Mikita is painting a spherical model of a human cell for a science fair. She uses 452.16 square inches of paint to evenly cover the outside of the cell with one coat of paint. What is the diameter of the cell model? (Use 3.14 for the value of π.)

6 in.
12 in.
24 in.
36 in.

Answer:

0.3736

Step-by-step explanation:

46.7 percent of  [tex]\frac{4}{5}[/tex] is 0.3736.

To find 46.7% of [tex]\frac{4}{5}[/tex].

So,

[tex]\frac{46.7}{100}[/tex] × [tex]\frac{4}{5}[/tex]

[tex]\frac{0.467}{100}[/tex] × [tex]\frac{4}{5}[/tex]

⇒ [tex]0.3736[/tex]

Therefore,  46.7% of  [tex]\frac{4}{5}[/tex] is 0.3736.

Know more about percentages here:

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Answer:

Step-by-step explanation:

(2x - 5)° + 45° = 180°

2x - 5 + 45 = 180

x = 70

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

Step-by-step explanation:

When x = 0,

3x + 7

= 3 ( 0 ) + 7

= 0 + 7

= 7

When x = 4,

3x + 7

= 3 ( 4 ) + 7

= 12 + 7

= 19

When x = 8,

3x + 7

= 3 ( 8 ) + 7

= 24 + 7

= 31

When x = 14,

3x + 14

= 3 ( 14 ) + 14

= 14 ( 3 + 1 )

= 14 ( 4 )

= 56

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

Tanθ =sin /cos

tan θ = 5/2 / y

tan (30°) = 5/2 /y

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

y=4.33

Answer:

Question 16

(a) x < 1 : the values of x are smaller than than 1 (e.g. possible values are 0, -1, -2, etc) and since the circle is not shaded it means that 1 isn't a possible value of x

(b) x [tex]\geq[/tex] -2 : the circle is filled therefore -2 is included in the answer

Question 17

(a) unfilled dot above -2 and arrow pointing to the left

(b) shaded circle above 4 with and arrow pointing to the right →

Answer: C

<BFE is 148 degrees

Step-by-step explanation:

We have angles <BFC (57 degrees) and <CFD (34 degrees), but what is <DFE?

1. The angle symbol in the vertexes shows that <BFC is congruent to <DFE, meaning that they are the same

2. Knowing this, we can safely say that <DFE is equal to 57 degrees because <BFC is also 57 degrees.

3. Now, we have all the angles we need to find out <BFE.

4. <BFC+<CFD+<DFE=<BFE

5. Substitute to get

57+34+57=<BFE

91+57=<BFE

148=<BFE

6. Now we know that the answer is 148 degrees.

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:

  arithmetic; common difference of 5

Step-by-step explanation:

It usually works well to check differences first. Here, they are ...

  8 -3 = 5

  13 -8 = 5

These are the same value, so the sequence is arithmetic with a common difference of 5.

Answer:

Range y≤-1

Domain all reals

Step-by-step explanation:

The range is the output values (y)

Y is less than or equal to -1

y≤-1

The domain is the values that the input can take

the arrows on the ends of the graph tells us x can take all real numbers

The range is the span of y-values. What is the smallest possible y-value and what is the largest possible y-value?

For this problem, the y-values start at -1 and decrease infinitely. Therefore, the range is y <= -1.

The domain is the span of x-values. What is the smallest possible x-value and what is the largest possible x-value?

For this problem, the parabola will keep expanding horizontally (or to the left and right). Therefore, the range is all real numbers.

Hope this helps!

Answer:

Option C

Step-by-step explanation:

thankful that there are graphing tools. see screenshot

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

9514 1404 393

Answer:

  y = -9x +49

Step-by-step explanation:

The slope of line b is the same as the slope of line a. That can be found using the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (-1 -8)/(2 -1) = -9

The y-intercept can be found from the given point using the formula ...

  b = y - mx

  b = 13 -(-9)(4) = 13 +36 = 49

Then the slope-intercept equation of line b is ...

  y = -9x +49

Answer:

135

Step-by-step explanation:

Given that :

Total score obtained by Peter, Jan and Maxim = 269

Let :

Peter's score = x

Jan's score = y

Maxim's score = z

x + y + z = 269

x > (y + z)

For x to be greater Than y + z ;

Then x > (269 / 2) ; x > 134.5

The least possible x score is 135

Hence, Peter's least possible score is 135.

Answer:

f(-1) = 2-3(-1) +1

= 7

f(-3)= 2-3(-3)+1

= 12

f(-1) = -1-1

= -2

f(-3) = -3-1

= -4

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]

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:

0.055 = 5.5% probability that exactly 5 employees were over 50.

Step-by-step explanation:

The employees are dismissed from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[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]

In this question:

Total of 7 + 18 = 25 employees, which means that [tex]N = 25[/tex]

7 over 50, which means that [tex]k = 7[/tex]

10 were dismissed, which means that [tex]n = 10[/tex]

What is the probability that exactly 5 employees were over 50?

This is P(X = 5). So

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 5) = h(5,25,10,7) = \frac{C_{7,5}*C_{18,5}}{C_{25,10}} = 0.055[/tex]

0.055 = 5.5% probability that exactly 5 employees were over 50.

Answer:

[tex]\pi[/tex]

Step-by-step explanation:

1. 2/2 =1 1 is the radius

2. [tex]A = \pi r^2[/tex]

3. [tex]A=\pi 1^2[/tex]

4. [tex]A=\pi[/tex]

Answer:

Step-by-step explanation:

The focus lies above the vertex, so the parabola opens upwards.

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.

Answer:

The speed of the plane is 150 miles per hour, while the speed of the car is 50 miles per hour.

Step-by-step explanation:

Since a plane can fly 450 miles in the same time it takes a car to go 150 miles, if the car travels 100 mph slower than the plane, to find the speed (in mph) of the plane the following calculation must be performed:

450 to 150 is equal to 3: 1, that is, the plane travels three times the distance of the car.

Therefore, since 100/2 x 3 equals 150, the speed of the plane is 150 miles per hour, while the speed of the car is 50 miles per hour.

Answer:

C, 6

Step-by-step explanation:

31-13 is 18, 18/3 is 6.

Answer:

6

Step-by-step explanation:

31-13= 18

18÷3 = 6

Answer from Gauthmath

Answer:

8 minuets

Step-by-step explanation:

24min/3miles = 8

Answer:

8 minutes.

Step-by-step explanation:

If we divide 24 minutes by 3 miles, your answer will be 8 minutes.

Answer:

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

Answer:

Always. Always.

Step-by-step explanation:

All circles conform to the same equations such as using pie to calculate circumference. Unlike a rectangle, for example, all ratios used in a circle are the same.