A sample of size n=10n=10 is drawn from a population. The data is shown below.

138.8

116.4

97

114.2

138.8

100.4

128.8

138.8

101.9

117.6



What is the range of this data set?

range =

What is the standard deviation of this data set? (Remember, it is a sample.) Please report the answer with appropriate rounding, rounding to two more decimal places than the original data. Please, please, please do not calculate the value by hand.

stdev =

Answer:

the answer is 90

Step-by-step explanation:

296-96=90

Answer:

8,000-24x

Step-by-step explanation:

Let

y ----> depreciated value of the car

x---> rate of depreciation

t ----> the time in months

we know that

The linear equation that represent this situation is

y=8,000-xt

For

t=2 years=2*12=24 months

substitute

y=8,,000-x(24)

y=8,000-24x

To find the number of people who did not like any of the three flavors, we need to subtract the number of people who liked at least one flavor from the total number of people.

To find the number of people who did not like any of the three flavors, we need to subtract the number of people who liked at least one flavor from the total number of people.

From the given information, we can create a Venn diagram to represent the preferences:

Picking it up from the explanation above, it becomes clear that 10 people liked both vanilla and strawberry, 10 people liked both strawberry and chocolate, and 15 people liked both vanilla and chocolate. We also know that 5 people liked all three flavors. Using this information, we can determine the number of people who liked at least one flavor by adding up the numbers in the overlapping circles: 10 + 10 + 15 + 5 = 40 people.

To find the number of people who did not like any of the three flavors, we subtract 40 from the total number of people who responded to the survey: 100 - 40 = 60 people.

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To find out how many people did not like any of the three flavors, we use the principle of inclusion-exclusion, resulting in 5 people who did not like vanilla, chocolate, or strawberry.

The student has asked a question related to combinations without repetition and the interpretation of survey results. To determine how many people did not like any of the three flavors (vanilla, chocolate, strawberry), we can use the principle of inclusion-exclusion. Here are the steps to solve this:

Therefore, 5 people did not like any of the three flavors.

Answer: Our required probability is 47.3%.

Step-by-step explanation:

Since we have given that

Probability of schools or district in a country use digital content = 86% = 0.86

Probability of schools or district uses digital content as a part of their curriculum out of 86% = [tex]\dfrac{11}{20}[/tex]

So, Probability that a selected school or district uses digital content and uses it as a part of their curriculum is given by

[tex]\dfrac{86}{100}\times \dfrac{11}{20}\\\\=0.86\times 0.55\\\\=0.473\\\\=47.3\%[/tex]

Hence, our required probability is 47.3%.

The probability that a randomly selected school or district uses digital content and uses it as part of their curriculum is 47.3% and this can be determined by using the given data.

Given :

The probability that a randomly selected school or district uses digital content and uses it as part of their curriculum is given by:

[tex]=\dfrac{11}{20}\times \dfrac{86}{100}[/tex]

Now, multiply 11 by 86 and also multiply 20 by 100 in the above expression.

[tex]=\dfrac{11\times 86}{20\times 100}[/tex]

SImplify the above expression.

[tex]=\dfrac{946}{2000}[/tex]

= 0.473

So, the probability that a randomly selected school or district uses digital content and uses it as part of their curriculum is 47.3%.

For more information, refer to the link given below:

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Answer: 0.8021

Step-by-step explanation:

The given problem is a binomial distribution problem, where

[tex]n=14,\ p=0.2, q=1-0.2=0.8[/tex]

The formula of binomial distribution is :-

[tex]P(X=r)=^{n}C_{r}p^{r}q^{n-r}[/tex]

The probability that the lot will fail inspection is given by :_

[tex]P(X\geq2)=1-(P(X\leq1))\\\\=1-(P(0)+P(1))\\\\[/tex]

[tex]=1-(^{14}C_{0}(0.2)^{0}(0.8)^{14-0}+^{14}C_{1}(0.2)^{1}(0.8)^{14-1})\\\\=1-((1)(0.8)^{14}+(14)(0.2)(0.8)^{13})\\\\=0.802087907\approx0.8021[/tex]

Hence, the required probability = 0.4365

Final answer:

Lester Hollar can assess the impact of the fitness program on absenteeism by conducting a paired samples t-test at a 0.05 significance level. If the p-value is less than 0.05, the program effectively reduced absences; otherwise, there is insufficient evidence to conclude its effectiveness.

Explanation:

Evaluating the Exercise Program’s Impact on Employee Absenteeism

Lester Hollar wishes to assess if the company’s fitness program led to a decline in employee absences. With a sample of eight participants, he analyzed absenteeism before and after the program’s implementation. To determine if absences have decreased, a hypothesis test at the 0.05 significance level (alpha) is conducted.

To evaluate the change in absences, two sets of absenteeism data are compared using a statistical test, such as the paired samples t-test. This test examines if the mean difference in absences before and after the program is statistically significant. If the p-value obtained from the test is less than the significance level of 0.05, the null hypothesis (no change in absences) would be rejected, suggesting that the exercise program was effective in reducing absences.

If Lester Hollar finds a p-value greater than 0.05, he would not reject the null hypothesis, indicating that there isn’t sufficient evidence to conclude the program's impact. It’s also important to estimate the p-value precisely as it gives a measure of the strength of evidence against the null hypothesis. However, without the specific data, we cannot calculate the p-value or make a definitive conclusion here.

Answer:

The area under the standard normal curve to the left of z=−2.94 and to the right of z=−2.28 is 0.9903 square units.

Step-by-step explanation:

We need to find the area under the standard normal curve to the left of z=−2.94 and to the right of z=−2.28.

The standard normal table represents the area under the curve.

[tex]P(z<-2.94)\cup P(z>-2.28)=P(z<-2.94)+P(z>-2.28)[/tex]          .....(1)

According to the standard normal table, we get

[tex]P(z<-2.94)=0.0016[/tex]

[tex]P(z>-2.28)=1-P(z<-2.28)=1-0.0113=0.9887[/tex]

Substitute these values in equation (1).

[tex]P(z<-2.94)\cup P(z>-2.28)=0.0016+0.98807=0.9903[/tex]

Therefore the area under the standard normal curve to the left of z=−2.94 and to the right of z=−2.28 is 0.9903 square units.

The area under the standard normal curve to the left of z  = −2.94 and to the right of z = −2.28 is 0.9903 square units.

It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.

The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.

The area under the standard normal curve to the left of z = −2.94 and to the right of z = −2.28 will be

The standard normal table represents the area under the curve.

[tex]\rm P(z < -2.94) \cap P(z > -2.28) = P(z < -2.94) + P(z > -2.28)[/tex] ...1

According to the standard normal table, we have

[tex]\rm P(z < -2.94) = 0.0016\\\\P(z > -2.94) = 1- P(z < -2.94) = 1-0.0113 = 0.9887[/tex]

Substitute these values in equation 1, we have

[tex]\rm P(z < -2.94) \cap P(z > -2.28) = 0.0016 + 0.9887 = 0.9903[/tex]

More about the normal distribution link is given below.

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ANSWER

[tex]80 {ms}^{ - 1} [/tex]

EXPLANATION

The average velocity of the ball is the rateof displacement over the total time.

The height of the ball, in feet, after t seconds is given by the function:

[tex]f(t)=-16t^2+192t[/tex]

At time t=1, the height of the ball is

[tex]f(1)=-16(1)^2+192(1)[/tex]

[tex]f(1)=-16+192 = 176ft[/tex]

At time t=6, the height of the ball is

[tex]f(6)=-16(6)^2+192(6)[/tex]

[tex]f(6)=-16(36)+192(6)[/tex]

[tex]f(6)=-576+1152 = 576[/tex]

The average velocity

[tex] = \frac{f(6) - f(1)}{6 - 1} [/tex]

[tex]= \frac{576- 176}{6 - 1} [/tex]

[tex]= \frac{400}{5} [/tex]

[tex] = 80 {ms}^{ - 1} [/tex]

Answer:

3rd option: 60 degrees

Step-by-step explanation:

We can see in the diagram that the angle on C is a supplementary angle, which means that the sum of 135 and internal angle will be equal to 180 degrees.

Let x be the internal angle,

Then

x+135 = 180

x = 180-135

x = 45 degrees

So now we know that two interior angles of the triangle.

Also we know that sum of all internal angles of triangle is 180 degrees.

Using the same postulate:

A+B+C = 180

75 + B + 45 = 180

120+B = 180

B = 180 - 120

B = 60 degrees

So,

third option is the correct answer ..

Answer:

It’s 120 I got it right on the test !

Answer:

Part 1) [tex]y=80,000(1.035)^{x}[/tex]

Part 2) The table in the attached figure

Part 3) The graph in the attached figure

Step-by-step explanation:

Part 1) Find the population function

In this problem we have a exponential function of the form

[tex]y=a(b)^{x}[/tex]

where

y ----> is the population

x ----> the time in years

a is the initial value (a=80,000 people)

b is the base (b=100%+3.5%=103.5%=1.035)

substitute

[tex]y=80,000(1.035)^{x}[/tex]  

Part 2) Construct the table

For x=0 years  

substitute in the function equation

[tex]y=80,000(1.035)^{0}=80,000\ people[/tex]  

For x=10 years

substitute in the function equation

[tex]y=80,000(1.035)^{10}=112.848\ people[/tex]

For x=20 years

substitute in the function equation

[tex]y=80,000(1.035)^{20}=159,183\ people[/tex]

For x=40 years

substitute in the function equation

[tex]y=80,000(1.035)^{40}=316,741\ people[/tex]

For x=50 years

substitute in the function equation

[tex]y=80,000(1.035)^{50}=446,794\ people[/tex]

For x=75 years

substitute in the function equation

[tex]y=80,000(1.035)^{75}=1,055,884\ people[/tex]

For x=100 years  

substitute in the function equation

[tex]y=80,000(1.035)^{100}=2,495,313\ people[/tex]

Part 3) The graph in the attached figure  

Answer:

First type of fruit drinks: 48 pints

Second type of fruit drinks: 32 pints

Step-by-step explanation:

Let's call A the amount of first type of fruit drinks. 55% pure fruit juice

Let's call B the amount of second type of fruit drinks. 80% pure fruit juice

The resulting mixture should have 65% pure fruit juice and 80 pints.

Then we know that the total amount of mixture will be:

[tex]A + B = 80[/tex]

Then the total amount of pure fruit juice in the mixture will be:

[tex]0.55A + 0.8B = 0.65 * 80[/tex]

[tex]0.55A + 0.8B = 52[/tex]

Then we have two equations and two unknowns so we solve the system of equations. Multiply the first equation by -0.8 and add it to the second equation:

[tex]-0.8A -0.8B = -0.8*80[/tex]

[tex]-0.8A -0.8B = -64[/tex]

[tex]-0.8A -0.8B = -64[/tex]

               +

[tex]0.55A + 0.8B = 52[/tex]

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

[tex]-0.25A = -12[/tex]

[tex]A = \frac{-12}{-0.25}[/tex]

[tex]A = 48\ pints[/tex]

We substitute the value of A into one of the two equations and solve for B.

[tex]48 + B = 80[/tex]

[tex]B = 32\ pints[/tex]

To create an 80-pint batch of 65% pure fruit juice, the Royal Fruit Company needs to solve two equations representing the volume and percent mixture of the two juices. These equations can be solved simultaneously to find the required volumes of each juice.

The subject of this question falls under Mathematics, particularly dealing with proportions and algebra. Given that the first type of juice is 55% pure fruit and the second type is 80% pure fruit, we can define our variables: let's denote X as the volume of the first type of drink and Y as the volume of the second one. We know that the total volume is 80 pints, so we have our first equation: X + Y = 80. The second equation derives from the percentage of fruit juice: 0.55X + 0.80Y = 0.65*80.

Now we can solve these two equations to find the volumes of X and Y. The solution to these equations will provide us with the volume needed from each of the two types of juice to achieve a 65% pure fruit juice drink.

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Answer:

a) 43

b) 5.7

c) 2.54

Step-by-step explanation:

The metric system is so easy to work with, everything is in base of 10, and all measures use a prefix. Here, we're talking about length, with the main measure being the meter.

1 m = 100 centimeters (centi- = 1/100)

1 m = 1000 millimeters (milli- = 1/1000)

So, for each centimeter, you have 10 millimeters.

a) How many millimeters are in 4.3 centimeters?

1 cm = 10 mm as shown above, so 4.3 cm = 43 mm

b) How many centimeters are in 57 millimeters?

10 mm = 1 cm so, 57 mm = 5.7 cm

c) Approximately how many centimeters are in an inch?

There are approximately 2.54 cm in an inch.  No real calculation to make here, it's just a unit conversion between systems, done following a known reference table.

Answer: 478

Step-by-step explanation:

The formula to calculate the standard error of the population mean is given by :-

[tex]S.E.=\dfrac{\sigma}{\sqrt{n}}[/tex], where [tex]\sigma[/tex] is the standard deviation and 'n' is the sample size.

Given: Mean : [tex]\mu=$\50,000[/tex]

Standard deviation : [tex]\sigma= $\4,000[/tex]

Sample size : [tex]n=70[/tex]

Now, the value of the standard error of the average annual salary is given by :-

[tex]S.E.=\dfrac{50000}{\sqrt{70}}=478.091443734\approx478[/tex]

Hence, the standard error of the average annual salary = 478

The value of the standard error of the average annual salary is calculated using the formula SE = population standard deviation / [tex]\sqrt{sample size}[/tex] ,which for a population standard deviation of $4,000 and a sample size of 70 employees, comes out to approximately $478.

To calculate the standard error of the average annual salary, you'd use the formula for the standard error of the mean when you know the population standard deviation: SE = σ /[tex]\sqrt{n}[/tex], where σ is the population standard deviation and n is the sample size.

In this case, the population standard deviation σ is $4,000, and the sample size n is 70 employees. Using the formula, we get SE = 4000 / [tex]\sqrt{70}[/tex], which will give us the standard error of the average annual salary.

Performing the calculation: SE = 4000 / [tex]\sqrt{70}[/tex] ≈ 4000 / 8.367 = 478.29, which when rounded to the nearest integer is $478. Therefore, the value of the standard error of the average annual salary is approximately $478.

Answer:

G.P. is, 450, 360, 288, 230.4,......

The sum is 2250.

Step-by-step explanation:

Given,

The first total spending in the resort city = $ 450 million,

Also, 80% of that revenue is again spent in the resort city, and of that amount approximately 80% is again spent in the same city, and so on.

Thus, there is a G.P. that represents the given situation,

450, 360, 288, 230.4,......

Which is an infinite geometric series having first term, a = 450,

Common ratio, r = 0.8,

Hence, the sum of the series,

[tex]S_n=\frac{a}{1-r}[/tex]

[tex]=\frac{450}{1-0.8}[/tex]

[tex]=\frac{450}{0.2}[/tex]

[tex]=2250[/tex]

Answer:

A. H(x) is an inverse of F(x)

Step-by-step explanation:

The given functions are:

[tex]F(x)=\sqrt{x-2}[/tex]

[tex]G(x)=(x-2)^2[/tex]

[tex]H(x)=x^2+2[/tex]

We compose F(x) and G(x) to get:

[tex](F\circ G)(x)=F(G(x))[/tex]

[tex](F\circ G)(x)=F((x-2)^2)[/tex]

[tex](F\circ G)(x)=\sqrt{(x-2)^2-2}[/tex]

[tex](F\circ G)(x)=\sqrt{x^2-4x+4-2}[/tex]

[tex](F\circ G)(x)=\sqrt{x^2-4x+2}[/tex]

[tex](F\circ G)(x)\ne x[/tex]

Hence G(x) is not an inverse of F(x).

We now compose H(x) and G(x).

[tex](F\circ H)(x)=F(H(x))[/tex]

[tex](F\circ H)(x)=F(x^2+2)[/tex]

[tex](F\circ H)(x)=\sqrt{x^2+2-2}[/tex]

We simplify to get:

[tex](F\circ H)(x)=\sqrt{x^2}[/tex]

[tex](F\circ H)(x)=x[/tex]

Since [tex](F\circ H)(x)=x[/tex], H(x) is an inverse of F(x)

Answer:

The area of this composite figure is [tex]64\ cm^{2}[/tex]

Step-by-step explanation:

we know that

If the composite figure is divided into two congruent trapezoids, then the area of the composite figure is equal to the area of one trapezoid multiplied by two

so

The area of the composite figure is

[tex]A=2[\frac{1}{2}(b1+b2)h][/tex]

[tex]A=(b1+b2)h[/tex]

substitute the values

[tex]A=(6+10)4[/tex]

[tex]A=64\ cm^{2}[/tex]

Answer:

64cm

Step-by-step explanation:

I looked at the guy's answer on top of mine and it was correct, go thank him!

Answer:

After how many years is the fish population 100?

x=3.97 years

Step-by-step explanation:

The fish population increases by a factor of 1.5 each year. We have the equation that represents this situation

[tex]f (x) = 20 (1.5) ^ x[/tex]

Where x represents the number of years elapsed f(x) represents the amount of fish.

Given this situation, the following question could be posed

After how many years is the fish population 100?

So we do [tex]f (x) = 100[/tex] and solve for the variable x

[tex]100 = 20 (1.5) ^ x\\\\\frac{100}{20} = (1.5)^x\\\\ 5= (1.5)^x\\\\log_{1.5}(5) = log_{1.5}(1.5)^x\\\\log_{1.5}(5) = x\\\\x =log_{1.5}(5)\\\\x=3.97\ years[/tex]

Observe the solution in the attached graph

Final answer:

To find the probability of the mean weight of 25 randomly selected ice cream cartons being greater than 20.06 ounces, we can use the Central Limit Theorem. By calculating the standard error, finding the z-score, and using a z-table or calculator, we can determine the probability.

Explanation:

To find the probability that the mean weight of 25 randomly selected ice cream cartons is greater than 20.06 ounces, we can use the Central Limit Theorem. According to the Central Limit Theorem, the distribution of sample means from a population with any distribution will be approximately normal, as long as the sample size is large enough.

First, we need to find the standard error of the mean (SE). The formula for SE is SE = standard deviation / √(sample size). In this case, the standard deviation is 0.3 ounces and the sample size is 25. So, SE = 0.3 / √25 = 0.06 ounces.

Next, we calculate the z-score, which measures how many standard deviations the mean is from the population mean. The formula for z-score is z = (sample mean - population mean) / standard error. In this case, the sample mean is 20.06 ounces, the population mean is 20.1 ounces, and the standard error is 0.06 ounces. So, z = (20.06 - 20.1) / 0.06 = -0.67.

We can use a z-table or a calculator to find the probability associated with the z-score. From the table or calculator, we find that the probability of getting a z-score greater than -0.67 is approximately 0.748. Therefore, the probability that the mean weight of the 25 ice cream cartons is greater than 20.06 ounces is approximately 0.748.

Answer:

F or G = {7,8,9,10,11,12,13,14}

n(F or G) = 8

n(S) = 12

By counting the no. of outcome

P(F or G) = n(F or G) / n(S)

P(F or G) = 8 /12

P(F or G) = 2/3

By using the general addition rule

P(F or G) = P(F) + P(G) - P(F and G)

= 6/12 + 4/12 - 2/12

= 2/3

Answer:

The area under the curve y=f(x) on [a,b] is [tex]\frac{1}{6}\ln(2)[/tex] square units.

Step-by-step explanation:

The given function is

[tex]f(x)=\tan(3x)[/tex]

where a=0 and b=pi/12.

The area under the curve y=f(x) on [a,b] is defined as

[tex]Area=\int_{a}^{b}f(x)dx[/tex]

[tex]Area=\int_{0}^{\frac{\pi}{12}}\tan (3x)dx[/tex]

[tex]Area=\int_{0}^{\frac{\pi}{12}}\frac{\sin (3x)}{\cos (3x)}dx[/tex]

Substitute cos (3x)=t, so

[tex]-3\sin (3x)dx=dt[/tex]

[tex]\sin (3x)dx=-\frac{1}{3}dt[/tex]

[tex]a=\cos (3(0))=1[/tex]

[tex]b=\cos (3(\frac{\pi}{12}))=\frac{1}{\sqrt{2}}[/tex]

[tex]Area=-\frac{1}{3}\int_{1}^{\frac{1}{\sqrt{2}}}\frac{1}{t}dt[/tex]

[tex]Area=-\frac{1}{3}[\ln t]_{1}^{\frac{1}{\sqrt{2}}[/tex]

[tex]Area=-\frac{1}{3}(\ln \frac{1}{\sqrt{2}}-\ln (1))[/tex]

[tex]Area=-\frac{1}{3}(\ln 1-\ln \sqrt{2}-0)[/tex]

[tex]Area=-\frac{1}{3}(-\ln 2^{\frac{1}{2}})[/tex]

[tex]Area=-\frac{1}{3}(-\frac{1}{2}\ln 2)[/tex]

[tex]Area=-\frac{1}{6}\ln 2[/tex]

Therefore the area under the curve y=f(x) on [a,b] is [tex]\frac{1}{6}\ln(2)[/tex] square units.

Answer:

The area of the glass in region BCIH is 11 to the nearest feet²

Step-by-step explanation:

* Lets explain the figure

- The window is a semicircle with center G and radius 6 feet

- There is a small semicircle with center G and radius GF

∵ GE is 6 feet and EF is 3 feet

∵ GE = GF + FE

∴ 6 = GF + 3 ⇒ subtract 3 from both sides

∴ 3 = GF

∴ The radius of the small semicircle is 3 feet

∵ m∠BGC = 45°

- The area of sector BGC is part of the area of the semicircle

∵ The area of semi-circle is 1/2 π r²

∵ The measure of the central angle of the semicircle is 180°

∵ The measure of the central angle of the sector BGC is 45°

∴ The sector = 45°/180° = 1/4 of the semi-circle

∴ The area of the sector is 1/4 the area of the semicircle

∵ The area of the semicircle = 1/2 π r²

∵ r = 6 feet

∴ The area of the semicircle = 1/2 π (6)² = 1/2 π (36) = 18 π feet²

∴ Area of the sector = 1/4 (18 π) = 4.5 π feet²

- The small sector HGI has the same central angle of the sector BGC

∴ The area of the sector HGI is 1/4 The area of the small semicircle

∵ The area of the small semicircle = 1/2 π r²

∵ r = 3 feet

∴ The area of the small semicircle = 1/2 π (3)² = 1/2 π (9) = 4.5 π feet²

∴ Area of the sector HGI= 1/4 (4.5 π) = 1.125 π feet²

- The area of the glass in region BCIH is the difference between the

  area of sector BGC and the area of the sector HGI

∴ The area of the glass in region BCIH = 4.5 π - 1.125 π ≅ 11 feet²

Answer:

11 feet to the nearest square foot.

Step-by-step explanation:

The area of sector BCG

= 45/180 * 1/2 π r^2

= 1/4 * 1/2 π r^2

= 1/8 * π * 6^2

= 4.5 π ft^2.

The radius of the inner semicircle is 6 - 3 = 3 feet.

The area of sector HIG = 1/4 * 1/2 π  3^2

= 1.125 π ft^2.

So the area of BCIH

= area of BCG - area HIG

=  4.5  π - 1.125  π

=  3.375  π

= 10.6 square feet.

Answer:

[tex]4a^{2}[/tex]

Step-by-step explanation:

We need to simplify the following expression:

[tex]y=\frac{32a^{3}b^{2}}{8ab^{2}}[/tex]

We know that: [tex]\frac{x^{a}}{x^{b}}=x^{a-b}[/tex]. Applying this rule, we have that:

[tex]y = \frac{32a^{3}b^{2}}{8ab^{2}} = 4a^{3-1}b^{2-2} = 4a^{2}[/tex]

Then, the solution is: [tex]4a^{2}[/tex]

Answer:

cool

Step-by-step explanation:

Answer:

$5151.42

Step-by-step explanation:

The formula you need is

[tex]A(t)=P(1+\frac{r}{n})^{(n)(t)}[/tex]

where A(t) is the amount after the compounding, P is the initial investment, r is the interest rate in decimal form, n is the number of compoundings per year, and t is time in years.  The info we have is

A(t) = 8000

P = ?

r = .09

t = 5

Filling in we have

[tex]8000=P(1+\frac{.09}{2})^{(2)(5)}[/tex]

Simplifying a bit and we have[tex]8000=P(1+.045)^{10}[/tex]

Now we will add inside the parenthesis and raise 1.045 to the 10th power to get

8000 = P(1.552969422)

Divide away the 155... on both sides to solve for P.

P = $5151.42

ANSWER

[tex]\frac{ {x}^{2} }{ 64 } + \frac{ {y}^{2} }{ 289 } = 1[/tex]

See attachment for the graph

EXPLANATION

The standard equation of the vertical ellipse with center at the origin is given by

[tex] \frac{ {x}^{2} }{ {b}^{2} } + \frac{ {y}^{2} }{ {a}^{2} } = 1[/tex]

where

[tex] {a}^{2} \: > \: {b}^{2} [/tex]

The ellipse has its vertices at (0,±17).

This implies that:a=±17 or a²=289

The foci are located at (0,±15).

This implies that:c=±15 or c²=225

We use the following relation to find the value of b²

[tex] {a}^{2} - {b}^{2} = {c}^{2} [/tex]

[tex] \implies \: 289 - {b}^{2} = 225[/tex]

[tex] - {b}^{2} = 225 - 289[/tex]

[tex] - {b}^{2} = - 64[/tex]

[tex] {b}^{2} = 64[/tex]

We substitute into the formula for the standard equation to get:

[tex]\frac{ {x}^{2} }{ 64 } + \frac{ {y}^{2} }{ 289 } = 1[/tex]

Answer:

Function which represents the product of these two numbers is:

(23+x)(28+2x)

Step-by-step explanation:

The first number is the sum of 23 and x

i.e. First number=23+x

The second number is 18 less than two times the first number.

i.e. Second number=2(23+x)-18

                                = 46+2x-18

                                = 28+2x

Product of the two numbers=(23+x)(28+2x)

Hence, function which represents the product of these two numbers is:

(23+x)(28+2x)

Answer:

  (-9, 6)

Step-by-step explanation:

It's all about pattern matching.

A circle centered at (h, k) with radius r has the equation ...

  (x -h)^2 + (y -k)^2 = r^2

Comparing this pattern to the equation you have, you can see that ...

Then the center is (h, k) = (-9, 6).

Answer:

 (-9, 6)

Step-by-step explanation:

i took the test

Answer:

  The bottleneck of this process is Workstation C, at 30 minutes per unit.

Step-by-step explanation:

The throughput of each workstation is ...

Since each process must be executed once per finished product, the bottleneck is the station with the lowest throughput. It is clearly Workstation C.

The bottleneck of this process is workstation D, where the time per unit is 15 minutes.

The bottleneck of this process is workstation D, where the time per unit is 15 minutes. This means that workstation D takes the longest time to complete one unit compared to other workstations. The bottleneck determines the maximum output rate of the entire process, as the other workstations cannot work faster than the slowest one.

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Answer:

Step-by-step explanation:

Given:

  Total interest earned on two investments is $29,220.

  An amount is invested at 7%.

  $24,000 more than 4 times that amount is invested at 8%.

Find:

  The amount invested at each rate.

Solution:

  Our strategy will be to define a variable representing the amount invested at 7%, use that variable to write an expression for the amount invested at 8%, then write an equation for the total return on the investments.

Let x represent the amount invested at 7%. Then (24,000+4x) will be the amount invested at 8%. The total interest earned will be ...

  interest on 7% account + interest on 8% account = total interest

  0.07x + 0.08(24000+4x) = 29220

  0.39x + 1920 = 29220 . . . . . . . . . . . simplify

  0.39x = 27300 . . . . . . . . . . . . . . . . . .subtract 1920

  x = 27300/0.39 = 70000 . . . . . . . . . divide by the coefficient of x

  24,000 +4x = 24,000 +280,000 = 304,000 . . . . amount invested at 8%

He invested $70,000 at 7% and $304,000 at 8%.

Check

The answer must satisfy ...

  7% interest + 8% interest = 29,220

  0.07×70,000 +0.08×304,000 = 4,900 +24,320 = 29,220 . . . . as required

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