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2 years ago

Factor the expression 4x + 32. Explain each step you take in the process.

2 answers:

6 0

4x+32

4 goes into 4 1 time. (4/4=1)
4 goes into 32 8 times. (32/4=8)
We can factor out 4 from both numbers.

4(1x+8)
aka 4(x+8)

harina [27]2 years ago

3 0

Answer:

Sample response: The GCF of 4x and 32 is 4, so the first step is to divide each term by 4. The quotients are x and 8. The factored expression will be 4(x + 8).

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At an ocean-side nuclear power plant, seawater is used as part of the cooling system. This raises the temperature of the water t

grandymaker [24]

Answer:

(a1) The probability that temperature increase will be less than 20°C is 0.667.

(a2) The probability that temperature increase will be between 20°C and 22°C is 0.133.

(b) The probability that at any point of time the temperature increase is potentially dangerous is 0.467.

Step-by-step explanation:

Let X = temperature increase.

The random variable X follows a continuous Uniform distribution, distributed over the range [10°C, 25°C].

The probability density function of X is:

$f(X)=\left \{ {{\frac{1}{25-10}=\frac{1}{15};\ x\in [10, 25]} \atop {0;\ otherwise}} \right.$

(a1)

Compute the probability that temperature increase will be less than 20°C as follows:

$P(X$

Thus, the probability that temperature increase will be less than 20°C is 0.667.

(a2)

Compute the probability that temperature increase will be between 20°C and 22°C as follows:

$P(20$

Thus, the probability that temperature increase will be between 20°C and 22°C is 0.133.

(b)

Compute the probability that at any point of time the temperature increase is potentially dangerous as follows:

$P(X>18)=\int\limits^{25}_{18}{\frac{1}{15}}\, dx\\=\frac{1}{15}\int\limits^{25}_{18}{dx}\,\\=\frac{1}{15}[x]^{25}_{18}=\frac{1}{15}[25-18]=\frac{7}{15}\\=0.467$

Thus, the probability that at any point of time the temperature increase is potentially dangerous is 0.467.

(c)

Compute the expected value of the uniform random variable X as follows:

$E(X)=\frac{1}{2}[10+25]=\frac{35}{2}=17.5$

Thus, the expected value of the temperature increase is 17.5°C.

7 0

2 years ago

A linear regression equation is calculated for a sample of n = 20 pairs of X and Y values.

Nata [24]

Answer: B) 18

Step-by-step explanation:

The degree of freedom for Standard error or df(Residual) is the sample size minus the number of estimated parameters ,.

df= n - p , where n= sample size , p = number of parameters.

According to the given problem , we have

Sample size : n=20

Number of parameters (x and y ): p= 2

Then, the df value for the standard error of estimate will be :

df= n-p =20-2=18

Thus , the df value for the standard error of estimate is 18 .

Hence, the correct answer is B) 18 .

3 0

2 years ago

Can someone help please

riadik2000 [5.3K]

Answer:

62 Sunday papers were sold

Step-by-step explanation:

Let x represent the number of Sunday papers sold. Then half that many, or x/2, is the number of Friday papers sold. The total revenue from the sales is the sum of products of quantity and price:

1.50 · x + 0.75 · (x/2) = 116.25

Multiplying by 2, this becomes ...

3.00x +0.75x = 232.50

3.75x = 232.50

Dividing by the coefficient of x gives ...

232.50/3.75 = x = 62

The number of Sunday newspapers sold is 62.

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2 years ago

The percentage of U.S. college freshmen claiming no religious affiliation has risen in recent decades. The bar graph shows the

emmainna [20.7K]

Answer: