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GenaCL600 [577]
3 years ago
10

A rectangle or piece of paper has a width is 3 inches less than its link it is cut in half along a diagonal to create two congru

ent right triangles with areas of 44 in.²
Mathematics
1 answer:
kolezko [41]3 years ago
3 0

The length and width of the rectangle is 11 in and 8 in respectively.

Step-by-step explanation:

Given,

The width of a rectangle is 3 in less than the length.

The area of each congruent right angle triangle = 44 in²

To find the length and width of the rectangle.

Formula

The area of a triangle with b base and h as height = \frac{1}{2}bh

Now,

Let, the width = x and the length = x+3.

Here, for the triangle, width will be its base and length will be its height.

According to the problem,

\frac{1}{2}×(x+3)×x = 44

or, x^{2} +3x = 88

or,x^{2} +3x-88 = 0

or, x^{2}+(11-8)x-88 = 0

or, x^{2}+11x-8x-88 =0

or, x(x+11)-8(x+11) = 0

or, (x+11)(x-8) = 0

So, x = 8 ( x≠-11, the length or width could no be negative)

Hence,

Width = 8 in and length = 8+3 = 11 in

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The graph models the daily high temperature, H(t), in Santiago, Chile, t days after the hottest day of the year. What does the p
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For this case we have a function of the form:
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3 years ago
At 95% confidence, how large a sample should be taken to obtain a margin of error of 0.03 for the estimation of a population pro
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Answer:

A sample of 1068 is needed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

The margin of error is:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

95% confidence level

So \alpha = 0.05, z is the value of Z that has a pvalue of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.

At 95% confidence, how large a sample should be taken to obtain a margin of error of 0.03 for the estimation of a population proportion?

We need a sample of n.

n is found when M = 0.03.

We have no prior estimate of \pi, so we use the worst case scenario, which is \pi = 0.5

Then

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.03 = 1.96\sqrt{\frac{0.5*0.5}{n}}

0.03\sqrt{n} = 1.96*0.5

\sqrt{n} = \frac{1.96*0.5}{0.03}

(\sqrt{n})^{2} = (\frac{1.96*0.5}{0.03})^{2}

n = 1067.11

Rounding up

A sample of 1068 is needed.

8 0
3 years ago
A person invests 9000 dollars in a bank. The bank pays 4.25% interest compounded daily. To the nearest tenth of a year, how long
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Answer:

The person must invest the money in the bank for 18 years to reach $19600, if a person invests 9000 dollars in a bank and the bank pays 4.25% interest compounded daily.

Step-by-step explanation:

4 0
3 years ago
Two three-digit numbers are made up of six different digits. The first digit of the second number is twice as big as the last di
topjm [15]

Answer:the smallest possible sum of the two numbers is 537

Step-by-step explanation:

Two three-digit numbers are made up of six different digits.

To interpret this, let the two three digit numbers be;

ABC and. DEF

The first digit of the second number is twice as big as the last digit of the first number.

Interpret;

D=2C

The first digit of the first number can be 1, the second digit 0 and the third digit 2.

102.

For the second number:

D=2C

The first digit is 4, second digit 3 and last digit 5 since no repetition of digits

435.

Answer:the smallest possible sum of the two numbers is

102+435= 537

7 0
3 years ago
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