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3 years ago

Factor this quadratic expression: a2 - 2a - 15

Mathematics

2 answers:

Mumz [18]3 years ago

8 0

A² - 2a - 15
= a² - 5a + 3a - 15
= a(a-5) + 3(a-5)
= (a-5)(a+3)

Sliva [168]3 years ago

7 0

A^2-2a-15

1. Ask: Which two numbers add up to -2 and multiply to -15?
-5 and 3

2. Rewrite the expression using the above
(a-5)(a+3)

Have a nice day :D

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Two dice are tossed. Find the probability of getting the sum of the

pogonyaev

Answer:

Step-by-step explanation:

If you are talking about a die with 6 faces, then 16 isn't possible. 12 is the highest possible number.

If you are talking about some other kind of die, you have to specify it.

I'm going to assume you made a mistake and meant 6.

There are 5 ways to get six

3 - 3

4 - 2

2 - 4

5 - 1

1 - 5

There are 36 ways of throwing 2 dice.

So the probability = 5/36 = 0.1389

If you really did mean 16 then the probability = 0

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3 years ago

A sample of 900 college freshmen were randomly selected for a national survey. Among the survey participants, 372 students were

Rufina [12.5K]

Answer:

a) $ME=2.58 \sqrt{\frac{0.413(1-0.413)}{900}}=0.0423$

b) $0.413 - 2.58 \sqrt{\frac{0.413(1-0.413)}{900}}=0.371$

Step-by-step explanation:

1) Data given and notation

n=900 represent the random sample taken

X=372 represent the students were pursuing liberal arts degrees

$\hat p=\frac{372}{900}=0.413$ estimated proportion of students were pursuing liberal arts degrees

$\alpha=0.01$ represent the significance level

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

p= population proportion of students were pursuing liberal arts degrees

2) Solution to the problem

The confidence interval would be given by this formula

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

For the 99% confidence interval the value of $\alpha=1-0.99=0.01$ and $\alpha/2=0.005$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=2.58$

The margin of error is given by:

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

If we replace we have:

$ME=2.58 \sqrt{\frac{0.413(1-0.413)}{900}}=0.0423$

And replacing into the confidence interval formula we got:

$0.413 - 2.58 \sqrt{\frac{0.413(1-0.413)}{900}}=0.371$

$0.413 + 2.58 \sqrt{\frac{0.413(1-0.413)}{900}}=0.455$

And the 99% confidence interval would be given (0.371;0.455).

We are confident (99%) that about 37.1% to 45.5% of students were pursuing liberal arts degrees.

7 0

3 years ago

Write the equation of the line in fully simplified slope-intercept form.

Leya [2.2K]

Answer:

$y = -\frac{1}{6}x +2$

Step-by-step explanation:

To write an equation into slope-intercept form, or y = mx + b format, we need to find the y-intercept of the line and its slope and substitute values for m and b.

1) First, find the y-intercept. The y-intercept is the point at which the line intersects the y-axis. Reading the graph, we can see that the line passes the y-axis at the point (0,2), thus that is the y-intercept.

2) Next, find the slope. Pick out two points on the graph to use for the slope formula, $\frac{y_2-y_1}{x_2-x_1}$ . I chose to work with (0,2) and (6,1). Now, substitute the two points' x and y values into the formula appropriately and solve:

$\frac{(1)-(2)}{(6)-(0)} \\= \frac{1-2}{6-0}\\= \frac{-1}{6}$

Thus, $-\frac{1}{6}$ is the slope.

3) Now, substitute the calculated values into the y = mx + b format. The b represents y-value of the y-intercept. The y-intercept is (0,2), thus substitute 2 for b. The coefficient of the x term, or m, represents the slope, thus substitute $-\frac{1}{6}$ for m. This will give the following equation of the line in slope-intercept format:

$y = -\frac{1}{6}x +2$

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3 years ago

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Answer:

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