Exponential function f is represented by the table. x -1 0 1 2 3 4 f(x) 7.5 7 6 4 0 -8 Function g is an exponential function passing through the points (0,27) and (3,0). Which statement correctly compares the behavior of the two functions on the interval (0, 3)? A. Both functions are positive and decreasing on the interval. B. Both functions are positive on the interval, but one function is increasing while the other is decreasing. C. Both functions are positive and increasing on the interval. D. One function is positive on the interval, and the other is negative.

Answer:

a) E(X) = 16.09 ft³

E(X²) = 262.22 ft⁶

Var(X) = 3.27 ft⁶

b) E(22X) = 354 dollars

c) Var(22X) = 1,581 dollars

d) E(X - 0.01X²) = 13.470 ft³

Step-by-step explanation:

The complete Correct Question is presented in the attached image to this solution.

a) Compute E(X), E(X2), and V(X).

The expected value of a probability distribution is given as

E(X) = Σxᵢpᵢ

xᵢ = Each variable in the distribution

pᵢ = Probability of each distribution

Σxᵢpᵢ = (13.5×0.20) + (15.9×0.59) + (19.1×0.21)

= 2.70 + 9.381 + 4.011

= 16.092 = 16.09 ft³

E(X²) = Σxᵢ²pᵢ

Σxᵢ²pᵢ = (13.5²×0.20) + (15.9²×0.59) + (19.1²×0.21)

= 36.45 + 149.1579 + 76.6101

= 262.218 = 262.22 ft⁶

Var(X) = Σxᵢ²pᵢ - μ²

where μ = E(X) = 16.092

Σxᵢ²pᵢ = E(X²) = 262.218

Var(X) = 262.218 - 16.092²

= 3.265536 = 3.27 ft⁶

b) E(22X) = 22E(X) = 22 × 16.092 = 354.024 = 354 dollars to the nearest whole number.

c) Var(22X) = 22² × Var(X) = 22² × 3.265536 = 1,580.519424 = 1,581 dollars

d) E(X - 0.01X²) = E(X) - 0.01E(X²)

= 16.092 - (0.01×262.218)

= 16.0926- 2.62218

= 13.46982 = 13.470 ft³

Hope this helps!!!

Answer:

I didn't know which one you wanted...

Step-by-step explanation:

1. Finding the x an y-intercepts

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

x-intercept(s): (2,0)

y-intercept(s): (0,−24)

2. Finding the slope and y-intercept

Use the slope-intercept form to find the slope and y-intercept.

Slope: 12

y-intercept: −24

Answer:

[tex] P(A) = 0.25, P(B= 0.3[/tex]

And if we want to find [tex] P(A \cap B)[/tex] we can use this formula from the definition of independent events :

[tex] P(A \cap B) =P(A) *P(B) = 0.25*0.3= 0.075[/tex]

And the best option would be:

[tex] P(A \cap B) =0.075[/tex]

Step-by-step explanation:

For this case we have the following events A and B and we also have the probabilities for each one given:

[tex] P(A) = 0.25, P(B= 0.3[/tex]

And if we want to find [tex] P(A \cap B)[/tex] we can use this formula from the definition of independent events :

[tex] P(A \cap B) =P(A) *P(B) = 0.25*0.3= 0.075[/tex]

And the best option would be:

[tex] P(A \cap B) =0.075[/tex]

Answer:

  both

Step-by-step explanation:

Both of the equations shown here are linear equations in standard form.

  5x + 3y = 210

  x + y = 60

Answer:

D. *6F

Step-by-step explanation:

C=(F-32)*5/9

30=(F-32)*5/9

F = (30*9)/5+32

F = 86

Answer:

The probability that neither box contains a prize is 0.5625 or 56.25%

Step-by-step explanation:

It's referred as to the case when the probability of success (or failure) of the event A doesn't interfere with the probability of B. In this question we'll assume there are enough boxes of cereal of each type to make the choosing of one of them affect very little the choosing of the other one.

Let's call p=0.25 to the probability of getting a cereal box with a prize, and q=0.75 to the negation of p, i.e. the probability of getting a ceral box without a prize. There are four possible combinations: {pp,pq,qp,qq}. We need to find the probability of the combination qq.  We compute it as the product of the individual probabilities

In other words, the probability that neither box contains a prize is 0.5625 or 56.25%

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Answer:

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)  

And replacing we got:

[tex]t=\frac{69.5-69}{\frac{11.2}{\sqrt{147}}}=0.541[/tex]  

Step-by-step explanation:

Information given

[tex]\bar X=69.5[/tex] represent the sample mean    

[tex]s=11.2[/tex] represent the sample standard deviation

[tex]n=69[/tex] sample size  

[tex]\mu_o =69[/tex] represent the value that we want to test

t would represent the statistic (variable of interest)  

Hypothesis to test

We want to check if the true mean is 69, the system of hypothesis would be:  

Null hypothesis:[tex]\mu =69[/tex]  

Alternative hypothesis:[tex]\mu \neq 69[/tex]  

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)  

And replacing we got:

[tex]t=\frac{69.5-69}{\frac{11.2}{\sqrt{147}}}=0.541[/tex]  

Answer:

The chance that there will be exactly 2 heads among the first five tosses and exactly 4 heads among the last 5 tosses is P=0.0488.

Step-by-step explanation:

To solve this problem we divide the tossing in two: the first 5 tosses and the last 5 tosses.

Both heads and tails have an individual probability p=0.5.

Then, both group of five tosses have the same binomial distribution: n=5, p=0.5.

The probability that k heads are in the sample is:

[tex]P(x=k)=\dbinom{n}{k}p^k(1-p)^{n-k}=\dbinom{5}{k}\cdot0.5^k\cdot0.5^{5-k}[/tex]

Then, the probability that exactly 2 heads are among the first five tosses can be calculated as:

[tex]P(x=2)=\dbinom{5}{2}\cdot0.5^{2}\cdot0.5^{3}=10\cdot0.25\cdot0.125=0.3125\\\\\\[/tex]

For the last five tosses, the probability that are exactly 4 heads is:

[tex]P(x=4)=\dbinom{5}{4}\cdot0.5^{4}\cdot0.5^{1}=5\cdot0.0625\cdot0.5=0.1563\\\\\\[/tex]

Then, the probability that there will be exactly 2 heads among the first five tosses and exactly 4 heads among the last 5 tosses can be calculated multypling the probabilities of these two independent events:

[tex]P(H_1=2;H_2=4)=P(H_1=2)\cdot P(H_2=4)=0.3125\cdot0.1563=0.0488[/tex]

Answer:

[tex] 3x - y = 5 [/tex]

Step-by-step explanation:

The two pint equation of a line:

[tex] y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1) [/tex]

We have

[tex] x_1 = 4 [/tex]

[tex] x_2 = 3 [/tex]

[tex] y_1 = 7 [/tex]

[tex] y_2 = 4 [/tex]

[tex] y - 7 = \dfrac{4 - 7}{3 - 4}(x - 4) [/tex]

[tex] y - 7 = \dfrac{-3}{-1}(x - 4) [/tex]

[tex] y - 7 = 3(x - 4) [/tex]

[tex] y - 7 = 3x - 12 [/tex]

[tex] 5 = 3x - y [/tex]

[tex] 3x - y = 5 [/tex]

Answer:

7,000,000,000

Step-by-step explanation:

since the closest number is less than 5 (1<5) you round down making the nearest billion 7

Answer:

7,000,000,000 OR 7 Billion

Step-by-step explanation:

Since the 1 is millions place and its less than 5, you need to round down meaning that 7,125,000,00 rounded to the nearest billion is 7 billion.

Answer:

The temperature that separates the bottom 12% from the top 88% is 97.5°F.

Step-by-step explanation:

We are given that human body temperatures are normally distributed with a mean of 98.2°F and a standard deviation of 0.62°F.

Let X = human body temperatures

So, X ~ Normal([tex]\mu= 98.2,\sigma^{2} = 0.62^{2}[/tex])

The z-score probability distribution for the normal distribution is given by;

                            Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = mean human body temperature = 98.2°F

           [tex]\sigma[/tex] = stnadard deviation = 0.62°F

Now, we have to find the temperature that separates the bottom 12% from the top 88%, that means;

        P(X < x) = 0.12       {where x is the required temperature}

        P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{x-98.2}{0.62}[/tex] ) = 0.12

        P(Z < [tex]\frac{x-98.2}{0.62}[/tex] ) = 0.12

Now, the critical value of x that represents the bottom 12% of the area in the z table is given as -1.1835, that is;

                    [tex]\frac{x-98.2}{0.62} = -1.1835[/tex]

                    [tex]{x-98.2}= -1.1835\times 0.62[/tex]

                     [tex]x = 98.2 -0.734[/tex] = 97.5°F

Hence, the temperature that separates the bottom 12% from the top 88% is 97.5°F.

Answer:

[tex]( x_1 , y_1 , z_1 ) = < -7 + 4\sqrt{3} , -4 + 2\sqrt{3} , 7 - 2\sqrt{3} >\\\\( x_2 , y_2 , z_2 ) = < -7 - 4\sqrt{3} , -4 - 2\sqrt{3} , 7 + 2\sqrt{3} >\\[/tex]

Step-by-step explanation:

Solution:-

- We are given a parametric form for the vector equation of line defined by ( t ).

- The line vector equation is:

                        L: < 3 + 2t , t + 1 , 2 -t >

- The same 3-dimensional space is occupied by a unit sphere defined by the following equation:

                          [tex]S: x^2 + y^2 + z^2 = 1[/tex]

- We are to determine the points of intersection of the line ( L ) and the unit sphere ( S ).

- We will substitute the parametric equation of line ( L ) into the equation defining the unit sphere ( S ) and solve for the values of the parameter ( t ):

                        [tex]( 3 + 2t )^2 + ( 1 + t )^2 + ( 2 - t)^2 = 1\\\\( 9 + 12t + 4t^2 ) + ( t^2 + 2t + 1 ) + ( 4 + t^2 -4t ) = 1\\\\t^2 + 10t + 13 = 0\\\\[/tex]

- Solve the quadratic equation for the parameter ( t ):

                       [tex]t = -5 + 2\sqrt{3} , -5 - 2\sqrt{3}[/tex]

- Plug in each of the parameter value in the given vector equation of line and determine a pair of intersecting coordinates:

                      [tex]( x_1 , y_1 , z_1 ) = < -7 + 4\sqrt{3} , -4 + 2\sqrt{3} , 7 - 2\sqrt{3} >\\\\( x_2 , y_2 , z_2 ) = < -7 - 4\sqrt{3} , -4 - 2\sqrt{3} , 7 + 2\sqrt{3} >\\[/tex]

Answer:

Answer is option 2

Step-by-step explanation:

We know that Angle M = Angle G (given in diagram)

We also know that Angle L in triangle LMN is equal to Angle L in triangle LGH

As two angles are equal in both triangles they are similar.

But why is it Triangle LGH instead of Triangle HGL?

As we know M=G therefore they should be in the same place in the name Of the triangle. In triangle LMN M is in the middle therefore Angle G should also be in the middle

Answer

so I need to know the coordinates for me to tell you the answer but I think I can still help you by explaining.

In order for E to become E' the rule for reflection over y=x is (y, x) so you basically switch the x and the Y to have E'. so for you to be able find out E, you need to witch the x and the y.

for example:

if E' was (-2, 3)

E in the pre image would be (3, -2)

hope this helps :)

Answer:

(-2,6)

Step-by-step explanation:

Just did it edge 2021

This is a great question!

When we are given ( r - c )( 3 ), we are being asked to take 3 as x in the functions r( x ) and c( x ), taking the difference of each afterwards -

[tex]r( 3 ) = ( 3 )^2 + 5( 3 ) + 14,\\x( 3 ) = ( 3 )^2 - 3( 3 ) + 4[/tex]

____

Let us calculate the value of each function, determine their difference, and multiply by 100, considering r( x ) and c( x ) are measured in hundreds of dollars,

[tex]r( 3 ) = 9 + 15 + 14 = 38,\\x( 3 ) = 9 - 9 + 4 = 0 + 4 = 4\\----------------\\( r - c )( 3 ) = 38 - 4 = 34,\\34 * 100 = 3,400( dollars )\\\\Solution = 3,400( dollars )[/tex]

Therefore, ( r - c )( 3 ) " means " that George's new store will have a profit of $3,400 after it's third month in business, given the following options,

( 1. The new store will have a profit of $3400 after its third month in business.  

( ​​2. The new store will have a profit of $2400 after its third month in business.

( 3. ​The new store will sell 2400 items in its third month in business.

( 4. The new store will sell 3400 items in its third month in business.

The required answer is , [tex](r-c)(5)[/tex] means the revenue less expenses in 5 months i.e. the new store will have a profit of $ 5400 after 5 months.

The substitution method is the algebraic method to solve simultaneous linear equations.

Given function is,

[tex]r(x) = x^2+5x+14[/tex]...(1)

And [tex]c(x) = x^2-4x+5[/tex]...(2)

Now, substituting the value into the equation (1) and (2).

[tex]r(5) = (5)^2+5(5)+14=64[/tex]

[tex]c(5) = (5)^2-4(5)+5=10[/tex]

Therefore,

[tex](r-c)(5)=r(5)-c(5)\\=64-10\\=54[/tex]

Now, [tex](r-c)(5)[/tex] means the revenue less expenses in 5 months i.e. the new store will have a profit of $ 5400 after 5 months.

Learn more about the topic Substitution:

https://brainly.com/question/3388130

Answer:

20 years old.

Step-by-step explanation:

Let us say that the man's age is represented by x and the son's age is represented by y.

As of now, x = 2y.

In 20 years, both ages will increase by 20. We can have an equation where the son's age increased by 20 equals 2/3 of the man's age plus 20.

(y + 20) = 2/3(x + 20)

Since x = 2y...

y + 20 = 2/3(2y + 20)

3/2y + 30 = 2y + 20

2y + 20 = 3/2y + 30

1/2y = 10

y = 20

To check our work, the man's age is currently double his son's, so the man is 40 and the son is 20. In 20 years, the man will be 60 and the son will be 40. 40 / 60 = 2/3, so the son's age is 2/3 of his father's.

So, the son's present age is 20 years old.

Hope this helps!

Answer:

  (x, y, z) = (13/7, 19/7, 25/7)

Step-by-step explanation:

You know that the vector whose components are the coefficients of the equation of the plane is perpendicular to the plane. That is (1, 2, 3) is a vector perpendicular to the plane.

The parametric equation for a line through (1, 1, 1) with this direction vector is ...

  (x, y, z) = (1, 2, 3)t +(1, 1, 1) = (t+1, 2t+1, 3t+1)

The point of intersection of this line and the plane will be the point in the plane closest to (1, 1, 1). That point has a t-value of ...

  (t +1) +2(2t +1) +3(3t +1) = 18

  14t +6 = 18

  t = 12/14 = 6/7

The point in the plane closest to (1, 1, 1) is ...

  (x, y, z) = (6/7+1, 2(6/7)+1, 3(6/7)+1)

  (x, y, z) = (13/7, 19/7, 25/7)

Answer:

[tex] g(x) = 2x+2[/tex]

Let's find g(a+h):

[tex] g(a+h)=2*(a+h) +2= 2a +2h +2[/tex]

And now let's find g(a)

[tex] g(a)= 2a+2[/tex]

And now finally:

[tex] g(a+h) = 2a +2h +2 -2a-2 = 2h +2-2= 2h[/tex]

Step-by-step explanation:

We have the following function given:

[tex] g(x) = 2x+2[/tex]

Let's find g(a+h):

[tex] g(a+h)=2*(a+h) +2= 2a +2h +2[/tex]

And now let's find g(a)

[tex] g(a)= 2a+2[/tex]

And now finally:

[tex] g(a+h) = 2a +2h +2 -2a-2 = 2h +2-2= 2h[/tex]

Answer:True

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

Because it can but does not

First find the distance it is reflected:

D = 20.0 x 10.0 /(20-10) = 200/10 = 20cm away.

Now calculate the magnification: -20/ 20 = -1

Now calculate the height:

-1 x 2.50 = -2.50

The negative sign means the image is inverted.

The mirrored image would be inverted, 2.50 cm tall and 20 cm in front of the mirror.

Answer:

HL (try HL, I believe that's the right answer)

Answer:

HL

Step-by-step explanation:

BRO TRUST ME

Answer:

Option A.

Step-by-step explanation:

We need to find the amount of oil for a sports car.

We know that,

1 quart = 4 cups

1 gallon = 4 quarts = 16 cups

Since, quart and cup are small units and they are not sufficient for a sports car because sports car needs more oil, therefore the amount of oil for a sports car is 5 gallons.

Therefore, the correct option is A.

Answer:

  a) 207 mph

  b) x = (1260-w)/1.17

  c) 1000 mb

Step-by-step explanation:

a) Put the pressure in the equation and solve.

  w(900) = -1.17(900) +1260 = 207

The wind speed for a hurricane with a pressure of 900 mb is 207 mph.

__

b) Solving for x, we have ...

  w = -1.17x +1260

  w -1260 = -1.17x

  x = (1260 -w)/1.17 . . . . inverse function

__

c) Evaluating the inverse function for w=90 gives ...

  x = (1260 -90)/1.17 = 1170/1.17 = 1000 . . . millibars

The approximate barometric pressure for a hurricane with a wind speed of 90 mph is 1000 millibars.

Answer:

C

Step-by-step explanation:

[tex]-5x-49\geq 113[/tex]

[tex]-5x\geq 162[/tex]

[tex]x\leq -32.4[/tex]

(Multiplying or dividing by a negative flips the sign).

Answer:

what's a bit

Step-by-step explanation:

Hey there! :)

Answer:

y = 1/4x - 3.

Step-by-step explanation:

Use the slope-formula to find the slope of the line:

[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Plug in two points from the line. Use the points (-4, -4) and (0, 3):

[tex]m = \frac{-3 - (-4)}{0 - (-4)}[/tex]

Simplify:

m = 1/4.

Slope-intercept form is y = mx + b.

Find the 'b' value by finding the y-value at which the graph intersects the y-axis. This is at y = -3. Therefore, the equation is:

y = 1/4x - 3.

Answer:

A) Null and alternative hypothesis

[tex]H_0: \mu=2\\\\H_a:\mu\neq 2[/tex]

B) M = 2.2 hours

C) s = 0.52 hours

D) P-value = 0.255

E) At a significance level of 0.05, there is not enough evidence to support the claim that the mean tree-planting time significantly differs from two hours.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the mean tree-planting time significantly differs from two hours.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=2\\\\H_a:\mu\neq 2[/tex]

The significance level is 0.05.

The sample has a size n=10.

The sample mean is M=2.2.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.52.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.52}{\sqrt{10}}=0.1644[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{2.2-2}{0.1644}=\dfrac{0.2}{0.1644}=1.216[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=10-1=9[/tex]

This test is a two-tailed test, with 9 degrees of freedom and t=1.216, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=2\cdot P(t>1.216)=0.255[/tex]

As the P-value (0.255) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

At a significance level of 0.05, there is not enough evidence to support the claim that the mean tree-planting time significantly differs from two hours.

Sample mean and standard deviation:

[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{10}(1.7+1.5+2.6+. . .+2.3)\\\\\\M=\dfrac{22}{10}\\\\\\M=2.2\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{9}((1.7-2.2)^2+(1.5-2.2)^2+(2.6-2.2)^2+. . . +(2.3-2.2)^2)}\\\\\\s=\sqrt{\dfrac{2.4}{9}}\\\\\\s=\sqrt{0.27}=0.52\\\\\\[/tex]

Answer:

  14

Step-by-step explanation:

Chords the same distance from the center of the circle have the same length. You are shown that half the chord length is 7, so the whole chord length is

  x = 14.