p(t) = t3 + 2; Find p(5)

Answer:

E: 2

F: 9

Step-by-step explanation:

E:

\(\left(\frac{1}{2}\right)^2=\frac{1^2}{2^2}=\frac{1}{2^2}\)

\(=8\cdot \frac{1}{2^2}\)

\(=\frac{8}{2^2}\)

\(=\frac{2^3}{2^2}\)

\(=2\)

F:

\(=\frac{1}{3}\cdot \:27\)

\(=9\)

Answer:

\(\frac{n+2}{8}\) has a remainder of 7 ⇒ B

Step-by-step explanation:

In m ÷ n = c + \(\frac{r}{n}\) ,

Let us use the facts above to solve the question

∵ \(\frac{n}{8}\) has a remainder of 5

→ Let us find the first number divided by 8 and give a reminder of 5

  that means let the quotient = 1

∵ n = (8 × 1) + 5 = 8 + 5

∴ n = 13

∵ \(\frac{n+x}{8}\) has a remainder of 7

→ Let us find the first number divided by 8 and give a reminder of 7

  that means let the quotient = 1

∵ n + x = (8 × 1) + 7 = 8 + 7

∴ n + x = 15

∵ n = 13

∴ 13 + x = 15

→ Subtract 13 from both sides

∴ 13 -13 + x = 15 - 13

∴ x = 2

∴ \(\frac{n+2}{8}\) has a remainder of 7

Answer:

x=2

Step-by-step explanation:

just add 5 to both sides of the equation

Answer:

( 0 < y < 23 / 6 ) mins

Step-by-step explanation:

Solution:-

We will define a variable ( x ) as the time it took for Jo Anne to give her speech at home.

The time taken to give her speech must always be less than 4 minutes. We can express this mathematically using an inequality as follows:

                              ( 0 < x < 4 ) minutes

Jo Anne gave her speech which was 10 seconds less than the one she practised at home. We will convert the time in seconds to minutes as follows:

                             \(10 s * \frac{min}{60 s} = \frac{1}{6} min\)

The time taken by Jo Anne to complete her speech in English class can be represented as:

                             y = x - 1/6

Using the range of time that Jo Anne could take in delivering her speech in the class would be:

                                    0 < x < 4

                            0 - 1/6 < y < 4 - 1/6

                            -1/6 < y < 23 / 6

Since time can not be less than zero. We correct the lower limit to " 0 " as follows:

                              ( 0 < y < 23 / 6 ) mins

The possible times for her speech of her at school vary between 0 and 3:50 minutes.

Since Jo Anne needs to do a speech in her English class that can't be more than 4 minutes long, and she timed herself when she practiced last night and was within the time limit, and in class, her speech was 10 seconds less than the one that she did at home, to determine what are the possible times for her speech at school the following calculation must be performed:

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If rectangle has sides measuring (2x +7) units and (5x +9) units then expression that represents the area of the rectangle is \(10x^2+53x+63\) and degree of this expression is 2 and we proved that it satisfy closure property .

A quadrilateral with four right angles is called rectangle .

Given that sides are (2x+7) and (5x+9)

Hence area of rectangle can be calculated as

\((2x+7)(5x+9)\\\\2x(5x+9)+7(5x+9)\\\\10x^2+18x+35x+63\\\\10x^2+53x+63\\\)

Now we can see that this is a second degree polynomial

We got polynomial   \(10x^2+53x+63\) by multiplying two polynomial (2x+7) and (5x+9) hence it's closure property .

If rectangle has sides measuring (2x +7) units and (5x +9) units then expression that represents the area of the rectangle is \(10x^2+53x+63\) and degree of this expression is 2 and we proved that it satisfy closure property .

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The challenge requires you to change the equation from f(t)=a(x-h)2 + k to the parabola function f(t)=a(x-h)2 + k.

The centripetal acceleration is therefore given by the equation ac= v2/r = 2gh/r at every point along the frictionless roller coaster, where h is the distance from the highest point and r is the local radius of curvature.

If f(t) = 4t2 -8t + 7 then

= (4t2 - 8t + 4) + 7 - 4

=4 (t2 - 2t + 1) + 3

= 4 (t-1) 2 +3

As a result, options C and D are no longer possible.

recognising the f (t),

The maximum/minimum value is at f'(t) = 0 and f'(t) = 8t - 8.

0 = 8t – 8

t = 1

figuring out whether f"(t) > 0 or if minimum, f"(t) 0 maximum

Since f"(t) = 8 > 0, the minimal

f(1) =4(1)^2 – 8(1) +7= 3

Consequently, the minimal height is 3.

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Answer: t=5 t=8

Step-by-step explanation:

The mean of the data set is   427.5

We know that the mean of the data set as computed is obtained from; 345+340+400+625/ 4=  427.5

To obtain the variance of the data.

We now have to take the difference of the values and square it.

345-427.5 = -82.5

340-427.5 =-87.5

400-427.5 = -27.5

625-427.5 =197.5

Thus;

Variance=σ2 =(-82.5)^2 + (-87.5)^2 + (-27.5)^2+ (197.5)^2 /4  

σ2=6806.25+7656.25+756.25+39006.25/4

σ2=13556.25

The variance is 13556.2

For  the Standard deviation (S.D) of the data;

σ = √13556.25

σ =116.43

The Standard deviation of the data is 116.4

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To rank the steps involved in transforming one couple to another couple in a parallel plane, here is the correct order:

Identify the initial couple and the desired final couple.

Determine the translation vector that will move the initial couple to the desired final couple.

Translate the initial couple using the determined translation vector. This will shift the entire couple in the parallel plane.

Verify that the translation has successfully moved the initial couple to the desired final couple.

If necessary, make any additional adjustments or transformations to align the initial and final couples precisely in the parallel plane.

Confirm that the final couple is now in the desired position and orientation relative to the initial couple, maintaining the parallelism of the plane.

By following these steps in order, you can effectively transform one couple to another in a parallel plane.

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Answer:

its c

Step-by-step explanation:

Answer:

C. 2/3

Step-by-step explanation:

To solve this, we should come up with a common denominator first.

The least common denominator (LCD) of the four fractions would be 120.

So, first multiply each fraction's denominator to get 120, and multiply the numerator by the same amount.

ex. 3/4

4 x 30 = 120

3 x 30 = 90

We get 90/120.

After doing this with each fraction, we get;

13/15 = 104/120

7/8 = 105/120

2/3 = 80/120

3/4 = 90/120

Now, it is easier to see which fraction has the least value (or the one that is the smallest. Your answer is 2/3, since 80/120 is the smallest out of the four.

To find the radius of convergence, we use the ratio test. The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is less than 1, then the series converges absolutely. If the limit is greater than 1, then the series diverges. If the limit is equal to 1, then the test is inconclusive.

In this case, we have the series (-1)^(n-1)/n5^n. Taking the absolute value of the ratio of consecutive terms, we get |((-1)^n)/(n+1)(5^(n+1))) / ((-1)^(n-1)/n5^n)| = 1/(5(n+1)). Taking the limit as n approaches infinity, we get 1/5. Since the limit is less than 1, the series converges absolutely.

The radius of convergence is equal to the reciprocal of the limit we just found, which is 5. Therefore, the series converges for all x values between -5 and 5.

To find the interval of convergence, we need to test the endpoints. When x=5, the series becomes (-1)^(n-1)/(5n), which is an alternating series. The alternating series test tells us that the series converges if the absolute value of the terms decreases and approaches zero. In this case, the terms are decreasing in absolute value but do not approach zero, so the series diverges at x=5.

When x=-5, the series becomes (-1)^(n-1)/(-5n), which is also an alternating series. The same reasoning as above tells us that the series converges at x=-5.

Therefore, the interval of convergence is [-5,5).

The radius of convergence of the series (-1)^(n-1)/n5^n is 5, and the interval of convergence is [-5,5). To find the radius of convergence, we used the ratio test and found that the limit of the absolute value of the ratio of consecutive terms is 1/5. To find the interval of convergence, we tested the endpoints and found that the series converges at x=-5 and diverges at x=5.

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The interval of convergence is [-5,5). We apply the ratio test to determine the radius of convergence. The ratio test asserts that the series converges absolutely if the limit of the absolute value of the ratio of consecutive terms is smaller than 1.

The series diverges if the limit is bigger than 1. The test is not convincing if the limit is equal to 1.The series in question is (-1)(n-1)/n5n. The result is |((-1)n)/(n+1)(5(n+1))] / ((-1)(n-1)/n5n)| = 1/(5(n+1) when we take the absolute value of the ratio of successive words. When we take the limit as n gets closer to infinity, we get 1/5. Since 1, the limit, the series completely converges.

The radius of convergence is equal to the reciprocal of the limit we just found, which is 5. Therefore, the series converges for all x values between -5 and 5.

To find the interval of convergence, we need to test the endpoints. When x=5, the series becomes (-1)\(^(n-1)/(5n)\), which is an alternating series. The alternating series test tells us that the series converges if the absolute value of the terms decreases and approaches zero. In this case, the terms are decreasing in absolute value but do not approach zero, so the series diverges at x=5.

When x=-5, the series becomes (-1)\(^(n-1)/(-5n),\)which is also an alternating series. The same reasoning as above tells us that the series converges at x=-5.

Therefore, the interval of convergence is [-5,5).

The radius of convergence of the series (-1)^(n-1)/n\(5^n\) is 5, and the interval of convergence is [-5,5). To find the radius of convergence, we used the ratio test and found that the limit of the absolute value of the ratio of consecutive terms is 1/5. To find the interval of convergence, we tested the endpoints and found that the series converges at x=-5 and diverges at x=5.

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Answer:

r≈3.95in

Step-by-step explanation:

The probability that it takes the player 2 tries to make a three-point shot is approximately 0.498.

This is a binomial probability problem. The probability of making a three-point shot is 0.462, and we want to know the probability that it takes the player exactly 2 tries to make a shot. We can use the formula for the probability mass function of a binomial distribution:

where X is the number of successful shots, k is the number of successful shots we're interested in, n is the total number of shots attempted, p is the probability of making a shot, and (n choose k) is the binomial coefficient, which is the number of ways to choose k successes from n trials.

In this case, we have n = 2, k = 1, and p = 0.462, so we can calculate:

Therefore, the probability that it takes the player 2 tries to make a three-point shot is approximately 0.498.

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Answer: Associative property of multiplication as it is showing that the value does not change although you move the parentheses.

Step-by-step explanation:

The interest earned increases with higher principal amounts, higher interest rates, and longer time periods.

Principal (P) | Interest Rate (r) | Time Period (t) | Interest Earned (I)

$1,000 | 2% | 1 year | $20

$5,000 | 4% | 2 years | $400

$10,000 | 3.5% | 3 years | $1,050

$2,500 | 1.5% | 6 months | $18.75

$7,000 | 2.25% | 1.5 years | $236.25

To calculate the interest earned (I), we can use the simple interest formula: I = P * r * t.

For the first row, with a principal of $1,000, an interest rate of 2%, and a time period of 1 year, the interest earned is calculated as follows: I = $1,000 * 0.02 * 1 = $20.

For the second row, with a principal of $5,000, an interest rate of 4%, and a time period of 2 years, the interest earned is calculated as follows: I = $5,000 * 0.04 * 2 = $400.

For the third row, with a principal of $10,000, an interest rate of 3.5%, and a time period of 3 years, the interest earned is calculated as follows: I = $10,000 * 0.035 * 3 = $1,050.

For the fourth row, with a principal of $2,500, an interest rate of 1.5%, and a time period of 6 months (0.5 years), the interest earned is calculated as follows: I = $2,500 * 0.015 * 0.5 = $18.75.

For the fifth row, with a principal of $7,000, an interest rate of 2.25%, and a time period of 1.5 years, the interest earned is calculated as follows: I = $7,000 * 0.0225 * 1.5 = $236.25.

These calculations show the interest earned for different savings principals, interest rates, and time periods.

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Answer:

4(8)(12)

384 is your answer ☺️

Driving a personal car would be the most cost-effective mode of transportation for this commute, with a total daily cost of approximately $4.60 ($3.60 for gas + $1 for travel time).

Based on the given information, the most cost-effective mode of transportation for this commute would be to drive a personal car. Taking public transportation or carpooling may be more environmentally friendly options, but they may not save as much money as driving alone.

Assuming an average speed of 60 miles per hour on the highway, the commute would take approximately 20 minutes each way, or 40 minutes round-trip. This means the total cost of travel time for each workday would be $40 ($60/hour x 2/3 hour).

Using a cost calculator such as GasBuddy, we can estimate that the cost of driving 20 miles per day (round-trip) would be around $3.60 per day, assuming an average fuel efficiency of 25 miles per gallon and a gasoline price of $2.50 per gallon.

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Answer:

-12

Step-by-step explanation:

Let x be "the number."  

"Three times a number" means 3x

"is 24 less than the number" means = x-24

Put them togehter:

3x = x-24

2x = -24

x = -12

Check:  Is 3(-12) = 24 less than -12?  YES.

Bisection method is a numerical method used to find the root of a function by repeatedly bisecting an interval and determining which subinterval the root lies in, until the root is found.

To find the time at which the number of people in the museum is at a maximum, we need to find when the rate at which people are entering the museum (f'(t)) is equal to the rate at which people are leaving the museum (g'(t)).

Setting f'(t) = g'(t), we get:

380(1.02^t) = 240 + 240 sin (π(t-4)/12)

Simplifying, we get:

1.58(1.02^t) = 1 + sin(π(t-4)/12)

We can use a graphing calculator or numerical methods to solve for t.

Using a graphing calculator, we can graph the functions y = 1.58(1.02^x) and y = 1 + sin(π(x-4)/12) and find the point of intersection on the interval 1 ≤ x ≤ 11.

Alternatively, we can use numerical methods such as the bisection method or Newton's method to approximate the solution.

Using either method, we find that the solution is t ≈ 9.446.

Therefore, the answer is (C) 9.446.

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Answer:

50°

Step-by-step explanation:

because there opposite to each other.

Answer: John has an object suspended in the air. It has a mass of 50 kilograms and is 50 meters above the ground. Calculate the object's potential energy.

Step-by-step explanation:

Calculate the potential energy for a 2 kg basketball dropping from a height of 3.5 meters with a velocity of 9.8 m/sec².

Step-by-step explanation:

r u adding them or not if so it will be 2 years:0 months

Answer: I believe its B

Please check before ok

hope this helped <3

The  displacement x of the moving puck is; 0.43 meters

The displacement is defined as the change in position of an object. It is also called a vector quantity and has a direction and magnitude

The parameters given here are;

The polar coordinate initial velocity vector; U = 2.35 m/s, -22°

Final velocity vector; V = 6.42 m/s, +50°

This suggests to us that Cartesian x axis is parallel to angle 0° and y axis is parallel to +90°.

Change of velocity component parallel to +90° =  magnitude*sinθ,.

Thus, the change of that velocity

Δv = |V|sin(50) - |U|sin(-22)

Δv = 6.42sin(50) - 2.35sin(-22)

Δv = 4.9 - (-0.88)

Δv = +5.8 m/s

The equation for displacement is;

s = ut +1/2at^2

where acceleration time t = Δt = 0.215 s

initial velocity u = |U|sin(-22) = -0.88 m/s

acceleration parallel to u is a = Δv/Δt = +5.8/Δt

a = 5.8/t m/s^2

Thus;

s = -0.88t + ¹/₂* 5.8/t * t²

s = -0.88t +2.9t

s = 2.0t

s = 2.0 * 0.215

s = 0.43 m

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The sum of measures of angles A and B is 90°

Hence the angles are complementary

Answer:

5.2 hours

Step-by-step explanation:

To find the solution, you need to multiply Aretha's time by 1.6, since Neal takes 1.6 as long to run the marathon.

3.25 × 1.6 = 5.2

In other words, Neal takes 5.2 hours to run the marathon. Let me know if I can help you with anything else, 'kay?

Answer:

76%

Step-by-step explanation:

Convert the fraction 19/25 into decimal

19/25 = 0.766

Multiply the decimal by 100: 0.76 × 100 = 76%

Answer:

76%

Step-by-step explanation:

19/25×100

76%

In order for you to get the percentage, you multiply the fraction of gotten out of total to 100