Calculate the minimum number of subjects needed for a research study regarding the proportion of respondents who reported a history of diabetes using the following criteria:

95% confidence, within 5 percentage points, and a previous estimate is not known.

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.

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

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

[tex]\huge❥︎\underbrace\mathfrak\red {SoLuTiOn}✈︎[/tex]

1)

[tex] £7 \: of \: £20 \\ \\ \fbox{considering as x} \\ \\ x\%of \: 20 = 7 \\ \\ x\% = \frac{7}{20} \times 100 \\ \\ x\% = \frac{7}{ \cancel{20}} \times \cancel{ 100} \\ \\ x\% = 7 \times 5 \\ \\ x\% = 35\%[/tex]

2)

[tex]28 \: kg \: of \: 40 \: kg \\ \\ \fbox{considering as x} \\ \\ x\% 40 = 28 \\ \\ x\% = \frac{28}{40} \times 100 \\ \\ x\% = \cancel \frac{28}{4 \cancel0} \times 10 \cancel0 \\ \\ x\% = 7 \times 10 \\ \\ x\% = 70\%[/tex]

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

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.

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.

9514 1404 393

Answer:

  1750 = 2 · 5³ · 7

Step-by-step explanation:

It is often helpful to start with divisibility rules when finding prime factors of a small composite number.

The least-significant digit is even, so we know 2 is a factor.

  1750/2 = 875

The least significant digit is 5, so we know 5 is a factor.

  875/5 = 175

  175/5 = 35

  35/5 = 7

7 is a prime number, so we're done.

The factorization is ...

  1750 = 2 · 5³ · 7

Answer:

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

y = ⅓x² → widest

y = -½x²

y = -9x² → narrowest

Answer:

c. infinitely many solutions

General Formulas and Concepts:

Pre-Algebra

Distributive Properties

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

2(h - 8) - h = h - 16

Step 2: Solve for h

Hello from  MrBillDoesMath!

Answer:    c  (infinitely many solutions)

Steps:

1) Simplify  the original  equation

       2(h-8)- h= h - 16

2.As 2 (h-8) = 2h- 16,  the equation in 1) is equivalent to  

      (2h-16) -h  = h - 16

 or

      (2h-h) - 16 = h - 16

or

      h - 16 = h -16

which is true for all values of h.

Regards,  MrB

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

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

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

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

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.

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!

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]

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

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

Answer:

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

Step-by-step explanation:

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

Answer:

5.7

Step-by-step explanation:

sine cosine tangent

soh cah toa

sine = opposite/hypotenuse

so sin(35)= x/10

you can multiply 10 to both sides to get rid of the 10 denominator on the right leaving you with 10sin(35)=x

be sure your calculator is in degrees.

put that into a calculator leaving you with 5.7

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:

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.

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]

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.

Answer:

The 95% confidence interval for the true difference between the mean home prices in the two areas is (-$29156.52, $1956.52).

Step-by-step explanation:

Before building the confidence interval, 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.

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.

First area:

33 homes, mean of $168,300, standard deviation of $37,825. Thus:

[tex]\mu_1 = 168300[/tex]

[tex]s_1 = \frac{37825}{\sqrt{33}} = 6584.5[/tex]

Second area:

33 homes, mean of $181,900, standard deviation of $25,070. Thus:

[tex]\mu_2 = 1819000[/tex]

[tex]s_2 = \frac{25070}{\sqrt{32}} = 4431.8[/tex]

Distribution of the difference:

[tex]\mu = \mu_1 - \mu_2 = 168300 - 181900 = -13600[/tex]

[tex]s = \sqrt{s_1^2+s_2^2} = \sqt{6584.5^2 + 4431.8^2} = 7937[/tex]

Confidence interval:

[tex]\mu \pm zs[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].  

The lower bound of the interval is:

[tex]\mu - zs = -13600 - 1.96*7937 = -29156.52 [/tex]

The upper bound of the interval is:

[tex]\mu + zs = -13600 + 1.96*7937 = 1956.52[/tex]

The 95% confidence interval for the true difference between the mean home prices in the two areas is (-$29156.52, $1956.52).

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]