Would anyone be willing to help me out with a few math questions? I'm up late and could really use the help!

Answers

Answer 1
State your questions and I’ll be happy to help

Related Questions

After Paul and Marlena got married, they decided they wanted to take a
Caribbean cruise to celebrate their ten year anniversary. The cruise will cost them
$5,800. How much should they deposit into an account now that pays 5.3%
interest, compounded daily, in order to have enough for their cruise in ten years?
A. $550.81
B. $2,431.23
C. $2,957.82
D. $3,414.04

PLEASEEE

Answers

Paul and Marlena should deposit approximately $2,431.23 into an account now to have enough for their cruise in ten years.

So, the correct answer is B. $2,431.23.

To calculate the amount Paul and Marlena should deposit into an account now in order to have enough for their cruise in ten years, we can use the formula for compound interest:

[tex]A = P(1 + r/n)^{ (nt)}[/tex]

Where:

A = the future value of the investment/loan, including interest

P = the principal amount (initial deposit)

r = the annual interest rate (in decimal form)

n = the number of times that interest is compounded per year

t = the number of years

In this case, the principal amount (P) is what we need to find.

The future value (A) is given as $5,800.

The interest rate (r) is 5.3% or 0.053 as a decimal.

The interest is compounded daily, so n = 365 (number of days in a year).

Using the formula, we can rearrange it to solve for P:

[tex]P = A / (1 + r/n)^{(nt)[/tex]

Substituting the given values:

[tex]P = 5800 / (1 + 0.053/365)^{(365\times 10)[/tex]

Calculating this expression:

P ≈ 2,431.23

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Which equation represents the volume of each cone?

Answers

The equation which represents the volume of each cone is as follows:

V = (1/3)πr²h

Explanation :

In this equation, "V" represents the volume of the cone, "r" represents the radius of the base, and "h" represents the height of the cone.

V represents the volume of the cone. Volume is a measure of the space occupied by an object, and in this case, it refers to the space inside the cone.

π (pi) is a mathematical constant approximately equal to 3.14159. It is used in calculations involving circles and spheres.

r represents the radius of the base of the cone. The radius is the distance from the center of the base to any point on its circumference. Squaring the radius, r², gives us the area of the base.

h represents the height of the cone. It is the perpendicular distance from the base to the vertex (top) of the cone.

When we multiply the area of the base (πr²) by the height (h) and divide the result by 3, we get the volume of the cone. The division by 3 is necessary because the volume of a cone is one-third the volume of a cylinder with the same base and height.

So, the equation V = (1/3)πr²h provides a way to calculate the volume of a cone based on its radius and height.

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A. johnny translated abcd 3 units to the right and 4 units up to a new position, efgh. draw and label efgh.

b. tom rotated abcd to a new position, ijkl, 90º clockwise about the origin, o. draw and label ijkl.

c. tony placed a smaller car, represented as mnop, on the coordinate plane. mnop is a dilation of abcd with its center at the origin and a scale factor of -0.5. draw and label mnop.

Answers

A. To obtain the position of EFGH, Johnny translated ABCD by 3 units to the right and 4 units up. To draw and label EFGH, simply shift each vertex of ABCD by this translation vector (3, 4).

B. Tom rotated ABCD by 90º clockwise about the origin, O, to get the position of IJKL. To draw and label IJKL, rotate each vertex of ABCD 90º clockwise around the origin. This can be achieved by switching the x and y coordinates of each vertex and negating the new x value.

C. Tony placed a smaller car, MNOP, on the coordinate plane. MNOP is a dilation of ABCD with its center at the origin and a scale factor of -0.5. To draw and label MNOP, multiply the coordinates of each vertex of ABCD by the scale factor -0.5, keeping the origin as the center.

Use The Fundamental Theorem of Calculus, Part 2 to evaluate / - (13 – 12) dt.

Answers

The value of the integral [tex]\int -1^1 (13 - 12) dt[/tex] is 26.

How to evaluate the integral?

To evaluate the integral [tex]\int-1^1 (13 - 12) dt[/tex] , we need to find an antiderivative of the integrand, which is simply:

∫ (13 - 12) dt = 13t - 12

Using this antiderivative, we can evaluate the definite integral by applying the theorem:

[tex]\int-1^1 (13 - 12) dt = [13t - 12]_{(-1)^1[/tex]

Evaluating this expression at the limits of integration (-1 and 1), we get:

[13(1) - 12] - [13(-1) - 12]

Simplifying, we get:

= 13 - 12 + 13 + 12

= 26

Therefore, the value of the integral [tex]\int-1^1 (13 - 12) dt[/tex] is 26.

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A consumer group is investigating two brands of popcorn, R and S. The population proportion of kernels that will pop for Brand R is 0. 90. The population proportion of kernels that will pop for Brand S is 0. 85. Two independent random samples were taken from the population. The following table shows the sample statistics. Number of Kernels in Samples Proportion from Sample that Popped Brand R 100 0. 92 Brand S 200 0. 89 The consumer group claims that for all samples of size 100 kernels from Brand R and 200 kernels from Brand S, the mean of all possible differences in sample proportions (Brand R minus Brand S) is 0. 3. Is the consumer group’s claim correct? Yes. The mean is 0. 92−0. 89=0. 3. Yes. The mean is 0. 92 minus 0. 89 equals 0. 3. A No. The mean is 0. 92+0. 892=0. 905. No. The mean is the fraction 0. 92 plus 0. 89 over 2 equals 0. 905. B No. The mean is 0. 92−0. 892=0. 15. No. The mean is the fraction 0. 92 minus 0. 89 over 2 equals 0. 15. C No. The mean is 0. 90+0. 852=0. 875. No. The mean is the fraction 0. 90 plus 0. 85 over 2 equals 0. 875. D No. The mean is 0. 90−0. 85=0. 5

Answers

The consumer group's claim that the mean of all possible differences in sample proportions (Brand R minus Brand S) is 0.3 is correct.

This can be calculated by subtracting the sample proportion of Brand S from the sample proportion of Brand R, resulting in a difference of 0.03 or 3%. This matches the consumer group's claim that the mean of all possible differences in sample proportions is 0.3. It is important to note that this result only applies to the specific samples taken and cannot be generalized to all samples from these brands.

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Consider the quadratic function: f(x)=x^2-6x+8
Identify the coordinates of the x(intercepts if any

Answers

Answer:

x-intercepts (4,0) (2,0)

y-intercepts (0,8)

Step-by-step explanation:

have a good day :)

Answer the following questions regarding convergence of series. It is possible that the correct answer would be "cannot be determined". (a) Suppse that sum Ak is a convergent series with known sum L Bk a convergent series with known
k=1
sum M. If L < M, does this guarantee that ax < bx for all k > 1? If not, provide a counter example.

Answers

L < M, as 1 < 1.25.  

a_2 = 1/4 > 1/8 = b_2, which shows that a_k < b_k is not guaranteed for all k > 1.

What is the detailed explaination of this answer?

(a) Given two convergent series Σa_k (with sum L) and Σb_k (with sum M) where k=1 to ∞, and L < M, we are asked if a_k < b_k for all k > 1. The answer is no, this is not guaranteed.

Counter example:
Consider the following two convergent series:

Series A: Σa_k, where a_1 = 1/2, a_2 = 1/4, a_3 = 1/8, ... (a geometric series with a common ratio of 1/2)

Series B: Σb_k, where b_1 = 1, b_2 = 1/8, b_3 = 1/16, ... (a geometric series with a common ratio of 1/2 starting from the second term)

Sum L for Series A:
L = a_1 / (1 - (1/2)) = 1

Sum M for Series B:
M = b_1 + (b_2 / (1 - (1/2))) = 1 + 1/4 = 1.25

In this case, L < M, as 1 < 1.25. However, a_2 = 1/4 > 1/8 = b_2, which shows that a_k < b_k is not guaranteed for all k > 1.

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For this problem, a table has been started for you based on the information given in the problem. use inductive reasoning to complete the table.



an electronics store finds that over a period of three months, sales of stereos decreased. in march, the store sold 325 stereos. in april, the store sold 280 stereos, and in may, the store sold 235 stereos.



month



stereos sold



march



325



april



280



may



235



june



july



august



incorrect feedback has been removed from the screen.


type your answers and then click or tap done.




make a conjecture about the number of stereos sold in june. fill in the blank text field 1


190



make a conjecture about the number of stereos sold in july.



make a conjecture about the number of stereos sold in august.

Answers

Using inductive reasoning, we can observe a pattern in the given data: the number of stereos sold decreases by 45 each month.

We can apply this pattern to make conjectures about the number of stereos sold in June, July, and August.

June: 235 (May's sales) - 45 = 190 stereos
July: 190 (June's sales) - 45 = 145 stereos
August: 145 (July's sales) - 45 = 100 stereos

So, the conjectures for the number of stereos sold are:
June: 190
July: 145
August: 100

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The base of a solid is the region in the first quadrant between the graph of y=2x
and the x-axis for 0≤x≤1. For the solid, each cross section perpendicular to the x-axis is a quarter circle with the corresponding circle’s center on the x-axis and one radius in the xy-plane. What is the volume of the solid?

Answers

The volume of the solid is A. [tex]\pi/3[/tex]

What is the volume of a solid?

The volume of a solid in geometry signifies the space it occupies inside a three-dimensional area. It denotes how much content can fill up its inner region, and as usual, measured in units like cubic feet, meters, or centimeters.

Finding the measurement formula varies from shape to shape but commonly involves multiplying width, height, and length. Given that many sectors rely on this term, such as engineering, architecture, and physics, understanding the concept of the volume of a solid weighs significantly.

If we take a cross-section of (x,y)perpendicular to the x-axis, with width dx, now the cross-section is a quarter circle with radius y.

Thus, the volume of the cross-section, since y = 2x becomes: [tex]\pi x^2 dx[/tex]

Now, the volume of the solid when integrated becomes: [tex]\frac{\pi }{3}[/tex]

Option A is correct.

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Frank keeps his pet iguana in a glass tank that is shaped like a rectangular prism.the height of the tank is 11 inches, the width is 34.5 inches, and the length is 25 inches.what is the best estimate for the volume of the tank in cubic feet?remember 12 inches = 1 foot.

Answers

The best estimate for the volume of the tank in cubic feet is 5.5 cubic feet.

The volume of the tank is:

V = l x w x h

where l is the length, w is the width, and h is the height.

Substituting the given values, we get:

V = 25 x 34.5 x 11 = 9547.5 cubic inches

To convert cubic inches to cubic feet, we divide by (12 x 12 x 12), since there are 12 inches in a foot and 12 x 12 x 12 cubic inches in a cubic foot:

V = 9547.5 / (12 x 12 x 12) cubic feet

V ≈ 5.5 cubic feet

Therefore, 5.5 cubic feet is the best estimate for the tank's cubic foot capacity.

Hence , the volume of the rectangular glass tank is 5.490 feet³

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A restaurant in Richmond, BC, lists the prices on its menus in fractions of a dollar. Three friends have lunch at the restaurant. Each of 3 friends orders a veggie mushroom cheddar burger for 11 % ( , with a glass of water to drink.
What was the total bill be fore taxes, in fractions of a dollar?

Answers

If each of the 3 friends orders a veggie mushroom cheddar burger for 11%, the cost of each burger would be:

11% of $1.00 = $0.11

Since the prices are listed in fractions of a dollar, we can express the cost of each burger as 11/100 of a dollar.

So, the total cost of 3 veggie mushroom cheddar burgers would be:

3 x 11/100 = 33/100 = $0.33

Assuming that the glass of water is free, the total bill before taxes would be $0.33 for the 3 burgers. However, it's important to note that this calculation is based on the assumption that the prices are listed in fractions of a dollar, which may not be the case. If the prices are listed in a different unit, the calculation would need to be adjusted accordingly.

a driveway consists of two rectangles one rectangle is 80 ft long and 15 ft wide the other is 30 ft long and 30 ft wide what is the area of the driveway ​

Answers

Answer: 2100 square feet

Step-by-step explanation:

To solve this question we must add the areas of the two rectangles.

area = length x width

Rect 1:

a = lw

  = 80 x 15 = 1200 square feet

Rect 2:

a = lw

  = 30 x 30 = 900 square feet

so in total, the driveway is 1200 + 900 = 2100 square feet

Answer:

To find the area of the driveway, we need to find the area of both rectangles and add them together.

The area of the first rectangle is:

80 ft x 15 ft = 1200 sq ft

The area of the second rectangle is:

30 ft x 30 ft = 900 sq ft

To find the total area of the driveway, we add the two areas together:

1200 sq ft + 900 sq ft = 2100 sq ft

Therefore, the area of the driveway is 2100 square feet.

Cam can't figure out what to eat. He is going to randomly select a piece of fruit from his pantry. There are
4
44 apples and
5
55 bananas in his pantry.
What is
P(select an apple
)
P(select an apple)start text, P, left parenthesis, s, e, l, e, c, t, space, a, n, space, a, p, p, l, e, end text, right parenthesis?
If necessary, round your answer to
2
22 decimal places.

Answers

If Cam randomly selects a piece of fruit from his pantry, the probability of selecting an apple is 4/9 or 0.44.

To find the probability of selecting an apple, we need to divide the number of apples by the total number of fruits in Cam's pantry.

Total number of fruits = number of apples + number of bananas = 4 + 5 = 9

P(select an apple) = number of apples / total number of fruits = 4/9

So, the probability of selecting an apple is 4/9 or approximately 0.44 when rounded to two decimal places.

Therefore, the probability is 4/9 or 0.44.

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Complete question is:

Cam can't figure out what to eat. He is going to randomly select a piece of fruit from his pantry. There are 4 apples and 5 bananas in his pantry.

What is P(select an apple)?

If necessary, round your answer to 2 decimal places.

What are the coordinates of the point on the directed line segment from (-3,-5) to (9,−8) that partitions the segment into a ratio of 2 to 1?

Answers

The coordinates of the point are (7,0).

How to solve for the coordinates

distance from (-3,-5) to (x,y) = 2 * distance from (x,y) to (9,-8)

Using the distance formula, we can write this equation as:

√[(x - (-3))^2 + (y - (-5))^2] = 2 * √[(9 - x)^2 + (-8 - y)^2]

Simplifying this equation, we get:

[tex](x + 3)^2 + (y + 5)^2 = 4[(9 - x)^2 + (-8 - y)^2][/tex]

Expanding and simplifying further, we get:

[tex]17x + 16y = 119[/tex]

So the coordinates of the point on the directed line segment from (-3,-5) to (9,-8) that partitions the segment into a ratio of 2 to 1 are:

x = (119 - 16y)/17

y = any value (since we can choose any value of y and then calculate x using the equation above)

For example, if we choose y = 0, then we get:

x = (119 - 16(0))/17 = 7

So the coordinates of the point are (7,0).

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What’s the answer I need help plsease

Answers

Answer: B

Step-by-step explanation:

Your original matrix:

1 0

0 1

after dilation

3 0

0 3

after reflection... it only changes sign of y because its reflected across x-axis

3 0

0 -3

B

1. bona drives tor 3 hours at 44mph. clare drives 144 mies in 4 hours. how
for would bena travel if she drove for 3 hours at the same speed os
claire
2. janet and andrew leave their home at the same time. janet has 60
milles to travel and drives at 40 mph. andrew have 80 miles to travel
and also drives at 40 mph
a) how long does janets journey take?
(b) how much longer does andrew spend driving than janeta

Answers

1) Bona can drive 108 miles if she drove for 3 hour at the same speed as Claire.

2) Janet would take 1.5 hour to complete the journey and Andrew spend half hour more driving than Janet.

1) Bona speed is 44mph

Time taken by Bona is 3 hour

distance travelled by Claire is 144 miles

Time taken by Claire is 4 hour

Claire's speed = distance / time

Claire's speed = 144/4

Claire's speed = 36 mph

Distance travelled by Bona = speed × time

Distance travelled by Bona = 36 × 3

Distance travelled by Bona = 108 miles

2) Janet distance = 60 miles

Janet speed = 40 mph

Time taken by Janet = distance / speed

Time taken by Janet = 60/40

Time taken by Janet = 1.5 hour

Janet would take 1.5 hour to complete the journey

Andrew distance = 80 miles

Andrew speed = 40 mph

Time taken by Andrew = distance / speed

Time taken by Andrew = 80/40

Time taken by Andrew= 2 hour

Andrew spend half hour more driving than Janet.

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Please help me with this math

Answers

Answer:

mean decreases by 15

median stays the same

The average weight of Carl, Carla, Carmen, Clark, and Cathy is 107.6 lb. Cathy weighs 115 lb. What is the average weight of the other four? Show your work.

Answers

Answer:

Step-by-step explanation:

Let's start by finding the total weight of all five people:

Total weight = Average weight x Number of people

Total weight = 107.6 x 5

Total weight = 538

We know that Cathy weighs 115 lb, so we can subtract her weight from the total weight to find the total weight of the other four people:

Total weight of other four = Total weight - Cathy's weight

Total weight of other four = 538 - 115

Total weight of other four = 423

To find the average weight of the other four, we can divide the total weight of the other four by the number of people:

Average weight of other four = Total weight of other four / Number of people

Average weight of other four = 423 / 4

Average weight of other four = 105.75 lb

Therefore, the average weight of the other four is 105.75 lb.

Q1. Consider the following options for characters in setting a password:
.
.


Digits = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9}


Letters = { a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, V, W, X, Y, z}


Special characters = 1 *, &, $. #}


Compute the number of passwords possible that satisfy these conditions:


• Password must be of length 6.


Characters can be special characters, digits, or letters,


Characters may be repeated.
.

Answers

There are 4,096,000,000 possible passwords of length 6 using special characters, digits, and letters, with characters allowed to be repeated.


To compute the number of passwords possible with a length of 6 using digits, letters, and special characters, with characters allowed to be repeated, follow these steps:

1. Count the number of options for each character type:
  - Digits: 10 (0-9)
  - Letters: 26 (a-z)
  - Special characters: 4 (*, &, $, #)

2. Combine the options for all character types:
  Total options per character = 10 digits + 26 letters + 4 special characters = 40

3. Calculate the number of possible passwords:
  Since characters may be repeated and the password has a length of 6, the number of possible passwords = 40^6 (40 options for each of the 6 character positions)

4. Calculate the result:
  Number of possible passwords = 40^6 = 4,096,000,000



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[tex]\frac{4}{-2} -\frac{3}{-6}[/tex]

Answers

The value of the fraction is 3/-2

What is a fraction?

A fraction can simply be described as the part of a whole variable, a whole number or a whole element.

The different types of fractions in mathematics are;

Mixed fractionsProper fractionsImproper fractionsComplex fractionsSimple fractions

From the information given, we have that;

4/-2 - 3/-6

find the lowest common factor

12 - 3/-6

subtract the value, we get;

9/-6

Divide the values into simpler forms

3/-2

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An egg is dropped from the roof of a building. The distance it falls varies directly with the square of the time it falls. It takes 1/2 second for the egg to fall eight feet, how long will it take the egg to fall 200 feet?

What does K equal? And how many seconds?

Answers

Answer:

16 seconds

Step-by-step explanation:

Which of the following Is closest to the volume of the shoebox?

How do you set up and solve?

Answers

Answer:

H

Step-by-step explanation:

You take each given side and multiply them all together

18.4 x 8.8 x 11 = approx 1782

Qn in attachment
.
..​

Answers

Answer: d

Step-by-step explanation:

Answer:

pls mrk me brainliest

Step-by-step explanation:

(⁠ ̄⁠(⁠エ⁠)⁠ ̄⁠)⁠ノ

Chandler earns $15.25 an hour as a hostess at a local restaurant. She
earns an additional $25 in tips each night from take-out orders.
Determine if this linear relationship is proportional. Explain.

Answers

No, this linear relationship is not proportional, because the ratio between Chandler's hourly wage and tips changes because the number of hours worked changes

Proportional relationships are those wherein the ratio between the two portions being as compared stays constant, no matter the values of those quantities.

In this case, we're evaluating Chandler's earnings primarily based on her hourly wage and her hints from take-out orders.

But, the ratio between Chandler's hourly wage of $15.25 and her tips of $25 per night varies relying on the number of hours she works.

For example, if Chandler works for 2 hours, her total income could be $30.50 (2 x $15.25) + $25 = $55.50.

If she works for four hours, her total earnings would be $61 (4 x $15.25) + $25 = $86. In this example, the ratio among her hourly salary and tips adjustments as her income increase with more hours worked.

Therefore, because the ratio between Chandler's hourly wage and tips changes because the number of hours worked changes, this linear relationship is not proportional.

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The value of a car is worth 40,000, and it declines by 3% every year. Which function best represents the the value of the hybrid car.


40000(0. 03)^t


40000(1. 03)^t

Answers

The function best represent the value of hybrid car that is worth 40000 and it declines by 3% every year is  [tex]40,000(0.97)^{t}[/tex]

The value of the car = 40,000

The value of car declines at the rate of 3% every year

function is represented as F(t)

F(t) = [tex]P( 1 - \frac{R}{100} )^{t}[/tex]

P is principal amount value of the car which is 40,000

R is rate at which it declines every year which is 3%

t is no. of year

Putting all the values in the equation we get

F(t) = [tex]40000(1-\frac{3}{100} )^{t}[/tex]

F(t) = [tex]40000(\frac{97}{100}) ^{t}[/tex]

F(t) = [tex]40000(0.97)^{t}[/tex]

The function represent the value of the hybrid car is [tex]40000(0.97)^{t}[/tex] .

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23- Find unit vectors that satisfy the stated conditions (a) Oppositely directed to v = (3,-4 ) and half the length of v.

Answers

The unit vector that is oppositely directed to v = (3, -4) and half its length is approximately u = (-0.5547, 0.8321).

How to find a unit vector that satisfies the given conditions?

To find a unit vector that is oppositely directed to v = (3, -4) and half its length, we can follow these steps:

Find the length of vector v:

|v| = sqrt(3^2 + (-4)^2) = 5

Divide vector v by 2 to get a vector with half its length:

v/2 = (3/2, -2)

To get a vector that is oppositely directed to v, we can reverse the direction of v/2:

-(3/2, -2) = (-3/2, 2)

Finally, we can find the unit vector in the direction of (-3/2, 2) by dividing it by its length:

|(-3/2, 2)| = sqrt((-3/2)^2 + 2^2) = sqrt(13/4)

u = (-3/2, 2) / sqrt(13/4) = (-3/2) * (2/sqrt(13))/2 + (2/sqrt(13)) * (1/2)

Therefore, the unit vector that is oppositely directed to v = (3, -4) and half its length is approximately u = (-0.5547, 0.8321).

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The coach recorded the time it took 14 students to run a mile. The times are as follows: 9:23, 8:15, 9:23, 9:01, 6:55, 7:20, 9:14, 6:21, 7:12, 7:34, 6:10, 9:15, 9:18. Use the data set to complete the frequency table. Then use the table to make a histogram

Answers

The histogram for the frequency table is illustrated below.

To create the frequency table, we need to count how many times each time appears in the data set. The time 9:23 appears twice, so we would put a frequency of 2 in the row corresponding to 9:23. We do this for each time in the data set.

Here is the completed frequency table:

Time Frequency

6:10 1

6:21 1

6:55 1

7:12 1

7:20 1

7:34 1

8:15 1

9:01 1

9:14 1

9:15 1

9:18 1

9:23 2

As you can see, each time appears only once or twice in the data set. This tells us that there is no dominant time that most students ran the mile in.

To create the histogram, we'll draw a bar above each time on the x-axis with a height equal to the frequency of that time. For example, there are two times of 9:23, so we'll draw a bar above 9:23 with a height of 2.

As you can see, the histogram shows a relatively even distribution of times. The most common times are around 9 minutes, but there are also several times below 8 minutes and one time below 7 minutes.

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The distance from city a to city b is 256. 8 miles. The distance from city a to city c is 739. 4 miles how much farther is the trip to city c than the trip to city b

Answers

Answer:

482.6 mi

Step-by-step explanation:

a to b = 256.8 mi

a to c = 739.4 mi

(a to c) - (a to b) = 739.4 - 256.8 = 482.6 mi

THIS IS FOR 20 POINTS
What is the value of a?


27.5


50


90


45

Answers

The measure of arc a must be 2 times measure of inscribed angle, which is 90 degrees.

What is arc?

In geometry, an arc is a segment of a circle's circumference. It is defined by two endpoints and all the points on the circle's circumference between them.

What is inscribed angle?

An inscribed angle is an angle formed by two chords in a circle that have a common endpoint.

According to given information:

For any inscribed angle in a circle, the measure of the angle is always half the measure of the arc that it intercepts. This is known as the inscribed angle theorem.

So, if we have an inscribed angle with a measure of 45 degrees, then the measure of its corresponding arc would be 2 times that, which is 90 degrees.

Therefore, if the inscribed angle is associated with arc a, and the measure of the corresponding angle is 45 degrees, then we know that the measure of arc a must be 2 times that, which is 90 degrees.

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Use Newton's method to approximate a root of the equation In (4x) = arctan(x -0.1) as follows. Let x1 = 0.1 be the initial approximation. The fourth approximation x4 is and the fifth approximation x5 is

Answers

To use Newton's method to approximate a root of the equation

In (4x) = arctan(x -0.1),

we will need to find the first derivative of the function f(x) = In(4x) - arctan(x-0.1). f(x) = In(4x) - arctan(x-0.1) f'(x) = 4/(4x) - 1/(1+(x-0.1)^2) Using the initial approximation x1 = 0.1,

We can find the second approximation x2: x2 = x1 - f(x1)/f'(x1) x2 = 0.1 - [In(4*0.1) - arctan(0.1-0.1)] / [4/(4*0.1) - 1/(1+(0.1-0.1)^2)] x2 = 0.1076

We can repeat this process to find the third approximation x3: x3 = x2 - f(x2)/f'(x2) x3 = 0.1076 - [In(4*0.1076) - arctan(0.1076-0.1)] / [4/(4*0.1076) - 1/(1+(0.1076-0.1)^2)] x3 = 0.1078

Now we can find the fourth approximation x4: x4 = x3 - f(x3)/f'(x3) x4 = 0.1078 - [In(4*0.1078) - arctan(0.1078-0.1)] / [4/(4*0.1078) - 1/(1+(0.1078-0.1)^2)] x4 = 0.1078

Finally, we can find the fifth approximation x5: x5 = x4 - f(x4)/f'(x4) x5 = 0.1078 - [In(4*0.1078) - arctan(0.1078-0.1)] / [4/(4*0.1078) - 1/(1+(0.1078-0.1)^2)] x5 = 0.1078

Therefore, the fourth approximation x4 is 0.1078 and the fifth approximation x5 is also 0.1078.

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