What is the area of the trapezoid?
5 cm
9 cm
45°
2 cm
(Not drawn to scale)
O 94.5 cm
O 7 cm
O 31.5 cm
O 81 cm

Composing f(x)=2x-8 and g(x)=1/2x+4 results in the identity function, f(g(x)) = x.

To compose the two functions, we substitute g(x) into f(x) in place of x:

f(g(x)) = 2(g(x)) - 8

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

= x + 8 - 8

= x

Therefore, composing the two functions results in the identity function, f(g(x)) = x.

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Answer:

Step-by-step explanation:

Its is

6CM wide. as to find the area we have to times the length x height :)

Answer:

wide = 6 cm

Step-by-step explanation:

\(t=tall=10\)

\(w=wide=?\)

\(P=perimeter=32\)

The equation:

\(P=2t+2w\)

\(32=2(10)+2w\\32=20+2w\)

\(32-20=2w\\12=2w\)

\(\frac{12}{2} =w\)

\(6=w\)

Hope this helps.

The linear equation that describes this situation is:

y = 2500 + 300*x

A general linear equation is written as:

y = ax + b

where a is the slope and b is the initial value.

Here we know that she starts with 2,500 points in the game, and then she wins 300 points for every minute.

Then the initial value is 2,500, and the slope is 300, then we can write the linear equation:

y = 2500 + 300*x

That is the correct option.

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The total number of adult leaders is 11.

When solving a simple equation, think of the equation as a balance, with the equals sign (=) being the fulcrum or center. A simple equation represents a relationship between two terms on either side of an equal sign. Simple equations also follow one or a combination of the four mathematical operations of addition, subtraction, multiplication and division. As mathematics becomes more complex in level, simple equations can become larger with additional terms and variables.

Types of simple equation:

Linear equation are the most common simple equation and typically consist of one or several terms on either side of an equal sign.

Exponential equations contain numerical terms and exponents and sometimes include variables, depending on the type of problem you are solving.

Given:

Number of cub = 28

Number of scouts is 6 more than twice the number of adult leaders

Let C = cub scouts

L = adult leaders

C = 6 + 2L

28 = 6 + 2L

28 - 6 = 2L

22 = 2 L

L = 11

Number of adult leaders are 11.

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Answer:

55

Step-by-step explanation:

i did the test and got 55. the actual answer is 55.49, but you have to round.

Answer:

\(x = 9\)

Step-by-step explanation:

The correct equation is:

\(2x = 1x + 9\)

Required

Solve for x

\(2x = 1x + 9\)

Collect Like Terms

\(2x - 1x = 9\)

\(x = 9\)

Hence, the solution to the equation is 9

Answer:

37.50

Step-by-step explanation:

The price per cup is $0.20.

To determine the price per cup, we need to first find the number of cups in a 2-quart carton of apple juice.

Since 1 quart is equal to 4 cups, a 2-quart carton contains 2 x 4 = 8 cups of apple juice.

Therefore, the price per cup of apple juice can be found by dividing the total cost of the carton by the number of cups:

$1.60 / 8 cups = $0.20 per cup

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Step-by-step explanation:

7equitacion h< y ⚽ de los siguientes dominios

Answer:

a. The 95% C.I. is approximately -5.83 < μ₁ - μ₂ < -0.57

b. Yes

c. The power of the test is 0.03836

d. The sample size can be considered adequate

Step-by-step explanation:

a. The given data in the study

Catalyst 1: 57.9, 66.2, 65.4, 65.4, 65.2, 62.6, 67.6, 63.7, 67.2, 71.0

Catalyst 2: 66.4 , 71.7, 70.3, 69.3, 64.8, 69.6, 68.6, 69.4, 65.3, 68.8

Using the Average, Standard Deviation function from Microsoft Excel, we have;

The mean for Catalyst 1, \(\overline x_1\) = 65.22

The standard deviation for catalyst 1, σ₁ = 3.444416

The mean for Catalyst 2, \(\overline x_2\) = 68.42

The standard deviation for catalyst 2, σ₂ = 2.22401

The 95% confidence interval on the difference in mean is given as follows;

\(\left (\bar{x}_1-\bar{x}_{2} \right ) \pm z_{c}\sqrt{\dfrac{\sigma _{1}^{2}}{n_{1}} + \dfrac{\sigma_{2}^{2}}{n_{2}}}\)

The critical-z for a 95% confidence interval = 1.96

Therefore, we have;

\(\left (65.22-68.42 \right ) \pm 1.96 \times \sqrt{\dfrac{3^{2}}{10} + \dfrac{3^{2}}{10}}\)

Therefore, we have;

The 95% C.I. is approximately -5.83 < μ₁ - μ₂ < -0.57

The test statistics is given as follows;

\(z=\dfrac{(\bar{x}_{1}-\bar{x}_{2})}{\sqrt{\dfrac{\sigma_{1}^{2} }{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}}\)

Therefore we have;

\(z=\dfrac{(65.22-68.42)}{\sqrt{\dfrac{3^{2} }{10}+\dfrac{3^{2}}{10}}} = -2.385\)

The p-value = P(Z<-2.39 or Z > 2.39) = 2P(Z<-2.39) = 2 × 0.00842 = 0.01684

b. From the confidence interval which range from approximately -5.83 to -0.57 and does not include 0, therefore, there is a difference in mean active concentration which depends on the choice of catalyst

c. The power of the test

 The sample mean difference is given as follows;

\(\left (\bar{x}_1-\bar{x}_{2} \right ) = \pm z_{c}\sqrt{\dfrac{\sigma _{1}^{2}}{n_{1}} + \dfrac{\sigma_{2}^{2}}{n_{2}}}\)

Therefore, we have;

\(\left (\bar{x}_1-\bar{x}_{2} \right ) = \pm 1.96 \times \sqrt{\dfrac{3^{2}}{10} + \dfrac{3^{2}}{10}} = \pm 2.6296\)

The z-value is given as follows;

\(z=\dfrac{(\bar{x}_{1}-\bar{x}_{2})-(\mu_{1}-\mu _{2} )}{\sqrt{\dfrac{\sigma_{1}^{2} }{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}}\)

μ₁ - μ₂ = 5

When \(\bar{x}_1-\bar{x}_{2} = 2.6296\)

\(z=\dfrac{2.6296-5}{\sqrt{\dfrac{3^{2} }{10}-\dfrac{3^{2}}{10}}} \approx -1.7667918\)

When \(\bar{x}_1-\bar{x}_{2} = -2.6296\)

\(z=\dfrac{-2.6296-5}{\sqrt{\dfrac{3^{2} }{10}-\dfrac{3^{2}}{10}}} \approx -5.686768\)

The power of the test is given by P = P(Z<-5.69) + P(Z>-1.77) = 0 + 0.03836 = 0.03836

The power of the test = 0.03836

d. The sample size is statistically adequate because the confidence interval of -5.83 < μ₁ - μ₂ < -0.57 has a value of -5 as a possible population difference in mean

The assumption of normality seems adequate because the confidence interval obtained by using the sample standard deviation is given as follows;

(-5.74, -0.66) which also contains -5 which is the difference in the population mean

Answer:

5x+30

Step-by-step explanation:

we just open the bracket and multiply

The total value of the furniture sold by Joyce last week is A = $ 6,733.33

Given data ,

Let's call the value of the furniture Joyce sold "x".

She receives 10% commission on the first $1,200 of sales, which is $120:

Commission on first $1,200 = 0.1 * 1200 = 120

The remaining sales that she earns commission on is the difference between the total value of the furniture sold and the first $1,200:

Remaining sales = x - 1200

She earns 15% commission on the remaining sales, which is 0.15 times the remaining sales:

Commission on remaining sales = 0.15 * (x - 1200)

Her total earnings from commission last week was $950. So we can write an equation:

Commission on first $1,200 + Commission on remaining sales = $950

Substituting the expressions we found for the two commissions, we get:

120 + 0.15(x - 1200) = 950

120 + 0.15x - 180 = 950

On simplifying the equation , we get

0.15x - 60 = 950

0.15x = 1010

x = 6,733.33

Hence , the value of the furniture Joyce sold last week was $6,733.33

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We will find the rate as follows:

So the rate is the distance divided by the time it took to traverse.

Answer:

9000

Step-by-step explanation:

The perimeter of triangle ABC could be either approximately 27.98 cm or approximately 14.66 cm, depending on the length of AB.

What is the perimeter?

The perimeter is a mathematical term that refers to the total distance around the outside of a two-dimensional shape. It is the length of the boundary or the sum of the lengths of all the sides of a closed figure.

Let's call the length of AB x and the length of BC y.

First, we can use the fact that CD is the height of the triangle to find the area of triangle ABC:

Area of triangle ABC = 1/2 * CD * AB

Substituting the given values, we have:

1/2 * 12 * x = 6x

So the area of triangle ABC is 6x square centimeters.

We can also use the fact that angle BCD is 30 degrees to set up a trigonometric equation involving x and y:

tan(30) = x/y

Simplifying, we get:

y = x/tan(30) = x/(1/√(3)) = √(3) * x

Now we can use the formula for the area of a triangle in terms of its sides:

Area of triangle ABC = 1/2 * AB * BC * sin(B)

where B is the angle between sides AB and BC. In this case, we know that angle BCD is 30 degrees, so angle BCA is 60 degrees, and angle ABC is 90 degrees. Therefore, we have:

Area of triangle ABC = 1/2 * x * √3 * x * sin(60)

Simplifying, we get:

Area of triangle ABC = 1/4 * √3 * x²

Since we already found that the area of triangle ABC is 6x square centimeters, we can set these two expressions equal to each other and solve for x:

6x = 1/4 * √(3) * x²

Multiplying both sides by 4/√3, we get:

24/√(3) * x = x²

Simplifying, we get:

x² - 24/√(3) * x = 0

Using the quadratic formula, we get:

x = (24/√(3) ± √((24/√(3))² - 410)) / 2*1

Simplifying, we get:

x = 16√(3) / 3 or x = 8 √(3) / 3

Since we are looking for the perimeter of triangle ABC, we need to find y as well. Using the equation we derived earlier, we have:

y = √(3) * x

Therefore, we have two possible triangles:

Triangle ABC1: AB = 16 √(3) / 3, BC = 16, and AC = 8 √7 / 3

Triangle ABC2: AB = 8 √3 / 3, BC = 8, and AC = 4 √7 / 3

The perimeter of each triangle is the sum of its side lengths. Therefore:

Perimeter of triangle ABC1 = 16 √3/ 3 + 16 + 8 √7 / 3 ≈ 27.98 cm

Perimeter of triangle ABC2 = 8 √3 / 3 + 8 + 4 √7 / 3 ≈ 14.66 cm

hence, the perimeter of triangle ABC could be either approximately 27.98 cm or approximately 14.66 cm, depending on the length of AB.

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Answer:

Step-by-step explanation:

the pouint and end

Answer:It would mean that one value would be 1, and the other would be 25, like a ratio. Example: 1:25, 2:50

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

21 = 3 x 7

12 = 2 x 6

4 = 2 x 7

( 21 x 12 ) / 14

= ( 3 x 7 x 2 x 6 ) / ( 2 x 7 )

= 3 x 6

= 18

Answer:

18

Step-by-step explanation:

See image attached for guide

21 x 1 2/14

Make 1 2/14 an improper fraction, add the denominator 1 under 21:

21/1 x 16/14

Multiply numerator x numerator, do the same for denominator:

21 x 16= 336

1 x 14 = 14

336/14

Simplify:

336/14 = 24

Hope this helps

Answer: draw the line using a ruler on which you have identified points 2 7/16 inches apart

Step-by-step explanation:  On your ruler graduated in inches with marks at 1/16-inch intervals, locate the 0 mark and the mark 1/16 inch before the half-inch mark between 2 and 3 inches.Draw your line along the edge of the ruler between the two marks you have identified: 0 and 2 7/16. The line will be 2 7/16 inches

The relationship in this problem is not proportional, as there are different ratios between the number of people and the number of cars washed.

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.

The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:

y = kx.

The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.

The ratios between the output and the inputs are given as follows:

Different ratios, hence the relationship is not proportional.

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Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.

A perfect square refers to a number that is the result of multiplying an integer by itself. In this case, 6^1 is equal to 6.

However, 6 is not a perfect square because it cannot be obtained by multiplying an integer by itself. The perfect squares up to 6^1 would be 1^2 = 1 and 2^2 = 4.

Using probability concepts, it is found that:

a) 0.43 = 43% probability that the patient experiences neither depression nor weight gain.

b) 0.3929 = 39.29% probability that the patient experiences depression given that the patient experiences weight gain.

c) 0.275 = 27.5% probability that the patient experiences weight gain given that the patient experiences depression.

d) No.

e) No.

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

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)  

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

Item a:

\(P(A \cup B) = P(A) + P(B) - P(A \cap B) = 0.4 + 0.28 - 0.11 = 0.57\)

\(p = 1 - P(A \cup B) = 1 - 0.57 = 0.43\)

0.43 = 43% probability that the patient experiences neither depression nor weight gain.

Item b:

\(P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{0.11}{0.28} = 0.3929\)

0.3929 = 39.29% probability that the patient experiences depression given that the patient experiences weight gain.

Item c:

\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.11}{0.4} = 0.275\)

0.275 = 27.5% probability that the patient experiences weight gain given that the patient experiences depression.

Item d:

\(P(A \cap B) \neq 0\), thus, the events are not mutually exclusive.

Item e:

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Answer:

Step-by-step explanation:

67

Alijah's taxable income puts him in the first tax bracket, over $8,350 but not surpassing $33,950. Hence, his tax due is a base of $835 plus 15% of the income that exceeds $8,350. This results in a total tax payable of $850. Option B is the correct answer.

Alijah's taxable income falls within the first bracket of the tax table given, being over $8,350 but not over $33,950.

This bracket requires him to pay a tax of $835.00 plus 15% of the amount over $8,350.

He has a surplus of $100 over the $8,350 threshold (i.e., $8,450 - $8,350), and 15% of $100 equals $15.

Therefore, the total tax he owes would be the fixed amount of $835.00 plus the $15.00 calculated, which sums up to $850.00.

Thus, looking at the provided options, option B ($850.00) would be the correct answer.

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a) P(psychology student)  = 1/3. b) P(psychology or anthropology student)  = 5/6. c) P(not sociology student)= 5/6

(a) The probability of choosing a psychology student is the number of psychology students divided by the total number of students:

P(psychology student) = 4/(6+2+4) = 4/12 = 1/3

(b) The probability of choosing a psychology student or an anthropology student is the sum of the number of psychology and anthropology students divided by the total number of students:

P(psychology or anthropology student) = (4+6)/(6+2+4) = 10/12 = 5/6

(c) The probability of not choosing a sociology student is the number of non-sociology students divided by the total number of students:

P(not sociology student) = (6+4)/(6+2+4) = 10/12 = 5/6

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Answer:

The mean cost of a five pound bag of shrimp is 40 dollars with a standard deviation of 8 dollars.

Step-by-step explanation:

a sample of 49 bags of shrimp is randomly selected, what is the probability that the sample mean would be less than 37.4 dollars? Round your answer to four decimal places.

Answer:

21.75 I think

Step-by-step explanation:

3x-8 = Mitch

x = Tom

3x -8 + x = 79

4x - 8 = 79

add eight to both sides

4x = 87

divide both sides by 4

x = 21.75

The grand mean fir the observations of the age of three different types of vehicles currently on the road: trucks, cars, and vans is Eight . So, correct option is option B.

The overall or pooled average is the average of multiple subsample averages, as long as the subsamples have the same number of data points. In ANOVA, the overall mean for a set of multiple subsamples is the mean of all observations. that is, each data point divided by the common sample size.

∑x = represented by the sum of the averages of all sets. Overall grand mean formula is

Grand mean = sum of all sample mean / total number of sentences

We have given that,

Autotrader would like to test difference exists in the age of three different types of vehicles.

let set A , set B and set C represents the ages of three different vichles i.e trunks , cars and vans respectively.

From table we get,

Mean of ages of trunks , A = 10

Mean of ages of cars , B = 8

Mean of ages of vans , C = 6

Grand mean = (10+8+6)/3 = 8

Hence, the grand mean is 8..

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