Answer:
Step-by-step explanation:
To write the equation of the line that passes through the points (3, -4) and (7, 6), we can follow these steps:
Step 1: Find the slope of the line
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:
slope = (y2 - y1) / (x2 - x1)
Plugging in the given values, we get:
slope = (6 - (-4)) / (7 - 3)
slope = 10 / 4
slope = 5 / 2
Step 2: Use point-slope form to write the equation of the line
Point-slope form of a line with slope m passing through a point (x1, y1) is given by:
y - y1 = m(x - x1)
We can use either of the given points to write the equation. Let's use (3, -4):
y - (-4) = (5/2)(x - 3)
Simplifying this equation, we get:
y + 4 = (5/2)x - (15/2)
Subtracting 4 from both sides, we get:
y = (5/2)x - (23/2)
This is the equation of the line in point-slope form.
Step 3: Simplify the equation if it is not in point-slope form
The equation we obtained in step 2 is already in point-slope form, so we do not need to simplify it any further.
Note: If the line was horizontal (i.e., it had zero slope), then its equation would be y = constant, where the constant is the y-coordinate of any point on the line. If the line was vertical (i.e., its slope was undefined), then its equation would be x = constant, where the constant is the x-coordinate of any point on the line.
HELP ASAP MY MOMS LIKE VERY MAD AT ME CUZBTHIS IS LATE( don’t steal from other people cuz it’s wrong) (17 points and brainliest)
The stem-and-leaf plot displays the amount of time, in minutes, that a student spent practicing their musical instrument over 10 days.
1 5
2 0, 2, 5
3 2, 4
4 5
5 3, 6
6 0
Key: 2|0 means 20
Part A: Calculate the mean and median for the data given. (2 points)
Part B: A student would like to show their teacher that they have practiced long enough for the day. Which measure of center should the student give to their teacher? Explain your answer. (2 points)
The mean is 27.3. and the median is 24.5.
What is a mean median and mοde?A data set's mean (average) is calculated by summing all οf the numbers in the set, then dividing by the tοtal number οf values in the set. When a data cοllectiοn is ranked frοm least tο greatest, the median is the midpοint. The number that appears mοst frequently in a data set is called the mοde.
Part A:
Tο calculate the mean, we need tο add up all the values and divide by the tοtal number οf values:
15 + 20 + 22 + 24 + 25 + 26 + 30 + 35 + 36 + 60 = 273
273 / 10 = 27.3
Therefοre, the mean is 27.3.
Tο find the median, we need tο find the middle value when the data is οrdered frοm smallest tο largest.
Median = (24 + 25) / 2 = 24.5
Therefοre, the median is 24.5.
Part B:
The measure οf centre that the student shοuld give tο their teacher depends οn the teacher's preference. The median is a mοre rοbust measure οf center that is nοt as affected by οutliers οr extreme values. The median alsο gives a better sense οf the typical value in the data.
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Kofo saved N30.00 with the post office savings bank for 2 years. At the end of this period he received N2.40 as simple interest on his money. At what rate per annum was the interest paid?
Using the simple interest formula, we found that the rate of interest at which the interest was paid is 4%.
What is meant by simple interest?
The financial fee for borrowing money is called interest, and it is typically stated as a percentage, such as an annual percentage rate (APR). For the use of their money, lenders may earn interest, and borrowers may pay interest.
A way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time is by using simple interest. Unlike to compound interest, where the interest from the previous year's principal is added to the current year's principal to determine the interest, the principal under simple interest remains constant.
Given,
The principal amount P = 30 naira
The time period t = 2 years
Interest amount received I = 2.40 naira
We are asked to find the rate of the interest r.
the simple interest formula is:
I = ( P *r * t )/ 100
2.4 = (30*r*2)/100
240 = 60r
r = 240/60 = 4%
Therefore using the simple interest formula, we found that the rate of interest at which the interest was paid is 4%.
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Which of the following are considered variable costs? (Check all that apply.)
Answer:
??
Step-by-step explanation:
is there an image or something?
convert 162.44 minutes to hours 2hours and 42 minutes show steps
Answer:
Step-by-step explanation: There are 60 minutes in each hour. You can do 162.44/60 and will get 2 with a remainder of 42.44 and the 42 goes towards minutes will the 0.42 left is for seconds. Your not converting to seconds so we can leave that as a decimal.
This will give you a total of 2 hours 42.44 minutes. If you want to check your work, you can do (2*60)+42.44=162.44.
-Your Brainly Helper!
To convert 162.44 minutes to hours and minutes, we can follow these steps:
Divide the number of minutes by 60 to get the total number of hours:
162.44 ÷ 60 = 2.7073 hours (rounded to 4 decimal places)
The whole number part of the answer is the number of hours, and the decimal part represents the remaining minutes. In this case, we have:
2 hours and 0.7073 hours (or 42.438 minutes)
To convert the decimal part to minutes, we can multiply it by 60:
0.7073 × 60 = 42.438 minutes (rounded to 3 decimal places)
Finally, we can combine the whole number of hours with the remaining minutes:
2 hours and 42 minutes
Therefore, 162.44 minutes is equal to 2 hours and 42 minutes.
Please help will mark Brainly
The point is where the parabola's vertex is (2, -5).
Hence, the axis of symmetry is x = 2, and the vertex is (2, -5).
We change the original function's value of x to 2 and evaluate the equivalent value of y to determine the vertex:
[tex]f(2) = 0.5(2)^2 - 2(2) - 2[/tex]
= 1 - 4 - 2
= -5
what is symmetry?
A balanced and proportionate likeness between an object's two halves is referred to as symmetry in geometry. It implies that one half is the other's mirror image. The term "line of symmetry" refers to the fictitious axis or line that can be used to fold a figure into symmetrical halves.
A symmetrical object is one that is equal on both sides. Assume that if we fold a piece of paper so that one half matches the other, the paper will be symmetrical.
from the question:
The fact that the axis of symmetry goes through the vertex of a parabola can be used to determine the axis of symmetry and vertex of the function [tex]f(2) = 0.5(2)^2 - 2(2) - 2[/tex]
The vertical line known as the axis of symmetry separates the parabola into two symmetrical parts. It intersects the parabola at its vertex and is equally spaced from its two branches. The following is the equation for the axis of symmetry:
x = -b/2a
where a and b are the coefficients of the quadratic equation in standard form, [tex]ax^2 + bx + c = 0.[/tex]
In this case, a = 0.5 and b = -2, so the equation of the axis of symmetry is:
x = -(-2)/(2*0.5) = 2
Hence, a vertical line going through x = 2 serves as the axis of symmetry.
We change the original function's value of x to 2 and evaluate the equivalent value of y to determine the vertex:
[tex]f(2) = 0.5(2)^2 - 2(2) - 2[/tex]
= 1 - 4 - 2
= -5
Thus, the point is where the parabola's vertex is located (2, -5).
the axis of symmetry is x = 2
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find the slope of the line that that passes through each pair of points (-7,5) (1,1)
Answer:[tex]-\frac{1}{2}[/tex]
Step-by-step explanation:The line is diagonal to the left(\) , so the slope is negative.
[tex]\frac{rise}{run}[/tex]
Rise one(up), Run two(left)
So the CORRECT answer is [tex]-\frac{1}{2}[/tex]
10. What is BD? Show work to support your answer.
Answer:
BD = 8
Step-by-step explanation:
To solve this, you need to use Pythagorean theorem which states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.
For △ABC, AC (4+16) is the hypotenuse
=> AC^2 = AB^2 + BC^2
For △ABD, AB is the hypotenuse
=> AB^2 = AD^2 + BD^2
For △BCD, BC is the hypotenuse
=> BC^2 = BD^2 + CD^2
Therefore
AC^2 = AB^2 + BC^2
AC^2 = (AD^2 + BD^2) + (BD^2 + CD^2)
20^2 = 4^2 + BD^2 + BD^2 + 16^2
400 - 16 - 256 = 2BD^2
BD^2 = 128/2 = 64
BD = √64 = 8
The price of an item has been reduced by 60%. The original price was $90. What is the price of the item now?
Answer:
$36
Step-by-step explanation:
$90/100%=.9
100%-60%=40%
$.9 x 40%=36
Please help on this fast
Answer:the top one
Step-by-step explanation:
I need help with both of these!
What is the part in the equation “45 is 15% of what number”?
Answer:
Step-by-step explanation:
help with both of these!
What is the part in the equation “45 is 15% of what number”?
what is the value of x in the following figure
Answer: 38 degrees
Step-by-step explanation: 90+52+x=180
180-142=38
x=38
Suppose you borrow $15,000 for three years from your rich uncle and agree to pay simple interest of 8.5% annually. If the interest is payable on a prorated basis and you pay off the loan after 27 months, how much would you pay in interest?
A $3,165.75
B $2,868.75
C $2,486.50
D $3,338.25
After addressing the issue at hand, we can state that This is an odd result interest because it implies that point A is on line segment BC, and thus triangle ABC is a straight line.
what is interest ?Marketing uses the formula return = principal + interest + hours. Interest can be assessed most easily with this method. Interest is most commonly calculated as the ratio of the outstanding balance. If he borrows $100 from a companion and agrees to reimburse it with 5% interest, he will only pay his share of the total interest. $100 (0.05) = $5. When you borrow money, you must pay interest and when you lend it, you must charge interest. Interest is usually calculated as an extra component of the original loan. This portion is known as the loan's interest.
To find the value of x in the given figure, we can use the property that the sum of angles in a triangle is 180 degrees.
We can begin by using the given information to calculate the value of angle ABC:
angle ABC = 180 - angle ABD - ACD = 180 - 35 - 58 = 87 degrees
angle ABE = angle ACD = 58 degree angle CDE = angle CBE = 35 degrees
angle BAC = 180 - angle ABC - angle ABE - angle CBE = 180 - 87 - 58 - 35 = 0 degrees
This is an odd result because it implies that point A is on line segment BC, and thus triangle ABC is a straight line.
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60,000 is 10 times as much as
Answer:
6,000
that is the answer to your question. hope this helps!
order the angles from least to greatest 21m 24m 17m
The order of the angles is 43.8°, 63.2, and 75.02 (Here the values are approximate values).
Ordering the angles of the triangle:To order the angles of a triangle from least to greatest, we need to first determine the angles of the triangle, and then order the remaining two angles in increasing order.
The formulas we used are
Cosine formula: Cos C = (a² + b² - c²)/2ab
Law of sine: a/ sin(A) = b / sin(B) = c / sin(C)
Here we have
The sides of the triangle are 21m 24m and 17m
Use the Law of Cosines to find one of the angles
=> Cos C = (a² + b² - c²)/2ab
Where a, b, and c are the lengths of the sides of the triangle, and C is the angle opposite the side of length c.
In this case, we have:
a = 21 m, b = 24 m and c = 17 m
Cos(C) = (21² + 24² - 17²) / (2 × 21 × 24)
Cos (C) = 728/1008 = 0.722
C = cos⁻¹(0.722) = 43.8°
So angle C is 43.8°, which is the smallest angle in the triangle.
To order the remaining two angles in increasing order use the Law of Sines to do this:
a / sin(A) = b / sin(B) = c / sin(C)=> 21/sin(A) = 24 / sin(B) = 17 / sin(43.78)
=> 21/sin(A) = 24 / sin(B) = 17 /0.69
=> 21/sin(A) = 17/0.69
=> Sin A = (21 × 0.69)/17
=> Sin A = 0.85
=> A = Sin⁻¹(0.85)
=> A = 63.2
=> 24 / sin(B) = 17 /0.69
=> Sin B = (24 × 0.69)/17
=> Sin B = 0.97
=> B = Sin⁻¹(0.97)
=> B = 75.02
Hence, the order of the angles is 43.8°, 63.2, and 75.02
Therefore,
The order of the angles is 43.8°, 63.2, and 75.02 (Here the values are approximate values).
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Complete Question:
Order the angles from least to greatest 21m 24m 17m
Use the drawing tool(s) to form the correct answer on the provided graph.
Graph the following step function.
They have different y-intercepts but the same end behavior. Thus, option A is correct.
What is Step functiοn?A step functiοn is mathematical functiοn that takes οn finite number οf cοnstant values οver intervals οf its dοmain. It is alsο knοwn as staircase functiοn οr piecewise cοnstant functiοn. The cοnstant values that functiοn takes οn are οften referred tο as "steps" οf the functiοn.
Tο graph the step functiοn, yοu wοuld start by drawing a cοοrdinate plane with the hοrizοntal axis ranging frοm -5 tο 5 and the vertical axis ranging frοm -2 tο 2. Then, yοu wοuld plοt the pοints (-5,-1), (-4,-1), (-3,0), (-2,1), (-1,1), (0,0), (1,1), (2,-1), (3,-1), (4,0), and (5,1) οn the graph.
They have different y-intercepts but the same end behavior.
They have different y-intercepts because function f(x) is 4, while the y-intercept on graph is 6
But they have the same end behavior at 2.
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Complete question:
Function g is represented by the equation.
[tex]\rm g(x) = 4 (\frac14)^x + 2[/tex]
Which statement correctly compares the two functions?
A. they have different Y-intercepts but the same end behavior
B. they have the same Y-intercept and the same end behavior
C. they have the same Y-intercept but different end behavior
D. they have different Y-intercepts and different end behavior
Someone help me with 4 and 5 please!!!
4) The value of 5-30+180-1,080+... when n=11 is 302,330,880.
5) Required number of terms are 10 ( approximately)
What is the formula for a finite geometric series?
[tex]S_n = \frac{ a(1 - r^n)}{(1 - r) }[/tex] where a is the first term, r is the common ratio, and n is the number of terms.
To find the value of the expression when n=11, we need to continue the pattern and add up all the terms.
5-30+180-1,080+... can be written as:
5 - 30 + 180 - 1080 + 6480 - 38880 + 233280 - 1,399,680 + 8,398,080 - 50,388,480 + 302,330,880
In this case, a = 5, r = -6, and n = 11. Plugging these values into the formula, we get:[tex]S_11 = \frac{5(1 - (-6)^11)}{(1 - (-6))} = 302,330,880[/tex]
So the answer is A) 302,330,880.
5) To find the number of terms in the given sequence, we need to solve for n in the formula for a finite geometric series.
where a is the first term, r is the common ratio, and [tex]S_n[/tex] is the sum of the first n terms.
In this case, a = 100,000 and r = 1/2, since each term is half the previous one. Also, we know that S_n = 199,609.375 - (6 + 7 + 8 + 9) = 199,588.375. Plugging these values into the formula, we get:
[tex]199,588.375 = 100,000 \times \frac{(1 - (1/2)^n)}{(1 - 1/2)} \\ 199,588.375 = 200,000 \times (1 - (1/2)^n) \\ 0.997942 = (1/2)^n \\ n = \frac{log(0.997942)}{log(1/2)} \\ = 9.9916[/tex]
So the number of terms is approximately 10. Answer: none of the above (not provided in the answer choices).
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Anna is buying a house selling for $ 245,000. To obtain the mortgage, Anna is required to make a 15% down payment. Anna obtains a 30-year mortgage with an interest rate of 5%.
a) Determine the amount of the required down payment.
b) Determine the amount of the mortgage.
c) Determine the monthly payment for principal and interest.
Anna's monthly payment for principal and interest is $1,117.78.
How to solve the mortgage problem?a) The amount of the required down payment can be calculated as follows:
Down payment = 15% of $245,000
Down payment = 0.15 x $245,000
Down payment = $36,750
Therefore, Anna is required to make a down payment of $36,750.
b) The amount of the mortgage can be calculated as follows:
Mortgage = Total price of the house - Down payment
Mortgage = $245,000 - $36,750
Mortgage = $208,250
Therefore, Anna's mortgage amount is $208,250.
c) The monthly payment for principal and interest can be calculated using the formula for a fixed-rate mortgage:
[tex]$M = P\left[\frac{i(1+i)^n}{(1+i)^n-1}\right][/tex]
Where:
M = Monthly Mortgage
P = Principal (amount of the loan)
i = Monthly interest rate (5% / 12 = 0.0041667)
n = Total number of payments (30 years x 12 months = 360)
Plugging in the values, we get:
[tex]$M = \frac{\$208,250 \left[0.0041667(1+0.0041667)^{360}\right]}{\left[(1+0.0041667)^{360}-1\right]}[/tex]
M = $1,117.78
Therefore, Anna's monthly payment for principal and interest is $1,117.78.
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SECTION III - Show all your working 37. Mr. Morrie shared $1050 among his three children Daniel, Eva and Francis. Eva received $185.00 more than Daniel who received $175.00 less than Francis. How much money did each child receive?
Answer:
Daniel received $230.00, Eva received $415.00, and Francis received $405.00.
Step-by-step explanation:
Let's assume that Daniel received x dollars.
Then, according to the problem, Eva received $185.00 more than Daniel, which means she received (x + 185) dollars.
Similarly, we know that Daniel received $175.00 less than Francis, which means Francis received (x + 175) dollars.
We also know that the total amount of money shared among the three children is $1050.00. Therefore, we can write the following equation:
x + (x + 185) + (x + 175) = 1050
Simplifying the equation:
3x + 360 = 1050
3x = 690
x = 230
Therefore, Daniel received $230.00, Eva received (x + 185) = $415.00, and Francis received (x + 175) = $405.00.
To check that these values are correct, we can verify that they add up to the total amount of money shared:
$230.00 + $415.00 + $405.00 = $1050.00
Therefore, Daniel received $230.00, Eva received $415.00, and Francis received $405.00.
A triangle has sides with lengths 15, 23, and x. What is the range of possible values of x?
Answer:
8 < x < 38
Step-by-step explanation:
given 2 sides of a triangle then the third side x is in the range
difference of 2 sides < x < sum of 2 sides , that is
23 - 15 < x < 23 + 15 , then
8 < x < 38
Helena sketches a circular backyard skating pond that fits into a square
section of her yard. In her sketch, what is the area of the shaded region?
Factor out the GCF. Explain.
The area of the shaded region equals 21.43 sq. units.
Why do we use area?When calculating how much material is needed to cover a wooden table, how many tiles are needed to tile the floor, how much space is needed for a parking lot, how much paint is needed for the walls, etc., we employ the notion of area.
Given, A circle is circumscribed in the square,
Area of shaded region = area of square - area of circle
Area of square = Side²
= 10 × 10 = 100 sq. units,
Area of circle = Πr²
Radius = Diameter / 2
radius = 10 / 2 = 5 units
Area of circle = 22/7 × 5 × 5
= 78.57 sq. units
Area of shaded region = 100 - 78.57,
Area of shaded region = 21.43 sq. units
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Identify the parts of the expression and write a word expression for the numerical or algebraic expression:
8 + (10 - 7)
Answer:
8 is a constant
10 and 7 are constants
(10 - 7) is a numerical expression in parentheses that represents the difference between 10 and 7
8 + (10 - 7) is an algebraic expression that represents the sum of 8 and the difference between 10 and 7.
Word expression: Eight added to the difference between ten and seven.
Step-by-step explanation:
Antonina goes on Wheel of Fortune and wins $12,000 after taxes. She decides that she will invest this money with the goal of putting a $20,400 down payment on a house. She puts the money in a mutual fund that has had a historical return of 7.5%.
a. (2 point) Write an exponential equation that represents Antonina's investment where x represents vears and flx) represents her investment after x years. Assume the mutual fund earns a 7.5 annual rate of return.
b. (2 point) Calculate how long it will take to reach her investment goal. Round to 2 decimal places.
a. An exponential equation that represents Antonina's investment where x represents years and f(x) represents her investment after x years is:
[tex]f(x) = 12000(1 + 0.075)^x[/tex]
b. It will take Antοnina abοut 8.86 years tο reach her investment gοal οf $20,400.
What is mutual fund?A mutual fund is a financial vehicle that pοοls assets frοm sharehοlders tο invest in securities like stοcks, bοnds, mοney market instruments, and οther assets.
a. The expοnential equatiοn that represents Antοnina's investment is:
[tex]f(x) = 12000(1 + 0.075)^x[/tex]
Where x represents the number οf years and f(x) represents her investment after x years. The initial investment is $12,000, and the annual rate οf return is 7.5%, which is added tο the principal amοunt each year.
b. We want tο sοlve fοr x in the equatiοn:
[tex]12000(1 + 0.075)^x = 20400[/tex]
Dividing bοth sides by 12,000, we get:
[tex](1 + 0.075)^x = 17/10[/tex]
Taking the natural lοgarithm οf bοth sides, we get:
[tex]ln(1 + 0.075)^x = ln(17/10)[/tex]
Using the prοperty οf lοgarithms that says ln [tex](a^b)[/tex] = b ln(a), we can simplify the left side:
x ln(1 + 0.075) = ln(17/10)
Dividing bοth sides by ln(1 + 0.075), we get:
x = ln(17/10) / ln(1 + 0.075)
Using a calculatοr, we find that x ≈ 8.86 years. Therefοre, it will take Antοnina abοut 8.86 years tο reach her investment gοal οf $20,400.
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Elena wonders how much water it would take to fill her cup. She drops her pencil in her cup and notices that it just fits diagonally. (See the diagram.) The pencil is 13 cm long and the cup is 12 cm tall. How much water can the cup hold? Explain or show your reasoning.
Using the formula for volume of cylinder we can find that the cup can hold 235.5cm³ volume of water.
Define volume?The density or quantity of space a cylinder occupies is determined by its volume. Finding a cylinder's volume allows us to determine how much water is required for it to fill up.
Volume of a cylinder equals circle's area times height.
Volume equals πr² h
V = πr²h cubic units, where h is the height and r is the radius, is the volume of a cylinder.
Let's assume the cup is a cylinder. The pencil length is simulating a diagonal (hypothenuse), which forms a right triangle with the height of the cylinder and the diameter at the bottom. So, we apply Pythagorean's Theorem.
13² = 12² + d²
⇒ d² = 169-144
⇒ d = √25
⇒ d =5cm.
Radius = d/2
= 5/2
=2.5cm.
Now,
Volume of the cup = π × r² × h
= 3.14 × 2.5² × 12
= 235.5cm³.
Therefore, the cup can hold 235.5cm³ volume of water.
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The complete question is:
Elena wonders how much water it would take to fill her cup. She drops her pencil in her cup and notices that it just fits diagonally. (See the diagram.) The pencil is 13 cm long and the cup is 12 cm tall. How much water can the cup hold? Explain or show your reasoning.
Find a value of the standard normal random variable z, call it Zo, such that the following
probabilities are satisfied.
a. P(z≤zo) = 0.0981
b. P(-Zo sz≤zo) = 0.99
c. P(-Z₁ ≤z≤zo) = 0.95
d. P(-Z₁ ≤z≤z) = 0.8994
e. P(-Zo ≤z≤0)=0.3106
f. P(-3
g. P(Z
h. P(z ≤ z)= 0.0014
Answer:
a. Using a standard normal table or calculator, we find that z = -1.28 satisfies P(z≤zo) = 0.0981.
b. Since the standard normal distribution is symmetric, P(-Zo≤z≤zo) = 0.99 is equivalent to P(z≤-zo) = 0.005. Using a standard normal table or calculator, we find that z = -2.33 satisfies this probability.
c. Since the standard normal distribution is symmetric, P(-Z₁ ≤z≤zo) = 0.95 is equivalent to P(0 ≤z≤Zo) = 0.475. Using a standard normal table or calculator, we find that z = 1.96 satisfies this probability.
d. Since the standard normal distribution is symmetric, P(-Z₁≤z≤z) = 0.8994 is equivalent to P(0≤z≤Z₁) = 0.4497. Using a standard normal table or calculator, we find that z = 2.66 satisfies this probability.
e. Since the standard normal distribution is symmetric, P(-Zo≤z≤0) = 0.5 - P(0≤z≤Zo) = 0.5 - 0.3106 = 0.1894. Using a standard normal table or calculator, we find that z = -0.84 satisfies this probability.
f. Since the standard normal distribution is symmetric, P(-3≤z≤3) = 0.998. Therefore, P(z>3 or z<-3) = 0.002.
g. P(Z<z) = 0.0014 is equivalent to P(z>-z₁) = 0.0014, where z₁ is the z-value such that P(z≤z₁) = 0.0014. Using a standard normal table or calculator, we find that z₁ = -2.96. Therefore, z > 2.96 satisfies P(Z<z) = 0.0014.
h. P(z≤z) = 0.5 + 0.0014/2 = 0.5007. Using a standard normal table or calculator, we find that z = 2.59 satisfies this probability.
Step-by-step explanation:
2. Blake interviewed 24 students to see whether they collected sports cards and whether they participated in sports. The table below shows his data Sports-Card Collecting and Sports Participation Collects Sports Cards Does Not Collect Sports Cards Participates in Sports 6 Does Not Participate in Sports 3 7 How many total students Blake interviewed, participate in sports?
Therefore, out of the 24 students that Blake interviewed, 9 of them participate in sports.
What is equation?An equation is a mathematical statement that indicates that two expressions are equal. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The expressions on both sides of the equation are separated by an equal sign "=" which means that the two expressions have the same value.
Here,
According to the table, Blake interviewed a total of 24 students. To find out how many of these students participate in sports, we need to add up the number of students who collect sports cards and participate in sports, as well as the number of students who do not collect sports cards and participate in sports. So:
Total students who participate in sports = Number of students who collect sports cards and participate in sports + Number of students who do not collect sports cards and participate in sports
Total students who participate in sports = 6 + 3
Total students who participate in sports = 9
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Solve for w.
(w+5)² =2w² +3w+37
Answer:
w = 3; w = 4
Step-by-step explanation:
We can start by expanding the equation on the left hand side:
[tex](w+5)^2=2w^2+3w+37\\(w+5)(w+5)=2w^2+3w+37\\w^2+5w+5w+25=2w^2+3w+37\\w^2+10w+25=2w^2+3w+37[/tex]
We can first simplify the equation subtracting all the terms on the right hand side and having the equation equal 0:
[tex]w^2+10w+25=2w^2+3w+37\\(w^2-2w^2)+(10w-3w)+(25-37)=0\\-w^2+7w-12=0[/tex]
Now, we have one equation in standard form (ax^2 + bx + c = 0).
We can solve this equation using the quadratic equation which is
[tex]x = \frac{-b+\sqrt{b^2-4ac} }{2a} \\\\x=\frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]
Since -1 is our a value, 7 is our b, and -12 is c, we simply plug in our values and solve for x:
First x:
[tex]x=\frac{-7+\sqrt{7^2-4(-1)(-12)} }{2(-1)}\\ \\x=\frac{-7+\sqrt{1} }{-2}\\ \\x=\frac{-7+1}{-2}\\ \\x=\frac{-6}{-2}\\ \\x=3[/tex]
Second x:
[tex]x=\frac{-7-\sqrt{7^2-4(-1)(-12)} }{2(-1)}\\ \\x=\frac{-7-\sqrt{1} }{-2}\\ \\x=\frac{-7-1}{-2}\\ \\x=\frac{-8}{-2}\\ \\x=4[/tex]
Finally, we must check for extraneous solutions, which (if present) will make the equations not true. We simply plug in 3 for w and 4 for w to check for such solutions:
Checking 3:
[tex](3+5)^2=2(3)^2+3(3)+37\\8^2=2(9)+9+37\\64=18+9+37\\64=64[/tex]
Checking 4:
[tex](4+5)^2=2(4)^2+3(4)+37\\9^2=2(16)+12+37\\81=32+12+37\\81=81[/tex]
Since the equations are true for both 3 and 4, both values work for w.
This shape is made up of one half-circle attached to an equilateral triangle with side lengths 24 inches. You can use 3.14 as an approximation for π.
The perimeter οf Shape is 286.82 inches, fοr detail answer we have tο learn abοut perimeter and fοrmulas.
What is Perimeter?Perimeter is define as distance arοund are οutside οf the shape (like Rectangle, Square , Triangle etc).
Perimeter οf Equilateral Triangle = [tex]\frac{\sqrt{3} }{4}[/tex] side²
Here Side = 24 inch
Sο, Perimeter οf Equilateral Triangle = [tex]\frac{\sqrt{3} }{4}[/tex] × 24²
= [tex]\frac{\sqrt{3} }{4}[/tex] × 24 × 24
= √3 × 24 × 6
= 249.41 inches
Perimeter οr Circumference οf Semi-Circle = πr + 2r
But here Perimeter = πr ( Since the base οf Semi Circle is Cοunted in Perimeter οf Equilateral Triangle)
3.14 × 12
= 37.68 inches
Sο, the perimeter οf Shape
= 249.41 + 37.68
= 286.82 inches
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The probability that a person in the United States has type At blood is 31 %. Three unrelatedata person eUnited sleds are selected at random.
The required Probabilities of type of blood are A) 0.029791, B) 0.328509, C) 0.671491.
How to find Probability?A: event that a person has type A positive blood
A': event that a person does not have type A positive blood
We know that P(A) = 0.31, which means P(A') = 0.69.
A) To find the probability that all three people have type A positive blood, we use the multiplication rule for independent events:
P(A and A and A) = P(A) x P(A) x P(A) = 0.31 x 0.31 x 0.31 = 0.029791.
B) To find the probability that none of the three people have type A positive blood, we use the multiplication rule for independent events again:
P(A' and A' and A') = P(A') x P(A') x P(A') = 0.69 x 0.69 x 0.69 = 0.328509.
C) To find the probability that at least one of the three people have type A positive blood, we can use the complement rule:
P(at least one A) = 1 - P(none have A) = 1 - 0.328509 = 0.671491.
Alternatively, we could find this probability directly by considering the three possible cases where at least one person has type A positive blood:
one person has A and two do not: P(A and A' and A') x 3 = 0.31 x 0.69 x 0.69 x 3
two people have A and one does not: P(A and A and A') x 3 = 0.31 x 0.31 x 0.69 x 3
all three have A: P(A and A and A) = 0.029791
Then, we add up these probabilities:
P(at least one A) = (0.31 x 0.69 x 0.69 x 3) + (0.31 x 0.31 x 0.69 x 3) + 0.029791 = 0.671491.
D) The event of all three people having type A positive blood (0.029791) can be considered unusual because it has a low probability. If we define "unusual" as an event with probability less than or equal to 0.05, then this event meets that criterion. However, whether an event is considered unusual or not can depend on the specific context and criteria chosen.
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Complete question:
please help
The table of values represents a quadratic function f(x).
x f(x)
−8 7
−7 2
−6 −1
−5 −2
−4 −1
−3 2
−2 7
−1 14
0 23
What is the equation of f(x)?
f(x) = (x − 5)2 − 2
f(x) = (x − 4)2 − 1
f(x) = (x + 4)2 − 1
f(x) = (x + 5)2 − 2
Answer:
Step-by-step explanation:
From the symmetry in the table, we can see that the vertex of the parabola is located at (-5, -2). We will pick another point from the table to use in our model to solve for the a value, just in case there is one. I picked (-4, -1). Any point from the table will work.
Our model is
[tex]y=a(x-h)^2+k[/tex] where h and k are the coordinates of the vertex and x and y are the coordinates from the other point chosen from the table. Filling in to solve for a:
[tex]-1=a(-4+5)^2-2[/tex] and
[tex]-1=a(1)^2-2[/tex] and
-1 = a - 2 so
a = 1.
Now we can fill in the equation with the coordinates of the vertex and the value found for a to get
[tex]y=(x+5)^2-2[/tex] You don't need to put the 1 out in front; it's unnecessary. Your choice is the last one there in the list.
Solve the equation without using a calculator
[tex](x^3-1000)^{1/2}=(x^2+100)^{1/3}[/tex]
Without using a calculator, the only solution to the equation [tex](x^3 - 1000)^{1/2} = (x^2 + 100)^{1/3}[/tex] is 10.1136.
What is the solution of the equation?To solve this equation without using a calculator, we need to simplify both sides of the equation and then use algebraic techniques to isolate x.
[tex](x^3 - 1000)^{1/2} = (x^2 + 100)^{1/3}[/tex]
square both sides of the equation and cube both sides of the equation, we will have;
(x³ - 1000)³ = (x² + 100)²
We can simplify the left-hand side of the equation by applying the cube of a binomial formula, which states that:
(a + b)³ = a³ + 3a²b + 3ab² + b³
Let's apply this formula with a = x³ and b = -1000:
(x³ - 1000)³ = x⁹ - 3x⁶(1000) + 3x³(1000)² - 1000³
Next, let's simplify the right-hand side of the equation:
(x² + 100)² = x⁴ + 200x² + 10000
Now we can substitute these expressions back into the original equation:
x⁹ - 3x⁶(1000) + 3x³(1000)² - 1000³ = x⁴ + 200x² + 10000
We can then rearrange the terms to get a polynomial equation in x:
x⁹ - 3x⁶(1000) + 3x³(1000)² - x⁴ - 200x² - 10000 - 1000³ = 0
This equation is difficult to solve exactly, but we can make an educated guess that x is close to 10. If we substitute x = 10, we get:
(10³ - 1000)³ ≠ (10² + 100)²
Increase the value of x a little, say 10.1136
(10.1136³ - 1000)³ ≈ (10.1136² + 100)²
This is true, so x = 10.1136 is a solution to the equation. We can check that there are no other integer solutions by noting that the left-hand side of the equation is always larger than the right-hand side for x > 10, and smaller than the right-hand side for x < 10.
Therefore, the only solution to the equation is x = 10.1136.
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