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3 years ago

3.

Mathematics

1 answer:

larisa [96]3 years ago

8 0

Answer:

a. 16 gallons

b. 32

Step-by-step explanation:

Let the full capacity of the tank is x gallons.

a. It is given that 12 gallons of water fill a tank to $\frac{3}{4}$ capacity.

Hence, we can write $\frac{3x}{4} = 12$

⇒ $x = \frac{4 \times 12}{3} = 16$ gallons.

b. If the tank is filled to capacity, then there will be 16 gallons of water, with which $\frac{16}{\frac{1}{2} } = 32$ numbers of half-gallon bottles of be filled with water. (Answer)

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What is the approximate length of the radius of a circle with a circumference of 63 inches?

Sergeeva-Olga [200]

Answer: 63/2π

Step-by-step explanation: C=πd

63=πd

D=63/π

r=1/2d

1/2×63/π=63/2π

5 0

3 years ago

Gianna put $1000 in a savings account for 18 months, The interest on the account is 3.5%. How much will Gianna earn in interest?

zimovet [89]

Answer:

amount of interest = 52.5

amount at the end of the period = 1052.5

Step-by-step explanation:

use the formula for simple interest

PRT/100

P is the principle

R is the rate of interest charged

T is the Time taken

18 months = 1 years 6 months ( 1.5 years)

1000 * 3.5 * 1.5 = 5250

5250/100 = 52.5

the amount of interest = 52.5

the amount she will have at the end of the period

= 1000 +52.5

= 1052.5

8 0

2 years ago

Question 3. Is it A B C, or D? Explain why

Agata [3.3K]

I think its: A
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4 0

2 years ago

Read 2 more answers

The bike store marks up the wholesale (lower price) cost of all of the bikes they sell by 30%.

mario62 [17]

Answer:

$100

Step-by-step explanation:

125 dollar bike will cost you 100 dollars if the sale for 20%.

125 x 0.20 = 25

25-125=100

Hope this helped!

8 0

2 years ago

The scores of individual students on the American College Testing (ACT) Program College Entrance Exam have a normal distribution

tekilochka [14]

Answer:

The probability that the average of the scores of all 400 students exceeds 19.0 is larger than the probability that a single student has a score exceeding 19.0

Step-by-step explanation:

Xi~N(18.6, 6.0), n=400, Yi~Ber(p); Z~N(0, 1);

$P(0\leq X\leq 19.0)=P(\frac{0-\mu}{\sigma} \leq \frac{X-\mu}{\sigma}\leq \frac{19-\mu}{\sigma}), Z= \frac{X-\mu}{\sigma}, \mu=18.6, \sigma=6.0$

$P(-3.1\leq Z\leq 0.0667)=\Phi(0.0667)-\Phi (-3.1)=\Phi(0.0667)-(1-\Phi (3.1))=0.52790+0.99903-1=0.52693$

P(Xi≥19.0)=0.473

$\{Yi=0, Xi< 19\\Yi=1, Xi\geq 19\}$

p=0.473

Yi~Ber(0.473)

$P(\frac{1}{n}\displaystyle\sum_{i=1}^{n}X_i\geq 19)=P(\displaystyle\sum_{i=1}^{400}X_i\geq 7600)$

Based on the Central Limit Theorem:

$\displaystyle\sum_{i=1}^{n}X_i\~{}N(n\mu, \sqrt{n}\sigma),\displaystyle\sum_{i=1}^{400}X_i\~{}N(7440, 372)$

Then:

$P(\displaystyle\sum_{i=1}^{400}X_i\geq 7600)=1-P(0$

$P(\displaystyle\sum_{i=1}^{n}Y_i=1)=P(\displaystyle\sum_{i=1}^{400}Y_i=1)$

Based on the Central Limit Theorem:

$\displaystyle\sum_{i=1}^{400}Y_i\~{}N(400\times 0.473, \sqrt{400}\times 0.499)=\displaystyle\sum_{i=1}^{400}Y_i\~{}N(189.2; 9.98)$

$P(\displaystyle\sum_{i=1}^{400}Y_i=1)\~{=}P(0.5$

Then:

the probability that the average of the scores of all 400 students exceeds 19.0 is larger than the probability that a single student has a score exceeding 19.0

7 0

3 years ago