What is the value of x in the figure? Enter your answer in the box. x =

Mathematics

1 answer:

Arada [10]2 years ago

5 0

Since we know that a right angle equals 90 degrees, we can solve for x.

90 - 22 = x
x = 68

See the image I've included for more details. :)

Hope this helps!

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Find 5 consecutive whole numbers if it is known that the sum of the squares of the first 3 numbers is equal to the sum of the

Sloan [31]

So... our numbers... let's say the first one is hmmm "a"
so the second and subsequent are
a
a+1
a+2
a+3
a+4

there, 5 consecutive whole numbers or integers for that matter

now, we know the sum of the square of the first three,
is the same as the sum of the square of the last two

so $\bf \begin{cases}
a\\
a+1\\
a+2\\
\textendash\textendash\textendash\textendash\\
a+3\\
a+4
\end{cases}\qquad (a)^2+(a+1)^2+(a+2)^2=(a+3)^2+(a+4)^2$

do a binomial theorem expansion on those, solve for "a"

8 0

2 years ago

Franchise Business Review stated over 50% of all food franchises earn a profit of less than $50,000 a year. In a sample of 130 c

nydimaria [60]

Answer:

We need a sample size of 564.

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 $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

$\pi = \frac{81}{130} = 0.6231$

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 $Z = 1.96$ .

Based upon a 95% confidence interval with a desired margin of error of .04, determine a sample size for restaurants that earn less than $50,000 last year.

We need a sample size of n

n is found when $M = 0.04$