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Alex17521 [72]
2 years ago
9

*The sum of two numbers is 400. If the first number is decreased by 20% and the second number is decreased by 15%, then the sum

would be 68 less. Find the numbers after the decrease.
Mathematics
2 answers:
Dahasolnce [82]2 years ago
8 0

Answer:

The two numbers are .8*160=128 and .85*240=204

Step-by-step explanation:

First sentence:                 x+y=400

Second sentence           .8x+.85y=400-68

Solve y in the first sentence:  y=400-x

Plug first into second:     .8x+.85(400-x)=332

Distribute:                        .8x+.85(400)-.85x=332

Combine like terms:        -.05x+.85(400)=332

Simplify(multiply):              -.05x+      340=332

Subtract 340 on both sides:    -.05x       =332-340

Simplify(subtract):                     -.05x        =-8

Divide both sides by -.05:              x        =-8/-.05

Simplify (division):                           x        = 160

So y=400-x=400-160=240

Vinil7 [7]2 years ago
8 0

Answer:

128 and 204. your welcome.

Step-by-step explanation:

Let x = the first number

Let y = the second number

So we can set up two equations:

x+y = 400

.8x + .85y = 400-68

Use substitution:

y = 400 - x

.8x + (.85)*(400-x) = 332

.8x + 340 -.85x = 332

8 = .05x

x = 160

So that makes y = 240

We want the decreased values so:

160*.8 = 128

240*.85 = 204

So the answers are 128 and 204

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Answer:

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Step-by-step explanation:

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Alternate Hypothesis, H_A : \mu > 210 seconds      {means that the sample is from a population of songs with a mean greater than 210 seconds}

The test statistics that will be used here is <u>One-sample z-test statistics </u>because we know about population standard deviation;

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Since the value of our test statistics is more than the critical value of z as 4.932 > 1.645, so <u><em>we have sufficient evidence to reject our null hypothesis</em></u> as it will fall in the rejection region.

Therefore, we conclude that the sample is from a population of songs with a mean greater than 210 seconds.

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