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3 years ago

The area of a square is numerically 45 more than the perimeter. find the length of the side

1 answer:

4 0

Area of square = l²
Perimeter of square = 4l

According to the question,
$l^2 = 45 + 4l \\\\ l^2 - 4l - 45 = 0 \\\\ l^2 -9l+5l-45=0 \\\\ l(l-9)+5(l-9) =0 \\\\(l-9)(l+5)=0$

Using zero product property,

Either,
$l-9 = 0 \\
~~~~~~l = 9$

Or,
$l+5=0 \\
~~~~~~l=-5$

Since length can't be negative, the length is 9

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A 5 divided by 48 lottery involves choosing 5 of the numbers from 1 through 48 and a 4 divided by 35 lottery involves choosing 4

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Answer:

4/35 lottery is easier to win.

Step-by-step explanation:

For the 5/48 lottery, the winning probability is $\frac{5}{48}$ ≈0.1042

For the 4/35 lottery, the winning probability is $\frac{4}{35}$ ≈ 0.1143

Since $\frac{4}{35}$ > $\frac{5}{48}$ , the lottery where one chooses 4 of the numbers 1 through 35 is easier to win.

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3 years ago

Can Fractions and ratios cannot have zero in the denominator?

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3 years ago

124 – 70 = n – 35 I need the answer i please this is very importend

Sliva [168]

Answer:

N=89

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3 years ago

Let f(x) = x2 and g(x) = x - 3. Evaluate (gºf)(-2). A. -20 B. 20 C. 7 D. 1

7nadin3 [17]

Answer:

D. 1

Step-by-step explanation:

Step 1: Find g of f(x)

g(f(x)) = (x²) - 3

Step 2: Plug in -2 as x

g(f(x))(-2) = (-2)² - 3

g(f(x))(-2) = 4 - 3

g(f(x))(-2) = 1

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3 years ago

The U.S. and many other countries have recently tightened airport security. A sociologist is interested in estimating the propor

melisa1 [442]

Answer:

0.0073 < 0.05, which means that we reject the null hypothesis and conclude that the true proportion of interest is higher than 0.7.

Step-by-step explanation:

Conduct a test to determine whether the true proportion of interest is higher than 0.7.

This means that the null hypothesis is: $H_{0}: p = 0.7$

And the alternate hypothesis is: $H_{a}: p > 0.7$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

0.7 is tested at the null hypothesis:

This means that $\mu = 0.7, \sigma = \sqrt{0.7*0.3}$

The sociologist found that 375 of the 500 travelers randomly selected and interviewed indicated that the airports were safe.

This means that $n = 500, X = \frac{375}{500} = 0.75$

Value of the z-statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{0.75 - 0.7}{\frac{\sqrt{0.7*0.3}}{\sqrt{350}}}$

$z = 2.44$

P-value of the test:

Probability of z being larger than 2.44, that is, a proportion larger than 0.75.

This is, looking at the z-table, 1 subtracted by the pvalue of Z = 2.44. S

Z = 2.44 has a pvalue of 0.9927

1 - 0.9927 = 0.0073

0.0073 < 0.05, which means that we reject the null hypothesis and conclude that the true proportion of interest is higher than 0.7.

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3 years ago