The perimeter of an equilateral triangle with a side length of 12 units is:

Answer:

Problem 1: We conclude that less than or equal to 50% of adult Americans without a high school diploma are worried about having enough saved for retirement.

Problem 2: We conclude that the volume of Google stock has changed.

Step-by-step explanation:

Problem 1:

We are given that in a recent survey conducted by Pew Research, it was found that 156 of 295 adult Americans without a high school diploma were worried about having enough saved for retirement.

Let p = proportion of adult Americans without a high school diploma who are worried about having enough saved for retirement

So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 50%    {means that less than or equal to 50% of adult Americans without a high school diploma are worried about having enough saved for retirement}

Alternate Hypothesis, [tex]H_A[/tex] : p > 50%     {means that a majority of adult Americans without a high school diploma are worried about having enough saved for retirement}

This is a right-tailed test.

The test statistics that would be used here is One-sample z-test for proportions;

                       T.S.  =  [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of adult Americans who were worried about having enough saved for retirement = [tex]\frac{156}{295}[/tex] = 0.53

           n = sample of adult Americans = 295

So, the test statistics =  [tex]\frac{0.53-0.50}{\sqrt{\frac{0.50(1-0.50)}{295} } }[/tex]

                                    =  1.03

The value of z-test statistics is 1.03.

Also, the P-value of the test statistics is given by;

              P-value = P(Z > 1.03) = 1 - P(Z [tex]\leq[/tex] 1.03)

                           = 1 - 0.8485 = 0.1515

Now, at a 0.05 level of significance, the z table gives a critical value of 1.645 for the right-tailed test.

Since the value of our test statistics is less than the critical value of z as 1.03 < 1.645, so we insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that less than or equal to 50% of adult Americans without a high school diploma are worried about having enough saved for retirement.

Problem 2:

We are given that a random sample of 35 trading days in 2014 resulted in a  sample mean of 3.28 million shares with a standard deviation of 1.68 million shares.

Let [tex]\mu[/tex] = mean daily volume in Google stock

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 5.44 million shares    {means that the volume of Google stock has not changed}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 5.44 million shares     {means that the volume of Google stock has changed}

This is a two-tailed test.

The test statistics that would be used here is One-sample t-test statistics because we don't know about the population standard deviation;

                       T.S.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean volume in Google stock = 3.28 million shares

            s = sample standard deviation = 1.68 million shares

           n = sample of trading days = 35

So, the test statistics =  [tex]\frac{3.28-5.44}{\frac{1.68}{\sqrt{35} } }[/tex]  ~ [tex]t_3_4[/tex]

                                    =  -7.606

The value of t-test statistics is -7.606.

Also, the P-value of the test statistics is given by;

              P-value = P([tex]t_3_4[/tex] < -7.606) = Less than 0.05%

Now, at a 0.05 level of significance, the t table gives a critical value of -2.032 and 2.032 at 34 degrees of freedom for the two-tailed test.

Since the value of our test statistics doesn't lie within the range of critical values of t, so we sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the volume of Google stock has changed.

Answer:

a)the proportion of student is 0.1082

b)

H1: p = .08

H2: p not equal to 0.08

H1: p =0 .08

H2: p < .08

H1: p =0 .08

H2: p >0 .08

c)z=1.45

d) the p value is 0.1470

e)null hypothesis cannot be accepted,There is no enough evidence to reject the  null hypothesis.

Step-by-step explanation:

CHECK THE ATTACHMENT FOR DETAILED EXPLANATION

Answer:

Largest integer in the interval [−∞, 31] is 31.

Step-by-step explanation:

Given the interval: [−∞, 31]

To find: The largest integer in this interval.

Solution:

First of all, let us learn about the representation of intervals.

Two kind of brackets can be used to represent the intervals. i.e. () and [].

Round bracket means not included in the interval and square bracket means included in the interval.

Also, any combination can also be used.

Let us discuss one by one.

1. [p, q] It means the interval contains the values between p and q. Furthermore, p and q are also included in the interval.

Smallest p

Largest q

2. (p, q) It means the interval contains the values between p and q. Furthermore, p and q are not included in the interval.

Smallest value just greater than p.

Largest value just smaller than q.

3. [p, q) It means the interval contains the values between p and q. Furthermore, p is included in the interval but q is not included in the interval.

Smallest value p.

Largest value just smaller than q.

4. (p, q] It means the interval contains the values between p and q. Furthermore, p is not included in the interval but q is included in the interval.

Smallest value just greater than p.

Largest value q.

As per above explanation, we can clearly observe that:

The largest integer which belongs to the following interval: [−∞, 31] is 31.

Answer:

the solutions to the inequality ys-x+1 are shaded on the graph. which point is B. (3 ,-2)

Answer:

Step-by-step explanation:

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have

[tex](-3;\ -8)\to x_1=-3;\ y_1=-8\\(4;\ 6)\to x_2=4;\ y_2=6[/tex]

Substitute:

[tex]m=\dfrac{6-(-8)}{4-(-3)}=\dfrac{6+8}{4+3}=\dfrac{14}{7}=2[/tex]

The formula for the slope m of the line that passes through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is the following:

[tex]m=\dfrac{y_1-y_2}{x_1-x_2}[/tex]

We have points (4,6) and (-3,-8). Let's plug these values into the formula for slope:

[tex]m=\dfrac{6-(-8)}{4-(-3)}[/tex]

[tex]=\dfrac{14}{7}=2[/tex]

The slope of the line passing through the two points is 2. Let me know if you need any clarifications, thanks!

Answer:

Step-by-step explanation:

Hello!

Miguel has four chips, two have the number "1", one has the number "3" and the other has the number "5"

If the experiment is "choosing two chips and looking at their numbers" there are the following possible outcomes:

S= {(1,1)(1,3)(1,5)(3,1)(5,1)(3,5)(5,3)}

The sample space for the experiment has 7 possible combinations.

a)

Be X: the amount of money Miguel will receive or owe.

If two chips with the same number are chosen he will receive $2

If the chips have different number he will owe $1

Looking at the possible outcomes listed above, out of the 7, in only one he will select the same number (1,1)

So the probability of him receiving $2 will be 1/7

Now out of the 7 possible outcomes, 6 will make Miguel owe $1, so you can calculate its probability as: 6/7

  xi  | $2 | -$1

P(xi) | 1/7 | 6/7

b)

To calculate the expected value or mean you have to use the following formula:

[tex]\frac{}{X}[/tex]= ∑[xi*P(xi)]= (2*1/7)(-1*6/7)= -4/7= $-0.57

c)

The expected value is $-0.57, meaning that Miguel can expect to owe $0.57 at the end of the game.

d)

To make the game fair you have to increase the probability of obtaining two chips with the same number. Any probability close to 50% will make the game easier. For example if you change the experiment so that for earning $2 the probability is 4/7 and for owing $1 the probability is 3/7, the expected earnings will be:

(2*4/7)+(-1*3/7)= $0.71

I hope this helps!

Answer:

3 is not a solution

Step-by-step explanation:

6x – 7 = 12?

Substitute 3 in for x and see if the equation is true

6*3 - 7 = 12

18-7 = 12

11 =12

This is false so 3 is not a solution

Explanation:

1. CS ≅ HR, ∠CHS ≅ ∠HCR, ∠CSH ≅ ∠HRC — given

2. ∆CRH ~ ∆HSC — AA similarity theorem

3. ∠SCH ≅ ∠RHC — corresponding angles of similar triangles are congruent

4. CH ≅ HC — reflexive property of congruence

5. ∆CRH ≅ ∆HSC — SAS congruence theorem

6. CR ≅ HS — CPCTC

Answer:

B

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos54° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{39}{AB}[/tex] ( multiply both sides by AB )

AB × cos54° = 39 ( divide both sides by cos54° )

AB = [tex]\frac{39}{cos54}[/tex] ≈ 66.35 → B

Answer: 0.476

Step-by-step explanation:

Let A = Event of choosing an even number ball.

B = Event of choosing an 8 .

Given, A lottery game has balls numbered 1 through 21.

Sample space: S= {1,2,3,4,5,6,7,8,...., 21}

n(S) = 21

Then, A= {2,4,6,8, 10,...(20)}

i.e. n(A)= 10

B= {8}

n(B) = 1

A∪B = {2,4,6,8, 10,...(20)} = A

n(A∪B)=10

Now, the probability of selecting an even numbered ball or an 8 is

[tex]P(A\cup B)=\dfrac{n(A\cup B)}{n(S)}[/tex]

[tex]=\dfrac{10}{21}\approx0.476[/tex]

Hence, the required probability =0.476

Answer:

Part A- 6

Part B- 3

Part C- 3/22100

Step-by-step explanation:

Part A-

Use the permutation formula and plug in 3 for n and 2 for k.

nPr=n!/(n-k)!

3P2=3!/(3-2)!

Simplify.

3P2=3!/1!

3P2=6

Part B-

Use the combination formula and plug in 3 for n and 2 for k.

nCk=n!/k!(n-k)!

3C2=3!/2!(3-2)!

Simplify.

3C2=3!/2!(1!)

3C2=3

Part C-

It is given that the total number of three-card hands that can be dealt from a deck of 52 cards is 22100. Use the fact that the probability of something equals the total successful outcomes over the sample space. In this case the total successful outcomes is 3 and the sample space is 22100.

I believe the answer is 3/22100

I honestly suck at probability but I tried my best.

Answer:

3.54%

Step-by-step explanation:

This question represents a binomial distribution. A binomial distribution is given by:

[tex]P(x)=\frac{n!}{(n-x)!x!} p^xq^{n-x}[/tex]

Where n is the total number of trials, p is the probability of success, q is the probability of failure and x is the number of success.

Given that:

A basketball player scores 70% of his shots on average, therefore p = 70% = 0.7. Also q = 1 - p = 1 - 0.7 = 0.3.

The total number of trials (n) = 20 shots

The probability that he scores at least 18 successful shots tonight if he gets 20 shots = P(x = 18) + P(x = 19) + P(x = 20)

P(x = 18) = [tex]\frac{20!}{(20-18)!18!}*0.7^{18}*0.3^{20-18}=0.0278[/tex]

P(x = 19) = [tex]\frac{20!}{(20-19)!19!}*0.7^{19}*0.3^{20-19}=0.0068[/tex]

P(x = 20) = [tex]\frac{20!}{(20-20)!20!}*0.7^{20}*0.3^{20-20}=0.0008[/tex]

The probability that he scores at least 18 successful shots tonight if he gets 20 shots = P(x = 18) + P(x = 19) + P(x = 20) = 0.0278 + 0.0068 + 0.0008 = 0.0354 = 3.54%

Answer:

84π mm^2

Step-by-step explanation:

formula for circumference is 2πr where r is the radius of circle

Given,The circumference of the base of a cylinder is 24π mm

Thus,

2πr= 24π mm

=> r = 24π mm/2π = 12 mm

________________________________________

A similar cylinder has a base with circumference of 60π mm.

radius for this cylinder will be

2πr= 60π mm

r =   60π mm/2π = 30mm

______________________________________________

Given

The lateral area of the larger cylinder is 210π mm2

lateral area of cylinder is given by  2πrl

where l is the length of cylinder

thus,

r for larger cylinder = 30mm

2π*30*l  = 210π mm^2

=> l = 210π mm^2/2π*30 = 3.5 mm

___________________________________________

the lateral area of the smaller cylinder

r = 12 mm

l = 3.5 mm as both larger and smaller cylinder are same

2πrl  =  2π*12*3.5 mm^2 = 84π mm^2 answer

Answer:

33.6pi mm2 is the correct answer

edge 2021

Step-by-step explanation:

The circumference of the base of a cylinder is 24π mm. A similar cylinder has a base with circumference of 60π mm. The lateral area of the larger cylinder is 210π mm2.

What is the lateral area of the smaller cylinder?

17.1π mm2

33.6π mm2

60π mm2

84π mm2

Answer:

D. 4 real roots and 0 complex roots

Step-by-step explanation:

If I assume that the function you are saying is

[tex]F(x)=x^4+x^3-5x^2+x-6[/tex]

There should be up to "4 roots," there can't be more or less than 4 total solutions. First, we need to check how many sign changes are there in this function. There are 3 positive real roots. Now lets check for negative roots.

[tex]F(-x)=x^4-x^3-5x^2-x-6[/tex]

There are is only 1 negative real root. Since we basically have 4 real roots, and the max is 4. There should be 4 real roots and 0 complex roots.

Answer:

15.9degrees

Step-by-step explanation:

in photo above

Answer:

[tex]\boxed{15.95\°}[/tex]

Step-by-step explanation:

The angle can be found by using trigonometric functions.

tan (θ) = [tex]\frac{opposite}{adjacent}[/tex]

tan (θ) = [tex]\frac{4}{14}[/tex]

θ = [tex]tan^{-1} \frac{4}{14}[/tex]

θ = 15.9453959

θ ≈ 15.95

Answer:

Volume: 112 m³.

Surface area: 172 m².

Step-by-step explanation:

The volume is the base times height times length. So, the volume will be 2 * 8 * 7 = 16 * 7 = 112 m³.

The surface area is 2lw + 2lh + 2wh. l = 8; w = 7; h = 2.

2(8)(7) + 2(8)(2) + 2(7)(2) = 2 * 56 + 2 * 16 + 2 * 14 = 112 + 32 + 28 = 112 + 60 = 172 m².

Hope this helps!

Answer:

the value of c is  20.155 such that 99% of all parcels are under the surcharge weight.

Step-by-step explanation:

Given that :

The mean value [tex]\mu[/tex] = 12

The standard deviation [tex]\sigma[/tex] = 3.5

Let Consider Q to be the weight of the parcel that is normally distributed .

Then;

Q [tex]\sim[/tex] Norm(12,3.5)

The objective is to determine thewight  value of c under which there is a surcharge

Also, let's not that 99% of all the parcels are below the surcharge

However ;

From the Percentiles table of Standard Normal Distribution;

At 99th percentile; the value for Z = 2.33

The formula for the Z-score is:

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

[tex]2.33 = \dfrac{X - 12}{3.5}[/tex]

2.33 × 3.5 = X - 12

8.155 = X - 12

- X = - 12 - 8.155

- X = -20.155

 X = 20.155

the weight  value of c under which there is a surcharge = X + 1 (0) since all the  pounds are below the surcharge

c = 20.155 + 1(0)

c = 20.155

Thus ; the value of c is  20.155 such that 99% of all parcels are under the surcharge weight.

Answer:16.1%

Step-by-step explanation:

Answer:

The investment needs the rate of growth to be approximately 16.1%.

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:C

Step-by-step explanation:

Pemdas

3+5(10)

5*10=50

3+50=53

Answer:

The answer is 15.6/31 or 1/2

Step-by-step explanation:

The data in the question is sufficient to find an answer for it.

1. I look at the temperature and rainfall chart for Brighton, United Kingdom.

2. Check for rainy season and dry season.

3. The rainy season lasts approximately 5 months while the dry season (which still has some rainfall) lasts approximately 7 months. All together, 12 months of the calendar year.

4. July happens to fall within the dry season. The temperature and rainfall statistics are observed.

The number of rainfall days is 15.6 and we know there are 31 days in July.

If the approximate number of days it rains in Brighton, in July, is 15.6 then the probability of rainfall in the month is 15.6/31 which is = 0.503 or 0.5

Therefore, there's a 50% chance of having rainfall in Brighton, on any day in the month of July.

In fraction, 0.5 = 1/2

Answer:

[tex]\boxed{Area\ of\ sector = 141.4\ cm^2}[/tex]

Step-by-step explanation:

Radius = r = 9 cm

Angle = θ = 200° = 3.5 radians

Now,

[tex]Area \ of \ sector = \frac{1}{2} r^2 \theta[/tex]

Area = 1/2 (9)²(3.5)

Area = 1/2 (81)(3.5)

Area = 282.7 / 2

Area of sector = 141.4 cm²

Answer:

45 pi cm^2 or 141.3 cm^2

Step-by-step explanation:

First find the area of the circle

A = pi r^2

A = pi (9)^2

A = 81 pi

A circle has 360 degrees

The shaded part has 200

The fraction that is shaded is

200/360 =5/9

Multiply by the total area

5/9 * 81 pi

45 pi

Using 3.14 for pi

141.3

45 pi cm^2 or 141.3 cm^2

Answer:

outside the circle i think

Step-by-step explanation:

Answer:

inside the circle

Step-by-step explanation:

Answer:

Rs. 32,000

Step-by-step explanation:

height = 4m

let length = x m

breadth = x/3 m

Area of the 4 walls = 2(length × height) + 2(breadth × height)

Area = 2(4×x) + 2(4 × x/3) = 8x + (8x)/3

Area = (32x)/3 m²

1 m² = Rs. 5

The cost for an area that is (32x)/3 m²=  (32x)/3  × 5 Rs.

The cost of plastering 4 walls at Rs.5 per m² = 640

(32x)/3  × 5  = 640

(160x)/3 = 640

x = length = 12

Area =  (32x)/3 m² = (32×12)/3 = 128m²

The cost of carpeting its floor at the rate of Rs. 250/m²:

= 128m² × Rs. 250/m² = 32,000

The cost of carpeting its floor at the rate of Rs. 250/m² = Rs. 32,000

Answer:

Barts total cost is (c)213.36

Step-by-step explanation:

First, you subtract 6% from $219

=204.92

add shipping,

+7.50

=213.36

Hope this helps <3

Answer:

C. $213.36

Step-by-step explanation:

The original price is $219 and the discount is 6% which is equal to $13.14

$219 - $13.14 + $7.50 (shipping cost) = $213.36

Answer:

A

Step-by-step explanation:

When subtracting 7 on the left of the equation, he also needs to subtract 7 from the right of the equation.

Step 2 should be:

⅓X +7 -7= 15 -7

What he is trying to do here by subtracting 7 is to move all the constants, that is numbers without any variables such as x, to one side of the equation.

⅓X= 8

X= 8 ×3

X= 24

Answer:

cars are dum

Step-by-step explanation:

Answer:

Perimeter= 40 units

Step-by-step explanation:

Ok

We are asked to look for the perimeter.

We have some clue given.

All at right angle and some sides are given it's full length.

We have the bae to be 11 unit

The height to be 7 unit.

What this mean is that taking either the base or the height should sum up to either 11 or 7 respectively.

Let's go for the other side of the height.

Let's take all the vertical height and sum it up to 7 because the right side is equal to 7.

So we have 7+7+11

But it's not complete yet.

We are given a dimension 2.

And the 2 is in two places so it's total 2*2= 4

The two is for a small base .

The base is actually an extra to the 11 of the other base.

So summing up

We have 2*11 + 2*7 + 2*2

Perimeter= 22+14+4

Perimeter= 40 units

Answer: Pi multiplied by the diameter of the circle

Step-by-step explanation:

Answer:

The formula for finding the circumference of a circle is [tex]C = 2\pi r[/tex]. You substitute the radius of the circle for [tex]r[/tex] and multiply it by [tex]2\pi[/tex].

Answer:

Probability of obtaining no more than two defective tubes = 0.816

Step-by-step explanation:

The Probability of obtaining no more than two defective tubes in a randomly selected sample of 15 tubes is obtained using the binomial distribution formula: nCr × p^r × q^(n -r).

Where n is number of samples;

r is maximum number of defective tubes, r ≤ 2;

p is probability of defective tubes = 10% or 0.1

q is probability of non-defective tubes, q = 1 - p

Further explanations and calculations are given in the attachment below: