A patio 20 feet wide has a slanted roof, as shown in the figure. Find the length of the roof if there is an 8-inch overhang. Show all work and round the answer to the nearest foot. Be sure to label your answer appropriately. Then write a sentence explaining your answer in the context of the problem.

Answer:

The 99%  confidence interval is  [tex]97.94 < \mu < 98.26[/tex]

Step-by-step explanation:

From the question we are told that

    The sample size is  n =  110

     The  sample mean is  [tex]\= x = 98.1 \ F[/tex]

       The standard deviation is  [tex]\sigma = 0.64 \ F[/tex]

Given that the confidence level is  99% the level of significance i mathematically evaluated as

                  [tex]\alpha = 100 - 99[/tex]

                  [tex]\alpha = 1\%[/tex]

                  [tex]\alpha = 0.01[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution, the values is  

          [tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.01 }{2} } = 2.58[/tex]

Generally the margin of error is mathematically represented as

           [tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]

substituting values

          [tex]E = 2.58 * \frac{ 0.64}{\sqrt{110} }[/tex]

          [tex]E = 0.1574[/tex]

Generally the  99% confidence interval  is mathematically represented as

               [tex]\= x - E < \mu < \= x + E[/tex]

substituting values

             [tex]98.1 - 0.1574 < \mu < 98.1 + 0.1574[/tex]

             [tex]97.94 < \mu < 98.26[/tex]

Answer:

Step-by-step explanation:

Step-by-step explanation:

n mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. ... For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with common difference of 2.

Answer:

Step-by-step explanation:

Since 8 is a factor of 24, 8 is the GCF of the pair, and 24 is the LCM of the pair.

__

The ratio 8/24 is reduced by observing that 24 = 8·3:

  8/24 = 8/(8·3) = (8/8)·(1/3)

  8/24 = 1/3

Answer:

The minimum sample size is  [tex]n =135[/tex]

Step-by-step explanation:

From the question we are told that

   The confidence interval is [tex]( lower \ limit = \ 0.44,\ \ \ upper \ limit = \ 0.51)[/tex]

    The margin of error is  [tex]E = 0.1[/tex]

Generally the sample  proportion can be mathematically evaluated as

     [tex]\r p = \frac{ upper \ limit + lower \ limit }{2}[/tex]

    [tex]\r p = \frac{ 0.51 + 0.44}{2}[/tex]

    [tex]\r p = 0.475[/tex]

Given that the confidence level is  98% then the level of significance can be mathematically evaluated as

         [tex]\alpha = 100 - 98[/tex]

        [tex]\alpha = 2\%[/tex]

        [tex]\alpha =0.02[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table  

   The value is

        [tex]Z_{\frac{\alpha }{2} } = 2.33[/tex]

Generally the minimum sample size is evaluated as

      [tex]n =[ \frac { Z_{\frac{\alpha }{2} }}{E} ]^2 * \r p (1- \r p )[/tex]

     [tex]n =[ \frac { 2.33}{0.1} ]^2 * 0.475(1- 0.475 )[/tex]

     [tex]n =135[/tex]

Answer:

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Answer:

Ok so to help you out, first, off you need to be sure that the sets domain and range use the proper variable. After that, you are going to want to just plug it into the equation. I am going to link a screenshot to the correct answer if you are still have trouble finding it.

Anyways hoped this helped and I got to this question in time c:

Answer:

Circle Equation : x² + y² = 21

Step-by-step explanation:

So we know that this circle goes through the point ( - 4, √5 ), with a center being the origin. Therefore, this makes the circle equation a bit simpler.

The first step in determining the circle equation is the length of the radius. Applying the distance formula, the radius would be the length between the given points. Another approach would be creating a right triangle such that the radius is the hypotenuse. Knowing the length of the legs as √5 and 4, we can calculate the radius,

( √5 )² + ( 4 )² = r²,

5 + 16 = r²,

r = √21

In general, a circle equation is represented by the formula ( x - a )² + ( y - b )² = r², with radius r centered at point ( a, b ). Therefore our circle equation will be represented by the following -

( x - 0 )² + ( y - 0 )² = (√21 )²

Circle Equation : x² + y² = 21

Answer:

m = 15

Step-by-step explanation:

m/9 + 2/3 = 7/3

Subtract 2/3 from each side

m/9 + 2/3  -2/3= 7/3 -2/3

m/9 = 5/3

Multiply each side by 9

m/9 *9 = 5/3 *9

m = 15

Answer:

1,377/2 and 688 1/17

Step-by-step explanation:

Answer:

t = 32,5 minutes

Step-by-step explanation:

Volume to fill =  13000000 Gal

5 pumps delivering  80000 gal/min

5 * 80000 = 400000 gal/min

If we divide the total volume by the amount of water delivered for the 5 pumps, we get the required time to fill the volume, then

t =  13000000/ 400000

t = 32,5 minutes

Answer:

a) 6.00

b) 3.00

c) 1.50

Step-by-step explanation:

Sample error of the mean is expressed mathematically using the formula;

SE = σ /√n where;

σ  is the standard deviation and n is the sample size.

a) Given σ = 18, n = 9

Standard error of the mean = σ /√n

Standard error of the mean = 18/√9

Standard error of the mean = 18/3

Standard error of the mean = 6.00

b) Given σ = 18, n = 36

Standard error of the mean = σ /√n

Standard error of the mean = 18/√36

Standard error of the mean = 18/6

Standard error of the mean = 3.00

c) Given σ = 18, n = 144

Standard error of the mean = σ /√n

Standard error of the mean = 18/√144

Standard error of the mean = 18/12

Standard error of the mean = 3/2

Standard error of the mean = 1.50

Answer:

90% confidence interval for the difference between the two population means

( -23.4166 , -6.5834)

Step-by-step explanation:

Step(i):-

Given first sample size n₁ = 100

Given mean of the first sample x₁⁻ = 178

Standard deviation of the sample S₁ = 35

Given second sample size n₂= 100

Given mean of the second sample x₂⁻ = 193

Standard deviation of the sample S₂ = 37

Step(ii):-

Standard error of two population means

        [tex]se(x^{-} _{1} -x^{-} _{2} ) = \sqrt{\frac{s^{2} _{1} }{n_{1} }+\frac{s^{2} _{2} }{n_{2} } }[/tex]

       [tex]se(x^{-} _{1} -x^{-} _{2} ) = \sqrt{\frac{(35)^{2} }{100 }+\frac{(37)^{2} }{100 } }[/tex]

        [tex]se(x^{-} _{1} -x^{-} _{2} ) = 5.093[/tex]

Degrees of freedom

ν  = n₁ +n₂ -2 = 100 +100 -2 = 198

t₀.₁₀ = 1.6526

Step(iii):-

90% confidence interval for the difference between the two population means

[tex](x^{-} _{1} - x^{-} _{2} - t_{\frac{\alpha }{2} } Se (x^{-} _{1} - x^{-} _{2}) , x^{-} _{1} - x^{-} _{2} + t_{\frac{\alpha }{2} } Se (x^{-} _{1} - x^{-} _{2})[/tex]

(178-193 - 1.6526 (5.093) , 178-193 + 1.6526 (5.093)

(-15-8.4166 , -15 + 8.4166)

( -23.4166 , -6.5834)

Answer:

the answer is 4

Step-by-step explanation:

so 1 rotation is like a circle 1 unit circle requires 4 quadrant to be in this is the most simplified i can get

Answer:

Solution : 4

Step-by-step explanation:

The question asks us how many polar coordinates are possible for one rotation. For one rotation there will be 4 polar coordinates, one present in each quadrant such that,

( r, theta ), ( r, theta ), ( - r, theta ), ( - r, theta )

Respectively if theta was q say,

( r, q ), ( r, - q ), ( - r, q ), ( - r, -q )

Therefore there are 4 sets of polar coordinates for one rotation, in each of the 4 quadrants.

Answer: A,C, and D

Step-by-step explanation:

Answer:

the answer to this question may be option B, C and D

Answer:

d. 60000000000

Step-by-step explanation:

Answer:

The answer is D. 60,000,000,000

Step-by-step explanation:

Answer:

= 18.2 miles per hour

Step-by-step explanation:

Speed = distance / time

            =82 miles / 4.5 hours

             =18.22222222 miles per hour

             Rounding

             = 18.2 miles per hour

Answer:

Given that

Distance = rate × time

82 = r × 4½

r = 18.2 mph

Answer:

20

Step-by-step explanation:

We can set up a percentage proportion to find the value of x.

[tex]\frac{12}{x} = \frac{60}{100}[/tex]

Now we cross multiply:

[tex]100\cdot12=1200\\\\1200\div60=20[/tex]

Hope this helped!

Answer:

The temperature of the 5th day was 3°C

Step-by-step explanation:

Mean temperature of the first 4 days = 8°C

Note that:

Mean = Sum of temperatures ÷ number of days

∴ 8 = sum of temperature ÷ 4

[tex]= 8 = \frac{sum\ of\ temperatures}{4}[/tex]

[tex]= sum\ of\ temperatures\ = 8\ \times\ 4 = 32[/tex]

Therefore the sum of the first 4 days = 32

Let the temperature of the next day (the fifth day) be m

Hence,

sum of the temperatures of first 5 days = 32 + m - - - - (1)

Next, the sum of the first 5 days can be calculated from the given average of the first 5 days as follows:

Mean temperature of the first 5 days = 7

[tex]Mean = \frac{sum\ of\ temperatures}{number \ of\ days}\\\\7 = \frac{sum\ of\ temperatures}{5} \\sum\ of\ temperatures\ = \ 7\ \times\ 5\ = 35\\sum\ of\ temperature\ of\ the\ first\ 5\ days\ =\ 35 - - - - - (2)[/tex]

Now, you will notice that equation (1) = equation (2)

∴ 32 + m = 35

m = 35 - 32 = 3

therefore, the temperature of the 5th day was 3°C

Answer:

  the product of a number and 33

Step-by-step explanation:

The operation "times" is what is used to form the product of two operands.

  "t times 33" is "the product of t and 33"

a ) Now as you can see, the white region is composed of a triangle and a rectangle. This triangle has a height of 5, as it is composed of the respective blank triangles. It's base is 5 meters as well, by properties of a rectangle - which is sufficient information to solve for the area of the triangle.

Area of Triangle : 1 / 2 [tex]*[/tex] 4 [tex]*[/tex] 5 = 2 [tex]*[/tex] 5 = 10 m²

The area of this rectangle will be 3 [tex]*[/tex] 4 = 12 m², considering it's given dimensions are 3 by 4. Therefore the area of this white region will be 10 + 12 = 22 m²

b ) Now this striped region will be the remaining area, or the area of the white region subtracted from the area of the outer rectangle.

Area of Outer Rectangle : 10 [tex]*[/tex] 4 = 40 m²,

Area of Striped Region : 40 - 22 = 18 m²

Answer:

Well a rhombus is considered a quadrilateral because it has 4 sides and 4 angles.

Just like a square and rectangle they both are quadrilaterals with 4 angles and sides.

A rhombus is considered a type of quadrilateral because it has four sides and four angles

As a general rule, a shape that is considered a quadrilateral must have:

Since a rhombus has four sides and four angles, then it is considered a type of quadrilateral

Read more about rhombus at:https://brainly.com/question/20627264

#SPJ6

Answer:

Known:

• a book have front, back and 200 pages

• front= 0.7 mm

• back= 0.7 mm

• each page= 0,14 mm

ask:

calculate the minimum thickness...?

answer:

a. 200 p × 0,14 = 28 mm

b. front + back = 0.7+0.7= 1.4 mm

Thickness= 28+1,4 = 29,4 mm

I hope this helps

if u have question let me know in comments^_^

Answer:

35/14

Step-by-step explanation: 35/14

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

Answer:

10 girls.

Step-by-step explanation:

Boys: 5x

Girls: 2x

next... 5x + 2x = 35

7x= 35

x=5

Answer. 10 girls.

Answer:

9%

Step-by-step explanation:

12x=6y eq 1

18x=9y eq 2

Answer:

[tex]L + \frac{5}{8} = 1[/tex]

Step-by-step explanation:

Given

A cup of coffee

Kelly drank 5/8 of the coffee

Required

Determine how much is left

Start by representing the amount of coffee left with L

Because the amount of coffee Kelly drank is in fraction (5/8), the total cup of coffee will equate to 1;

Hence, the addition equation as requested in the question to represent the scenario is

[tex]L + \frac{5}{8} = 1[/tex]

Answer:

5/2

Step-by-step explanation:

5^(-3). 2^2.5^6 / (2^3.5^2)

By the law of indices,

=5^(-3+6-2).2^(2-3)

=5^1.2^(-1)

=5. 2^-1

=5/2

Answer:

measure

Step-by-step explanation:

The collection of quantitative or numerical data that describes a property of an object or event is called a measured/measurement.

The SI Unit is a metric system. An example of an SI Unit is the kilogram, centimeter, second, etc.

Measurements are made by comparing a particular quantity with an SI unit or assigning numbers to certain objects in a way that reflects its value.

Answer:

The probability that none of the LED light bulbs are​ defective is 0.7374.

Step-by-step explanation:

The complete question is:

What is the probability that none of the LED light bulbs are​ defective?

Solution:

Let the random variable X represent the number of defective LED light bulbs.

The probability of a LED light bulb being defective is, P (X) = p = 0.03.

A random sample of n = 10 LED light bulbs is selected.

The event of a specific LED light bulb being defective is independent of the other bulbs.

The random variable X thus follows a Binomial distribution with parameters n = 10 and p = 0.03.

The probability mass function of X is:

[tex]P(X=x)={10\choose x}(0.03)^{x}(1-0.03)^{10-x};\ x=0,1,2,3...[/tex]

Compute the probability that none of the LED light bulbs are​ defective as follows:

[tex]P(X=0)={10\choose 0}(0.03)^{0}(1-0.03)^{10-0}[/tex]

                [tex]=1\times 1\times 0.737424\\=0.737424\\\approx 0.7374[/tex]

Thus, the probability that none of the LED light bulbs are​ defective is 0.7374.

Answer:

The area of the house is A. 1,108