Rewrite the expression in the form y^n (y^4)^2

The mean resting pulse rate for men is 72 beats per minute. A simple random sample of men who regularly work out at Mitch's Gym

BARSIC [14]

Answer:

We conclude that the mean resting pulse rate for men is 72 beats per minute.

Step-by-step explanation:

We are given that he mean resting pulse rate for men is 72 beats per minute. Assume that the standard deviation of the resting pulse rates of all men who work out at Mitch's Gym is known to be 2.6 beats per minute.

A simple random sample of men who regularly work out at Mitch's Gym is obtained and their resting pulse rates (in beats per minute) are listed below;

87, 89, 69, 63, 70, 65, 88, 84, 58, 53, 66, 70.

Let $\mu$ = mean resting pulse rate for men.

SO, Null Hypothesis, $H_0$ : $\mu$ = 72 beats/minute {means that the mean resting pulse rate for men is 72 beats per minute}

Alternate Hypothesis, $H_A$ : $\mu$ < 72 beats/minute {means that the mean resting pulse rate for men is less than 72 beats per minute}

The test statistics that would be used here One-sample z-test statistics as we know about population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean mean resting pulse rate = $\frac{\sum X}{n}$

= $\frac{87+ 89+ 69 +63 +70 +65+ 88+ 84+ 58+ 53+ 66+ 70}{12}$ = 71.83 beats/minute

$\sigma$ = population standard deviation = 2.6 beats per minute

n = sample of men = 12

So, the test statistics = $\frac{71.83 - 72}{\frac{2.6}{\sqrt{12} } }$

= -0.23

The value of z test statistics is -0.23.

Also, P-value of the test statistics is given by;

P(Z < -0.23) = 1 - P(Z $\leq$ 0.23)

= 1 - 0.59095 = 0.40905

Now, at 0.05 significance level the z table gives critical value of -1.645 for left-tailed test.

Since our test statistic is more than the critical value of z as -0.23 > -1.645, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the mean resting pulse rate for men is 72 beats per minute.

3 0

3 years ago

Rolando is 17. In four years, his age will be 3/2 the age of his sister Marisa. How old will Marisa be in three years

Bess [88]

To find the answer, we can first find the age of Rolando in four year:

17+4
=21

We can then proceed to find the current age of Marisa,which is 3/2 of Rolando’s age calculated above:

Let Marisa’s age be y.

3/2 y =21
y = 21 × 2/3
y = 42/3
y = 14

Therefore Marisa is currently 14 years old.

In three years, Marisa would be:

14+3
=17

Therefore, she will be 17 years old.

Hope it helps!

5 0

3 years ago

Last week, a skate shop originally sold a skateboard for $120. Today, there is a sale and the same skateboard costs $96. What is

Tamiku [17]

120 - 96 = 24

Now we have to find what percent of 120 24 is.

x × 120 = 24
x = 0.2

0.2 means 20%.

The discount is 20% off.

8 0

3 years ago

3х - 30 = у 7y - 6 = 3х

mars1129 [50]

Answer:

Step-by-step explanation:

This one is simple substitution... at least, substitution is the easiest method. The first equation is 3x – 30 = y and the second is 7y – 6 = 3x

As I look, I see 3 ways to use substitution to solve this:

substitute 7y – 6 for 3x
substitute 3x – 30 for y
solve 3x – 30 = y for 3x and make it equal to 7y – 6

We're going to only use 1 method for the sake of time. Try the other two on your own. Assuming you don't make any mistakes, they will work.

Method 1:

3x – 30 = y

7y – 6 = 3x — initial system of equations

7y – 6 – 30 = y — substitute 7y – 6 for 3x

7y – 6 – 30 = y — marking like terms, bold for constants, underlined for variables

7y – 36 = y — combining the constants and simplifying

Here, you could diverge into multiple paths: add 36 to both sides, subtract y from both sides, divide by 6 OR subtract 7y from both sides and divide by –6 . For the sake of time, I'm subtracting 7y, though I don't like dealing with negatives.

7y – 7y – 36 = y – 7y — subtract 7y from both sides

–36 = –6y — simplify

–36 ÷ –6 = –6y ÷ –6 — divide by –6 on both sides

y = 6 — simplify

Again, we can diverge here: substitute y into 3x – 30 = y or substitute y into 7y – 6 = 3x

I'm going to choose 3x – 30 = y but it will work either way, should you take the time (if you have it) to chase down every path this problem can take.

3x – 30 = y — initial equation

3x – 30 = 6 — substitute 6 for y

3x – 30 + 30 = 6 + 30 — add 30 to both sides to isolate 3x

3x = 36 — simplify the expression

3x ÷ 3 = 36 ÷ 3 — divide both sides by 3 to isolate x

x = 12 — simplify

So, we have x = 12 and y = 6 . We know they work for 3x – 30 = y but not if they work for 7y – 6 = 3x . Let's substitute those in to see if (12, 6) really is the solution point.

7y – 6 = 3x — original equation

7(6) – 6 ≟ 3(12) — substitute 6 for y and 12 for x

42 – 6 ≟ 36 — simplify by multiplying

36 = 36 ✔ — simplify by combining like terms on left side

Success! It works! We have found our solution!

I hope this helps increase your understanding of the concept. Have a great day!

8 0

3 years ago

A photo album costs $10.49 before discount and tax.

Gemiola [76]

Answer:

Total after tax and discount is $7.78

Step-by-step explanation:

(10.49×0.3)= 3.15

10.49 - 3.15 = 7.34

(7.34×0.06)= 0.44

7.34 + 0.44 = 7.78

7 0

3 years ago