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3 years ago

45 is 20% of what number?

1 answer:

5 0

$x-\ number\\\\
20\%x=45\\\\
\frac{20}{100}x=45\\\\
0.2x=45\ \ \ | divide\ by\ 0.2\\\\
x=225\\\\
45\ is\ 20\% \ of\ 225.$

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How many quart are 8/1/4 gallons

Westkost [7]

Given:

Consider the given gallons are $8\dfrac{1}{4}$ gallons.

To find:

The number of quarts in $8\dfrac{1}{4}$ gallons.

Solution:

We know that,

1 gallons = 4 quarts

Using this conversion, we get

$8\dfrac{1}{4}\text{ gallons}=4\times 8\dfrac{1}{4}\text{ quarts}$

$8\dfrac{1}{4}\text{ gallons}=4\times \dfrac{32+1}{4}\text{ quarts}$

$8\dfrac{1}{4}\text{ gallons}=4\times \dfrac{33}{4}\text{ quarts}$

$8\dfrac{1}{4}\text{ gallons}=33\text{ quarts}$

Therefore, there are 33 quarts in $8\dfrac{1}{4}$ gallons.

6 0

3 years ago

Forty percent of households say they would feel secure if they had $50,000 in savings. you randomly select 8 households and ask

Kay [80]

Answer:

Let X be the event of feeling secure after saving $50,000,

Given,

The probability of feeling secure after saving $50,000, p = 40 % = 0.4,

So, the probability of not feeling secure after saving $50,000, q = 1 - p = 0.6,

Since, the binomial distribution formula,

$P(x=r)=^nC_r p^r q^{n-r}$

Where, $^nC_r=\frac{n!}{r!(n-r)!}$

If 8 households choose randomly,

That is, n = 8

(a) the probability of the number that say they would feel secure is exactly 5

$P(X=5)=^8C_5 (0.4)^5 (0.6)^{8-5}$

$=56(0.4)^5 (0.6)^3$

$=0.12386304$

(b) the probability of the number that say they would feel secure is more than five

$P(X>5) = P(X=6)+ P(X=7) + P(X=8)$

$=^8C_6 (0.4)^6 (0.6)^{8-6}+^8C_7 (0.4)^7 (0.6)^{8-7}+^8C_8 (0.4)^8 (0.6)^{8-8}$

$=28(0.4)^6 (0.6)^2 +8(0.4)^7(0.6)+(0.4)^8$

$=0.04980736$

(c) the probability of the number that say they would feel secure is at most five

$P(X\leq 5) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)$

$=^8C_0 (0.4)^0(0.6)^{8-0}+^8C_1(0.4)^1(0.6)^{8-1}+^8C_2 (0.4)^2 (0.6)^{8-2}+8C_3 (0.4)^3 (0.6)^{8-3}+8C_4 (0.4)^4 (0.6)^{8-4}+8C_5(0.4)^5 (0.6)^{8-5}$

$=0.6^8+8(0.4)(0.6)^7+28(0.4)^2(0.6)^6+56(0.4)^3(0.6)^5+70(0.4)^4(0.6)^4+56(0.4)^5(0.6)^3$

$=0.95019264$

8 0

3 years ago

Suppose that $1800 is borrowed for three years at an interest rate of 2% per year, compounded continuously. Find the amount owed

Schach [20]

1908

Step-by-step explanation:2% of 1800 is 36 36 x 3 is 108 + 1800 =1908

5 0

2 years ago

If a farmer sells 9.8 KL of apples and pears at the farmers market. 4/5 of this weight is apples,and the rest are pears. How man

faltersainse [42]

Answer:

1.96

Step-by-step explanation:

A farmer sells 9.8 kl of apples and pears

4/5 of this weight is apples, while the rest are pears

Therefore the wight of pears can be calculated as follows

Let x represent the weight of pears

9.8= 4/5×9.8 + x

9.8= 0.8×9.8+x

9.8= 7.84+x

9.8-7.84= x

x= 1.96

8 0

3 years ago

How many hours are there in ten quarters of an hour?

svlad2 [7]

Answer:

2 1/2 hours

Step-by-step explanation:quarters means 1/4 and there are 4 of them in each hours so if you have 10 quarters of a hour they add up to 2 hours and a half, because 2 hours times 4 equals 8 quarters and then add the other 2 quarters and you get half

6 0

3 years ago