Let W be the region bounded by z=100−y^2, y=10x^2, and the plane z=0. Calculate the volume of W as a triple integral in the order dzdydx. (Give your answer in exact form. Use symbolic notation and fractions where needed.)

Answer:

[tex]t=\frac{4.2-4}{\frac{0.5}{\sqrt{25}}}=2[/tex]

The degrees of freedom are given by:

[tex] df =n-1=25-1=24[/tex]

And the p value would be given by:

[tex] p_v = P(t_{24}>2) =0.0285[/tex]

And since the p value is lower than the significance level we have enough evidence to conclude that the true mean for this case is significantly hiher than 4. And the claim for this case is not appropiate      

Step-by-step explanation:

Data provided

[tex]\bar X=4.2[/tex] represent the sample mean for the weigths

[tex]s=0.5[/tex] represent the sample standard deviation

[tex]n=25[/tex] sample size      

[tex]\mu_o =4[/tex] represent the value that we want to analyze

[tex]\alpha[/tex] represent the significance level for the hypothesis test.    

t would represent the statistic

[tex]p_v[/tex] represent the p value for the test

System of hypothesis

We want to conduct a hypothesis in order to check if the true mean weigth is less than 4 or not, the system of hypothesis would be:      

Null hypothesis:[tex]\mu \leq 4[/tex]      

Alternative hypothesis:[tex]\mu > 4[/tex]      

The statistic for this case is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)      

Replacing the info given we got:

[tex]t=\frac{4.2-4}{\frac{0.5}{\sqrt{25}}}=2[/tex]  

The degrees of freedom are given by:

[tex] df =n-1=25-1=24[/tex]

And the p value would be given by:

[tex] p_v = P(t_{24}>2) =0.0285[/tex]

And since the p value is lower than the significance level we have enough evidence to conclude that the true mean for this case is significantly hiher than 4. And the claim for this case is not appropiate

Answer:

There is a relationship between the age of a young adult and the type of movie preferred.

Step-by-step explanation:

In this case we need to test whether there is a significance relationship between the age of a young adult and the type of movie preferred.

The hypothesis can be defined as:

H₀: Age of a young adult and movie preference are independent.

Hₐ: Age of a young adult and movie preference are not independent.

The test statistic is given as follows:

[tex]\chi^{2}=\sum\limits^{n}_{i=1}{\frac{(O_{i}-E_{i})^{2}}{E_{i}}}[/tex]

Consider the table below.

The formula to compute the expected frequencies is:

[tex]E_{i}=\frac{\text{Row Total}\times \text{Column Total}}{\text{Total}}[/tex]

The Chi-square test statistic value is:

[tex]\chi^{2}=\sum\limits^{n}_{i=1}{\frac{(O_{i}-E_{i})^{2}}{E_{i}}}=2.6013[/tex]

The significance level of the test is, α = 0.05.

The degrees of freedom of the test is,

df = (r - 1)(c - 1)

   = (3 - 1)(3 - 1)

   = 2 × 2

   = 4

Compute the p-value as follows:

p-value = 0.6266

*Use a Chi square table.

As the p-value is more than the significance level the null hypothesis was failed to be rejected.

Thus, concluding that there is a relationship between the age of a young adult (18 to 35 years old) and the type of movie preferred.

To seed the entire lawn, you will need 11.4 packages of grass seed.

To determine the number of packages of grass seed needed, we need to find the area of the lawn. The area of a rectangle is given by the formula length * width. In this case, the length is 400 feet and the width is 285 feet. Multiplying these values together, we get an area of 114,000 square feet. Now, we can determine the number of packages needed by dividing the area of the lawn by the area covered by one package of seed. Since one package covers 10,000 square feet, we divide 114,000 by 10,000 to get 11.4 packages.

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A total of 12 packages needed.

To determine how many packages of grass seed are needed to seed a lawn of 400 feet by 285 feet, follow these steps:

Calculate the lawn's total area by multiplying its length by its width: 400 feet * 285 feet = 114,000 square feet.

Since one 50-pound package of grass seed is enough for 10,000 square feet, divide the lawn's total area by 10,000 square feet to find the number of packages needed: 114,000 square feet / 10,000 square feet per package = 11.4 packages.

Because you can't purchase a fraction of a package, you'll need to round up to the nearest whole number, which means you require 12 packages of grass seed to cover the entire lawn.

It's also important to consider the seeding rate when determining the amount of seed required. However, in this case, the seeding rate is not needed since the question specifies one package covers a set amount of square footage.

Answer:

  c.  6

Step-by-step explanation:

The degree of a vertex is the number of arc ends that intercept it. (The other end of the arc is irrelevant.)

Vertex A is connected to B (1), D (2), F (1), and itself (2). There are a total of 6 arc ends that meet vertex A. Its degree is 6.

Answer: 2,820 (use the profit equation from the first question )

Answer:

for  edg its 3x - 180 and the other one is  2820

Step-by-step explanation:

bc i just took it

Given that $1.50 is the cost of one kilogram of rice and that one kilogram equals about 2.20462 pounds, the cost of one pound of rice will be about $0.68.

To convert the costs from kilogram to pound, you need to know that one kilogram equals about 2.20462 pounds. Hence, if rice costs $1.50 per kilogram, we can calculate the cost per pound by dividing $1.50 by 2.20462.

This results in a cost of approximately $0.68 per pound of rice.

So, if you're looking to purchase a pound of rice under this cost scheme, it would set you back about $0.68.

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Answer:

62

Step-by-step explanation:

length of rectangle = 2* diameter = 24

width  = diameter = 12

area = 24*12 - 2 * pi * 6^2 = 61.8

Your answer would be the second option, 62.

To answer this we need to find the area of the 2 circles, and then subtract this from the area of the rectangle to find the shaded area.

The equation for the area of a circle is πr², so for one circle this would be π × 6² = 36π. Since we're taking π = 3.14, this comes out as 113.04 as the area for once circle, which means the area for both circles would be 113.04 × 2 = 226.08.

To find the area of the rectangle, we need to notice that the height of the rectangle is the diameter of one circle, and the width is 2 multiplied by the diameter of the circle, because there are 2 diameters right next to each other. The diameter of one circle is 6 × 2 = 12, so this is the height, which means the width of the rectangle is 12 × 2 = 24. This means the area of the rectangle is 24 × 12 = 288.

Now the last step is to do 288 - 226.08 = 61.9 = 62.

I hope this helps!

Answer:

2 sq. ft. ?

Step-by-step explanation:

hope we can be friends

can i please get brainliest

Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 25235

For the alternative hypothesis,

µ > 25235

This is a right tailed test.

Since the population standard deviation is not given, the distribution is a student's t.

Since n = 100,

Degrees of freedom, df = n - 1 = 100 - 1 = 99

t = (x - µ)/(s/√n)

Where

x = sample mean = 27524

µ = population mean = 25235

s = samples standard deviation = 6000

t = (27524 - 25235)/(6000/√100) = 3.815

We would determine the p value using the t test calculator. It becomes

p = 0.000119

Since alpha, 0.05 > than the p value, 0.000119, then we would reject the null hypothesis. There is sufficient evidence to support the claim that student-loan debt is higher than $25,235 in her area.

Answer:

3 ft

Step-by-step explanation:

Answer:

it will take 1095 seconds to wash 18 dishes using a pipelined approach

Step-by-step explanation:

Let represent the identity of those three people with :

A

B

C

Now; let the function assigned to those  the people be:

A = Rinse

B =Scrub with soap

C = Dry

For the first dish pipeline

A(RInse) = 15 seconds

B (Scrub with soap) = 30 seconds

A(RInse) = 15 seconds

C(Dry) = 15 seconds

The total time taken to complete one dish to wash = (15 +30+  15+15)seconds = 75 seconds

However ; A cannot take the second dish for rinse until the first dish has not been rinse for the second time by A,   A can only start rinse from the second dish when the first dish is at C for dry

SO; for the second dish:

B (Scrub with soap) = 30 seconds

A(RInse) = 15 seconds

C(Dry) = 15 seconds

B (Scrub with soap) = 30 seconds

A(RInse) = 15 seconds

C(Dry) = 15 seconds

Similiarly ; for the third dish

B (Scrub with soap) = 30 seconds

A(RInse) = 15 seconds

C(Dry) = 15 seconds

B (Scrub with soap) = 30 seconds

A(RInse) = 15 seconds

C(Dry) = 15 seconds

B (Scrub with soap) = 30 seconds

A(RInse) = 15 seconds

C(Dry) = 15 seconds

Therefore, the total time taken to was 18 dishes = time to wash the first dish + time remaining for 17 dishes

= 75 +(30+15+15)×17

= 1095 seconds

Hence, it will take 1095 seconds to wash 18 dishes using a pipelined approach

To wash 18 dishes using a pipelined approach, you can assign each friend a different task and work on multiple dishes simultaneously. The total time taken would be 75 seconds.

In order to wash 18 dishes using a pipelined approach, you can assign each friend a different task and work on multiple dishes simultaneously. Here is the step-by-step process:

The total time taken to wash the dishes using this pipelined approach can be calculated as follows:

Total time = (15 seconds) + (30 seconds) + (15 seconds) + (15 seconds)

Total time = 75 seconds

Since the pipelined approach allows you to work on multiple dishes simultaneously, the time taken to wash 18 dishes would be the same as washing a single dish, which is 75 seconds.

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Answer:

  6

Step-by-step explanation:

The degree of 8m^2n^4 is the sum of the exponents of the variables:

  2 + 4 = 6

The monomial has degree 6.

Answer:

B

Step-by-step explanation:

21/25

Work Shown:

21/25 = 84/100 after multiplying top and bottom by 4

Since 84/100 = 84%, this means 21/25 = 84% as well

Alternatively, you can use a calculator or long division to find that 21/25 = 0.84 = 84%

Answer:

x =89

Step-by-step explanation:

The sum of the angles of a quadrilateral are 360 degrees

88+154+x+29 = 360

Combine like terms

271 +x = 360

271+x-271 = 360-271

x =89

Answer:

We conclude that we fail to reject [tex]H_0[/tex] as there is not sufficient evidence to warrant support of the claim that less than 10 percent of the test results are wrong.

Step-by-step explanation:

We are given that among 317 tested​ subjects, results from 25 subjects were wrong.

We have to test the claim that less than 10 percent of the test results are wrong.

Let p = proportion of subjects that were wrong.

So, Null Hypothesis, [tex]H_0[/tex] : p = 10%     {means that 10 percent of the test results are wrong}

Alternate Hypothesis, [tex]H_A[/tex] : p < 10%     {means that less than 10 percent of the test results are wrong}

The test statistics that would be used here One-sample z proportion statistics;

                      T.S. =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p (1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of test results that were wrong = [tex]\frac{25}{317}[/tex] = 0.08

           n = sample of tested subjects = 317

So, test statistics  =  [tex]\frac{0.08-0.10}{\sqrt{\frac{0.08 (1-0.08)}{317} } }[/tex]

                              =  -1.31

The value of z test statistics is -1.31.

Now, the P-value of the test statistics is given by the following formula;

                P-value = P(Z < -1.31) = 1 - P(Z [tex]\leq[/tex] 1.31)

                              = 1 - 0.9049 = 0.095

Now, at 0.05 significance level the z table gives critical value of -1.645 for left-tailed test. Since our test statistics is more than the critical value of z as -1.31 > -1.645, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that we fail to reject [tex]H_0[/tex] as there is not sufficient evidence to warrant support of the claim that less than 10 percent of the test results are wrong.

Answer:

Check the explanation

Step-by-step explanation:

here are 6 possible sequences of removing 3 marbles. Let R be the red marble, B be the blue marble and G be the green marble. The possible sequences are: RBG, RGB, BGR, BRG, GRB and GBR.

Let A denotes Event 1 and B denotes Event 2.

The favorable cases for A are: BGR, BRG, GRB and GBR.

So, P(A) = 4/6 = 2/3.

The favorable cases for B are: RBG, RGB, BRG and GRB.

So, P(B) = 4/6 = 2/3.

The probability of both events happening is P(A \cap B).

Favorable cases for (A \cap B) are BRG and GRB.

Thus, P(A \cap B) = 2/6 = 1/3.

The probability of either of these events happening is P(A \cup B).

Favorable cases for (A \cup B) are RBG, RGB, BRG, BGR, GRB and GBR.

Thus, P(A \cup B) = 6/6 = 1.

Also, P(A \cap B) \neq P(A) P(B).

So, A and B are not independent.

Hence, Option (D) is the only true statement. (Ans).

We have been given that a virus has infected 400 people in the town and is spreading to 25% more people each day. We are asked to write an exponential function to model this situation.

Since the number of infected people is increasing, so our model will be exponential growth model.

An exponential growth function is in form [tex]y=a(1+r)^x[/tex], where,

y = Final amount,

a = Initial amount,

r = Growth rate in decimal form,

x = Time.

Let us convert 25% into decimal form.

[tex]25\%=\frac{25}{100}=0.25[/tex]

The initial number of infected people is [tex]400[/tex], so our function would be [tex]y=400(1+0.25)^x[/tex].

[tex]y=400(1.25)^x[/tex]

To find the number of infected in 10 days, we will substitute [tex]x=10[/tex] in our given formula as:

[tex]y=400(1.25)^{10}[/tex]

[tex]y=400(9.3132257461547852)[/tex]

[tex]y=3725.290298\approx 3725[/tex]

Therefore, there will be approximately 3725 infected people in 10 days.

The number of people that will be infected in 10 days is approximately 3725. This represents exponential growth.

Step 1

To model the spread of the virus using an exponential function, we start with the initial number of infected people and the daily growth rate. The exponential growth formula is:

[tex]\[ P(t) = P_0 \times (1 + r)^t \][/tex]

Where:

- [tex]\( P(t) \)[/tex] is the number of people infected after t days

- [tex]\( P_0 \)[/tex] is the initial number of infected people

- [tex]\( r \)[/tex] is the growth rate

- t is the time in days

Given:

- Initial number of infected people, [tex]\( P_0 = 400 \)[/tex]

- Daily growth rate, r = 0.25  (since 25% more people are infected each day)

The exponential function becomes:

[tex]\[ P(t) = 400 \times (1 + 0.25)^t \][/tex]

[tex]\[ P(t) = 400 \times (1.25)^t \][/tex]

Step 2

To find the number of people infected in 10 days [tex](\( t = 10 \))[/tex]:

[tex]\[ P(10) = 400 \times (1.25)^{10} \][/tex]

Calculating this:

[tex]\[ P(10) = 400 \times (1.25)^{10} \][/tex]

Using a calculator:

[tex]\[ (1.25)^{10} \approx 9.3132 \][/tex]

[tex]\[ P(10) = 400 \times 9.3132 \approx 3725.28 \][/tex]

So, the number of people infected in 10 days is approximately 3725.

Known :

r = 2

Asked :

C = ...?

Answer :

C = 2πr

= 2 × 3.14 × 2

= 12.56

So, tge circumference of circle is 12.56

Hope it helpful and useful :)

Answer:

[tex]4\pi[/tex]

Step-by-step explanation:

The equation for the circumference of a circle is 2[tex]\pi[/tex]r. I remember it as Cherry Pies Are (r) Square. If you plug in 2 for r, it should get you the answer

Answer:

THE ANSWER IS 4n - 13

Answer:

because your just adding a zero at the end.

Step-by-step explanation:

Adding 6+3 is like adding 60+30 because both utilize the place value system and the commutative property of addition where units are added to units and tens to tens, respectively.

The question of adding 6+3 is similar to adding 60+30 due to the property of place value and the commutative property of addition. In both cases, you are adding units that are consistent within their respective places. In single-digit addition, such as 6+3, you are adding units to units. Similarly, in the addition of multi-digit numbers like 60+30, you are adding tens to tens. This is much like the property A+B=B+A, which holds true for ordinary numbers, meaning you'll get the same result regardless of the order in which you add them.

Answer:

We are tryng to proof if more than half of all seniors think their job prospects are good so that would be the alternative hypothesis and the complement rule would be the null hypothesis.:  

Null hypothesis:[tex]p\leq 0.5[/tex]  

Alternative hypothesis:[tex]p > 0.5[/tex]  

Step-by-step explanation:

Information provided

n=100 represent the random sample ofcollege senior selected

X=53 represent the college seniors who say good

[tex]\hat p=\frac{53}{100}=0.53[/tex] estimated proportion of seniors who think their job prospects are good

[tex]p_o=0.5[/tex] is the value that we want to test

z would represent the statistic

[tex]p_v[/tex] represent the p value

System of hypothesis

We are tryng to proof if more than half of all seniors think their job prospects are good so that would be the alternative hypothesis and the complement rule would be the null hypothesis.:  

Null hypothesis:[tex]p\leq 0.5[/tex]  

Alternative hypothesis:[tex]p > 0.5[/tex]  

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing the info given we have:

[tex]z=\frac{0.53 -0.5}{\sqrt{\frac{0.5(1-0.5)}{100}}}=0.6[/tex]  

The p value for this case would be given by

[tex]p_v =P(z>0.6)=0.274[/tex]  

Answer:

The 90% confidence interval for the average monthly residential water usage for all households in this city is between 4401.3 gallons and 4598.7 gallons.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.9}{2} = 0.05[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.645*\frac{600}{\sqrt{100}} = 98.7[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 4500 - 98.7 = 4401.3 gallons

The upper end of the interval is the sample mean added to M. So it is 4500 + 98.7 = 4598.7 gallons

The 90% confidence interval for the average monthly residential water usage for all households in this city is between 4401.3 gallons and 4598.7 gallons.

We have been given that the perimeter of a semicircle is 25.71 cm. We are asked to find the value of the radius.

We know that perimeter of a semicircle is [tex]\pi r+2r[/tex], where r is radius of perimeter.

Upon equating perimeter of semicircle formula with 25.71, we will get:

[tex]\pi r+2r=25.71[/tex]

[tex]3.142r+2r=25.71[/tex]

[tex]5.142r=25.71[/tex]

[tex]\frac{5.142r}{5.142}=\frac{25.71}{5.142}[/tex]

[tex]r=5[/tex]

Therefore, the radius of the semicircle is 5 cm.

Answer:

D is the answer

Step-by-step explanation:

If every year the value decreases by $1,500 that variable will change, but the price he bought the car at will not. That is why the x variable(standing for years) would go into the 1,500. And if each year the value decreases the answer would be D

Answer:  D. y=18,000 - 1,500x

Step-by-step explanation: the answer is d.) because the cars value will go down as time pas, so 1,500 represent the money and x could represent one year and you subtract it from 18,000 which is the original  value of the car.

Answer:

4cm; 1.79 cm.

Step-by-step explanation:

Okay, this question is about the Calculation involving the volume of a box with a square base and a height.

So, the volume of the box = length × width × height ---------------------------(1).

Therefore, we are going to make use of Equation (1) to determine the solution to this question, so that we have;

For Box A; We are given our volume to be equal to 32cm^3, height = 2cm, length and width = x cm.

For Box B = 32 = 2x^2.

x^2 = 16..

x = 4.

Note that Length = width.

For box B=> 32 = 10x^2.

x = √3.2 cm. = 1.79 cm.

Final answer:

The height of Box A with a base area of 32 square centimeters is 1 cm.

Explanation:

To find the height of Box A, we need to use the formula for the volume of a rectangular box, which is V = length * width * height. Given that the base area of Box A is 32 cm2 and assuming that the volume of Box A is equal to the volume of Box B, we can express their volumes as proportional to each other based on their dimensions.

Box A has a volume of 32 cm³ with a base area of 32 square centimeters.

Volume of Box A = Base Area x Height = 32 cm² x Height = 32 cm³

Height of Box A is 1 cm.

Answer:

9² − x²

x(9-x)+9(9-x)

Step-by-step explanation:

The area of the shaded light gray square =

= the area of the whole square - the area of the shaded dark gray square

= 9² - x²

since x(9-x)+9(9-x) = 9x - x² + 9² - 9x = 9² - x²

then x(9-x)+9(9-x) is also a right answer.

Answer:

The answer is 9² - x² and x(9 - x) + 9(9 - x)

Step-by-step explanation:

Here, In a Figure, two square is given first which is small and shaded dark gray and second which is big and shaded light gray.

Now, For area of Small Square.

Length (l) = x

A = l²

A = (x)²

A = x²

Now, For area of Big Square.

Length (l) = 9

A = l²

A = (9)²

A = 81

Then, To find are of Shaded light gray square

Area of Big Square - Area of Small Square.

9² - x²

Thus, The answer is 9² - x² and

x(9 - x) + 9(9 - x)

-TheUnknownScientist

Answer:

orchestra​ seats = 140 seats

main​ seats = 350 seats

balcony seats = 210 seats

Step-by-step explanation:

Let x = number of orchestra seats

Let y = number of main seats

Let z = number of balcony seats

Theater has 700 seats. Thus;

Total seat equation is;

x + y + z = 700 - - - - (1)

We are told Orchestra seats sell for $ 50, main seats for $ 40, and balcony seats for $ 25 and a gross revenue of $26,250

Thus ;

all seats revenue equation is;

50x + 40y + 25z = 26250 - - - (eq2)

Now, we are told that, when all the main and balcony seats are​ sold, but only half the orchestra seats are​ sold, the gross revenue is $ 22,750

Thus, we have;

½(50x) + 40y + 25z = 22,750

Which gives ;

25x + 40y + 25z = 22,750 ---(eq3)

Solving the 3 equations simultaneously, we have;

x = 140

y = 350

z = 210

Answer:

x=\frac{-3}{2}

Step-by-step explanation:

We have been given with the expression (1/3)^x=(27)^x+2

Now, to solve the equation firstly we have to make the base same on both sides

(1/3)^x=3^{-x}

27 can be written as 3^3

27^x=(3^3)^x=3^{3x}

Hence, given expression can be rewritten as

3^{-x}=3^{3(x+2)}

Now since, base is same we can equate the powers on both sides

-x=3(x+2)\\ \Rightarrow-x= 3x+6\\ \Rightarrow -x-3x=6\\-4x=6\Rightarrow x=\frac{-3}{2}

Therefore given expression (1/3)^x=(27)^x+2 is equivalent to x=\frac{-3}{2}

Equivalent means the simplified form of any given expression

The equation is equivalent to [tex]\(\boxed{3^x = 3^{-3x+2}}\)[/tex]

To solve the equation [tex]\((\frac{1}{3})^x = 27^{(x+2)}\)[/tex], we first need to express [tex]\(27\)[/tex] as a power of [tex]\(3\)[/tex], as [tex]\(27 = 3^3\)[/tex]. Then, we rewrite the equation as:

[tex]\[\left(\frac{1}{3}\right)^x = (3^3)^{(x+2)}\][/tex]

Now, we apply the properties of exponents, specifically the power of a power rule which states [tex]\((a^m)^n = a^{m \times n}\)[/tex], to simplify the expression:

[tex]\[\left(\frac{1}{3}\right)^x = 3^{3(x+2)}\][/tex]

Now, we have the same base on both sides of the equation. We can set the exponents equal to each other:

[tex]\[x = 3(x+2)\][/tex]

Now, let's solve for [tex]\(x\)[/tex]:

[tex]\[x = 3x + 6\][/tex]

[tex]\[x - 3x = 6\][/tex]

[tex]\[-2x = 6\][/tex]

[tex]\[x = \frac{6}{-2}\][/tex]

[tex]\[x = -3\][/tex]

Complete correct question:

Which equation is equivalent to [tex]( 1/3 )^x=27^{x+2}[/tex] ?

[tex]3^x=3^{-3x+2}[/tex]

[tex]3^x=3^{3x+6}[/tex]

[tex]3^{-x} =3^{3x+2}[/tex]

[tex]3^{-x} =3^{3x+6}[/tex]

Final answer:

Descriptive and inferential statistics both analyze research data and are used together in scientific studies to summarize, describe, and make predictions about a population based on sample data.

Explanation:

Understanding the similarities between descriptive statistics and inferential statistics is fundamental in scientific investigations. Although these two types of statistics serve different purposes, they share some common ground. Both are used to analyze data collected from a research study and help in making decisions or drawing conclusions about that data.

Descriptive statistics summarize and describe the main features of a dataset. Common descriptive measures include the mean, median, mode (measures of central tendency), and the range, standard deviation, and variance (measures of dispersion). On the other hand, inferential statistics use a random sample of data from a population to make inferences about the overall population. It includes various hypothesis tests and confidence intervals to determine the probability of the occurrence of a particular event.

Both descriptive and inferential statistics rely on the same underlying data collection principles and are often used in tandem. Descriptive statistics generally precede inferential statistics in the data analysis process, providing a foundation for further analysis. Moreover, they both employ graphical and numerical methods to present and summarize data, ensuring the findings are communicated in a clear and easily understood manner.

Ultimately, understanding both types of statistics allows researchers to accurately describe, summarize, and make predictions or generalizations regarding their data, which are crucial steps in any scientific study.