The number that belongs in the green box

Answer:

\( \frac{6}{x} = \frac{8}{24} \)

\(8x = 144\)

\(x = 18\)

\( \frac{8}{24} = \frac{y}{12} \)

\(24y = 96\)

\(y = 4\)

So x = 18 and y = 4.

Answer: 32

Step-by-step explanation:

5+3*(5-2)^2

5+3*(3)^2

5+3*9

5+27

32

Answer:

32

Step-by-step explanation:

5 + 3 * (5 - 2)^2

5 + 3 * 3^2

5 + 3 * 9

5 + 2

= 32

~Let's change 9.9² to 10² since we have to estimate.~

We know that:

Solving the expression:

The estimated value of 9.9² × 1.79 is 179.

~Let's change √97.5 to √100 and 1.96 to 2 since we have to estimate.~

We know that:

Solving the expression:

The estimated value of √97.5 ÷ 1.96 is 5.

Answer:

2. 1/16

3. 729

4. x^11

6. x^3

7. 32768

8. x^6

9. 675

The total area of the composite figure is;  94.485 sq.units

The given composite shape is made up of a rectangle and the quadrant of a circle.

Formula for area of rectangle is;

A_r = Length * Width

Thus;

A_r = 8 * 7

A_r = 56 sq.units

The formula for the area of the quadrant of a circle is;

A_quad = ¹/₄πr²

Thus;

A_quad = ¹/₄π * 7²

A_quad = 38.485 sq.units

Total area of composite figure = 56 sq.units + 38.485 sq.units

= 94.485 sq.units

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Explanation:

Part A.

f(x) gives us the average test score, so to calculate the average test score n your math class after test 2, we need to replace x by 2 in f(x), then:

Therefore, the test average for your math class is 79.4

Part B.

To find the test average for your science class after test 2, we need to know what is the value of g(x) when x is equal to 2.

Since g(x) is 84 when x is 2, the test average for your science class is 84.

Part C.

After completing test 4, the average of the math class is:

On the other hand, we can see that after a new test, the average of the science class g(x) decreases by 2. So, after completing test 4 g(x) will be

Answer:

F(2b-1) = 4b² - 6b + 4

Step-by-step explanation:

Replace all the x with 2b-1

F(x) = x² - 2x + 4

F(2b-1) = (2b-1)² - 2(b) + 4

= 4b² - 4b + 1 - 2b + 4

= 4b² - 6b + 4

Answer:

C. 58 degrees

To find the measure of angle R in triangle QRS, we can use the fact that the sum of the angles in a triangle is 180 degrees.

Given:

Q = 8x

m/R = 14x + 2 degrees

m/S = 10x + 50 degrees

The sum of angles Q, R, and S is 180 degrees:

Q + R + S = 180

Substituting the given values:

8x + (14x + 2) + (10x + 50) = 180

Simplifying the equation:

8x + 14x + 2 + 10x + 50 = 180

32x + 52 = 180

32x = 180 - 52

32x = 128

x = 128/32

x = 4

Now that we have the value of x, we can substitute it back into the given expressions to find the measures of angles Q, R, and S.

Q = 8x = 8 * 4 = 32 degrees

m/R = 14x + 2 = 14 * 4 + 2 = 58 degrees

m/S = 10x + 50 = 10 * 4 + 50 = 90 degrees

Therefore, the measure of angle R is 58 degrees. So, the correct answer is C. 58°.

I hope you do great and pass this Unit test!!

1) The length of the side DE by similar triangle theorem is; Option C: 20

3) If RY = b + 4 and SE =20, then the value of b is; 6

Similar triangles are defined as triangles that have the same shape, but their sizes may vary. Thus, we can say that equilateral triangles, squares of any side lengths are as well examples of similar objects. This means that, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

1) ΔABC ~ ΔDEF

We are given the similar triangles ABC and DEF.

We are also told that ΔABC ~ ΔDEF.

Now, If AB = 10, AC = 8 and DF = 16

Thus, by similar triangle theorem, we can apply it to the attached triangle to get;

AB/DE = AC/DF

DE = (AB * DF)/AC

DE = (10 * 16)/8

DE = 20

3) Now, by using the concept of similar triangles, since we are given that;

R is the midpoint of line SH.

Y is the midpoint of line EH

RY = b + 4

SE =20

(b + 4)/20 = 1/2

Cross multiply to get;

2(b + 4) = 20

2b + 8 = 20

2b = 20 - 8

b = 12/2

b = 6

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There is percent decrease of 30%

50 pounds to 35 pounds

Original amount = 50 pounds

New amount= 35 pounds

Since, New amount is less than the original amount, this is a percentage of decrease.

Change in amount = 35 -50

Change in amount = -15 pounds

Substitute the given values we have;

% change = (change/original value) x 100

% change = -(15/50) x 100

% change = - 30%

Therefore, there is percent of decrease which is 30%.

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The value of X and Y are not independent of each other.

To determine if X and Y are independent or not from each other with the given information, we have to check if the given joint density function satisfies the following property:

f(x,y) = g(x) × h(y)

where g(x) and h(y) are the marginal density functions of X and Y respectively.

If the above equation holds, then X and Y are said to be independent of each other.If not, X and Y are dependent on each other.

Let's find the marginal density functions of X and Y.

The marginal density function of X:

fX(x) = ∫f(x,y)dy

∫0∞xe^-(x+y)dy = x

∫0∞e^-(x+y)dy∫0∞e^-(x+y)dy = x

The marginal density function of Y:fY(y) = ∫f(x,y)dx∫0∞xe^-(x+y)dx = e^-y

The joint density function doesn't satisfy the property:

f(x,y) ≠ g(x) × h(y)f(x,y) = x × e^-(x+y)

fX(x) = x

fY(y) = e^-y

Since the joint density function can not be expressed as the product of the marginal density functions of X and Y, X and Y are dependent on each other.

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Answer: JK=10

Step-by-step explanation:

JL=JK+KL

13=JK+3

13-3=JK+3-3

JK=10

x = # of days Maria worked

x + 5 = # of days Fred worded

$16(x + 5) + $18x = $1780

Let's distribute the $16

$16x + $80 + $18x = $1780

Combine like terms

$34x + $80 = $1780

Subtract $80 from both sides.

$34x = $1700

Divide both sides by $34

x = 50 days

Maria worked 50 days

Answer:

a³ + 5c

Step-by-step explanation:

That would be, symbolically, a³ + 5c

Using a significance level of 0.05, we can conclude that fails to reject the null hypothesis. There is not sufficient evidence to support the claim that the proportion of urban gardens visited by native bees is different than 25%. The correct option is d).

Based on the given information, Sarah has calculated a p-value of 0.178 and is using a significance level of 0.05. The p-value is a measure of the strength of evidence against the null hypothesis. In hypothesis testing, if the p-value is less than the chosen significance level (0.05 in this case), it suggests that the observed data is statistically significant and provides evidence to reject the null hypothesis.

On the other hand, if the p-value is greater than the significance level, it indicates that the observed data is not statistically significant, and there is insufficient evidence to reject the null hypothesis.

In this scenario, since the p-value (0.178) is greater than the significance level (0.05), the best conclusion is to "Fail to reject the null hypothesis." This means that there is not sufficient evidence to support the claim that the proportion of urban gardens visited by native bees is different than 25%. The data collected does not provide strong enough evidence to conclude that there has been a significant change in the proportion over the five-year period.

Therefore, the correct answer is D. "Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that the proportion of urban gardens visited by native bees is different than 25%."

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Answer:

\(\frac{1}{\sqrt{2}}\)

Step-by-step explanation:

Answer:

\(\Large \boxed{2. \ x=\pm \sqrt{k}}\)

Step-by-step explanation:

\(x^2 =k\)

k is a real number.

We take the square root of both sides of the equation.

\(\sqrt{x^2 } =\pm \sqrt{k}\)

Simplifying the equation.

\(x=\pm \sqrt{k}\)

Answer:

x = ±√k

Step-by-step explanation:

If:

\(x^2 = k\)

We'll take square root on both sides

=> \(\sqrt{x^2} = +/- \sqrt{k}\)

=> x = ±√k

Answer:

\(5 \div 11 \times 6 \div 7 = \frac{30}{77} \)

Answer:

\(Total\ length = 8\frac{5}{8}\ miles\)

Step-by-step explanation:

Given

See attachment for ski trails

Required

Total length of \(2\frac{7}{8}\) ski trails

From the attached figure, there are 3 skis with length \(2\frac{7}{8}\ miles\)

So:

The total length is:

\(Total\ length = 3 * 2\frac{7}{8}\)

Express fraction as improper fraction

\(Total\ length = 3 * \frac{23}{8}\)

\(Total\ length = \frac{3 *23}{8}\)

\(Total\ length = \frac{69}{8}\)

\(Total\ length = 8\frac{5}{8}\ miles\)

Answer:

-2-\(\frac{2}{a}\)

Step-by-step explanation:

I broke up the fractions so that it is easier.

\(\frac{1}{a-1}\) - \(\frac{1}{a+1}\) - \(\frac{2}{2a+1}\) - \(\frac{2}{2a-1}\) = (\(\frac{1}{a}\) - \(\frac{1}{1}\)) - (\(\frac{1}{a}\) + \(\frac{1}{1}\)) - (\(\frac{2}{2a}\) + \(\frac{2}{1}\)) - (\(\frac{2}{2a}\) - \(\frac{2}{1}\))

Now I remove the brackets. One plus and one minus make one minus and two minus makes one plus.

(\(\frac{1}{a}\) - \(\frac{1}{1}\)) - (\(\frac{1}{a}\) + \(\frac{1}{1}\)) - (\(\frac{2}{2a}\) + \(\frac{2}{1}\)) - (\(\frac{2}{2a}\) - \(\frac{2}{1}\)) =\(\frac{1}{a}\) - \(\frac{1}{1}\) - \(\frac{1}{a}\) - \(\frac{1}{1}\) - \(\frac{2}{2a}\) - \(\frac{2}{1}\) - \(\frac{2}{2a}\) + \(\frac{2}{1}\)

Remove redundancies. (\(\frac{1}{a}\) - \(\frac{1}{a}\) = 0)

\(\frac{1}{a}\) - \(\frac{1}{1}\) - \(\frac{1}{a}\) - \(\frac{1}{1}\) - \(\frac{2}{2a}\) - \(\frac{2}{1}\) - \(\frac{2}{2a}\) + \(\frac{2}{1}\) = -\(\frac{2}{1}\) -\(\frac{4}{2a}\)

Simplify the fractions.

-\(\frac{2}{1}\) -\(\frac{4}{2a}\)  = -2-\(\frac{2}{a}\)

When rounding a number to 2 decimal places, we are essentially keeping only the first two digits after the decimal point and discarding the rest. The third digit after the decimal point is the one that affects the rounding decision.

In this case, the number y is rounded to 9.68, which means that the third digit after the decimal point is either 5 or greater than 5. If it is 5 or greater, we round up the second digit after the decimal point. If it is less than 5, we simply truncate the decimal part.

To find the upper bound of y, we need to add 0.005 to 9.68, which is the smallest possible value for the third digit that would cause rounding up:

9.68 + 0.005 = 9.685

Therefore, the upper bound of y is 9.685.

To find the lower bound of y, we need to subtract 0.005 from 9.68, which is the largest possible value for the third digit that would not cause rounding up:

9.68 - 0.005 = 9.675

Therefore, the lower bound of y is 9.675.

Hence, the upper and lower bounds of y are 9.685 and 9.675, respectively.

Answer:

11

Step-by-step explanation:

Step 1:

\(\frac{11}{15}\) = 0.7333333333333

Answer:

Miguel has $63

Lisbeth has $11

David has $21

Step-by-step explanation:

let Miguel share be M

let Lisbeth share be L

let David share be D

from the question, we know that

M=3D

L=D-10.

M+L+D=95

thus,

3D+(D-10)+D= 95

3D+D-10+D= 95

5D-10 = 95

5D= 95+10

5D= 105

D= 105/5

D= 21.

thus,

M = 3D = 3×21

= $63

L = D-10 = 21-10

= $11

(63+21+11)$ = $95

Answer:

mass is 58kg

Step-by-step explanation:

Answer:

Yes, it is possible that the triangles ABC and DEF are similar. To check if two triangles are similar, one must check if all the corresponding angles are equal. To do this, we need to find the measure of triangle ABC's interior angles. We can use the Triangle Sum Theorem, which states that the sum of any triangle's three interior angles is equal to 180 degrees. So, if we subtract 22 + (2X) + 55 from 180, we get 180 - 77 = 103. Therefore, triangle ABC's interior angle measures are 22, (2X), and 103.

To determine if the two triangles are similar, we must also find the interior angle measures of triangle DEF. We can do this by subtracting 11 + 5 + (5.5X) from 180, which gives us 180 - 16.5 = 163.5. Therefore, triangle DEF's interior angle measures are 11, 5, and 163.5.

Now, since all the pairs of corresponding angles are equal (22 and 11; 2X and 5; and 103 and 163.5), the triangles ABC and DEF do have the possibility of being similar.

The probability of exactly 16 students having jobs in the sample is 0.204 and the probability of 16 or more students having jobs in the sample is 0.334.

Let X be the number of KSU students with jobs in a random sample of 20 students. Since each student in the sample can be either employed or not employed, X follows a binomial distribution with parameters n = 20 (the sample size) and p = 0.50 (the probability of a student having a job).

To find the probability of exactly 16 students having jobs in the sample, we can use the binomial probability mass function

P(X = 16) = (20 choose 16) * 0.5^16 * 0.5^(20-16) = 0.204

To find the probability of 16 or more students having jobs in the sample, we can use the cumulative distribution function

P(X ≥ 16) = 1 - P(X < 16) = 1 - ∑(i=0 to 15) (20 choose i) * 0.5^i * 0.5^(20-i) = 0.334

Based on the sample data, it appears that the proportion of KSU students with jobs is higher than the professor's conjectured value of 0.50. However, we cannot conclusively reject the professor's conjecture based on a single sample of 20 students.

We would need to conduct a hypothesis test with appropriate statistical significance level to determine if the difference between the sample proportion and the conjectured value is statistically significant or not.

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Taking the inverse Laplace transform of Y(s), we get:  y(t) = (f(t) + 3e²3t - 4e²4t) u(t - 1) where u(t - 1) is the unit step function (equal to 0 for t < 1 and equal to 1 for t >= 1).

To solve the differential equation y'' - 7y' + 12y = f(t), we first take the Laplace transform of both sides:

L[y''] - 7L[y'] + 12L[y] = L[f(t)]

Using the properties of the Laplace transform and the initial conditions, we can simplify the left-hand side as follows:

s²2 Y(s) - s y(0) - y'(0) - 7 (s Y(s) - y(0)) + 12 Y(s) = L[f(t)]

s²2 Y(s) - s - 7s Y(s) + 12 Y(s) = L[f(t)]

Y(s) (s²2 - 7s + 12) = L[f(t)] + s

Solving for Y(s), we get:

Y(s) = (L[f(t)] + s) / (s²2 - 7s + 12)

To find the inverse Laplace transform of Y(s), we factor the denominator:

s²2 - 7s + 12 = (s - 3)(s - 4)

Using partial fractions, we can write Y(s) as:

Y(s) = A/(s - 3) + B/(s - 4)

where A and B are constants. Multiplying both sides by the denominator (s - 3)(s - 4) and setting s = 3 and s = 4, we can solve for A and B:

A = (L[f(t)] + 3) / (4 - 3) = L[f(t)] + 3

B = (L[f(t)] + 4) / (3 - 4) = -L[f(t)] - 4

Therefore, Y(s) can be written as:

Y(s) = (L[f(t)] + 3)/(s - 3) - (L[f(t)] + 4)/(s - 4)

Taking the inverse Laplace transform of Y(s), we get:

y(t) = (f(t) + 3e²3t - 4e²4t) u(t - 1)

where u(t - 1) is the unit step function (equal to 0 for t < 1 and equal to 1 for t >= 1).

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Answer:

To calculate the gradient of a straight line you choose two points on the line itself.

From the two points we calculate:

The difference in height (y co-ordinates) ÷ The difference in width (x co-ordinates).

If the answer is a positive value then the line is uphill in direction.

If the answer is a negative value then the line is downhill in direction.

Step-by-step explanation: