The value of z can be determined by solving the equation 7z-94 = 2z+76, which yields z=35.
To determine the value of z in the given equation, it is necessary to solve the equation 7z-94 = 2z+76. Begin by subtracting 2z from both sides of the equation, which yields 7z-2z-94 = 76. Simplifying this yields 5z-94 = 76. To solve for z, add 94 to both sides of the equation, which yields 5z = 170. Dividing both sides by 5 yields z = 34. Since the equation is not asking for an exact value, it can be rounded to the nearest whole number, which is 35. Therefore, the value of z is 35.
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Do what the picture says and right answer gets brainilest!!!
Answer:
Below
Step-by-step explanation:
See image attached
The table below represents the number of NFL teams that won or lost their first game of the season. What is the probability that a team selected won their first game, given the team is from the AFC?
The prοbability that a team selected wοn their first game, given the team is frοm the AFC, is 2/3 οr apprοximately 0.67.
What is Prοbability?Prοbability is a measure οf the likelihοοd οf an event οccurring, expressed as a number between 0 and 1. A prοbability οf 0 means the event is impοssible, and a prοbability οf 1 means the event is certain.
Out οf the tοtal number οf teams that wοn their first game, 12 are frοm the AFC and 6 are frοm the NFC. Out οf the tοtal number οf teams that lοst their first game, 4 are frοm the AFC and 10 are frοm the NFC.
Therefοre, the tοtal number οf AFC teams is 12 + 4 = 16, and the tοtal number οf NFC teams is 6 + 10 = 16.
If we randοmly select a team that wοn their first game, the prοbability that the team is frοm the AFC is:
P(AFC) = number οf AFC teams / tοtal number οf teams
= 16 / (16 + 16)
= 1/2
The prοbability that the team selected wοn their first game and is frοm the AFC is:
P(wοn first game AND AFC) = number οf AFC teams that wοn first game / tοtal number οf teams that wοn first game
= 12 / (12 + 6)
= 12/18
= 2/3
Therefοre, the prοbability that a team selected wοn their first game, given the team is frοm the AFC, is 2/3 οr apprοximately 0.67.
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(4^2)+6×(5^2)−(3^3)÷(3^2)=
Answer: (16)➕6✖(25)➖(9)
In the table below, find the slope, y-intercept, and equation for each racer.
Hint: Time is going to be your independent x / the x-axis. Distance is going to be your dependent y / the y-axis.
Therefore , the solution of the given problem of slope comes out to be y = 15x + 10.
Explain slope.A line's steepness is determined by its slope. In gradient based equations, a situation known as gradient overflow can happen. One can determine the slope by dividing the sum of a run (width differential) and rise (climbing distinction) between two places. The equation with the hill variation, y = mx + b, is used to model the fixed path issue. where grade is mm, a = bc, and the line's y-intercept is situated; (0, b).
Here,
A racer:
Due to the fact that the race begins at the beginning, the y-intercept
is 0.
We can select any two locations from the table and use the following formula to determine the slope:
=> Slope Equals (Distance Change) / (change in time)
As an illustration, if we select the coordinates (1, 10) and (3, 40), we obtain:
=> slope = (40 - 10) / (3 - 1) = 30 / 2 = 15
As a result, Racer A's calculation is:
=> y = 15x
Runner B:
As an illustration, if we select the coordinates (1, 25) and (3, 55), we obtain:
=> slope = (55 - 25) / (3 - 1) = 30 / 2 = 15
As a result, Racer B's calculation is:
=> y = 15x + 20
Runner B
The race begins at a distance of 10 feet, so the y-intercept is 10.
We can select any two locations from the table and use the following formula to determine the slope:
Slope Equals (Distance Change) / (change in time)
As an illustration, if we select the coordinates (1, 35) and (3, 65), we obtain:
=> slope = (65 - 35) / (3 - 1) = 30 / 2 = 15
As a result, Racer C's equation is:
=> y = 15x + 10
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What point on the number line is one fourth of the way from the point 0 to the point −3? −0.25 −0.5 −0.75 −1
Answer: 0.75
Step-by-step explanation: Hope this helps :D
Answer: -0.75
Step-by-step explanation:
1/4th of the way to point 0,-3 from 0
-3/4=-0.75, therefore, the answer is C, -0.75.
Suppose demand d for a company's product at cost x is predicted by the function d(x) = 0. 36x2 + 810, and that the price p that the company can charge for the product is given by p(x) = x + 14. Find the company's revenue function
The revenue for a company's product is the amount of money the company earns from selling the product. R(x) = 0.36x^3 + 824x. This is the equation that tells us how much the company will earn in revenue for the product at a certain cost.
R(x) = 0.36x^3 + 824x
The revenue for a company's product is the amount of money the company earns from selling the product. To find the revenue function for a company, we can use the demand and price functions given. The demand function tells us how much of the product customers are willing to buy at a certain cost, while the price function tells us how much the company can charge for the product. R(x) = 0.36x^3 + 824x + 824x. This is the equation that tells us how much the company will earn in revenue for the product at a certain cost.
At x = 10,
R(10) = 0.36(10^3) + 824(10) + 824
R(10) = 3600 + 8240 + 824
R(10) = 17,664
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Which expression is equivalent to (4xexponent2yexponent3)exponent2?
Please refer to the photo attached
Answer:
Below
Step-by-step explanation:
You will need to multiply the exponents in the parens by 2 and square 4 so it is 16
16 x^(2*2) y^(3*2) = 16 x^4 y^6
What is the total amount due on 20000 which has been invested for five years at 10% annual interest?
Therefore , the solution of the given problem of amount comes out to be 30000 is the new amount.
What is an amount?aggregate attempting to determine the length of time needed, overall amount or quantity. The amount in front of you or being thought about is very active. the final outcome, its significance, or its meaning. three accountings: principal, interest, and the third. Word versions include amounts, amounting, and amounted. supple word How much something is, how often you possess
Here,
The straightforward interest formula can be used to determine the total amount owing on $20,000 that has been invested for five years at 10% annual interest:
=> Sum total = Principal + Interest
where Principal represents the amount invested initially and Interest represents the interest collected over the course of five years.
Since the interest gained annually is 10% of the principal, the total interest earned over the course of five years is as follows:
=> Interest is calculated as follows:
=> Interest = P*R*T
=> Interest = 20000 * 0.10 * 5
=> Interest = 10000
Total amount = 20000 +10000 = 30000
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Giving Brainliest!!!
Answer:294
Step-by-step explanation:
Answer:
[tex]294m^2[/tex]
Step-by-step explanation:
Volume of a cube is side x side x side or [tex]s^3[/tex]
now we find the value of one side
[tex]s^3 = 343m^3\\s = \sqrt[3]{343m^3} \\s = 7m\\[/tex]
Now we have a side value we can find the surface area of this cube which is
Surface area = [tex]6 * s^2[/tex]
= [tex]6 * (7m)^2[/tex]
= [tex]6 * 49m^2[/tex]
= [tex]294 m^2[/tex]
Hope this helps!
Brainliest and a like is much appreciated!
5(x-y)+4=7 what is the value of x-y
Step-by-step explanation:
We can solve for x-y by isolating the term on one side of the equation and simplifying:
5(x-y) + 4 = 7
5(x-y) = 7 - 4
5(x-y) = 3
Next, we can divide both sides by 5:
x - y = 3/5
Therefore, the value of x-y is 3/5.
enter your answer and show all the steps that you use to solve this in the space provided.
find the surface area of the cone. Use 3.14 for π height 7in diameter 8in and below it says drawing not to scale??
The surface area of the cone is 305.30 inches squared.
How to find the surface area of a cone?The height of the cone is 7 inches and the diameter of the cone is 8 inches. Therefore, let's find the surface area of the cone as follows:
surface area of the cone = πr(r + l)
where
r = radiusl = slant heightHence,
r = 8 / 2 = 4 inches
l² = 7² + 4²
l = √49 + 16
l = √65
l = 8.0622577483
l = 8.06 inches
Therefore,
surface area of the cone = 3.14 × 8.06(4 + 8.06)
surface area of the cone = 25.3154893297(12.06)
surface area of the cone = 305.304801316
surface area of the cone = 305.30 inches squared
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PLEASE HELPP!!
Given the Following hexagon
Calculate the missing angles.
Trey and matt each have a rectangular prism the base if treys is 4 by 7 by 12 the base of matts prism is 6 by 10 by 3 whose rectangular prism will require more material to construct
Trey's rectangular prism will require more material to be constructed.
To determine which rectangular prism will require more material to construct, we need to calculate the surface area of each prism.
The surface area of a rectangular prism is given by the formula,
SA = 2×l×w + 2×l×h + 2×w×h
where l, w, and h are the length, width, and height of the prism, respectively.
For Trey's prism, the length is 12, the width is 7, and the height is 4. Therefore, the surface area of Trey's prism is:
SA of Trey = 2(12 x 7) + 2(12 x 4) + 2(7 x 4) = 336
For Matt's prism, the length is 10, the width is 6, and the height is 3. Therefore, the surface area of Matt's prism is,
SA of Matt = 2(10 x 6) + 2(10 x 3) + 2(6 x 3) = 192
Comparing the surface areas, we see that Trey's prism requires more material to construct since its surface area is larger than Matt's prism. Therefore, Trey's rectangular prism requires more material to construct than Matt's rectangular prism.
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Q27) A retailer receives some products from three suppliers - $1, S2 and S3. The probability of successfully delivering the products in time by the suppliers are 0.85 for S1, 0.82 for S2 and 0.91 for S3. No supplier's delivery is impacted by any other supplier's delivery. The manufacturer orders 500 units of a raw material from $1, 120 units from S2 and 156 units from S3. What is the expected loss for the retailer given that failure to receive the materials in time will cost the manufacturer $20 per unit for the product supplied by $1, $30 for the product supplied by 52 and $10 for the product supplied by S3.
Expected loss for the retailer is $2288.4
There are three suppliers named S1, S2, and S3 who provide raw materials to a retailer. The probability of supplying the raw materials on time for S1, S2, and S3 are 0.85, 0.82, and 0.91 respectively. Let’s suppose that the retailer orders 500 units of raw material from S1, 120 units from S2, and 156 units from S3. The loss for the retailer is $20, $30, and $10 respectively for S1, S2, and S3. To find out the expected loss for the retailer, we can use the formula given below:Expected loss = (probability of loss) × (value of loss) + (probability of no loss) × (value of no loss)Let’s calculate the expected loss for each supplier separately.Supplier S1: The probability of not receiving raw material on time from S1 is 1 - 0.85 = 0.15. The expected loss due to S1 can be calculated as follows:Expected loss for S1 = (0.15) × (500 units) × ($20 per unit) = $1500Supplier S2: The probability of not receiving raw material on time from S2 is 1 - 0.82 = 0.18. The expected loss due to S2 can be calculated as follows:Expected loss for S2 = (0.18) × (120 units) × ($30 per unit) = $648Supplier S3: The probability of not receiving raw material on time from S3 is 1 - 0.91 = 0.09. The expected loss due to S3 can be calculated as follows:Expected loss for S3 = (0.09) × (156 units) × ($10 per unit) = $140.4Therefore, the total expected loss for the retailer can be calculated by adding the losses from all three suppliers.Total expected loss = $1500 + $648 + $140.4 = $2288.4Thus, the expected loss for the retailer is $2288.4.
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What is the perimeter of the figure with vertices D(-4, 5), E(-4, -6) and F(3, -6)?
The perimeter of the figure with vertices D(-4, 5), E(-4, -6) and F(3, -6) is given as follows:
31.04 units.
How to calculate the perimeter of a polygon?The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.
The vertices of the polygon in this problem are given as follows:
D(-4, 5), E(-4, -6) and F(3, -6).
Hence the side lengths are given as follows:
DE = 11 units -> x constant, subtract y.DF = sqrt((-4 - 3)² + (5 - (-6))²) = 13.04 units.EF = 7 units, y constant, subtract x.Hence the perimeter of the polygon is given as follows:
11 + 13.04 + 7 = 31.04 units.
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Use synthetic division to write (6x+5)/(x+7) in the form quotient +( remainder )/( divisor ).
[tex](6x+5)/(x+7)\\[/tex] can be represented as in the form quotient [tex]+( remainder )/( divisor )[/tex] as [tex]6 + 47/(x+7)[/tex] using division.
The methods below show how to use synthetic division to write (6x+5)/(x+7) in the form quotient +(remainder)/(divisor):
The divisor, x+7, should be written in the following format: (a, b, c,... 0), where the final term is 0 and the other terms are the polynomial coefficients in descending order of degree. The divisor is already present in this form in this instance.Using the same format as the divisor and a 0 coefficient for any missing terms, write the dividend, 6x+5, in the same format. The dividend can therefore be expressed as (6, 5).Reduce the dividend's first period, which is six years.Multiply the first coefficient of the dividend by the amount that was just brought down, and then place the answer under the second coefficient of the payout. So, we multiply 7 by 6 to obtain 42, which we then place in the payout under the number 5.To determine the new dividend coefficient value, add the two coefficients from the previous step. Because of this, 5 + 42 = 47.Repeat steps 4 and 5 as necessary to process all of the dividend's terms. The leftover is the last coefficient in the dividend, and together with the other coefficients, it makes up the quotient. In this instance, the remainder is 47 and the quotient is 6.So, (6x+5)/(x+7) is the divisor x+7 divided by the quotient 6 plus the remainder 47. Hence, we can write:
(6x+5)/(x+7) = 6 + 47/(x+7)
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help please i really appreciate it
Answer:
B
Step-by-step explanation:
Find the Primeter and area
For rectangle type books, the difference in the heights of their stacks of books is 15 3/4 inches.
What exactly is a rectangle?
A rectangle is a type of quadrilateral (a four-sided polygon) that has four straight sides and four right angles. It is a two-dimensional shape, meaning it lies flat in a plane, and is defined by its two sets of parallel sides, each pair of which are equal in length.
In a rectangle, opposite sides are parallel and congruent (equal in length), and adjacent sides are perpendicular (meet at a right angle). The diagonals of a rectangle bisect each other (divide each other into two equal parts) and are congruent.
The area of a rectangle is calculated by multiplying its length and width, while its perimeter is found by adding the lengths of all its sides. The area of a rectangle is A = l x w, where A is the area, l is the length, and w is the width.
Now,
To solve this problem, we need to first find out the height of Rick's stack of books. We know that his stack is 3 times as tall as Trevor's stack, so:
Rick's stack = 3 x Trevor's stack
Rick's stack = 3 x 7 7/8 inches
Rick's stack = 23 5/8 inches
Now that we know the height of both stacks, we can find the difference between them:
Difference = Rick's stack - Trevor's stack
Difference = 23 5/8 inches - 7 7/8 inches
Difference = 15 6/8 inches
Difference = 15 3/4 inches
Therefore, the difference in the heights of their stacks of books is 15 3/4 inches.
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MNPQ is a rectangle. Find the value of x.
*
The original price of a laptop was £200.
The price of the laptop was reduced by 10% in sale.
A) work out 10% of the original price of the laptop.
B)work out the sale price of the laptop.
Answer:
A) £20
B) £180
Step-by-step explanation:
The original price is £200. The price was reduced by 10% so the sale price is 90% of the original price.
A) Price Reduction = 200 * 0.1 = £20
B) Sale Price = Original Price - Price Reduction = 200 - 20 = £180
Original Price * Percent Paid = 200 * 0.9 = £180
URGENT!!
3. Suppose ABC=EFG, and EG=7x-11, AB 5x -9. GF=3x-1 and AC=2x+4 . Find the value of x and the lengths of the sides of EFG.
Part I: Sketch the triangles below.
Part II: Use measures for AC and EG to find the value of x. Show your work.
Part III: Find the lengths of the sides of EFG. Show your work.
Part IV: Explain how to find the lengths of the sides of ABC.
Part II: Value of x=0
Part III: the lengths of the sides of EFG as EF = G = 11 and EG = -11.
Part IV: the lengths of the sides of ABC as AB = -9, GF = -1, and AC = 4.
What is value?Value can be used to find the solution to an equation or to compare two or more values.
Part II: To find the value of x, we need to use measures for AC and EG. We can use the equation AC = 2x + 4 to solve for x.
We can rearrange the equation to 2x = AC - 4, and then substitute in the value of AC, which is 2x + 4.
This gives us 2x = 2x + 4 - 4, or 0 = 0
x = 0.
Part III: To find the lengths of the sides of EFG, we can use the equation EF = G + 7x - 11.
Substituting in the value of x, which is 0, we get
EF = G + 7 * 0 - 11,
or EF = G - 11.
Since EG = 7x - 11, substituting in the value of x gives us
EG = 7 * 0 - 11,
or EG = -11.
So EF = G and EG = -11
Part IV: To find the lengths of the sides of ABC, we can use the equation AB = 5x - 9, substituting in the value of x as 0.
This gives us AB = 5 * 0 - 9,
or AB = -9.
Since GF = 3x - 1 and AC = 2x + 4, substituting in the value of x gives us GF = 3 * 0 - 1,
or GF = -1,
and AC = 2 * 0 + 4
or AC = 4.
So AB = -9, GF = -1, and AC = 4, giving us the lengths of the sides of ABC as AB = -9, GF = -1, and AC = 4.
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(x + 2y ) 2 some one answer this please I need help
Answer:
x² + 4xy + 4y²
Step-by-step explanation:
(x + 2y )²
= (x + 2y) (x + 2y)
= x² + 2xy + 2xy + 4y²
= x² + 4xy + 4y²
So, the answer is x² + 4xy + 4y²
A square on the coordinate plane has vertices at (−5, 5), (5, 5), (5, −5), and (−5, −5). A dilation of the square has vertices at (−10, 10), (10, 10), (10, −10), and (−10, −10). Find the scale factor and the perimeter of each square
the perimeter of the original square is 40 units, and the perimeter of the dilated square is 80 units.
To find the scale factor of the dilation, we can compare the corresponding side lengths of the two squares. The distance between the points (-5,5) and (5,5) is 10 units, which is also the length of the side of the original square. The distance between the points (-10,10) and (10,10) is 20 units, which is the length of the side of the dilated square. Therefore, the scale factor is:
Scale factor = Length of dilated square side / Length of original square side = 20 / 10 = 2
This means that the dilated square is twice as large as the original square.
To find the perimeter of the original square, we can add up the length of each side. Each side of the square has a length of 10 units, so the perimeter is:
Perimeter of original square = 4 × length of one side = 4 × 10 = 40 units
To find the perimeter of the dilated square, we can use the same method. Each side of the dilated square has a length of 20 units, so the perimeter is:
Perimeter of dilated square = 4 × length of one side = 4 × 20 = 80 units
Therefore, the perimeter of the original square is 40 units, and the perimeter of the dilated square is 80 units.
Dilation is a transformation that changes the size of an object but leaves its shape unchanged. In this case, the dilation of the square resulted in a larger square that was similar to the original square, meaning that the corresponding angles in the two squares were equal. The scale factor of the dilation determined the ratio of the side lengths of the two squares, and the perimeter of each square was proportional to its side length. Dilations are used in geometry to create similar figures and to scale up or down an object in size.
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These triangles are similar. I need to know what x is.
The value of x as per the similarity of triangles is = 7.1.
What is similarity of triangles?If two triangles' sides have the same ratio or proportion and their angles are the same (corresponding angles), then the triangles will resemble one another (corresponding sides).
Similar triangles may have varied side lengths when compared individually, but they must all have the same ratio of their side lengths and equal angles.
Now in the figure, the triangles are similar.
So, sides of the triangles will be proportional to each other.
Now, 9/15 = 4.3/x
⇒ x = (4.3 × 15)/ 9
⇒ x = 7.1
Therefore, the value of x as per the similarity of triangles is = 7.1.
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Find the probability of obtaining exactly four tails when flipping four coins. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth
The probability of obtaining exactly four tails {( T,T,T,T)}, when flipping four coins is equals to the 1/16 = 0.0625.
Independent Events : If the result of one event does not influence the result of another event, then the events are referred to as independent. In other words, it can be said that both events can happen simultaneously without interference. Probability is defined as a chance of occurrence of an event. Let E be the event that exactly four tails when flipping four coins. As we know that, when One coin is flip, total outcomes = 2 = { H,T}
So, 4 coins flipped, total possible outcomes = 16
Probability of getting tail on flipping one coin = 1/2
That is exactly four tails when flipping four coins are independent events. Therefore, the probability of obtaining four tails in a row in 4 flips of a coin is the product of probability in 4 flips. Since each flipping of a coin is independent, so
the probability of obtaining exactly four tails when flipping four coins = P(X = 4)
=( 1/2)(1/2)(1/2)(1/2) = (1/2)⁴
= 0.0625
Hence, required probability is 0.0625.
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A curve has the equation y= x² + ax + b, where a and b are numbers. The turning point of the curve is (5, 4). Work out the values of a and b.
The values of a and b are -10 and 29, respectively of the curve.
What do you mean by turning point of a quadratic curve ?
The turning point of a quadratic curve is the point at which the curve changes direction from going up to going down, or vice versa. It is also known as the vertex of the parabola. The x-coordinate of the turning point is given by -b/2a, and the y-coordinate is the value of the function at that point.
Finding the values of a and b :
Given that the turning point of the curve is (5,4), we can write the following equations:
[tex]4 = 5^2 + 5a + b[/tex] (since the turning point lies on the curve)
[tex]0 = 2(5) + a[/tex] (since the derivative of the curve at the turning point is 0)
Simplifying the second equation gives us:
[tex]a = -10[/tex]
Substituting this value of a in the first equation, we get:
[tex]4 = 5^2 - 50 + b[/tex]
[tex]b = 29[/tex]
Therefore, the values of a and b are -10 and 29, respectively.
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Eighteen individuals are scheduled to take a driving test at a particular DMV office on a certain day, eight of whom will be taking the test for the first time. Suppose that six of these individuals are randomly assigned to a particular examiner, and let X be the number among the six who are taking the test for the first time. a. What kind of a distribution does X have (name and values of all parameters)?
b. Compute c. Calculate the mean value and standard deviation of X.
The distribution of X is a hypergeometric distribution, he probability that exactly 2 of the 6 individuals assigned to the examiner are taking the test for the first time is 0.317 and the mean value of hypergeometric distribution is 1.187.
a. The distribution of X is a hypergeometric distribution with the following parameters:
N = 18 (total number of individuals)
K = 8 (number of individuals taking the test for the first time)
n = 6 (number of individuals randomly assigned to a particular examiner)
b. The probability mass function of a hypergeometric distribution is given by:
P(X = x) = (K choose x) * ((N-K) choose (n-x)) / (N choose n)
So, for example, the probability that exactly 2 of the 6 individuals assigned to the examiner are taking the test for the first time is:
P(X = 2) = (8 choose 2) * (10 choose 4) / (18 choose 6) = 28 * 210 / 18564 = 0.317
c. The mean value of a hypergeometric distribution is given by:
E(X) = n * (K/N) = 6 * (8/18) = 2.667
The standard deviation of a hypergeometric distribution is given by:
SD(X) = sqrt(n * (K/N) * ((N-K)/N) * ((N-n)/(N-1))) = sqrt(6 * (8/18) * (10/18) * (12/17)) = 1.187
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e population of Matteson in t years can be m What is the population of Matteson now?
Cannot be determined
The population of Matteson can be calculated using the given formula: m(t) = 11410 + 220t. However, the current population of Matteson is not given in the question, so it cannot be calculated using the given formula. Therefore, the population of Matteson now cannot be determined based on the given information.
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i need help on geometry, an explanation on the answer would be helpful, thanks.
The following are the correct measures for the angles and arc length:
m∠DFA = 58°
m∠COB = 114°
m∠EOB = 122°
arc CE = 124°.
How to evaluate for the measures of the angles and arcm∠CED = [360 - 2(124)]/2 {angles at a point}
m∠CED = 56°
m∠A = [360 - 2(114)]/2 {angles at a point}
m∠A = 66°
m∠F = 180 - (56 + 66) {sum of interior angles of a triangle}
m∠F = 58°
The lines touching the circle at point C, B, and E respectively are tangents, hence the radii are perpendicular to each lines so;
angles m∠OCA, m∠OBA, m∠OBF, and m∠OEF are all equal to 90°
m∠COB = 360° - (90 + 90 + 66)° {sum of interior angles of a quadrilateral}
m∠COB = 114°
m∠EOB = 360° - (90 + 90 + 58)° {sum of interior angles of a quadrilateral}
m∠EOB = 122°
m∠CDE = 180° - arcCE
56° = 180° - arcCE
arcCE = 180° - 56°
arc CE = 124°.
Therefore, the correct measures of the angles and arc length are:
m∠DFA = 58°
m∠COB = 114°
m∠EOB = 122°
arc CE = 124°
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Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player. Josiah predicted the number of rock songs on his MP3 player to be 300 songs. Which statements about his solution are true? Select three choices. Josiah’s Music Sample 1 Sample 2 R & B 5 R & B 4 Pop 4 Pop 3 Classical 3 Classical 5 Jazz 2 Jazz 4 Rock 6 Rock 4 Josiah’s work: StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction. StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction. 300 = x. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5. He did not multiply the numerator and denominator by the correct number to equal 1,500. His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion. He can only solve the proportion by multiplying the numerator and denominator by a common multiple. He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500.
Answer:
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Step-by-step explanation:
Based on the information provided, the three true statements about Josiah's solution are:
"300 = x." - This statement is true because Josiah predicted that there were 300 rock songs on his MP3 player.
"He did not multiply the numerator and denominator by the correct number to equal 1,500." - This statement is true because in his proportion, Josiah multiplied the numerator and denominator by 30, which is not a multiple of 1,500.
"He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500." - This statement is true because to set up a proportion with 1,500 as the denominator, Josiah should have multiplied the numerator and denominator by a multiple of 1,500. In this case, 75 is a multiple of 1,500, so multiplying by 75 would have been the correct approach.