Simplify: 6x^-2

a) 1/6x^2
b) 6/x^2
c) x^2/6
d) 1/36x^2

Answers

Answer 1

Answer:

The correct answer choice is option B. 6/x^2

Step-by-step explanation:

Simplify: 6x^-2a) 1/6x^2b) 6/x^2c) X^2/6d) 1/36x^2
Answer 2

Answer:

6/x^2

Step-by-step explanation:

6 * x^-2

We know that a^ -b = 1/a^b

6 * 1/x^2

6/x^2


Related Questions

The gross domestic product (GDP) of the United States is defined as

Answers

The gross domestic product (GDP) of the United States is defined as the market value of all final goods and services produced within the United States in a given period of time.

Answer:

the market value of all final goods and services produced within the United States in a given period of time.

I’ll mark you as a brain list please help

Answers

Answer:

just ignore this whole thing

Answer: There is a pattern if you look closely :)

So yhe required answer would be 7^-1

Step-by-step explanation:

Triangles P Q R and S T U are shown. Angles P R Q and T S U are right angles. The length of P Q is 20, the length of Q R is 16, and the length of P R is 12. The length of S T is 30, the length of T U is 34, and the length of S U is 16.
Using the side lengths of △PQR and △STU, which angle has a sine ratio of Four-fifths?

∠P
∠Q
∠T
∠U

Answers

Answer:

[tex]\angle P[/tex]

Step-by-step explanation:

Given

[tex]\triangle PRQ = \triangle TSU = 90^o[/tex]

[tex]PQ = 20[/tex]     [tex]QR = 16[/tex]    [tex]PR = 12[/tex]

[tex]ST = 30[/tex]       [tex]TU = 34[/tex]    [tex]SU = 16[/tex]

See attachment

Required

Which sine of angle is equivalent to [tex]\frac{4}{5}[/tex]

Considering [tex]\triangle PQR[/tex]

We have:

[tex]\sin(P) = \frac{QR}{PQ}[/tex] --- i.e. opposite/hypotenuse

So, we have:

[tex]\sin(P) = \frac{16}{20}[/tex]

Divide by 4

[tex]\sin(P) = \frac{4}{5}[/tex]

Hence:

[tex]\angle P[/tex] is correct

Answer:

A or <P

Step-by-step explanation:

on edge 2021

Find mBAF help ASAP.

Answers

Answer:

I think

c. 164

Step-by-step explanation:

m<BAC=m<FAE = 25

m< CAD=m< DAE= 57

m<BAF= 25+25+57+57=164

URGENT!!!!!! 15 POINTDS

Answers

Answer:

Option C

Step-by-step explanation:

thankful that there are graphing tools. see screenshot

I’m pretty sure it’s c

Look at the figure below: an image of a right triangle is shown with an angle labeled y degrees If sin y° = s divided by 8 and tan y° = s divided by t, what is the value of cos y°?
cos y° = 8s
cos y° = 8t
cos y°= t / 8
cos y°=8 / t

Answers

Answer:

Cos y = t / 8

Step-by-step explanation:

Using the hints given in the question, the omitted tribagke will look like the triangle attached on the picture ;

From trigonometry :

Sin y = opposite / hypotenus

Sin y = s / 8

Opposite side = s ; hypotenus = 8

Tan y = opposite / Adjacent

Tan y = s / t

Adjacent side = t

Then ;

Cos y = Adjacent / hypotenus

Hence,

Cos y = t / 8

Answer:

the answer is :

cos y°= t / 8

Step-by-step explanation:

I promise! I got this right, and.....you are welcome.

HELP PLEASE BE CORRECT

Answers

Answer:

12

Step-by-step explanation:

Scale factor of 4

CD = 3

3 · 4 = 12

Length of C'D' is 12 units

Answer:

12 units

Step-by-step explanation:

The original segment CD = 3 units

Scale factor is 4.

3 x 4 = 12

A certain species of virulent bacteria is being grown in a culture. It is observed that the rate of growth of the bacterial population is proportional to the number present. If there were 3000 bacteria in the initial polulation and the number doubled after the first 60 minutes, how many bacteria will be present after 2 hours

Answers

Answer:

12000 bacteria

Step-by-step explanation:

Recall that

60 minutes = 1 hour

Given that the rate of growth of the bacterial population is proportional to the number present.

If there were 3000 bacteria in the initial population and the number doubled after the first 60 minutes

Then after 60 minutes, the number of bacteria present would be

= 3000 * 2

= 6000

In another 60 minutes, the number would have doubled again, thus the number present then would be

= 6000 * 2

= 12000

Hence after 120 minutes, the number of bacteria present is 12000. 120 minutes is same as 2 hours

convert 2m 50cm 15mm in cm

Answers

Answer:

251.5 cm

Step-by-step explanation:

1 m = 100 cm

1 cm = 10 mm

2 m + 50 cm + 15 mm =

= 2 m * (100 cm)/m + 50 cm + 15 mm * (1 cm)/(10 mm)

= 200 cm + 50 cm + 1.5 cm

= 251.5 cm

Which of the following is equivalent to the expression - 1/4-(2/5 + 3/7)?

Answers

Given:

The expression is:

[tex]-\dfrac{1}{4}-\left(\dfrac{2}{5}+\dfrac{3}{7}\right)[/tex]

To find:

The expression that is equivalent to the given expression.

Solution:

We have,

[tex]-\dfrac{1}{4}-\left(\dfrac{2}{5}+\dfrac{3}{7}\right)[/tex]

Using the distributive property, we get

[tex]=-\dfrac{1}{4}-\dfrac{2}{5}-\dfrac{3}{7}[/tex]

Taking LCM, we get

[tex]=\dfrac{-35-56-60}{140}[/tex]

[tex]=\dfrac{-151}{140}[/tex]

Therefore, the expression [tex]-\dfrac{151}{140}[/tex] is equivalent to the given expression expression.

Note: There are more than one equivalent expressions.

A survey sampled men and women workers and asked if they expected to get a raise or promotion this year. Suppose the survey sampled 200 men and 200 women. If 98 of the men replied Yes and 72 of the women replied Yes, are the results statistically significant so that you can conclude a greater proportion of men expect to get a raise or a promotion this year?

a. State the hypothesis test in terms of the population proportion of men and the population proportion of women.
b. What is the sample proportion for men? For women?
c. Use α= 0.01 level of significance. What is the p-value and what is your conclusion?

Answers

Answer:

a)

The null hypothesis is: [tex]H_0: p_M - p_W = 0[/tex]

The alternative hypothesis is: [tex]H_1: p_M - p_W > 0[/tex]

b) For men is of 0.49 and for women is of 0.36.

c) The p-value of the test is 0.0039 < 0.01, which means that the results are statistically significant so that you can conclude a greater proportion of men expect to get a raise or a promotion this year.

Step-by-step explanation:

Before solving this question, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Men:

98 out of 200, so:

[tex]p_M = \frac{98}{200} = 0.49[/tex]

[tex]s_M = \sqrt{\frac{0.49*0.51}{200}} = 0.0353[/tex]

Women:

72 out of 200, so:

[tex]p_W = \frac{72}{200} = 0.36[/tex]

[tex]s_W = \sqrt{\frac{0.36*0.64}{200}} = 0.0339[/tex]

a. State the hypothesis test in terms of the population proportion of men and the population proportion of women.

At the null hypothesis, we test if the proportion are similar, that is, if the subtraction of the proportions is 0, so:

[tex]H_0: p_M - p_W = 0[/tex]

At the alternative hypothesis, we test if the proportion of men is greater, that is, the subtraction is greater than 0, so:

[tex]H_1: p_M - p_W > 0[/tex]

b. What is the sample proportion for men? For women?

For men is of 0.49 and for women is of 0.36.

c. Use α= 0.01 level of significance. What is the p-value and what is your conclusion?

From the sample, we have that:

[tex]X = p_M - p_W = 0.49 - 0.36 = 0.13[/tex]

[tex]s = \sqrt{s_M^2+s_W^2} = \sqrt{0.0353^2 + 0.0339^2} = 0.0489[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{s}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error, so:

[tex]z = \frac{0.13 - 0}{0.0489}[/tex]

[tex]z = 2.66[/tex]

P-value of the test and decision:

The p-value of the test is the probability of finding a difference above 0.13, which is the p-value of z = 2.66.

Looking at the z-table, z = 2.66 has a p-value of 0.9961.

1 - 0.9961 = 0.0039.

The p-value of the test is 0.0039 < 0.01, which means that the results are statistically significant so that you can conclude a greater proportion of men expect to get a raise or a promotion this year.

A survey is created to measure dietary habits. The survey asks questions about each meal and snack consumed for each day of the week. The survey seems like a good representation of measuring dietary habits. This survey would be considered to have high ______ validity.

Answers

Answer:

Face validity

Step-by-step explanation:

In quantitative research in mathematics, we have four major types of validity namely;

- Content Validity

- Construct validity

- Criterion validity

- Face validity.

Now;

> Construct validity seeks to find out if the tool used in measurement is a true representation of what is really going to be measured.

> Content Validity seeks to find out whether a test covers every part of a particular subject being tested.

> Face validity seeks to find out how true a test is by looking at it on the surface.

> Criterion validity seeks to find out the relationship of a particular test to that of another test.

Now, in this question, we are told that The survey seems like a good representation of measuring dietary habits after just asking questions about each meal and snack they consumed for the week. Thus, it is a face validity because it just appears true on the surface to be a good representation but we don't know if it is effective until we go deep like content validity

PLEASE HELPPP!!!! WILL GIVE BRAINLIEST!!!!!!!!!!

Answers

I also need help anyone can help

A number increased by a% and decreased by 80% is 400. What is the number?

will give brainliest

Answers

Answer:

If we have a given number N, and we increase it by x%, then the new number is:

N + (x%/100%)*N

While if we decrease it by x%, the new number will be:

N - (x%/100%)*N

Now, we know that:

"A number increased by a% and decreased by 80% is 400. What is the number?"

First, we can not solve the problem, because we have two unknown values, the original number and the "a%", which I guess is a typo.

So, to be general with my answer, let's assume that the actual question is:

"A number increased by 50% and decreased by 80% is 400. What is the number?"

Then, if our original number is N and we increase it by 50%, the new number will be:

N + N*(50%/100%)

N + N*0.5

N*(1 + 0.5)

N*(1.5)

Now we decrease it by 80%, and that will be equal to 400, then:

N*1.5 - N*(1.5)*(80%/100%) = 400

N*1.5 - N*1.5*0.8 = 400

N*(1.5 - 1.5*0.8) = 400

N*(0.3) = 400

N = 400/0.3 = 1,333.33...

Remember that this is a kinda general solution, so you can understand how to solve this type of problem.

The average time to serve a customer at a fast-food restaurant is 4.35 minutes. The standard deviation of the service time is 2.5 minutes. What is the coefficient of variation of the service time

Answers

Answer: 0.5747

Step-by-step explanation:

Given: Average time to serve a customer[tex](\mu)=4.35[/tex] minutes

standard deviation of the service time [tex](\sigma)=[/tex] 2.5 minutes

coefficient of variation = [tex]\frac{\sigma}{\mu}[/tex]

[tex]=\dfrac{2.5}{4.35}\\\\=\dfrac{250}{435}\\\\=0.5747[/tex]

Hence, the required coefficient of variation= 0.5747

A certain manufacturing process yields electrical fuses of which, in the long run
15% are defective. Find the probability that in a random sample of size n=10, fuses
selected from this process, there will be
(i) No defective fuse
(ii) At least one defective fuse
(iii) Exactly two defective fuses
(iv) At most one defective fuse

Answers

Answer:

i) 0.1969 = 19.69% probability that there will be no defective fuse.

ii) 0.8031 = 80.31% probability that there will be at least one defective fuse.

iii) 0.2759 = 27.59% probability that there will be exactly two defective fuses.

iv) 0.5443 = 54.43% probability that there will be at most one defective fuse.

Step-by-step explanation:

For each fuse, there are only two possible outcomes. Either it is defective, or it is not. The probability of a fuse being defective is independent of any other fuse, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

15% are defective.

This means that [tex]p = 0.15[/tex]

We also have:

[tex]n = 10[/tex]

(i) No defective fuse

This is [tex]P(X = 0)[/tex]. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{10,0}.(0.15)^{0}.(0.85)^{10} = 0.1969[/tex]

0.1969 = 19.69% probability that there will be no defective fuse.

(ii) At least one defective fuse

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

We already have P(X = 0) = 0.1969, so:

[tex]P(X \geq 1) = 1 - 0.1969 = 0.8031[/tex]

0.8031 = 80.31% probability that there will be at least one defective fuse.

(iii) Exactly two defective fuses

This is P(X = 2). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{10,2}.(0.15)^{2}.(0.85)^{8} = 0.2759[/tex]

0.2759 = 27.59% probability that there will be exactly two defective fuses.

(iv) At most one defective fuse

This is:

[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{10,0}.(0.15)^{0}.(0.85)^{10} = 0.1969[/tex]

[tex]P(X = 1) = C_{10,1}.(0.15)^{1}.(0.85)^{9} = 0.3474[/tex]

Then

[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.1969 + 0.3474 = 0.5443[/tex]

0.5443 = 54.43% probability that there will be at most one defective fuse.

16. Jorge plans to paint a bedroom wall that is shaped like a trapezoid. The bottom edge of the wall is 22.5 feet long, and the top edge of the wall is 9.5 feet long. If the wall is 8 feet tall, what is the area of the wall? Round your answer to the nearest hundredth if necessary.

Answers

Answer:

128 square feet

Step-by-step explanation:

length of the bottom edge of the wall (a) = 22.5 feet

length of the top edge of the wall (b) = 9.5 feet

height of the wall (h) = 8 feet

then

area of the wall = [(a + b)/2] * h

                         = [ (22.5 + 9.5)/2] * 8 square feet

                          = (32/2) * 8 square feet

                          = 16 * 8 square feet

                          = 128 square feet

order the group of quadratic functions from widest to narrowest graph

Answers

Answer:

"The coefficient with the largest absolute value is the most narrow graph."

y = ⅓x² → widest

y = -½x²

y = -9x² → narrowest

Instructions: State what additional information is required in order
to know that the triangles in the image below are congruent for the
reason given
Reasory. HL Postulate

Answers

Answer:

TU ≅ CB

Step-by-step explanation:

HL Postulates that when a leg and the hypotenuse of a right triangle are congruent to a corresponding leg and hypotenuse of another, then both right triangles are congruent.

Both right triangles shown in the diagram above is indicated to possess corresponding lengths of a leg, that is side UV ≅ side BA

We need an additional information that shows that the hypotenuse, TU, of ∆TUV is congruent to the hypotenuse, CB of ∆CBA.

Therefore, additional information needed is TU ≅ CB

Hi please somebody help me with this equation with explanation thank you

Answers

Answer:

[tex]{ \tt{ \frac{1}{24} m - \frac{2}{3} = \frac{3}{4} }} \\ \\ { \tt{ \frac{1}{24} m = \frac{17}{12} }} \\ m = 34[/tex]

Step 1: Find a common denominator

---The common denominator here is 24. So, we need to transform all of the fractions to have a denominator of 24.

1/24m - 16/24 = 18/24

Step 2: Solve

1/24m - 16/24 = 18/24

1/24m = 34/24

m = 34/24 x 24/1

m = 34

Hope this helps!

The sum of the 3rd and 7th terms of an A.P. is 38, and the 9th term is 37. Find the A.P?​

Answers

Let a be the first term in the arithmetic progression. Then each successive term differs from a by a fixed number c, so that

• first term = a

• second term = a + c

• third term = (a + c) + c = a + 2c

• fourth term = (a + 2c) + c = a + 3c

and so on. In general, the n-th term in the AP is a + (n - 1) c.

The sum of the 3rd and 7th terms is 38, so that

(a + 2c) + (a + 6c) = 38

==>   2a + 8c = 38

==>   a + 4c = 19 … … … [1]

The 9th term is 37, so

a + 8c = 37 … … … [2]

Subtracting [1] from [2] eliminates a and lets you solve for c :

(a + 8c) - (a + 4c) = 37 - 19

4c = 18

c = 18/4 = 9/2

Solve for a using either equations [1] or [2] :

a + 8 (9/2) = 37

a + 36 = 37

a = 1

Then the n-th term in the AP is 1 + 9/2 (n - 1) or 9/2 n - 7/2, where n ≥ 1.

Which number produces an irrational number when added to 0.4

Answers

Answer:

0.31311311131111....

Step-by-step explanation:

We need to tell a number which when adds to 0.4 makes it a Irrational Number . We know that ,

Rational number :- The number in the form of p/q where p and q are integers and q is not equal to zero is called a Rational number .

Irrational number :- Non terminating and non repeating decimals are called irrational number .

Recall the property that :-

Property :- Sum of a Rational Number and a Irrational number is Irrational .

So basically here we can add any Irrational number to 0.4 to make it Irrational . One Irrational number is ,

[tex] \rm\implies Irrational\ Number = 0.31311311131111... [/tex]

So when we add this to 0.4 , the result will be Irrational . That is ,

[tex] \rm\implies 0.4 + 0.31311311131111 ... = 0.731311311131111 .. [/tex]

The answer is gonna be 0.3

Use the figure to find y.

Answers

Tanθ =sin /cos

tan θ = 5/2 / y

tan (30°) = 5/2 /y

[tex]y = \frac{5 \sqrt{3} }{2} [/tex]

y=4.33

a new extended-life light bulb has an average service life of 700 hours, with a standard deviation of 50 hours. if the service life of these light bulbs approximates a normal distribution, about what percent of the distribution will be between 600 hours and 900 hours

Answers

Answer:

Hence the distribution will be between 600 hours and 900 hours is 74.9%.

Step-by-step explanation:

the angle between two lines is 60 degree. if the slope of one of them is 1. find the slope of other line​

Answers

Answer:

-3.73

Step-by-step explanation:

solution:

Given:

Angle between two lines=60⁰

slope of first line=1

Or, tanA=1

Or, A= tan inverse (1)

so, A=45⁰

so, angle of inclination of first line=45⁰

Now,

angle of inclination of second line= A+ 60⁰

= 45⁰+60⁰

=105⁰

so, slope of second line = tan105.

= -3.73

Help me! Thanks! Show work too! Please!

Answers

Answer:

(2, 79) (12, 24)

24-79/12-2=-55/10

m=-0.55

24=-6,6+b

30.6=b

y=-0.55x+30.6

Step-by-step explanation:

you multiply

using the equation to represent your answer

PLEASE HELP

Identify the 15th term of the arithmetic sequence in which a. = 10 and ao = 20.

Answers

Answer:

The 15th term is 160

Step-by-step explanation:

The details are not clear. So, I will make the following assumptions

[tex]d = 10[/tex] ---- common difference

[tex]a_1 = 20[/tex] ---- first term

Required

The 15th term

This is calculated as:

[tex]a_{n} = a + (n - 1) * d[/tex]

Substitute 15 for n

[tex]a_{15} = a + (15 - 1) * d[/tex]

[tex]a_{15} = a + 14 * d[/tex]

Substitute values for d and a

[tex]a_{15} = 20 + 14 * 10[/tex]

[tex]a_{15} = 20 + 140[/tex]

[tex]a_{15} = 160[/tex]

15. What is the solution to k+(-12) = 42? (1 point)
k=-54
k=-30
k= 30
k=54

Answers

Answer:

k = 54

Step-by-step explanation:

k + (-12) = 42

Remove parenthesis and addition sign

k - 12 = 42

Add 12 to both sides

K = 54

[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]

k+(-12)=42

k-12=42

k=42+12

k=54

According to the WHO MONICA Project the mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg (Kuulasmaa, Hense & Tolonen, 1998). Assume that blood pressure is normally distributed.
a.) State the random variable.
b.) Find the probability that a person in China has blood pressure of 135 mmHg or more.
c.) Find the probability that a person in China has blood pressure of 141 mmHg or less.
d.) Find the probability that a person in China has blood pressure between 120 and 125 mmHg.
e.) Is it unusual for a person in China to have a blood pressure of 135 mmHg? Why or why not?
f.) What blood pressure do 90% of all people in China have less than?

Answers

Answer:

a) Mean blood pressure for people in China, which has mean 128 and standard deviation 23.

b) 0.3821 = 38.21% probability that a person in China has blood pressure of 135 mmHg or more.

c) 0.714 = 71.4% probability that a person in China has blood pressure of 141 mmHg or less.

d) 0.0851 = 8.51% probability that a person in China has blood pressure between 120 and 125 mmHg.

e) Since |Z| = 0.3 < 2, it is not unusual for a person in China to have a blood pressure of 135 mmHg.

f) 90% of all people in China have a blood pressure of less than 157.44 mmHg.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg

This means that [tex]\mu = 128, \sigma = 23[/tex]

a.) State the random variable.

Mean blood pressure for people in China, which has mean 128 and standard deviation 23.

b.) Find the probability that a person in China has blood pressure of 135 mmHg or more.

This is 1 subtracted by the p-value of Z when X = 135, so:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{135 - 128}{23}[/tex]

[tex]Z = 0.3[/tex]

[tex]Z = 0.3[/tex] has a p-value of 0.6179.

1 - 0.6179 = 0.3821

0.3821 = 38.21% probability that a person in China has blood pressure of 135 mmHg or more.

c.) Find the probability that a person in China has blood pressure of 141 mmHg or less.

This is the p-value of Z when X = 141, so:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{141 - 128}{23}[/tex]

[tex]Z = 0.565[/tex]

[tex]Z = 0.565[/tex] has a p-value of 0.7140.

0.714 = 71.4% probability that a person in China has blood pressure of 141 mmHg or less.

d.) Find the probability that a person in China has blood pressure between 120 and 125 mmHg.

This is the p-value of Z when X = 125 subtracted by the p-value of Z when X = 120, so:

X = 125

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{125 - 128}{23}[/tex]

[tex]Z = -0.13[/tex]

[tex]Z = -0.13[/tex] has a p-value of 0.4483.

X = 120

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{120 - 128}{23}[/tex]

[tex]Z = -0.35[/tex]

[tex]Z = -0.35[/tex] has a p-value of 0.3632.

0.4483 - 0.3632 = 0.0851

0.0851 = 8.51% probability that a person in China has blood pressure between 120 and 125 mmHg.

e.) Is it unusual for a person in China to have a blood pressure of 135 mmHg? Why or why not?

From item b, when X = 135, Z = 0.3.

Since |Z| = 0.3 < 2, it is not unusual for a person in China to have a blood pressure of 135 mmHg.

f.) What blood pressure do 90% of all people in China have less than?

The 90th percentile, which is X when Z has a p-value of 0.9, so X when Z = 1.28.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.28 = \frac{X - 128}{23}[/tex]

[tex]X - 128 = 1.28*23[/tex]

[tex]X = 157.44[/tex]

90% of all people in China have a blood pressure of less than 157.44 mmHg.

4 The equation of a curve is y= (3-20)^3 + 24.
(a) Find an expression for dy/dx.​

Answers

g tau .......................

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