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3 years ago

Will Mark Brilliant!

Mathematics

1 answer:

pochemuha3 years ago

8 0

Answer:

87.8

Step-by-step explanation:

I assume you know how to do this so I didn't show any steps. Have a nice night. :)

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If pq = 23 and uv = 1/23, find the value of u×q×v×p. Explain which properties you used

zhannawk [14.2K]

Remember that multiplication is commutative, which means the order in which we multiply things doesn't matter.

The order of u × q × v × p (which we can abbreviate uqvp) isn't as important as the fact that we're multiplying all four values together. We could just as easily rewrite the expression as pquv, and it'd represent the same value.

To find this value then, we can simply multiply pq and uv - the values we already know - together.

If we start with the expression pq = 23, we can multiply either side by uv (taking advantage of the multiplication property of equality) to get

pquv = 23uv

And since we know that uv = 1/23, we can use the substitution property of equality to replace the uv on the right side with 1/23:

pquv = 23(1/23)

The inverse property of multiplication states that any number multiplied by its inverse (its reciprocal) gives us 1. 23 and 1/23 are reciprocals of each other, so 23(1/23) = 1, which means

pquv = 1

Finally, going back to the second paragraph, we can use the commutative property of multiplication to rearrange the left side of the equation, giving us the solution

uqvp = 1

3 0

3 years ago

Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the popu

tia_tia [17]

Answer:

The minimum head breadth that will fit the clientele is 4.4 inches.

The maximum head breadth that will fit the clientele is 7.8 inches.

Step-by-step explanation:

Let X = head breadths of men that is considered for the helmets.

The random variable X is normally distributed with mean, μ = 6.1 and standard deviation, σ = 1.

To compute the probability of a normal distribution we first need to convert the raw scores to z-scores using the formula:

$z=\frac{x-\mu}{\sigma}$

It is provided that the helmets will be designed to fit all men except those with head breadths that are in the smallest 4.3% or largest 4.3%.

Compute the minimum head breadth that will fit the clientele as follows:

P (X < x) = 0.043

⇒ P (Z < z) = 0.043

The value of z for this probability is:

z = -1.717

*Use a z-table.

Compute the value of x as follows:

$z=\frac{x-\mu}{\sigma}\\-1.717=\frac{x-6.1}{1}\\x=6.1-(1.717\times 1)\\x=4.383\\x\approx4.4$

Thus, the minimum head breadth that will fit the clientele is 4.4 inches.

Compute the maximum head breadth that will fit the clientele as follows:

P (X > x) = 0.043

⇒ P (Z > z) = 0.043

⇒ P (Z < z) = 1 - 0.043

⇒ P (Z < z) = 0.957

The value of z for this probability is:

z = 1.717

*Use a z-table.

Compute the value of x as follows:

$z=\frac{x-\mu}{\sigma}\\1.717=\frac{x-6.1}{1}\\x=6.1+(1.717\times 1)\\x=7.817\\x\approx7.8$

Thus, the maximum head breadth that will fit the clientele is 7.8 inches.

5 0

3 years ago

Determine which of the following are functions. Select all that apply.

Murljashka [212]

Answer:

(4x-32),-2,1-13)6

Step-by-step explanation:

6 0

3 years ago

Add any three numbers of the following and answer should be 60?

mina [271]

Six, twenty- two, and thirty

3 0

3 years ago

Read 2 more answers

If c(x) = 4x – 2 and d(x) = x^2+ 5x, what is (c circle d) (x)?

Xelga [282]

Answer:

4x² + 20x - 2

Step-by-step explanation:

To evaluate (c ￮ d)(x), substitute x = d(x) into c(x)

c(x² + 5x)

= 4(x² + 5x) - 2

= 4x² + 20x - 2

7 0

3 years ago