Does the graph represent a function?

Answer:

A. Juan wins the race

B. At about 7 minutes J(t )= A(t)

C. 2 minutes

Step-by-step explanation:

A. Juan wins the race. This is because she covers the distance in a shorter time interval than Antonio

B. At about 7 minutes J(t )= A(t). to get this, just look at the point that the two curves intersect on the graph, and trace it down to the time axis to read off the time.

C. J(t) is greater than A(t) with about 2 minutes. To get this, we just subtract the time Juan arrived at the finish line from the time Antonio arrived, this is = 15 -13 = 2 minutes

a)

The integral

∫

1

2

3

�

+

1

3

�

−

2

∫

1

2

​

3x−2

​

3x+1

​

 evaluates to

14

3

3

−

2

3

1

3

14

​

3

​

−

3

2

​

1

​

.

To evaluate the integral, we can use the substitution

�

=

3

�

−

2

u=3x−2. This implies

�

�

=

3

�

�

du=3dx. We also need to change the limits of integration.

When

�

=

1

x=1, we have

�

=

3

(

1

)

−

2

=

1

u=3(1)−2=1.

When

�

=

2

x=2, we have

�

=

3

(

2

)

−

2

=

4

u=3(2)−2=4.

The integral becomes

∫

1

2

3

�

+

1

3

�

−

2

�

�

=

∫

1

4

1

�

�

�

3

∫

1

2

​

3x−2

​

3x+1

​

dx=∫

1

4

​

u

​

1

​

3

du

​

.

Simplifying, we have

1

3

∫

1

4

�

−

1

2

�

�

3

1

​

∫

1

4

​

u

−

2

1

​

du.

Integrating with respect to

�

u gives

1

3

⋅

2

�

1

2

∣

1

4

3

1

​

⋅2u

2

1

​

∣

∣

​

1

4

​

.

Evaluating at the limits, we have

2

3

(

4

1

2

−

1

1

2

)

=

14

3

3

−

2

3

1

3

2

​

(4

2

1

​

−1

2

1

​

)=

3

14

​

3

​

−

3

2

​

1

​

, which is the final result.

The integral

∫

1

2

3

�

+

1

3

�

−

2

∫

1

2

​

3x−2

​

3x+1

​

 evaluates to

14

3

3

−

2

3

1

3

14

​

3

​

−

3

2

​

1

​

 using the substitution

�

=

3

�

−

2

u=3x−2.

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The expression 2x^5 - 7x^3 - (4x^2 - 3x^3) when evaluated is 2x^5 - 10x^3 - 4x^2

From the question, we have the following parameters that can be used in our computation:

\left(2x^{5}-7x^{3}\right)-\left(4^{x2}-3x^{3}\right)

Express properly

So, we have

2x^5 - 7x^3 - (4x^2 - 3x^3)

Open the bracket

So, we have

2x^5 - 7x^3 - 4x^2 - 3x^3

Evaluate the like terms

2x^5 - 10x^3 - 4x^2

Hence, the solution is 2x^5 - 10x^3 - 4x^2

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Answer:

Step-by-step explanation:

I can't find the mean absolute value. But the absolute value is never negative unless there is a minus sign outside the absolute value bars.

So the mean is those 5 salaries added and then divide by 5

           28

           21.8

           21.1

           19

           15.5

Total  105.4

The mean = 105.4 / 5 = 21.08

The absolute mean is the same thing. Both are plus. If you have a definition for the mean absolute value, please post it and I'll come back and edit my answer.

Answer:

Part A 73  Part B 113

Step-by-step explanation:

The standard deviation measures the spread of data points around the mean. It considers all data points, not just the farthest or nearest ones. A higher standard deviation indicates a greater spread.

The standard deviation is a statistical measure that tells us how much the data points in a set vary from the mean. It provides information about the spread or dispersion of the data. To calculate the standard deviation, we take the square root of the variance, which is the average of the squared differences between each data point and the mean.

By considering all data points, the standard deviation provides a comprehensive measure of how spread out the data is. Therefore, the statement "The difference between the mean and the data point farthest from the mean" is incorrect, as the standard deviation does not focus on just one data point.

The statement "The difference between the mean and the data point nearest to the mean" is also incorrect because the standard deviation takes into account the entire data set. The statement "The difference between the mean and the median" is incorrect as well, as the standard deviation is not specifically related to the median.

Hence, the correct answer is "None of the above."

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To find the variance of the random variable X + 3Y - 4, we need to calculate the variances of X and Y and consider their covariance.

Let's start by calculating the variances of X and Y. Since X and Y are the numbers shown when two dice are tossed, each with six sides, their variances can be found using the formula for the variance of a discrete random variable:

Var(X) = E(X^2) - [E(X)]^2

Var(Y) = E(Y^2) - [E(Y)]^2

For a fair six-sided die, E(X) = E(Y) = (1 + 2 + 3 + 4 + 5 + 6) / 6 = 3.5.

Next, we calculate the second moments:

E(X^2) = (1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2) / 6 = 15.17

E(Y^2) = (1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2) / 6 = 15.17

Now, let's calculate the covariance between X and Y. Since the two dice are independent, the covariance is zero: Cov(X, Y) = 0.

Finally, we can calculate the variance of X + 3Y - 4:

Var(X + 3Y - 4) = Var(X) + 9Var(Y) + 2Cov(X, Y)

Substituting the values, we have:

Var(X + 3Y - 4) = 15.17 + 915.17 + 20 = 169.53

Rounding to the nearest whole number, the variance is approximately 170.

Therefore, none of the given options (a, b, c, d) match the correct variance value of 170.

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Probability of the intersection of events A and B (p(a ∩ b)) is 0 when events A and B are mutually exclusive.

To find the probability of the intersection of events A and B (p(a ∩ b)) when p(a) = 0.50 and p(b) = 0.30, and events A and B are mutually exclusive, follow these steps:

1. Recognize that mutually exclusive events have no overlap and cannot occur at the same time.
2. Apply the definition of mutually exclusive events: p(a ∩ b) = 0 for mutually exclusive events.

So, the probability of the intersection of events A and B (p(a ∩ b)) is 0 when events A and B are mutually exclusive.

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Answer:

350

Step-by-step explanation:

350 because there are 1/12 of VIP seats and there are 600 so 600 times 1/12 is 6,600.

Then you minus off the 600 VIP seats so you get 6000

next you do 600 divided bu 12 because of the 1st tier seats and 2nd tier seats combined which then you get 50

lastly you do 50 times 7 because of the ration 7:5 1st tier seats to 2nd tier seats so then you get 350

please mark brainliest i need one last one

Simple interest is p15612.12 and compound interest is p16500.If I was were Mr. henry ,I will choose offer of 2%.

1.To calculate simple interest, multiply the principal (initial amount) by the number of years, the interest rate, and the interest rate.

Contrarily, compound interest is computed by first adding the interest from earlier periods to the principal, and then computing the interest for the subsequent period on the updated sum.

Consider Mr. Henry investing P150,000 in ABC Bank at an annual simple interest rate of 2%:

Year 1: Interest earned is P3,000 (P150,000 x 2%).

Year 2: Interest earned is P3,000 ($150,000 x 2%).

Year 3: Interest earned is P3,000 ($150,000 x 2%).

Year 4: Interest earned is P3,000 ($150,000 x 2%).

Year 5: Interest earned is P3,000 ($150,000 x 2%).

Interest earned overall: P15,000

After five years, the total will be P150,000 plus P15,000, or P165,000.

Let's imagine Mr. Henry makes a P150,000 investment in Union Bank at a 2% yearly compound rate:

Year 1: P150,000 multiplied by 2% yielded P3,000 in interest, for a total of P153,000.

Year 2: P153,000 multiplied by 2% to be P3,060 in interest, for a total of P156,060.

Year 3: P156,060 multiplied by 2% to equal P3,121.20 in interest, for a total of P159,181.20.

Year 4: P159,181.20 multiplied by 2% yielded P3,183.624 in interest, for a total of P162,364.824.

Year 5: P162,364.824 multiplied by 2% yields P3,247.29696 in interest, for a total of P165,612.12096.

Interest earned in whole was P15,612.12096.

2 .If I were Mr. Henry, I would pick the 2% compounded annual offer from Union Bank. This is so that after five years, the total sum will be larger due to compound interest. Compound interest increases the amount on which interest is computed in the following period by adding the interest from prior periods to the principal. Due to this, the interest earned during the subsequent period will increase, and so on. As a result, after a certain amount of time, interest accrues more quickly and the overall amount is higher.

  Therefore , simple interest is p15612.12 and compound interest is p16500.If I was were Mr. henry ,I will choose offer of 2% .

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The time that you will arrive at your destination, given the distance of the trip and the average speed, is 2 pm

To find the time of arrival by using the car going at 90 km /h, you need to find the time that the whole trip would take.

The time the trip would take is found by the formula:

= Distance of trip / Average speed

= 495 / 90

= 5 . 5 hours

0.5 hours is 30 minutes so this is 5 hours 30 minutes.

The time you will arrive is therefore:

= 8 : 30 + 5 hours 30 minutes

= 2 pm

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The perimeter of the parallelogram is 35 cm.

The length of the continuous line that a parallelogram's boundary forms are considered to be its perimeter. The same unit applies to it as it does to its sides. A closed shape made up of four line segments is referred to as a quadrilateral. If the opposing sides of a quadrilateral are parallel and the same length, the shape is referred to as a parallelogram.

Given, the area of the parallelogram = 62 cm²

We know the area of the parallelogram = base × height

62 = b × 6.2 cm

b = 62/6.2

b = 10 cm

So, the perimeter of the parallelogram is given by

P = 7.5 + 10 + 7.5 + 10 cm

P =  35 cm

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The first quartile would be drawn at 3 and the median would be drawn

at 4.

What is the median in math?

Scores of group of students                        Frequency

                1                                                           0

                2                                                          2

                3                                                          2

                4                                                          4

                5                                                          3

                6                                                          1

                7                                                          1

First three set of scores from 1 to 3 comes under first quartile.

Median is in the center.

Last three set of scores comes under third quartile.

Therefore, the first quartile would be drawn at 3.

And the median would be drawn at 4.

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Answer:

jenny earned a total of $103.05.

Step-by-step explanation:

jenny charges 9.15 an hour to babysit todllers and 7.4 an hour to babysit school -aged children. if jenny babysat toddlers for 9 hours and school -aged childrenfor 6, she earned in all 83.55.

The proof shown below shows that "the square of a number that is two more than a multiple of 3 is one more than a multiple of 3."

In this exercise, you are required to proof that "the square of a number that is two more than a multiple of 3 is one more than a multiple of 3." Therefore, we would translate the word problem into an equation and then factorize it completely as follows;

(3n + 2)² = (3n + 2)(3n + 2)

Opening the bracket through expansion, we have the following:

(3n + 2)² = 9n² + 6n + 4

(3n + 2)² = 9n² + 6n + 3 + 1

Factorizing the equation as a multiple of 3, we have the following:

(3n + 2)² = 3(3n² + 2n + 1) + 1

(3n + 2)² = 1 more than a multiple of 3.

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The area of the walkway is 24π square meters.

To find the area of the walkway, we need to subtract the area of the inner circle from the area of the outer circle.

The inner circle has a radius of 5 meters, so its area can be calculated using the formula for the area of a circle: A_inner = π * \((r_inner)^{2}\).

A_inner = π * \(5^{2}\) = 25π square meters.

The outer circle has a radius equal to the sum of the inner radius and the width of the walkway. In this case, the outer radius is 5 + 2 = 7 meters.

The area of the outer circle can be calculated in the same way: A_outer = π * \((r_outer)^{2}\).

A_outer = π * \(7^{2}\) = 49π square meters.

Now, we can find the area of the walkway by subtracting the area of the inner circle from the area of the outer circle: A_walkway = A_outer - A_inner.

A_walkway = 49π - 25π = 24π square meters.

The area of the walkway is 24π square meters, where π (pi) is a mathematical constant approximately equal to 3.14159.

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Answer:

0.27

Step-by-step explanation:

To solve this problem, we will use Set Theory Approach to Probability.

Let U = the Sample Space which consists of all possible tests.

Of course U = {1,2,3 .... ,30}

So, no elements in that.

U = n = 30

Let Q = the event bearing a multiple of 4 No winning ticket, and,

R = the case that has the No. 19 winning ticket

∴

Q  = { 4,  8, 12 , 16 , 20, 24 , 28} ,  and

R  = {19} , so that

Q ∩ R  = ϕ

P(Q ∩R ) = 0

As, n(Q) = 7 , n(R) = 1  , we have,

P (Q) = \(\frac{n (A)}{n(U)}\) = \(\frac{7}{30}\),  and P (R) = \(\frac{1}{30\\}\)

P (Q∪R) = P(Q ) + P(R) − P(A∩B) = \(\frac{7}{30}\) +  \(\frac{1}{30\\}\) − 0 = \(\frac{8\\}{30\\}\)

≅ 0.27 .

Answer:Answer is C

Step-by-step explanation:

If a cross-section is parallel to the base it will be a triangle because the bases are triangles.

Answer:

x^2 + 7/2 + 15 is the answer.

Step-by-step explanation:

Make the number that is equal to x be on the side of the x, then multiply those to values.

x = -6

x= 5/2

(x + 6)*(x - 5/2)

Now, distribute the x to the x and the negative 5/2, and add that to 6 distributed to x and negative 5/2. Simplify.

\(x^{2} + -\frac{5}{2}x + 6x + 15\\\\x^{2} + \frac{7}{2} + 15\)

#teamtrees #WAP (Water And Plant)

The number of the seats within the 25th row is 227.

According to the statement

We have to seek out that the quantity of seats are within the twenty-fifth row of the left section.

So, For this purpose, we all know that the

According to the information:

The number of seats within the first row of the left section of the Ming-Sun Theater is 9.

As with the middle section, the amount of seats in each succeeding row is 2 over the row ahead of it.

From this information, the equation become to search out the seats is:

Number of seats within the given row(x) = 9x+2

And the number of seats is: Number of seats within the 25th row(25) = 9(25)+2

Number of seats within the 25th row(25) = 225+2

Number of seats within the 25th row(25) = 227.

So, The amount of the seats within the 25th row is 227.

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Answer:

18

Step-by-step explanation:

6(7e+3)=6*7e + 6*3=42e + 18

The amount of money that Carly would have left if she doesn't buy any packs of baseball cards is $20.

In order to calculate the amount of money that Carly would have left if she doesn't buy any packs of baseball cards, we would determine the cost of each baseball card as follows:

Translating the word problem into an algebraic expression, we have;

x - n = 16

x - 2n = 12

Solving the simultaneous equations by elimination, we have:

n = 4

Therefore, Carly's minimum balance is given by:

x - n = 16

x = 16 + n

x = 16 + 4

x = $20.

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Complete Question:

The graph shows the relationship between the total amount of money that Carly will have left, y, if she buys x packs of baseball cards. How much money will she have if she doesn't buy any packs of baseball cards?

Answer:

$20

Step-by-step explanation:

2375 is the amount of his investment and 625 is his total profit

The discount on the shares is 5%, so the price of each share is 100 - (5/100)100 = 95.

The total price Yoezer paid for the shares is 2595 = 2375.

To calculate Yoezer's total profit, we need to find the total dividend he received and the price he sold the shares for.

The dividend rate is 15%, so Yoezer received a dividend of (15/100)100 = 15 on each share.

The total dividend he received is 1525 = 375.

The price Yoezer sold the shares for was increased by a premium of 5%, so the selling price was 100 + (5/100)100 = 105.

The total selling price for the shares is 10525 = 2625.

Yoezer's total profit is the selling price minus the price he paid for the shares plus the dividends he received. This is 2625 - 2375 + 375 = 625.

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Answer:

Step-by-step explanation:

The standard form of the ellipse equation is (x-h)²/a² +(y-k)²/b² =1

This equation is for a horizontal ellipse. (a) is always bigger than (b) in ellipses. Because (a²) is under the x, that's why this ellipse is horizontal.

Now, let's answer the questions:

1. The center coordinates are (h,k) which are (4,-2) by comparing the two equations.

2. length of the major axis = 2a , let's find (a)

if you compare the two equations, a²=36 , that means a=6

Then 2a=12

3. length of the minor axis = 2b , let's find (b)

if you compare the two equations, b²=16 , that means b=4

Then 2b=8

4. the sum of the local radii = length of the major axis = 12

5. to find the foci, we have to find the value of (c), we have to use the equation a²=b²+c²

plugin a² and b², 36=16+c² , solve it, c=√20 =2√5

Now, to find the coordinates of the foci, we have to add and subtract the (c) value from the x-coordinate of the center while the y-coordinate stays the same (because this ellipse is horizontal).

the coordinates of the foci are (4+2√5 , -2) and (4-2√5 , -2)

6. the vertices are the end points of the major and the minor axes. To find the vertices on the major axis, add the value of (a) to the x-coordinate of the center while the y-coordinate stays the same.

(4+6,-2) and (4-6,-2) , this leads to (10,-2) and (-2,-2)

To find the vertices on the minor axis, add the value of (b) to the y-coordinate of the center while the x-coordinate stays the same.

(4,-2+4) and (4,-2-4) , this leads to (4,2) and (4,-6)

7. eccentricity (e)=c/a =(2√5)/6 = (√5)/3

Answer:

H:Median

Step-by-step explanation:

We know that Median means the middle, and we know that lines AB or in the middle of the page.

The area of the triangle by the given points i.e. P(1,1,1) , Q(-2,-7,-1) and R(-7,-1,4) is √4773/2. The area of the triangle is \(\frac{1}{2}\)  |PQ × PR|.

From the points that is  given in the question with the adjacent sides,

P(1,1,1) , Q(-2,-7,-1) and R(-7,-1,4)

Area of the triangle = \(\frac{1}{2}\)  |PQ × PR|

then, from the above points,

PQ = <-3,-8,-2>

and PR = <-8,-2,3>

now, The matrices can be written as,

PQ × PR = \(\left[\begin{array}{ccc}i&j&k\\-3&-8&-2\\-8&-2&3\end{array}\right]\)  

by calculating the above matrices we get,

= -28i + 25j - 58k

| PQ × PR | = \(\sqrt{28^{2} + 25^{2} + 58^{2}\)

=√4773

However, the Area of the triangle = √4773 / 2

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The question is-

Find the area of the triangle determined by the points P(1,1,1) , Q(-2,-7,-1) and R(-7,-1,4).

Answer:

b

Step-by-step explanation:

circumference= 2πr

37.8cm = 2πr

r= 6 cm

Area= πr^2

area = 113cm^2

Answer:

12

Step-by-step explanation:

3.60/0.30=12