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3 years ago

Solve for u. |5u + 15| = 10

Mathematics

1 answer:

Rudiy273 years ago

6 0

Answer:

-1 and -5

Step-by-step explanation:

You must account for negative u values (which the abs nullifies).

So $5u+15=10$ and $5u+15=-10$ is what we have to solve for.

As for usual equations, isolate the u variable.

5u + 15 = 10

5u + 15 (-15) = 10 (-15)

5u = -5

$\frac{5u}{5}=\frac{-5}{1}$

u = -1

Now you can do the same operation for the other equation and you should get u = -5.

Let's make sure we did it right by replacing u with one of our solutions (-1 or -5).

$|5(-1)+15| = 10\\10 = 10$

That's true. What about the other one?

$|5(-5)+15|=10\\10=10$

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4 years ago

Laura takes very good care of her vehicles. She owns a blue van and a red truck. Although she bought them both new, she has owne

MrRissso [65]

The age of the van owned = 12 years

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Step-by-step explanation:

Here, the given question is INCOMPLETE.

Laura takes very good care of her vehicles. She owns a blue van and a red truck. Although she bought them both new, she has owned the truck for 17 years longer than she has owned the van. If the sum of the ages of the vehicles is 41 years, how old is the van and how old is the truck?

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So, according to the question:

The number of years she has owned truck = S + 17 years

Now, Sum of the age of ( Truck + Van) = 41 years

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6 0

3 years ago

(a) An article in a medical journal suggested that approximately 14% of such operations result in complications. Using this esti

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This question is incomplete, the complete question is;

Surgical complications: A medical researcher wants to construct a

99.5% confidence interval for the proportion of knee replacement surgeries that result in complications.

- An article in a medical journal suggested that approximately 14% of such operations result in complications. Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.08?

Answer: a sample of operations needed is 149

Step-by-step explanation:

Given that;

confidence interval = 99.5% = 0.995 so

margin of error E = 0.08

p = 14% = 0.14

now we obtain the critical value of z t the 99.5 confidence interval

∝ = 1 - confidence interval

∝ = 1 - 0.995

∝ = 0.005

∝/2 = 0.0025

obtaining the area of probability in the right tail

Area of probability to the right is = 1 - 0.0025 = 0.9975

from probability table; critical value of t =2.81

using the formula

n = p( 1 - p ) [ (z_∝/2)/E)² ]

so we substitute

n = 0.14 ( 1 - 0.14 ) [ 2.81 / 0.08 )²

n = (0.14 × 0.86 ) × 1233.7656

n = 148.5453 ≈ 149

Therefore , a sample of operations needed is 149

4 0

3 years ago