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4 years ago

The product of two natural numbers is 1000. None of them is divisible by 10. Find their sum.

1 answer:

5 0

Two numbers make up the factors of 1000. In order that neither of the numbers be divisible by ten, each must contain powers of only one of the prime factors of 10, namely, 2 OR 5.

So let's see what we can cook up. The obvious answer is

1000 = 10 * 10 * 10

1000 = 2*5 * 2*5 * 2*5

1000 = 2^3 * 5^3

1000 = 8 * 125 Are there any others?

I don't think so. The answer then comes to 8 + 125 = 133

You might argue that -8 * - 125 would also work. But the question says natural numbers not integers.

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Find the a. MEAN and b. STANDARD DEVIATION for the data set. Round to two decimal places.

Dafna11 [192]

Answer:

Explained below.

Step-by-step explanation:

(10)

The data set is:

S = {124, 94, 129, 109, 114}

The mean and standard deviation are:

$\bar x=\frac{1}{n}\sum x=\frac{1}{5}\times [124+94+...+114]=114\\\\s=\sqrt{\frac{1}{n-1}\sum ( x-\bar x)^{2}}$

$=\sqrt{\frac{1}{5-1}\times [(124-114)^{2}+(94-114)^{2}+...+(114-114)^{2}]}\\=\sqrt{\frac{750}{4}}\\=13.6931\\\approx 13.69$

The correct option is B.

(11)

According to the Empirical 95% of the data for a Normal distribution are within 2 standard deviations of the mean.

So, the adult male's height is in the same range as about 95% of the other adult males whose heights were measured.

The correct option is B.

(12)

Let the score be X.

Given:

μ = 100

σ = 26

$X=\mu-2\sigma$

$=100-(2\times 26)\\=100-52\\=48$

The correct option is B.

(13)

Let X be the prices of a certain model of new homes.

Given: $X\sim N(150000, 2300^{2})$

Compute the percentage of buyers who paid between $147,700 and $152,300 as follows:

$P(147700$

$=P(-1$

According to the 68-95-99.7, 68% of the data for a Normal distribution are within 1 standard deviations of the mean.

The correct option is D.

(14)

Compute the percentage of buyers who paid more than $154,800 as follows:

$P(X>154800)=P(\frac{X-\mu}{\sigma}>\frac{154800-150000}{2400})$

$=P(Z>2)\\=0.975\\$

According to the 68-95-99.7, 95% of the data for a Normal distribution are within 2 standard deviations of the mean. Then the percentage of data above 2 standard deviations of the mean will be 97.5% and below 2 standard deviations of the mean will be 2.5%.

The correct option is D.

(15)

The z-score is given as follows:

$z=\frac{x-\mu}{\sigma}$

5 0

3 years ago

What is the total cost of a sweatshirt if the regular price is $42 and the sales tax is 5 1/2

leonid [27]

Answer:

$44.31

Step-by-step explanation:

Regular Price = $42

Sales Tax Rate = 5 1/2% or 5.5%

The total cost would be the regular price PLUS the sales tax. We find the sales tax by finding 42's 5.5%.

First, converting percentage to decimal (dividing by 100):

5.5% = 5.5/100 = 0.055

Now finding 5.5% of $42:

42 * 0.055 = $2.31

Now, the total price is the SUM of regular and this sales tax:

Total Price = 42 + 2.31 = $44.31

6 0

3 years ago

Can someone please help me?? I don’t understand what the order is? And or the symmetry

Vika [28.1K]

It is probably a rectangle so u see the answer would make s eve but in your mind does it

3 0

3 years ago

21. Mickey earned $475 from mowing lawns last summer. He deposited this money in an

Dennis_Churaev [7]

Answer:

first, u need to know the formula for compound interest, which is:

$A = P(1 + \frac{r}{100})^{n}$

where A is the final amount

P- initial amount

r- percent compounded(interest)

and

n- number of years

we have

$A = 475(1 + \frac{3.8}{100})^{4}$

3.8/100 = 0.038

1+0.038 =1.038

1.038^4 = 1.160885573136

475 * 1.160885573136 = 551.4206472396‬

approximately $551.42

5 0

4 years ago

Justin has two coupons for a phone.

Ghella [55]

Answer:

1) Coupon A gives the lower price.

The price with coupon A is less than the price with coupon B.

Step-by-step explanation:

Here, according to the given details:

Coupon A : $45 rebate on $65 phone

So, the actual paid price for phone = $65 - $45 = $20

If we apply Coupon A , the cost of the phone = $20

Coupon B : 65% off on $65 phone

Now, calculating 65% of 65, we get:

$\frac{65}{100} \times 65 = 42.25$

So, the discounted amt on $65 phone is $42,25

So, the actual paid price for phone = $65 - $42.25 = $22.75

If we apply Coupon B , the cost of the phone = $22.75

Hence, Coupon A gives the lower price.

The price with coupon A is less than the price with coupon B.

3 0

3 years ago