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3 years ago

7. What is the slope of the line that passes through the pair of points (3, 8) and (9, 5) ? (1 point)

2 answers:

5 0

7. D
8. D
9. D
10.C

for 7 & 8 you use the equation
$\frac{y2 - y1}{x2 - x1}$
your points are (3,8) & (9,5)

so you plug the numbers in
y2= 5
y1=8

x2=9
x1=3
you subtract them get a fraction and that is your slope

9 & 10
use the equation
$y - y1 = m(x - x1)$
plug you numbers in for y1 and x2 m is your slope plug it in and that is your equation

wariber [46]3 years ago

3 0

7. (D). -1/2
8. (D). -22/6
10. (D). y-2=3(x+5)
11. (C). y+2=-1/2(x+4)

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Please help f(x)=x^2+x-1 g(x)=-3x+12 Find g(f(x))

Alecsey [184]

Answer: -3x^2-3x+9

Step-by-step explanation:

-3(x^2+x-1)+12 = -3x^2-3x-3+12 = -3x^2-3x+9

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3 years ago

The digit 5 appears twice in the number 255,120. How does the total value of the 5 on the right compare to the total value of th

maksim [4K]

Answer:

The value of the first " $5$ " in the number $255,\!120$ is ten times that of the second " $5\!$ " in this number.

Step-by-step explanation:

What gives the number " $255,\!120$ " its value? Of course, each of its six digits has contributed. However, their significance are not exactly the same. For example, changing the first $\verb!5!$ to $\verb!6!$ would give $2\mathbf{6}5,\!120$ and increase the value of this number by $10,\!000$ . On the other hand, changing the second $\verb!5!\!$ to $\verb!6!\!$ would give $25\mathbf{6},\!120$ , which is an increase of only $1,\!000$ compared to the original number.

The order of these two digits matter because the number " $255,\!120$ " is written using positional notation. In this notation, the position of each digits gives the digit a unique weight. For example, in $255,\!120\!$ :

$\begin{array}{|r||c|c|c|c|c|c|}\cline{1-7}\verb!Digit!& \verb!2! & \verb!5! & \verb!5! & \verb!1! & \verb!2! & \verb!0!\\\cline{1-7}\textsf{Index} & 5 & 4 & 3 & 2 & 1& 0 \\ \cline{1-7} \textsf{Weight} & 10^{5} & 10^{4} & 10^{3} & 10^{2} & 10^{1} & 10^{0}\\\cline{1-7}\end{array}$ .

(Note that the index starts at $0$ from the right-hand side.)

Using these weights, the value $255,\!120$ can be written as the sum:

$\begin{aligned}& 255,\!120\\ &= 2 \times 10^{5} + 5 \times 10^{4} + 5 \times 10^{3} + 1 \times 10^{2} + 2 \times 10^{1} + 0 \times 10^{0} \\&=200,\!000 + 50,\!000 + 5,\!000 + 100 + 20 + 0 \end{aligned}$ .

As seen in this sum, the first " $5$ " contributed $50,\!000$ to the total value, while the second " $5\!$ " contributed only $5,\!000$ .

Hence: The value of the first " $5$ " in the number $255,\!120$ is ten times that of the second " $5\!$ " in this number.

7 0

3 years ago

Read 2 more answers

Many elementary school students in a school district currently have ear infections. A random sample of children in two different

Marta_Voda [28]

Answer:

Step-by-step explanation:

The summary of the given data includes;

sample size for the first school $n_1$ = 42

sample size for the second school $n_2$ = 34

so 16 out of 42 i.e $x_1$ = 16 and 18 out of 34 i.e $x_2$ = 18 have ear infection.

the proportion of students with ear infection Is as follows:

$\hat p_1 = \dfrac{16}{42}$ = 0.38095

$\hat p_2 = \dfrac{18}{34}$ = 0.5294

Since this is a two tailed test , the null and the alternative hypothesis can be computed as :

$H_0 :p_1 -p_2 = 0 \\ \\ H_1 : p_1 - p_2 \neq 0$

level of significance ∝ = 0.05,

Using the table of standard normal distribution, the value of z that corresponds to the two-tailed probability 0.05 is 1.96. Thus, we will reject the null hypothesis if the value of the test statistics is less than -1.96 or more than 1.96.

The test statistics for the difference in proportion can be achieved by using a pooled sample proportion.

$\bar p = \dfrac{x_1 +x_2}{n_1 +n_2}$

$\bar p = \dfrac{16 +18}{42 +34}$

$\bar p = \dfrac{34}{76}$

$\bar p = 0.447368$

$\bar p + \bar q = 1 \\ \\ \bar q = 1 -\bar p \\ \\\bar q = 1 - 0.447368 \\ \\\bar q = 0.552632$

The pooled standard error can be computed by using the formula:

$S.E = \sqrt{ \dfrac{ \bar p \bar q}{ n_1} + \dfrac{\bar p \bar p}{n_2} }$

$S.E = \sqrt{ \dfrac{ 0.447368 * 0.552632}{ 42} + \dfrac{ 0.447368 * 0.447368}{34} }$

$S.E = \sqrt{ \dfrac{ 0.2472298726}{ 42} + \dfrac{ 0.2001381274}{34} }$

$S.E = \sqrt{ 0.01177284105}$

$S.E = 0.1085$

The test statistics is ;

$z = \dfrac{\hat p_1 - \hat p_2}{S.E}$

$z = \dfrac{0.38095- 0.5294}{0.1085}$

$z = \dfrac{-0.14845}{0.1085}$

z = - 1.368

Decision Rule: Since the test statistics is greater than the rejection region - 1.96 , we fail to reject the null hypothesis.

Conclusion: There is insufficient evidence to support the claim that a difference exists between the proportions of students who have ear infections at the two schools

5 0

3 years ago

What is the probability of getting zero heads in six tosses? What is the probability of getting exactly two heads in six tosses?

alexira [117]

Answer:

The probability of getting zero heads in six tosses is 0.015625.

The probability of getting exactly two heads in six tosses is 0.234375.

Step-by-step explanation:

Using the Minitab software for computing the desired probabilities.

We take n=6 and p=1/2 because we have six tosses and in binomial distribution the probability of success p remains constant in each trial whereas the probability of success in this case is getting heads.

When a coin is tossed then there are two possible outcomes head or tail.

So,

p= P(heads)=1/2=0.5

The probability of getting zero heads in six tosses is computed by considering the following steps:

In Minitab

Calc >Probability Distributions > Binomial

Select n=6 and p=0.5 and select input constant=0 and bubble the probability and by clicking OK we get the following output:

Probability Density Function

Binomial with n = 6 and p = 0.5

x P( X = x )

0 0.015625

So, the probability of getting zero heads in six tosses is 0.015625.

The probability of getting exactly two heads in six tosses is computed by considering the following steps :

In Minitab

Calc >Probability Distributions > Binomial

Select n=6 and p=0.5 and select input constant=2 and bubble the probability and by clicking OK we get the following output:

Probability Density Function

Binomial with n = 6 and p = 0.5

x P( X = x )

2 0.234375

So, the probability of getting exactly two heads in six tosses is 0.234375.

7 0

4 years ago

If line q has a slope of -3/8, what is the slope of any line perpendicular to to q?

Contact [7]

Answer:

The slope of line perpendicular to line q is 8/3.

Step-by-step explanation:

Given that:

Slope of a line q is -3/8

Slope is the steepness of any line.

Let,

x be the slope of line perpendicular to line q.

The product of slopes of two perpendicular lines is equal to -1.

$\frac{-3}{8}x = -1$

Multiplying both sides -8/3

$\frac{-8}{3}*\frac{-3}{8}x=-1*\frac{-8}{3}$

x = 8/3

Hence,

The slope of line perpendicular to line q is 8/3.

7 0

3 years ago