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3 years ago

Find X. BC is the tangent

Mathematics

2 answers:

pav-90 [236]3 years ago

7 0

Answer:

x = 9

Step-by-step explanation:

The angle formed by the tangent BC and the radius AB is right at B

Thus ΔABC is right with AC as the hypotenuse

Using Pythagoras' identity in the right triangle

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, hence

AC² = AB² + BC² ← substitute given values

(x + 6)² = x² + 12² ← expand squared parenthesis on left side

x² + 12x + 36 = x² + 144 ( subtract x² from both sides )

12x + 36 = 144 ( subtract 36 from both sides )

12x = 108 ( divide both sides by 12 )

x = 9

Arturiano [62]3 years ago

4 0

Check the picture below.

let's recall that the point of tangency with the radius chord is always a right-angle.

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Data for the estimated number of HIV cases worldwide between 1988 and 1996 suggests exponential growth in the number of cases ov

Eduardwww [97]

Answer:

d. 52.5 million cases

Step-by-step explanation:

from the data output in the question, we have the regression equation to be

log y = -151.281 + 0.076577x

y is the number of hiv cases which is in millions

x is the year of the hiv case

x = 1998

we put the value of x in the regression equation

log y = -151.281 + 0.076577(1998)

log y = -151.281 + 153.000846

log y = 1.719846

since the result is in log form,

$y=10^{1.791846}$

y = 52.5 million cases

3 0

3 years ago

PLEASE HELP GEOMETRY PLEASE! SHOW WORK!!

MissTica

Answer:

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Step-by-step explanation:

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7 0

3 years ago

You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the

Vesna [10]

Answer:

A sample size of at least 1,353,733 is required.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , 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 .

The margin of error is:

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

98% confidence level

So $\alpha = 0.02$ , z is the value of Z that has a pvalue of $1 - \frac{0.02}{2} = 0.99$ , so $Z = 2.327$ .

You would like to be 98% confident that you esimate is within 0.1% of the true population proportion. How large of a sample size is required?

We need a sample size of at least n.

n is found when M = 0.001.

Since we don't have an estimate for the proportion, we use the worst case scenario, that is $\pi = 0.5$

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

$0.001 = 2.327\sqrt{\frac{0.5*0.5}{n}}$

$0.001\sqrt{n} = 2.327*0.5$

$\sqrt{n} = \frac{2.327*0.5}{0.001}$

$(\sqrt{n})^{2} = (\frac{2.327*0.5}{0.001})^{2}$

$n = 1353732.25$

Rounding up

A sample size of at least 1,353,733 is required.

5 0

3 years ago

Carlos and Mike work part time as salespeople for an electronics store. Carlos earns $7.25 per hour plus a $10 bonus. Mike earns

galina1969 [7]

Carlos and Mike earn same amount for 10 hours of part time work

Solution:

Let "x" be the number of hours worked by Carlos and mike

Given that,

Carlos earns $7.25 per hour plus a $10 bonus

Thus, total amount earned by Carlos for "x" hours is given by:

total earned = 7.25(number of hours) + $ 10

total earned = 7.25x + 10 ----- eqn 1

Mike earns $7.75 per hour plus a $5 bonus

Thus, total amount earned by Mike for "x" hours is given by:

total earned = 7.75(number of hours) + $ 5

total earned = 7.75x + 5 ------- eqn 2

To find number of hours, they earn same amount, equate eqn 1 and eqn 2

7.25x + 10 = 7.75x + 5

7.75x - 7.25x = 10 - 5

0.5x = 5

x = 10

Thus for 10 hours, they earn the same amount

3 0

3 years ago

How do you add and subtract polynomials?

bekas [8.4K]

Reverse the sign of each term you are subtracting and then add as usual. Hope this helps!

4 0

3 years ago