All categories

2 years ago

Which of the following is the correct graph of the solution to the inequality -13> -5x+2> -28?

Mathematics

1 answer:

anyanavicka [17]2 years ago

4 0

Answer:

first option

Step-by-step explanation:

solving the inequality

- 13 > - 5x + 2 > - 28 ( subtract 2 from each interval )

- 15 > - 5x > - 30

divide each interval by - 5 , reversing the symbols as a result of dividing by a negative quantity.

3 < x < 6

since the symbol is < then end values will be an open circle with the values between shaded blue, that is the first graph

You might be interested in

For funcitons f(x)=2x+3 and g(x)=-3x-2, please find (f∘g)(-1)

ratelena [41]

Answer:

$\displaystyle (f\circ g)(-1) = 5$

Step-by-step explanation:

We are given the two functions:
$\displaystyle f(x) = 2x + 3\text{ and } g(x) = -3x - 2$

And we want to find:
$\displaystyle (f\circ g)(-1)$

Recall that this is equivalent to:
$\displaystyle (f\circ g)(-1) = f(g(-1))$

Hence, find g(-1):
$\displaystyle \begin{aligned} g(x) & = -3x - 2\\ \\ g(-1) & = -3(-1) - 2\\ \\ & = (3) - 2 \\ \\ & = 1 \end{aligned}$

Substitute:
$\displaystyle f(g(-1)) = f(1)$

Find f(1):

$\displaystyle \begin{aligned} f(x) & = 2x+ 3 \\ \\ f(1) & = 2(1) + 3 \\ \\ & = 5\end{aligned}$

In conclusion:
$\displaystyle (f\circ g)(-1) = 5$

5 0

3 years ago

Use vectors to show that, for any triangle1 in R², the points2 that are 2/3 of the way from a vertex to the midpoint of the oppo

Anit [1.1K]

Answer:

True

Step-by-step explanation:

the centroid divides each median into segments with a 2:1 ratio(means 2/3)

6 0

3 years ago

Add the sum of 1 and one nineth part of 72 to the sum of 72 and one fourth of 72.

meriva

Answer:

Step-by-step explanation:

1/9 of 72 = 8

1/4 of 72 = 18

1 + 8 = 9

72 + 18 = 90

90 + 9 = 99

I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!

3 0

3 years ago

D. 10.83<br> Math question Please Help don't Guess

shepuryov [24]

Remark

You need to do some trig to get the final answer. There is no way around it. You can however, solve the first part with the Pythagorean Theorem.

Step One

Find AB

AB^2 = DB^2 + AD^2

AB^2 = 7.5^2 + 4.9^2

AB^2 = 56.25 + 24.01

AB^2 = 80.26

AB = sqrt(80.26)

AB = 8.9588

Step Two

Move to the triangle on your right. Find x

Tan(C)= opposite / adjacent

Tan(55.8) = AB/adjacent

Tan(55.8) = 8.9588/ x Multiply both sides by x

x * tan(55.8) = 8.9588 Divide by tan(55.8)

x = 8.9588/tan(55.8)

x = 6.09

Answer: A

5 0

3 years ago

Exercise 5.2. Suppose that X has moment generating function

soldi70 [24.7K]

Answer:

a) Mean, E(X) = - 0.5

Variance = = 9.25

b) $M_{X}(t)=E(e^{tX})$

⇒ $=\sum e^{tx}p(x)$

⇒ $=\frac{1}{2}+\frac{1}{3}e^{-4t}+\frac{1}{6}e^{5t}$

Step-by-step explanation:

Given:

moment generating function of X as:

MX(t) = $\frac{1}{2} + \frac{1}{3}e^{-4t} + \frac{1}{6} e^{5t}$

a) Now

Mean, E(X) = $M_{X}'(t=0)$

Thus,

$M_{X}'(t)=\frac{1}{3}(-4)e^{-4t}+\frac{1}{6}(5)e^{5t}$

$M_{X}'(t)=\frac{-4}{3}e^{-4t}+\frac{5}{6}e^{5t}$

also,

$E(X^{2})=M_{X}''(t=0)$

Thus,

$M_{X}''(t)=\frac{-4}{3}(-4)e^{-4t}+\frac{5}{6}(5)e^{5t}$

$M_{X}''(t)=\frac{16}{3}e^{-4t}+\frac{25}{6}e^{5t}$

Therefore,

Mean, E(X) = $M_{X}'(t=0)=\frac{-4}{3}e^{-4(0)}+\frac{5}{6}e^{5(0)}$

Mean, E(X) = - 0.5

and

$E(X^{2})=M_{X}''(t=0)=\frac{16}{3}e^{-4(0)}+\frac{25}{6}e^{5(0)}$

$E(X^{2})$ = 9.5

also,

Variance(X) = E(X²) - E(X)²

⇒ 9.5 - (-0.5)²

= 9.25

b) Now,

Let f(x) be the PMF of X

Thus,

$M_{X}(t)=E(e^{tX})$

⇒ $=\sum e^{tx}p(x)$

⇒ $=\frac{1}{2}+\frac{1}{3}e^{-4t}+\frac{1}{6}e^{5t}$

Therefore,

at x = 0, P(x) = $\frac{1}{2}$

at x= - 4 ,P(x) = $\frac{1}{3}$

at x = 5, P(x) = $\frac{1}{6}$

Thus,

E(X) = $\sum xP(x)=0(\frac{1}{2})+(-4)(\frac{1}{3})+5(\frac{1}{6})$

E(X) = - 0.5

also, $E(X^{2})=\sum x^{2}P(x)=0^{2}(\frac{1}{2})+(-4)^{2}(\frac{1}{3})+5^{2}(\frac{1}{6})$

$E(X^{2})$ = 9.5

Hence,

Var(X) = E(X²) - E(X)²

⇒ 9.5 - (-0.5)²

= 9.25

4 0

4 years ago