Points D, B, and E are collinear. Find the value of a so that points A, B, and C
are collinear.

Answer:

40/30

Step-by-step explanation:

[tex] \tan(c) = \frac{40}{30} = \frac{4}{3} [/tex]

Answer:

yup

Step-by-step explanation:

Answer: 25g/cm3

Step-by-step explanation: The formula for density is mass÷volume. There is no need to convert the mass since it is already in grams.

Answer:

B' = (3, -3)

Step-by-step explanation:

If the coordinate (a,b) is dilated by a factor of k, the resulting coordinate will be ()ka, ka)

Given the coordinate (1, -1). When dilated by a factor of 3, the resulting coordinate will be;

B' = 3B

B' = 3(1, -1)

B' = (3(1), 3(-1))

B' = (3, -3)

Answer:

5.3%

Step-by-step explanation:

The first step is to find the z score corresponding to $200.

[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{200-144.05}{34.52}\approx 1.62[/tex]

The next step is to find the area under the standard normal curve to the right of z = 1.62.  Some graphing calculators can do this, and there are tables that will help, although many of those show areas to the left of a particular z-score.

Calculator (TI-83/84)

See the attached image.

The command uses 1 x 10^99 as "positive infinity" and calculates the area under the normal curve from 1.62 all the way to the right.

Table

See attached table.  This table shows areas to the left of a certain z-score.

Find the entry for 1.62 (it's on page 2 highlighted with a red box).  The table says the area to the left of 1.62 is 0.9474.

But the area under the entire curve is 1!

This important fact means that the area to the right of z = 1.62 is 1 - 0.9474 = 0.0536, about 5.3%

(To get the area to the right of z, subtract the area to the left of z from 1.)

Answer:

1st option

Step-by-step explanation:

From the graph the zeros are x = - 3 and x = 1 , then the corresponding factors are

(x + 3) and (x - 1) , so

y = a(x + 3)(x - 1) ← a is a multiplier

To find a substitute a point on the graph into the equation

Using (0, - 1.5 ) , then

- 1.5 = a(3)(- 1) = - 3a ( divide both sides by - 3 )

0.5 = a

Then

f(x) = 0.5(x + 3)(x - 1)

Answer:

8 sides

Step-by-step explanation:

(n-2)×180=1080

180n-360=1080

180n=1080+360

180n=1440

n=1440/180

n=8 sides

it's an octagon

Answer:

It has 8 sides

Step-by-step explanation:

This is because the formula is 180(n-2) where n is the amount of sides. An octagon has 8 sides so the sum of the angles is 180(8-2)=180(6)=180×6=1080 degrees

Hope that helps :)

Answer:

48 cm

Step-by-step explanation:

Answer:48 cm

Step-by-step explanation:

a^2+b^2=c^2

a^2+16^2=20^2

a^2+256=400

a^2= 144

a = 12

12+16+20=48

The answer to all the questions is explained below with justifications.

In statistics, the process of hypothesis testing involves putting an analyst's presumption about a population parameter to the test. The type of data used and the purpose of the study will determine the methodology the analyst uses.

a) The null hypothesis[tex](H_o)[/tex] is that 71.3% or more of American families owned their homes.

The alternative hypothesis[tex](H_1)[/tex]is less than 71.3% of American families owned their homes.

b) The type I error is the null hypothesis is true but we assumed it to be false that is 71.3% or more of American families owned their homes but the council did not provide tax breaks.

The type II error is the null hypothesis is false and we assumed it to be true

that is less than 71.3% of American families owned their homes and the council provides tax breaks.

c) The consequences of the type II error would be the council will provide tax breaks to more people and it would cost them a large amount of money.

d) Type II error is more serious in this context as the council has to lay off a large amount as compared to individual homeowners who already can afford to buy a house.

e) For type I error house owners will be harmed and for type II error counsel will be harmed.

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The provided expression can be simplified in the form 2y4/x4 option ( B) Using the integer exponent characteristics,  = [x[tex]^\frac{1}{8}[/tex] . y⁸]  is the right answer.

In mathematics, integer exponents are exponents that fall under the integer category. It's possible for the number to be either positive or undesirable. The positive integer exponents in this example dictate how many times that base number must be multiplied by itself.

It's possible for the number to be either positive or undesirable. The positive integer exponents in this example dictate how many instances the base number must be multiplied by itself.

= [x[tex]^\frac{1}{4}[/tex] . y¹⁶][tex]^\frac{1}{2}[/tex]

= [x[tex]^\frac{1}{8}[/tex] . y⁸]

The provided expression can be simplified in the form 2y4/x4 option ( B) Using the integer exponent characteristics,  = [x[tex]^\frac{1}{8}[/tex] . y⁸]  is the right answer.

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Answer:

80

Step-by-step explanation:

Because it is more than 45 and the only one that is more that 45 is 80

Answer:

4

Step-by-step explanation:

Add each sample separately

A.17   B. 47   C. 39 D. 52 E. 45

Then you add them all together which totals 200 sick days

We know that they surveyed 5 schools and 10 students at random from each one. So we want to know the mean of sick days the students took not the schools in all.

So we divide 200/50

And get a mean of 4.

So each student took an average of 4 sick days each in the country.

Answer:

B, Rectangle.

Answer:

number 3

Step-by-step explanation:

it helped us try to learn hieroglyphics

Answer:

x=3

Step-by-step explanation:

3 cubed is 27

Answer:

Step-by-step explanation:

It is D, I did this quiz once

Step-by-step explanation:

to find the equation of any line we have to first find the slope. the slope formula is:

[tex] \frac{y2 - y1}{x2 - x1} [/tex]

our slope here would be 8/13

now we input the points in the equation

y = mx + b

then we find b to be -3(7/13)

so the final equation would be:

[tex]y = \frac{8x}{13} - 3( \frac{7}{13} )[/tex]

For her research, a geneticist has to raise a stock of fruit flies. She presently has 200 fruit flies in stock;

The mathematical function she may use to calculate is given as

f(n)=log1.38(n/200)

Which function could she use to calculate, the number of days required for her stock to grow to n fruit flies?

Generally, the equation for the final value is mathematically given as

A=Ao(1+u)^t

Therefore

n=200(1+0.38)*t

log(1.38^t)=log(n/200)

t=log1.38(n/200)

In conclusion, The function she could use to calculate is

f(n)=log1.38(n/200)

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Answer:

-4 and 12 are the zeros of the quadratic.

Step-by-step explanation:

What value does X need to be so (x+4) is 0? -4

What value does X need to be so (x-12) is 0? 12

Answer:

6.28

Step-by-step explanation:

½ × 3.47²

Answer:

I think its C

Step-by-step explanation:

The fast of the radius of balloon increasing is 480 cm³ / sec.

Given data :

V = [tex]\frac{4}{3}[/tex] π r³

we know [tex]\frac{dr}{dt}[/tex] = 30 cm/ sec

we want [tex]\frac{dV}{dt}[/tex] when r = 2cm

Differentiate V = [tex]\frac{4}{3}[/tex] π r³ implicitly with respect to t

[tex]\frac{dV}{dt}[/tex] (V) = [tex]\frac{dr}{dt}[/tex] ( [tex]\frac{4}{3}[/tex] π r³ )

[tex]\frac{dV}{dt}[/tex] = [tex]\frac{4}{3}[/tex] π x 3r² [tex]\frac{dr}{dt}[/tex] = 4 π r² [tex]\frac{dr}{dt}[/tex]

Plug in what you know and solve for what you don't know.

[tex]\frac{dV}{dt}[/tex] = 4π ( 2 )² ( 30 / sec ) =

= 120 x 4 .π cm³ / sec

= 480 cm³ / sec

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The number of hours that the team trians per week is 17 hours.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

Since the the swim tea spends 1/2h in the gym followed by 1 1/4 in the pool. On Saturday there is no gym work but double the swim team time. The number of hours will be:

( 1 1/4 + 1/2 + 2 1/2) × 4

= 4.25 × 4

= 17 hours.

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Answer:

The null hypothesis is [tex]H_0: \mu = 14[/tex]

The alternate hypothesis is [tex]H_a: \mu < 14[/tex]

The test statistic is t = -1.95.

The p-value is of 0.0292. This means that for a level of significance of 0.0292 and higher, there is sufficient evidence to conclude that the  highlighters wrote for less than 14 continuous hours.

Step-by-step explanation:

Suppose a consumer product researcher wanted to find out whether a highlighter lasted less than the manufacturer's claim that their highlighters could write continuously for 14 hours.

At the null hypothesis, we test if the mean is 14 hours, that is:

[tex]H_0: \mu = 14[/tex]

At the alternate hypothesis, we test if the mean is less than 14 hours, that is:

[tex]H_a: \mu < 14[/tex]

The test statistic is:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.

14 is tested at the null hypothesis:

This means that [tex]\mu = 14[/tex]

X = 13.6 hours, s = 1.3 hours. Sample of 40:

In addition to the values of X and s given, we have that [tex]n = 40[/tex]

Test statistic:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{13.6 - 14}{\frac{1.3}{\sqrt{40}}}[/tex]

[tex]t = -1.95[/tex]

The test statistic is t = -1.95.

P-value:

The p-value of the test is the probability of finding a sample mean lower than 13.6, which is a left tailed test, with t = -1.95 and 40 - 1 = 39 degrees of freedom.

Using a calculator, the p-value is of 0.0292. This means that for a level of significance of 0.0292 and higher, there is sufficient evidence to conclude that the  highlighters wrote for less than 14 continuous hours.

Answer:

It's neither:

x =√ 9.000 = 3.00000 or :

x =√ 9.000 = -3.00000 or :

x =√ 8.000 = 2.82843 or :

x =√ 8.000 = -2.82843

Four solutions

Answer:

x^4 - 17x^2 + 72 = (x^2 - 9)(x^2 - 8)

Step-by-step explanation:

First, we need to find two numbers that multiply to give us 72 and whose sum is -17. We can see that 8 and 9 multiply to give us 72, and their sum is 8 + 9 = 17. Since we want the sum to be negative, we need to change one of the signs. So we write -(8 + 9) = -17.

Next, we write the expression as the product of two binomials. We factor out the common factor x^2 from the first two terms: x^4 - 17x^2 + 72 = x^2(x^2 - 17) + 72

Now, we complete the square in the first binomial. To do this, we need to add and subtract (17/2)^2 = (8.5)^2 = 72.25 inside the bracket:

x^2(x^2 - 17) + 72 = x^2(x^2 - 17 + 72.25 - 72.25) + 72 = x^2(x^2 - 17 + 72.25) - 72.25 + 72

Now we can rewrite the square of a binomial :

x^2(x^2 - 17 + 72.25) = x^2((x-8.5)^2)

Finally, we can combine the two binomials

x^2((x-8.5)^2) + 72 = (x^2(x-8.5)^2) + 8(9)

So the expression x^4 - 17x^2 + 72 factors completely as (x^2 - 9)(x^2 - 8)

Hope this helps!

Answer:

60%

Step-by-step explanation:

Answer:

106.2

Step-by-step explanation:

A 18% increase of a number is the same as multiplying it by 1.18.

If we multiply 90 by 1.18 we get:

90 * 1.18

106.2

Answer:

What about Pythagorean Theorem?