Which is the correct classification and decimal expansion of StartFraction 5 Over 8 EndFraction?

if a rug was 5 times as long as thia record sheet, how long would it be? measure the length of this record sheet in centimeters.

vlada-n [284]

Answer:

If a rug was 5 times as long as this record sheet. The length of this record sheet in centimeters is 100x centimeter

Solution:

Given that a rug was 5 times than the record sheet.

Let assume the length of the record sheet = x units

Then from given information,

Length of the rug = 5x units

Conversion of measure of record sheet in centimeter completely depends upon in which unit the length is given.

Suppose the given length is in meters, than need to multiply the given length by 100 to get the length in centimeter that is

x meter = $x \times 100$ = 100x cm

Conversion factor will change accordingly to the unit of given length which needs to be convert into centimeter.

4 0

3 years ago

A certain pen has been designed so that true average writing lifetime under controlled conditions (involving the use of a writin

Morgarella [4.7K]

Answer:

(a) We reject our null hypothesis.

(b) We fail to reject our null hypothesis.

(c) We fail to reject our null hypothesis.

Step-by-step explanation:

We are given that a certain pen has been designed so that true average writing lifetime under controlled conditions (involving the use of a writing machine) is at least 10 hr.

A random sample of 18 pens is selected.

Let $\mu$ = true average writing lifetime under controlled conditions

So, Null Hypothesis, $H_0$ : $\mu \geq$ 10 hr {means that the true average writing lifetime under controlled conditions is at least 10 hr}

Alternate Hypothesis, $H_A$ : $\mu$ < 10 hr {means that the true average writing lifetime under controlled conditions is less than 10 hr}

The test statistics that is used here is one-sample t test statistics;

T.S. = $\frac{\bar X -\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean

s = sample standard deviation

n = sample size of pens = 18

n - 1 = degree of freedom = 18 -1 = 17

Now, the decision rule based on the critical value of t is given by;

If the value of test statistics is more than the critical value of t at 17 degree of freedom for left-tailed test, then we will not reject our null hypothesis as it will not fall in the rejection region.

If the value of test statistics is less than the critical value of t at 17 degree of freedom for left-tailed test, then we will reject our null hypothesis as it will fall in the rejection region.

(a) Here, test statistics, t = -2.4 and level of significance is 0.05.

Now, at 0.05 significance level, the t table gives critical value of -1.74 at 17 degree of freedom.

Here, clearly the value of test statistics is less than the critical value of t as -2.4 < -1.74, so we reject our null hypothesis.

(b) Here, test statistics, t = -1.83 and level of significance is 0.01.

Now, at 0.051 significance level, the t table gives critical value of -2.567 at 17 degree of freedom.

Here, clearly the value of test statistics is more than the critical value of t as -2.567 < -1.83, so we fail to reject our null hypothesis.

(c) Here, test statistics, t = 0.57 and level of significance is not given so we assume it to be 0.05.

Now, at 0.05 significance level, the t table gives critical value of -1.74 at 17 degree of freedom.

Here, clearly the value of test statistics is more than the critical value of t as -1.74 < 0.57, so we fail to reject our null hypothesis.

8 0

2 years ago

If f(x) = 7 + 4x and g (x) = StartFraction 1 Over 2 x EndFraction, what is the value of (StartFraction f Over g EndFraction) (5)

Degger [83]

Answer:

$\frac{f}{g}(5)$ = 270 ⇒ Last answer

Step-by-step explanation:

* If f(x) = 7 + 4x

* If g(x) = $\frac{1}{2x}$

* We want to find $\frac{f}{g}(5)$

- Lets find at first $\frac{f}{g}(x)$

∵ f(x) = 7 + 4x

∵ g(x) = $\frac{1}{2x}$

∴ $\frac{f}{g}(x)=\frac{7+4x}{\frac{1}{2x}}$

- Lets divide the numerator by the denominator

∵ The numerator is 7 + 4x

∵ The denominator is $\frac{1}{2x}$

∴ (7 + 4x) ÷ $\frac{1}{2x}$

- Lets reverse the division sign to multiplication sign and reciprocal

the fraction after the division sign

∴ (7 + 4x) × $\frac{2x}{1}$

∴ $\frac{f}{g}(x)$ = 2x(7 + 4x)

∴ $\frac{f}{g}(x)$ = 14x + 8x²

- Now substitute x by 5

∴ $\frac{f}{g}(5)$ = 14(5) + 8(5)² = 70 + 200 = 270

∴ $\frac{f}{g}(5)$ = 270

4 0

3 years ago

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5,000 is 1/10 of blank

Olin [163]

Answer:

blank = 50,000

Step-by-step explanation:

6 0

3 years ago

Esther drove to work in the morning at an average speed of 45 miles per hour. She returned home in the evening along the same ro

nydimaria [60]

The key is Esther travelled the same distance - x - in both her morning and evening commute.

45(time she took in the morning, or p) = x
30(time she took in the evening, or q) = x

Therefore 45(p) = 30(q), or divide both sides by 5 and get 9(p) = 6(q). I know you can divide it further, but these numbers are small enough and it's not worth the time.

Since the whole trip took an hour, (p + q) = 60min, and so, p = 60-q.

Therefore 9(60-q) = 6q or 540-9q = 6q. So 540 = 15q, which makes q = 36. If q = 36, then by (p+q)=60, p (the time she took in the morning) must equal 24.

45 miles per hour, her speed in the morning, times (24/60) hours, her time, makes 18 miles travelled in the morning. If you check, 30 miles per hour times (36/60) hours also makes 18 miles in the evening.

Hope that makes a little sense. And I also hope it's right

7 0

3 years ago

Read 2 more answers