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Answer:

23

Step-by-step explanation:

since the number is relatively prime to the product of the first 20 positive numbers

It number must not have factor of (1-20)

Therefore the smallest possible number is the next prime after 20

Answer is 23

The smallest positive integer that is greater than 1 and relatively prime to the product of the first 20 positive integers is,

⇒ 23

The highest number that divides exactly into two more numbers, is called  Greatest common factors.

Since, The number is relatively prime to the product of the first 20 positive numbers means a number which must not have factor of (1 - 20).

Hence, The smallest possible number is the next prime after 20 is, 23

Therefore, The smallest positive integer that is greater than 1 and relatively prime to the product of the first 20 positive integers is,

⇒ 23

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Complete question is;

A researcher studying public opinion of proposed Social Security changes and asks a random sample of 30 adult Americans whether or not they support the proposed changes. To say that the distribution of the sample proportion of adults who respond​ yes, is approximately​ normal, how many adult Americans does the researcher need to sample in the following​ cases

(a) if 37​% of all adult Americans support the changes?

(b) 25% of all adults Americans support the changes?

Answer:

A) 13 adults

B) 23 adults

Step-by-step explanation:

A) We are given;

p = 37% = 0.37

Since we are told that this is an approximately normal distribution, we will use the formula;

np(1 - p) ≥ 10

Thus;

0.37n(1 - 0.37) ≥ 10

n ≥ 10/(0.63 × 0.37)

n ≥ 42.9

We need a whole number, thus n = 43

From the question, we have already 30 adults , so the required number of adults are; 43 - 30 = 13 adults

B) We are given;

p = 25% = 0.25

Since we are told that this is an approximately normal distribution, we will use the formula;

np(1 - p) ≥ 10

Thus;

0.25n(1 - 0.25) ≥ 10

n ≥ 10/(0.75 × 0.25)

n ≥ 53.33

n ≈ 53

From the question, we have already 30 adults , so the required number of adults are; 53 - 30 = 23 adults

Answer:

θ ≈ 40°

Step-by-step explanation:

Since, sinθ = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

cosθ = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

tanθ = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

In the picture attached,

Measures of adjacent side and opposite side of the triangle have been given. Therefore, tangent rule will be applied in the given triangle.

tanθ = [tex]\frac{19}{23}[/tex]

θ = [tex]\text{tan}^{-1}(\frac{19}{23})[/tex]

θ = 39.56

θ ≈ 40°

Answer:

251 inches

Step-by-step explanation:

c = 2πr

c = 2(3.14)(5) = 31.4

31.4 x 8 rev. = 251 inches

Answer:

8*4*3=96 boxes in total

Step-by-step explanation:

I think. I just multiplies the 3 numbers. Hope this helps (:

Answer:

8*4*3=96 boxes in total

Step-by-step explanation:

I just multiplies the 3 numbers.

Answer: a) a 90% confidence interval for the proportion of dog owners who take more pictures of their dog than of their significant others or friends is (0.656,0.704).

b) a 95% confidence interval for the proportion of dog owners who are more likely to complain to their dog than to a friend is (0.459,0.521).

Step-by-step explanation:

Confidence interval for a population proportion is given by:-

[tex]\hat{p}\pm z(\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}})[/tex]

, where [tex]\hat{p}[/tex] = sample proportion , n= sample size, z= critical z-value.

As per given,

a) n=1000

Sample proportion of dog owners say they take more pictures of their dog than of their significant others or friends =[tex]\hat{p}=\dfrac{680}{1000}=0.68[/tex]

critical value for 90% confidence = 1.645  [By table]

A 90% confidence interval for the proportion of dog owners who take more pictures of their dog than of their significant others or friends.

[tex]0.68\pm (1.645)\sqrt{\dfrac{0.68(1-0.68)}{1000}}\\\\\approx0.68\pm0.024=(0.68-0.024,0.68+0.024)=(0.656,0.704)[/tex]

Hence, a 90% confidence interval for the proportion of dog owners who take more pictures of their dog than of their significant others or friends is (0.656,0.704).

b) Sample proportion of dog owners say they are more likely to complain to their dog than to a friend =[tex]\hat{p}=\dfrac{490}{1000}=0.49[/tex]

critical value for 95% confidence = 1.96  [By table]

A 95% confidence interval for the proportion of dog owners who are more likely to complain to their dog than to a friend:

[tex]0.49\pm (1.96)\sqrt{\dfrac{0.49(1-0.49)}{1000}}\\\\\approx0.49\pm0.031=(0.49-0.031,0.49+0.031)=(0.459,0.521)[/tex]

Hence, a 95% confidence interval for the proportion of dog owners who are more likely to complain to their dog than to a friend is (0.459,0.521).

Answer:  C

Step-by-step explanation:

h · k(x) = 2(3x - 5)(-2x + 1)

           = (6x - 10)(-2x + 1)

           = -12x² + 6x + 20x - 10

           = -12x² + 26x - 10

Answer:

C

Step-by-step explanation:

h(x) × k(x)

= 2(3x - 5)(- 2x + 1) ← expand factors using FOIL

= 2(- 6x² + 3x + 10x - 5)

= 2(- 6x² + 13x - 5) ← distribute parenthesis by 2

= - 12x² + 26x - 10 → C

Answer:

[tex]B'(x,y) = (0,-2)[/tex]

Step-by-step explanation:

Given

The attached grid

Translation rule: [tex](x,y) = (x + 5, y - 2)[/tex]

Required

Determine the coordinates of B'

First, we have to write out the coordinates of B

[tex]B(x,y) = (-5,0)[/tex]

Next is to apply the translation rule [tex](x,y) = (x + 5, y - 2)[/tex]

[tex]B(x,y) = (-5,0)[/tex] becomes

[tex]B'(x,y) = B(x+5,y-2)[/tex]

Substitute -5 for x and 0 for y

[tex]B'(x,y) = (-5+5,0-2)[/tex]

[tex]B'(x,y) = (0,-2)[/tex]

Answer:

  52/3.

Step-by-step explanation:

There are (54·53)/2 = 1431 ways the 2 jokers can be placed in the 54-card deck. We can consider those to see how the number of cards between them might work out.

Suppose we let J represent a joker, and - represent any other card. The numbers of interest can be found as follows:

For jokers: JJ---... there are 0 cards between. This will be the case also for ...

  -JJ---...

  --JJ---...

and so on, down to ...

 ...---JJ

The first of these adjacent jokers can be in any of 53 positions. So, the probability of 0 cards between is 53/1431.

__

For jokers: J-J---..., there is 1 card between. The first of these jokers can be in any of 52 positions, so the probability of 1 card between is 52/1431.

__

Continuing in like fashion, we find the probability of n cards between is (53-n)/1431. So, the expected number of cards between is ...

  [tex]E(n)=\sum\limits_{n=0}^{53}{\dfrac{n(53-n)}{1431}}=\dfrac{53}{1431}\sum\limits_{n=0}^{53}{n}-\dfrac{1}{1431}\sum\limits_{n=0}^{53}{n^2}\\\\=\dfrac{53(53\cdot 54)}{1431(2)}-\dfrac{1(53)(54)(107)}{1431(6)}=53-\dfrac{107}{3}\\\\\boxed{E(n)=\dfrac{52}{3}}[/tex]

Answer:

30 cm

Step-by-step explanation:

1 inch is 2.54 centimeters, and 2.54 times 12 is 30.48, which would be the closest.

The following metric units of measure is 30 cm

The correct option is (A)

Measurement” is the act of determining a target's size, length, weight, capacity, or other aspect.

Step 1: Write the conversion as a fraction.

Step 2: Multiply or divide, as required.

Step 3: Cancel the units (same units from top and bottom)

Step 4: Write the simplified answer with its correct unit.

Now, as we know that

1 inch = 2.54 cm

So, we can write

12 inch = 2.54 * 12

12 inch= 30.48 cm

Hence, the closest unit is  30 cm in the given metric system.

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Answer: Binomial distribution

Step-by-step explanation:

The binomial appropriation is a likelihood circulation that sums up the probability that a worth will take one of two free qualities under a given arrangement of boundaries or suspicions. The hidden suspicions of the binomial dispersion are that there is just a single result for every preliminary, that every preliminary has a similar likelihood of achievement, and that every preliminary is totally unrelated, or autonomous of one another.

Answer:

a=11/5 OR 5.5

Step-by-step explanation:

Answer:

I think it is [tex]\frac{6x-18}{x^{4} }[/tex]

Step-by-step explanation:

Answer:

x = 80

y = 130

Step-by-step explanation:

The 2 angles are supplementary. so, x-30 + x+50 = 180.

We solve and get 2x = 180-20

x = 80

y = x+50, because of parallel rules.

y = 130

Answer:

x = 80

y = 130

Step-by-step explanation:edge 2020

Answer:

x=2

Step-by-step explanation:

12-10=2

Answer:

x=2

Step-by-step explanation:

10=12-x

Subtract 12 from each side

10-12 = 12-12-x

-2 =-x

Multiply by -1

2 = x

Answer:

b. [tex]g(x)=f(x)-5[/tex]

Step-by-step explanation:

You have that the function f(x) has its y-intercept for y=3.

Furthermore, you have that g(x) is a transformation of f(x) with y-intercept for y=-2.

In this case you have that f(x) has been translated vertically downward.

The general way to translate a function vertically in the coordinate system is:

[tex]g(x)=f(x)+a[/tex]      (1)

being a positive or negative.

if g(x) has its y-intercept for y=-2, and the y-intercept of f(x) is for y=3, then the value of a in the equation (1) must be a = -5, which is the difference between both y-intercepts, in fact:

a = -2 -3 = -5

Then, the answer is:

b. [tex]g(x)=f(x)-5[/tex]

Answer: g(x) = f(x) - 5

Step-by-step explanation:

just took this

Answer: y > 2x + 1

Step-by-step explanation:

In the graph first, we can see two things:

The line is not solid (so the values in the line are not included), and the shaded part is above, so we will be using the symbol:

y > f(x)

Now, in the line we can see that when x = 0, y = 1.

So the linear equation must be something like:

f(x) = a*x + 1

The only one that has an y-intercept equal to 1 is y > 2x + 1

Answer:

C or y>2x +1

Step-by-step explanation:

edge

ok its 45.15% trust me

Answer:

Step-by-step explanation:

This curve alone does  not give exact percentages with the exception of P(z=0) = .50 or 50%

A Pictorial where 'some' of the % have been added for helps more...  

However, most often one needs to use a table, calculator, or an Excel function ect to find exact Percentage,

P(x > 4000) = P(z = 0) =  .50  or 50 % |using above pictorial

Using Calculator etc:  Here, am using the Excel NORMSDIST function to find the Percentages:

P(z=3/5 - z=-3/5) =  .7257 - .2742 =.4515 or 45.15%

Answer:

Well all even numbers between 0 and 8 are,

2, 4, 6, 8

Meaning if the button is pressed 4 times 2, 4, 6, or 8 will be outputted.

When press button 4 times. Then output of the program will be,  [tex](2,4,6,2)[/tex]

Any number that can be exactly divided by 2 is called as an even number.

Given that, When a button is pressed, a computer program outputs a random even number greater than 0 less than 8.

Even numbers greater than 0 less than 8 are,

                             [tex]=2,4,6[/tex]

When press button 4 times. Then output of the program will be,

                     [tex]=(2,4,6,2)[/tex]

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Answer:

Proper: 15/4

Improper: 3 3/4

Step-by-step explanation:

Well to solve the following question,

5/12 + (5/12 + 3/4)

We solve the part in the parenthesis first,

5/12 + 3/4 = 14/4

Simplified -> 7/2

5/12 + 7/2

= 45/12

Simplified -> 15/4

Thus,

the answer is 15/4 or 3 3/4.

Hope this helps :)

Answer:

Step-by-step explanation:

[tex]\frac{5}{12}+\left(\frac{5}{12}+\frac{3}{4}\right)\\\\=\frac{5}{12}+\frac{5}{12}+\frac{3}{4}\\\\\mathrm{Add\:similar\:elements:}\:\frac{5}{12}+\frac{5}{12}=2\times \frac{5}{12}\\=2\times \frac{5}{12}+\frac{3}{4}\\\\=\frac{5\times \:2}{12}\\\\=\frac{10}{12}\\\\=\frac{10}{12}\\\\=\frac{5}{6}+\frac{3}{4}\\L.C.M =12\\\mathrm{Adjust\:Fractions\:based\:on\:the\:LCM}\\\\\frac{5}{6}=\frac{5\cdot \:2}{6\times \:2}=\frac{10}{12}\\\\\frac{3}{4}=\frac{3\times \:3}{4\times \:3}=\frac{9}{12}\\[/tex]

[tex]\\=\frac{10}{12}+\frac{9}{12}\\\mathrm{Since\:the\:denominators\:are\:equal\\\:combine\:the\:fractions}:\\\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\\\=\frac{10+9}{12}\\\\=\frac{19}{12}[/tex]

Answer:

The answer is below

Step-by-step explanation:

Twenty-five blood samples were selected by taking every seventh blood sample from racks holding 187 blood samples from the morning draw at a medical center. The white blood count (WBC) was measured using a Coulter Counter Model S. The mean WBC was 8.636 with a standard deviation of 3.9265. (a) Construct a 90% confidence interval for the true mean using the FPCF. (Round your answers to 4 decimal places.) The 90% confidence interval is from to

Answer:

Given:

Mean (μ) = 8.636, standard deviation (σ) = 3.9265, Confidence (C) = 90% = 0.9, sample size (n) = 25

α = 1 - C = 1 - 0.9 = 0.1

α/2 = 0.1/2 = 0.05

From the normal distribution table, The z score of α/2 (0.05) corresponds to the z score of 0.45 (0.5 - 0.05) which is 1.645

The margin of error (E) is given by:

[tex]E=z_{\frac{\alpha}{2} }*\frac{\sigma}{\sqrt{n} }\\ \\E=1.645*\frac{3.9265}{\sqrt{25} }=1.2918[/tex]

The confidence interval = μ ± E = 8.636 ± 1.2918 = (7.3442, 9.9278)

The 90% confidence interval is from 7.3442 to 9.9278

Answer:

A. Eric rode 2 more miles per week than Kim rode

Step-by-step explanation:

Number of miles Kim rode bicycle in 9 weeks = 135 miles

Let x be the number of miles per week.

135miles => 9 weeks

x miles => 1 week

[tex] x = \frac{135}{9} [/tex]

[tex] x = 15 [/tex]

Kim rode the bicycle 15 miles per week

Number of miles Eric rode bicycle in 6 weeks = 102 miles

Let x be the number of miles per week Eric rides the bicycle.

102 miles => 6 weeks

x miles => 1 week

[tex] x = \frac{102}{6} [/tex]

[tex] x = 17 [/tex]

Kim rode the bicycle 17 miles per week

Comparing the number of miles per week they rode, we would conclude that: "Eric rode 2 more miles per week than Kim rode".

Answer:

8n6

step by step explanation.

Answer:

[tex]n = 0.949[/tex]. The waist-to-hip ratio indicates that length of her waist circumference is equal to the 94.9 % of length of her hip circumference.

Step-by-step explanation:

The waist-to-hip ratio of Rachel is:

[tex]n = \frac{37\,in}{39\,in}[/tex]

[tex]n = \frac{37}{39}[/tex]

[tex]n = 0.949[/tex]

The waist-to-hip ratio indicates that length of her waist circumference is equal to the 94.9 % of length of her hip circumference.

The length of her waist circumference is 94.9% the length of her hip circumference.

From the information given, Rachel's waist circumference is 37 inches and her hip circumference is 39 inches.

Therefore, her waist to hip ratio will be calculated thus:

n = 37/39

n = 0.949

This implies that the length of her waist circumference is 94.9% the length of her hip circumference.

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Answer:

Her eye discourses; I will answer it.

I am too bold; ’tis not to me she speaks:

Two of the fairest stars in all the heaven,

Having some business, do entreat her eyes

To twinkle in their spheres till they return.

Step-by-step explanation:

Answer:

95% confidensce interval of the mean (two-tail) =  [132.2, 139.2]

Step-by-step explanation:

Given:

N = size of sample = 61

m = sample mean = 135.7

s = sample standard deviation 13.7

Need 95% confidence interval

Solution.

alpha (95% confidence interval) = 0.05

(1-alpha/2) = 0.975   [two sided]

Equation for confidence interval of the mean

= m +/- t(1-alpha/2,N-1) * s / sqrt(N)

= 135.7 +/- 2.0003 * 13.7 / sqrt(60)

= [132.16, 139.24]

Answer: C y>3x+1

Step-by-step explanation:

From all the given options , only C contains inequality with '>' sign .

Hence, y>3x+1 is the inequality has a dashed boundary line when graphed.

hence, the correct option is C.

Answer:

9 is the answer

Step-by-step explanation:

got a delivery of 60ib...but dont have enough .thats why he or she sells 29..totally he or she have 38ib of carrots ...so when we subtract 38_29

its =9

Answer:

n = 13

Step-by-step explanation:

24 = 3 (n-5)

3n  - 15 = 24

3n = 24 +15

3n = 39

n = 39/3

n = 13

Answer:

[tex]\boxed{\sf n=13}[/tex]

Step-by-step explanation:

[tex]\sf 24=3(n-5)[/tex]

[tex]\sf Expand \ brackets.[/tex]

[tex]\sf 24=3n-15[/tex]

[tex]\sf Add \ 15 \ to \ both \ sides.[/tex]

[tex]\sf 24+15=3n-15+15[/tex]

[tex]\sf 39=3n[/tex]

[tex]\sf Divide \ both \ sides \ by \ 3.[/tex]

[tex]\sf \frac{39}{3} =\frac{3n}{3}[/tex]

[tex]\sf 13=n[/tex]