- 3(4 - 9)

Evaluate.

Car A and Car B enter a freeway simultaneously. Their velocities, measured in miles per minute, are given by \(VA(t) = 0.4 + 0.2t - 0.02t^2 \\\)and \(VB(t) = -0.1 + 0.3t - 0.02t^2\) respectively, where t represents time in minutes. After 5 minutes, Car A has traveled a certain distance, Car B has traveled a certain distance, and we need to determine who is ahead and by how much.

To find the distances traveled by Car A and Car B, we need to calculate the definite integrals of their respective velocity functions over the interval [0, 5]. The integral of VA(t) over this interval gives us the distance traveled by Car A, and the integral of VB(t) gives us the distance traveled by Car B.

Integrating\(VA(t) = 0.4 + 0.2t - 0.02t^2\)with respect to t from 0 to 5:

∫\([0,5] (0.4 + 0.2t - 0.02t^2) dt = [0.4t + 0.1t^2 - (0.02/3)t^3]\)evaluated from 0 to 5

= \((0.4(5) + 0.1(5)^2 - (0.02/3)(5)^3) - (0.4(0) + 0.1(0)^2 - (0.02/3)(0)^3)\)

= 2 + 1.25 - (0.02/3)(125)

= 3.25 - 0.8333

≈ 2.42 miles (rounded to 2 decimal places)

Similarly, integrating\(VB(t) = -0.1 + 0.3t - 0.02t^2\) over the same interval:

∫\([0,5] (-0.1 + 0.3t - 0.02t^2) dt = [-0.1t + 0.15t^2 - (0.02/3)t^3]\)evaluated from 0 to 5

\(= (-0.1(5) + 0.15(5)^2 - (0.02/3)(5)^3) - (-0.1(0) + 0.15(0)^2 - (0.02/3)(0)^3)\\= -0.5 + 1.875 - (0.02/3)(125)= 1.375 - 0.8333\\=0.54 miles\) (rounded to 2 decimal places)

Therefore, Car A has traveled approximately 2.42 miles, Car B has traveled approximately 0.54 miles, and Car A is ahead of Car B by approximately 1.88 miles (rounded to 2 decimal places).

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The solution to the system of equations is:x = -3 and y = 2.

To solve the following system of equations using matrix inverse:4x + 5y = 143x - 2y = -1

Using the matrix inverse, we can rewrite the system of equations into a matrix equation:

AX = B

where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix.

The variable matrix X can be found by multiplying the inverse of A to the constant matrix B, which is:X = A⁻¹B

To use matrix inverse, let us first obtain the coefficient matrix A, constant matrix B, and inverse of matrix A.

Then we will use these matrices to obtain the variable matrix X.

A = [4 5; 3 -2]

B = [14; -1]

A⁻¹ = (1/22) [-2 -5; -3 4]

X = A⁻¹BX = (1/22)[-2 -5; -3 4][14; -1]= [-3; 2]

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Answer:

y=6x+5  →equation 1

y=4x+5 → equation 2

you can either substitute equation 1 in 2 or equation 2 in 1

substituting equation 1 in 2,

y = 4x + 5

6x + 5 = 4x + 5

6x - 4x = 5 - 5

2x = 0

x = 0/2

x = 0

substituting x = 0 in equation 1, (to get y)

y = 6x + 5

y = 6(0) + 5

y = 0 + 5

y = 5

hope it helps you!!

Answer: 12.357312274

Step-by-step explanation:

Answer:

The unit rate is $6.25

Step-by-step explanation:

d = cost of each dvd

4d = 25

/ 4    / 4

d = 6.25

Each dvd costs $6.25

Check your answer:

4(6.25) = 25

25 = 25

This statement is true, which makes our answer true.

Hope this helps!

Answer:

6n^2 or 6n squared

Step-by-step explanation:

To find the greatest common factor we have to first find out all the factors for every other number.

Factors - Numbers you can multiply to find that number.

For example, we have 6n^3 what numbers can be multiplied to find that number?

It takes the person 40 minutes to travel 10 miles at a rate of 15 miles per hour

We can use the formula:

time = distance / speed

where "distance" is the distance traveled and "speed" is the speed at which the person is traveling.

In this case, the person rode their bike 10 miles south at a speed of 15 miles per hour.

Plugging these values into the formula, we get:

time = 10 miles / 15 miles per hour

Simplifying, we get:

time = 40 minutes

Therefore, it takes them 40 minutes

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Angle-Angle-Side (AAS) Theorem has two sides and a non-included angle.

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Answer:

4 is in the p and 2 in the not p

Step-by-step explanation:

the one with the 40 in p the one with the 12 in p the one with 8 in the p and the one with the 12 with a 3 is in the p the others are in no p.

Answer:

This will be your answer, I apologize for the late response. Nonetheless, I wish whoever needs this good luck.

I hope I've helped! :)

The skip interval should be 40 if the sampling frame has 2000 names and the desired sample size is 50.

Systematic sampling is a type of sampling which uses the probability method where researchers select members of the group or population at a regular interval.

To determine the skip interval, it is necessary to first determine the sample size. Then the skip interval can be determined by dividing the total population by the target/desired sample size. Therefore;

skip interval = population / target sample size

Substituting the given values;

skip interval = 2000 / 50

skip interval = 40

Hence, the skip interval is calculated to be 40 if the frame has 2000 names and the desired sample size is 50.

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We'd be able to fit 4 cabinets total if there is no space in between them.

Compared to multiplication, division is the opposite. When you divide 12 into three equal groups, you get four in each group if three groups of four add up to 12, which they do when you multiply.The primary objective of division is to count the number of equal groups that are created or the number of individuals in each group after a fair distribution.

Given that: Carl heinrich has lateral filing cabinets that need to be placed along 1 wall of a storage closet.  that the filing cabinets are each 1 and a half feet wide, and the wall is 6 feet long

We know that we have a total of 18 feet that we want to break up so to speak amongst 1 and a half foot, so 1.5 foot wide cabinets.

So we will take 6 and divide that by 1.5 and we get a value of exactly 4 point. So double checking that when we have 4 times 1.5,we get a value of exactly 6 point, so you'd be able to fit 6 or part me we'd be able to fit 4 cabinets total if there is no space in between them.

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Answer:

Step-by-step explanation:

I think that you cut off the leading number in the BD segment 8cm appears to be truncated....

if that number was in the image....

BC would be sqrt(52.3 ^2 + ?.8^2)

if you  have BC then

sin(θ)/BC = sin(90)/18.6

Answer:

Table A

Step-by-step explanation:

It grows at a steady rate by 1 for x, the other ones grow exponentially.

Answer:

The volume of the cube is 21952.

Step-by-step explanation:

V = L x W x H

because a cube's sides are all the same, the length, width, and height are also the same. So we use the formula:

V= S^3

(S standing for side)

we know the height is 28 and as all sides measure the same we use the equation:

V= 28^3

28^3 = 21952

So, V= 21952

Answer:

irrational

Explanation:

What a rational is:

a number that can be given as the ratio of two integers

We know that √2 cannot be given as a ratio of two integers.

(√7 also cannot be given as a ratio of two integers)

[What an irrational number is:

a number that cannot be given as the ratio of two integers]

This makes √2 and √7 irrational numbers.

When subtracting √2 from anything, (other than √2) you end up with an irrational number. [or √7]

0 - √2 = irrational

10204 - √2 = irrational

4 - √2 = irrational

So, when subtracting √2 from √7, (finding the difference between the two), we are left with an irrational number.

Answer: x = 0; x = 3

Step-by-step explanation:

x^2 - 3x = 0

1. x is a common factor, so factor it out

x(x - 3) = 0

2. set both factors equal to zero

x = 0

x - 3 = 0

3. final answer

x = 0

x = 3

There are 30 possible schedules for Bob to play basketball on Wednesday or Monday or both.

Define the event A as playing basketball on Wednesday, and the event B as playing basketball on Monday. Since Bob can play basketball on either day, we want to count the number of schedules that include at least one of these events, which is equivalent to finding the union of the events A and B.

By the inclusion-exclusion principle, we can compute the number of schedules that include either A or B or both as:

|A ∪ B| = |A| + |B| - |A ∩ B|

To find |A|, we note that Bob can play basketball on any 3 of the remaining 6 days, which gives us:

|A| = C(6,3) = 20

Similarly, |B| = C(6,3) = 20, since the choices for playing basketball on the other days are the same.

To find |A ∩ B|, we note that Bob can play basketball on any 2 of the remaining 5 days, since Monday and Wednesday are already occupied. This gives us:

|A ∩ B| = C(5,2) = 10

Substituting these values into the formula for |A ∪ B|, we get:

|A ∪ B| = 20 + 20 - 10 = 30

Therefore, there are 30 possible schedules for Bob to play basketball on Wednesday or Monday or both.

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Answer:

-40

Step-by-step explanation:

The Concept here is Complex Numbers

where \(\sqrt{-1}=i \ and \ i^{2} = -1\)

Then \(\sqrt{-4}=\sqrt{4i^{2} } =\sqrt{(2i)^{2} } =2i\)

Also \(\sqrt{-25}=\sqrt{25i^{2} } =\sqrt{(5i)^{2} } =5i\)

Then \((\sqrt{-4} )(4\sqrt{-25} )=(2i)(4*5i)=40i^{2} =40*-1=-40\)

Glad to Help:)

p= 610/62, or 9.84 hope this hopes (5)

Answer:

the answer is 5.

Step-by-step explanation:

hope this helps..

The solution to the differential equation dy/dx = e^(5x + 4y) by separation of variables is y = (1/4)ln(1 - Ce^(5x)).

To solve the given differential equation by separation of variables, we start by separating the variables and integrating both sides. We get ∫dy = ∫e^(5x + 4y)dx. Integrating both sides gives us y = (1/4)ln(1 - Ce^(5x)), where C is the constant of integration. This is the solution to the differential equation.

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Answer:

Slope is 8/9

hope this helps!

Answer:

The figures are congruent because a 270° rotation about the origin and then a reflection over the x-axis will map ΔABC onto ΔLMN.

It is a function because all the domain inputs are unique to their respective range outputs.

Answer:

the answer is -1/4x which isn't on there

Step-by-step explanation:

If we share $60 in the ratio 3:1, then each person will get is $45 and $15 respectively

Given,

The total amount = $60

The ratio = 3:1

Then the amount given to first person = 3x

The amount given to the second person = x

Given that the total amount is 60

Then  the equation will become

x+3x=60

4x=60

x=\(\frac{60}{4}\)

x=15

The amount given to the first person = 3x

Substitute the value of x in the equation

The amount given to the first person =3x

=3×15

= $45

The amount given to the second person =x

= $15

Hence, if we share $60 in the ratio 3:1, then each person will get is $45 and $15 respectively

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