Which equation shows a proportional relationship between x and y?
A. y=-3x-2
B. y=9
C. y=3x+1
D. y=4x
​

To find f(x), we need to integrate f''(x) twice, taking into account the given initial conditions.

f(x) = (2/3)x^3 - 4cos(x) + 7x + 9

1. First, we find f'(x) by integrating f''(x):

f''(x) = 4x + 4cos(x)

∫(4x + 4cos(x)) dx = 2x^2 + 4sin(x) + C₁

Now, we use the initial condition f'(0) = 7:

2(0)^2 + 4sin(0) + C₁ = 7

C₁ = 7

So, f'(x) = 2x^2 + 4sin(x) + 7

2. Next, we find f(x) by integrating f'(x):

f'(x) = 2x^2 + 4sin(x) + 7

∫(2x^2 + 4sin(x) + 7) dx = (2/3)x^3 - 4cos(x) + 7x + C₂

Now, we use the initial condition f(0) = 5:

(2/3)(0)^3 - 4cos(0) + 7(0) + C₂ = 5

C₂ = 5 + 4 = 9

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.

As we know, The volume of the square prism is twice the volume of the cylinder

To determine the relationship between the volume of the square prism and that of the cylinder, we need to find both volumes.

The volume of the square prism is V = Ah where A is the cross-sectional area and h its height. Since A = 314 square units,

V = 314 × h = 314h

Also, the volume of the cylinder is V = A'h where A' is the cross-sectional area of the cylinder and h' its height. Since the A' = 50π square units,

V' = 50π × h' = 50πh'

The ratio of the volume of the square prism to that of the cylindrical prism is V/V' = 314h/50πh'

Since the height of the square prism equals that of the cylinder, h = h'.

So, V/V' = 314h/50πh .

V/V' = 314/50π

if we take π = 3.14,

V/V' = 314/(50 × 3.14)

V/V' = 100/50

V/V' = 2

So, V = 2V'

Thus, the volume of the square prism is twice the volume of the cylinder.

So, the answer is D.

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Answer:

D. The volume of the square prism is twice the volume of the cylinder.

Step-by-step explanation:

took the test, got it right, comment below if you would like a step by step explanation

Answer:

52.93

Step-by-step explanation:

Answer:

There are a total of 740 faculty members at the college.

Step-by-step explanation:

Answer:

this doesn't make any sense

Step-by-step explanation:

The values of b, angle C and angle A are 6.3, 49° and 80° respectively

The Cosine Rule says that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

b² = c²+a²-2abcos C

b² = 5²+8²-2(5)(8)cos 51

b² = 25+64-80cos51

b² = 89-50.35

b² = 39.35

b = 6.3

Using sine rule

8/sinA = 6.3/sin51

8× sin51 = 6.3sinA

6.2 = 6.3sin A

sinA = 6.2/6.3

sinA = 0.984

A = sin^-1( 0.984)

A = 80°( nearest degree)

angle C = 180-(51+80)

= 180-131

= 49°

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Answer:

poosjsjdwjqisnsjjdd

Step-by-step explanation:

Answer:

what's the question?

Answer:

25

Step-by-step explanation:

1 = 1^2

4 = 2^2

9 = 3^2

16 = 4^2

Next will be    25  =  5^2

The experimental probability of a coin toss showing heads in this experiment is 1/2. Thus, the correct answer is B. 1/2.

To find the experimental probability of a coin toss showing heads, we need to calculate the ratio of the number of heads to the total number of tosses.

In the given data, we can count the number of heads, which is 10.

The total number of tosses is 20.

The experimental probability of a coin toss showing heads is given by:

(Number of heads) / (Total number of tosses) = 10/20 = 1/2

Therefore, the experimental probability of a coin toss showing heads in this experiment is 1/2.

Thus, the correct answer is B. 1/2.

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Answer: y=2/5x+1

Step-by-step explanation: (5,3) 2/5

y=mx+b

3=2/5(5)+b 2/5x5=10/5=2

3=2+b

3-2=b

1=b

answer : y=2/5x+1

The relationship between the confidence interval and the margin of error is that the margin of error determines the width of the confidence interval.

The margin of error is a measure of the uncertainty associated with a sample statistic, such as the mean or proportion. It represents the maximum amount by which the sample statistic may differ from the true population parameter, with a certain degree of confidence. The confidence interval, on the other hand, is a range of values that is likely to contain the true population parameter, with a certain degree of confidence. The width of the confidence interval is determined by the margin of error.

Therefore, none of the options given in the question is correct. The width of the confidence interval is typically calculated by multiplying the margin of error by a factor that depends on the desired level of confidence. For example, a 95% confidence interval is typically calculated by multiplying the margin of error by 1.96, which corresponds to a confidence level of 95%. In summary, the margin of error determines the width of the confidence interval, but the relationship between the two is not as simple as any of the options given in the question.

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As we know that

♦ Area of rectangle = Length × breadth

Substituting known values ,

⇒ 144x⁴ = 12x ( Length )

⇒ 144x⁴ / 12x = Length

⇒ 12x³ = Length

⇒ Length = 12 x³

Answer:

The quadratic equation x2 + 8x + 16 = 0 is a perfect square trinomial, which means it can be factored as (x+4)²=0. Therefore, the nature of the quadratic equation is a perfect square trinomial, and it has one real root with a multiplicity of 2.

The quadratic equation x2 - 24x + 144 = 0 can be factored as (x-12)²=0, which is also a perfect square trinomial. Therefore, the nature of the solutions is a perfect square trinomial, and it has one real root with a multiplicity of 2.

The quadratic equation x2 - 25 = 0 can be factored as (x+5)(x-5)=0, which means it has two real roots: x=5 and x=-5.

The quadratic formula determines the solutions to the quadratic equation in terms of its coefficients. The formula is x = (-b ± √(b²-4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.

The roots of the quadratic equation 2x2 + 5x + 3 = 0 can be found by factoring it as (2x+3)(x+1)=0, which means the roots are x=-3/2 and x=-1.

Step-by-step explanation:

So, 4,200 meters is the closest distance to the work. Therefore, option C is the correct answer.

Given that, Michelle lives 4.5 miles from work Kelly lives 5.6 kilometres from work Staci lives 4,200 meters from work Kyle lives 670,000 centimetres from work.

Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are.

Now, convert miles, kilometres and centimetres into the same unit meters.

Where,

1 mile = 1,609 meters

1 kilometer = 1000 meters

1 meter = 100 centimeters

Now, 4.5 miles = 4.5 × 1,609 = 7,240.5 meters

5.6 kilometres = 5.6 × 1000 = 5600 meters

670,000 centimeters = 670,000/100 = 6700 meters

So, 4,200 meters is the closest distance to the work. Therefore, option C is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

Michelle lives 4.5 miles from work. Kelly lives 5.6 kilometres from work. Staci lives 4,200 meters from work. Kyle lives 670,000 centimetres from work.

1 mile = 1,609 meters

1 kilometer = 1000 meters

1 meter = 100 centimeters

Part A: Which employee lives the closest to work?

A. Michelle

B. Kelly

C. Staci

D. Kyle

The population of rabbits by the year 2023  is 13985.

We have to use the following exponential function. This will be:

y = a b^t

In 2008 means, t=0

So we have 7100 = a b^0

a = 7100

y = 7100b^t

In 2013 means t = 2013-2008 =5

8900 = 7100 b⁵

b⁵ = 89/71

b = 1.046

So the equation will be

y = 7100 (1.046)^t

For 2023, t=2023-2008= 15

y = 7100(1.046)¹⁵

= 13985

The population is 13985.

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Answer:

40%

Step-by-step explanation:

% of students drive to school

= no of students who drive/ total students× 100

=250/250+375×100

=250/625×100

=40%

Step-by-step explanation:

The answer has to be 4.

4×4=16

4+4+4×4=16

Growth factor is the factor by which the quantity is multiplied by itself by the number of times of that factor. The growth factor of the function is 6. Thus the option 3 is the correct option.

Given information-

The given function is,

\(f(x)=\dfrac{1}{3} \times (6)^x\)

Growth factor is the factor by which the quantity is multiplied by itself by the number of times of that factor.

For a function,

\(A(x)=c\times a^x\)

Here \(c\) is the initial value and the \(a\) is the growth factor of the function.

Compare given function with above function,

\(f(x)=\dfrac{1}{3} \times (6)^x\)

Here 1/3 is the initial value of the function and 6 is the growth factor of the function.

Hence the growth factor of the function is 6. Thus the option 3 is the correct option.

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Answer:

6 or c

Step-by-step explanation:

on edge

Answer:

2

Step-by-step explanation:

It is 2 because -2x + 10 has a rate of change of -2 while 2 has a rate of change of 0 (it never changes).

In backtracking with conflict-directed back-jumping, the search for a solution to a problem is performed using a depth-first search algorithm. The variable order you mentioned, (a1, h, a4, f1, a2, f2, a3, t), represents the sequence in which variables are assigned values during the search. The value order, (red, green, blue), indicates the order in which the algorithm will try assigning different values to the variables.

Conflict-directed back-jumping is an improvement over basic backtracking, as it helps reduce the search space by identifying and jumping over irrelevant parts of the search tree. When a conflict (i.e., an unsolvable assignment) is encountered, the algorithm doesn't simply backtrack to the previous variable but rather identifies the cause of the conflict and jumps back to the most recent variable responsible for the conflict. This allows the algorithm to skip parts of the search tree that are guaranteed not to yield a solution.

In summary, backtracking with conflict-directed back-jumping is an efficient search technique that uses a specific variable and value order to assign values during the search. It improves upon basic backtracking by identifying the cause of conflicts and jumping back to the most recent relevant variable, thus reducing the search space and time complexity.

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Answer: 1 / 8806

Step-by-step explanation: not no noticeable way of it being a mixed number.

Answer: we can conclude that the two vectors are parallel because they have the same direction.

Step-by-step explanation:

a) To find the constant k such that the system has no solution, we can use the determinant of the system as a criterion.

So, the system will have no solution if and only if the determinant is equal to zero and the equation is as follows:

| 1 - 3 | 2 | 1 || -1 k | 0 | = 0

Expanding the above determinant, we get:

|-3k| - 0 | = 0

We can see that the determinant is zero for any value of k.

So, there are infinitely many solutions.

b) We are given the system:

x - 3y = 2-x + k

y = 0

Now, we will rewrite the system using vectors as follows:

⇒ r. = r0 + td

Where d = (1, -3) and r0 = (2, 0)

Then, the equation x - 3y = 2 can be written as:

r. = (2, 0) + t(1, -3)

Next, we will substitute the value of k in the system to find the equation of the second line.

We know that the system has no solution for

k = 0.

So, the equation of the second line is:

r. = (0, 0) + s(3, 1)

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Question:

Answer:

This is pretty simple, just multiply 9.0 by $13.95, which will give you the answer of $125.55.

* I am not responsible if you get this question wrong, for you are the one who asked the question. *

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If this helped, your welcome! Please know that I might be wrong, and if I am, I am truly sorry for that. But If you would, please make me brainliest.

I hope you have a great rest of your day! If there is an issue with this question, be happy to comment. <3

-niaxfandoms

Harry needs to pay $ 125.55 in total for the 9.0 pizzas he ordered at $ 13.95 each.

To calculate how much Harry needs to pay, multiply the number of pizzas (9.0) by the cost of each pizza ($ 13.95).

Total cost = Number of pizzas × Cost per pizza

Total cost = 9.0 × $ 13.95

To find the product, we can treat 9.0 as a whole number and then multiply:

Total cost = 9 × $ 13.95

Now, calculate the product:

Total cost = $ 125.55

Harry needs to pay $ 125.55 in total for the 9.0 pizzas he ordered at $ 13.95 each.

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Given:

Clicks = 50

Impressions = 5000

To find:

The CTR percentage.

Solution:

We know that,

\(CTR=\dfrac{\text{Clicks}}{\text{Impressions}}\times 100\)

Substituting the given values, we get

\(CTR=\dfrac{50}{5000}\times 100\)

\(CTR=\dfrac{1}{100}\times 100\)

\(CTR=1\%\)

Therefore, the correct option is A.

The dimensions of the marble is thus 10∛18 cm when the volume is 18000 cm³.

An object's capacity is the amount of material it can hold inside, while an object's volume is the amount of space it takes up. Here, the cubic unit is used to measure either of the two.

Cubic units are used to measure volume. The quantity of cubes needed to completely fill any given figure, such as blocks in a box, is its volume.

As there is no  definite shape is given we can assume that the shape is cube.

Volume of cube = a³

given the volume 18000cm³

dimensions of the marble,

a × a × a = 18000

a³ = 18000

a = ∛18000

a = 10∛18

a = 26.21

Hence, the dimensions of the marble is thus 10∛18 cm when the volume is 18000 cm³.

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Answer:

44 questions

Step-by-step explanation:

Part 1: She got 16 questions correct, which was 4/5 of the number of part 1 questions.

Let x = total number of questions in part 1

4/5x = 16

Divide both sides by 4/5

x = 16 ÷ 4/5

= 16 × 5/4

= 20

x = 20

There are 20 questions in part 1

She got 16 questions correct, which was 2/3 of the number of part 2 questions.

Let y = number of questions in part 2

2/3y = 16

Divide both sides by 2/3

y = 16 ÷ 2/3

= 16 × 3/2

= 24

y = 24

There are 24 questions in part 2

The total number of questions on Stephanie’s exam = part 1 + part 2

= 20 + 24

= 44 questions

Answer:

3b/2 + 3

Step-by-step explanation:

The formula to calculate perimeter of rectangle is 2l + 2w

The length is half the width so length is 1/2 (b/2 +1), which when simplified is b/4 + 1/2

Using the formula to calculate perimeter you can substitute and calculate

p= 2l + 2w

p= 2(b/4 + 1/2) + 2(b/2 + 1)

p= 2b/4 +2/2 + 2b/2 +2

p= 1/2b + 1 + b + 2

p= 3/2b + 3

Simplified it's 3b/2 +3