There are 20 girls on the basketball team. of these, 17 are over 16 years old, 12 are taller than 170 cm, and 9 are both older than 16 and taller than 170 cm. how many of the girls are older than 16 or taller than 170 cm?

The equation of the horizontal line that passes through the point ( -2 , 5 ) is

y = 5

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the equation of line be represented as A

Now , let the point be A ( x₁ , y₁ )

The value of A ( x₁ , y₁ ) = A ( -2 , 5 )

Now , the slope of the line m is given by

Since , the line is a horizontal line , the slope of the line m = 0

Slope m = 0

Now , the equation of line is given by the equation

y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 5 = 0 ( x + 2 )

y - 5 = 0

Adding 5 on both sides of the equation, we get

y = 5

Therefore, the value of A is y = 5

Hence ,

The equation of the horizontal line that passes through the point ( -2 , 5 ) is y = 5

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The slope of line containing the points (-2, 5) and (4, -4) is [tex]\frac{-3}{2}[/tex].

A slope of a line is the change in y coordinate with respect to the change in x coordinate.

[tex]m = \frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]

Where,

m is the slope of line.

[tex](x_{1} ,y_{1} )[/tex] and [tex](x_{2},y_{2})[/tex] are the two points.

According to the given question.

We have two points (-2,5) and (4,-4).

Therefore, the slope of the line containing the points (-2, 5) and (4, -4) is given by

[tex]m = \frac{-4-5}{4-(-2)}[/tex]

⇒[tex]m = \frac{-9}{6}[/tex]

⇒[tex]m =\frac{-3}{2}[/tex]

Hence, the slope of line containing the points (-2, 5) and (4, -4) is [tex]\frac{-3}{2}[/tex].

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Final answer:

The volume of a cube with side length 2.5 units can be calculated using the formula V = s³, resulting in a volume of 15.625 cubic units.

Explanation:

To find the volume of a cube with a side length of 2.5 units, we can use the formula for the volume of a cube, which is V = s³, where V represents volume and s represents the side length of the cube.

Using this formula:

s = 2.5 units

V = 2.5³ = 2.5 × 2.5 × 2.5 = 15.625 units³

So, the volume of the cube is 15.625 cubic units.

6.  z=2a-p

7.  w= A/L

8.  w= v/Lh

9.  t= (A-P)/PR

Answer:

You should change the direction of the sign.

Step-by-step explanation:

This is a general rule for all inequalities. Whenever multiplying or dividing by a negative, always change the direction of the sign

To find the probability of passing the quiz, we need to determine the minimum number of correct answers needed to achieve a passing grade. The probability of guessing the correct answer for each question is 1/5, so the probability of getting exactly 12 correct answers is calculated using the binomial probability formula.

To find the probability of passing the quiz, we need to determine the minimum number of correct answers needed to achieve a passing grade. Since a passing grade is 60%, this corresponds to 12 correct answers out of 20. The probability of guessing the correct answer for each question is 1/5, so the probability of getting exactly 12 correct answers is given by the binomial probability formula:

P(X = k) = (nCk) * p^k * (1-p)^(n-k)

Using this formula, we can calculate the probability of passing the quiz.

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The problem can be solved using binomial distribution principles where the number of trials is the total number of questions (20), success is answering a question correctly, and the probability of success is 1/5 since the answers are guessed randomly. Calculate the cumulative binomial probability for getting 12 (minimum passing grade at 60%) to 20 (total questions) correct answers. This gives the probability of passing the test.

The question asks about the probability of passing a 20 question quiz with each question having 5 possible answers, by making random guesses. To pass the quiz, a grade of 60% is required which means at least 12 questions need to be answered correctly. Since the answers are guessed randomly, the chance of picking the correct answer for each question is 1/5 or 0.2.

We can treat this problem as a binomial distribution problem, where the success is answering a question correctly. In this case, the number of trials is n=20 (the total number of questions), the number of success k is 12 or more (the minimum number of correct answers required to pass), and the probability of success p is 0.2 (since there are 5 multiple choice options per question).

Calculating the cumulative binomial probability for k=12 to n=20, we get the required probability of passing the test. Given that we have to calculate multiple probabilities and sum them, this problem might be easier to solve if you have statistical software or a calculator that can compute binomial distributions.

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Answer:

Ben's house is at point -2

Step-by-step explanation:

Given that Anna lives 2.5 miles to the east of her school, and Ben lives 2 miles to the west of the same school

When Anna draws a map with a number line connecting her house to Ben’s house, with school marked as 0 then to the east would be +2.5

Since Ben lives 2 miles to the west, Ben would be marked as negative -2.

(West denotes negative in number line)

So answer is Ben's house is at point -2

Ben's house is at the point -2 on the map of number line.

A number line is pictorially represented as a horizontal straight line where numbers are placed at equal distance. Usually integers are placed in the number line with negative numbers placed to the left of 0 and positive numbers placed to the right of 0.

Number lines are used in performing basic operations in mathematics such as addition, multiplication, subtraction and division.

Here, it is given that Anna lives 2.5 miles to the east of her school and Ben lives 2 miles to the west of the same school.

So school is a common point here with respect to which both of their distance to house are marked.

On the number line school is at 0.

Anna's and Ben's house lies two opposite sides from the school.

So if one of their houses is at the positive side, the house of other one's will be at the negative side.

Given that, Anna's house is at positive side at the point +2.5.

Then clearly Ben's house will be at the negative side and the point will be -2 since it is 2 miles away from the school.

Hence, Ben's house will be at the negative side of the number line at point -2.

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Answer:

constant of variation(k) is, 250.

[tex]y = \frac{250}{x}[/tex]

Step-by-step explanation:

The inverse variation says that:

[tex]y \propto \frac{1}{x}[/tex]

then, the equation is in the form of :

[tex]y = \frac{k}{x}[/tex]        ....[1] where, k is the constant of variation

As per the statement:

Suppose that y varies inversely with x.

then,

by definition of inverse variation we have;

[tex]y = \frac{k}{x}[/tex]

When x = 2.5 and y = 100 then

Substitute these in [1] we have;

[tex]100 = \frac{k}{2.5}[/tex]

Multiply 2.5 both sides we have;

[tex]250 = k[/tex]

or

k = 250

⇒[tex]y = \frac{250}{x}[/tex]

Therefore, the constant of variation is, 250 and the equation we get [tex]y = \frac{250}{x}[/tex]

To find the number of nickels in the piggy bank, you can set up a system of equations based on the total number of coins and the total value of all the coins. By solving this system, you can determine the number of nickels.

To find the number of nickels in the piggy bank, we need to set up a system of equations. Let's use n to represent the number of nickels and d to represent the number of dimes.

The total value of the nickels can be calculated by multiplying the number of nickels (n) by the value of each nickel, which is $0.05. So, the value of the nickels is 0.05n.

The total value of the dimes can be calculated by multiplying the number of dimes (d) by the value of each dime, which is $0.10. So, the value of the dimes is 0.10d.

We can set up two equations based on the given information:

Equation 1: n + d = 33 (total number of coins)

Equation 2: 0.05n + 0.10d = 2.40 (total value of all coins)

Now we can solve this system of equations to find the number of nickels (n).

Multiplying Equation 1 by 0.05 gives us: 0.05n + 0.05d = 1.65

Subtracting Equation 2 from this gives us: 0.05d - 0.10d = 1.65 - 2.40

Simplifying, we get: -0.05d = -0.75

Dividing both sides by -0.05, we find: d = 15

Substituting this value back into Equation 1, we get: n + 15 = 33

Subtracting 15 from both sides, we find: n = 18

Therefore, there are 18 nickels in the piggy bank.

To find the number of nickels in the piggy bank, set up a system of equations and solve. There are 18 nickels in the piggy bank.

To find the number of nickels in the piggy bank, you need to set up a system of equations based on the information given. Let's assume that the number of nickels is represented by 'n' and the number of dimes is represented by 'd'. From the problem, we know that there are 33 coins in total, so we can write the equation 'n + d = 33'. We also know that the value of the nickels, in cents, is 5n and the value of the dimes, in cents, is 10d. Since the total value of the coins is $2.40, we can write the equation '5n + 10d = 240'. Now we can solve this system of equations to find the number of nickels.

To solve the system of equations, we can use the substitution method. Rearrange the first equation to get 'n = 33 - d', and substitute this expression for 'n' in the second equation: '5(33 - d) + 10d = 240'. Simplify the equation to get '165 - 5d + 10d = 240'. Combine like terms to get '5d = 75'. Divide both sides by 5 to get 'd = 15'. Substitute this value of 'd' back into the first equation to find 'n': 'n + 15 = 33', 'n = 18'.

Therefore, there are in the piggy bank.

K is the middle letter of the triangle JKL so it would be the same as the middle letter of the triangle EFG

so K = F

 F = 62 degrees, so K = 62 degrees

Both triangles are congruent so the corresponding angle will be the same K is the mid-latter of JKL thus K will be the same as the mid-later of EFG therefore, K=F=62°.

If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent or to be in the relation of congruence.

As per the given question,

△EFG≅△JKL

Now it is known that all corresponding angles in two congruent triangles are the same.

Now K is the mid-latter of JKL thus K will be the same as the mid-later of EFG.

Mid latter of EFG = F

Given that m∠F = 62°

Therefore, m∠K = m∠F = 62°

Hence "Both triangles are congruent so the corresponding angle will be the same K is the mid-latter of JKL thus K will be the same as the mid-later of EFG therefore, K=F=62°".

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Final answer:

The most likely function of the cells in this pulse-chase experiment is to synthesize, process, and degrade or secrete proteins. This is deduced from the movement of radioactivity from the ER to the Golgi apparatus, then to lysosomes and the extracellular space over time.

Explanation:

Based on the data provided, which stem from a pulse-chase experiment, we can infer the most likely function of the cells. Initially, radioactivity is high in the endoplasmic reticulum (ER), indicating that newly synthesized proteins, likely labeled with radioactive amino acids, are present there.

As time progresses, radioactivity moves to the Golgi apparatus, implying that proteins are being processed and modified.

Eventually, the highest levels of radioactivity are found in the lysosomes and then the extracellular space, suggesting that these proteins are being degraded and secreted respectively.

This sequence of events indicates that the cells are involved in synthesizing, processing, and secreting proteins, with some being targeted for degradation in lysosomes.

This is a fundamental part of the protein secretory pathway in cells. The data reveal the dynamic movement of molecules within the cell, reflecting the pathway from synthesis to secretion or degradation.

Answer:

C.The county gives all public school teachers a $2,000 raise without adjusting taxes.

Step-by-step explanation:

100% on edge

The correct answer is Option (C).The county gives all public school teachers a $2,000 raise without adjusting taxes.

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the interior angles of a triangle need to equal 180 degrees

Answer is B

Answer:

180 is the answer

Answer:

y ≤ x – 4  will be the linear inequality is represented by the graph.

Step-by-step explanation:

Given : graph.

To find :  Linear inequality equations .

Solution : We have given graph,

We can see from graph here y intercept is -4 and solid line shaded below ,

Since , For shaded below graph we can say equation have less than equal sign. and y intercept -4.

Therefore, y ≤ x – 4  will be the linear inequality is represented by the graph.

Answer:

B

Step-by-step explanation:

because the line goes through -4 evenly

Answer:

84,000,000

Step-by-step explanation:

Answer: 24.52%

Step-by-step explanation: Convert times into decimals by dividing the seconds by 60. (7:45 = 7.75 | 5:51 = 5.85) Subtract 7.75 and 5.85 which equals 1.9

1.9/7.75 = 0.2451612903

Rounded to 0.2452 = 24.52%