Let XT(a, A) with probability density function f. Find E [f(X)] in terms of a and X.

a. Phoebe's car has the greater acceleration at first.

b. The maximum distance by which the other car was ahead was approximately 0.69 feet

c. The maximum difference in velocities does not occur at the same time as the maximum distance the two cars are apart.

d. The car that was ahead at first (Calvin's car) does not regain the lead.

Acceleration is the rate at which an object changes its velocity. In other words, it's the amount of change in velocity per unit of time. The standard unit of acceleration is meters per second squared (m/s²).

a Since \(e^{t}\) is always positive and increasing, while 3\(t^{2}\) is positive but increasing at a slower rate, we can conclude that Phoebe's car has the greater acceleration at first.

b We can do this by taking the derivative of the difference and setting it equal to zero:

(su(t) - sp(t))' = 3\(t^{2}\) - \(e^{t}\) = 0

Solving for t, we get t ≈ 0.85 seconds. Plugging this value back into the distance functions, we find that at this time Phoebe was ahead of Calvin by approximately 0.69 feet.

c. The maximum difference in velocities does not occur at the same time as the maximum distance the two cars are apart.

d. Yes, the car that was ahead at first does eventually regain the lead, since both cars have unbounded distance functions.

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Answer:

its C

Step-by-step explanation:

Using exponential function it will take approximately 2.6 years for the population to reach 26676

Exponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function). An exponential function can be in one of the following forms.

The formula given in this question is

P(t) = 988(3.5)ˣ

The time it will take to reach a population of 26676 is

26676 = 988(3.5)ˣ

x = 2.6 years

It will take approximately 2.6 years

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The expression is f(y) = 80y.

We have a school canteen.

We have to write down an expression for the cost in pence of y cups of tea.

A function in mathematics is a relation involving two variables, such that one variable is dependent on the other for its value.

According to the question -

Number of cups of tea = y

Cost of one cup = 80 pence.

Therefore, the function representing the cost in pence of y cups of tea =

f(y) = 80y

Hence, the expression is 80y.

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As per the given costs, 80 notebooks were sold at the student government fundraiser.

Let the number of notebooks sold be = N

Let the number of t-shirts sold be = T

Setting the equation, representing the total number of items sold

N + T = 90

or N = 90 - T.

Setting the equation, representing the total amount -

6N + 12T = 600

Substituting this value of N into the second equation -

6(90 - T) + 12T = 600

540 - 6T + 12T = 600

6T = 600 - 540

6T = 60

T = 60 / 6

T = 10

Substituting the value of T back into the first equation to find the value of n or total notebooks -

N + 10 = 90

N = 90 - 10

N = 80

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Answer:

b) 1/6

Step-by-step explanation:

You need to multiply the results from the question a) by 2.

1*2=2

----------

6*2=12

=2/12

now simplify it

2/12

=1/6

Hope this  helps <3

The number of pounds of copper in 120 pounds of brass is 78 pounds.

Given that, a certain type of brass contains 65% copper.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

120 pounds of the brass given

Number of pounds of copper

= 65% of 120

= 65/100 ×120

= 0.65 ×120

= 78 pounds

Hence, the number of pounds of copper in 120 pounds of brass is 78 pounds.

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Out of the given differential equations, only equation 3 is separable, and equation 4 is linear. The rest are nonlinear and neither separable nor linear.

The first-order differential equation dy/dx + exy = x2y2 is neither separable nor linear. It is a nonlinear ordinary differential equation. The presence of the term x2y2 in the equation makes it nonlinear, and the term exy makes it non-separable.

The differential equation y + ex * sin(x) = x3y' is neither separable nor linear. It is a nonlinear ordinary differential equation. The presence of the term ex * sin(x) and the term y' (derivative of y) make it nonlinear, and the term y makes it non-separable.

The differential equation ln(x) - x2y = xy' is separable but not linear. The terms ln(x) and x2y make it nonlinear, but it can be separated into two parts, one containing x and y and the other containing x and y'. Therefore, it is separable.

The differential equation dy/dx + cos(y) = tan(x) is linear but not separable. The terms cos(y) and tan(x) make it nonlinear, but it can be written in the form dy/dx + P(x)y = Q(x), where P(x) = cos(y) and Q(x) = tan(x). Therefore, it is a linear differential equation.

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Answer:

190

Step-by-step explanation:

quotient: 120/3=40

product: 15*10=150

adding them:150+40=190

Answer:

190

Step-by-step explanation:

quotient: 120/3=40

product: 15*10=150

adding them:150+40=190

The First step in adding and subtracting the rational expression is making the denominator equal .

The Rational Expression is defined as the expression that is written in the p/q form , where q ≠ 0 .

Let us understand adding and subtracting of the rational expression by an Example .

For Example : add the rational expressions 2/3 and 1/4 .

The First Step in adding them is to make the denominator equal ,

to make the denominator equal , we take LCM ,

the LCM of 3 and 4 is 12 ,

the rational expression become ⇒ 8/12 and 3/12 .

On adding , we get ; (8 + 3)/12 = 11/12 .

On subtracting , we get ; (8 - 3)/12 = 5/12 .

Therefore , making the denominator equal is the first step for adding and subtracting rational expressions .

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The value of the triple integral ∭E​2xdV over the region E is π.

We have,

To evaluate the triple integral ∭E​2xdV, where E is bounded by the paraboloid x = y² + z² and the plane x = 1, we need to determine the limits of integration.

The plane x = 1 intersects the paraboloid x = y² + z² when x = 1.

Substituting x = 1 into the paraboloid equation gives:

1 = y² + z²

This equation represents a circle in the yz-plane with a radius of 1.

So, we can express the bounds for y and z as follows:

-1 ≤ y ≤ 1

-√(1 - y²) ≤ z ≤ √(1 - y²)

For the x-coordinate, since we are integrating over the entire region between the paraboloid and the plane, the limits are 0 ≤ x ≤ 1.

Now, we can set up the triple integral:

∭E​2xdV = ∫[0,1]∫[-1,1]∫[-√(1 - y²), √(1 - y²)] 2x dz dy dx

Integrating with respect to z first:

∭E​2xdV = ∫[0,1]∫[-1,1] [2xz] evaluated from -√(1 - y²) to √(1 - y²) dy dx

Simplifying:

∭E​2xdV = ∫[0,1]∫[-1,1] 2x(√(1 - y²) - (-√(1 - y²))) dy dx

∭E​2xdV = ∫[0,1]∫[-1,1] 4x√(1 - y²) dy dx

Now, integrating with respect to y:

∭E​2xdV = ∫[0,1] [4x(π/2)] dx

∭E​2xdV = 2π∫[0,1] x dx

∭E​2xdV = 2π[x²/2] evaluated from 0 to 1

∭E​2xdV = 2π(1/2 - 0) = π

Therefore,

The value of the triple integral ∭E​2xdV over the region E is π.

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The substitution method involves using the expression of one variable extracted from one equation into the other equation.

We have the equation

- 7 x - 14 = 7 y

which can be easily solved for "y" by dividing both sides by "7" :

- x - 2 = y

Then we can substitute the y variable in the second equation:

so we replace y with (- x - 2) in the other equation as shown below:

10 = - 10 x - 5 y

10 = - 10 x - 5 (- x - 2)

use distributive property to remove the parenthesis:

10 = - 10 x + 5 x + 10

10 = - 5 x + 10

subtract 10 from both sides to isolate the term in "x"

0 = - 5 x

divide bothe sides by "-5"

0 = x

Then x = 0, and we can use this value to solve for "y" in the substitution equation:

y = - x - 2

y = - (0) - 2

y = -2

Then the answer is:

x = 0 and y = - 2

Answer:

1/5

Step-by-step explanation:

It's just the inverse of the number or 1 over the number you have

There is no statistically significant difference between Mr. Goodman’s evaluations and the History Department’s as we fail to reject the null hypothesis and value of p in which p-value = 0.5893.

H0: There is no difference in Mr. Goodman’s evaluations and the History Department’s

H- There is a significant difference between Mr. Goodman’s evaluations and the History Department’s

Applying the chi-square test:

            relative  observed  expected        residual                      Chisquare

Cat frequency(p) Oi        Ei=total x p  R2i=(Oi-Ei)/√Ei    R2i=(Oi-Ei)2/Ei

1's         0.100          11.000        12.500           -0.42                         0.180

2's        0.150         14.000         18.750           -1.10                         1.203

3's       0.340         47.000       42.500            0.69                       0.476

4's       0.410          53.000       51.250            0.24                         0.060

total     1.000         125              125                                               1.9196

Through the attached file as well as shown above we get the value of X2 equal to 1.9196.

Test statistic X2 = 1.9196.

P value through Chi-Square Distribution table = 0.5893

No, it can't be concluded that there is a statistically significant difference between Mr. Goodman’s evaluations and the History Department’s as we fail to reject the null hypothesis.

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Answer:

both

Step-by-step explanation:

that's the answer to the question

\(answer = 62 \\ solution \\ \: let \: < 3 \: be \: x \\ x + 118 = 180(sum \: of \: angle \: in \: triangle) \\ or \: x = 180 - 118 \\ x = 62 \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment\)

Answer:

angle 3 = 31

because there are three angles in a triangle if we add 118+31=149 and it has the capacity for a third angle.

Answer:

14w

Step-by-step explanation:

Width = w

Length is 6 time its width. so, multiply w by 6

length = 6*w = 6w

Perimeter of rectangle = 2* (length + width)

                                        = 2*(6w + w)

                                        = 2*7w

                                         = 14w

Answer:

y=3x+3

Step-by-step explanation:

i use point (-1,0) and (0,3) then 3-0/0-(-1)=3/1=3 so (0,3) 3 is the y intercept plug in so y=3x+3is the equation

Answer:

See below

Step-by-step explanation:

Find two convenient points to calculate the slope:

0,3   and   -1,0         slope =  m =  (3-0) / ( 0 - -1) = 3

  and the y axis intercept = 3   (from looking at graph)

line equation is   y = mx + b             ( where b is the y-axis intercept)

                     y = 3x + 3

Juliet will have  13 cups mixture of the orange juice and water .

Given :-

Juliet already has 9 cups of orange juice , and she adds 32 fluid ounces of water into the  cup of orange uice syrup.

So, we have to find that how much cups of syrup does Juliet had ,

So, we know that

1 cup = 8 ounces

but she adds 32 ounces of water which means

= No. of ounces added / no. of ounces in a glass

= 32 / 8

= 4

therefore ,

9 + 4 = 13 glasses.

which means she has 13 glasses of the syrup made up of water and orange juice .

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The standard deviation is 16.54 if the population of customers ages is 45, 76, 30, 22, 51, 40, 63, 66, and 41.

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

\(\rm SD = \sqrt{\dfrac{ \sum (x_i-X)^2}{N}\)

SD is the standard deviation

xi is each value from the data set

X is the mean of the data set

N is the number of observations in the data set.

It is given that:

The data set:

45, 76, 30, 22, 51, 40, 63, 66, 41

From the formula:

∑(x(i) - X)² = 2463.55

N = 9

SD = √(2463.55/9)

SD = 16.54

Thus, the standard deviation is 16.54 if the population of customers ages is 45, 76, 30, 22, 51, 40, 63, 66, and 41.

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The probability that the student owns 3 pets is 0.0272.

Poisson distribution is a type of probability distribution that is often used in the analysis of events that are rare. A Poisson distribution can be used to estimate the probability of a given number of events occurring in a fixed time or space when the average rate of occurrence is known.

The parameter of a Poisson distribution is the average rate of occurrence of the event in question. It is equal to the expected value and the variance of the distribution.The number of pets that a randomly selected student owns has a Poisson distribution with parameter 0.8.

Therefore,λ = 0.8.

The probability that the student owns 3 pets is given by;

P(X=3) = (λ³ * e^-λ) / 3!

P(X=3) = (0.8³ * e^-0.8) / 3!

P(X=3) = (0.512 * 0.4493) / 6

P(X=3) = 0.0272

Therefore, the probability that the student owns 3 pets is 0.0272.

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The correct option for this question is B. There has been a rise in three-point shots, and players tend to score more points now.

Why it is?

The factor that makes it challenging to make a fair comparison between a current NBA star and an NBA star from the 1990s is:

B. There has been a rise in three-point shots, and players tend to score more points now.

The increase in three-point shots has significantly changed the way the game is played and the strategies used by teams, which makes it difficult to compare the performance of players from different eras.

Players in the current NBA tend to score more points because of the increased emphasis on the three-point shot, while players from the 1990s may have had different strengths and styles of play that were more effective in that era. Therefore, it is challenging to make a fair comparison between players from different eras based solely on their statistics.

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Answer:

please see analysis

Step-by-step explanation:

You can do this with a proportion. It takes 5/6 of a gallon to paint 1 wall and you want to know how much of a wall can you paint with 1/2 gallon. So set up the proportion:

5/6 / 1 = 1/2 / x

cross multiplying gets you 5/6x = 1/2

multiply by the reciprocal of 5/6 to isolate x - which is 6/5. 1/2 times 6/5 = 3/5

Answer: so wich line do we need to answer

Step-by-step explanation:

(a) Purchase of the investment:

1 Available-for-Sale Securities $80,728

2 Cash (Payment for the investment) $80,728

(b) Receipt of annual interest and discount amortization:

1 Cash (Receipt of annual interest) $8,700

2 Discount on Bonds Payable (Amortization) $1,272

3 Investment Revenue (Interest Income) $7,428

(a) Journal entry for the purchase of the investment:

Date: January 1, 2020

Account Titles                  Debit     Credit

----------------------------------------------

Available-for-Sale Investments  $80,728

Cash                            $80,728

(b) Journal entry for the receipt of annual interest and discount amortization:

Date: End of the year (Assuming December 31, 2020)

Account Titles               Debit   Credit

-------------------------------------------

Cash                          $10,400

Interest Revenue              $7,728

Discount on Bonds Investment  $2,672

The cash received is the annual interest payment calculated as 10% of the face value of the bonds ($87,000 x 10%).

(c) Journal entry for the year-end fair value adjustment:

Date: End of the year (Assuming December 31, 2020)

Account Titles             Debit     Credit

------------------------------------------

Fair Value Adjustment                 $2,150

Unrealized Gain or Loss               $2,150

The fair value adjustment account is credited to increase its balance to reflect the increase in the fair value of the investment.

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Step-by-step explanation:

please refer to the sketch

\({ \qquad\qquad\huge\underline{{\sf Answer}}} \)

When two lines intersects, they have a plane common to

both of them, hence we can say that both the lines lie in the same plane.

So, the given statement is True