Answers
Explanation
A dilation is when you create a second figure from an original figure using a scale factor. The corresponding sides of both the dilated figure and the original figure are proportional, so the two figures are similar.
Figure F is proportional as the dashed line indicates, it goes through zero.
Figure F is a scale factor of 2 based on
Image side/ pre image side
F = 4/2 = 2 and 6/3 = 2
The other two figures are not proportional and do not share a scale factor
G = 5/2 = 2 1/2 and 7/3 = 2 1/3
H = 7/2 = 3 1/2 and 8/3 = 2 2/3
The figure similar to figure E after dilation is figure F.
What are transformations?The transformation, or f: X X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the picture X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation. A function can be moved in one way or another using translation, rotation, reflection, and dilation. A function can also be scaled using rotation around a point. Two-dimensional mathematical figures move about a coordinate plane according to transformations.
We know that when a figure is dilated the ratio of their sides are same, that is they are proportional.
From the graph we observe that the line passes through the point F and E. Thus, the sides of the figure are proportional or in linear relation with each other.
Hence, the figure similar to figure E after dilation is figure F.
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Related Questions
Leeanne plans to sell her car and places an x-line ad. The newspaper charges p dollars for the
first k lines and e dollars per extra line, to run the ad for a week.
When x > k, write an algebraic expression for the cost of running the ad for a week.
a.
b. When x
Answers
Answer:
a. When x > k, the cost of running the ad for a week can be expressed as:
C = p + e(x - k)
where C is the cost in dollars, p is the cost per k lines, e is the cost per extra line, and (x - k) is the number of extra lines over k.
b. When x ≤ k, the cost of running the ad for a week can be expressed as:
C = p
where C is the cost in dollars and p is the cost per k lines. Since the number of lines x is less than or equal to k, there are no extra lines and the cost is simply the base cost of p dollars for k lines.
Hope this helped! I'm sorry if it's wrong. If you need more help, ask me! :]
Find the sum or difference
Answers
The sum or difference of [tex]$-2x^2+x+6$[/tex] and [tex]$(5x^2-4x-2)$[/tex] is [tex]3x^2 - 3x + 4$.[/tex]
What is sum?
In mathematics, the term "sum" refers to the result obtained by adding two or more numbers or quantities together. It also be used to refer to the total amount of something, such as the sum of money you have in your bank account, or the sum of the lengths of all the sides of a polygon.
To find the sum or difference of [tex]-2x^2+x+6 + (5x^2-4x-2)[/tex] we need to combine like terms.
[tex]-2x^2+x+6 + (5x^2-4x-2) &\\\\= (-2x^2 + 5x^2) + (x - 4x) + (6 - 2)[/tex]
[tex]&= 3x^2 - 3x + 4[/tex]
Therefore, the sum or difference of [tex]$-2x^2+x+6$[/tex] and [tex]$(5x^2-4x-2)$[/tex] is [tex]3x^2 - 3x + 4$.[/tex]
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If Bill starts work at 8:15, works until 4:45, and has 90 minutes of breaks. How many hours does Bill work in 5 days?
Answers
If Bill starts work at 8:15, works until 4:45, and has 90 minutes of breaks. Bill works for 36.25 hours in 5 days.
What is work per day?Work per day typically refers to the amount of time or effort expended by an individual during a typical working day.
According to question:First, let's find out how many hours Bill works in one day.
From 8:15 AM to 4:45 PM, Bill works for 8 hours and 30 minutes (since there are 60 minutes in an hour, we can convert the 45 minutes to 0.75 hours, so 8 hours and 45 minutes is the same as 8.75 hours):8 hours and 45 minutes - 90 minutes of breaks
= 7 hours and 15 minutes
= 7.25 hours of work per day.
To find out how many hours Bill works in 5 days, we can simply multiply his daily hours by the number of days:7.25 hours per day x 5 days = 36.25 hours.
Therefore, Bill works for 36.25 hours in 5 days.
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Identify which functions have complex roots by selecting the function names on the provided coordinate plane.
Answers
From the graphs in the given coordinate plane, the functions that have complex roots are function b, function d and function f.
Determining the functions that have complex rootsFrom the question, we are to determine the functions that have complex roots in the given coordinate plane.
In a quadratic graph, if the vertex of the quadratic function lies above the x-axis, and the parabola opens upward, there will be NO x-intercepts. The graph will have complex roots.
Also, if the vertex of the quadratic function lies below the x-axis, and the parabola opens downward , there will be NO x-intercepts.
The graph will have complex roots.
In the given coordinate plane, the functions that have complex roots are function b, function d and function f.
Hence, the functions b, d, and f have complex roots.
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Please I really need help the blank boxes are from 0-9.
Answers
For no solution 7x+10
For one solution8x+0
For infinite solution 7x+5
Define infinite solutionAn infinite solution is a solution to a system of equations that has an infinite number of possible solutions. In other words, any value for the variables in the system will satisfy all the equations.
2x+5+2x+3x
On adding the values with variables, x=7
On adding constant values=5
2x+5+2x+3x=7x+5
For no solution
7x+5=7x+10
For one solution
7x+5=8x
x=5
For infinite solution
7x+5=7x+5
Hence, For no solution 7x+10
For one solution 8x+0
For infinite solution 7x+5.
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Consider the system of equations x^2 + y^2 = 25 and y = 4x + b.
Find two values of b, one positive and one negative, so that the
system is inconsistent.
Answers
The two values of b that make the system inconsistent are b = -4.79 (negative) and b = 4.79 (positive). This is found by setting the discriminant of the quadratic equation in x to be negative.
We can solve this problem by substituting y = 4x + b into the first equation:
x² + (4x + b)² = 25
Expanding the square and simplifying, we get:
x² + 16x² + 8bx + b² - 25 = 0
Combining like terms, we get a quadratic equation in x:
17x² + 8bx + (b² - 25) = 0
For the system to be inconsistent, this quadratic equation must have no real solutions (i.e., the discriminant must be negative). Therefore, we need:
(8b)² - 4(17)(b² - 25) < 0
Simplifying and solving for b, we get:
64b² - 4(17b² - 425) < 0
98b² < 1700
b² < 1700/98
b < ±sqrt(1700/98)
b < ±4.79
Therefore, the two values of b that make the system inconsistent are:
b = -4.79 (negative)
b = 4.79 (positive)
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I dont know what 28x76 is
Answers
Answer:
28
x 76
----
168 (units digit of 76 multiplied by 28)
1408 (tens digit of 76 multiplied by 28)
----
2128
Therefore, 28x76 is equal to 2128.
Step-by-step explanation:
Any answers ??? I can’t do it
Answers
The missing value that completes the frequency table is 100
What is a Frequency Table?A frequency table is just a two-column "t-chart" or table that lists all of the potential outcomes and their corresponding frequencies as seen in a sample.
How to solve:
From the graph given,
The battery life(hours) from x = 15 to x= 20 has a frequency of 130
The battery life(hours) from x= 28 to x= 30 has a frequency of 100
It can be inferred that from the battery life of the different models, the missing value is 100 and when you crosscheck the data, you would find this is correct and accurate.
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be sure to simplify your answer
Answers
To find f(-6), we need to substitute -6 for x in the expression for f(x):
f(x) = 2x^2 + 5x - x/3
f(-6) = 2(-6)^2 + 5(-6) - (-6)/3
f(-6) = 2(36) - 30 + 2
f(-6) = 72 - 30 + 2
f(-6) = 44
Therefore, f(-6) = 44.
The table contains the number of M&M’s of each color that were found in a case.
M&M Distribution
Blue Brown Green Orange Red Yellow Total
399 538 364 393 507 351 2552
Round answers to four decimal places, if necessary.
Find the probability of choosing a green or red M&M.
P(green or red) =
Find the probability of choosing a blue, red, or yellow M&M.
P(blue, red, or yellow) =
Find the probability of not choosing a brown M&M.
P(not brown) =
Find the probability of not choosing a green M&M.
P(not green) =
Answers
(a) P(green or red) = 0.3946
(b) P(blue, red, or yellow) = 0.7606
(c) P(not brown) = 0.7807
(d) P(not green) = 0.6559
What is probability?
Probability is a branch of mathematics that deals with the study of randomness and uncertainty in events. It is the measure of the likelihood or chance that an event will occur. Probability is expressed as a number between 0 and 1, where 0 indicates that the event will not occur and 1 indicates that the event will occur with certainty.
The total number of M&M's is 2552.
(a) P(green or red) = P(green) + P(red)
= 364/2552 + 507/2552
= 0.2692
(b) P(blue, red, or yellow) = P(blue) + P(red) + P(yellow)
= 399/2552 + 507/2552 + 351/2552
= 0.4917
(c) P(not brown) = 1 - P(brown)
= 1 - 538/2552
= 0.7891
(d) P(not green) = 1 - P(green)
= 1 - 364/2552
= 0.8575
Hence,
(a) P(green or red) = 0.3946
(b) P(blue, red, or yellow) = 0.7606
(c) P(not brown) = 0.7807
(d) P(not green) = 0.6559
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The accompanying table shows the numbers of male and female students in a certain region who received bachelor's degrees in a certain field in a recent year. A student is selected at random. Find the probability of each event listed in parts (a) through (c) below.
Answers
0.571
Given data: The accompanying table shows the numbers of male and female students in a certain region who received bachelor's degrees in a certain field in a recent year. A student is selected at random. Find the probability of each event listed in parts (a) through (c) below.Table:Males FemalesTotalsFreshman 12 25 37Sophomore 14 18 32Junior 17 14 31Senior 9 12 21Totals 52 69 121a) A freshman is selected at random.b) A senior male is selected at random.c) A female is selected at random.a) For part a, we have to find the probability of selecting a freshman at random. The total number of students is 121. And the number of freshmen is 37. The probability of selecting a freshman at random is:37/121 = 0.306b) For part b, we have to find the probability of selecting a senior male at random. The total number of seniors is 21. And the number of senior males is 9. The probability of selecting a senior male at random is:9/121 = 0.074c) For part c, we have to find the probability of selecting a female at random. The total number of females is 69. And the total number of students is 121. The probability of selecting a female at random is:69/121 = 0.571Therefore, the probability of each event is:a) 0.306b) 0.074c) 0.571
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WRITING Explain how to tell which side of a right triangle is adjacent to an acute angle and which side is the hypotenuse.
Answers
The side which clοses tο the acute angle will be the adjacent side tο the acute angle and the lοngest side is the Hypοtenuse.
What are Sides οf a right-angled triangle?
In a right-angled triangle, there are three sides. One side is called the hypοtenuse and the οther twο sides are adjacent tο the right angle and are called the legs οf the triangle.
In a right triangle, the side οppοsite the right angle is always the lοngest side and is called the hypοtenuse. The twο οther sides are called the legs οf the triangle, and οne οf the legs is adjacent tο each οf the acute angles.
Tο determine which side is adjacent tο a specific acute angle, yοu need tο identify which οf the twο legs is clοsest tο that angle. The side clοsest tο the angle is the adjacent side.
Fοr example, if yοu have a right triangle with acute angles A and B, and leg AB is adjacent tο angle A, then leg BC is adjacent tο angle B.
Alternatively, yοu can use the trigοnοmetric functiοns sine, cοsine, and tangent tο determine the relatiοnship between the sides οf a right triangle and its angles.
The side which clοses tο the acute angle will be the adjacent side tο the acute angle and the lοngest side is the Hypοtenuse.
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Karen has two dogs. The larger dog weighs 1. 4 pounds more than the smaller dog. The combined weight of the two dogs is 12. 6 pounds
Answers
The weight of the smaller dog is 5.6 pounds.
Let the weight of the smaller dog be x, then,
The weight of the larger dog = 1.4 pounds.
The combined weight of the dogs = 12.6 pounds.
Therefore,
The sum of the weight of the larger dog and smaller dog = the combined weight of the dogs.
That is,
1.4 + x + x = 12.6
1.4 + 2x = 12.6
2x = 12.6 - 1.4
2x = 11.2
x = 11.2 ÷ 2
x = 5.6.
Hence, the weight of the smaller dog is 5.6 pounds.
?
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Your question is incomplete, and the complete question would be:
Karen has two dogs. the larger dog weighs 1.4 pounds more than the smaller dog. the combined weight of the two dogs is 12.6 pounds. what is the weight of the smaller dog?
. A right triangle has a perimeter of 198 cm. Knowing the hypotenuse is 85 cm, find the lengths of the other sides. 8. Around a square swimming pool a rubber mat of uniform width is placed whose area is equal to the area of the pool. What is the width of the mat if the area of the pool is 289 m2 ?
Answers
Width of the mat is 0.75 m
Answer:Triangle problemGiven a right triangle, perimeter = 198 cm Hypotenuse = 85 cmLet the other sides of the triangle be a and b respectively.To find the value of a and bSolutionWe know that, in a right triangle with sides a and b, and hypotenuse c Pythagoras Theorem can be usedc² = a² + b²Formula for perimeter of a triangle is P = a + b + cFrom the given values, we can substitute the values for P and c.198 = a + b + 85 198 - 85 = a + b 113 = a + bTo get the values of a and b, we need one more equation We can use Pythagoras theorem since it is a right triangle85² = a² + b²7225 = a² + b²a² = 7225 - b²b² = 7225 - a²Substitute b² into the previous equation113 = a + b7225 = a² + (7225 - a²)7225 = 2a²a² = 7225 / 2a = √(7225 / 2) = √(36125 / 8) = 75.59 cmNow that we have found the value of a, we can find b using the Pythagoras Theorem85² = 75.59² + b²b² = 85² - 75.59²b = √(85² - 75.59²) = 49.79 cm Therefore, a = 75.59 cm, b = 49.79 cmWidth of rubber matA square swimming pool has an area of 289 m²The area of the pool can be expressed as (side)²Therefore, side = √289 = 17 mLet the width of the rubber mat be w. Since it is uniform, it will be the same on all sides. Area of the pool and mat = (side + 2w)² - side² = 289From the above equation, we can solve for w:4w(side) + 4w² = 0+ 4w² + 4w(side) - 289 = 04(w + side/2)² - 289 = 0(w + side/2)² = 289 / 4w + side/2 = ±17/2 w + side/2 = 8.5 or w + side/2 = -8.5side/2 can never be negative, therefore we can consider only w + side/2 = 8.5 w = 8.5 - side/2w = 8.5 - 17/2 = 0.75m Width of the mat is 0.75 m
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The graph shows a straight line.
a) What is the equation of the straight
line shown?
b) Another straight line has equation
y = 3x + 5
Complete the following statement: -5
'y = 3x + 5 passes through (0,
c) A straight line has the same gradient
as y = 3x + 5 and it passes through
the point (0, 12).
What is the equation of this straight line? y=
5
5 x
Answers
The equation of the straight line with the same gradient as [tex]y = 3x + 5[/tex] and passing through the point [tex](0, 12)[/tex] is [tex]y = 3x + 12[/tex]
What are equations used for?A mathematical equation, such as 6 x 4 Equals 12 x 2, states that two quantities or units are similar. A noun that ranks. When two or more components must be taken into account together in to fully understand or describe the whole scenario, this is known as an equation.
a) To find the equation of the straight line shown, we need to determine its slope (or gradient) and [tex]y-[/tex]intercept. We can do this by choosing two points on the line and using the point-slope formula:
slope [tex]=[/tex] (change in y) / (change in x)
Let's choose the points [tex](1, 3)[/tex] and [tex](4, 7)[/tex] from the line.
slope [tex]= (7 - 3) / (4 - 1) = 4 / 3[/tex]
Now we can use the point-slope formula with one of the points to find the equation:
[tex]y - y1 = m(x - x1)[/tex]
where m is the slope and (x1, y1) is one of the points on the line.
Let's use the point (1, 3):
[tex]y - 3 = (4/3)(x - 1)[/tex]
Simplifying:
[tex]y = (4/3)x + 1[/tex]
So, the equation of the straight line shown is [tex]y = (4/3)x + 1[/tex].
b) To complete the statement "[tex]y = 3x + 5[/tex] passes through [tex](0, -5)[/tex]", we need to substitute [tex]x = 0[/tex] and [tex]y = -5[/tex] into the equation and verify that it is true:
[tex]y = 3x + 5[/tex]
[tex]-5 = 3(0) + 5[/tex]
[tex]-5 = 5 - 5[/tex]
[tex]-5 = -5[/tex]
Since the equation is true, we can say that the point [tex](0, -5)[/tex] is on the line [tex]y = 3x + 5[/tex].
c) We know that the gradient of the line we want to find is the same as [tex]y = 3x + 5[/tex], which is [tex]3[/tex]. We also know that it passes through the point [tex](0, 12)[/tex].
Using the point-slope formula with [tex]m = 3[/tex] and [tex](x1, y1) = (0, 12)[/tex]:
[tex]y - 12 = 3(x - 0)[/tex]
Simplifying:
[tex]y = 3x + 12[/tex]
So, the equation of the straight line with the same gradient as [tex]y = 3x + 5[/tex]and passing through the point [tex](0, 12)[/tex] is [tex]y = 3x + 12[/tex].
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Given: S is on the segment RT. RS = x + 2, ST = 3x + 1, and RT = 15.
Answers
On solving the question we have that We can see that RS + ST = RT, equation confirming that S is on segment RT: RT = RS + ST = 5 + 10 = 15
What is equation?A math equation is a mechanism for connecting two statements and indicating equivalence with the equals sign (=). To explain the connection between the two sentences put on each side of a letter, a statistical method can be employed. The software and the logo are usually interchangeable. 2x - 4 equals 2, for example. An equation is a logical expression that asserts the equality of some mathematical expressions in algebra. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14.
Because S is on the section RT, we know that RS + ST = RT. As a result, we may construct the following equation:
RS + ST = 3x + 1 + (x + 2) = 15
To simplify this equation, we can combine similar terms:
4x + 3 = 15
Subtraction of 3 from both sides yields:
4x = 12
When we divide both sides by 4, we get:
x = 3
RS = x + 2 = 5 and ST = 3x + 1 = 10 as a result.
We can see that RS + ST = RT, confirming that S is on segment RT:
RT = RS + ST = 5 + 10 = 15
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Divya is cooking dinner. she goes to the market to buy ingredients. the price per pound of different ingredients is shown in the table below. Diyva recipe calls for 3.25 pounds of beef, 0.65 pounds of onions, 0.2 pounds of potatoes, 0.15 pounds of tomatoes, and 0.33 pounds of asparagus How much will diyva pay for all the ingredients in the recipe?
Answers
Step-by-step explanation:
Divya is cooking dinner. she goes to the market to buy ingredients. the price per pound of different ingredients is shown in the table below. Diyva recipe calls for 3.25 pounds of beef, 0.65 pounds of onions, 0.2 pounds of potatoes, 0.15 pounds of tomatoes, and 0.33 pounds of asparagus How much will diyva pay for all the ingredients in the recipe?
PLEASE SHOW WORK!!!!!!!!!
Answers
Answer:
K
Step-by-step explanation:
[tex]c + d \: - 2(c + d) \\ = c + d - 2c - 2d \\ = - c - d \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
please somebody help
Answers
The factored forms of the equations and the intercepts would be:
g(x) = x² - 4x - 21:
Factored ⇒ g(x) = (x - 7)(x + 3) x - intercept ⇒ x = 7 or x = -3y - intercept ⇒ (0,- 21)h(x) = x² + 8x + 12:
Factored ⇒ h(x) = (x + 2)(x + 6) x - intercept ⇒ (-2,0) and (-6,0) y - intercept ⇒ (0 ,12 ) How to find the factored versions and intercepts ?For g(x) = x² - 4x - 21:
To find the factored form, we need to factor the quadratic expression:
g(x) = (x - 7)(x + 3)
To find the x-intercepts, we set g(x) = 0 and solve for x:
(x - 7)(x + 3) = 0
x = 7 or x = -3
To find the y-intercept, we set x = 0 and evaluate g(x):
g(0) = (0 - 7)(0 + 3) = -21
Therefore, the y-intercept of g(x) is (0,-21).
For h(x) = x² + 8x + 12:
h(x) = (x + 2)(x + 6)
To find the x-intercepts, we set h(x) = 0 and solve for x:
(x + 2)(x + 6) = 0
x = -2 or x = -6
To find the y-intercept, we set x = 0 and evaluate h(x):
h(0) = (0 + 2)(0 + 6) = 12
Therefore, the y-intercept of h(x) is (0,12).
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Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation 15 . Find
P 9
, which is the IQ score separating the bottom9%from the top 91%
. The IQ score that separates the bottom 9% from the top 91% is P 9
=
(Round to the nearest hundredth as needed.) Assume that adults have IQ
scores that are normally distributed with a mean of 105 and a standard deviation of 15 . Find the third quartile
Q 3
which is the IQ score separating the top 25% from the others. The third quartile, Q 3
is . (Round to one decimal place as needed.)
Answers
Value of Q3 is approximately 114.1 given mean and standard deviation.
We must identify the IQ score that separates the bottom 9% from the top 91% in order to determine P9. The normal distribution of IQ scores has a mean of 100 and a standard deviation of 15, as is well known. The z-score for the 9th percentile can be calculated using a calculator or a typical normal distribution table.
[tex]z = invNorm(0.09) = -1.34[/tex]
The formula for converting a z-score to an IQ score is as follows:
IQ equals z * standard deviation + mean, or -1.34 * 15 + 100, or 79.1.
P9 is therefore roughly 79.1.
We must identify the IQ score that distinguishes the top 25% from the rest in order to determine Q3. Assuming a normal distribution, IQ values have a mean of 105 and a standard deviation of 15. Since the top 25% and the 75th percentile are the same, we can use a calculator or a conventional normal distribution table to determine the z-score that represents the 75th percentile:
[tex]z = invNorm(0.75) = 0.67[/tex]
We can then use the formula for transforming a z-score to an IQ score:
IQ = z * standard deviation + mean = 0.67 * 15 + 105 = 114.05
Therefore, Q3 is approximately 114.1.
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1. Draw a scatter plot that shows a positive linear association and clustering.
2. Draw a scatter plot that shows a negative non-linear association and no clustering.
Answers
The grouping of data or sample points is a component of the machine learning process known as clustering.
What is Clustering?The task of arranging a set of objects into an identical group in a way that makes them more similar to one another than those found in different groups is known as cluster analysis or clustering.
A scatter plot is an unique type of plot or mathematical diagram that displays data for usually 2 parameters for a collection of data. It uses Cartesian coordinates.
Coordinates, it is a set or group of values that show an exact or accurate position.
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A cleaning process reduces the amount of chlorine in contaminated water by 5% per hour. Using ????0 for the initial amount of chlorine, find an exponential function ????(????) that gives the amount of chlorine remaining after t hours
Answers
a) A(5) = 10 * e^(-0.05*5)
b) 7.776
To solve the given problem, the initial amount of chlorine should be assumed as 'P0' and the exponential function should be written in the form of y = P_0 * e^(kt) where P_0 is the initial amount of chlorine and k is the rate of change. Therefore, for the given problem, the exponential function can be given by: y = P_0 * e^(-0.05t) where P_0 is the initial amount of chlorine and t is the number of hours. This equation will give the amount of chlorine remaining after t hours. The formula for exponential decay is given by:A(t) = A₀ * e^(-kt) Where A(t) is the amount after time t, A₀ is the initial amount, k is the rate of decay, and t is the time elapsed. To calculate the remaining amount of chlorine after a certain number of hours, we'll utilize the formula above .Let's start with the given information: An exponential function that gives the amount of chlorine remaining after t hours is to be found. P₀ = the initial amount of chlorine, which is 10.We can also figure out the rate of decay from the given information. The amount of chlorine is reduced by 5% per hour, which means the rate of decay is 0.05. We need to put a negative sign in front of the rate of decay to indicate that it is decreasing. Let's use the formula to find the amount of chlorine remaining after 5 hours. Then, substitute A₀ = 10, k = -0.05, and t = 5 into the equation above to obtain A(5) = 10 * e^(-0.05*5) = 7.776.So, the amount of chlorine remaining after 5 hours is 7.776.
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A company's profit (in millions of dollars) can be represented by y=x^2 -16x +67 where x is the number of years since the company started. When did the company have a profit of 7 million dollars?
Answers
For given quadratic equation, the company had a profit of 7 million dollars in either its 6th year or its 10th year of operation.
What exactly are quadratic equations?
A quadratic equation is a second-degree polynomial equation of the form:
ax²+ bx + c = 0
where x is the variable and a, b, and c are constants, with a ≠ 0. The term "quadratic" comes from the Latin word "quadratus", which means "square". In other words, a quadratic equation is an equation that involves the square of the variable x.
Now,
We are given that the profit of the company (in millions of dollars) can be represented by the equation y = x² - 16x + 67, where x is the number of years since the company started.
We want to find when the company had a profit of 7 million dollars.
So, we can set y = 7 in the equation:
7 = x² - 16x + 67
Rearranging and simplifying:
x² - 16x + 60 = 0
Now, we can solve for x using the quadratic formula:
x = (-(-16) ± √((-16)^2 - 4(1)(60))) / 2(1)
x = (16 ± √(16)) / 2
x = 8 ± 2
Therefore, the solutions are x = 10 or x = 6.
This means that the company had a profit of 7 million dollars in either its 6th year or its 10th year of operation.
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Solve 5(p−3q)<12 for q
Answers
The value of q in the question is q>-12/15
What is an inequality?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions
The given inequality is 5(p−3q)<12
Opening the bracket we have
5p - 15q < 12
The solution can only be gotten if we assume p = 0
the substitute p=0 in the inequality to have
-15q < 12
dividing both sides by -15 to have
-15q/-15 < 12/-15
therefore q > 12/-15
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help me find the missing sides to solve this equation
Answers
For the equilateral triangles we have:
1) x = 5, y = √50
2) a = 2, b = √8
3)y = 8, x = √128
4) a = b = 7/√2
How to find the missing sides?We can see some triangles, remember that for a right triangle whose angles are 45°, we have an equilateral triangle.
So the two legs have the same measure.
1) Here we can see that x = 5, and the hypotenuse is given by:
y^2 = 5^2 + 5^2
y^2 = 50
y = √50
2) Here we have a = 2, then the hypotenuse is:
b^2 = 2^2 + 2^2
b^2 = 8
b = √8
3) Here we have y = 8, then the hypotenuse is:
x^2 = 8^2 + 8^2
x^2 = 128
x = √128
On the last triangle we can see that the hypotenuse is 7, and we know that a = b
then:
7^2 = a^2 + b^2
7^2 = a^2 + a^2
49 = 2*a^2
(49/2) = a^2
√(49/2) = a
7/√2 = a = b
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help me with these five question and get brainlist and 100 points
Answers
Answer:
a) 7/9 * 2
Because 7*2/9 = 1.555556, which is less than 2.
All the other options' products are greater than 2.
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PLEASE HELP ASAP WILL GIVE BRAINLIEST
Answers
Answer:
3x+5x=8x
-3t+-t=-4t
3p+3p=6p
2n+n=3n
5g+-g=4g
7y+y=8y
4+12=16
Step-by-step explanation:
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Find the surface area of the rectangular prism.
A storage container is in the shape of a rectangular prism. The container has a length of 5 feet, and a width of 9 feet, and a height of 8 feet. What is the surface area of the container?
360 ft2
314 ft2
157 ft2
22 ft2
ANswer __________________
Answers
The surface area οf the cοntainer is 314 ft².
What is rectangle?A rectangle is a geοmetric shape that has fοur sides and fοur right angles (90 degrees) with οppοsite sides being parallel and equal in length. It is a type οf quadrilateral, a pοlygοn with fοur sides.
Tο find the surface area οf a rectangular prism, we need tο add the areas οf all six faces. The fοrmula fοr the surface area οf a rectangular prism is:
Surface area = 2lw + 2lh + 2wh
where l is the length, w is the width, and h is the height οf the rectangular prism.
Substituting the given values, we get:
Surface area = 2(5)(9) + 2(5)(8) + 2(9)(8)
Surface area = 90 + 80 + 144
Surface area = 314 square feet
Therefοre, the surface area οf the cοntainer is 314 ft².
Answer: 314 ft².
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The populations P (in thousands) of Horry County, South Carolina, from 1971 through 2018 can be modeled by P-75.9e0.0316 where t represents the year, with t= 1 corresponding to 1971.
(a) Use the model to find the population in 1980, 1990, 2000, and 2010. (Round your answers to the nearest whole number.)
1980
1990
2000
2010
(b) According to the model, when will the population of Horry County reach 390,000? (Round your answer down to the nearest year.)
(c) Do you think the model is valid for long-term predictions of the population? Explain.
O Yes, as t increases, the population increases rapidly.
O Yes, as t increases, the population decreases rapidly.
O Yes, as t increases, the population remains constant.
O No, as t increases, the population decreases rapidly.
O No, as t increases, the population increases rapidly.
Answers
a) The populations in 1980, 1990, 2000, and 2010 are 157,000, 218,000, 269,000, and 308,000 respectively.
b) the population will reach 390,000 in 270 years
c) No, as t increases, the population increases rapidly
How to find the populations as required(a) To find the population in 1980, 1990, 2000, and 2010, we substitute the corresponding values of t into the given model and round the answers to the nearest whole number.
Population in 1980: P = 75.9e^(0.0316*10) = 156,604
Population in 1990: P = 75.9e^(0.0316*20) = 217,643
Population in 2000: P = 75.9e^(0.0316*30) = 269,099
Population in 2010: P = 75.9e^(0.0316*40) = 308,227
(b) To find when the population of Horry County will reach 390,000, we need to solve the equation 390 000 = 75.9e^(0.0316t) for t.
Taking the natural logarithm of both sides, we get:
ln(390,000/75.9) = 0.0316t
Simplifying, we get:
t = ln(390,000/75.9)/0.0316 ≈ 270.395
Rounding down to the nearest whole year, we get that the population will reach 390,000 in 270 years
(c) The model assumes that the population growth rate will remain constant over time. However, in reality, population growth rates can be affected by a variety of factors, such as changes in birth and death rates, immigration, emigration, and natural disasters.
Therefore, it is unlikely that the model will be valid for long-term predictions of the population. The model can provide a good estimate of the population for the short-term, but it is not reliable for predictions far into the future.
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the daily high temperature for chattanooga is normally distributed with mean 79 and standard deviation 4. find the probability that a randomly chosen temperature is between 70 and 75.
Answers
The probability of randomly selecting a temperature between 70 and 75 is approximately 0.8291.
To find the probability that a randomly chosen temperature is between 70 and 75, we need to use the z-score formula as shown below:
z = (x - μ) / σ
Where:x = 70 and 75μ = 79σ = 4z1 = (70 - 79) / 4 = -2.25z2 = (75 - 79) / 4 = -1P(70 < x < 75) = P(-2.25 < z < -1)
To find the probability for the above inequality, we need to use a calculator. We know that the probability of the standard normal distribution is equal to 1.
Hence, P(-2.25 < z < -1) = Φ(-1) - Φ(-2.25) = 0.8413 - 0.0122 ≈ 0.8291. Therefore, the probability is about 0.8291.
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