Given the following information, find the length of the missing side. Leave your answer as a simplified radical.

Answer:

a) The margin of error for a 90% confidence interval when n = 14 is 18.93.

b) The margin of error for a 90% confidence interval when n=28 is 12.88.

c) The margin of error for a 90% confidence interval when n = 45 is 10.02.

Step-by-step explanation:

The t-distribution is used to solve this question:

a) n = 14

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 14 - 1 = 13

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 13 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.7709

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 1.7709\frac{40}{\sqrt{14}} = 18.93[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The margin of error for a 90% confidence interval when n = 14 is 18.93.

b) n = 28

27 df, T = 1.7033

[tex]M = T\frac{s}{\sqrt{n}} = 1.7033\frac{40}{\sqrt{28}} = 12.88[/tex]

The margin of error for a 90% confidence interval when n=28 is 12.88.

c) The margin of error for a 90% confidence interval when n = 45 is

44 df, T = 1.6802

[tex]M = T\frac{s}{\sqrt{n}} = 1.6802\frac{40}{\sqrt{45}} = 10.02[/tex]

The margin of error for a 90% confidence interval when n = 45 is 10.02.

9514 1404 393

Answer:

Step-by-step explanation:

It is useful to remember the form for the square of a binomial.

  (a +b)² = a² +2ab +b²

  (a -b)² = a² -2ab +b²

__

1. (5 +√3)² = 5² +2·5·√3 +(√3)² = 25 +10√3 +3

  = 28 +10√3

__

2. (√6 -5√3)² = (√6)² -2·√6·5√3 +(5√3)² = 6 -30√2 +75

  = 81 -30√2

__

3. (6 +3√2)² = 6² +2·6·3√2 +(3√2)² = 36 +36√2 +18

  = 54 +36√2

Answer:

x=3

Explanation

2x+1=7

Step 1: Subtract 1 from both sides.

2x+1−1=7−1

2x=6

Step 2: Divide both sides by 2.

2x/2  =  6/2

x=3

plz mark me as brainliest

Answer:

Step-by-step explanation:

The sides of a quadrilateral always add up to 360°.

Missing angle = 360-115-97-68 = 80°

Answer:

D. 80°

Step-by-step explanation:

A quadrilateral always add up to 360°

To find the missing value we first have to add the given number up:

115 + 97 + 68 = 280°

Now we minus our value from 360° :

360° - 280° = 80°

Hope this helps!

Answer:

she starts with $25

every three games she spends $1.50 (.50 per game)

Step-by-step explanation:

i mean i cant really explain it, its kinda self explanatory

Answer:

The answer to the question provided is 7.

Step-by-step explanation:

[tex]7x + 9 = 8x + 2 \\ \frac{ - 8x \: \: \: \: = - 8x}{ - 1x + 9 = 2 } \\ \frac{ \: \: \: \: \: \: \: \: - 9 = - 9}{ \frac{ - 1x}{ - 1} = \frac{ - 7}{ - 1} } \\ x = 7[/tex]

[I apologize if this isn't the answer]

Answer: 17 feet long 14 feet wide

The model has a scale of 1 : 16 so you can use a calculator like this one to find the exact length. https://www.ginifab.com/feeds/cm_to_inch/scale_converter.html

Answer:

x=2.32

Step-by-step explanation:

-1.32+x=1

add 1.32 to both sides

1.32 cancels itself out

so you are left with x=2.32

Answer:

15 weeks

Step-by-step explanation:

I just answered this one not too long ago

It will take 15 weeks for Emanuel to lose at most 251 pounds.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

For example, 3x + 5 = 15.

Given that, Emanuel is trying to lose weight, he starts 2017 weighing 296 pounds.

If he plans to burn enough calories to lose 3 pounds per week,

We need to find that how many weeks will pass before Emanuel is at most 251 pounds,

So, let the number of weeks be x,

We will use here the concept of equations solving,

So, establishing the equations,

296 - 3x = 251

296 - 251 = 3x

45 = 3x

x = 15

Hence, it will take 15 weeks for Emanuel to lose at most 251 pounds.

Learn more about equations, click;

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Answer:

64

Step-by-step explanation:

8x4 is 32 multiplied by 2 is 64

V=LxWxH

(length x Width x Height)

Answer:

Total volume of 80 balls = 2,263.2 inch³

Step-by-step explanation:

Given:

Diameter of lead ball = 6 inch

Number of ball need = 80

Find:

Total volume of 80 balls

Computation:

Radius of lead ball = Diameter / 2

Radius of lead ball = 6 / 2

Radius of lead ball = 3 inch

Volume of lead ball = πr²

Volume of lead ball = (22/7)(3)²

Volume of lead ball = (22/7)(9)

Volume of lead ball = 28.29 inch³ (Approx.)

Total volume of 80 balls = 80 x Volume of lead ball

Total volume of 80 balls = 80 x 28.29

Total volume of 80 balls = 2,263.2 inch³

Answer:

6/40=3/20

Step-by-step explanation:

Answer:

F

Step-by-step explanation:

answer:

shape f !

step-by-step explanation:

hi there!

the question is asking us which shape matches shape a right, now if we look closely we already know that shapes d and b look like they match each other rather then shape a

shape a - 2, 2, 4

so they are out of the equation ( checking how long the sides are )

shape d - 3, 3, 3

shape b - 3, 3, 3

shapes e and c look like they match each other but just to make sure, i counted how long the each side was for both of them

( going by blocks )

shape c - 2, 3, 4,

shape e - 2, 3, almost 5

which does leave us left with shape f, but just to make sure.. lets count it!

shape f - 2, 2, 4,

which is the same numbers that shape a has!

shape f = shape a

hope this helps you!! and if i made a mistake reading the problem or doing the problem then please tell me :) have a good day

Answer:

1. 2=x+41

‐x=41‐2

x=‐39

2. 2=4+7×

‐7×=4‐2

7×=2

3. 2=10×+8

‐10×=8‐2

‐5×=3

5×=‐3

4.2=×+141

‐x+2=141

‐x=139

Answer: 21.625

Step-by-step explanation:

The percentage of 21 (5/8)% in decimal form is 173/800.

We have,

The percentage means the required value out of 100.

It is calculated by dividing the required value by the total value and multiplying by 100.

The given percentage expression.

21(5/8) %

Divide by 100 to remove the %.

This can be written as,

21(5/8) / 100

Now,

21(5/8)

= (21 x 8 + 5) / 8

Simply the fraction.

= 173/8

Now,

173/8 / 100

Simplify the fraction.

= 173/800

Thus,

The percentage of 21 (5/8)% in decimal form is 173/800.

Learn more about percentages here:

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Answer:

y = 3x+4

Step-by-step explanation:

slope formula is changes of y over the changes of x

[tex] \large \boxed{m = \frac{y_2-y_1}{x_2-x_1} }[/tex]

m is slope in y = mx+b.

Substitute the coordinate points in.

[tex] \large{m = \frac{7 + 2}{1 + 2} } \\ \large{m = \frac{9}{3}} \\ \large{m = 3}[/tex]

Since we know the slope, we rewrite by substituting m = 3 in the slope-intercept form.

[tex] \large{y = mx + b} \\ \large{y = 3x + b}[/tex]

Then we either substitute one of given coordinate points to find the value of b. I will substitute (1,7) in the equation.

[tex] \large{7 = 3(1)+ b} \\ \large{7 = 3 + b} \\ \large{7 - 3 = b} \\ \large{4 = b}[/tex]

Then rewrite the equation from y = 3x+b by substituting the value of b.

[tex] \large{y = 3x + b} \\ \large{y = 3x + 4}[/tex]

Square and Rectangle

I hope this helps you

Answer:

y=45

Step-by-step explanation:

Answer:

=45

Step-by-step explanation:

Answer:

im not sure but i think it is A...

Answer:

the square root of 23 is 4.8 or if you need the longer one it's 4.79583152331

Answer:

z=529

Step-by-step explanation:

Let's solve your equation step-by-step.

√z=23

Solve Square Root.

√z=23

z=232(Square both sides)

z=529

Check answers. (Plug them in to make sure they work.)

z=529(Works in original equation)

9514 1404 393

Answer:

  70 cm³

Step-by-step explanation:

Amanda's container holds ...

  V = LWH = (10 cm)(10 cm)(13.5 cm) = 1350 cm³

Mary's container holds ...

  (8 cm)(8 cm)(20 cm) = 1280 cm³

The larger box holds 1350 -1280 = 70 cm³ more popcorn.

Answer:

5x+11

Step-by-step explanation:

Hope this helped!!!

Answer:

2x+14

Step-by-step explanation:

hope this helps!

have a great day!!

Answer:

50

Step-by-step explanation:

Given

Total number of US houses = 500

If 10% were affected by fuel oil

Total number affected by fuel oil = 10% of 500

Total number affected by fuel oil = 0.1 * 500

Total number affected by fuel oil = 50

Hence 50 houses were affected by fuel oil

Step-by-step explanation:

The surface area increases by 100

if x y and z are side lengths and it is a rectangle.

Then finding the surface area would normally be 2xy+2yz+2xz

But then increasing each side length by a factor of 10 means multiplying it together

2x(10)y(10)+2y(10)z(10)+2x(10)z(10)

200xy+200yz+200xz and that is 100 times greater than the normal surface area.

Volume:

(x)(y)(z)=normal volume

x(10)y(10)z(10)=increased value

1000xyz=new volume

that is 1000 times greater than the previous volume

Hope that helps :)