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2 years ago

Will mark brain list if answer

Mathematics

1 answer:

Natali5045456 [20]2 years ago

7 0

The fractional form of the rational number 0.1515... is:

15/99

<h3>How to write 0.1515... as the quotient of two integer numbers?</h3>

I will do all the steps, not only the one in the picture.

First, we identify that we have a number where the decimals do a repeating pattern.

That number in our case is 0.1515...

That repeating pattern is "15".

First we need to identify the number of digits in the pattern, and we can see that is 2, thus we define n = 2

Now we multiply our number by 10^n (10^2 in this case).

0.1515...*10^2 = 0.1515...*100 = 15.1515...

Notice that we still have the pattern, so we can subtract the original number to remove it:

15.1515... - 0.1515... = 15

Ok, now we can rewrite the left side as:

15.1515... - 0.1515... = 100*0.1515... - 0.1515...

= (100 - 1)*0.1515... = 99*0.1515...

And we know that is equal to 15, then we can write:

99*0.1515... = 15

If we isolate the original number in the left side we will get:

0.1515... = 15/99

That is the fractional form of the rational number.

If you want to learn more about rational numbers:

brainly.com/question/12088221

#SPJ1

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3 years ago

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Answer: 1. 0.0256

2. 0.4096

Step-by-step explanation:

Binomial probability formula , to find the probability of getting x successes:

$P(x)=^nC_xp^x(1-p)^{n-x}$ , where n= Total number of trials

p= Probability of getting success in each trial.

Let x be the number of customers will make purchase.

As per given , we have

p= 0.20

n= 4

1. The probability that 3 of the next 4 customers will make a purchase will be:-

$P(x=3)=^4C_3(0.20)^3(1-0.20)^{4-3}$

$P(x=3)=(4)(0.20)^3(0.80)^{1}\ \ [\because\ ^nC_{n-1}=n]$

$P(x=3)=(4)(0.008)(0.80)=0.0256$

Hence, the probability that 3 of the next 4 customers will make a purchase = 0.0256

2. The probability that none of the next 4 customers will make a purchase will be :

$P(x=0)=^4C_0(0.20)^0(1-0.20)^{4-0}$

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3 years ago

The table shows the height of 5 students in inches what is the mean absolute deviation for these numbers

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Answer:

Step-by-step explanation:

To find the mean absolute deviation (MAD), first find the mean (or average).

μ = (59 + 71 + 68 + 75 + 67) / 5

μ = 68

Next, subtract the mean from each value and take the absolute value.

|59 − 68| = 9

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3 years ago

The following prices, in dollars, of 7.5-cubic-foot refrigerators were recorded from a random sample. 314 305 344 283 285 310 3

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Answer:

$t=\frac{310.9-300}{\frac{31.09}{\sqrt{10}}}=1.109$

The degrees of freedom are given by:

$df=n-1=10-1=9$

And the p value would be given by:

$p_v =P(t_{9}>1.109)=0.148$

Since the p value is higher than the significance level of 0.05 we don't have enough evidence to conclude that the true mean is significantly higher than $300 because we FAIL to reject the null hypothesis.

Step-by-step explanation:

Information given

314 305 344 283 285 310 383 285 300 300

We can calculate the sample mean and deviation with the following formula:

$\bar X =\frac{\sum_{i=1}^n X_i}{n}$

$s =\sqrt{\frac{\sum_{i=1}^n (x_i -\bar X)^2}{n-1}}$

$\bar X=310.9$ represent the sample mean

$s=31.09$ represent the standard deviation for the sample

$n=10$ sample size

$\mu_o =300$ represent the value to test

$\alpha=0.05$ represent the significance level

t would represent the statistic

$p_v$ represent the p value

Hypothesis to test

We want to verify if the true mean is greater than 300, the system of hypothesis would be:

Null hypothesis: $\mu \leq 300$

Alternative hypothesis: $\mu > 300$

The statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

Replacing the info given we got:

$t=\frac{310.9-300}{\frac{31.09}{\sqrt{10}}}=1.109$

The degrees of freedom are given by:

$df=n-1=10-1=9$

And the p value would be given by:

$p_v =P(t_{9}>1.109)=0.148$

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3 years ago