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3 years ago

Hi 1-5 already done!!!!!!!!!!

Mathematics

1 answer:

Scilla [17]3 years ago

3 0

Answer:

According to tangents secant segments theorem,

11) x(16+x) = (x + 6)^2

x (16+x) = (x + 6)^2

16x + x^2 = x^2 + 2(6)(x) + 6^2

16x + x^2 = x^2 + 12x + 36

16x - 12x + x^2 - x^2 = 36

4x = 36

x = 36/4

x = 4

13) x(x + 5) = (x + 2)^2

x^2 + 5x = x^2 + 2x 2(2)(x) + 2^2

x^2 + 5x = x^2 + 4x + 4

x^2 -x^2 + 5x - 4x = 4

x = 4

14) x + 8( x + 8 + 32) = (3x) ^2

x + 8(x + 40) = 9x^2

x(x + 8) + 40(x + 8) = 9x^2

x^2 + 8x + 40x + 320 = 9x^2

x^2 + 48x + 320 =9x^2

48x + 320 = 9x^2 - x^2

48x + 320 = 8x^2

Dividing the whole eq. by 8,

6x = 40 = x^2

0 = x^2 - 6x - 40

0 = x^2 - 10x + 4x - 40

0 = x(x - 10) + 4(x - 10)

x - 10 = 0 OR x + 4 = 0

x = 10 OR x = - 4

length cannot be negative, so,

x = 10

15) (x + 3) ( x + 3 + 15) = (2x) ^2

(x + 3) (x + 18) = 4x^2

x(x + 18) + 3(x + 18) = 4x^2

x^2 + 18x + 3x + 54 = 4x^2

x^2 + 21x + 54 = 4x^2

0 = 4x^2 - x^2 - 21x - 54

0 = 3x^2 - 21x - 54

Dividing the whole eq. by 3,

x^2 - 7x - 18 = 0

x^2 - 9x + 2x - 18 = 0

x(x - 9) + 2 (x - 9)

x + 2 = 0 Or x - 9 = 0

x = -2 or x = 9

length cannot be negative,so,

x = 9

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Suppose that a researcher is designing a survey to estimate the proportion of adults in your state who oppose a proposed law tha

irinina [24]

Answer:

$n=\frac{0.5 (1-0.5)}{(\frac{0.02}{1.96})^2}= 2401$

So without prior estimation for the population proportion, using a confidence level of 95% if we want a margin of error about 2% we need al least a sample size of 2401.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

Solution to the problem

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

If solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

The margin of error desired for this case is $ME= \pm 0.02$ equivalent to 2% points

For this case we need to assume a confidence level, let's assume 95%. And since we don't have prior estimation for the population proportion of interest the best value to do an approximation is $\hat p =0.5$

In order to find the critical value we need to take in count that we are finding the margin of error for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=\pm 1.96$

Now we have all the values needed and if we replace into equation (b) we got:

$n=\frac{0.5 (1-0.5)}{(\frac{0.02}{1.96})^2}= 2401$

So without prior estimation for the population proportion, using a confidence level of 95% if we want a margin of error about 2% we need al least a sample size of 2401.

5 0

3 years ago

How do you solve substitution problems in Pre Algebra

Rus_ich [418]

You multiply both of the equations until you have two of the same term the same like for example, say I have 4x and 5x. You want to multiply until both have the same number, so multiply 5x by four, then multiply 4x by five, and you will get 20x, then both of those cancel out and you will be left with the other variable, and you just solve like a normal equation.

4 0

3 years ago

Read 2 more answers

The mean age of 5 people in a room is 40 years. A person enters the room. The mean age is now 40. What is the age of the person

ad-work [718]

Answer:

Step-by-step explanation:

5 people in the room have 5*40 = 200 years altogether

a new person is X years old.

Now 6 people have (200 + x) years altogether.

Mean age of 6 people is (200+x)/6. and it is also = 40.

So,

(200+x)/6 = 40

200 + x = 240

x = 40

6 0

3 years ago

Is the answer a, b, c, or d.

ale4655 [162]

The correct answer is d.

We have the following system of linear equations:

(I) $4x+7y=-14$
(II) $8x+5y=8$

Let's use the elimination method, then let's multiply the equation (1) $\times(-2)$ and subtracting (I) and (II):

(I) $-2(4x+7y)=-2(-14)$
∴ $-8x-14y=28$

(I) $-8x-14y=28$
(II) $8x+5y=8$
____________________
(III) $-9y=36$

∴ $y=-4$

We can find the value of x by substituting y either in (I) or (II). Thus, from (I):

$4x+7(-4)=-14$
∴ $4x-28=-14$
∴ $4x=14$
∴ $x=\frac{14}{4}$
∴ $\boxed{x=\frac{7}{2}}$

Let's substitute the values of x and y into (I) and (2)

(I) $4(\frac{7}{2})+7(-4)=14-28=-14$
(II) $8(\frac{7}{2})+5(-4)=28-20=8$

Finally the answer is:

$\boxed{x=\frac{7}{2} \rightarrow x= 3 \frac{1}{2}}$

4 0

2 years ago

What is the value of x in the figure? (2x+15)°

Deffense [45]

Answer:

(2x + 15)° = 180°

2x = 180 - 15

2x = 165

x = 165/2

x = 82.5

6 0

2 years ago