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Answer:

{58.02007 , 61.97993]

Step-by-step explanation:

Data are given in the question

Sample of cars = n = 121

Average speed = sample mean = 60

Standard deviation = sd = 11

And we assume

95% confidence t-score = 1.97993

Therefore

Confidence interval is

[tex]= [60 - \frac{1.97993 \times 11}{\sqrt{121} }] , [60 + \frac{1.97993 \times 11}{\sqrt{121} }][/tex]

=  {58.02007 , 61.97993]

Basically we applied the above formula to determine the confidence interval

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:

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.

Learn more about this units here:

https://brainly.com/question/19786378

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Answer:

Side length: 3 cm.

Surface area: 54 cm squared.

Step-by-step explanation:

The formula for a cube is the side length cubed, since the formula for a rectangular prism is length times width times height. Those three measurements are the same for a cube.

So, since the volume is 27 cm cubed, we can say that the side length of the cube is the cube root of 27 cm cubed, or 3 cm.

There are 6 sides on a cube, and every cube has the same area. Since the side length of the cube is 3 cm, the area of one side of the cube is 3 * 3 = 9 cm squared. 9 * 6 = 54 cm squared.

Hope this helps!

Answer:

8n6

step by step explanation.

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: 1020000

step-by-step explanation:

(7.8*10^5+(2.4*10^5)                                         given expression

(7.8*10^5)+(2.4*10^5)                                        group with parenthesis

(7.8+2.4)*10^5                                                   combine like terms

10.2*10^5                                                           preform addition

10.2*100000                                                     evaluate the exponent

1020000                                                           multiply out

Answer:

(4, -8).

Step-by-step explanation:

If point W were to be rotated 90 degrees, it would rotate 90 degrees clockwise. The current point of W is (-2, 4). After a 90 degree rotation about the origin, the point will be (4, 2).

y = -3 is a horizontal line where y = -3. The y-value of the newly rotated point is 2. That is five units above the line where y = -3. So, a reflection would result in a y-value of y = -3 - 5 = -8. The x-value does not change.

So, the coordinate of W' is (4, -8).

Hope this helps!

Answer:

a

  The null hypothesis is  

         [tex]H_o : \mu = 21[/tex]

The Alternative  hypothesis is  

           [tex]H_a : \mu< 21[/tex]

b

     [tex]\sigma_{\= x} = 0.8944[/tex]

c

   [tex]t = -2.236[/tex]

d

  Yes the  mean population is  significantly less than 21.

Step-by-step explanation:

From the question we are given

           a set of  data  

                               20  18  17  22  18

       The confidence level is 90%

       The  sample  size  is  n =  5  

Generally the mean of the sample  is  mathematically evaluated as

        [tex]\= x = \frac{20 + 18 + 17 + 22 + 18}{5}[/tex]

       [tex]\= x = 19[/tex]

The standard deviation is evaluated as

        [tex]\sigma = \sqrt{ \frac{\sum (x_i - \= x)^2}{n} }[/tex]

         [tex]\sigma = \sqrt{ \frac{ ( 20- 19 )^2 + ( 18- 19 )^2 +( 17- 19 )^2 +( 22- 19 )^2 +( 18- 19 )^2 }{5} }[/tex]

         [tex]\sigma = 2[/tex]

Now the confidence level is given as  90 %  hence the level of significance can be evaluated as

         [tex]\alpha = 100 - 90[/tex]

        [tex]\alpha = 10[/tex]%

         [tex]\alpha =0.10[/tex]

Now the null hypothesis is  

         [tex]H_o : \mu = 21[/tex]

the Alternative  hypothesis is  

           [tex]H_a : \mu< 21[/tex]

The  standard error of mean is mathematically evaluated as

         [tex]\sigma_{\= x} = \frac{\sigma}{ \sqrt{n} }[/tex]

substituting values

         [tex]\sigma_{\= x} = \frac{2}{ \sqrt{5 } }[/tex]

        [tex]\sigma_{\= x} = 0.8944[/tex]

The test statistic is  evaluated as  

              [tex]t = \frac{\= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]

substituting values

              [tex]t = \frac{ 19 - 21 }{ 0.8944 }[/tex]

              [tex]t = -2.236[/tex]

The  critical value of the level of significance is  obtained from the critical value table for z values as  

                   [tex]z_{0.10} = 1.28[/tex]

Looking at the obtained value we see that [tex]z_{0.10}[/tex] is greater than the test statistics value so the null hypothesis is rejected

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:

Step-by-step explanation:

To decipher how many eggs you have left, we must read the statement well.

I have 5 eggs if I break 2 eggs it is to cook them and when they are cooked they will be eaten, so we simply do the following:

5 -2= 3

Now you only have 3 eggs left.

Step-by-step explanation:

Given:

5 eggs

Required:

Number of eggs after breaking, cooking and eating 2.

Solution:

I won't count the eggs as 6.

Broken=cooked=eaten=2

5-2=3

Hope it helps ;) ❤❤❤

Answer:

y = 60 *x

Step-by-step explanation:

The rate is 180 miles / 3 hours = 60 miles per hour

Check by dividing 300 miles / 5 hours = 60 miles per hour

y = 60 *x  where y is miles and x = time

Answer:

Step-by-step explanation:

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]

Learn more about the even numbers here:

https://brainly.com/question/581879

Answer:

1. 55 degrees, 2. 316 degrees

Step-by-step explanation:

When it shows interior angles on a triangle it adds up to 180 degrees

When it shows exterior angles on a triangle it adds up to 360 degrees

1. ? = 55 degrees

85 + 40 = 125

180 - 125 = 55

2. ? = 316 degrees

Inside of triangle:

14 + 30 = 44

180 - 44 = 136 degrees

Exterior of triangle:

360 - 14 = 346 degrees

360 - 30 = 330 degrees

360 - 44 = 316 degrees

Answer:

linear

Step-by-step explanation:

Answer:

Positive is 1

Negative is-1

Step-by-step explanation:

Answer:

1) [tex](a+ib)(a-ib)[/tex]

2) [tex]a^2+i^2b[/tex]

Step-by-step explanation:

1) [tex]a^2+b^2[/tex]

=> [tex]a^2 - (-1)b^2[/tex]      (We know that -1 = [tex]i^2[/tex] )

=> [tex]a^2-i^2b^2[/tex]

=> [tex](a)^2-(ib)^2[/tex]

Using Formula [tex]a^2 -b^2 = (a+b)(a-b)[/tex]

=> [tex](a+ib)(a-ib)[/tex]

2) [tex]a^2-b[/tex]

=> [tex]a^2+(-1)b[/tex]      (We know that -1 = [tex]i^2[/tex] )

=> [tex]a^2+i^2b[/tex]  (It cannot be simplified further)

Answer:

[tex]\boxed{(a+ib)(a-ib)}[/tex]

[tex]\boxed{a^2+i^2b}[/tex]

Step-by-step explanation:

[tex]a^2 + b^2[/tex]

Rewrite expression.

[tex]a^2- (-1)b^2[/tex]

Use identity :  [tex]-1=i^2[/tex]

[tex]a^2- i^2 b^2[/tex]

Factor out square.

[tex]a^2-(ib)^2[/tex]

Apply difference of two squares formula : [tex]a^2-b^2 =(a+b)(a-b)[/tex]

[tex](a+ib)(a-ib)[/tex]

[tex]a^2-b[/tex]

Rewrite expression.

[tex]a^2+(-1)b[/tex]

Use identity :  [tex]-1=i^2[/tex]

[tex]a^2+i^2b[/tex]

Answer:

x=1

y=1

Step-by-step explanation:

Please look at the image below for solutions⬇️

Answer:

Step-by-step explanation:

Add the equations in order to solve for the first variable . Plug this value into the equations in order to solve for the remaining variables.

Point form

(x, 2-x)

Answer:

7.81

Step-by-step explanation:

its a triangular shape

let x = 4 + 2 = 6

let y = 5

length between two points = h

h² = x² + y²

h² = 6² + 5²

h = sqrt of 61

h = 7.81

Answer: $951,064.06 would be your answer.

Step-by-step explanation: Hope that helped!

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]

Incomplete question. I've made some assumptions to provide clarity.

Answer:

a. $45,743.07

b. $44,843.07

Step-by-step explanation:

Let's assume Victor is a single filer with an income of $100,000.

Using the 2017 tax bracket rates for single filers, Victor would be expected to pay:

- 10 percent on the first $9,325 = 10% x 9525 =$932.5

- plus 15 percent of the amount between $9,326 and $37,950 (37950-9326) x 15% = $4293.6

- plus 25 percent of the amount between $37,951 and $91,900 (91900-37,951 ) x25% = $13487.25

- plus 28 percent of the amount over $91,901-$191,650 (191650-91901) x 28% = 27929.72

Total=  $46,643.07

Minus $900 tax credit= $46,643.07-$900= $45,743.07

Minus $900 charitable contribution = $45,743.07-$900= $44,843.07

Answer:

[tex]B= 3.14 * 4^4 = 50.24cm^2\\h = 16cm\\V=B*h=50.24*16=803.84cm^3[/tex]

Step-by-step explanation:

The area of the base is the area of a circle with a radius equal to 4 cm. It means that the area can be calculated as:

[tex]B = 3.14 * r^2\\B= 3.14 * 4^4 = 50.24cm^2[/tex]

The height of the cylinder is shown in the picture, it is equal to 16 cm.

Finally, the volume of the cylinder can be calculated as:

[tex]V = B*h=50.24*16 = 803.84cm^3[/tex]

Where B is the base and h is the height of the cylinder.

Answer:

2007

Step-by-step explanation:

If the number of visitors was, say, 100 people in 2003, then in 2005 that number would have gone up to 300 people, which is a 200% increase. And that number would have gone up to 900 people in 2007, which is an 800% increase.

Answer:

2007

NOT YOU TRYING TO GET THE AOPS PREALGEBRA 2 ANSWER

I stan though :D

Answer:

65 dinners are expected to show up

The standard deviation of the distribution is 3.13

Step-by-step explanation:

Given

Proportion = 15%

Population = 77

Required

Expected Number that'll show up

Standard Deviation

If 15% won't show up; then

100% - 15% = 85% will show up

Expected Number, E(x) of Dinner is calculated as thus;

[tex]E(x) = np[/tex]

Where [tex]p = 85\%[/tex] (calculated above)

and [tex]n = 77[/tex]

Convert p to decimal

[tex]p = 0.85[/tex]

So;

[tex]E(x) = 0.85 * 77[/tex]

[tex]E(x) = 65.45[/tex]

[tex]E(x) = 65[/tex]

65 dinners are expected to show up

Calculating Standard Deviation, SD

Standard Deviation is calculated as;

[tex]SD = \sqrt{np(1-p)}[/tex]

Substitute 0.85 for p and 77 for n

[tex]SD = \sqrt{77 * 0.85 * (1-0.85)}[/tex]

[tex]SD = \sqrt{77 * 0.85 * 0.15}[/tex]

[tex]SD = \sqrt{9.8175}[/tex]

[tex]SD = 3.13328900678[/tex]

[tex]SD = 3.13[/tex] (Approximated)

The standard deviation of the distribution is 3.13

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:

Option D.

Step-by-step explanation:

The given quadratic equation is

[tex]y=x^2+7x+10[/tex]

We need to draw the graph of given equation by using graphing calculator as shown below.

From the graph it is clear that the parabola intersect the x-axis at points (-2,0) and (-5,0). So, the x-intercepts are (-2,0) and (-5,0).

Therefore, the correct option is D.

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: [tex]\dfrac{1}{5}[/tex]

Step-by-step explanation:

From, the circle graph in the attachment below,

The percentage of portion taken by 6 (dark blue) = 20%  

So, the probability of pulling out a tile with a 6 on it = percentage of portion taken by 6 (dark blue) = 20%     [Probability can also be written as a percentage]

[tex]=\dfrac{20}{100}\\\\=\dfrac{1}{5}[/tex]  [we divide a percentage by 100 to convert it into fraction]

Hence, the probability of pulling out a tile with a 6 on it = [tex]\dfrac{1}{5}[/tex]

Answer:

The answer is below

Step-by-step explanation:

Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation . Assume that the population has a normal distribution. Round the confidence interval limits to the same number of  decimal places as the sample standard deviation.

Answer: Given that:

Sample size (n) = 14, mean ([tex]\mu[/tex]) = 161.3, standard deviation ([tex]\sigma[/tex]) = 12.6

Confidence(C)= 90% = 0.9

α = 1 - C = 1- 0.9 = 0.1

α/2 = 0.1 / 2 = 0.05

The z score of α/2 correspond to a z score of 0.45 (0.5 - 0.05). This gives:

[tex]z_{\frac{\alpha}{2} }=1.645[/tex]

The margin of error (E) is given by the formula:

[tex]E=z_{\frac{\alpha}{2} }\frac{\sigma}{\sqrt{n} } =1.645*\frac{12.6}{\sqrt{14} }=5.5[/tex]

The confidence interval = μ ± E = 161.3 ± 5.5 = (155.8, 166.8)

The confidence interval is between 155.8 lb and 166.8 lb. There is a 90% confidence that the mean is between 155.8 lb and 166.8 lb.