The Pew Research Center interviewed a random sample of 1,546 adult Americans to determine the average time they spent sleeping per night. The sample mean was found to be 7.2 hours of sleep, with a sample standard deviation of 1.4 hours. Construct a 95% confidence interval for the true mean. Interpret your confidence interval in words.

Answer:

x = 11

Step-by-step explanation:

2x - 8 = 14

2x = 22

x = 11

Tell me if I am wrong.

Can I get brainliest

Answer:

Let that number be 'x'

Now first part of the question tells us that 8 less than twice a number which is"x".

so twice a number would be 2x

then 8 less than would 2x-8

and the given result of the equation is 14

so the equation iis 2x-8=14

2x=14+8

2x=22

x=22/2

x=11 So the number is 11

Hope you find it helpful

Answer:

Step-by-step explanation:

hello :

*   64 = 4^3   so : g(x) =  (∛4^3)^x = 4^x

*   16=4²        so :  f(x) = (√4²)^x = 4^x

the functions f(x) and g(x) are equivalent

Answer:

59

Step-by-step explanation:

As far as I know every triangle has to equal 180°

So if you add 98+23 you would get 121

subtract that from 180 and get 59

Hope this helps!

The sample is from the right population, his customers. However, because he is surveying such a small number of people and only asking his best customers (who are probably the most satisfied, or they would not buy so much from him), the results are going to be biased, most likely positive, and not representative of his entire customer base.

No, Because, when to do some sort of analysis (such as this one), you need to take (for example) a Random sample from the population of the problem that is being analyzed.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Pete is conducting a survey to determine his customers’ overall satisfaction about the quality of his company’s products.

Let an example a Random sample from the population of the problem that is being analyzed.

In this example (problem), Pete wants to evaluate overall satisfaction of customers, so he should not send the surveys only to the customers who have purchased the largest number of items, but to the randomly selected customers, in order to obtain representative results of the overall satisfaction.

If he sends the surveys only to the customers who have bought the largest number of items, he will obtain very high satisfaction of customers, as results, of course, and this will not be representative results.

Learn more about the mathematical expression visit:

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To find the length of the slide, you can use trigonometry and the angle of depression. The length can be found using the tangent function, and rounding to the nearest whole number gives an answer of approximately 9 feet.

To find the length of the slide, we can use trigonometry and the angle of depression. We can use the tangent function, which is opposite over adjacent, to find the length of the slide. In this case, the opposite side is the height of the slide (12 feet) and the adjacent side is the length of the slide. So we have:

tan(53 degrees) = opposite/adjacent

tan(53 degrees) = 12/adjacent

To solve for the length of the slide, we can rearrange the equation:

adjacent = 12/tan(53 degrees)

Using a calculator, we can find that the length of the slide is approximately 9 feet when rounded to the nearest whole number.

Answer: 15,700 is 1/10 of 157,000 (A)

Step-by-step explanation:

The relationship between 15,700 and 157,000 is that 15,700 is 1/10 of 157,000

1/10 × 157,000 = 15,700

A 15,700 is 1/10 of 157,000

= 1/10 × 157,000

= 15700 (Correct)

15700 equals 15700

B 157,000 is 1/10 of 15,700

= 1/10 × 15700 = 1570 (Wrong)

1570 is not equal to 157000

C 15,700 is 1/100 of 157,000

= 1/100 × 157,000 = 1570 (Wrong)

1570 is not equal to 15700

D 157,000 is 1/100 of 15,700

1/100 × 15700 = 157 (Wrong)

157 is not equal to 157000

Answer:

  b = -1

Step-by-step explanation:

Your equation is ...

  (5^3)b -1 = 5^b -3

This is a mix of exponential and linear terms, and cannot be solved algebraically.

___

We suspect you might mean ...

  5^(3b -1) = 5^(b -3)

We can equate the exponents to find a value for b:

  3b -1 = b -3

  2b = -2 . . . . add 1-b to both sides

  b = -1 . . . . . . divide by 2

Answer:

389.846

Step-by-step explanation

Sorry if its wrong

Answer:

1-4380   2-219   3-15.44    4-37.1     5-6.13      7-58.67     8-160.33

Step-by-step explanation:

Answer:

4.583 *10^9

Step-by-step explanation:

for scientific notation, the number has to be 1<x<10

so in this case, move the decimal point behind the 4. since there are 3 other non 0 digits behind the 4, write it as 4.583

now count how many spaces there are after the 4 and put that as the exponent for 10

Answer:

4.58 x 106

Step-by-step explanation:

i hope this help

Answer:

t = 16

Step-by-step explanation:

–4(t − 12) + 12 = –4

-12                     -12

-4(t - 12) = -16

/-4             /-4

t - 12 = 4

+12      +12

t = 16

or

–4(t − 12) + 12 = –4

distribute the -4

-4t + 48 + 12 = -4

simplify

-4t + 60 = -4

-60          -60

-4t = -64

/-4     /-4

t = 16

Answer:

64/3

Step-by-step explanation:

Answer: The portion of skiing is 36 degrees (36°)

Step-by-step explanation: In order to calculate the value of any of the given variables in degrees, we must calculate it as a fraction of the total and then convert it to a degree measure in relation to a total of 360 degrees. (Please note that a pie chart has a total of 360 degrees measurement for all the variables given)

The variables are;

Soccer - 5

Jogging - 20

Walking - 10

Skiing - 5

Football - 10

Total - 50

Therefore, the fraction that represents skiing is given as

Skiing = 5/50

Skiing = 1/10

Calculating this portion in degrees becomes,

Skiing = 1/10 x 360

Skiing = 36 degrees (36°)

Answer:

x = 36° represents the proportion of hours spent on skiing.

Step-by-step explanation:

Solution:-

- The time taken for various activities is to be represented using a pie chart.

- The individual times for various activities are given:

          Soccer : 5 hours

          Jogging : 20 hours

          Walking : 10 hours

          Skiing : 5 hours

          Football : 10 hours

=========================

      Total time : 50 hours

=========================

- An entire pie chart is represented by a circle. Where the angle representation of a complete circle is 360° - mapping the total number of hours taken for all activities.

- So,               360° ............. Total Time = 50 hours

- So we will use direct proportions to evaluate the angle representation for the number of hours spent on skiing for a pie chart:

                      x ................. Skiing time = 5 hours

            ======================================

                     50*x = 5*360

                     x = 36°

Final answer:

Situations A (40 km/hr for 3 hours), B (60 km/hr for 2 hours), and C (30 km/hr for 4 hours) represent a total distance of 120 km when applying the formula D = S * t. Situation D (25 km/hr for 5 hours) does not represent the required distance of 120 km.

Explanation:

The distance traveled can be calculated using the formula D = S * t where S is the speed and t is the total time. To find out which situations represent a total distance of 120 km, we will apply this formula to each of the given situations.

After calculating each situation, we can see that situations A, B, and C each yield a total distance of 120 km, while situation D yields a total distance of 125 km, which is not the distance we are looking for.

Answer:

486

Step-by-step explanation:

it multiplies by 3 each time

Answer:

486

Step-by-step explanation:

I just did 6/2 and got three and that was the rate of change so I multiplied 3 to  2 to get 6 and then multiplied 3 again to get 18 and kept going until I got to 162 and multiplied that to 3 to get 486.

Answer: The dimensions are that of a right triangle.

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

you can solve by checking with the Pythagorean theorem (a^2 + b^2= c^2)

24 and 45 are the legs because the hypotenuse is the largest side so they will be substituted for a and b. if c is equal to 51 then it would be a right triangle

24^2 + 45^2= c^2

576 + 2025 = c^2

2601 = c^2

51 = c

because c = 51 and 51 was the hypotenuse on the triangle previously mentioned 24 45 51 is a right triangle

Answer:

2

Step-by-step explanation:

2

Answer:

The answer to your question is below

Step-by-step explanation:

Data

1) AB = 6   BC = 4   AE = 9  ED = ?

Use proportions to solve this problem

              AB / AE = 6/9    (AB + BC) / (AE + ED) = (6 + 4) / (9 + ED)

-Equal both proportions

                              6/9 = 10 / (9 + ED)

-Solve for ED

                             9 + ED = 10(9)/ 6

-Simplification

                             9 + ED = 90/6

                             9 + ED = 15

                                   ED = 15 - 9

-Result

                                   ED = 6

2.-   AB = 12   AC = 16  ED = 5  AE = ?

Use proportions to solve this problem

             AE / AB = AE / 12          AD/AC = (AE + 5) / 16

-Equal both proportions

                          AE/12 = (AE + 5 ) / 16

-Solve for AE

                         16AE = 12(AE + 5)

                         16AE = 12AE + 60

                         16AE -12AE = 60

                                     4AE = 60

                                       AE = 60/4

-Result

                                      AE = 15                          

Answer:

120 in or 60in or 60^2

Step-by-step explanation:

brainly pls

Answer:

8/8

Step-by-step explanation:

8/8 is equal to one, so it would mean he would get to play his favorite board games for a full hour.

7/8 is only about 50 or so minutes, which is less than an hour.

If Tom chooses 8/8 of an hour, he will get to play longer.

Answer:

 The lower supports are Congruent Rectangles and the area of the two supports is 24 square meters.

The upper arch can be decomposed as one semicircle with radius 6 meters minus a semicircle with radius 3 meters.

The area of the archway is (13.5 π + 24) square meters.

Step-by-step explanation:

See attachment for the firgure,

In order to determine the area of archway = The area of upper support + area of lower support.

As given, the lower support are two congruent rectangles consists of dimension 3 m × 4 m

Therefore, the area of lower support can be written as,

The area of lower support = 3 × 4 + 3 × 4 = 12 + 12 = 24 square m.

Now, the upper support arch can be decomposed as the two concentric semi circles having radius 3 m and 6 m,

Hence, the area of the upper support = Area of semi circle having radius i.e 6 m - Area of semi circle having radius i.e 3 m

=> π6²/2 - π3²/2= 27π/2= 13.5π square m

Therefore, the area of the archway =  (13.5 π + 24) square meters

Answer:

1. congruent rectangles

2. 24

3. 6

4. 13.5

Step-by-step explanation:

Got it right, have a nice day!

Answer:

work out the following questions

Step-by-step explanation:

a.

[tex] \frac{3}{4} \times \frac{1}{2} [/tex]

[tex] \frac{3}{8} [/tex]

Now

b.

[tex] \frac{4}{7} \times \frac{21}{40} [/tex]

Now here we can see 21 is 3 times of 7 and 40 is 10 times of 4 so

[tex] \frac{3}{10} [/tex]

Hope this helps.

Explanation of how to calculate the volume of a rectangular prism with given dimensions.

The volume of a rectangular prism is calculated by multiplying its length, width, and height.

Given dimensions: length = 6/5 cm, width = 8/3 cm, height = 15/4 cm

Volume = (6/5) cm x (8/3) cm x (15/4) cm = 24 cm³

Answer:

1^7 is the answer you are looking for

Step-by-step explanation:

Answer: I am pretty sure it is 35 min

Step-by-step explanation:

Answer

Trent spent 35 minutes on his work.

Step-by-step explanation:

Answer:

[tex](x+3)^{2}+6[/tex]

Step-by-step explanation:

The given expression is:

[tex]x^2+6x+15[/tex]

We have to re-write the given expression in form of perfect square. The above equation can be rewritten as:

[tex](x^2+6x)+15\\\\ =(x^2+2(x)(3))+15[/tex]

The general formula of a perfect square is:

[tex](a+b)^{2}=a^{2}+2(a)(b)+b^{2}[/tex]

Comparing previous two equations we can conclude that:

We have the square of first term(x), we have twice the product of first term(x) and second term(3). The square of second term(3) is missing. We can rewrite the previous equation as:

[tex](x^2+2(x)(3))+9+6\\\\ =(x^2+2(x)(3)+9)+6\\\\ =(x^2+2(x)(3)+3^{2})+6\\\\ =(x+3)^{2}+6[/tex]

This is the required form of the given expression.

Answer: AC : BC = 22 : 33 = 2 : 3

Step-by-step explanation:

Since we have given that

AB = 3x-4

AC= 2x+12

BC = 7x-2

And AB: AC = 1 : 2

and To show : AC : BC = 2 : 3

So, it becomes ,

[tex]\dfrac{AB}{AC}=\dfrac{3x-4}{2x+12}=\dfrac{1}{2}\\\\2(3x-4)=2x+12\\\\6x-8=2x+12\\\\6x-2x=12+8\\\\4x=20\\\\x=\dfrac{20}{4}\\\\x=5[/tex]

So, AC: BC becomes:

[tex]\dfrac{AC}{BC}=\dfrac{3x-4}{7x-2}=\dfrac{2(5)+12}{7(5)-2}=\dfrac{22}{33}=\dfrac{2}{3}[/tex]

Hence, proved.

Step-by-step explanation:

First find x:

AB:AC=1:2

2(3x-4)=2x+12

6x-8=2x+12

4x-8=12

4x=20

x=5

Substitute:

AC=2x+12

=(2x5)+12

=10+12

=22

BC=7x-2

=(7x5)-2

=35-2

=33

22/33=2/3

Therefore AC:BC = 2:3

The correct answer is 2%. The store donated 2% of $7,400 to charity.

To find out what percent of $7,400 was donated to charity, we need to divide the amount donated by the total sales and then multiply by 100 to convert it into a percentage.

Let's denote the percent donated as P. The amount donated is given as $148, and the total sales are $7,400. The relationship between the percent donated, the total sales, and the amount donated can be expressed as:

[tex]\[ P \times 7,400 = 148 \][/tex]

To find P, we divide both sides of the equation by 7,400:

[tex]\[ P = \frac{148}{7,400} \][/tex]

Now, we calculate the value of P:

[tex]\[ P = \frac{148}{7,400} = \frac{2}{100} \] \[ P = 0.02 \][/tex]

To express P as a percentage, we multiply by 100:

[tex]\[ P = 0.02 \times 100 \] \[ P = 2\% \][/tex]

Answer:

Option C is the right choice where length of the arc is 25/18π.

Step-by-step explanation:

Given:

Length of the radius of the circle, [tex]r[/tex] = 2 unit

Angle between the arc, [tex]\theta[/tex] = 125°

We have to find the arc length.

Let the arc length JL be "a" unit.

Formula to be used:

Arc length = (Circumference times angle ) / 360°

Using the above formula and plugging the values.

⇒ Arc length, JL, 'a' = [tex]2\pi r\times (\frac{\theta}{360})[/tex]

⇒ [tex]a=2\pi r\times (\frac{\theta}{360})[/tex]

⇒ [tex]a=2\pi (2)\times (\frac{125}{360})[/tex]

⇒ [tex]a=4\pi \times (\frac{125}{360})[/tex]

⇒ [tex]a=\frac{4\pi \times 125}{360}[/tex]

⇒ [tex]a=\frac{500\pi }{360}[/tex]

⇒ [tex]a=\frac{50\pi }{36}[/tex]

⇒ [tex]a=\frac{25\pi }{18}[/tex]          ... reducing to lowest term.

So,

The length of the arc JL is 25/18π and option C is the right choice.

Answer:

220 ft^3

Step-by-step explanation:

Assuming a rectangular tank,

V = l*w*h

   = 8*5*5.5

   =220 ft^3

Answer: 150 shots.

Step-by-step explanation: Since her three-point shot probably is 30%, we can assume that for any total of three-point shots, only 30% of them will be "correctly shot."

Here are two methods of how to find the answer, depending on how your teacher is teaching you to calculate percentages.

Method A. Proportions

Therefore, let's make a proportion. Out of 500 shots, only 30% will be made.

[tex]\frac{30}{100} =\frac{x}{500}[/tex]

Solve for x, which in a proportion, is done by cross-multiplying and then dividing.

[tex](30 * 500) / 100[/tex]

[tex]= 150[/tex]

Out of all the 500 shots, only 150 can be made by her prediction.

Method B. Simple multiplication

30% is equal to 0.3

Therefore, you multiply [tex]0.3 * 500[/tex], which you get [tex]150[/tex].