Question 1:

An athlete runs in a straight line along a flat surface. He starts from rest and for 20 seconds accelerate at a constant rate. In this first 20 seconds he covers a distance of 100m. For the next 10 seconds he runs at a constant speed and then decelerates at a constant rate for 5 seconds until he stops.


a) What is the total distance that he ran? Another athlete runs along the same track, starting from rest and she accelerates at the same rate as her friend. She however only accelerates for 10 seconds before running at a constant speed.

b) How long does it take her to run 100m?​

A customer would  be charged $ 52 for an international phone call that started at 9:35 p.m. and ended at 11:15 p.m. the same day.

Charge for first 5 charged = $ 4.50

Charge for additional time = $ 0.50 per minute

Starting time = 9:35 p.m.

End time = 11:15 p.m.

Total minutes = 100 minutes

Total charge = 4.50 + (95 x 0.50)

                  = 4.50 + 47.50

                  = 52.00

Hence, a customer would  be charged $ 52 for an international phone call that started at 9:35 p.m. and ended at 11:15 p.m. the same day i.e. for 100 minutes.

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Answer:

Yes it is 7 cuz it has the equation of 3-5a

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Plug in -3 as a

h(-3) = (3+15)/3

h(-3) = 18/3

h(-3) = 6

The statement is true.

When the block is in equilibrium, each spring is stretched an additional ∆x. This implies that the forces from the two springs are balanced, and the block is not experiencing any net force in the equilibrium position.

When the block is set into oscillation with amplitude a, it will pass through its equilibrium point during the oscillation. At the equilibrium point, the displacement of the block is zero, and it changes direction. At this point, the block has its maximum speed v, as it is accelerating towards the equilibrium position.

The speed of the block decreases as it moves away from the equilibrium position, reaches zero at the maximum displacement (amplitude), and then starts accelerating towards the equilibrium point again. Therefore, when the block passes through its equilibrium point, it has its maximum speed v.

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There are 52 cards in the deck.

Picking the 6 of spades or 9 of clubs are two of the possible cards you could pick.

Your probability is 2/52 or 1/26 or 3.8461538461538%.

Answer:

It is an obtuse angle

Step-by-step explanation:

It is an obtuse angle because if any angle on a triangle is greater than 90 degrees, then it is called obtuse.

Answer:

I think the answer you're looking for is 86400

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

i am not sure but i think so

The areas of the composite figures are listed below:

In this problem we need to determine the areas of composite figures, which are the result of adding and subtracting geometric figures, whose area formulas are listed below:

Rectangle

A = b · h

Triangle

A = 0.5 · b · h

Circle

A = π · r²

Semicircle

A = 0.5π · r²

Quarter of a circle

A = 0.25π · r²

Square

A = l²

Where:

Now we proceed to determine the area of each figure:

Area 1

A = 30 · 20 - 6 · 14

A = 600 - 84

A = 516

Area 2

A = π · (8 cm)² - π · (3 cm)²

A = (64 - 9) · π cm²

A = 55π cm²

Area 3

A = (14 m)² - 4 · (5 m)²

A = 196 m² - 100 m²

A = 96 m²

Area 4

A = 0.5π · (7 m)² + 0.5 · (14 m) · (11 m)

A = 29.5π m² + 77 m²

A = (29.5π + 77) m²

Area 5

A = (7 ft) · (10 ft) + (3 ft) · (4 ft)

A = 70 ft² - 12 ft²

A = 58 ft²

Area 6

A = (28 cm)² - 4 · 0.25π · (14 cm)²

A = 784 cm² - 196π cm²

A = 588 cm²

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Answer:

To solve the inequality:

-10 - 66h ≥ -3

We can begin by isolating the variable h on one side of the inequality. First, we can add 10 to both sides:

-10 + 10 - 66h ≥ -3 + 10

Simplifying, we get:

-66h ≥ 7

Next, we can divide both sides by -66, remembering to reverse the inequality since we are dividing by a negative number:

h ≤ -7/66

Therefore, the solution to the inequality is h ≤ -7/66.

Step-by-step explanation:

Answer:

n=0

Step-by-step explanation:

n+-5= -5

n-5= -5

n= -5 +5

n=0

Form A

H(t) = -8(t – 2)² + 37

Form B

H(t)= -8t² + 32t + 5

a. From form A, the vertex of the parabola is at (2, 37). This means that the maximum height is 37 feet and it's reached after 2 seconds.

b. The initial height corresponds to t = 0 seconds. Replacing t = 0 into form B:

H(0)= -8(0)² + 32(0) + 5 = 5 ft

That is, the initial height was 5 ft

The number of days before they will be on the same schedule to run again together is given as follows:

15 days.

Considering periodic events, they will repeat on the same day for the least common factor of the periods of each event.

The periods for this problem are given as follows:

As 3 and 5 are prime numbers, the least common factor is given as follows:

3 x 5 = 15 days.

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Answer:

Eliana saves at a greater rate because her unit rate of $42 per week is greater than Lana's unit rate of $40 per week

hope this helps =3

sorry if im wrong

Answer:

Step-by-step explanation:

1.

a.9 ^3/2 = 27

b. 27 ^1/3 = 3

c. 125 ^2/3 = 25

b , c , a

2.

64 ^1/2 x 10 ^-2

8 x 1/100 = 2/25

3.

16 ^1/2 x 2 ^-3

4 x 1/8 = 1/2

4.

8 ^x = 2

2 ^3x = 2^1

3x = 1

x = 1/3

Answer:

10.50x + 15 = y

Step-by-step explanation:

x = amount of hours spent babysitting.

y = total amount of money.

The predicted cost for a student attending a arts college with 1,500 students and a rank of 4.5 can be calculated using the given regression model: Tuition = 7 + 4*Rank - 0.20*Size + 8*Private - 0.4*LibArts.

In this case, Rank = 4.5, Size = 1.5 (since it's measured in 1,000s), Private = 1 (since it's a private college), and LibArts = 1 (since it's a liberal arts college). Plugging these values into the model, the predicted tuition cost would be: Tuition = 7 + 4*(4.5) - 0.20*(1.5) + 8*1 - 0.4*1 = $26.1 thousand.

If the student switches from her current private liberal arts college to a public, non-liberal arts college with a rank 0.5 lower and 15,000 more students, we need to adjust the Size and Rank variables accordingly. Assuming the student's current college is still private, the new values would be Rank = 4.5 - 0.5 = 4 and Size = 1.5 + 15 = 16.5 (since it's measured in 1,000s). With the new values, we can calculate the predicted tuition cost for the public college: Tuition = 7 + 4*(4) - 0.20*(16.5) + 8*0 - 0.4*0 = $22.4 thousand.

To determine how much money the student saves in tuition, we calculate the difference between the predicted costs of the two colleges: $26.1 thousand - $22.4 thousand = $3.7 thousand. Therefore, by switching from her current private liberal arts college to a public, non-liberal arts college with a lower rank and larger size, the student saves $3.7 thousand in tuition.

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The given series \(\sigma_n=1^\infty 5/n^3\) is convergent.

The series given is:

Σₙ= \(1^\infty\) 5/n³

The nth partial sum of this series is given by:

\(S_n = \sigma_k=1^n 5/k^3\)

To calculate the first eight terms of the sequence of partial sums, we substitute n = 1, 2, 3, ..., 8 in the expression for Sₙ:

Rounding each partial sum to four decimal places, we get:

Based on these partial sums, it appears that the series is convergent. As we compute more and more terms of the sequence of partial sums, we observe that the sums increase, but at a decreasing rate, which suggests convergence.

To show that the series is convergent, we need to show that the sequence of partial sums approaches a finite limit as n approaches infinity.

We can use the Integral Test to show that the series converges. According to the Integral Test, if the series \(\sigma_n=1^\infty a_n\)  is a series of non-negative terms and the integral from 1 to infinity of a continuous, positive, decreasing function f(x) is finite, then the series converges.

In this case, we can use f(x) = 5/x³ as the function and integrate from 1 to infinity:

Integral from 1 to infinity of 5/x³ dx = [5/(-2x²)] from 1 to infinity

= \(-5/2 \lim (x- > \infty)[1/x^2 - 1/1]\)

= 5/2

Since the integral of f(x) is finite, the series \(\sigma_n=1^\infty 5/n^3\) converges by the Integral Test.

Therefore, the given series is convergent, as observed from the partial sums, and the sum of the series can be found by taking the limit of the sequence of partial sums as n approaches infinity.

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The answer is point C is further from point A than point B

A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates,

Given here: The points A(-5,8) ,  B(1,0) C(-10,16)

length of AB= \(\sqrt{(-5-1)^2+(8-1)^2}\)

                    =9.22 units

Similarly length of AC= \(\sqrt{(-5+10)^2+(8-16)^2}\)

                                    = 9.433

Hence, point C is further from point A than point B

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Answer:

55r737tdfrrgutyrvytuyt

Answer:

  (6, 3) and (6, -4)  or  (-4, 3) and (-4, -4)

Step-by-step explanation:

You want the coordinates of the remaining two vertices of a rectangle with area 35 square units, the endpoints of one side being (1, 3) and (1, -4).

A rectangle is a quadrilateral with adjacent sides at right angles. The area of it is the product of its length and width.

The given side is a vertical line (x=1) with points on it that are 7 units apart:

  3 -(-4) = 7

The area being 35 square units means the length of an adjacent side must be ...

  LW = 35

  7W = 35

  W = 35/7 = 5 . . . . units

The opposite side of the rectangle will be 5 units away, on a vertical line that is either x = 1+5 = 6, or x = 1 -5 = -4.

The y-coordinates of the endpoints of the opposite side will be the same as the y-coordinates of the given points. That is because the top and bottom edges of the rectangle are horizontal lines.

For the rectangle to the right of the given line, the missing coordinates are (6, 3) and (6, -4).

For the rectangle to the left of the given line, the missing coordinates are (-4, 3) and (-4, -4).

__

Additional comment

The attachment shows the two possible sets of answers.

Answer:

4 will replace?

Step-by-step explanation:

as 3-2=1

6-4=2

4-1=3

8-2=6

again

3-2=1

so

6-x=2

6-2=x

4

plz mark it as brainliest answer

In 2006, the five mainline Protestant churches accounted for 83% of the total Protestant membership.

In 2006, the combined membership of the five mainline Protestant churches (Baptist, Episcopal, Lutheran, Methodist, and Presbyterian) was approximately 65% of the total Protestant membership. This can be expressed as a formula:

Proportion of Mainline Protestant Membership = (Baptist Membership + Episcopal Membership + Lutheran Membership + Methodist Membership + Presbyterian Membership) / Total Protestant Membership

To calculate the proportion of mainline Protestant membership in 2006, we can apply the formula:

Proportion of Mainline Protestant Membership = (9,277,000 + 2,231,000 + 5,255,000 + 8,422,000 + 2,866,000) / (14,280,000 + 9,277,000 + 2,231,000 + 5,255,000 + 8,422,000 + 2,866,000)

Proportion of Mainline Protestant Membership = 29,106,000 / 35,050,000

Proportion of Mainline Protestant Membership = 0.83, or 83%

Therefore, in 2006, the five mainline Protestant churches accounted for 83% of the total Protestant membership.

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Answer:

\((x - y)(x + y + 1)\)

Step-by-step explanation:

\(x(x + 1) - y(y + 1)\)

\(=> x^{2} + x - y^{2} - y\)

Lets re-arrange it.

\(=> x^{2} - y^{2} + x - y\)

Now , lets expand x² - y².

\(=> (x + y)(x - y) + (x - y)\)

Taking ( x - y ) common ,

\(=> (x - y)(x + y + 1)\)

Answer:

\(x(x + 1) - y(y + 1) \\ → {x}^{2} + x - {y}^{2} - y \\→( {x}^{2}- {y}^{2}) + (x - y) \\→ (x - y)(x + y) + (x - y) \\→ \boxed{ (x - y)(x + y + 1)}✓\)

Answer:

A. False

B. True

C. False

D. False

E. True

Step-by-step explanation:

A. The diameter would be 6 inches.

B. Circumference = Diameter × 2

C. Area = Pi * Radius^2, NOT Pi^2.

D. Same as C.

E. Area = 3.14 × 1.5 × 1.5 = 7.065

Given the topological spaces X = {D, O, R, K} with the topology Tx and Y = {M, A, T, H} with the topology Jy, we are asked to determine whether the set E = {0, K} is open in X and open in Y.

To determine whether the set E = {0, K} is open in the topological spaces X and Y, we need to check if E belongs to the respective topologies, Tx and Ty.

In X, the topology Tx is given by: Tx = {Ø, {0}, {D, O}, {O, R}, {D, O, R}, X}. We can see that E = {0, K} is not explicitly listed in Tx. Therefore, E is not open in X since it does not belong to the topology.

In Y, the topology Ty is given by: Jy = {0, {M}, {M, A}, {M, A, T}, Y}. Again, E = {0, K} is not explicitly listed in Ty. Hence, E is not open in Y as it does not belong to the topology.

In both cases, the set E = {0, K} is not open in the respective topological spaces X and Y because it is not a member of the defined topologies.

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Answer:

3m + 4 is the answer obtained after combining like terms

We would need to perform a total of 72 evaluations to calculate the conditional probability P(Z|X, Y).

To calculate the conditional probability P(Z|X, Y) we need to evaluate the probability P(X, Y, Z) and the probability P(X, Y).

Next, we shall use these probabilities to calculate the conditional probability using Bayes' theorem:

P(Z|X, Y) = P(X, Y, Z) / P(X, Y)

Then, to evaluate P(X, Y, Z), we check all possible combinations of X, Y, and Z.

Given:

X has 3 potential outcomes

Y has 4 potential outcomes

Z has 5 potential outcomes

That is 3 x 4 x 5 = 60 possible combinations

Finally, to evaluate P(X, Y), we use the possible combinations of X and Y:

3 x 4 = 12.

Therefore, we would perform 60 evaluations to calculate P(X, Y, Z) and 12 evaluations to calculate P(X, Y), which is a total of 72 evaluations to calculate the conditional probability P(Z|X, Y).

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