Find the area of the rectangle, the side lengths are (z+9)(3z+8).

Answer:

18-cup jug of water for $3.78

Step-by-step explanation:

3-gallon jug of water for $16.80

3 gallon = 48 cups

16.80 / 48 = $0.35 per cup

18-cup jug of water for $3.78

3.78 / 18 = $0.21 per cup

So, 18-cup jug of water for $3.78 is a better buy.

If you have previous taxable wages of $102,000 and your current taxable wages are $1,100, your Social Security tax would be $6,324 for the previous wages and $68.20 for the current wages.

To calculate the Social Security tax, we need to know the tax rate for Social Security and the taxable wages. Let's assume the Social Security tax rate is 6.2% for both the employee and the employer.

Given that your taxable wages for Social Security purposes are $1,100, and your previous taxable wages are $102,000, we can determine the Social Security tax amount.

First, we need to calculate the Social Security tax on the previous taxable wages of $102,000. Multiply $102,000 by 6.2% (0.062) to find the Social Security tax for that amount:

Social Security tax = $102,000 x 0.062 = $6,324

Next, we calculate the Social Security tax on the current taxable wages of $1,100. Multiply $1,100 by 6.2% to find the tax amount:

Social Security tax = $1,100 x 0.062 = $68.20

Therefore, if you have previous taxable wages of $102,000 and your current taxable wages are $1,100, your Social Security tax would be $6,324 for the previous wages and $68.20 for the current wages.

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Answer:

a

  The null hypothesis is  

         \(H_o : \mu = 21\)

The Alternative  hypothesis is  

           \(H_a : \mu< 21\)

b

     \(\sigma_{\= x} = 0.8944\)

c

   \(t = -2.236\)

d

  Yes the  mean population is  significantly less than 21.

Step-by-step explanation:

From the question we are given

           a set of  data  

                               20  18  17  22  18

       The confidence level is 90%

       The  sample  size  is  n =  5  

Generally the mean of the sample  is  mathematically evaluated as

        \(\= x = \frac{20 + 18 + 17 + 22 + 18}{5}\)

       \(\= x = 19\)

The standard deviation is evaluated as

        \(\sigma = \sqrt{ \frac{\sum (x_i - \= x)^2}{n} }\)

         \(\sigma = \sqrt{ \frac{ ( 20- 19 )^2 + ( 18- 19 )^2 +( 17- 19 )^2 +( 22- 19 )^2 +( 18- 19 )^2 }{5} }\)

         \(\sigma = 2\)

Now the confidence level is given as  90 %  hence the level of significance can be evaluated as

         \(\alpha = 100 - 90\)

        \(\alpha = 10\)%

         \(\alpha =0.10\)

Now the null hypothesis is  

         \(H_o : \mu = 21\)

the Alternative  hypothesis is  

           \(H_a : \mu< 21\)

The  standard error of mean is mathematically evaluated as

         \(\sigma_{\= x} = \frac{\sigma}{ \sqrt{n} }\)

substituting values

         \(\sigma_{\= x} = \frac{2}{ \sqrt{5 } }\)

        \(\sigma_{\= x} = 0.8944\)

The test statistic is  evaluated as  

              \(t = \frac{\= x - \mu }{ \frac{\sigma }{\sqrt{n} } }\)

substituting values

              \(t = \frac{ 19 - 21 }{ 0.8944 }\)

              \(t = -2.236\)

The  critical value of the level of significance is  obtained from the critical value table for z values as  

                   \(z_{0.10} = 1.28\)

Looking at the obtained value we see that \(z_{0.10}\) is greater than the test statistics value so the null hypothesis is rejected

Answer:

y=3/4

Step-by-step explanation:

4x/3 = x/y

or, 1/y= 4/3

or, y=3/4

Answer:

y = \(\frac{3}{4}\)

Step-by-step explanation:

Express the ratios in fractional form

\(\frac{x}{y}\) = \(\frac{4x}{3}\) ( cross- multiply )

4xy = 3x ( divide both sides by 4x )

y = \(\frac{3x}{4x}\) = \(\frac{3}{4}\)

Answer:

I think it is -12

Multiply -0.75 (3 quarters) by 16.

The negative cancels out the positive number.

Since the exponent is not saying multiply the number by itself a number of times, we could make a hypothesis that this is just multiplication.

Normally, this ↑ is not the case, but here, I could make an exception.

I hope this helps you, let me know if you need something else.

Answer:

12 i think

Step-by-step explanation:

Answer:

I need help with this!!!!!

Step-by-step explanation:

The other person said 12 but how what if its not. ?

Linear equations are represented by straight line.

The required graph is graph (a).

The given parameters are:

\(\mathbf{Rate =15}\)

Let x represents the number of weeks, and y represents the number of words in week x.

So, we have:

\(\mathbf{y = Rate \times x}\)

Substitute 15 for Rate

\(\mathbf{y = 15\times x}\)

\(\mathbf{y = 15x}\)

The above equation means that:

\(\mathbf{(x,y) = (0,0)(1,15),(2,30)....}\)

The graph that represents the above ordered pair is graph (a).

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Answer:

im lost

Step-by-step explanation:

;;..

To find the domain and range of a function f(x), we need to consider the values that x can take and the corresponding values of f(x).

The domain of a function is the set of all possible input values, or x-values, for which the function is defined. In other words, it is the set of values that x can take without resulting in an undefined output. Typically, the domain is specified by any restrictions on the input, such as square roots, fractions, logarithms, or division by zero.

The range of a function is the set of all possible output values, or y-values, that the function can produce. In other words, it is the set of values that f(x) can take on, as x varies over the domain.

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Given question is incomplete. Subject may be asking: Write the domain and range of function f(x).

The perimeter and the area of rectangle EFGH are 24 cm and 35 square cm

From the question, we have the following parameters that can be used in our computation:

Side length, AB = 5 cm

Extension AE=AH=FC=GC = 2cm

Using the above as a guide, we have the following:

Dimension of the rectangle = 5 cm By (5 + 2) cm

So, we have

Dimension of the rectangle = 5 cm By 7 cm

The perimeter is then calculated as

P = 2 * (5 + 7) = 24 cm

The area is calculated as

A = 5 * 7 = 35 square cm

Hence, the perimeter and the area of rectangle EFGH are 24 cm and 35 square cm

See attachment for figure

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Answer:

sweefe

Step-by-step explanation:

EFEFEEa

Answer:

The question has some missing details such as ; Use cylindrical shells to find the volume of the remaining solid if the remaining solid is 8cm high. I have however solved it using the value of 8cm, you can use the same approach to solve for the volume irrespective of the value of the height you are given.

Step-by-step explanation:

The detailed step by step analysis and appropriate Integration by susbtitution in order to get the volume of the remaining solid is as shown in the attached file.

Answer:

126

Step-by-step explanation:

\(V = A * h = \frac{1}{4} * \pi * d^{2} * h = A * h = \frac{1}{4} * 3.14 * 36 * 5 = 141.3\\ \\V_{empty} = A * h = \frac{1}{4} * \pi * d^{2} * h = \frac{1}{4} * \pi * 4 * 5 = 15.7\)

\(V_{full} = V - V_{empty} = 141.3 - 15.7 = 125.6 \approx 126\)

The value of measure of x in the triangle is,

⇒ x = 4√3 units

We have to given that,

A triangle is shown in image.

Now, WE can formulate by trigonometry formula we get;

⇒ tan 30° = Opposite / Base

⇒ tan 30° = 4 / x

⇒ 1/√3 = 4/x

⇒ x = 4√3 units

Thus, The value of measure of x in the triangle is,

⇒ x = 4√3 units

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First, it is important to know the prices of each of the instruments in order to determine the number of djembe drums you had sold. Since it is not given here. I will give a general equation where you just substitute the prices. It would be as follows:

326 = 12x + 6(y) + (xx)z

where x is the price for a set of maracas

           y is the price for a set of claves

          xx is number of djembe drums sold

          z is the prices for each djembe drum

Hope this helps. Have a nice da

Answer:

(14*12)+(5*6)+16x

Step-by-step explanation:

First, you get the price of every instrument.

(Shown in the picture)

Maracas: $14

Claves: $5

Djembe Drums: $16

Then multiply the price to how many instruments you sold.

14*12 (Maracas)

5*6 (Claves)

You don't know what how many djembe drums you sold, so put an x right next to 16.

To get the total of $326 in that equation, you do: (14*12)+(5*6)+16x.

I hope it helps.

Answer:

Not perpendicular and not parallel.

Step-by-step explanation:

The equations are not perpendicular because the slopes of the two lines are not negative reciprocals.

The equations are not parallel because the slopes of the two lines are not equal.

Answer:

150

Step-by-step explanation:

Answer:

Hope it helps you with something.

Step-by-step explanation:

The slope of the secant line PQ passing through points P(4, 28) and Q(x, x² + x + 8) can be found using the formula:

slope of PQ = (change in y) / (change in x) = [(y₂ - y₁) / (x₂ - x₁)]

where (x₁, y₁) = (4, 28) and (x₂, y₂) = (x, x² + x + 8).

Substituting the values, we get:

slope of PQ = [(x² + x + 8 - 28) / (x - 4)]

simplifying, we get:

slope of PQ = [(x² + x - 20) / (x - 4)]

Now, we can find the slope of PQ for different values of x:

When x = 2:

slope of PQ = [(2² + 2 - 20) / (2 - 4)] = [(-14) / (-2)] = 7

Therefore, the slope of PQ when x = 2 is 7.

When x = 3:

slope of PQ = [(3² + 3 - 20) / (3 - 4)] = [(-14) / (-1)] = 14

Therefore, the slope of PQ when x = 3 is 14.

Hence, the slope of the secant line PQ for x = 2 is 7, and for x = 3 is 14.

Answer: -12x4y4 (option 3)

Step-by-step explanation:

The graph's function g(x) has a single x-intercept, a y intercept, a vertical asymptote, an oblique asymptote, and both.

Asymptotes are points along a line that a curve approaches but never touches. The term "asymptote" refers to the point at which a function's graph converges. Asymptotes are often not necessary when graphing functions.

There are three distinct asymptotes.

Asymptote horizontal (HA) - Given that it is horizontal, its equation has the form y = k. The horizontal asymptote is the point at which the function f(x) tends to zero.

As it is a vertical line, the vertical asymptote's equation has the form x = k. When the denominator of a rational function approaches towards 0, vertical asymptotes are defined.

The equation for the slanting asymptote (also known as the oblique asymptote) is y = mx + b since the line is inclined.

given the information,

Let's write the function as g. (x)

The value of g (x) is right now.

g (x) = ( -4x² + 36) / (x + 3)

We gain by simple.

g (x) = -4x² - 4×9) / (x + 3)

We gain more after additional simplification.

g (x) = -4 (x + 3) (x - 3) / (x + 3)

g (x) = -4x + 12

There is now a vertical asymptote for the function at (0, 12)

There is a horizontal asymptote for the function at (3, 0)

The function is so resolved.

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The complete question is:

G(x)=-4x^2+36/x+3

What key features does f(x), shown in the graph, share

with g(x), shown in the equation? Select three options.

at least one x-intercept

at least one y-intercept

Dan oblique asymptote

O a vertical asymptote

the domain of x

Answer:

Step-by-step explanation:

Answer:

dat easy

Step-by-step explanation:

Let's say John drove 2 miles. He had to pay the base fee of $18.99 and $.75(2) = $1.50, so he paid $20.49 total.

We are given his total, though, and asked to find the mileage.

18.99 + .75m = 199.74

-18.99 -18.99

.75m = 180.75

.75 .75

m = 241

So, John drove 241 miles.

Hope this helps!

I

The measure of the angle A is 70 degrees if the DR is the tangent to the circle option (A) 70 degrees is correct.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

It is given that:

Join the points B and O and then join points D and O

Angle A = (1/2)Angle BOD

Angle B = 140 degrees

Angle A = (1/2)140 degrees

Angle A = 70 degrees

Thus, the measure of the angle A is 70 degrees if the DR is the tangent to the circle option (A) 70 degrees is correct.

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A statistical question that can result in numerical data is How many times did you go swimming this year? So, the correct option is A).

The statistical question that can result in numerical data is "How many hours this week did you spend on homework?" and "How many times did you go swimming this year?".

These questions involve counting or measuring quantities, which can be represented using numerical data. The other two questions do not involve numerical data and therefore cannot be considered statistical questions that result in numerical data. So, the correct answer is B).

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Answer:

How many pink erasers do the students in your class have?

Answer:

He saved 12.2 dollars

Step-by-step explanation:

Answer:

William saved $12.20

Step-by-step explanation:

Its easy if you know mental math!

Answer:

\((\frac{1}{2}+\frac{\sqrt{3}}{2}i)^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Step-by-step explanation:

Convert 1/2 + i√3/2 to rectangular form

\(\displaystyle z=a+bi=\frac{1}{2}+\frac{\sqrt{3}}{2}i\\\\r=\sqrt{a^2+b^2}=\sqrt{\biggr(\frac{1}{2}\biggr)^2+\biggr(\frac{\sqrt{3}}{2}\biggr)^2}=\sqrt{\frac{1}{4}+\frac{3}{4}}=\sqrt{1}=1\\\\\theta=\tan^{-1}\biggr(\frac{b}{a}\biggr)=\tan^{-1}\biggr(\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\biggr)=\tan^{-1}(\sqrt{3})=\frac{\pi}{3}\\\\z=\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\)

Use DeMoivre's Theorem

\(\displaystyle z^n=r^n(\cos(n\theta)+i\sin(n\theta))\\\\z^5=1^5\biggr(\cos\biggr(\frac{5\pi}{3}\biggr)+i\sin\biggr(\frac{5\pi}{3}\biggr)\biggr)\\\\z^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Answer:

2

Step-by-step explanation:

good right solve and rate my answer

The probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing is 8/25 or 0.32 (rounded to the nearest millionth).

1. Calculate the total number of students on the Student Government Board by summing up the numbers in the table:

  Total Students = 2 + 2 + 2 + 4 + 0 + 3 + 4 + 2 = 19

2. Calculate the total number of graduate students on the Student Government Board:

  Total Graduate Students = 2 + 0 = 2

3. Calculate the total number of students living in on-campus housing:

  Total On-Campus Housing = 2 + 2 + 0 + 4 + 2 = 10

4. Calculate the probability of selecting a graduate student from the Student Government Board by dividing the total number of graduate students by the total number of students:

  Probability of Graduate Student = Total Graduate Students / Total Students = 2 / 19

5. Calculate the probability of selecting a student living in on-campus housing by dividing the total number of students in on-campus housing by the total number of students:

  Probability of On-Campus Housing = Total On-Campus Housing / Total Students = 10 / 19

6. Calculate the probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing by summing up the probabilities from steps 4 and 5:

  Probability = Probability of Graduate Student + Probability of On-Campus Housing = 2 / 19 + 10 / 19

7. Simplify the fraction if necessary. In this case, the fraction cannot be simplified further, so the final probability is 2 / 19 + 10 / 19 = 12 / 19.

8. Convert the fraction to a decimal by dividing the numerator by the denominator: 12 / 19 ≈ 0.631578947, which rounds to 0.632 (rounded to the nearest thousandth).

9. Finally, express the probability as a fraction in lowest terms: 12 / 19 is already in lowest terms.

Therefore, the probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing is 12/19 or approximately 0.632 (rounded to the nearest thousandth).

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The percentage of the red roses did Fancy Flowers Florist use to decorate for the grand opening at the museum is 80%

A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction.

Given that, a flower shop received a shipment of 250 red roses, they will use 200 out of this for decorating for the grand opening of the Historical Museum,

We need to find the percentage of the red roses used there,

So, the percentage of the red roses used in decoration =

200 / 250 x 100

= 0.8 x 100

= 80%

Hence. the percentage of the red roses did Fancy Flowers Florist use to decorate for the grand opening at the museum is 80%

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Answer:

Step-by-step explanation:

Answer:

x or 1x.

Step-by-step explanation:

The rate of change is slope.

Slope=m

y=mx+b

y=x+5

x is the same thing as 1x. So...