The quadratic function y = –10x2 + 160x – 430 models a store’s daily profit (y) for selling a T-shirt priced at x dollars. What equation do you need to solve to find the selling price or prices that would generate $50 in daily profit? What method would you use to solve the equation? Justify your choice.

The missing angles and side of the triangle are;

m∠FXD = 44°

EG = 14

m∠FZG = 32°

We are told that the angle bisectors of ΔXYZ are XG, YG and ZG

The parameters are;

∠DYE = 94°

∠FXG = 22°

Thus;

m∠FXD = 2* 22°

m∠FXD = 44°

The sum of angles in a triangle is 180 degrees. Thus;

m∠FZE + 94 + 22 = 180

m∠FZE = 180 - (94 + 22)

m∠FZE = 64°

Thus;

m∠FZG = 64°/2

m∠FZG = 32°

The incenter of a triangle lies at equal distances from the three line segments forming the sides of the triangle, and also from the three lines containing those segments. Thus;

DG = EG = FG = 14

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\(m\angle E=\sin \dfrac{\sqrt{10}}{2\sqrt5}=\sin \dfrac{\sqrt2}{2}=45^{\circ}\)

If the radius of sphere B is five times the radius of sphere A, then the ratio of the volume of sphere B to the volume of sphere A is 125. So, Option C is correct.

The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere and π is a mathematical constant approximately equal to 3.14159.

If the radius of sphere B is five times the radius of sphere A, then we can express this relationship mathematically as r₂ = 5r₁, where r₁ is the radius of sphere A.

Using the formula for the volume of a sphere, we can then calculate the ratio of the volume of sphere B to the volume of sphere A as follows:

V₂/V₁ = [(4/3)πr₂^3] / [(4/3)πr₁^3]

= (r₂/r₁)^3

= (5r₁/r₁)^3

= 5^3

= 125

Therefore, the ratio of the volume of sphere B to the volume of sphere A is 125. This means that sphere B has a volume that is 125 times larger than the volume of sphere A, because the relationship between the volumes of spheres is proportional to the cube of their radii. Therefore, option C is correct.

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Complete question is:

If the radius of sphere B is five times the radius of sphere A, then the ratio of the volume of sphere B to the volume of sphere A is

Select one:

A. 0.008

B. 25

C. 125

D. 5

E. 0.2.

the range of the function in the graph is:

-4 ≤ y ≤ 2

For a function y = f(x), we define the range as the set of the outputs. This is, the set of the possible values of y.

Now, remember that the values of y are on the vertical axis. So if we want to know the range, we just need to look at the vertical axis and see which ones are the allowed values.

If we look at the graph, we can see that the minimum value of y is:

y = -4

And we can see that the maximum value of y is:

y = 2

Then the range of the function in the graph is:

-4 ≤ y ≤ 2

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Answer:

positive 7

Step-by-step explanation:

You would need to wait approximately 51.33 years from now to grow your initial investment of $39,000 to $174,000 at an interest rate of 10% per year.

To calculate the number of periods (years) required to grow an initial investment to a desired future value, we can use the formula for compound interest:

FV = PV * \((1 + r)^n\)

Where:

FV is the future value

PV is the present value (initial investment)

r is the interest rate per period

n is the number of periods

In this case:

PV = $39,000

FV = $174,000

r = 10% per year

Let's calculate the number of periods (years):

FV = PV * \((1 + r)^n\)

174,000 = 39,000 * \((1 + 0.10)^n\)

Divide both sides by 39,000:

4.4615 = \((1.10)^n\)

Take the logarithm of both sides to solve for n:

log(4.4615) = n * log(1.10)

n ≈ log(4.4615) / log(1.10)

n ≈ 2.1270 / 0.0414

n ≈ 51.33 (rounded to two decimal places)

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$7.50

The expected amount paid to the player is $7.50. This is calculated by taking the probability of each outcome multiplied by the amount paid for that outcome, and then summing them all together. The probabilities are as follows:

The expected amount paid is therefore: (0.75 x $5) + (0.0625 x $10) + (0.0039 x $20) + (0.0001 x $30) + (0.00001 x $50) = $7.50

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The total surface area of the apparatus is approximately 16454.87 mm².

To calculate the total surface area of the apparatus, we need to find the surface area of the two metal cubes and the surface area of the cylinder.

Each metal cube has six faces, and since they are identical, we only need to calculate the surface area of one cube. The surface area of a cube can be found by multiplying the length of one edge by itself and then multiplying by 6. In this case, the length of each edge is 30 mm, so the surface area of one cube is:

Surface area of cube = 6 * (30 mm * 30 mm) = 6 * 900 mm² = 5400 mm²

Now, let's calculate the surface area of the cylinder. The surface area of a cylinder can be found by adding the areas of the two circular bases and the lateral surface area. The formula for the lateral surface area of a cylinder is given by 2 * π * radius * height.

In this case, the radius of the cylinder is equal to the length of one edge of the cube, which is 30 mm, and the height of the cylinder is also 30 mm (since the cubes are fixed to the cylinder). Therefore, the lateral surface area of the cylinder is:

Lateral surface area of cylinder = 2 * π * 30 mm * 30 mm = 1800π mm²

The total surface area of the apparatus is the sum of the surface area of the two cubes and the surface area of the cylinder:

Total surface area = 2 * surface area of cube + surface area of cylinder

= 2 * 5400 mm² + 1800π mm²

≈ 10800 mm² + 5654.87 mm²

≈ 16454.87 mm²

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Answer:

10

Step-by-step explanation:

Answer:

5+5=10

Step-by-step explanation:

use addition to add 5 and 5

Answer: I think a

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Step-by-step explanation:

From 5:43 pm to 6 pm is 17 minutes

from 6 pm to 6;32 pm is 32 minutes more

17 + 32 = 49 mis.

In Algebra 2, students typically use a scientific calculator.

A scientific calculator has advanced functions beyond basic arithmetic operations.

Some of the functions commonly used in Algebra 2 include logarithms, exponents, trigonometric functions, and statistical calculations. Therefore, a scientific calculator with these functions would be most useful for Algebra 2.

Examples of calculators that are often used in Algebra 2 include the TI-84 Plus , the TI-Nspire CX, the Casio fx-9750GII, and the HP Prime Graphing Calculator.

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Answer:

Step-by-step explanation:

3245

S has 3 elements - 3, {1, 4}, and 2 - so its power set will contain 2³ = 8 elements. (B)

Answer:

28

Step-by-step explanation:

The y, Cost, seems to increase by 6 every ride. Using this idea adding 6 to 22 gives 28.

28

Step-by-step explanation:

1 -> 16 = 15 + 1

2 -> 22 = 20 + 2

3 -> 28 = 25 + 3

4 -> 34 = 30 + 4

Therefore, the width of the asymptote rectangle is 8 units, and its height is 4 units.

To determine the width and height of the asymptote rectangle for the given hyperbola, we need to identify the standard form of the hyperbola equation. The standard form for a hyperbola is given by:

(x - h)^2 / a^2 - (y - k)^2 / b^2 = 1 or

(y - k)^2 / b^2 - (x - h)^2 / a^2 = 1

Comparing the given equation x^2 − 4y^2 − 2x − 15 = 0 to the standard form, we can rearrange it as follows:

(x^2 - 2x) - 4y^2 = 15

(x^2 - 2x + 1) - 4y^2 = 16

Next, we complete the square for the x-terms:

(x - 1)^2 - 4y^2 = 16

Now, we can rewrite the equation in the standard form:

(x - 1)^2 / 16 - y^2 / 4 = 1

From the standard form, we can determine the values of a and b. In this case, a^2 = 16, so a = 4, and b^2 = 4, so b = 2.

The width of the asymptote rectangle is equal to 2a, which is 2 * 4 = 8 units.

The height of the asymptote rectangle is equal to 2b, which is 2 * 2 = 4 units.

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Answer:

2r² - 60r - 45 = 0

Step-by-step explanation:

Hang on this is going to be convoluted

------------------------------

Area of pond

a = πr²

Area of path

a = πr²/10

Combined Area

a = πr² + πr²/10

a = π(r² + r²/10)

---------------------------

The Combined Area can also be expressed as

a = π(r + 1.5)²

a = π(r² + 3r + 2.25)

-----------------------------

Set the areas equal

π(r² + r²/10) = π(r² + 3r + 2.25)

Divide both sides by π

r² + r²/10 = r² + 3r + 2.25

Subtract r² from both sides

r²/10 = 3r + 2.25

Multiply both sides by 20

2r² = 60r + 45

Subtract 60r + 45 from both sides

2r² - 60r - 45 = 0

If the p-value is less than α, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the mean price of used cars at this particular dealership is statistically different from the national average. If the p-value is greater than α, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a significant difference.

To test whether the mean price of used cars at this particular dealership differs from the national mean, we can use a hypothesis test.

Let μ be the population mean price for used cars at the dealership, and let μ0 be the national mean price for used cars, which is given as $10,192.

We want to test the null hypothesis H0: μ = μ0 against the alternative hypothesis Ha: μ ≠ μ0, at a significance level of α = 0.05.

We can use a two-tailed t-test for the mean to test this hypothesis, assuming that the population standard deviation is unknown and using the sample standard deviation s as an estimate. The test statistic can be calculated as:

t = (X - μ0) / (s / √(n))

where X is the sample mean, s is the sample standard deviation, and n is the sample size.

Under the null hypothesis, the test statistic follows a t-distribution with n-1 degrees of freedom. We can then calculate the p-value associated with the observed test statistic, and compare it with the significance level α.

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To calcuate the calories in one cheeseburger and one order of fries from a popular fast-food restaurant, you would need to know the specific nutritional information for these items. However, I can provide you with some average values.

Typically, a cheeseburger at a fast-food restaurant has around 300-400 calories. The calories in a cheeseburger come from the meat patty, cheese, bun, and any additional toppings or sauces.

Similarly, an order of fries contains roughly 200-300 calories. Calories in fries are primarily derived from the potatoes and oil used for frying.

Keep in mind that these are approximate values and can vary depending on the restaurant and serving sizes. To get exact information, you can check the restaurant's website or ask for a nutritional information pamphlet.

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Answer:

The maximum number of rides is 16

Step-by-step explanation:

She has a total of $50 and spends $3 for the cake and $5 for admission. She has to spend $2.50 for every ride.

Your equation would be set up as:

$50=$5+$3+$2.50x

You would combine like terms and get

$50=$8+$2.50x

Subtract the $8 from $50 and you get

$42=$2.50x

Divide each number by 2.50 and you get

16.8=x, you cannot have a decimal as an answer since she cannot ride eight tenths of a ride so the maximum number of rides is 16

Answer:

pls upload photo for your question

We subtracted the probability of X being less than or equal to 1 from the probability of X being less than or equal to 2 to obtain the probability that X equals 2.

The given cumulative distribution function for the discrete random variable X tells us the probability of X being less than or equal to a particular value of x. To find the probability that X equals 2, we need to calculate the difference between the probability of X being less than or equal to 2 and the probability of X being less than or equal to 1.

P(X = 2) = P(X ≤ 2) - P(X ≤ 1) = 0.44 - 0.30 = 0.14

Therefore, the probability that X equals 2 is 0.14 or 14%.

It is important to note that the cumulative distribution function is defined for discrete random variables, where the values of X are countable and finite. The function assigns probabilities to each value of X. The probability of any value of X is obtained by subtracting the probability of the previous value from the probability of the current value. In this case, we subtracted the probability of X being less than or equal to 1 from the probability of X being less than or equal to 2 to obtain the probability that X equals 2.

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right triangle

The sides of a right triangle in a simple way, so that if the lengths of any two sides are known the length of the third side can be found.

hope it helps.

Answer:

(0,6), (0,4), (0,-10)

Step-by-step explanation:

#x

#y

#z

Answer:

x = 14

m∠A = 38°

m∠C = 71°

m∠D = 71°

Step-by-step explanation:

Answer:

AC=AD=71, CD=38

Step-by-step explanation:

AC=AD

5x+1=7x-27

2x=28

x=14

AC=5*14+1=71=AD

CD=3*14-4=38

Answer:

1st 2nd 4th 5th and 6th

Step-by-step explanation:

for 1st and 5th the absolute values are 7 and 2nd opposite of -7 is 7 and positive 7 is 7