In a random sample of 964 young adults aged 18-29, it was found that 196 of them were married. Construct a 99% confidence interval for the proportion of married young adults aged 18-29.

Answer:

  62.3538

Step-by-step explanation:

There is nothing to solve. If you need a decimal value, you can use a calculator or table of square roots.

Answer:

x=2

Step-by-step explanation:

5(2x - 3) = 5

Divide by 5

5/5(2x - 3) = 5/5

2x-3 = 1

Add 3 to each side

2x-3 +3 = 1+3

2x = 4

Divide by 2

2x/2 = 4/2

x =2

Answer:

x = 2

Step-by-step explain:

5(2x-3) = 5

Divide both sides by 5

2x-3 = 1

Add 3 to both sides

2x = 4

Divide both sides by 2

x = 2

Answer:

[tex]17.5-1.796\frac{3.61}{\sqrt{12}}=15.63[/tex]    

[tex]17.5+1.796\frac{3.61}{\sqrt{12}}=19.37[/tex]    

Step-by-step explanation:

Data given

20 13 21 18 19 22 19 15 12 12 18 21

We can calculate the sample mean and deviation with the following formulas:

[tex]\bar X =\frac{\sum_{i=1}^n X_i}{n}[/tex]

[tex]s= \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]

And we got:

[tex]\bar X = 17.5[/tex] represent the sample mean

[tex]\mu[/tex] population mean (variable of interest)

s=3.61 represent the sample standard deviation

n=12 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

The degrees of freedom are given by:

[tex]df=n-1=12-1=11[/tex]

Since the Confidence is 0.90 or 90%, the significance is [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], the critical value would be given by [tex]t_{\alpha/2}=[/tex]

Now we have everything in order to replace into formula (1):

[tex]17.5-1.796\frac{3.61}{\sqrt{12}}=15.63[/tex]    

[tex]17.5+1.796\frac{3.61}{\sqrt{12}}=19.37[/tex]    

Answer:

3c - 7

Step-by-step explanation:

c - the number of miles Lawrence biked

Tammy biked seven less than three times the number of miles that Lawrence biked.

So, 3 x c (the # of miles Lawrence biked) - 7 (she biked seven less)

The answer is 3c - 7.

Answer:

The probability that he requires 18 shots is 0.04785

Step-by-step explanation:

To answer this, we shall be using the negative binomial distribution

From the question;

P = 0.25 , r = 6

q will be 1-p = 1-0.25 = 0.75 Which is the probability of missing a target on any trial

P(X = 18) = (18-1)C(6-1) (0.25)^6 (0.75)^(18-6)

P(X = 28) = 17C5 (0.25)^6 (0.75)^12) = 0.04785

Answer:

29.4

Step-by-step explanation:

Answer:

2.94

Step-by-step explanation:

4.2 × 0.7 = 2.94

Answer:

Q1 is: 2.2 percent per minute

Q2 is: 35 minutes

Step-by-step explanation:

For the first question, take 89 percent, and subtract 23 from it, then divide by 30 minutes for the rate per minute.

For the second question take 23 percent, find out how much is left until 100 percent (77 percent) and use the rate from the last question (2.2 percent per minute), to find out how much time charging 77 percent takes. (You get 35 by using: 77 divided by 2.2)

Answer:

Step-by-step explanation:

Let's solve this by eliminating z, then we'll go from there.

Add 6 times the second equation to the first.

  (3x -3y +6z) +6(x +2y -z) = (3) +6(4)

  9x +9y = 27 . . . simplify

  x + y = 3 . . . . . . divide by 9 [eq4]

Add 13 times the second equation to the third.

  (5x -8y +13z) +13(x +2y -z) = (2) +13(4)

  18x +18y = 54

  x + y = 3 . . . . . . divide by 18 [eq5]

Equations [eq4] and [eq5] are identical. This tells us the system is dependent, and has an infinite number of solutions. We can find them in terms of z:

  y = 3 -x . . . . solve eq5 for y

  x +2(3 -x) -z = 4 . . . . substitute into the second equation

  -x +6 -z = 4

  x = 2 - z . . . . . . add x-4

  y = 3 -(2 -z)

  y = z +1

So far, we have written the solutions in terms of z. If we use the parameter "a", we can write the solutions as ...

  x = 2 -a

  y = 1 +a

  z = a

_____

Check

First equation:

  3(2-a) -3(a+1) +6a = 3

  6 -3a -3a -3 +6a = 3 . . . true

Second equation:

  (2-a) +2(a+1) -a = 4

  2 -a +2a +2 -a = 4 . . . true

Third equation:

  5(2-a) -8(a+1) +13a = 2

  10 -5a -8a -8 +13a = 2 . . . true

Our solution checks algebraically.

Answer:

A

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (1, 0) , thus

y = a(x - 1)² + 0

To find a substitute the coordinates of the y- intercept (0, 1) into the equation

1 = a(- 1)² = a , thus

a = 1

y = (x - 1)² → A

Considering it's y-intercept and vertex, the equation of the parabola is given by:

[tex]y = (x - 1)^2[/tex]

The equation of a quadratic function, of vertex (h,k), is given by:

[tex]y = a(x - h)^2 + k[/tex]

In which a is the leading coefficient.

In this problem, the vertex is (1,0), hence h = 1, k = 0 and:

[tex]y = a(x - 1)^2[/tex]

The y-intercept is of 1, hence, when x = 0, y = 1, so:

[tex]y = a(x - 1)^2[/tex]

[tex]1 = a(0 - 1)^2[/tex]

[tex]a = 1[/tex]

Hence, the equation is:

[tex]y = (x - 1)^2[/tex]

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Answer:

[tex]\boxed{\sf \ \ \ -\dfrac{15}{104} \ \ \ }[/tex]

Step-by-step explanation:

hello,

first of all let's assume that r is different from 0 as this is not allowed to divide by 0

[tex]\dfrac{1}{13r}=\dfrac{-8}{15}[/tex]

multiply by 13r it comes

[tex]\dfrac{13r}{13r}=1=\dfrac{-8*13r}{15}[/tex]

now multiply by 15

[tex]-8*13r=15\\<=> r = \dfrac{-15}{8*13}=-\dfrac{15}{104}[/tex]

hope this helps

Answer:[tex]r=-\frac{104}{15}[/tex] or -6.93333....

Step-by-step explanation:

[tex]\mathrm{Multiply\:both\:sides\:by\:}13[/tex]

[tex]13\cdot \frac{1}{13}r=13\left(-\frac{8}{15}\right)[/tex]    =-104/15

simplify

[tex]r=-\frac{104}{15}[/tex]

MARK BRAINLIEST PLEASE

Answer:

D(4,-3)

Step-by-step explanation:

Given three of the vertices of the square: A(4, -7), B(8, -7),C(8, -3)

Let the coordinate of the fourth vertex be D(x,y).

We know that diagonals of a square are perpendicular bisector. So, the midpoint of both diagonals is the same.

The diagonals are BD and AC

Midpoint of BD = Midpoint of AC

[tex]\left(\dfrac{8+x}{2},\dfrac{-7+y}{2}\right) =\left(\dfrac{4+8}{2},\dfrac{-7+(-3)}{2}\right)\\ \left(\dfrac{8+x}{2},\dfrac{y-7}{2}\right) =\left(\dfrac{12}{2},\dfrac{-10}{2}\right)\\ \left(\dfrac{8+x}{2},\dfrac{y-7}{2}\right) =\left(6,-5\right)\\$Therefore$:\\\dfrac{8+x}{2}=6\\8+x=12\\x=12-8\\x=4\\$Similarly$\\\dfrac{y-7}{2}=-5\\y-7=-5*2\\y-7=-10\\y=-10+7=-3[/tex]

The coordinates of the fourth vertex is D(4,-3)

Answer:

(4,-3)

Step-by-step explanation:

Answer:

Z = -2.054 and Z = 2.054

Step-by-step explanation:

Z-score:

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Middle 96%

The normal distribution is symmetric, so:

From the: 50 - (96/2) = 2nd percentile

To the: 50 + (96/2) = 98th percentile

2nd percentile:

Z with a pvalue of 0.02. So Z = -2.054.

98th percentile:

Z with a pvalue of 0.98. So Z = 2.054.

Z = -2.054 and Z = 2.054

Answer:

Step-by-step explanation:

For private Institutions,

n = 20

Mean, x1 = (43120 + 28190 + 34490 + 20893 + 42984 + 34750 + 44897 + 32198 + 18432 + 33981 + 29498 + 31980 + 22764 + 54190 + 37756 + 30129 + 33980 + 47909 + 32200 + 38120)/20 = 34623.05

Standard deviation = √(summation(x - mean)²/n

Summation(x - mean)² = (43120 - 34623.05)^2+ (28190 - 34623.05)^2 + (34490 - 34623.05)^2 + (20893 - 34623.05)^2 + (42984 - 34623.05)^2 + (34750 - 34623.05)^2 + (44897 - 34623.05)^2 + (32198 - 34623.05)^2 + (18432 - 34623.05)^2 + (33981 - 34623.05)^2 + (29498 - 34623.05)^2 + (31980 - 34623.05)^2 + (22764 - 34623.05)^2 + (54190 - 34623.05)^2 + (37756 - 34623.05)^2 + (30129 - 34623.05)^2 + (33980 - 34623.05)^2 + (47909 - 34623.05)^2 + (32200 - 34623.05)^2 + (38120 - 34623.05)^2 = 1527829234.95

Standard deviation = √(1527829234.95/20

s1 = 8740.22

For public Institutions,

n = 20

Mean, x2 = (25469 + 19450 + 18347 + 28560 + 32592 + 21871 + 24120 + 27450 + 29100 + 21870 + 22650 + 29143 + 25379 + 23450 + 23871 + 28745 + 30120 + 21190 + 21540 + 26346)/20 = 25063.15

Summation(x - mean)² = (25469 - 25063.15)^2+ (19450 - 25063.15)^2 + (18347 - 25063.15)^2 + (28560 - 25063.15)^2 + (32592 - 25063.15)^2 + (21871 - 25063.15)^2 + (24120 - 25063.15)^2 + (27450 - 25063.15)^2 + (29100 - 25063.15)^2 + (21870 - 25063.15)^2 + (22650 - 25063.15)^2 + (29143 - 25063.15)^2 + (25379 - 25063.15)^2 + (23450 - 25063.15)^2 + (23871 - 25063.15)^2 + (28745 - 25063.15)^2 + (30120 - 25063.15)^2 + (21190 - 25063.15)^2 + (21540 - 25063.15)^2 + (26346 - 25063.15)^2 = 1527829234.95

Standard deviation = √(283738188.55/20

s2 = 3766.55

This is a test of 2 independent groups. Let μ1 be the mean out-of-state tuition for private institutions and μ2 be the mean out-of-state tuition for public institutions.

The random variable is μ1 - μ2 = difference in the mean out-of-state tuition for private institutions and the mean out-of-state tuition for public institutions.

We would set up the hypothesis. The correct option is

-B. H0: μ1 = μ2 ; H1: μ1 > μ2

Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(x1 - x2)/√(s1²/n1 + s2²/n2)

t = (34623.05 - 25063.15)/√(8740.22²/20 + 3766.55²/20)

t = 9559.9/2128.12528473889

t = 4.49

The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [8740.22²/20 + 3766.55²/20]²/[(1/20 - 1)(8740.22²/20)² + (1/20 - 1)(3766.55²/20)²] = 20511091253953.727/794331719568.7114

df = 26

We would determine the probability value from the t test calculator. It becomes

p value = 0.000065

Since alpha, 0.01 > than the p value, 0.000065, then we would reject the null hypothesis. Therefore, at 1% significance level, the mean out-of-state tuition for private institutions is statistically significantly higher than public institutions.

Answer:

Step-by-step explanation:

A) The constant of proportionality in terms of minutes per bracelet is

15/3 = 5 minutes per bracelet

B) The constant of proportionality represents man hour rate

C) let k = constant of proportionality, t = time in minutes and b = number of bracelets produced. Therefore,

t = kb

D) the constant of proportionality in terms of number of bracelets per minute is

3/15 = 1/5

E) The constant of proportionality represents production rate

F) let k = constant of proportionality, t = time in minutes and b = number of bracelets produced. Therefore,

b = kt

G) The constants of proportionality are reciprocals

H) Two equations are equivalent if they have the same solution. They are not equivalent. By inputting the different values of k, the solutions will always be the same. Therefore, they are equivalent.

Answer:the sample answers, change them up so you dont get in trouble

A To find the constant of proportionality in minutes per bracelet, divide the total time by the number of bracelets:

constant of proportionality=15 MINUTES/3 BRACELETS=5  minutes per bracelet.

B The proportionality constant of 5 minutes per bracelet means it takes Olivia 5 minutes to make 1 bracelet.

C Here’s one way to set up the equation:

time = constant of proportionality × number of bracelets

Let m be time in minutes and let b be the number of bracelets. Substitute the variables (m and b) and the value of the proportionality constant (5 minutes per bracelet) into the equation: m = 5b.

thats all ik srry

Step-by-step explanation:

Answer:

See below under "explanation".

General Formulas and Concepts:

Algebra I

Functions

Average Rate of Change Formula:
[tex]\displaystyle \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}[/tex]

Step-by-step explanation:

*Note:

The function is unclear, so I will provide 2 possible answers.

Step 1: Define

Identify given.

[tex]\displaystyle \begin{aligned}1. \ f(x) & = \sqrt{x} + 4 \\2. \ f(x) & = \sqrt{x + 4} \\\end{aligned}[/tex]

[tex]\displaystyle \text{Interval: } 2 \leq x \leq 6[/tex]

Step 2: Find Average Rate of Change

For the 1st function:

[tex]\displaystyle\begin{aligned}\text{Average Rate of Change} & = \frac{\big( \sqrt{b} + 4 \big) - \big( \sqrt{a} + 4 \big)}{b - a} \\& = \frac{\big( \sqrt{6} + 4 \big) - \big( \sqrt{2} + 4 \big)}{6 - 2} \\& = \frac{\sqrt{6} - \sqrt{2}}{4} \\& = 0.258819 \\& \approx \boxed{0.26} \\\end{aligned}[/tex]

∴ the average rate of change, if using the 1st defined function, will be approximately 0.26.

For the 2nd function:

[tex]\displaystyle\begin{aligned}\text{Average Rate of Change} & = \frac{\sqrt{b + 4} - \sqrt{a + 4} }{b - a} \\& = \frac{\sqrt{6 + 4} - \sqrt{2 + 4}}{6 - 2} \\& = \frac{\sqrt{10} - \sqrt{6}}{4} \\& = 0.178197 \\& \approx \boxed{0.18} \\\end{aligned}[/tex]

∴ the average rate of change, if using the 2nd defined function, will be approximately 0.18.

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Topic: Algebra I

Answer:

The time period is 13 years.

Step-by-step explanation:

Interest rate (r )= 5% or 5%/12 = 0.42% per months

The investment amount (Present value) = $10500

Final expected amount (future value) = $20000

Since we have given the initial amount and final amount. Therefore we have to calculate the time period for which the initial amount is kept in the bank.

Use the below formula to find the time period.

Future value = present value (1 + r )^n

20000 = 10500(1+0.0042)^n

1.9047619 = (1+0.0042)^n

1.9047619 = 1.0042^n

n = 153.74 months.

Time in years = 153.74 / 12 = 12.8 years or 13 years (round off)

Answer:

1140 ways.

Step-by-step explanation:

The applicable formula is: (n +r - 1)C(r-1), where n is the number of identical items (the candies), and r is the possible number of recipients (the kids).

The 17 identical candies, can be distributed among the 4 children in :  

=(17 + 4 - 1)C(4–1) = 20C3 ways.

= 20!/((20–3)!*3!) ways.

= 20*19*18*17!/(17!*(3*2*1)) = 20*19*18/6 ways

= 20*19*3 ways.  

=1140 ways.

Answer:

5

Step-by-step explanation:

(14 × 5 × 4) ÷ (28 × 2)

Solve brackets.

280 ÷ 56

Divide.

= 5

Answer:

Step-by-step explanation:

Using Secant-Secant theorem we can find the value of x.

The product of one segment and its external segment is equal to the product of the other segment and its external segment.

5 × 3 = x × 4

15 = 4x

15/4 = x

3.75 = x

Hey there! :)

Answer:

56 m².

Step-by-step explanation:

To find the area, simply split the figure into a triangle and rectangle. Solve for the areas separately:

Solve for the rectangle: (A = l × w)

A = 8 × 5

A = 40 m²

Solve for the triangle: (A = 1/2 (bh))

A = 1/2(4 · 8)

A = 1/2(32)

A = 16 m².

Add up the two areas:

40 + 16 = 56 m².

Answer:

Area of triangle+ the area of rectangle

Step-by-step explanation:

Since, area of triangle is 1/2×base×height in right angled triangle, 1/2×4×8: 1/2×32= 16m²

Area of rectangle is length × breadth= 5×8: 40 m²

Area of the shape is 40m²+16m²= 56m²

Answer:

$-4.90.

Step-by-step explanation:

Fathi has $1.10. Each sheet costs him $0.25. He wants to print 47 pages.

If he prints double sided, then he will use 47 / 2 = 23.5 sheets of paper. But he can't print a half-sheet, so he will use 24 sheets of paper.

Each sheet costs $0.25. 0.25 * 24 = 6. The printing will cost him $6.

Since he only has $1.10, his remaining balance will be 1.1 - 6 = -4.9. The balance on his printing account will be $-4.90.

Hope this helps!

Answer:

-1.90

Step-by-step explanation:

Khan Academy

I got it right for sure

Answer:

1. The 99% confidence interval is from 941.527 to 958.473

2. The 99% confidence interval is from 933.054 to 966.946

3. The 99% confidence interval is from 916.108 to 983.892

Step-by-step explanation:

The confidence interval is given by

[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\[/tex]

Where [tex]\bar{x}[/tex] is the sample mean and Margin of error is given by

[tex]$ MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $ \\\\[/tex]

Where n is the sample size,

s is the sample standard deviation,

[tex]t_{\alpha/2[/tex] is the t-score corresponding to some confidence level

The t-score corresponding to 99% confidence level is

Significance level = α = 1 - 0.99 = 0.01/2 = 0.005

Degree of freedom = n - 1 = 13 - 1 = 12

From the t-table at α = 0.005 and DoF = 12

t-score = 3.055

1. 99% Confidence Interval when s = 10

The margin of error is

[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{10}{\sqrt{13} } \\\\MoE = 3.055\cdot 2.7735\\\\MoE = 8.473\\\\[/tex]

So the required 99% confidence interval is

[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 8.473\\\\\text {confidence interval} = 950 - 8.473, \: 950 + 8.473\\\\\text {confidence interval} = (941.527, \: 958.473)\\\\[/tex]

The 99% confidence interval is from 941.527 to 958.473

2. 99% Confidence Interval when s = 20

The margin of error is

[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{20}{\sqrt{13} } \\\\MoE = 3.055\cdot 5.547\\\\MoE = 16.946\\\\[/tex]

So the required 99% confidence interval is

[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 16.946\\\\\text {confidence interval} = 950 - 16.946, \: 950 + 16.946\\\\\text {confidence interval} = (933.054, \: 966.946)\\\\[/tex]

The 99% confidence interval is from 933.054 to 966.946

3. 99% Confidence Interval when s = 40

The margin of error is

[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{40}{\sqrt{13} } \\\\MoE = 3.055\cdot 11.094\\\\MoE = 33.892\\\\[/tex]

So the required 99% confidence interval is

[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 33.892\\\\\text {confidence interval} = 950 - 33.892, \: 950 + 33.892\\\\\text {confidence interval} = (916.108, \: 983.892)\\\\[/tex]

The 99% confidence interval is from 916.108 to 983.892

As the sample standard deviation increases, the range of confidence interval also increases.

Answer:

1 + 6v

Step-by-step explanation:

1+5v+v​

Combine like terms

1 + 6v

Answer:

6v + 1

Step-by-step explanation:

1 + 5v + v

Apply rule : a = 1a

1 + 5v + 1v

Combine like terms.

5v + 1v + 1

(5 + 1)v + 1

(6)v + 1

6v + 1

Answer:

y=x-1

Step-by-step explanation:

since the slope is just one up and one over and it's positive it would just be x

and since the intercept is just -1 it would be y=x-1

Answer:

here,

a=b+12

b=a-12----> equation (i)

b= c+4

putting the value of b from the equation (I)

a-12=c+4

a=c+4+12

a=c+16

hope this helps...

Good luck on your assignment...

The value of a + c is 16.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

a=b+12

So, b=a-12 ---- equation (i)

and, b= c+4

Substitute the value of b from the equation (I)

a-12=c+4

a=c+4+12

a=c+16

Hence, the value of a+ c is 16.

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Answer:

jc is 40 i think

Step-by-step explanation:

Answer:

40(Maybe)

Step-by-step explanation:

I'm not 100% sure that 40 is correct but I'm pretty sure it is.

Answer:

Step-by-step explanation:

Ron needs to lose 35 kgs in order to be 105 kgs. 35000 grams equals 35 kgs. Divide 35000 by 500 and you get 70 weeks.

To double check it, 500 grams equals 0.5 kgs. 0.5*70=35. This equation represents weight lost per week*time=total weight loss.

The explaination might not be the best but I hope it helped you:)

Answer:

a) 294

b) 180

c) 75

d) 174

e) 105

Step-by-step explanation:

I assume that for each problem, the first digit can't be 0.

a) There are 6 digits that can be first, 7 digits that can be second, and 7 digits that can be third.

6×7×7 = 294

b) This time, no digit can be used twice, so there are 6 digits that can be first, 6 digits that can be second, and 5 digits that can be third.

6×6×5 = 180

c) Again, each digit can only be used once, but this time, the last digit must be odd.

If only the last digit is odd, there are 3×3×3 = 27 possible numbers.

If the first and last digits are odd, there are 3×4×2 = 24 possible numbers.

If the second and last digits are odd, there are 3×3×2 = 18 possible numbers.

If all three digits are odd, there are 3×2×1 = 6 possible numbers.

The total is 27 + 24 + 18 + 6 = 75.

d) If the first digit is 3, and the second digit is 3, there are 1×1×6 = 6 possible numbers.

If the first digit is 3, and the second digit is greater than 3, there are 1×3×7 = 21 possible numbers.

If the first digit is greater than 3, there are 3×7×7 = 147 numbers.

The total is 6 + 21 + 147 = 174.

e) If the first digit is 3, and the second digit is greater than 3, then there are 1×3×5 = 15 possible numbers.

If the second digit is greater than 3, there are 3×6×5 = 90 possible numbers.

The total is 15 + 90 = 105.

Answer:

[tex]32.9-2.365\frac{4.9}{\sqrt{8}}=28.80[/tex]    

[tex]32.9+2.365\frac{4.9}{\sqrt{8}}=37.00[/tex]    

Step-by-step explanation:

Information given

[tex]\bar X=32.9[/tex] represent the sample mean for the sample  

[tex]\mu[/tex] population mean (variable of interest)

s=4.9 represent the sample standard deviation

n=8 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

the degrees of freedom are given by:

[tex]df=n-1=8-1=7[/tex]

Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and the critical value for this cae would be [tex]t_{\alpha/2}=2.365[/tex]

Now we have everything in order to replace into formula (1):

[tex]32.9-2.365\frac{4.9}{\sqrt{8}}=28.80[/tex]    

[tex]32.9+2.365\frac{4.9}{\sqrt{8}}=37.00[/tex]    

Answer:

Option B

Step-by-step explanation:

Again, another great question! Here we are given the following system of equations, bound by quadrant 1 -

[tex]\begin{bmatrix}2x+7y\le \:70\\ 8x+4y\le \:136\end{bmatrix}[/tex]

Convert this to slope - intercept form -

[tex]\begin{bmatrix}y\le \frac{70-2x}{7}\\ y\le \:2\left(-x+17\right)\end{bmatrix}[/tex]

Now the graphed solution of this intersects at a shaded region with which there are 3 important point that lie on the border. They are the following -

( 0, 10 ),

( 15, 9 ),

( 17, 0 )

When these point are plugged into the main function f ( x, y ) = 2x + 6y, the point ( 15, 9 ) results in the greatest solution of 84. Thus, it is our maximum point -

Option B