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3 years ago

Which statements are true of the function f(x) = 3(2.5)x? Check all that apply.

Mathematics

2 answers:

pentagon [3]3 years ago

5 0

Answer:

a) the function is exponential

c)the function increases by a factor of 2.5 for each unit increase in x

d)the domain of the function is all real numbers

Step-by-step explanation:

e2020 :))))

brainliest? like? rate?

disa [49]3 years ago

4 0

This is an exponential function since the x is in the exponent's place instead of in the place of a "regular" variable. The first statement is true.

The initial value of this particular function is 3 (the other number is the multiplier), so choice 2 is NOT true.

The function increases by its multiplier, which is 2.5, so statement 3 is true.

The equation allows us to enter any x value we want to determine the y, so the domain is in fact all real numbers. So, this statement is also true.

If you were to graph this on a calculator, you would see that the range, the "allowed" y values for our function, do not touch or ever drop below the x-axis. That means that the range is all numbers greater than 0. So that statement is false. No matter what value we pick for x, we will NEVER get back a negative y value or that y = 0. For example, if x = 0, y = 3; if x = -5, y = .03; if x = -10, y = .0003; if x = 5, y = 292.97; if x = -100, $y = 4.8208*88888810^{-40}$ . Y will never be equal to 0 or less than 0.

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For the family picnic, Dana's mom buys a box of 12 forks, a box of 18 spoons, and a box of 24 knives. How many boxes of each wil

SOVA2 [1]

Answer:

Step-by-step explanation:

This is assuming the following:

1) fork boxes comes with 12 count.

2) spoon boxes comes in 18 count.

3) knife boxes comes in 24 count.

Find the least common factor:

12: 12, 24, 36, 48, 60, 72

18: 18, 36, 54, 72

24: 24, 48, 72

72 is the least common factor shared by all these numbers.

3 0

2 years ago

Read 2 more answers

What is the equation of a line perpendicular to:

Nataly [62]

Step-by-step explanation:

"perpendicular" means it creates a right angle (90°) with the original line.

a key element is the slope (the incline) of the line.

it is the factor of x (here 1/4 for the original line) and is defined as the ratio of "y coordinate change / x coordinate change" when going from one point on the line to another.

the given slope of 1/4 means that for every increase in x by 4 units y increases by 1 unit.

now if you want to draw a few random lines, and then draw lines that cross them with a right angle, you will see very quickly the relationship of the slopes of the crossing lines :

for the slope of the perpendicular line x and y of the original slope trade places (the ratio turns "upside-down") and the sign of the slope flips (if the original line goes up, then the perpendicular line goes down and vice versa. so + turns into -, and - into +).

so, our original slope 1/4 turns into -4/1 = -4.

we still have infinite possibilities to draw such a perpendicular line (more up or more down on the coordinate grid).

to finally "nail" one particular line we need to use the given point and solve for the y-intercept.

the general slope-intercept form is

y = ax + b

a is the slope, b is the y-intercept (the y value for x = 0).

so, using the slope (-4) and the point (2, 5) we have

5 = -4×2 + b = -8 + b

13 = b

so, the full equation is

y = -4x + 13

7 0

2 years ago

Please help on this!!

dexar [7]

3^8=6,561
6,561 •3=19,683

The highest altitude of an altocumulus cloud is 19,683 feet.

8 0

3 years ago

The lifetime X (in hundreds of hours) of a certain type of vacuum tube has a Weibull distribution with parameters α = 2 and β =

stich3 [128]

I'm assuming $\alpha$ is the shape parameter and $\beta$ is the scale parameter. Then the PDF is

$f_X(x)=\begin{cases}\dfrac29xe^{-x^2/9}&\text{for }x\ge0\\\\0&\text{otherwise}\end{cases}$

a. The expectation is

$E[X]=\displaystyle\int_{-\infty}^\infty xf_X(x)\,\mathrm dx=\frac29\int_0^\infty x^2e^{-x^2/9}\,\mathrm dx$

To compute this integral, recall the definition of the Gamma function,

$\Gamma(x)=\displaystyle\int_0^\infty t^{x-1}e^{-t}\,\mathrm dt$

For this particular integral, first integrate by parts, taking

$u=x\implies\mathrm du=\mathrm dx$

$\mathrm dv=xe^{-x^2/9}\,\mathrm dx\implies v=-\dfrac92e^{-x^2/9}$

$E[X]=\displaystyle-xe^{-x^2/9}\bigg|_0^\infty+\int_0^\infty e^{-x^2/9}\,\mathrm x$

$E[X]=\displaystyle\int_0^\infty e^{-x^2/9}\,\mathrm dx$

Substitute $x=3y^{1/2}$ , so that $\mathrm dx=\dfrac32y^{-1/2}\,\mathrm dy$ :

$E[X]=\displaystyle\frac32\int_0^\infty y^{-1/2}e^{-y}\,\mathrm dy$

$\boxed{E[X]=\dfrac32\Gamma\left(\dfrac12\right)=\dfrac{3\sqrt\pi}2\approx2.659}$

The variance is

$\mathrm{Var}[X]=E[(X-E[X])^2]=E[X^2-2XE[X]+E[X]^2]=E[X^2]-E[X]^2$

The second moment is

$E[X^2]=\displaystyle\int_{-\infty}^\infty x^2f_X(x)\,\mathrm dx=\frac29\int_0^\infty x^3e^{-x^2/9}\,\mathrm dx$

Integrate by parts, taking

$u=x^2\implies\mathrm du=2x\,\mathrm dx$

$\mathrm dv=xe^{-x^2/9}\,\mathrm dx\implies v=-\dfrac92e^{-x^2/9}$

$E[X^2]=\displaystyle-x^2e^{-x^2/9}\bigg|_0^\infty+2\int_0^\infty xe^{-x^2/9}\,\mathrm dx$

$E[X^2]=\displaystyle2\int_0^\infty xe^{-x^2/9}\,\mathrm dx$

Substitute $x=3y^{1/2}$ again to get

$E[X^2]=\displaystyle9\int_0^\infty e^{-y}\,\mathrm dy=9$

Then the variance is

$\mathrm{Var}[X]=9-E[X]^2$

$\boxed{\mathrm{Var}[X]=9-\dfrac94\pi\approx1.931}$

b. The probability that $X\le3$ is

$P(X\le 3)=\displaystyle\int_{-\infty}^3f_X(x)\,\mathrm dx=\frac29\int_0^3xe^{-x^2/9}\,\mathrm dx$

which can be handled with the same substitution used in part (a). We get

$\boxed{P(X\le 3)=\dfrac{e-1}e\approx0.632}$

c. Same procedure as in (b). We have

$P(1\le X\le3)=P(X\le3)-P(X\le1)$

and

$P(X\le1)=\displaystyle\int_{-\infty}^1f_X(x)\,\mathrm dx=\frac29\int_0^1xe^{-x^2/9}\,\mathrm dx=\frac{e^{1/9}-1}{e^{1/9}}$

Then

$\boxed{P(1\le X\le3)=\dfrac{e^{8/9}-1}e\approx0.527}$

7 0

3 years ago

What is the exact volume of a cone whose base radius is 9 feet and whose height is 13 feet? Show your work.

Radda [10]

Answer:

<u>The volume of the cone is 1,102.7 feet³ (cubic)</u>

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Radius = 9 feet

Height = 13 feet

2. What is the exact volume of the cone?

We will use the following formula to calculate the volume of the cone:

Volume of the cone = π * Radius² * Height/3

Volume of the cone = 3.1416 * 9² * 13/3

Volume of the cone = 3.1416 * 81 * 13/3

Volume of the cone = 3.1416 *9² * 13/3

<u>Volume of the cone = 1,102.7 feet³ (cubic)</u>

6 0

2 years ago