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3 years ago

15

Factor −1/2 out of −1/2x+6.

1 answer:

Minchanka [31]3 years ago

6 0

Answer:

Step-by-step explanation:

socratic.org/questions/how-do-you-factor-1-2-out-of-1-2x-6#630699

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Find the range of <br> y = 2x + 1 <br> a. All real numbers <br> b. All positive number

Debora [2.8K]

B. All positive numbers

3 0

3 years ago

Mrs. Daly's reading classes were surveyed about their reading preferences. The data is summarized in the table below.

andriy [413]

Answer:

Required probability is 0.19

Step-by-step explanation:

The two-way table for the given data is,

Fiction Non-Fiction Total

9th grade 35 8 43

10th grade 52 12 64

Total 87 20 107

It is required to find the probability of the students who prefer to read non-fiction novels, given that they are in 9th grade.

That is, to find the conditional probability $P(Non-fiction| 9th\ grade)$ .

Now, $P(A|B)=\dfrac{P(A\bigcap B)}{P(B)}$

So, we get,

$P(Non-fiction| 9th\ grade)=\dfrac{(Non-fiction\bigcap 9th\ grade)}{P(9th\ grade)}\\\\P(Non-fiction| 9th\ grade)=\dfrac{8}{43}\\\\P(Non-fiction| 9th\ grade)=0.19$

<h3>Thus, the required probability is 0.19.</h3>

5 0

3 years ago

Given the following three points, find by the hand the quadratic function they represent (0,6, (2,16, (3,33)

Lisa [10]

Answer:

$f(x) = 4x^2 - 3x + 6$

Step-by-step explanation:

Quadratic function is given as $f(x) = ax^2 + bx + c$

Let's find a, b and c:

Substituting (0, 6):

$6 = a(0)^2 + b(0) + c$

$6 = 0 + 0 + c$

$c = 6$

Now that we know the value of c, let's derive 2 system of equations we would use to solve for a and b simultaneously as follows.

Substituting (2, 16), and c = 6

$f(x) = ax^2 + bx + c$

$16 = a(2)^2 + b(2) + 6$

$16 = 4a + 2b + 6$

$16 - 6 = 4a + 2b + 6 - 6$

$10 = 4a + 2b$

$10 = 2(2a + b)$

$\frac{10}{2} = \frac{2(2a + b)}{2}$

$5 = 2a + b$

$2a + b = 5$ => (Equation 1)

Substituting (3, 33), and c = 6

$f(x) = ax^2 + bx + x$

$33 = a(3)^2 + b(3) + 6$

$33 = 9a + 3b + 6$

$33 - 6 = 9a + 3b + 6 - 6$

$27 = 9a + 3b$

$27 = 3(3a + b)$

$\frac{27}{3} = \frac{3(3a + b)}{3}$

$9 = 3a + b$

$3a + b = 9$ => (Equation 2)

Subtract equation 1 from equation 2 to solve simultaneously for a and b.

$3a + b = 9$

$2a + b = 5$

$a = 4$

Replace a with 4 in equation 2.

$2a + b = 5$

$2(4) + b = 5$

$8 + b = 5$

$8 + b - 8 = 5 - 8$

$b = -3$

The quadratic function that represents the given 3 points would be as follows:

$f(x) = ax^2 + bx + c$

$f(x) = (4)x^2 + (-3)x + 6$

$f(x) = 4x^2 - 3x + 6$

6 0

4 years ago

HELP! what is the unit rate???

UkoKoshka [18]

The unit rate for that equation is .33

8 0

3 years ago

Read 2 more answers

Of all the students enrolled at the American dream, 9% are playing a music instrument. There are 330 students in ADS. How many s

Genrish500 [490]

Exactly 29.7, but you can't have 7/10 of a student so you round to 30. So 30 students are playing a music instrument because 330 times 0.09 is about 30

5 0

4 years ago