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2 years ago

Sam has 30 coins, all nickels and dimes. Together they are worth $2.40 how many nickels and dimes does he have

Mathematics

1 answer:

Aliun [14]2 years ago

4 0

Answer:

20 dimes and 8 nickels

Step-by-step explanation:

20 dimes = 10 x 20 = $2.00 and 8 nickels = 40 cents.

total is 2.40

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Prove the following statement.

jolli1 [7]

<h2>Step-by-step explanation:</h2>

As per the question,

Let a be any positive integer and b = 4.

According to Euclid division lemma , a = 4q + r

where 0 ≤ r < b.

Thus,

r = 0, 1, 2, 3

Since, a is an odd integer, and

The only valid value of r = 1 and 3

So a = 4q + 1 or 4q + 3

Case 1 :- When a = 4q + 1

On squaring both sides, we get

a² = (4q + 1)²

= 16q² + 8q + 1

= 8(2q² + q) + 1

= 8m + 1 , where m = 2q² + q

Case 2 :- when a = 4q + 3

On squaring both sides, we get

a² = (4q + 3)²

= 16q² + 24q + 9

= 8 (2q² + 3q + 1) + 1

= 8m +1, where m = 2q² + 3q +1

Now,

We can see that at every odd values of r, square of a is in the form of 8m +1.

Also we know, a = 4q +1 and 4q +3 are not divisible by 2 means these all numbers are odd numbers.

Hence , it is clear that square of an odd positive is in form of 8m +1

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2 years ago

A set of numbers is shown below: {0, 0.4, 1, 2, 3} Which of the following shows all the numbers from the set that make the inequ

klemol [59]

Answer:

{1,2,3}

Step-by-step explanation:

The others will not show all the numbers from the set to make the inequality true

8 0

2 years ago

HELP ME WRITE AN EQUATION FOR THIS GRAPH

kramer

Answer:

lol

Step-by-step explanation:

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2 years ago

How much time will Alex need to walk to his school, which is 2 1/4 miles away from his house, if he would walk with the speed of

mojhsa [17]

It would take him 30 mins

4 0

2 years ago

The clearance between a pin and the collar around it is important for the proper performance of a disc drive for small computers

hichkok12 [17]

Answer:

(a) The distribution of (Y - X) is N (0.001, 0.0005).

(b) The probability that the pin will not fit inside the collar is 0.023.

Step-by-step explanation:

The random variable X is defined as the diameter of the pin and the random variable Y is defined as the diameter of the collar.

The distribution of X and Y is:

$X\sim N(0.525, 0.0003)\\Y\sim N(0.526, 0.0004)$

The random variables X and Y are independent of each other.

(a)

Compute the expected value of (Y - X) as follows:

$E(Y-X)=E(Y)-E(X)=0.526-0.525=0.001$

The mean of (Y - X) is 0.001.

Compute the variance of (Y - X) as follows:

$V(Y-X)=V(Y)+V(X)-2Cov(X,Y)\\=V(Y)+V(X);\ X\ and\ Y\ are\ independent\\=0.0003^{2}+0.0004^{2}\\=0.00000025$

$SD(Y-X)=\sqrt{0.00000025}=0.0005$

The standard deviation of (Y - X) is 0.0005.

Thus, the distribution of (Y - X) is N (0.001, 0.0005).

(b)

Compute the probability of [(Y - X) ≤ 0] as follows:

$P(Y-X\leq 0)=P(\frac{(Y-X)-\mu_{Y-X}}{\sigma_{Y-X}}\leq \frac{0-0.001}{0.0005})=P(Z$

*Use a z-table for the probability value.

Thus, the probability that the pin will not fit inside the collar is 0.023.

8 0

2 years ago