Basketballs cost 24$. a physical education teacher spent 312$ on basketballs for the school.

Which equation can be used to determine the number (n) of basketballs the physical education teacher purchased?

A. 24+n=312
B. 24/n =312
C. 24n= 312
D. 24 =312-n
URGENT!!!

The value of x in the triangle is 8.8493 units.

Trigonometry deals with the relationships between the sides and angles of triangles.

The three primary trigonometric functions are sine, cosine, and tangent, which are ratios of the sides of a right triangle. These functions are often abbreviated as sin, cos, and tan.

Using the given triangle:

11.6² =  x² + 7.5²    (Pythagoras theorem)

x² = 11.6² - 7.5²

x² = 78.31

x = √78.31

x = 8.8493 units

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It is not possible for a subset of A to contain elements of Ac

To answer the question, "Can a subset of A contain elements of Ac?" we must first understand what these terms mean.

A subset of A is a set that contains only elements that are also in A. On the other hand, Ac is the complement of A, which is the set of all elements that are not in A. Therefore, an element that is in Ac is not in A.

Now, let us consider the possibility of a subset of A containing elements of Ac. If an element is in Ac, it is not in A. Therefore, it cannot be in any subset of A, as all elements of a subset must be in A. This means that it is not possible for a subset of A to contain elements of Ac.

In summary, It is not possible for a subset of A to contain elements of Ac because the complement of A includes all the elements that are not in A. Therefore, any element that is in Ac cannot be in any subset of A

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Complete Question:

Can a subset of A contain elements of Ac? Give reason.

Answer:

Kailey flipping heads: 3/4 as a fraction, 0.75 as a decimal, and 75% as a percent.

Olivia flipping tails: 9/20 as a fraction, 0.45 as a decimal, and 45% as a percent.

Step-by-step explanation:

Kailey flipped heads 15 times and tails 5 times.

First, find the total amount of times that Kailey flipped the coin.

15+5=20

Kailey flipped the coin 20 times.

Out of those 20 times, she flipped heads 15 times. We can rewrite this as:

[tex]\frac{15}{20}[/tex]

and simplify it:

[tex]\frac{3}{4}[/tex]

3/4 as a decimal is 0.75, and to find the percentage, simply multiply the decimal form by 100.

We can find that 3/4 as a percentage is 75%.

So, the probability of Kailey flipping heads is:

3/4 as a fraction, 0.75 as a decimal, and 75% as a percent.

Olivia flipped heads 11 times and tails 9 times.

Let's find how many times she flipped the coin.

11+9=20

Olivia flipped the coin 20 times.

Out of 20 times, Olivia flipped tails 9 times.

This can be rewritten as:

[tex]\frac{9}{20}[/tex]

This fraction is already in simplest form.

To find what 9/20 is as a decimal, divide 9 by 20. You'll get 0.45.

Now, multiply 0.45 by 100 to find the percent. You'll get 45%.

So, the probability of Olivia flipping tails is:

9/20 as a fraction, 0.45 as a decimal, and 45% as a percent.

The smallest number possible is 42.5 pound.

We have,

42 pounds 8 ounce.

We know 1 pound = 16 ounce

So, 42 pounds 8 ounce

= 42 + 8/16

= 42 + 1/2

= 42+ 0.5

= 42.5 pounds

Now, dividing by 5 we get

= 42.5/5

= 8.5

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Answer:

I put the equation on math-way and it gave me this:

Answer:

Starting at (0, 1), go up 4 units, then right 3 units. You will end at (3, 5). Plot that point, and then draw a line that goes through the two points.

Answer: To write the equation of a line parallel to AB through a given point, we need to follow these steps:

Find the slope of the line AB. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:

m = (y2 - y1)/(x2 - x1)

Let the coordinates of points A and B be (x1, y1) and (x2, y2) respectively. Then, the slope of the line AB is:

m = (y2 - y1)/(x2 - x1)

Since we want to find the equation of a line parallel to AB, the slope of this line will also be equal to m.

Let the given point be (x0, y0). Using the point-slope form of the equation of a line, we can write the equation of the line passing through (x0, y0) with slope m as:

y - y0 = m(x - x0)

Substituting the value of m found in step 1, we get:

y - y0 = (y2 - y1)/(x2 - x1) * (x - x0)

This is the equation of the line parallel to AB passing through the point (x0, y0).

Note that we assume that the line passing through A and B exists and is not vertical. If the line is vertical, then its slope is undefined, and we cannot find the equation of a parallel line using this method. In that case, we need to use a different method to find the equation of the line.

Step-by-step explanation:

The expression that can be used to find the total number of sundaes made by the students is option B, 3 x 22.

In mathematics, an expression is a combination of variables, numbers, and mathematical operations that can be evaluated to produce a value. It can be as simple as a single number or variable, or it can be more complex and involve multiple variables and operations. Expressions can be used to represent a wide variety of mathematical concepts and relationships, and are an essential part of algebra, calculus, and other branches of mathematics.

The number of sundaes that can be made by one student is 3 x 3 = 9 (since each student chooses one of 3 syrups and one of 3 candy toppings).

Since there are 22 students in each class, the total number of sundaes made by one class is 22 x 9 = 198. Since there are 3 classes, the total number of sundaes made by all the students is 3 x 198 = 594.

Therefore, the expression that can be used to find the total number of sundaes made by the students is option B, 3 x 22.

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Length of the new rectangle = 28 x 2 = 56,Width of the new rectangle = 7 x 2 = 14These are indeed the dimensions of the new rectangle we considered, so we can conclude that it is similar to the given rectangle.

How to solve the question?

In order for two rectangles to be similar, their corresponding sides must be in proportion. This means that the ratio of the length to the width in one rectangle must be equal to the ratio of the length to the width in the other rectangle.

Let's consider a rectangle with a length of 56 and a width of 14. We can check if this rectangle is similar to the given rectangle by calculating the ratio of the length to the width in each rectangle:

Ratio in the given rectangle = 28/7 = 4

Ratio in the new rectangle = 56/14 = 4

As we can see, the ratio of the length to the width is the same in both rectangles. Therefore, the rectangle with a length of 56 and a width of 14 is similar to the given rectangle.

To confirm this, we can calculate the dimensions of the new rectangle by scaling up the dimensions of the given rectangle by a factor of 2. That is, we can multiply the length and width of the given rectangle by 2:

Length of the new rectangle = 28 x 2 = 56

Width of the new rectangle = 7 x 2 = 14

These are indeed the dimensions of the new rectangle we considered, so we can conclude that it is similar to the given rectangle.

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We can conclude:

a) For an initial population size of 286, the population will trend towards extinction.

b) For an initial population size of 16, the population will exhibit unbounded growth in finite time.

What is differential equations?

Differential equations are mathematical equations that describe the relationship between an unknown function and its derivatives (or differentials).

The modified logistic equation is given by:

dP/dt = aP - bP²

where P is the population size, and a and b are positive constants.

To determine the limiting behavior of the population, we need to analyze the phase portrait of the differential equation. This can be done by finding the equilibria of the system, and then examining the direction of the vector field near each equilibrium.

The equilibria of the system occur when dP/dt = 0. This leads to two possible equilibria:

P = 0, and P = a/b

The direction of the vector field near each equilibrium can be determined by examining the sign of dP/dt for values of P slightly greater and less than the equilibrium value.

Near P = 0, dP/dt = aP > 0 for P > 0, indicating that the population will grow in this region.

Near P = a/b, dP/dt = -bP² < 0 for P slightly greater than a/b, indicating that the population will decrease in this region.

Based on this analysis, we can conclude:

a) For an initial population size of 286, the population will trend towards extinction. This is because 286 is larger than a/b, so the population starts in the region where the vector field is pointing towards extinction.

b) For an initial population size of 16, the population will exhibit unbounded growth in finite time.

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As per the triangle, the length of the other, shorter leg is 3.46 units.

We know that a is twice the length of b, so we can write:

a = 2b

We also know that c is the square root of three times b, or:

c = √3b

Now, let's say we're given the length of the longer leg, a. We can use our equation a = 2b to solve for b:

a = 2b

b = a/2

So, we know that the shorter leg is half the length of the longer leg. For example, if a is 8, then b is 4.

To double-check our answer, we can use the equation for the hypotenuse:

c = √3b

c = √3(4)

c = 2√3 = 3.46

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The relative error in calculating the area of the rectangle is 0.0155.

The relative error means ratio of the absolute error of the measurement to the actual measurement.

The actual area of the rectangle is:

= 10 ft x 8 ft

= 80 sq ft

The measured area is:

= 10.46 ft x 7.53 ft

= 78.7638 sq ft

The relative error derive by the following formula:

= (Real - Measured)/Real

= (80 - 78.7638)/80

= 0.0154525

= 0.0155.

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Answer:

b

Step-by-step explanation:

Answer: by watching videos

Step-by-step explanation:

Answer: Watch a video or do your best to scroll down as soon as the website loads. The scrolling worked for me before but you get about 5 seconds before you can't see it anymore.

Step-by-step explanation:

The solution to the initial value problem is [tex]y = 4e^{(5x^{10})[/tex]. The domain of the function is all real numbers.

Ordinary differential equations of the first order only take into account the dependent variable y's first derivative with regard to the independent variable x. They could be written as follows:

f(x,y) = dy/dx

where the supplied function of both x and y is f(x,y). There are numerous methods for solving first-order ordinary differential equations, which are crucial in many branches of science and engineering. One such method is variable separation. Other methods include Bernoulli equations, integrating components, and precise equations.

The given differential function is:

[tex]dy/dx = 10x{^9}y[/tex]

Separating the variables we have:

dy/y = 10x^9 dx

Now, integrating on both sides:

[tex]]int dy/y = \int 10x^9 dx\\ln (y) = 5x^{10} + C[/tex]

Solving for y:

[tex]y = ke^{(5x^{10})[/tex]

Now, for the initial values y = 4 and x = 0 we have:

[tex]4 = ke^{(0)}[/tex]

k = 4

Hence, the solution to the initial value problem is [tex]y = 4e^{(5x^{10})}[/tex].

The domain of the function is all real numbers.

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The measure of DE, given that Triangle ABC is similar to Triangle DEF, is 53. 09 units .

To find the measure of DE, you need to use the corresponding sides of BC and EF to find the scale factor that shows the difference in the sizes of corresponding sides.

The scale factor is:

= 31 / 8

= 3. 875

Now, since the value of the corresponding side of AB is 13.7 units, the measure of DE would be :

= 13. 7 x 3. 875

= 53. 09 units

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If [tex]5[/tex] grammes are rounded to the closest tenth, that would be  [tex]0.175[/tex] ounces.

The conversion factor that states [tex]1[/tex] gramme is about equivalent to [tex]0.035[/tex]ounces can be used to convert grammes to ounces.

we may multiply  [tex]5[/tex] by  [tex]0.035[/tex] to convert [tex]5[/tex] grammes to ounces:

[tex]5 grams \times 0.035 \ oz/gram = 0.175[/tex] ounces

It's vital to remember that the ratio of 1 gramme to  [tex]0.035[/tex] ounces is merely an estimate; the precise ratio is 1 gramme to [tex]0.03527396195[/tex] ounces.

However, utilizing the streamlined conversion factor of [tex]1[/tex] gramme to [tex]0.035[/tex] ounces is accurate enough for the majority of routine uses.

Therefore,If [tex]5[/tex] grammes are rounded to the closest tenth, that would be  [tex]0.175[/tex] ounces.

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Answer:

There are 775 - 91 + 1 = 685 integers.

In the given range, the smallest multiple of 14 is 98, and the largest multiple of 14 is 770. ((770-98)/14) + 1 = 49 multiples of 14.

So the probability of choosing a multiple of 14 from this range is 49/685.

The probability that exactly one of the computers will be defective is 0.141

To calculate the probability of exactly one defective computer being selected out of four computers, we can use the binomial distribution formula

P(X = k) = (n choose k) × p^k × (1 - p)^(n - k)

where P(X = k) is the probability of exactly k successes (in this case, one defective computer), n is the total number of trials (in this case, four computers being selected), p is the probability of success (in this case, the probability of selecting a defective computer), and (n choose k) is the binomial coefficient, which represents the number of ways to choose k items out of n.

The probability of selecting a defective computer is 4/15, since there are 4 defective computers out of 15 in total. Therefore, the probability of selecting exactly one defective computer out of four is:

P(X = 1) = (4 choose 1) × (4/15)^1 × (11/15)^3

= 4 × 4/15 × 1331/3375

= 0.141

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The given question is incomplete, the complete question is:

A computer retail store has 15 personal computers in stock. A buyer wants to purchase 4 of them. Unknown to either the retail store or the buyer, 4 of the computers in stock have defective hard drives. Assume that the computers are selected at random. What is the probability that exactly one of the computers will be defective?

According to the price, it will take 3.75 hours for the prices of both stocks to be the same, assuming they continue to increase and decrease at the same rates.

To find out when the prices of both stocks will be the same, we need to set up an equation where the prices of both stocks are equal. Let's call the number of hours it takes for the prices to be equal "t".

For stock A, the price after "t" hours can be expressed as:

Price of stock A = $12.73 + ($0.06 x t)

For stock B, the price after "t" hours can be expressed as:

Price of stock B = $13.48 - ($0.14 x t)

To find the time when the prices of both stocks are equal, we can set the two equations equal to each other and solve for "t".

$12.73 + ($0.06 x t) = $13.48 - ($0.14 x t)

Simplifying this equation, we get:

$0.20 x t = $0.75

Dividing both sides by $0.20, we get:

t = 3.75 hour

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The radius of the pool is changing at a rate of 3 / (20π) cm/min when the radius is 10 cm.

To solve this problem, we'll use the given information and the area formula for a circle.
Write the formula for the area of a circle:

[tex]A = \pi r^2[/tex],

where A is the area and r is the radius.
Differentiate both sides of the equation with respect to time (t): [tex]dA/dt = d(\pi r^2)/dt.[/tex]
Apply the chain rule on the right side: [tex]dA/dt = 2\pi r(dr/dt),[/tex]

where dr/dt is the rate of change of the radius.
Plug in the given values:

dA/dt = 3 cm²/min (given) and r = 10 cm (given at the moment of interest).
Solve for dr/dt:
3 = 2π(10)(dr/dt).

Isolate dr/dt:
dr/dt = 3 / (20π)
Simplify:
dr/dt = 1 / (20π/3) = 3 / (20π).

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According to the table, the "Under 18" age group constitutes 24% of the total population, which is nearly 25 percent. Therefore, the answer is "nearly 25 percent".

The percentage of the population under the age of 18 can be calculated by dividing the total number of people in that age group by the total population, then multiplying by 100 to obtain a percentage.

From the table, we see that the total number of people under 18 is 74,181,467.

The total population is the sum of the total numbers in all age groups, which is 74,181,467 + 30,672,088 + 82,134,554 + 81,489,445 + 40,267,984 = 308,745,538.

Dividing the total number of people under 18 by the total population and multiplying by 100 gives

(74,181,467 / 308,745,538) × 100 ≈ 24%.

Therefore, nearly 25% of the population was under the age of 18 in 2010.

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The surface area of the cylinder is approximately 50.2 square cm

The formula for the surface area of a cylinder is:

Surface area = 2πr^2 + 2πrh

where r is the radius of the cylinder and h is the height of the cylinder.

In this case, the radius is 2 cm and the height is also 2 cm.

Substituting these values into the formula, we get:

Surface area = 2π(2)^2 + 2π(2)(2)

Surface area = 8π + 8π

Surface area = 16π

So, we have

Surface area ≈ 16(3.14)

Surface area ≈ 50.2

Therefore, the surface area of the cylinder is approximately 50.2 square cm when rounded to the nearest tenth.

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The surface area of the prism is 78 square units, which corresponds to option A.

You provided three dimensions: 5 units, 3 units, and 3 units. I assume these are the dimensions of a rectangular prism.

Let's label the dimensions: length (l) = 5 units, width (w) = 3 units, and height (h) = 3 units.

There are two bases, and their areas are equal:

Base Area = l * w = 5 * 3 = 15 square units

There are also three pairs of lateral faces. The areas of the lateral faces are:

Two faces with dimensions l and h: 2 * (l * h) = 2 * (5 * 3) = 30 square units

Two faces with dimensions w and h: 2 * (w * h) = 2 * (3 * 3) = 18 square units

Now, add the areas of all the faces together:

Surface Area = Base Area * 2 + Lateral Area = 15 * 2 + 30 + 18 = 30 + 30 + 18 = 78 square units

So, the surface area of the prism is 78 square units, which corresponds to option A.

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The rate of change of the circular area is increasing at a constant rate of 12π square feet per second when the radius is exactly 3 feet.

To solve this problem, we need to use the formula for the area of a circle:

[tex]A = πr^2[/tex],

where A is the area and r is the radius.

We also need to use the chain rule of differentiation because we are dealing with a changing radius over time.

First, we can find the rate of change of the area with respect to time (dA/dt) by differentiating the formula for the area:

dA/dt = 2πr(dr/dt)

where dr/dt is the rate of change of the radius with respect to time, which is given as 2 feet per second in the problem.

Therefore, we can substitute these values into the formula to get:

dA/dt = 2π(3)(2)

dA/dt = 12π

So, the rate of change of the circular area is increasing at a constant rate of 12π square feet per second when the

radius is exactly 3 feet.

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The amount that the Jones family would pay in the 18th month would be $1,233.45

Prior to determining the required payment for the 18th month, it is paramount to calculate the collective minimum payments by the Jones family during the course of seventeen months.

First, find the amount that had been paid in total by the Jones in 17 months to be :

= Monthly payment x minimum monthly payment

= 17 x 25

= $ 425

The balance after 17 months is :

= $ 1 , 658. 45 - $ 425

= $ 1, 233. 45

The remaining balance of $ 1, 233. 45 would have to be paid in the 18th month.

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The surface area of the square pyramid is 384 cm squared.

The surface area of the square base pyramid can be found as follows:

surface area of the square base pyramid = base area + 2al

where

Therefore,

base area = 12 × 12

base area = 144 cm²

Hence,

surface area of the square base pyramid = 144 + 2 × 12 × 10

surface area of the square base pyramid = 144 + 240

surface area of the square base pyramid = 384 cm²

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Selina will get £153.78 of interest by the end of 3 years.

To calculate the total amount of interest Selina will get by the end of 3 years, we need to use the compound interest formula:

A = P[tex](1 + r/n)^{(nt)}[/tex]

where:

A = the amount of money at the end of the time period

P = the principal amount (the amount initially invested)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time period (in years)

In this case, we have:

P = £2000 (the amount initially invested)

r = 2.5% per annum = 0.025 (as a decimal)

n = 1 (the interest is compounded annually)

t = 3 (the time period is 3 years)

So, plugging in the values into the formula, we get:

A = 2000[tex](1 + 0.025/1)^{(1×3)}[/tex]

= 2000[tex](1.025)^{3}[/tex]

= 2000(1.07689)

= £2,153.78 (rounded to the nearest penny)

To find the total amount of interest Selina will get, we need to subtract the principal amount from the final amount:

Total interest = £2,153.78 - £2,000

= £153.78

Therefore, Selina will get £153.78 of interest by the end of 3 years.

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