4 What quantity represents the total change in the volume of water in the birdbath after
two days? Write your answer as a mixed number.
When these two numbers are subtracted, the difference is 2 3/4, which is the total change in the volume of water in the birdbath after two days. This can be written as a mixed number, which would be 2 3/4.
The total change in the volume of water in the birdbath after two days can be determined by subtracting the starting volume of water (1 1/2) from the ending volume of water (4 1/4).
The total change in the volume of water in the birdbath after two days is an important figure to calculate in order to understand the amount of water that has been added or removed from the birdbath. To calculate this figure, one must subtract the starting volume of water from the ending volume of water. In this scenario, the starting volume of water was 1 1/2 and the ending volume of water was 4 1/4. When these two numbers are subtracted, the difference is 2 3/4, which is the total change in the volume of water in the birdbath after two days. This can be written as a mixed number, which would be 2 3/4. This figure is important to know as it can help one determine how much water has been added or removed from the birdbath over a certain period of time.
the complete question is :
A birdbath is filled to the top. On Day 1, the volume of water in the bowl decreases by 7/8 cup. On Day 2, the volume in the bowl decreases by 3/4 cup. What number represents the total change in the volume of water in the bowl after two days? Write your answer as a mixed number.
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Very urgent urgent urgent
explain also
The expressions for the dimensions of the rectangular composite figure, indicates;
a) The simplified expression for the shaded region is; (3·x + 36) cm²
b) x = 17
c) Please find attached the drawing of the figure, showing the dimensions, created with MS Word
d) The area of the shaded region cannot be 39 cm², because that will make the length of the small rectangle -1 cm.
What is a composite figure?A composite figure is a figure that comprises of two or more simpler figures.
The figure can be considered as a composite figure, comprising of a small rectangular unshaded region within a shaded larger rectangle.
The area of the shaded region is the difference between the area of the large rectangle and the area of the unshaded rectangle, which can be found as follows;
Area of a rectangle = Length × Breadth
Length of the large rectangle = (x + 5) cm
Breadth of the large rectangle = 6 cm
Area of large rectangle = 6 cm × (x + 5) cm = (6·x + 30) cm²
Area of the unshaded area = 3 cm × (x - 2) cm = (3·x - 6) cm²
Area of the shaded region, A, is therefore;
A = (6·x + 30) cm² - (3·x - 6) cm² = (3·x + 36) cm²
The expression for the shaded area is; (3·x + 36) cm²b) The shaded area = 87 cm², therefore;
(3·x + 36) = 87
3·x = 87 - 36 = 51
x = 51/3 = 17
The value of x is 17c) The dimensions of the figures are therefore;
x = 17
Length of the large rectangle = (17 + 5) cm = 22 cmLength of the unshaded region = (17 - 2) cm = 15 cmPlease find attached the drawing of the shape created with MS Word
d) The area of the shaded region is; (3·x + 36)
Therefore, if the area of the shaded region is 39, we get;
(3·x + 36) = 39
x = (39 - 36)/3 = 1
x = 1
The length of the unshaded region is; (x - 2)
The length of the unshaded region becomes; (1 - 2) = -1, which is not a natural number and therefore, not possible
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Complete the identity. Cos(2pi-x) =?
PLEASE I NEED HELP ASAP!
The identity of cos (2π-x) = -cosx
What are trigonometric identities?Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation.
for example;
cos 2 θ + sin 2 θ = 1
1 + cot 2 θ = csc 2 θ
1 + tan 2 θ = sec 2 θ
For cos(2π -x)
π = 180°
2π = 2× 180
= 360°
Therefore cos ( 360-x) will have the identity -cos x.
This is because 360° has an equivalent as 0 in trigonometry.
Therefore cos( 0-x)
= -cosx
therefore the identity of cos (2π-x) is -cos(x).
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(-4+-7)(-3) shown work
Answer:
33
Step-by-step explanation:
First, you multiply 3 into the other equation (remember, anytime there is a parentheses by each like there is shown, it will be multiplication.) So -3 * -7 is 21 because a negative and a negative is a positive. Then -3 * -4 which is 12. Add 21 and 12 together and you get 33!
I hoped this helped <3
A car is stopped at a red light.when the light turns green,the car speed up to 80m/s in 5s.what is the acceleration of the car
Given
Required
Equation
solution
Answer
Answer:
Given:
Initial velocity, u = 0 (since the car is stopped)
Final velocity, v = 80 m/s
Time taken, t = 5 s
Required:
Acceleration, a
Equation:
We can use the following equation to calculate the acceleration:
a = (v - u) / t
where u is the initial velocity, v is the final velocity, and t is the time taken.
Solution:
Substituting the given values, we get:
a = (80 - 0) / 5
a = 16 m/s²
Answer:
The acceleration of the car is 16 m/s².
(^2 is just another version of ²)
Hope this helped! Sorry if it didn't. If you need more help, ask me! :]
Anyone know how to solve these both? Ik it’s a lot but I really need help bc I’m like super tired.
(please separate each question from each other so I can actually read it)
a. If Kayla runs on the inside she would run for about 400.96 meters
b. If Emi runs on the outer edge, in one lap, she would run for about 463.76 meters
c. The difference = 62.80 m
we have to find the perimeter of the outer edgeThis is = 200 + (2π * 42 / 2) + (2π * 42 / 2)
= 200 + 84 π
= 200 + 84 * 3.14
= 463.76 meters
Next we have to solve for the perimeter of the inside edge
200 + (2 π * 32 / 2) + (2 π * 32 / 2)
= 200 + 64π
= 400.96
The difference is given as 463.76 - 400.96
= 62.80 m
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Hector is training for a race that is 10 kilometers long. On Saturday he ran 2.5 km. He plans to add 0.5 km to his distance every Saturday. Hector tracks his progress by adding 0.5 every week. 2.5 + 0.5 = 3.0 3.0 + 0.5 = 3.5 ⋮ 9.5 + 0.5 = 10 Which equations are equivalent to his weekly addition of 0.5 km and would correctly determine how many weeks it will take Hector to reach 10 km if he starts at 2.5 km and adds 0.5 km every week? Select all that apply. 0.5x + 2.5 = 10 0.5 – 2.5 = 10x 10 = 2.5 + 0.5x 2.5x + 0.5 = 10 2.5x – 0.5 = 10
According to the given information, it will take Hector 15 weeks to reach 10 km if he starts at 2.5 km and adds 0.5 km every week.
What is an equation?
An equation is a mathematical statement that shows that two expressions are equal. It typically consists of two sides separated by an equals sign (=), where each side contains an expression that may contain variables, constants, or mathematical operations. The goal of solving an equation is to find the value(s) of the variable(s) that make the equation true.
The equation that correctly determines how many weeks it will take Hector to reach 10 km is 0.5x + 2.5 = 10, where x is the number of weeks.
To verify, we can solve for x:
0.5x + 2.5 = 10
0.5x = 10 - 2.5
0.5x = 7.5
x = 7.5/0.5
x = 15
Therefore, it will take Hector 15 weeks to reach 10 km if he starts at 2.5 km and adds 0.5 km every week.
The other equations are not equivalent to Hector's weekly addition of 0.5 km:
0.5 – 2.5 = 10x is not equivalent because it does not involve adding 0.5 every week.
2.5x + 0.5 = 10 is not equivalent because it does not take into account Hector's starting distance of 2.5 km.
2.5x – 0.5 = 10 is not equivalent because it does not involve adding 0.5 every week and it also does not take into account Hector's starting distance of 2.5 km.
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Three students are comparing how fast their social media posts spread the results are on the table.
1. Write an exponential function to represent the spread of Ben's social media post.
2. Write an exponential function to represent the spread of Carter's social media post.
3. Graph each function using at least three points for each curve. All graphs should be placed together on the same coordinate plane, so be sure to label each curve. You may graph your equation by hand on a piece of paper and scan your work, or you may use graphing technology.
4. Using the functions for each student, predict how many shares each student's post
will be received on Day 3 and then on Day 10. Justify your answers.
5. If Amber decides to mail copies of her photo to the 45 residents of her grandmother's assisted living facility, the new function representing her photo shares is f(x) = 3(4)x + 45. How does this graph compare with the original graph of
Amber's photo share?
6. Based on your results, which students' post travels the fastest? How is this shown
in the equation form of the functions?
7. If you had to choose, would you prefer a post with fewer friends initially but more
shares, like Amber, or more friends initially but fewer shares? Justify your answer with your calculations from
previous questions.
The spread of Carter's social media post is f(x) = 3(3)x. On Day 3, Ben's post will be received 8 shares and Carter's post will be received 27 shares. On Day 10, Ben's post will be received 524 shares and Carter's post will be received 729 shares.
What is exponential function?Amber's new function of f(x) = 3(4)x + 45 will produce a graph with a steeper slope than the original graph of Amber's photo share. Carter's post travels the fastest, as his equation form has the highest exponential rate. Depending on the goal of the post, one might prefer a post with fewer friends initially but more shares, such as Amber, or more friends initially but fewer shares, such as Ben.
Exponential function is a mathematical function that increases or decreases exponentially. It is an equation of the form y = ax^b, where a is the base and b is the exponent, and x is the independent variable.
1. The exponential function to represent the spread of Ben’s social media post is f(x) = 3(2)x.
2. The exponential function to represent the spread of Carter’s social media post is f(x) = 3(3)x.
3. The graph of Ben’s post will have a curve that increases exponentially as the x-values increase, while the graph of Carter’s post will have a curve that increases exponentially faster than Ben’s as the x-values increase. Three points that can be used to graph each curve are (0, 3), (1, 9), and (2, 27) for Ben’s post and (0, 3), (1, 9), and (2, 27) for Carter’s post.
4. On Day 3, Ben’s post will have 81 shares (f(3) = 3(2^3) = 81), and Carter’s post will have 243 shares (f(3) = 3(3^3) = 243). On Day 10, Ben’s post will have 59049 shares (f(10) = 3(2^10) = 59049), and Carter’s post will have 59049 shares (f(10) = 3(3^10) = 59049). This is shown in the equation form of the functions because each function is in the form of a(b^x). For Ben’s post, a = 3, b = 2, and for Carter’s post, a = 3, b = 3. As the x-values increase, the value of b increases exponentially and so the total number of shares increases exponentially.
5. Amber’s new function representing her photo shares is f(x) = 3(4)x + 45. The graph of this function will be different from the original graph of Amber’s photo share because it is no longer an exponential function - it is a linear function. The graph will have a constant rate of increase as the x-values increase, reflecting that the number of shares is increasing by a constant number with each additional day.
6. Based on the results, Carter’s post travels the fastest. This is shown in the equation form of the functions because Carter’s post has a larger value of b (3) than Ben’s post (2), indicating that Carter’s post is increasing exponentially faster than Ben’s post.
7. It would depend on the situation, but generally speaking it would be preferable to have more friends initially and fewer shares, like Amber. This is because if a post has few friends initially and more shares, the post will spread faster, but there is no guarantee that the post will continue to spread after it reaches its peak. If a post has more friends initially and fewer shares, the post will spread more slowly, but it is more likely to continue to spread for a longer period of time.
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On a map, two cities are 2.8 inches apart. The map has a scale of 1 inch to 25 miles. How far apart, in inches, would the same two citites on a map that has a scale oof 1 inch to 40 miles
The distance on the map where the scale is 1 inch to 40 miles is 1.75 inches.
How far will be the two cities on the other map?First we know that the cities are at 2.8 inches apart on a map whose scale is 1 inch to 25 miles, then the real distance between the two cities is:
[tex]D = (2.8)\times25\text{mi}= 70 \ \text{mi}[/tex]
Now we move to a map where each inch is 40 miles, to find the distance in inches, we can take the quotient between the real distance and the scale, it gives:
[tex]D = (\dfrac{70\text{mi}}{40\text{mi}} ) \ \text{inches}[/tex]
[tex]D = 1.75 \ \text{inches}[/tex]
The distance on the other map is 1.75 inches.
The amount of shore at a local beach changes an average of -3/4 foot each year. What is the change in the amount of shore after 7 years and 4 months ( 7 1/3)
The change in the amount of shore after 7 years and 4 months is -5.4975 feet.
First, let us convert the values into the same quantities
7 1/3 years = 7 + 1/3 years = 7.33 years
The change in shore after 7 years and 4 months can be calculated as
Change in amount of shore = (average change per year) x (number of years)
Change in amount of shore = (-3/4 foot/year) x (7.33 years)
Change in amount of shore = -5.4975 feet.
Therefore, the change in the amount of shore after 7 years and 4 months is approximately -5.4975 feet.
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When customers buy a book from an online bookstore,
they pay a $6 shipping fee in addition to the cost of the
book.
The total cost is the book price plus $6.
Let x=book price
Let y = total cost
Which equation represents the situation?
A. y = 6x
B. y=x+6
C. y =
D. y=x-6
The equation that represents the situation is y = x + 6.
What is equations ?An equation is a mathematical statement that shows the equality between two expressions. It consists of two sides separated by an equal sign (=) and can involve numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.
According to given information :The equation that represents the situation is B. y = x + 6.
The problem states that the total cost, y, is the book price, x, plus a $6 shipping fee. We can express this as:
y = x + 6
Option A, y = 6x, suggests that the total cost is only determined by the book price multiplied by 6, which is not what the problem states.
Option C, y = , is not a valid equation as it does not include any terms to determine the value of y.
Option D, y = x - 6, suggests that the total cost is the book price minus $6, which is not what the problem states either.
Therefore, the equation that represents the situation is y = x + 6.
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(2x +3) ² - (2x -5)²
Answer:
[tex]32x-16[/tex]
Step-by-step explanation:
[tex](2x+3)^{2} - (2x-5)^{2}[/tex]
expand the equation.
[tex](2x+3)(2x+3) - (2x-5)(2x-5)[/tex]
then distribute.
[tex](4x^{2} +6x + 6x+9) - (4x^2 - 10x - 10x + 25)[/tex]
finally simplify the equation.
= [tex]32x-16[/tex]
Find the measure of the arc or angle indicated pt.2
Answer:
angle=80 degrees
Step-by-step explanation:
if we know the arc is 160 degrees than we know we want to find the interior angle, then we must divide 160/2 to get the measure of the indicated angle.
ANSUR II 2012
ANSUR is an abbreviation of "anthropometric survey." The ANSUR II study was conducted in 2012. (See also the preceding ANSUR I data set.) This data set consists of body measurements from 6068 U.S. Army personnel (first five rows shown here, not all data columns shown). AGE is in years, WEIGHT is in kilograms (kg), for GENDER 1=male and 0=female, for WRITING HAND 1=right and 2=left and 3=both, and the other body measurements are in millimeters (mm). Additional detail on body measurements can be found at TriolaStats.com/ansur. Data are from the U.S. Army.
TI-83/84 list names (ANSUR2)*: A2AGE, A2HT, A2WGT, A2FTL, A2HC, A2CC, A2NC, A2WC, A2SW, A2SH, A2SKH, A2SEH, A2NHT, A2PPD, A2ARM, A2WH, A2GND
*NOTE: TI lists are limited to 500 rows due to calculator memory constraints.
AGE HEIGHT WEIGHT FOOT LENGTH HEAD CIRC CHEST CIRC SHOULDER WIDTH SITTING HT ARM SPAN WRITING HAND GENDER (1=M)
41 1776 81.5 273 583 1074 493 928 1782 1 1
35 1702 72.6 263 568 1021 479 884 1745 2 1
42 1735 92.9 270 573 1120 544 917 1867 2 1
31 1655 79.4 267 576 1114 518 903 1708 1 1
21 1914 94.6 305 566 1048 524 919 2035 1 1
A2AGE, A2HT, A2WGT, A2FTL, A2HC, A2CC, A2NC, A2WC, A2SW, A2SH, A2SKH, A2SEH, A2NHT, A2PPD, A2ARM, A2WH, A2GND
The ANSUR II study was conducted in 2012 and consisted of body measurements from 6068 U.S. Army personnel. In the data set, AGE is in years, WEIGHT is in kilograms (kg), GENDER is identified as 1=male and 0=female, WRITING HAND is 1=right and 2=left and 3=both, and the other body measurements are in millimeters (mm). The following data list names are provided for TI-83/84: A2AGE, A2HT, A2WGT, A2FTL, A2HC, A2CC, A2NC, A2WC, A2SW, A2SH, A2SKH, A2SEH, A2NHT, A2PPD, A2ARM, A2WH, A2GND.
The first five rows of the data set are provided here for reference:
AGE HEIGHT WEIGHT FOOT LENGTH HEAD CIRC CHEST CIRC SHOULDER WIDTH SITTING HT ARM SPAN WRITING HAND GENDER (1=M)
41 1776 81.5 273 583 1074 493 928 1782 1 1
35 1702 72.6 263 568 1021 479 884 1745 2 1
42 1735 92.9 270 573 1120 544 917 1867 2 1
31 1655 79.4 267 576 1114 518 903 1708 1 1
21 1914 94.6 305 566 1048 524 919 2035 1 1
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Sphere A has a radius of 2 cm. Sphere B has a radius of 4 cm.he radius of Sphere B is doubled that of sphere A. How many times greater is the volume of B? times
Volume of Sphere B is 8 times greater than the volume of Sphere A
What does sphere refer to?
A sphere is symmetrical and round in form. All of its surface points are equally spaced from the centre, making it a three-dimensional solid. Depending on the radius, it has a surface area and a volume. No faces, corners, or edges exist on it.
It is sometimes referred to as the second cousin of a circle, the sphere is a three-dimensional form. Round, without boundaries, and solid in shape, a sphere is spherical. Examples of spherical shapes include a playing ball, a balloon, and even light bulbs.
Sphere A: V = 4π (2³)/3 = 32π/3
Sphere B: V = 4π (4³)/3 = 4π(64)/3 = 256π/3
volume of Sphere B / volume of Sphere A = (256π/3)/(32π/3) = 8
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6^3x- 8^(x+1) show all your work, and round your final answer to four decimal places and check your solution.
Therefore , the solution of the given problem of expressions comes out to be x ≈ 0.6309.
What does an expression actually mean?Calculations that combine joining, removing, and random subdivision must be done with ever-changing factors. They could accomplish the following if they united: An programme, some data, and a mathematical problem. Formulas, components, and arithmetic operations like adds, subtractions, mistakes, and groupings can all be found in a declaration of truth.
Here,
We can rewrite this equation as follows in order to answer it using the properties of logarithms:
We can now use a substitution to simplify the problem. Let y = 8^x.
By finding x, we obtain:
=> y = (6³ˣ))/8
This equation can be made simpler by applying the formula 8 = 23:
=> y = (6³ˣ))/(2³)
=> y = (3³ˣ)/(2³)
=> 6³ˣ - (3³ˣ)/(2³) = 0
=> (6³ˣ)*(2³) - (3³ˣ) = 0
=> (2³)/(3³ˣ) - 1 = 0
=> log((2³)/(3³ˣ)) = log(1)
=> log(2³) - log(3³ˣ) = 0
Simplifying, we get:
=> 3log(2) - 3xlog(3) = 0
By multiplying both parts by 3log(3), we obtain:
=> x = (log(2))/(log(3))
Using a calculator, we can calculate this expression to four decimal places:
=> x ≈ 0.6309
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A shop owner had three boxes, containing a total of 1500 plastic cups. The number of plastic cups in Box A to the total number of plastic cups was 3:10. He sold 330 plastic cups from Box B and sold 1/3 of the plastic cups in Box C. The number of plastic cups left in Box B to the number of plastic cups left in Box C was 3:1. How many plastic cups were there in Box B at first?
The initial number of cups in Box B at first is given as follows:
810 cups.
How to obtain the initial number of cups?The initial number of cups in box B is obtained solving a system of equations, for which the variables A, B and C represents the amounts of each box.
A shop owner had three boxes, containing a total of 1500 plastic cups. The number of plastic cups in Box A to the total number of plastic cups was 3:10, hence the initial amount of Box A is given as follows:
0.3 x 1500 = 450 cups.
Then:
B + C = 1500 - 450
B + C = 1050.
He sold 330 plastic cups from Box B and sold 1/3 of the plastic cups in = Box C. The number of plastic cups left in Box B to the number of plastic cups left in Box C was 3:1, hence:
(B - 330)/(2C/3) = 3
B - 330 = 2C
C = 0.5B - 165
Replacing into B + C = 1050, the value of B is given as follows:
B + 0.5B - 165 = 1050
B = 1215/1.5
B = 810.
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Consultant`s Prediction (in %) Actual Market Outcome Prior Probabilities Rise Stable Fall Raise 0.6 0.7 0.2 0.1 Stable 0.3 0.2 0.6 0.2 Fall 0.1 0.1 0.2 0.7 Hint: The sum of getting a `Raise report` is given by the sum of the probabilities of getting a `Raise report` under each outcome multiplied respectively by the probability of getting that outcome. Use the Bayes Theorem to revise the consultant`s prediction. Should you choose to pay for this additional information? Produce a revised Decision tree for the board to make a decision. You should discuss on your decision on to use or not to use the consultant firm and each strategy.
If the company has limited resources or is not particularly concerned with precision, it may decide to forego the additional information and rely on its prior probabilities to make decisions
Bayes TheoremBayes Theorem is a statistical technique that enables one to find the probability of an event given another event that is known to have happened. The theorem states that the probability of an event A happening given that another event B has already occurred is equivalent to the probability of event B happening given that event A has already occurred multiplied by the probability of A happening divided by the probability of B happening. The revised decision tree can be produced to make a decision. However, before that, we need to find the sum of getting a Raise report for each outcome of the prior probabilities. This is shown in the table below:Consultant`s Prediction (in %)Actual Market OutcomePrior ProbabilitiesRiseStableFallRaise0.60.70.20.10.70.140.1260.0280.0140.20.30.20.60.240.0600.0180.1260.03 0.03150.0060.00210.07Total 0.34 0.36 0.30 1.00To revise the consultant's prediction using Bayes theorem, we can use the following formula:P(Stable | Raise) = (P(Raise | Stable) * P(Stable)) / (P(Raise | Stable) * P(Stable) + P(Raise | Rise) * P(Rise) + P(Raise | Fall) * P(Fall)) = (0.140 * 0.30) / (0.140 * 0.30 + 0.126 * 0.34 + 0.028 * 0.36) = 0.2906 or 29.06%The probability of getting a stable report given a raise report is 29.06%. This value can also be calculated for getting a fall report given a raise report using the same formula, which gives a probability of 24.51%.To make a decision on whether to use the consultant firm or not, we can use the revised decision tree. The tree shows that the probability of getting a raise report is only 34%, and given that we get a raise report, the probability of getting a stable report is 29.06% while the probability of getting a fall report is 24.51%.If the company decides to use the consultant firm, they will have to pay for the additional information. This cost needs to be weighed against the benefits of having this information, which will depend on the goals and priorities of the company. If the company values precision and accuracy in its decision-making process and is willing to pay for it, then it may choose to use the consultant firm. However, if the company has limited resources or is not particularly concerned with precision, it may decide to forego the additional information and rely on its prior probabilities to make decisions.
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n is an integer greater than 1
Prove algebraically that n²-2-(n-2)2 is always an even number.
Answer:
Starting with the expression n² - 2 - (n - 2)², we can simplify it by expanding the second term using the formula for the square of a binomial:
n² - 2 - (n - 2)² = n² - 2 - (n² - 4n + 4)
Next, we can combine like terms:
n² - 2 - (n² - 4n + 4) = n² - n² + 4n - 6
Simplifying further, we get:
n² - 2 - (n - 2)² = 4n - 6
To prove that this expression is always even, we can show that it can be written in the form 2k, where k is an integer.
So, let's rewrite the expression as:
4n - 6 = 2(2n - 3)
Since 2n - 3 is an integer (because n is an integer greater than 1), we have shown that 4n - 6 can be written in the form 2k, where k is an integer.
Therefore, we have proved algebraically that n² - 2 - (n - 2)² is always an even number.
I NEED HELP ON THIS ASAP! PLEASE HELP!! I WILL GIVE YOU BRAINLIEST!!
A system of inequalities to represent the constraints of this problem are x ≥ 0 and y ≥ 0.
A graph of the system of inequalities is shown on the coordinate plane below.
How to write the required system of linear inequalities?In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of HD Big View television produced in one day and number of Mega Tele box television produced in one day respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of HD Big View television produced in one day.Let the variable y represent the number of Mega Tele box television produced in one day.Since the HD Big View television takes 2 person-hours to make and the Mega TeleBox television takes 3 person-hours to make, a linear equation to describe this situation is given by:
2x + 3y = 192.
Additionally, TVs4U’s total manufacturing capacity is 72 televisions per day;
x + y = 72
For the constraints, we have the following system of linear inequalities:
x ≥ 0.
y ≥ 0.
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Data was collected on the weight, in ounces, of kittens for the first three months after birth. A line of fit was drawn through the scatter plot and had the equation w = 4.05 + 0.4d, where w is the weight of the kitten in ounces and d is the age of the kitten in days. What is the w-intercept of the line of fit and its meaning in terms of the scenario? 4.05; for each additional day after the kitten is born, its weight is predicted to increase by 4.05 ounces 4.05; a kitten who is just born is predicted to weigh 4.05 ounces 0.4; for each additional day after the kitten is born, its weight is predicted to increase by 0.4 ounces 0.4; a kitten who is just born is predicted to weigh 0.4 ounces
Answer: B - A kitten who is just born is predicted to weigh 4.05 ounces
Step-by-step explanation:
Amy is looking into investing a portion of her recent bonus into the stock market. While researching different companies, she discovers the following standard deviations of one year of daily stock closing prices.
Garden Statues Express: Standard deviation of stock prices =$1.05
=
$
1.05
Masterful Pocketwatches: Standard deviation of stock prices =$9.83
=
$
9.83
Based on the data and assuming these trends continue, which company would give Amy a stable long-term investment?
To determine which company would give Amy a stable long-term investment, we need to compare the standard deviations of the stock prices for both companies. A lower standard deviation indicates that the stock price is more stable and has less variability.
From the given information, we can see that the standard deviation of stock prices for Garden Statues Express is $1.05, while the standard deviation of stock prices for Masterful Pocketwatches is $9.83. This means that Garden Statues Express has a much lower standard deviation, and thus a more stable stock price, compared to Masterful Pocketwatches.
Therefore, if Amy is looking for a stable long-term investment, she should consider investing in Garden Statues Express.
I need help with this question
Answer:
range = 60
Step-by-step explanation:
the range of the data set is the difference between the largest and smallest values in the set.
the largest value = 140 ( denoted by the line on furthest right )
the smallest value = 80 ( denoted by line on left )
range = 140 - 80 = 60
What are the finance charges?
$3. 79
$4. 68
$5. 32
$7. 50
In the case of the example given, the finance charge is $5.32, which is the amount of money that will be charged for borrowing the money for the given period.
Finance charges refer to the fees and interest associated with borrowing money or making a purchase on credit. Finance charges are usually expressed as a percentage of the total amount borrowed or purchased, and they are calculated based on the interest rate and the length of the loan term. In the case of the example given, the finance charge is $5.32, which is the amount of money that will be charged for borrowing the money for the given period. The finance charge is calculated by multiplying the interest rate by the amount borrowed and then dividing it by the total number of days in the loan term.
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At a scout jamboree, dinner is served from tinned food. each tin of soup is shared between 2 scouts. each tin of frankfurters is shared between 3 scouts and each tin of fruit is shared between 4 scouts. if 117 tins are opened to feed all the scouts, how many scouts attended the jamboree
By answering the above question, we may state that As a result, there equation were 108 scouts who attended the jamboree.
What is equation?A math equation is a mechanism for connecting two claims by using the equals sign (=) to indicate equivalence. A mathematical statement that establishes the equivalence of two mathematical expressions is known as an equation in algebra. The equal symbol, for example, splits the numbers 3x + 5 and 14. A mathematical formula can be used to describe the relationship between two phrases written on opposite sides of a letter. The logo and programme are frequently the same. 2x - 4 Equals 2, for example.
Because each tin is divided by four scouts, the number of fruit tins necessary will be one-fourth of the number of scouts. As a result, the quantity of tins of fruit required is x/4.
The total number of tins opened, according to the query, is 117. Based on the preceding data, we can construct the following equation:
x/2 + x/3 + x/4 = 117
To remove the denominators, multiply both sides by 12 (the LCM of 2, 3, and 4).
6x + 4x + 3x = 1404
When we simplify, we get:
13x = 1404
By multiplying both sides by 13, we get:
x = 108
As a result, there were 108 scouts who attended the jamboree.
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Geometric Sequence
Need help with number 5
The sum of the perimeters of all squares is 80 ft.
What is perimeter?
Perimeter is the distance around the outer boundary of a two-dimensional shape, such as a rectangle, square, triangle, or circle. It is the total length of all the sides of the shape.
Starting with a square with a perimeter of 40 ft, we can find the length of one side by dividing the perimeter by 4:
[tex]\frac{40ft}{4} = 10ft[/tex]
So, the original square has a side length of 10 ft.
Connecting the midpoints of the sides of this square creates a new square with half the side length of the original square. Each side of this new square is the hypotenuse of a right triangle with legs equal to half the side length of the original square (i.e., 5 ft).
Using the Pythagorean theorem, we can find the length of each side of the new square:
[tex]s^2 = (5 ft)^2 + (5 ft)^2[/tex]
[tex]s^2 = 50 ft^2[/tex]
[tex]s = \sqrt{50}ft[/tex]
So, the second square has a side length of [tex]\sqrt{50}ft[/tex], which is approximately 7.07 ft.
Continuing this process, each subsequent square will have half the side length of the previous square. Therefore, the side length of the third square will be half the side length of the second square, which is:
[tex]\frac{1}{2}[/tex] * [tex]\sqrt{50}ft[/tex] = [tex]\sqrt{25}ft[/tex] = 5 ft.
The side length of the fourth square will be half the side length of the third square, which is: [tex]\frac{1}{2}[/tex] * 5 ft = 2.5 ft. And so on.
The perimeters of the squares are:
The perimeter of the first square is 40 ft.
The perimeter of the second square is 4 * [tex]\sqrt{50}ft[/tex], which is approximately 28.28 ft.
The perimeter of the third square is 4 * 5 ft = 20 ft.
The perimeter of the fourth square is 4 * 2.5 ft = 10 ft.
We can see that the perimeter of each subsequent square is half the perimeter of the previous square. So, the series for the perimeters of the squares is a geometric series with a first term of 40 ft and a common ratio of 1/2.
Using the formula for the sum of an infinite geometric series, we can find the sum of the perimeters of all squares:
S = a / (1 - r)
where a is the first term (40 ft) and r is the common ratio (1/2). Plugging in these values, we get:
S = 40 ft / (1 - 1/2)
S = 80 ft
Therefore, the sum of the perimeters of all squares is 80 ft.
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true/false. the basic calculation for obtaining a response bias is to the number of legitimately completed questionnaires returned divided by the total number of sample members provided a chance to participate.
The statement "The basic calculation for obtaining a response bias is not to divide the number of legitimately completed questionnaires returned by the total number of sample members provided a chance to participate." is False
Instead, the basic calculation for obtaining a response bias is to subtract the response rate from 100%. The response rate is calculated by dividing the number of legitimately completed questionnaires returned by the total number of sample members provided a chance to participate.
So, the formula for calculating response bias is:
Response bias = 100% - (number of legitimately completed questionnaires returned / total number of sample members provided a chance to participate)
In other words, response bias is the percentage of sample members who did not participate or did not complete the questionnaire legitimately. It is important to calculate response bias in order to understand how representative the sample is of the population.
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Hi. please I need help and it's urgent
a particle is projected with an initial speed of 45m/s² at an angle of elevation ∅ given by sin inverse(0.5). find the greatest height reached by the particle
Answer:
(i) 25.83 m
(ii) 178.9 m
(iii) 4.592 s
Step-by-step explanation:
You want the greatest height, the range, and the time of flight of a particle launched at 45 m/s at an angle of arcsin(0.5) from the horizontal.
Vertical speedThe vertical speed is the speed in the direction of launch multiplied by the sine of the angle from the horizontal. Here, it is ...
(45 m/s)(sin(arcsin(0.5))) = 22.5 m/s
(i) Maximum heightThe maximum height is the height at which all of the initial vertical kinetic energy is converted to potential energy:
h = v²/(2g)
h = (22.5 m/s)²/(2·9.8 m/s²) ≈ 25.83
The maximum height is about 25.83 meters.
(iii) Time of flightThe time of flight is twice the time it takes to reach the maximum height. That time is the height divided by the average vertical speed, which average is half the initial vertical speed.
T = 2 × (25.83 m)/(11.25 m/s) ≈ 4.592 s
The time of flight is about 4.592 seconds.
(ii) RangeThe range is the product of the time of flight and the horizontal speed. The horizontal speed is the speed in the launch direction multiplied by the cosine of the angle from the horizontal.
cos(α) = √(1 -sin(α)²) = √(1 -(1/2)²) = √(3/4)
R = (45 m/s)√(3/4)·4.592 s = 178.949 m
The horizontal range of the particle is about 178.9 meters.
Therefore , the solution of the given problem of angle comes out to be the particle's horizontal range is approximately 178.9 metres.
An angle meaning is what?A tilt is a form in Euclidean geometry made up of two sides, but rather cylindrical faces, that divide at the barrier's centre and apex. At their junctions, two rays may combine to form an angle. Angle is another outcome of two entities interacting. Dihedral shapes best describe them. A two-dimensional curve can be created by arranging two line beams in various configurations at their ends.
Here,
Lateral momentum
The launch speed is compounded by the sine of the angle from the horizontal to obtain the vertical speed. This is it...
=> 22.5 m/s = (45 m/s)(sin(arcsin(0.5)))
I The tallest person
The height at which all of the original vertical kinetic energy is transformed into potential energy is known as the maximum height.
=> h = v²/(2g) (2g)
=> h = (22.5 m/s)²/(2·9.8 m/s²) ≈ 25.83
The highest point is roughly 25.83 metres high.
(ii) Flight time
The duration of flying is twice as long as the time required to ascend to the highest point. The height divided by the average vertical speed, which is half of the original vertical speed, yields that time.
=> T = 2 × (25.83 m)/(11.25 m/s) ≈ 4.592 s
The journey lasts for approximately 4.592 seconds.
=> (iii) Scope
The range is calculated by multiplying the flight duration by the horizontal speed. The cosine of the angle from the horizontal compounded by the speed in the direction of launch gives the horizontal speed.
=>Cos(x) = (1 - sin(x)2) = (1 -(1/2)2) = Cos(x) = (3/4)
=> R = (45 m/s)√(3/4)·4.592 s = 178.949 m
The particle's horizontal range is approximately 178.9 metres.
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Please Help!!!!!
Type the inverse of the matrix. Use decimals. If no inverse exists type "none".
In response to the question, we may say that Therefore, the inverse of the given matrix is: [ 0.0 1.5 -1.0 ], [ 1.0 -2.0 2.0 ] and [-1.0 1.5 -2.0 ]
what is matrix?An arrangement of integers in rows and columns is known as a matrix. learns about matrices' components and dimensions and first presents them. A matrix is a rectangular grid with integers arranged in rows and columns. For example, Matrix A contains two rows and three columns. The origin of its moniker is due to its single row and 1 n row matrix arrangement. For example, a row matrix of order 1 by 4 is A = [1 2 4 5]. The row matrix P = [-4 -21 -17] of order 1-by-cubic is another example.
Let's begin by calculating the determinant of the matrix:
[tex]det(A) = 1(41 - 30) - 2(40 - 20) + 3(10 - 21)\\det(A) = 4 - 0 - 6\\det(A) = -2\\[/tex]
Since the determinant is not zero, an inverse exists. Let's find the adjugate matrix:
[tex]adj(A) = [dof(A)]^T\\[/tex]
where dof(A) is the matrix of cofactors of A.
[tex]dof(A) = [(-1)^(1+1)0, (-1)^(1+2)2, (-1)^(1+3)(-2),\\(-1)^(2+1)(-3), (-1)^(2+2)4, (-1)^(2+3)(-3),\\(-1)^(3+1)2, (-1)^(3+2)(-4), (-1)^(3+3)*4]\\dof(A) = [0, -2, 2, 3, 4, -3, 2, -4, 4]\\[/tex]
Therefore,
[tex]adj(A) = [0 -3 2; -2 4 -4; 2 -3 4]\\[/tex]
Finally, we can find the inverse matrix by multiplying the adjugate matrix by the reciprocal of the determinant:
[tex]A^(-1) = (1/det(A)) * adj(A)\\A^(-1) = (-1/2) * [0 -3 2; -2 4 -4; 2 -3 4]\\A^(-1) = [0.0 1.5 -1.0; 1.0 -2.0 2.0; -1.0 1.5 -2.0]\\[/tex]
Therefore, the inverse of the given matrix is:
[ 0.0 1.5 -1.0 ]
[ 1.0 -2.0 2.0 ]
[-1.0 1.5 -2.0 ]
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Answer
[ 1.25 -0.75
-0.5 0.5 ]
Step-by-step explanation:
4.02 Lesson check ! (9)
Hence, in response to the provided question, we can say that As a result, arithmetic progression the usual difference is d = -30.
what is arithmetic progression?The difference between subsequent terms in a string will never vary, and this is referred like an arithmetic progression. The sequences 5, 7, 9, 11, 13, through 15 are examples of arithmetic progressions with a tolerance of 2. Arithmetic progression (A.P.) is a progression that has a set tolerance between any 2 consecutive values. Numerical progression may fall into one of two main types: finite-length arithmetic series A finite geometry progression is a series with just a fixed number of terms. The series' terms can be used to calculate the early, late, leniency, and number of term.
A) The sequence is, indeed, arithmetic.
We can find the common difference by subtracting any two consecutive terms:
109 - 9 = 100
209 - 109 = 100
309 - 209 = 100
As a result, the typical difference is d = 100.
A) The sequence is, indeed, arithmetic.
We can find the common difference by subtracting any two consecutive terms:
-32 - (-2) = -30 \s-62 - (-32) = -30 \s-92 - (-62) = -30
As a result, the usual difference is d = -30.
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