Ten seventh graders and 15 eighth graders were selected for the elite choir ensemble.
a. Write the ratio of seventh graders to eighth graders who were selected for the
elite choir.
b. Write the ratio of seventh graders to total students who were selected for the
elite choir.
c. Write the ratio of eighth graders to total students who were selected for the elite
choir.

By using the unitary method, we found that 60 items were sold at $25 each, while 90 items were sold at $5 each at the charity's craft fair.

In this problem, we know the total number of items sold and the total revenue earned. Let's assume that the number of items sold at $5 each is x, and the number of items sold at $25 each is y. Therefore, we can write two equations based on this information:

x + y = 150 (Equation 1)

5x + 25y = 1950 (Equation 2)

Equation 1 represents the total number of items sold, while Equation 2 represents the total revenue earned from the sale. Now, we can use the unitary method to find the value of y, which represents the number of items sold at $25 each.

Let's rearrange Equation 2 to solve for y:

5x + 25y = 1950

25y = 1950 - 5x

y = (1950 - 5x)/25

Now, we can substitute this expression for y into Equation 1:

x + (1950 - 5x)/25 = 150

Simplifying this equation, we get:

25x + 1950 - 5x = 3750

20x = 1800

x = 90

Therefore, we know that 90 items were sold at $5 each. Now, we can use Equation 1 to find the number of items sold at $25 each:

y = 150 - x

y = 150 - 90

y = 60

Hence, 60 items were sold at $25 each.

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The best prediction possible for the number of times the spinner will not land on yellow is 18.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

Assuming that the spinner is fair and all outcomes are equally likely, we can calculate the probability of the spinner not landing on yellow in one spin by adding up the probabilities of all other outcomes, which are green, blue, and red.

The probability of the spinner not landing on yellow in one spin is:

P(not yellow) = P(green) + P(blue) + P(red)

= 1/6 + 1/3 + 1/6

= 1/2

Therefore, the expected number of times the spinner will not land on yellow in 36 spins is:

E(not yellow) = 36 x P(not yellow)

= 36 x 1/2

= 18

So the best prediction possible for the number of times the spinner will not land on yellow is 18. However, it's important to note that this is just a prediction based on probabilities, and the actual number of times the spinner doesn't land on yellow in 36 spins may vary.

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Answer:

£12063.57

Step-by-step explanation:

The value of Alfred’s car after 12 years can be calculated using the formula for exponential decay: Final Value = Initial Value * (1 - rate of depreciation)^(number of years). Plugging in the values we get: Final Value = 13960 * (1 - 0.0075)^12. Therefore, after 12 years, Alfred’s car will be worth approximately £12063.57.

The means of a stock that has a beta measure of 2.5 is 2.5%.

A beta measure of 2.5 indicates that the stock is 2.5 times as volatile as the market.

This means that if the market goes up by 1%, the stock is expected to go up by 2.5%.

The beta measure is a measure of the volatility of a stock relative to the market.

If the market goes down by 1%, the stock is expected to go down by 2.5%.

Therefore,

The stock is considered to be more risky than the average stock in the market.

A beta measure of 2.5 indicates that the stock is 2.5 times as volatile as the market.

This means that if the market goes up by 1%, the stock is expected to go up by 2.5%.

Conversely, if the market goes down by 1%, the stock is expected to go down by 2.5%.

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The two coterminal angles for 3/4 radians are (3π + 4)/4 and (-5π + 4)/4 radians.

Coterminal angles are two or more angles that have the same initial and terminal sides, but differ by a multiple of 360 degrees or 2π radians. In other words, coterminal angles are angles that overlap each other when drawn in standard position (with their initial side on the positive x-axis).

To find two coterminal angles with 3/4 radians, we can add or subtract multiples of 2π radians (which is equivalent to a full circle).

One positive coterminal angle is obtained by adding 2π radians to 3/4 radians:

3/4 + 2π = 3/4 + 8π/4 = 3/4 + 2π

Simplifying, we get:

3/4 + 2π = (3π + 4)/4

Therefore, one positive coterminal angle is (3π + 4)/4 radians.

One negative coterminal angle is obtained by subtracting 2π radians from 3/4 radians:

3/4 - 2π = 3/4 - 8π/4 = 3/4 - 2π

Simplifying, we get:

3/4 - 2π = (-5π + 4)/4

Therefore, one negative coterminal angle is (-5π + 4)/4 radians.

Hence, the two coterminal angles for 3/4 radians are (3π + 4)/4 and (-5π + 4)/4 radians.

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The decimal that represents the fraction of the $30.00 Maggie spent is 0.6.

Now, let's talk about decimals. Decimals are a way of expressing parts of a whole number in a fraction of 10. For example, 0.5 is the same as 1/2. In your situation, Maggie spent $18.00 out of $30.00. To figure out what decimal represents the fraction of the $30.00 Maggie spent, we need to divide the amount she spent by the total amount she had.

So, we can write this as a fraction:

$18.00 / $30.00

To turn this fraction into a decimal, we divide the numerator (top number) by the denominator (bottom number) using long division or a calculator.

$18.00 / $30.00 = 0.6

Another way to say this is that Maggie spent 60% of the money she had in her wallet.

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Answer:

2.36 miles

Step-by-step explanation:

radius, r = 3 miles∅ = 45°Length of an arc = ∅/360 * 2πr= 45/360 * 2 * 3.14 * 3= 2.36 miles

The area of the cement part is 24 m².

Area is the region bounded by a plane shape.

To calculate the area of the part with cement. we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the area is 24 m².

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Step-by-step explanation:

x = -4     ( the value of the x-coordinate of the vertex is the axis of symmetry for normal up or down opening parabolas)

Answer:

≈ $26

Step-by-step explanation:

13% = 0.13

199.99 x 0.13 = $25.9987

So, 13% markup is ≈ $26

1) The equation (x + 6)² + (y + 4)² = 36 represents a circle centered at the point (-6, -4) with a radius of 6. Therefore, the signal is located at the point (-6, -4).

2) The range of the signal refers to the maximum distance that the signal can travel before it becomes too weak to be detected. In this case, the range of the signal is equal to the radius of the circle, which is 6. This means that any point on the circle (x + 6)² + (y + 4)² = 36 is 6 units away from the signal located at (-6, -4).

To visualize this, imagine the signal as a point source located at (-6, -4), and the range of the signal as a circle centered at the signal with a radius of 6. Any point on this circle represents the farthest distance that the signal can reach and still be detected.

In summary, the signal is located at (-6, -4) and its range is 6 units, as represented by the circle (x + 6)² + (y + 4)² = 36.

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Answer: 1. 48.356 2. 75.3982236862

Step-by-step explanation:

Radias*2 pi

The amount that each charity gets is $25.

The charity raise simply define as we raise funds in the form of small amounts of money from a huge crowd of people within a specific period of time.

For example, if 100 people donate $50 each to your crowdfunding campaign in two weeks, you will be able to raise $5000.

To find the amount that each charity got, we have to divide the total charity amount raised in the proportion given, i.e., 1/6.

Each charity gets 1/6 of the total amount raised, which is $150.

So, we need to divide $150 by 6:

$150 ÷ 6 = $25

Therefore, each charity received $25.

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The value of x is approximately 10.57 and the value of y is approximately 15.25.

In mathematics, a chord is a straight line segment that connects two points on a curve. More specifically, a chord is a line segment that has its endpoints on the curve.

The term "chord" is most commonly used in the context of circle geometry, where a chord is a line segment that connects two points on the circumference of a circle. In this context, the length of a chord can be calculated using the Pythagorean theorem, given the lengths of the radii of the circle and the distance between the endpoints of the chord.

In a circle, if four chords are connected to form a quadrilateral, then opposite angles of the quadrilateral are supplementary. Using this property, we can set up the following equation:

105 + (7y + 1) + (7x + 1) + (4y + 14) = 180

Simplifying and solving for x and y, we get:

7x + 4y + 122 = 180

7x + 4y = 58 ......(1)

Also, we know that the opposite angles of a cyclic quadrilateral are supplementary. Therefore, we can set up the following equations:

105 + (4y + 14) = 180 ......(2)

(7y + 1) + (7x + 1) = 180 ......(3)

Simplifying and solving for y in equation (2), we get:

4y + 119 = 180

4y = 61

y = 15.25

Substituting this value of y in equation (3) and solving for x, we get:

(7x + 1) + (7*15.25 + 1) = 180

7x + 106 = 180

7x = 74

x = 10.57

Therefore, the value of x is approximately 10.57 and the value of y is approximately 15.25.

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Answer:

5 1/4

Step-by-step explanation:

The x-axis and y-axis are two parallel number lines that meet at (0, 0) to form the shape of the letter t.

Geometric objects and mathematical equations are represented on the coordinate plane, a two-dimensional graph. It is made up of the x-axis and y-axis, two parallel number lines that meet at the starting point (0, 0). The horizontal coordinate is represented by the x-axis, while the vertical coordinate is represented by the y-axis. They combine to create the Cartesian coordinate system.

Positive numbers are labelled to the right of the origin and negative values are labelled to the left of the origin on the x-axis. Positive numbers are written above the origin of the y-axis, and negative numbers are written below it. An ordered pair (x, y), where x denotes the horizontal coordinate and y denotes the vertical coordinate, is used to represent each point on the coordinate plane.

For graphing linear equations, quadratic equations, and other functions, the coordinate plane is a helpful tool. Additionally, it is employed to depict geometric forms like polygons, circles, and lines. The distance between two points, the slope of a line, and other significant features of mathematical objects can be calculated by graphing points on the coordinate plane. With applications in physics, engineering, economics, and computer science, the coordinate plane is a fundamental idea in mathematics.

The graph is shown below when y=1.

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Graph attached below,

The coordinates of the plane is

x       y

1       -3.5

2      -3

4      -2

6      -1.

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here the given equation is y = [tex]\frac{1}{2}x-4[/tex].

Now put x= 1 then y = [tex]\frac{1}{2}\times1-4 =\frac{1-8}{2}=\frac{-7}{2}=-3.5[/tex]

Now put x=2 then [tex]y=\frac{1}{2}\times2-4=1-4=-3[/tex]

Now put x=4 then [tex]y=\frac{1}{2}\times4-4=2-4=-2[/tex]

Now put x=6 then [tex]y=\frac{1}{2}\times6-4=3-4=-1[/tex]

Then coordinates of the plane is

x       y

1       -3.5

2      -3

4      -2

6      -1.

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The answer is 24. To calculate this, 8 1/2% needs to be converted to a decimal by dividing it by 100.

Numbers are often used to measure and compare objects, and they can be used to solve problems and make predictions.

8 1/2% is equal to 0.04.

To calculate the number of poetry books for children, multiply 0.04 by 600.

0.04 x 600 = 24

To find the number of poetry books for children, the decimal equivalent of 8 1/2% needs to be multiplied by the total number of poetry books.

In conclusion, 8 1/2% of 600 poetry books is equal to 24 books.

To calculate this, 8 1/2% needs to be converted to a decimal by dividing it by 100.

Then, the decimal needs to be multiplied by the total number of poetry books. This will give the answer, which can be rounded down if necessary.

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Answer: If you want me to evaluate its 18x - 2

Hope it helped :D

The number of ways to arrange the letters of PENCIL when the first letter can't be N or L is option (B) 480.

The word PENCIL has 6 letters, here we have to use permutation method.  If all the letters are used, there are 6! = 720 ways to arrange them. However, the first letter can’t be N or L. This means that there are only 4 choices for the first letter (P, E, C, or I). After choosing the first letter, there are 5 letters left to arrange,

So there are 5! = 120 ways to arrange them.

Therefore, the total number of ways to arrange the letters of PENCIL when the first letter can’t be N or L is

4 x 5! = 4 x 120 = 480

Therefore, the correct option is (B) 480.

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Answer:

I would say convenience sampling. It's hard to tell. Sampling every other person is like systematic sampling, BUT convenience sampling would be to sample people that are easy to reach.

Answer:

The answer is 59 ½

Step-by-step explanation:

4×4×4-2×1 ½×1 ½

= 64 - 2× 3/2 × 3/2

= 64 - 9/2

= 128/2 - 9/2

= 119/2

= 59 ½ in3

Hope this helped :)

Answer:

6 inches

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

The explanation is in the picture

Answer:

  2

Step-by-step explanation:

You want the average rate of change of f(x) = -x² -2x +6 on the interval [-7, 3].

The average rate of change of f(x) on the interval [a, b] is computed as ...

  m = (f(b) -f(a))/(b -a)

For the given function f(x), this is ...

  m = (f(3) -f(-7))/(3 -(-7)) = (-9 -(-29))/10 = 20/10 = 2

The average rate of change of f(x) on the interval [-7, 3] is 2.

__

Additional comment

The derivative of the function is f'(x) = -2x -2. The midpoint of the interval is x = (-7 +3)/2 = -2. The value of the derivative at the midpoint is equal to the average rate of change on the interval:

  -2(-2) -2 = 4 -2 = 2 . . . . average slope between x=-7 and x=3.

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The correct expression showing the total area of the five rooms is A. (3 x 14²) + (2 x 17²), which simplifies to 1918 square feet.

An expression is a combination of numbers, symbols, and operators (such as addition, subtraction, multiplication, and division) that represent a mathematical calculation. An expression can be a single number, a variable, or a combination of both, and can be used to represent mathematical formulas, equations, or relationships.

In the given question,

C. (3 × 17²) + (2 × 14²)

To find the total area of the five rooms, we need to add the area of each room. The area of a square is found by squaring the length of one side.

For the three rooms with sides of 14 feet each, the area of each room is:

14^2 = 196 square feet

So the total area of these three rooms is:

3 × 196 = 588 square feet

For the two rooms with sides of 17 feet each, the area of each room is:

17^2 = 289 square feet

So the total area of these two rooms is:

2 × 289 = 578 square feet

Therefore, the total area of all five rooms is:

588 + 578 = 1166 square feet

Option C, (3 × 17²) + (2 × 14²), gives the correct expression for this calculation.

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The rejection of the null hypothesis in a hypothesis test that claims the mean gestation period for a fox is more than 48.9 weeks implies there is sufficient evidence to support the claim, indicating a statistically significant difference between the observed sample mean and the hypothesized mean.

If a hypothesis test is performed that rejects the null hypothesis that the mean gestation period for a fox is 48.9 weeks or less, it means that there is sufficient evidence to support the claim that the mean gestation period for a fox is more than 48.9 weeks.

The rejection of the null hypothesis implies that the observed sample mean is significantly different from the hypothesized mean, and this difference is unlikely to have occurred by chance alone. The statistical test used to evaluate the hypothesis would have produced a p-value less than the significance level, indicating that the evidence against the null hypothesis is strong.

Therefore, the scientist can conclude that there is evidence to support their claim that the mean gestation period for a fox is more than 48.9 weeks, and this finding could have important implications for understanding fox reproductive biology and management.

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The required equation in the given situation is C = 35 + 2.50m where C is the total cost and m is the number of miles driven.

Equation: A declaration that two expressions with variables or integers are equal.

In essence, equations are questions and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

A formula would be 3x - 5 = 16, for instance.

The equation would be:

C is the total cost and m is the miles driven.

We know that:
Charge of the truck: $35

Charge per mile: $2.50

Then, form the equation as follows:

C = 35 + 2.50m

Therefore, the required equation in the given situation is C = 35 + 2.50m where C is the total cost and m is the number of miles driven.

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The amount of fencing, dirt and sod for the baseball field are;

Length of fencing ≈ 1410.5 feet

Area of the sod ≈ 118017.13 ft²

Area of of the field covered with dirt ≈ 7,049.6 ft²

The fencing of a baseball field is the outer enclosure of the field, which typically, is located along the outfield boundary.

The amount of fencing, dirt, and sod can be found using the formula for finding the circumference of a circle and the area of a circle as follows;

Area of a circle = π × r²

Circumference of a circle = 2 × π × r

Where r is the radius of the circle

The area of a quarter of a circle is therefore; Area of a circle ÷ 4

The perimeter of a quarter of a circle is; The perimeter of a circle ÷ 4

Fencing = (1/4) × 2 × π × 380 + 2 × 15 + 2 × 380 + (1/4) × 2 × π × 15

Fencing = 190·π + 790 + 7.5·π = 197.5·π + 790 ≈ 1410.5

Grass = π/4 × (380 - 6)² + 87² - π/4 × (87 + 30)² + 2 × 380 × 15 + π/4 × 15² - (3/4) × π × 10² - 25·π = 31528·π + 18969 ≈ 118017.13

Dirt; π/4 × 380² - π/4 × (380 - 6)² + π/4 × (87 + 30)²- 87² + π·100 = (18613·π - 30276)/4 ≈ 7049.6

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The tax on the belt buckle is $1.56

What is Rate?

In general terms, a rate is a measure of the relationship between two quantities that are measured in different units. A rate expresses how much of one thing there is per unit of another thing. For example, miles per hour is a rate that expresses how many miles are traveled in one hour.

To calculate the tax on the belt buckle, we need to multiply the price of the belt buckle by the sales tax rate:

Tax = Price x Tax rate

In this case, the price of the belt buckle is $25 and the sales tax rate is 6.25%. To convert the tax rate from a percentage to a decimal, we need to divide it by 100:

Tax rate = 6.25% ÷ 100 = 0.0625

Now we can calculate the tax on the belt buckle:

Tax = Price x Tax rate

= $25 x 0.0625

= $1.56

Therefore, the tax on the belt buckle is $1.56. The total cost of the belt buckle including tax would be $25 + $1.56 = $26.56.

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