Jason left for school and forgot his math homework on the kitchen table. His mother found the homework 10 minutes later after jason left, and started driving 36 mph to catch him. Jason bikes 12 mph. If Jason's school is 2.5 miles from his apartment, how fast must his mother drive to catch him at the school door?

The equation of a line that passes through two points is given by:

Plugging the values of the points given we have that:

Therefore the equation of the line is:

Step-by-step explanation:

i think it might be 50% i am not sure

So, you will need to make a monthly payment of 1312.26 for 36 months to pay off the balance.

If you choose to buy the TV, you must pay a deposit equal to 50000, or 20% of the entire price. Your deposit will therefore be 0.20 x 50000, or 10000.

The remaining 40,000 will be paid off over the course of 36 months at a 12% annual interest rate that is compounded each month. We must apply the following calculation to get the monthly payment:

Payment is equal to (PV x r x (1+r)n) / (1+rn - 1)

where n is the total number of payments, r is the monthly interest rate (12% / 12 = 1% per month), and PV is the present value (the balance that remains) (36 months).

When we change the values, we obtain:

Payment: (40000 x 0.01 x (1+0.01)36) / (1+0.01)36-1) = 1312.26

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Answer: 92º

Step-by-step explanation:

Since the sum of the angles of a triangle is always 180 degrees, we can use the following equation:

56º + 32º + xº = 180º

or

180º - (56º + 32º) = xº

Tertiary consumers are one level above primary producers in a food chain. In a food chain, the transfer of energy and nutrients occurs from one trophic level to another.

The trophic levels are categorized into producers, primary consumers, secondary consumers, and tertiary consumers.

Primary producers, such as plants or algae, are the first trophic level in a food chain. They convert energy from sunlight into organic matter through photosynthesis. Primary consumers, also known as herbivores, are the organisms that feed directly on primary producers.

Secondary consumers are the next trophic level and they feed on primary consumers. They are usually carnivores or omnivores that consume herbivores.

Finally, tertiary consumers occupy the highest trophic level in a food chain. They are the top predators that feed on secondary consumers. These can include large carnivores or even apex predators.

Therefore, tertiary consumers are one level above primary producers in the food chain. They represent the organisms that obtain energy by consuming other organisms higher up in the trophic hierarchy.

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The equation of the line that passes through the point (8,2) and is parallel to the line x+4y = 28 is y = -x/4+4.

According to the question,

We have the following information;

Point thorough which line is passing = (8,2)

Equation of the line:

x+4y = 28

Now, we will convert this equation into the slope-intercept form:

4y = -x+28

Dividing by 4 on both sides of the equation:

y = -x/4+28/4

y = -x/4+7

Slope of the line = -1/4

We know that the following formula is used to find the equation of the line:

(y-y') = m(x-x')

(y-2) = -1/4(x-8)

y-2 = -x/4+2

Adding 2 on both sides:

y = -x/4+4

Hence, the equation of the line that passes through the point (8,2) and is parallel to the line x+4y = 28 is y = -x/4+4.

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Answer:

4

Step-by-step explanation:

-5 - ( - 9 ) is the same as -5 + 9

so the answer is 4

Answer:

4 bhsshhshshshshshshshehshhsbsbs

The 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.

Population: The containers of blueberries that are being sent to Stop and Shop.

Sample: The 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.

Therefore, the 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.

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The price of carrots per ounce is $0.24 .

Ounce is an unit of mass in the Imperial System. It is widely used throughout the world and is one of the oldest units of measurement to still exist. The unit ounce is derived from uncia, a unit of measurement in roman times.

The ounce(abbreviated oz) is equal to approximately 28.35 grams and 16 ounces make up a pound.

Now it is given that a 2-pound bag of carrots cost $7.68 .

Therefore price per pound of carrots=$7.68÷2

Price per pound=$ 3.84 .

Now we know that 16 ounces make up a pound.

Price of carrots per ounce=  $3.84 ÷16

Price per ounce=  $ 0.24

Therefore the price of carrots per ounce is $0.24

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\( = 3 \sqrt{49} \times \sqrt{81} \\ = 3(7) \times 9 \\ = 21 \times 9 \\ = 189 \)

HOPE THIS HELPS

Answer:

779264 k-tons

Step-by-step explanation:

First year ====> no change

  then each of the next 9 years decrease by 4 %  ( leaving 96%)

       this is a geometric sequence with

  r = .96   and a1 = 93000  and n =  10 terms

sum of sequence =   a1 (1-r^n) / ( 1-r) = 779264  kilotons

Answer:A standard form is a form of writing a given mathematical concept like an equation, number, or an expression in a form that follows certain rules. Representing very large or very small numbers concisely, the standard form is used. For example, 4.5 billion years is written as 4,500,000,000 years.

Step-by-step explanation:

Answer:

12 hours

Step-by-step explanation:

1 pair per hour ?

The value of variance in the above formula: σ(X) = √(b-a) / √12. This is our standard deviation (σ(X)).

The probability density function, over the given interval, can be found using the formula below:  

f(x) = 1 / (b - a) over [a, b]

Let's start with finding the expected value (E(X)).

Formula for E(X):

E(X) = ∫xf(x)dx over [a, b]

We can substitute f(x) with the formula we obtained in the question.  

E(X) = ∫x(1/(b-a))dx over [a, b]

Next, we can solve the above integral.

E(X) = [x²/2(b-a)] between limits a and b, which simplifies to:

E(X) = [b² - a²] / 2(b-a)  = (b+a)/2

This is our expected value (E(X)).

Next, we will find the expected value (E(X²)).

Formula for E(X²):E(X²) = ∫x²f(x)dx over [a, b]

Substituting f(x) in the above formula: E(X²) = ∫x²(1/(b-a))dx over [a, b]

Solving the above integral, we get:

E(X²) = [x³/3(b-a)] between limits a and b

E(X²) = [b³ - a³] / 3(b-a)  

= (b² + ab + a²) / 3

This is our expected value (E(X²)).

Now we can find the variance and standard deviation.

Variance: Var(X) = E(X²) - [E(X)]²

Substituting the values we have found:

Var(X) = (b² + ab + a²) / 3 - [(b+a)/2]²

Var(X) = (b² + ab + a²) / 3 - (b² + 2ab + a²) / 4

Var(X) = [(b-a)²]/12

This is our variance (Var(X)).

Standard deviation: σ(X) = √Var(X)

Substituting the value of variance in the above formula:

σ(X) = √(b-a) / √12

This is our standard deviation (σ(X)).

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Explanation:

Let's say your first selection was red. If you have really good luck, you'll pick 7 more red and the answer would be 8. However, we need to consider the opposite side of the spectrum. We need to consider the worst possible scenario and having the worst luck ever. In this scenario, we don't match colors until the very last possible moment. If you pick red first, then you cannot pick red again until you've picked blue, yellow and black/white.

There are a few ways to consider the worst case scenario. One way is to form a table as shown below. See the attached image. Each row represents the colors "red, blue, yellow, black/white" in that exact order. This could be one way to select the items. For this row, we haven't selected a repeat color. Red is selected first. Each row repeats itself, although the black/white gets exhausted after 4 rows.

By the 7th row, we have 7 red, 7 blue and 7 yellow. We don't need a full 8th row to reach our goal. We can stop once we reach the highlighted cell I marked in the table. That cell represents picking the 8th red. You could replace that highlighted cell with "blue" or "yellow" and still achieve the goal because you'd get 8 of that color. I'm just picking on red since it's the first one listed.

If you count out the items, you should count out 33 total. Ignore the stuff after the highlighted cell in row 8.

We have a 7 by 3 rectangle that has 7*3 = 21 items. Then the highlighted cell bumps the count up to 21+1 = 22. Finally, the four black/white items are counted as well to get to 22+4 = 26 as the final answer

We need to make 26 selections to guarantee that we selected 8 of the same color. Again, this is because we're considering a scenario in which we get the worst luck ever and don't make any color matches until the last possible moment.

The volume of the triangular prism is 216 cubic meters.

To find the volume of a triangular prism, we need to multiply the area of the triangular base by the length of the prism.

Calculate the area of the triangular base.

The base of the triangular face is given as 8 meters, and the height is 9 meters. We can use the formula for the area of a triangle: area = (1/2) * base * height.

Plugging in the values, we get:

Area = (1/2) * 8 meters * 9 meters = 36 square meters.

Multiply the area of the base by the length of the prism.

The length of the prism is given as 12 meters.

Volume = area of base * length of prism = 36 square meters * 12 meters = 432 cubic meters.

Adjust for the shape of the prism.

Since the prism is a triangular prism, we need to divide the volume by 2.

Adjusted Volume = (1/2) * 432 cubic meters = 216 cubic meters.

Therefore, the volume of the triangular prism is 216 cubic meters.

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Answer:

l = 194999.45

Step-by-step explanation:

I'm going to assume that you meant 3.14 by 3,14.

336,765 = 3.14 × 0.55 × (l + 0.55)

336,765 ÷ (3.14 × 0.55) = l + 0.55

(336,765 ÷ (3.14 × 0.55)) - 0.55 = l

l = 194999.45

Answer:

21

Step-by-step explanation:

An isosceles triangle has 2 sides of the same length, those sides being the sides that aren't the base. The perimeter is the total length of all 3 sides of the triangle. We know that the base is 5 inches, and that one side is 8. Because the triangle is isosceles, we know that the others ide is also 8 inches. Therefore, the perimeter is 8+8+5, which is 21.

Answer:

21 in.

Step-by-step explanation:

If the triangle is isosceles, then two of its three sides are of equal length.  We can assume that the side lengths are 5 in., 8 in and 8 in.  Summing these up, we get total length 21 in.  That's the perimeter of the triangle.

The appropriate domain for the function is 0 ≤ x ≤ 7.

Given the function F(x) = 1/2x(14-2x), we can determine the area of the rectangular fenced-in area with width x feet and length 1/2(14-2x) feet.

The area of a rectangle is calculated by multiplying its length and width, which is represented by the function F(x).

To find appropriate domain values for the function, we need to consider the physical constraints of the problem.

Since the width (x) and length (1/2(14-2x)) must be non-negative, we can set up the following inequalities: 0 ≤ x 0 ≤ 1/2(14-2x)

Solving the second inequality, we get: 0 ≤ 14 - 2x 2x ≤ 14 x ≤ 7

Therefore, the appropriate domain for the function is 0 ≤ x ≤ 7.

This means the width of the rectangle can be any value between 0 and 7 feet, inclusive.

The function F(x) will then give the corresponding area in square feet for the fenced-in rectangle with the specified width.

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The function F(x) = ½x(14 - 2x) represents the area of a rectangular fenced area with a given width and length. You can find and interpret values of the function by substituting different values of x. The appropriate domain for the function is determined by considering the restrictions on x, in this case, 0 ≤ x ≤ 7.

The given function F(x) = ½x(14 - 2x) represents the area in square feet of a rectangular fenced area, where the width of the rectangle is x feet and the length is ½(14 - 2x) feet.

Therefore, the appropriate domain is 0 ≤ x ≤ 7.

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The area of each piece is 66.35.

What is the area of the circle?

The area of a circle is the space encircled or encompassed by its circumference. It has a square unit of measurement. Every geometric shape has a distinct area.

Here, we have

Given: a 26-inch diameter pizza is cut into 8 equal pieces.

we have to find the area of each piece.

A = πr²

We know that the diameter of the pizza is 26 inches, so the radius must be half that value: 13 inches. So:

A = (3.141)(13)²

A = 530.82 inches squared

Now that we know the area, we simply divide it by 8, as there are 8 equal pieces, and so each piece must have an equal area. This gives us:

= 530.82/8

= 66.35

Hence, the area of each piece is 66.35.

Question- A pizza with a 26-inch diameter is cut into 8 equal sizes. Determine the area of one slice.

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Answer:

223.67

Step-by-step explanation:

1.)  Probabilities range from 0 to 1, denoting impossibility and certainty, respectively.

2.) The sum of probabilities of all possible outcomes is equal to 1.

1.) Individual probabilities will always have values between 0 and 1. This property is known as the "probability bound." Probability is a measure of uncertainty or likelihood, and it is represented as a value between 0 and 1, inclusive.

A probability of 0 indicates impossibility or no chance of an event occurring, while a probability of 1 represents certainty or a guaranteed outcome.

Any probability value between 0 and 1 signifies varying degrees of likelihood, with values closer to 0 indicating lower chances and values closer to 1 indicating higher chances. In simple terms, probabilities cannot be negative or greater than 1.

2.) The sum of the probabilities of all individual outcomes must equal 1. This principle is known as the "probability mass" or the "law of total probability." When considering a set of mutually exclusive and exhaustive events, the sum of their individual probabilities must add up to 1.

Mutually exclusive events are events that cannot occur simultaneously, while exhaustive events are events that cover all possible outcomes. This property ensures that the total probability accounts for all possible outcomes and leaves no room for uncertainty or unaccounted possibilities.

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the rate of change of the radius at the instant the volume equals 36π cm³ is 7 / (36π) cm/sec.

The volume V of a sphere with radius r is given by the formula V = (4/3)πr³. We are given that the rate of change of the volume is 7 cm³/sec. Differentiating the volume formula with respect to time, we get dV/dt =(4/3)π(3r²)(dr/dt), where dr/dt represents the rate of change of the radius with respect to time.

We are looking for the rate of change of the radius, dr/dt, when the volume equals 36π cm³. Substituting the values into the equation, we have: 7 = (4/3)π(3r²)(dr/dt)

7 = 4πr²(dr/dt) To find dr/dt, we rearrange the equation: (dr/dt) = 7 / (4πr²) Now, we can substitute the volume V = 36π cm³ and solve for the radius r: 36π = (4/3)πr³

36 = (4/3)r³

27 = r³

r = 3  Substituting r = 3 into the equation for dr/dt, we get: (dr/dt) = 7 / (4π(3)²)

(dr/dt) = 7 / (4π(9))

(dr/dt) = 7 / (36π)

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Answer:

The value of H(F(-2)) is 379

Step-by-step explanation:

Soln,

Given,

F(x)= 2x^2+4x+10

G(x)= 3x-11

H(x)= 3x^2+x^2-21

Now,

F(-2) = 2(-2)^2 + 4×(-2) + 10

= 2×4 + (-8) + 10

= 8-8+10

= 18 - 8

= 10

Again,

H(F(-2)) = 3x^2 + x^2 - 21

Putting the value of F(-2) , we get

H(10) = 3×10^2 + 10^2 - 21

= 3×100 + 100 - 21

= 300 + 100 - 21

= 400 - 21

= 379

Therefore, H(F(-2)) = 379.

Multiple regression analysis is applied when analyzing the relationship between one dependent variable and two or more independent variables. The goal is to determine the extent to which the independent variables predict the dependent variable.

Multiple regression analysis is a statistical technique used to explore and quantify the relationship between a dependent variable and multiple independent variables. It allows researchers to examine how changes in one or more independent variables impact the dependent variable, while controlling for the effects of other variables. By estimating the coefficients for each independent variable, the analysis provides insights into the strength, direction, and significance of their relationships with the dependent variable. This method is commonly employed in various fields, such as economics, social sciences, and business, to understand complex relationships and make predictions based on the interplay of multiple factors.

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Answer:

18 I think

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Reagan brought 2 caramel brownies.

Solve using a proportion.

\(\frac{?}{20}\)=\(\frac{10}{100}\)

You're trying to find how many brownies he brought were caramel. We know Reagan brought a total of 20 brownies. Therefore since you don't know how many caramel brownies he brought, the fraction would be ?/20. Next, you know he brought brownies in which 10% were caramel. In proportions, the denominator would be 100% since that is the total percentage. Therefore, the proportion would be 10%/100%. Now we just have to cross multiply.

Proportion:

\(\frac{?}{20}\)=\(\frac{10}{100}\)

10 x 20 = 200

200/100= 2

Thus, Reagan brought 2 caramel brownies.

Answer:

D. 8

Step-by-step explanation:

32^(3/5) is the same as \(\sqrt[5]{32}\)^3.

 \(\sqrt[5]{32}\) = 2 because 2^5=32

2^3 = 8

Simplify the expression.

Rewrite 32 as 2⁵.

\(\bf{\left(2^{5}\right)^{\frac{3}{5} } }\)

Apply the power rule and multiply exponents, (αᵐ)ⁿ=αᵐⁿ.

\(\bf{2^{5}^{(\frac{3}{5} )} }\)

Cancel the common factor of 5.

Cancel the common factor.

\(\bf{2^{\not{5}}^{(\frac{3}{5} )} }\)

Substitute the expression.

\(\bf{2^{3} \ \ \to \ Calculate \ power. }\)

Raise 2 to the power of 3.

We conclude that the correct option is "D".

Answer:

the angle of 1 is 68 degrees

Answer:

\(\boxed {\boxed {\sf m \angle 1 = 68 \textdegree}}\)

Step-by-step explanation:

The 3 interior angles of a triangle must add to 180 degrees.

We don't know the measure of angle 1. We can say the measure of angle 2 is 61° and the measure of angle 3 is 51°.

Add the numbers on the left side.

We want to isolate the measure of angle 1.

112 is being added, so we must perform the inverse operation of subtraction.

The measure of angle 1 is 68 degrees.

Answer:

4

Step-by-step explanation:

We are asked to find a slope whilst given a graph.

To solve for slope, we must pick two coordinate points that are not decimals and following the formula of rise over run, which in basic terms y over x.

So based on what I see, I can see (1, 1) and (2, 5).

The rise over run is as followed :

\(\frac{y2 - y1}{x2 - x1}\)

2 and 1 meaning the first and second number within the coordinate, so substitute :

\(\frac{5 - 1}{2 - 1}\)

\(\frac{4}{1}\)

Divide :

\(4\)

4 is our slope.