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Travka [436]
3 years ago
15

What is the simplified form of the following expression? (3/5)3

Mathematics
1 answer:
ratelena [41]3 years ago
7 0

Answer:

The simplified form of the expression (3/5)³  = 27/125

Step-by-step explanation:

The given expression is (3/5)³

3/5 is a proper fraction.

(3/5)³ can be written as,

(3/5)³ = 3³/5³

<u>To find  3³ and 5³</u>

3³ = 3*3*3 = 27

5³ =5*5*5 =125

<u>To find the simplified form of (3/5)³ </u>

(3/5)³  = 27/125

The simplified form of the expression (3/5)³  is 27/125

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Use the model below to estimate the average annual growth rate of a certain country's population for 1950, 1988, and 2010, where
Morgarella [4.7K]

Answer:

The average annual growth rate of a certain country's population for 1950, 1988, and 2010 are 2.398, 0.9985 and 0.2236 respectively.

Step-by-step explanation:

The given equation is

Y=-0.0000084x^3+0.00211x^2-0.205x+8.423

Where Y is the annual growth rate of  a certain country's population and x is the number of years after 1900.

Difference between 1950 and 1900 is 50.

Put x=50 in the given equation.

Y=-0.0000084(50)^3+0.00211(50)^2-0.205(50)+8.423

Y=2.398

Therefore the estimated average annual growth rate of the country's population for 1950 is 2.398.

Difference between 1988 and 1900 is 88.

Put x=88 in the given equation.

Y=-0.0000084(88)^3+0.00211(88)^2-0.205(88)+8.423

Y=0.9984752\approx 0.9985

Therefore the estimated average annual growth rate of the country's population for 1988 is 0.9985.

Difference between 2010 and 1900 is 110.

Put x=110 in the given equation.

Y=-0.0000084(110)^3+0.00211(110)^2-0.205(110)+8.423

Y=0.2236

Therefore the estimated average annual growth rate of the country's population for 2010 is 0.2236.

8 0
3 years ago
Two rectangles are similar. One has a length of 12 cm and a width of 9 cm, and
il63 [147K]

Answer:

10.7

Step-by-step explanation:

Let x be the missing side.

The rectangles are similar. Wich means:

● 8/9 = x/12

Cross multiply

● 9x = 8×12

● 9x = 96

Divide both sides by 9

● 9x/9 = 96/9

● x = 10.666

Round it to the nearest unit

● x = 10.7

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3 years ago
There are _____ taste buds. Each of these contains _____ taste receptors
alexgriva [62]
5; 5,000 to 10,000




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4 0
3 years ago
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a sample of 546 boys aged 6–11 was weighed, and it was determined that 89 of them were overweight. A sample of 508 girls aged 6–
AleksAgata [21]

Answer:

p-value:  0.6527

Step-by-step explanation:

Hello!

You have two samples to study, from each sample the weight of each child was measured and counted the total of overweight kids (x: "success") in each group:

Sample 1 (Boys aged 6-11)

n₁= 546

x₁= 89

^p₁= x₁/n₁ = 89/546 ≅0.16

Sample 2 (girls aged 6-11)

n=508

x= 74

^p= x/n = 74/508 ≅ 0.15

If the hypothesis statement is "The proportion of boys that are overweight differs from the proportion of girls that are overweight", the test hypothesis is:

H₀: ρ₁ = ρ₂

H₁: ρ₁ ≠ ρ₂

This type of hypothesis leads to a two-tailed rejection region, then the p-value will also be two-tailed. To calculate the p-value you have to first calculate the value of the statistic under the null hypothesis, in this case, is a test for the difference between two proportions:

Z=<u>      (^ρ₁ - ^ρ₂) - (ρ₁ - ρ₂)        </u> ≈ N(0;1)

    √(ρ` * (1 - ρ`) * (1/n₁ + 1/n₂))

ρ`=<u> x₁ + x₂  </u> = <u>  89+74     </u> = 0.154 ≅ 0.15

     n₁ + n₂     546 + 508

Z⁰ᵇ =<u>          (0.16-0.15) - (0)                    </u>

       √(0.15 * (1 - 0.15) * (1/546 + 1/508))

Z⁰ᵇ = 0.45

I've mentioned before that in this test you have a two-tailed p-value. The value calculated (0.45) corresponds to the right or positive tail and the left tail is symmetrical to it concerning the distribution mean, in this case, is 0, so it is -0.45. To obtain the p-value you need to calculate the probability of both values and add them:

P(Z>0.45) + P(Z<-0.45) = (1- P(Z<0.45)) + P(Z<-0.45) = (1-0.67364) + 0.32636 = 0.65272 ≅ 0.6527

p-value:  0.6527

Since there is no signification level in the problem, I'll use the most common to reach a decision. α: 0.05

Since the p-value is greater than α, you do not reject the null Hypothesis, in other words, there is no significative difference between the proportion of overweight boys and the proportion of overweight girls.

I hope it helps!

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3 years ago
What is the answer to (4)(‐4)=
hram777 [196]

Answer:

-16

Step-by-step explanation:

A (positive * negative) is a negative. Keep that in mind ^-^

5 0
3 years ago
Read 2 more answers
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