A facilities manager at a university reads in a research report that the mean amount of time spent in the shower by an adult is 5 minutes. He decides to collect data to see if the mean amount of time that college students spend in the shower is significantly different from 5 minutes. In a sample of 8 students, he found the average time was 5.55 minutes and the standard deviation was 0.75 minutes. Using this sample information, conduct the appropriate hypothesis test at the 0.05 level of significance. Assume normality.

Answer:

Proved

Step-by-step explanation:

The options are not given. So, I will solve from scratch

Given

[tex]\frac{secx-1}{tan x}= \frac{tanx}{secx+1}[/tex]

Required

Prove

Multiply the right-hand side by [tex]\frac{secx + 1}{secx + 1}[/tex]

[tex]\frac{secx-1}{tan x} * \frac{secx + 1}{secx + 1}= \frac{tanx}{secx+1}[/tex]

Apply difference of two squares on the numerator

[tex]\frac{sec^2 x - 1}{(tanx)(secx + 1)} =\frac{tanx}{secx+1}[/tex]

In trigonometry:

[tex]tan^2x = sec^2x - 1[/tex]

So, we have:

[tex]\frac{tan^2 x}{(tanx)(secx + 1)} =\frac{tanx}{secx+1}[/tex]

[tex]\frac{tan x * tan x}{(tanx)(secx + 1)} =\frac{tanx}{secx+1}[/tex]

tan x cancels out

[tex]\frac{tan x}{secx + 1} =\frac{tanx}{secx+1}[/tex]

Proved

Answer:

-1<x<4

BLUE

Step-by-step explanation:

Answer:

ummmmm if im not wrong 34

Step-by-step explanation:

Answer:

+2 or adding 2 each step

So it is a linear function

Step-by-step explanation:

-2 + 2 = 0

0 + 2 = 4

4 + 2 = 6

So forth..

Answer:

Arithmetic sequence.

Step-by-step explanation:

Answer:

Approximately [tex]5.7[/tex] inches

Step-by-step explanation:

The crossbar and two given lengths form a right triangle. We know this because we see a right angle marked on the diagram in between the two given sides.

In this case, we have a right triangle with legs of [tex]4[/tex] and [tex]4[/tex], and we need to find the hypotenuse. By the Pythagorean Theorem ([tex]a^{2} +b^{2} =c^{2}[/tex], where [tex]a[/tex] and [tex]b[/tex] are the legs and [tex]c[/tex] is the hypotenuse), we get:

[tex]4^{2} +4^{2} =c^{2}[/tex]

[tex]16+16=c^{2}[/tex] (Evaluate exponents)

[tex]32=c^{2}[/tex] (Combine like terms)

[tex]\sqrt{32}=\sqrt{c^{2}}[/tex] (Take the square root of both sides of the equation to get rid of [tex]c[/tex]'s exponent)

[tex]c=4\sqrt{2} ,c=-4\sqrt{2}[/tex]

The latter solution is an extraneous solution because the side lengths of a triangle cannot be negative. Therefore, the answer is [tex]4\sqrt{2} \approx 5.7[/tex] inches. Hope this helps!

Answer:

760 inches squared

Step-by-step explanation:

surface area -

4(14 x 10) + 2( 10 x 10) = 560+200=760

Answer:

I think 40 units

Step-by-step explanation:

hope you have a wonderful day

Answer:

3 cm

Step-by-step explanation

1800 /30·20=3cm

Answer:

80in²

Step-by-step explanation:

Hey There!

So the first step of this problem is to find the width of the scale drawing

To do so we need to find the scale factor

To find the scale factor we divide the length of the room by the length of the scale factor

32/8=4

so the scale factor is 4

now to find the width

40/4=10

so the width of the scale drawing is 10 in

now we can find the area given the length and the width

10x8=80in²

so we can conclude that the area of the scale drawing is 80in²

Answer: Charity is 36 years old today.

Step-by-step explanation:

Let x = Present age of daughter.

Age of Charity = 4x

Age of her husband = 4x+6

After 10 years,

Age of daughter = x+10

Age of Charity = 4x+10

Age of her husband = 4x+6+10=4x+16

As per given,

[tex]x+10+4x+10+4x+16=117[/tex]

[tex]9x+36=117\\\\ 9x=117-36\\\\ 9x=81\\\\ x=9[/tex]

Present age of Charity = 4(9)=36 years

Hence, Charity is 36 years old today.

Answer:

Step-by-step explanation:

Step by Step Solution. Calculate Greatest Common Factor for : 138, 345. Factorize of the above numbers : 138 = 2 • 3 • 23. 345 = 3 • 5 • 23. Build a prime factors table. ...

Why learn this.

Terms and topics. GCF calculator.

Related links. Greatest common factor (GCF) explained | Arithmetic (video) | Khan Academy. LCM on Purplemath.

Answer:

69 I believe.

Step-by-step explanation:

Since my name is in this question, I'll answer it :)

Answer:

Yes, she's right.

Step-by-step explanation:

2/8 is simplified to 1/4. Between 1 and 1/2, it is 1/4. So yes, I (Candice) was right. :)

Answer:

18 stamps

Step-by-step explanation:

3/5(30) = 90/5 = 18

Answer:

Step-by-step explanation:

The chart tells you Zack has 30 stamps in total.

3/5 are animal stamps.

So you do

30 x 3/5 = 90 / 5 = 18

OR

30 / 5 x 3 = 6 x 3 = 18

Hope that helps!

Answer:

150 cookies

Step-by-step explanation:

The girl scout troupe could have baked between 100 to 150 cookies. Therefore, the largest amount they could have baked is 150 cookies. The amount on how many lemon crunch and chocolate macadamia nut cookies they made doesn't matter here.

Hope this helps!

Answer:

40

Step-by-step explanation:

Answer:

40

to solve this question

let the unknown number be x

Then,. x * 15% = 6

x * 15/100 = 6

x = 6*100/15

c = 40

hope it helps

Answer:

£9.80

Step-by-step explanation:

The computation of the total value is shown below:

Given that

The value of 20p coins is £2.80

So the value of 50p would be

= £2.80 × 50 ÷ 20

= £7

Now the total value is

= £2.80 +  £7

= £9.80

Answer:

20.5 m^2

Step-by-step explanation:

entire back yard area = 7 x 6.5 = 45.5 m^2

45.5 - 25 = 20.5 m^2

i might be wrong but you have to do proportions, i got 45 minute

Step-by-step explanation:

set it,it up by 30 minutes over 4 miles and x over 6 miles then you multiply by 6 and 30 which is 180 then divide by 4 and i got 45

Answer:

Step-by-step explanation:

Use formula

The distance between home and school:

Noah's time to reach home:

Difference in time:

Answer:

2x + 21

Step-by-step explanation:

Given :

Plant 1 : production level) 5x + 17

Plant 2 : production level = 3x - 4

To how much more plant 1 produces than plant 2 ; subtract production of plant 2 from plant 1

(5x + 17) - (3x - 4)

Open the bracket

5x + 17 - 3x + 4

5x - 3x + 17 + 4

2x + 21

Answer:

Step-by-step explanation:

Explanations are below

Step 1

7x + 2x^2 + 3x^2 - 2x  Observe the equation

Step 2

7x + 2x^2 + 3x^2 - 2x  Combine the like terms

(2x^2+3x^2)+(7x+-2x)

Step 3

(2x^2+3x^2)+(7x+-2x)  Simplify by adding and subtracting

Answer: 5x^2+5x

Answer:

similar shape!!!!

Step-by-step explanation:

Answer:

Dialation

Step-by-step explanation:

Dilation is an increase in size, but does not change the shape

Answer:

Each book cost $3.55

Step-by-step explanation:

Answer: 45 miles per hour

Step-by-step explanation:

Answer: if you are trying to find the hourly rate it's 45/hr. If your looking for minute rate it's .75/min. If you are looking for seconds rate it's .0125/sec

Step-by-step explanation: divide 135 by 3 for hourly rate. Divide 45 by 60 for minute rate. Divide .75 by 60 to to get seconds rate.

Answer:

25 [tex]in^{2}[/tex]

Step-by-step explanation: we can move the little triangle on the side to the missing part of the square and it says the length of the little triangle is 2 so we can do 2+3 since the height of the square with the missing side is 3. then we end up with the height being 5 and the base being 5. we know that A=bh so we can do A=5x5 and get 25 in squared

pls mark me branliest!!

Answer:

25ft2

Step-by-step explanation:

Answer:

ok

Step-by-step explanation:

Answer:

y = 2x - 5

Step-by-step explanation:

use the formula y - y1 = m (x - x1)

Answer:

2.345×0.023

2.345..........3 decimal point

0.023........3 decimal point

    2345

×       23               1.    first we change it whole number for multiply.

····················          2.count the decimal point.here  6 decimal points are there.

+ 7 0 3  5          3.we got the answer 53935.here only 5 digits are there.

4 6 9 0 0         4.now we add one zero backside  053935

····························5 . final answer is   0.053935

 5  3  9  3   5

···························

answer is =0.053935

Step-by-step explanation:

Answer:

It is only a solution to y = x - 2, not -3x - 2y = -8

Step-by-step explanation:

I) Check y = x - 2:

y = x - 2

2 = 4 - 2

As you can see, (4, 2) is a solution to this system.

II) Check -3x - 2y = -8:

-3x - 2y = -8

(-3)(4) - (2)(2) = -8

-12 - 4 =/= 8

-12 - 4 = -16, not 8. So (4, 2) is not a solution to this system.

Answer:

1 megámetro = 1000000 metros

Step-by-step explanation: