Helllp im doing my exam !

The area of a rectangle is 980 in squared. the ratio of the length to the width is 5 : 4. find the length and the width.

ella [17]

Answer: The length of the rectangle is 35 in.

The width of the rectangle is 28 in.
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Explanation:
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The formula for the area, "A", of a rectangle:

Area (A) = length (L) * width (w) ;

that is: " A = L * w " ;

A = 980 in² (given);

ratio of the length to the width is: " 5 : 4 " (given);

→ Find the length (L) and the width (w).
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→ 980 in² = (5x) * (4x) ;

in which: " 980 in² " is the area of the triangle;

" 5x" = the length (L) of the rectangle, for which we shall solve;

" 4x" = the width (w) of the rectangle, for which we shall solve.
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If we find solve for "x" ; we can solve for "5x" and "4x" (the "length" and the "width", respectively); by plugging in the solved value for "x" ;
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→ 980 in² = (5x) * (4x) ;

↔ (5x) * (4x) = 980 in² ;

→ (5x) * (4x) = (5) * (4) * (x) * (x) = 20 * x² = 20x² ;

→ 20x² = 980 ;

Divide each side by "10" ; by canceling out a "0" on each side of the equation:

→ 2x² = 98 ;

Now, divide each side of the equation by "2" ;

→ 2x² / 2 = 98 / 2 ;

to get:

→ x² = 49 ;

Now, take the "positive square root" of each side of the equation; (since a "length or width" cannot be a "negative value") ;
to isolate "x" on one side of the equation; & to solve for "x" ;

→ ⁺√(x²) = √49 ;

to get:

→ x = 7 ;
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Now, we can solve for the "length" and the "width" ;

→ The length is: "5x" ;

5x = 5(7) = " 35 in " ;
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→ The width is: "4x" ;

4x = 4(7) = "28 in."
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Let us check our answer:

→ A = L * w ;

→ 980 in² = ? 35 in. * 28 in. ?? ;

Using a calculator: "35 * 28 = 980" . Yes! ;
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{ Also note: " in * in = in² " ? Yes! } .
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3 0

3 years ago

A report indicated that 37% of adults had received a bogus email intended to steal personal information. Suppose a random sample

fiasKO [112]

Answer:

5.05% probability that no more than 34% had received such an email.

Step-by-step explanation:

We use the binomial approximation to the normal to solve this problem.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .