If f(x)=9x-6 and g(x)=x+6/9
f(g(x))
g(f(x))

The sample mean, population mean, population standard deviation, and sample size are required to calculate the value of the test statistic and are provided as  \(\bar{x}\)  = 62.5, μ = 63.2, σ = 3.3, and n = 79, respectively, and then we can calculate the test statistic using the formula t = (\(\bar{x}\) - μ) / (σ / √n).

We must calculate the value of the test statistic in order to determine whether the women's rights organization's assertion on the average retirement age for executives is supported by enough evidence.

Describe the theories:

The null hypothesis (H0) is that women CEOs retire on average at age 63.2. Alternative Hypothesis (H1): Women executives retire on average at a younger age than 63.2.

Determine the test statistic by:

The following formula is used to obtain the test statistic for comparing means:

t = (\(\bar{x}\) - μ) / (σ / √n)

where \(\bar{x}\) is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Given:

\(\bar{x}\) = 62.5 (sample mean)

μ = 63.2 (population mean)

σ = 3.3 (population standard deviation)

n = 79 (sample size)

Substituting the values into the formula, we get:

t = (62.5 - 63.2) / (3.3 / √79)

Calculating this expression, we find the value of the test statistic.

Determine the critical value:

To determine the critical value, we need to specify the significance level (α). In this case, the significance level is 0.10. We will use a one-tailed test because the alternative hypothesis states that the mean age of retirement is less than 63.2.

Using a t-distribution table or a statistical calculator, we can find the critical value corresponding to a one-tailed test with a significance level of 0.10 and the degrees of freedom (df) equal to n-1.

Compare the test statistic with the critical value:

If the absolute value of the test statistic is greater than the critical value, we reject the null hypothesis.

Otherwise, we fail to reject the null hypothesis.

By comparing the calculated test statistic with the critical value, we can determine whether there is sufficient evidence to support the organization's belief.

Note: Since the values of the test statistic and critical value are not provided in the question, it is not possible to provide the specific result without performing the calculations.  

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well, we know all three points are colinear, so the slope from the first two points is the same slope from either to the (c , -9) point, let's check the slope of the first two points given

\((\stackrel{x_1}{-5}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{1})~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{10}-\underset{x_1}{(-5)}}} \implies \cfrac{1 +3}{10 +5}\implies \cfrac{4}{15}\)

so then, the slope from say hmmmm let's use (-5 , -3), the slope from (-5 , -3) and (c , -9) must also be the same 4/15

\((\stackrel{x_1}{-5}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{c}~,~\stackrel{y_2}{-9}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-9}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{c}-\underset{x_1}{(-5)}}} \implies \hspace{5em}\cfrac{-9 +3}{c +5}~~ = ~~\stackrel{slope}{\cfrac{4}{15}}\implies \cfrac{-6}{c+5}=\cfrac{4}{15} \\\\\\ -90=4c+20\implies -110=4c\implies \cfrac{-110}{4}=c\implies -\cfrac{55}{2}=c\)

Answer:

are you looking for a mixed number if so its 2 4/5

Step-by-step explanation:

Answer:

Yeah, the answer is f(0) = -3

Answer:

16 deliveries

Step-by-step explanation:

238 ≤ 10d + 78

160 ≤ 10d

16 ≤ d

Thus, he needs to make at least 16 deliveries to make at least $238 in one day.  Any less than 16 deliveries will cause him to fall short of his goal and any more than 16 deliveries will cause him to exceed his goal.

Answer:

Step-by-step explanation:

What is 3-3×6+2 please?

remember PEMDAS

3 - 3 × 6 + 2 =    (solve multiplication)

3 - 18 + 2 =         (solve addition)

3 - 16 =              (solve subtraction)

-13                     (result)

Answer:

389/6

Step-by-step explanation:

thts the answer

Answer:

.16 or 4/25

Step-by-step explanation:

Answer:

4/25

Step-by-step explanation:

\(\frac{4}{5}\)×\(\frac{1}{5}\)

multiply tops together and denominators together and get \(\frac{4}{25}\)

Answer:

g>5/8

Step-by-step explanation:

Step 1: Simplify both sides of the inequality.

-8g-6<-11

Step 2: Add 6 to both sides.

−8g−6+6<−11+6

−8g<−5

Step 3: Divide both sides by -8.

−8g/−8<−5/−8

= g<5/8

Answer:

Y = 4

Step-by-step explanation:

5x-y=54

50-y=54

circle y and subtract 50 from itself then subtract 50 from 54.

after subtracting you should have y=4

Answer: 5,200,000

Step-by-step explanation:

10^6 = 1,000,000

So, 5.2 * 10^6 = 5.2 * 1,000,000

= 5,200,000

A translation followed by a reflection

Answer:

84 + 84(0.22)

Step-by-step explanation:

In order to find the amount of the tip you need to do 84x0.22 then you add that on to the original price

Answer:

$180

Step-by-step explanation:

If the perimeter is 30 yards and each yard costs $6 you times 30 and 6 and you get $180

Answer:

Step-by-step explanation:

(-3, -6) (0, -4)

(-4 + 6)/(0 + 3)= 2/3

y + 4 = 2/3(x - 0)

y + 4 = 2/3x - 0

y = 2/3x - 4

answer is c

Answer: Type I error

Step-by-step explanation:

A type 1 error is also referred to as the false positive and it is when a true null hypothesis is incorrectly rejected by the researcher.

On the other hand, type II error which is also refered to as the false-negative is when a null hypothesis which is false is failed to be rejected by the researcher but rather accepted.

Based on the information given in the question, since the data leads to the rejection of the null hypothesis such was later found out to be true, then a type I error has occured.

Answer:

4+2/3-1 = 3

Step-by-step explanation:

hopefully it helped

Step-by-step explanation:

mark it as the brainliest

Answer:

i need help with this too

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer is A for both

Answer:

multiply equation 1by -3 and multiply equation 2 by 1

-3×2x+3y×-3=13×-3

-6x+4y=0

-6x-9y=-39

-6x+4y=0

Step-by-step explanation:

-13y=-39

divide both side by -13

-13y/-13=-39/-13

y=3

put answer of y in equation 1

2x+3y=13

2x+3×3=13

2x+9=13

take like terms of the equation

2x=13-9

2x=4

divide both side by 2

2x/2=4\2

x=2

(x,y)=(2,3)

The correct answer is Option 1.

To find the x-intercept of the equation 3x + 5y = 9, we set y = 0 and solve for x.When y = 0, the equation becomes 3x + 5(0) = 9, which simplifies to 3x = 9.Solving for x, we get x = 3.The x-intercept of the equation 3x + 5y = 9 is (3, 0).

What is x-intercept ?

An x-intercept is a point where a graph or a line crosses the x-axis. It is the value of the independent variable (x) when the dependent variable (y) is equal to zero. In other words, it is the point at which a function or equation intersects the x-axis, and its coordinates are of the form (x, 0). To find the x-intercept of a graph or equation, you can set y=0 and solve for x.

To find the x-intercept of the equation 3x + 5y = 9, we need to set y = 0 and solve for x.

So, we have:

3x + 5(0) = 9

3x = 9

x = 3

Therefore, the x-intercept of the equation 3x + 5y = 9 is (3,0), which means the point where the line intersects the x-axis is (3,0).

To verify, we can graph the equation and see that the point (3,0) is indeed on the x-axis.

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The smaller number is 6 .

The larger number is 22

Let's let x be the smaller number and y be the larger number.

From the problem, we know that one number is eight less than five times the other, so we can write:

y = 5x - 8

We also know that the sum of the two numbers is 28, so we can write:

x + y = 28

Now we have two equations in two variables. We can solve for one of the variables in terms of the other, and substitute that expression into the other equation to eliminate one variable.

Let's solve the first equation for x

x = (y + 8)/5

Now we can substitute this expression for x into the second equation:

(y + 8)/5 + y = 28

Multiplying both sides by 5 to eliminate the fraction, we get:

y + 8 + 5y = 140

Combining like terms, we get:

6y + 8 = 140

Subtracting 8 from both sides, we get:

6y = 132

Dividing both sides by 6, we get:

y = 22

Now we can use the equation y = 5x - 8 to solve for x:

22 = 5x - 8

Adding 8 to both sides, we get:

30 = 5x

Dividing both sides by 5, we get:

x = 6

Therefore, the smaller number is 6 and the larger number is 22.

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Step-by-step explanation:

\( \frac{1 + \cot(x) }{ \cos(x) } - \csc(x) = \sec(x) \)

\( \frac{1}{ \cos(x) } + \frac{ \cot(x) }{ \cos(x) } - \csc(x) = \sec(x) \)

\( \sec(x) + \frac{1}{ \sin(x) } - \csc(x) = \sec(x) \)

\( \sec(x) + \csc(x) - \csc(x) = \sec(x) \)

\( \sec(x) = \sec(x) \)

Answer:

Area of the shape is 244.98cm² is B

Step-by-step explanation:

Area of shape=Area of semi circle+Area of trapezoid

A=1/2 πr² + 1/2(a+b)h

A=1/2×3.142×7² + 1/2(14+18)10.5

A=1/2×3.142×49 + 1/2×32×10.5

A=76.98+168

A=76.98+168

A=244.98cm²

Answer:

d = 3h - 6

Step-by-step explanation:

Given formula:

\(h=\dfrac{d}{3}+2\)

Subtract 2 from both sides:

\(\implies h-2=\dfrac{d}{3}+2-2\)

\(\implies h-2=\dfrac{d}{3}\)

Multiply both sides by 3:

\(\implies (h-2) \times 3=\dfrac{d}{3} \times 3\)

\(\implies 3(h-2)=d\)

Apply the distributive law  \(a(b-c)=ab-ac\)

\(\implies 3h-6=d\)

\(\implies d=3h-6\)

Answer:

\(d=3h-6\)

Step-by-step explanation:

\(h=\frac{d}{3}+2\)

\(h-2=\frac{d}{3}+2\)

                 -\(2\)

\(h-2=\frac{d}{3}\)

\((h-2)*3=\frac{d}{3}*3\)

\(3(h-2)=d\)

\(3h-6=d\)

\(d=3h-6\)

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The actual distance represented by 23.7 cm on the map is 355.5 km.

To find the ratio of the amount of money Mabaso has to the amount of money Thabo has and the amount of money Ally has, we can divide each amount by the smallest amount (which is R35) to simplify the ratio.

Mabaso has R140, Thabo has R70, and Ally has R35.

The ratio of Mabaso's money to Thabo's money is:

R140 ÷ R35 = 4

The ratio of Mabaso's money to Ally's money is:

R140 ÷ R35 = 4

Therefore, the ratio of the amount of money Mabaso has to the amount of money Thabo has and to the amount of money Ally has is 4:1:1.

To calculate the percentage discount of a steel table, we need to find the difference between the original price and the discounted price, and then divide it by the original price. Finally, we multiply the result by 100 to get the percentage.

Original price: R750

Discounted price: R600

Discount: R750 - R600 = R150

Percentage discount: (R150 ÷ R750) × 100 = 20%

So, the table has a 20% discount on Black Friday.

To convert 125 grams to kilograms, we divide the amount in grams by 1,000 (since there are 1,000 grams in a kilogram).

125 g ÷ 1,000 = 0.125 kg

Therefore, 125 grams is equal to 0.125 kilograms.

If a green grocer packs 12 apples in a plastic bag and has 285 apples, we divide the total number of apples by the number of apples per bag to determine the number of bags needed.

Number of bags needed: 285 apples ÷ 12 apples/bag = 23.75 bags

Since we can't have a fraction of a bag, we round up to the nearest whole number. Therefore, the green grocer would need 24 bags.

If the scale of a map is 1,500,000 and the measurement on the map is 23.7 cm, we can use the scale to determine the actual distance.

1 cm on the map represents 1,500,000 cm in reality.

23.7 cm on the map represents x cm in reality.

x = 23.7 cm × 1,500,000 cm = 35,550,000 cm

To convert cm to km, we divide by 100,000 (since there are 100,000 cm in a kilometer).

35,550,000 cm ÷ 100,000 = 355.5 km

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Answer:

The maximum profit the florist will earn from selling celebration bouquets is $725.

The florist will break-even after one-dollar decreases when her profit is zero. From the graph, this occurs at x = 10. So the florist will break-even after 10 one-dollar decreases.

The interval of the number of one-dollar decreases for which the florist makes a profit from celebration bouquets is (0, 10). This is because the profit is positive for values of x between 0 and 10, and becomes negative after 10.

Step-by-step explanation:

The mean absolute deviation of Robin's scores is 5.2.

The mean absolute deviation (MAD) is the mean (average) distance between each data value and the mean of the data set.

To determine the MAD, we subtract the mean of the data set from each data value and sum the absolute values obtained.

Then we divide the sum of the absolute values by the number of the data values to determine the mean absolute deviation.

Robin's Scores   Distance from the Mean

99                              8

108                             1

102                             5

107                             0

119                             12

Sum =                      26

Number of Data Values = 5

The mean = 107 since 107 - 107 = 0

Mean Absolute Deviation (MAD) = 26/5 = 5.2

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