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every year 20 fewer students eat in the school cafeteria. assuming this trend continues, write a multiplication expression to show the change in the number of students over the next 4 years. Express this change as an integer.

The cost of plain wrapping paper is $13 and the cost of holiday wrapping paper is $18

Chloe:

Number of plain wrapping paper sold = 2

Number of holiday wrapping paper sold = 10

Total income = $206

Eduardo:

Number of plain wrapping paper sold = 3

Number of holiday wrapping paper sold = 5

Total income = $129

Let x represent the cost of plain wrapping paper and y represent the cost of holiday wrapping paper:

Formulating the equations:

2x+10y = 206-----(1)

3x+5y = 129------(2)

Multiplying (2) with 2 and subtracting with (1) we get:

2x+10y = 206

6x+10y = 258

4x = 52

x = 13

So cost of plain wrapping paper is $13

holiday wrapping paper = $18

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Answer:

10% of 12 = 0.1 * 12 = 1.2

10% of 20 = 0.1 * 20 = 2

The correct option is B, The null hypothesis to test if the population variances differ is population variance 1 differs from population variance 2.

Variance is calculated as the average of the squared differences of each data point from the mean. In other words, variance measures how far the data points are from their average value. A high variance indicates that the data points are spread out over a wider range, while a low variance indicates that the data points are clustered more tightly around the mean.

Variance is an important concept in statistical analysis because it helps to assess the reliability of data and to make inferences about the population from a sample. It is also used in many areas of research, such as finance, economics, and engineering, to measure the risk or uncertainty associated with a set of data. Variance is closely related to other statistical measures such as standard deviation, covariance, and correlation, and is often used in conjunction with these measures to gain a deeper understanding of the data.

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Complete Question:-

Before comparing means, we need to test the relationship of the population variances. what null hypothesis would you use to determine if the population variances differ?

a. population variance 1 equals population variance 2

b. population variance 1 differs from population variance 2

c. population variance 1 is less than population variance 2

d. population variance 1 exceeds population variance 2

We can find the 7 parts of a circle can by: drawing a straight line through the circle so as to identify each of its parts.

The parts of a circle.

The parts of a circle are the properties that can be used to describe a circle. These properties can be deduce from the circle itself.

Some parts of a circle are: circumference, radius, diameter, chord, tangent, arc, segment, sector etc. Each part mentioned can be define as:

The parts of a circle can be determined by: drawing a straight line through it and identify each part as explained above.

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The translation is as shown in the figure in option B

Translation transformation is a type of geometric transformation that moves every point of a figure the same distance and direction. This transformation does not change the size, shape, or orientation of the figure, but only its position in space.

The transformation required ahs the rule defined as

Applying the rule arrives the image in option B

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Step-by-step explanation:

\( {30.5}^{2} = {x}^{2} + {19.1}^{2} \\ 930.25 = {x}^{2} + 364.81 \\ {x}^{2} = 930.25 - 364.81 \\ {x}^{2} = 565.44 \\ x = \sqrt{565.44} \\ \\ x = 23.78\)

Answer: 0.00000%4

Step-by-step explanation:

Answer:

Hi, I'm Za'Riah! I will gladly assist you with your problem. (see explanation)

Step-by-step explanation:

To convert a decimal to a percent, move the decimal point two places to the right and put a percent sign “%” at the end.

0.4 = 40%

Hope this helped!

The value of the expression when x = 7 is 70

Algebraic expressions are expressions made up of variables, terms, coefficients, factors and constants.

They are also made up of mathematical operations such as addition, multiplication, division, subtraction, etc.

Given the expression;

2x^2- 5x - 3

To determine the the value, we substitute the value of x a 7 into the expression, we have;

2(7)² - 5(7) - 3

expand the bracket

2(49) - 25 - 3

98 - 25 - 3

Find the difference

70

Thus, the value of the expression when x = 7 is 70

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Answer:

Option D

Step-by-step explanation:

H(x) = 3^(2x)

G(x) = reflecting H(x) across the y-axis and shifting 2 units down

=>G(x) = 3^(-2x) - 2

3^(2x) and 3^(-2x) - 2 are valid with all values of x.

=> There is no change in the domain of H(x) and G(x), in which all values of x satisfy H(x) and G(x).

3^(-2x) > 0

=> G(x) =  3^(-2x) - 2 > -2

=> Range of G(x) is from -2 to inifinity

Answer:

D.

Step-by-step explanation:

Well lets graph it first,

Look at the image below↓

So the red line is the new line which has been reflected and shifted down 2.

Meaning the domain turns into positive numbers but still remains infinite.

And the range changes

So we can cross out A and B.

Before the range was lower than 1 and now its (-2,∞)

Thus,

answer choice D is correct.

Hope this helps :)

Answer: 12%

Step-by-step explanation:

21/175=

(21/7)/(175/7)=

3/25=

12/100=0.12

0.12*100=12%

Answer:

ion know

Step-by-step explanation:

The value of x using similar triangles theorem is = 13/3.

Triangles that resemble one another but may not be exactly the same size are said to be comparable triangles.

When two objects have the same shape but different sizes, they can be said to be comparable.

This indicates that comparable shapes superimpose one another when amplified or de-magnified.

The term "Similarity" refers to this characteristic of like shapes.

Now in the given figure,

the proportion of the triangles' side is same.

So, 12/4 = 13/x

x = 13/3

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Answer:

100

Step-by-step explanation:

So in this problem, we have 5 base 10 blocks and 50 ones.

To find out the product we have to count by tens:

10, 20, 30, 40, 50

So 5 base 10 blocks = 50

Now we add the base ten blocks and the ones together:

50 + 50 = 100

So the answer is 100

There are 11 questions worth 5 points and 3 questions worth 15 points.

To find the correct number of questions:

Let, 5-point questions are x and 15 marks questions are y.

The total points are 100 so the other equation will be:

Now, multiply equation (1) by 5 and then subtract it by equation (2) as follows:

Therefore, there are 11 questions worth 5 points and 3 questions worth 15 points.

Now,

So, questions worth 15 marks are 3 then, and questions worth 5 marks will be 14 - 3 that is 11.

Therefore, there are 11 questions worth 5 points and 3 questions worth 15 points.

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Answer:

The equation is \(L + B = \$800\)

Andrea will donate $200 for business scholarships and $600 for liberal arts scholarships.

Step-by-step explanation:

Given

Represent Liberal Arts with L and Business with B

From the question, we have that:

\(L = 3 * B\)

and

\(Total = \$800\)

Required

Determine how much she donates for each

The total L + B is 800

i.e.

\(L + B = \$800\)

Substitute 3 * B for L

\(3 * B + B = \$800\)

\(3 B + B = \$800\)

\(4B = \$800\)

Solve for B

\(B =\$800/4\)

\(B =\$200\)

Recall that :

\(L = 3 * B\)

\(L = 3 * \$200\)

\(L = \$600\)

Answer: x = 9/11

Step-by-step explanation:

First, distribute 9 to x and -1

9x - 9 = 2

Then add 9 to both sides

9x = 11

Then divide both sides by 9

x = 9/11

Hope it helps :)

Answer:

Step-by-step explanation:

28/4 = 7

40/4 = 10

Then:

28:40 in simplest terms is:

7:10

Answer:

\( \sf \: 7 : 10 \)

Step-by-step explanation:

Now we have to,

→ simplify ratio into simplest form.

The given ratio,

→ 28 : 40

Let's simplify the given ratio,

→ 28 : 40

→ (28) ÷ 4 : (40) ÷ 4

→ (7) : (10)

→ 7 : 10

Therefore, the ratio is 7 : 10.

Answer:

\((x+3)(x-3)\)

Step-by-step explanation:

This equation is called a "difference in perfect squares".

The resulting answer should be: \((x + y)(x-y)\) where the y variable is the square root of the given number. In this instance, the integer 9

So knowing that the square root of 9 is 3 we can plug in 3 for both of the y spots which results in our answer.

If you wish to check this answer you can peform the "FOIL" method (first, outside, inside, last) in order to solve the equation which would result in:

\(x^{2}-9\)

I hope this helped! Feel free to ask questions if needed!

Answer:

I think it is D(A traditional Spanish government.)

Step-by-step explanation:

sorry if i'm wrong

Answer:

a

Step-by-step explanation:

Answer:

72

Step-by-step explanation:

We will first have to find the fraction of the whole land goats use. If we add 2/5 and 1/4, we will get 13/20. Simplifying the expression 1-13/20 gets 7/20, which is the total fraction of land the goat and sheep has. The goat will then get 7/20*1/7 of the whole land, which is 1/20. The sheep will then get 7/20*6/7 of the entire land, which is 3/10. Because 1/20 of the whole land is 12 acres, the farmer has 240 acres. SImplifying the expression 240*3/10 gets 72 acres

tan(41π/36) can be written in terms of the tangent of a positive acute angle as (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

To express tan(41π/36) in terms of the tangent of a positive acute angle, we need to find an angle within the range of 0 to π/2 that has the same tangent value.

First, let's simplify 41π/36 to its equivalent angle within one full revolution (2π):

41π/36 = 40π/36 + π/36 = (10/9)π + (1/36)π

Now, we can rewrite the angle as:

tan(41π/36) = tan((10/9)π + (1/36)π)

Next, we'll use the tangent addition formula, which states that:

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))

In this case, A = (10/9)π and B = (1/36)π.

tan(41π/36) = tan((10/9)π + (1/36)π) = (tan((10/9)π) + tan((1/36)π)) / (1 - tan((10/9)π)tan((1/36)π))

Now, we need to find the tangent values of (10/9)π and (1/36)π. Since tangent has a periodicity of π, we can subtract or add multiples of π to get equivalent angles within the range of 0 to π/2.

For (10/9)π, we can subtract π to get an equivalent angle within the range:

(10/9)π - π = (1/9)π

Similarly, for (1/36)π, we can add π to get an equivalent angle:

(1/36)π + π = (37/36)π

Now, we can rewrite the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Since we are looking for an angle within the range of 0 to π/2, we can further simplify the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Therefore, tan(41π/36) can be written in terms of the tangent of a positive acute angle as the expression given above.

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Answer:

− 0.21

Step-by-step explanation:

Convert to a fraction, then convert to a decimal by dividing the numerator by the denominator.

Answer:

8 < 2

Step-by-step explanation:

8x + 5 > 15

8x > 15 - 5

8x > 10

x < 2

cmiiw

Answer:

D. 3

hope this helps

have a good day :)

Step-by-step explanation:

The angles of a triangle with side lengths 5 , 12 and 13 are 90°, 22.63°, 67.38°.

In trigonometry, the law of cosines, also known as the law of cosines or cosine formula, basically relates the length of a triangle to one cosine of its angle. It states that if we know the lengths of two sides of a triangle and the angle between them, we can determine the length of the third side. c² = a²+ b² – 2ab cosγ

where a, b, c are the sides of the triangle and γ is the angle between a and b, see image above.

To find the length of a side of a triangle, take △ABC according to the cosine formula, which can be written as follows.

We have , a = 5 , b = 12 , c= 13

cos α =( 12² + 13² - 5² )/2×12×13= 288/312

=> α = cos⁻¹(0.923 ) = 22.63°

cos β = (5² + 13² - 12² )/2×13×5 = 50/130

=> β = cos⁻¹(5/13) = 67.38°

cos γ = (12² + 5² - 13² )/2×12×5= 0

=> γ = cos⁻¹(0) = 90°

Hence, the required angles are 90°, 22.63°, 67.38°.

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Answer:

Around 13.7

Step-by-step explanation:

The cosine of an angle in a right triangle is equivalent to the length of the adjacent side divided by the length of the hypotenuse. In this case, this means:

\(\cos 70= \dfrac{x}{40} \\\\x=40\cdot \cos 70\approx 13.7\)

Hope this helps!

It is given that:

Since both sides are having a base 2, the base 2 can be used to solve the equation.

Option A is correct.

Uisbg multiple line and angle theorems, the values of each of the 14 angles are given.

Using the geometry theorems :

1.)

∠2 is a right angle = 90°

2.)

∠1 + ∠2 + ∠3 = 180° (sum of angle on a straight line)

90 + ∠1 + 54° = 180°

∠1 = (180 - 144) = 36°

(∠2 and ∠5) ; (∠3 and ∠6) ; (∠1 and ∠4) are vertically opposite ;

Hence,

∠4 = 36°

∠5 = 90°

∠6 = 54°

∠3 = ∠8 = 54° (corresponding angles)

∠9 + ∠8 = 180° (sum of angle on a straight line)

∠9 = (180 - 54) =126°

∠7 = ∠9 = 126° (vertically opposite angles)

∠8 = ∠10 = 54° (vertically opposite angles)

∠4 = ∠13 = 36° (corresponding angles )

∠12 + ∠13 = 180° (sum of angle on a straight line)

∠12 = (180 - 36) =126°

∠11 = ∠13 = 36° (vertically opposite angles)

∠12 = ∠14 = 126° (vertically opposite angles)

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