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3 years ago

If c varies directly as the square root of d, and c=14, when d = 64, find c when d= 324

Mathematics

1 answer:

zubka84 [21]3 years ago

5 0

Answer:

c = 31.5

Step-by-step explanation:

Given c varies directly as $\sqrt{d}$ then the equation relating them is

c = k $\sqrt{d}$ ← k is the constant of variation

To find k use the condition c = 14 when d = 64, then

14 = k × $\sqrt{64}$ = 8k ( divide both sides by 8 )

1.75 = k

c = 1.75 $\sqrt{d}$ ← equation of variation

When d = 324 , then

c = 1.75 × $\sqrt{324}$ = 1.75 × 18 = 31.5

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A publisher reports that 55% of their readers own a laptop. A marketing executive wants to test the claim that the percentage is

Irina18 [472]

Answer:

We fail to reject the null hypothesis, we accept H₀

Step-by-step explanation:

Population proportion p₀ = 55 % p₀ = 0,55

Sample size n = 280

Sample mean p = 51 % p = 0,51 q = 0,49

n*p and n*q are both bigger than 10 therefore we can approximate the binomial distribution to a normal distribution

Test Hypothesis

Null Hypothesis H₀ p = p₀

Alternative Hypothesis Hₐ p ≠ p₀

Significance level is α = 0,05 but we have a two-tail test then

α/2 = 0,025

z(c) = - 1,96

Computing z(s)

z(s) = ( p - p₀ ) / √(p*q)/n

z(s) = ( 0,51 - 0,55 ) / √(0,51*0,49)/280

z(s) = - 0,04 * 16,73 / 0,5

z(s) = - 1,34

Comparing

z(s) and z(c)

- 1,34 < - 1,96

| z(s) | < | z(c)|

Then z(s) is in the acceptance region, we accept H₀

6 0

3 years ago

In a recent year, the population of California was about 2.52 x 10^7 people. Its land area is about 4.05 x 10^5 km^2. What was t

andrezito [222]

The population of California = $2.52 \times 10^7$ people.

Land area of California = $4.05 \times 10^5km^2$ .

We have to determine the average number of people per square kilometer.

Average number of people per square kilometer =

Land area of California $\div$ Population of California

= $4.05 \times 10^5 \div 2.52 \times 10^7$

= $1.6 \times 10^{-2}$

Therefore, the average number of people per square kilometer is $1.6 \times 10^{-2}$ .

It is represented in scientific notation as Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.

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3 years ago

3/4x+7/8=4 1/4 please help me

Orlov [11]

Answer:

4 1/2

Step-by-step explanation:

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2 years ago

What is the length of angle EF in the right triangle below

salantis [7]

Answer:

E. √180

Step-by-step explanation:

Using Pythagoras' theorem

a^2 + b^2 = c^2 (c = hypotenuse, a and b are legs)

a^2 = c^2 - b^2

a^2 = 18^2 - 12^2

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a^2 = 180

a = √180

Answer

E. √180

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4 years ago

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Answer:

Step-by-step explanation:

Hey there!

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3 years ago

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