Mathematics College

The ratio of the number of miles run to the number of miles biked is equivalent for each row in the table. What is the relationship between distances biked and distances run?

Answers

Answer 1

The relationship between distances biked and distances run is

D(bike) = 2 × D(run)

Here, we have been shown that when distance run is, lets say x then distance run is 2x

When distance run is 2 then distance biked is 4, twice as distance run.

Again in distance run 3[tex]\frac{1}{2}[/tex], distance biked is 7, so this proves that

D(bike) = 2 × D(run)

What is the importance of distance?

The measurement of distance between two objects or points can be quantitative or occasionally qualitative. Distance in physics or common language can refer to a physical length or an assumption based on other factors (e.g. "two counties over").

Since spatial thinking is a rich source of conceptual metaphors in human thought, the term is also frequently used metaphorically to denote a measure of the degree of separation or the statistical distance between two similar objects (such as edit distance between strings of text or statistical distance between probability distributions) (as exemplified by distance between people in a social network).

A metric space is a mathematical concept that is used to define the majority of these conceptions of distance, both literal and figurative.

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Related Questions

PLEASE HELP FAST I ONLY HAVE ONE HOUR!!!!!!

Answers

It’s the first one !!!!!!!!!!!!

a contractor purchases 3 dozen pairs of padded work gloves for $44.28. she incorrectly calculates the unit price as $14.76 per pair of the expense report. what is the correct unit price? what is the error?

Answers

The unit price of the pairs of padded will be $1.23 per pair. The error is the price of the pairs of pads should have been divided by 12.

What is the value of the expression?

When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.

For $44.28 a contractor buys 3 dozen pairs of cushioned work gloves.

The unit price of the pairs of padded will be given as,

⇒ $44.28 / (12 x 3)

⇒ $1.23 per pair

The unit price of the pairs of padded will be $1.23 per pair.

The error is the price of the pairs of pads should have been divided by 12.

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change the subject. make x the subject

Answers

Answer:

X= 1/y

Step-by-step explanation:

[tex]y = 1 - \frac{1}{ \sqrt{1} - \frac{1}{1 - x} } \\ y = 1 - \frac{1}{1 - \frac{1}{1 - x} } \\ y - 1 = - \frac{1}{1 - \frac{1}{1 - x} } \\ y - 1 = - \frac{1}{ \frac{1 - x - 1}{1 - x} } \\ y - 1 = - \frac{1 - x}{ - x} \\ y - 1 = \frac{1 - x}{x} \\ yx - x = 1 - x \\ yx = 1 \\ x = \frac{1}{y} [/tex]

FG is perpendicular to DM, if DF = 4R, FM = r + 21, and DF = FM, what is the value of R?

Answers

Answer:

(r+21 ) / 4

Step-by-step explanation:

as we can see DF = FM
and DF = 4R , FM =r+21

so,
4R = r+21
=> R= (r+21)/4

There is a real number whose product with every real numbers equal zero
a. Some ___ has the property that is __.
b. There is a real number a such that the product of á __.
c. There is a real number á with the property that for every real number b __.

Answers

There is a real number whose product with every real number equals zero

a. Some real number has the property that its product with every real number equals 0.

b. There is a real number a such that the product of á and any real equals zero.

c. There is a real number á with the property that for every real number b, the product of a and b equals zero.

Which of the following statements are true?
a) 25:35 = 45:55
b) 105: 30 = 49: 14
c) 45:48 = 60:64

Answers

Answer choice C is true.

100 POINTS PLEASE ANSWER QUICK
Use the box plot below to answer the questions.

Part A: Estimate the IQR for the male data.

Part B: Estimate the difference between the median values of each data set.

Part C: Describe the distribution of the data and if the mean or median would be a better measure of center for each.

Answers

The median is a better measure of center for the male's data, while the mean is a better for the female's data.

What are quartiles?

When we get data which can be compared relatively with each other, for finding quartiles, we arrange them in ascending or descending order.

Quartiles are then selected as 3 points such that they create four groups in the data, each groups approximately possessing 25% of the data.

(a) The IQR of the male's data

From the given male's boxplot, we have the following data elements;

Upper quartile (Q3) = 14

Lower quartile (Q1) = 2

Then the IQR is calculated as:

IQR = Q3 - Q1

So, we have:

IQR = 14 - 2

IQR = 12

Hence, the IQR for the given males' data is 12

(b) The difference between the median values can be calculated as;

Median of male's data = 14

Median of female's data = 9

The difference (d) between the median values is;

d = 14 - 9

d = 5

Hence, the difference between the median values of each data set is 5

It is found that the median is a better measure of center for the male's data, while the mean is a better measure of center for the female's data.

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The median is a better measure of center for the male's data, while the mean is a better for the female's data.

What are quartiles?

When we get data which can be compared relatively with each other, for finding quartiles, we arrange them in ascending or descending order.

Quartiles are then selected as 3 points such that they create four groups in the data, each groups approximately possessing 25% of the data.

(a) The IQR of the male's data

From the given male's boxplot, we have the following data elements;

Upper quartile (Q3) = 14

Lower quartile (Q1) = 2

Then the IQR is calculated as:

IQR = Q3 - Q1

So, we have:

IQR = 14 - 2

IQR = 12

Hence, the IQR for the given males' data is 12

(b) The difference between the median values can be calculated as;

Median of male's data = 14

Median of female's data = 9

The difference (d) between the median values is;

d = 14 - 9

d = 5

Hence, the difference between the median values of each data set is 5

(c) The distribution of data

It is found that the median is a better measure of center for the male's data, while the mean is a better measure of center for the female's data.

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If f(1)=6f(1)=6 and f(n)=f(n-1)-2f(n)=f(n−1)−2 then find the value of f(6)

Answers

The value of function f(n) = f(n - 1) - 2, at n = 6 is f(6) = -4

In this question,

we have been given a function f(n) = f(n - 1) - 2

Also, we have been given the value of function f(n) for n = 1

i.e., f(1) = 6

We need to find the value of f(6).

For n = 2,

f(2) = f(2 - 1) - 2

f(2) = f(1) - 2

f(2) = 6 - 2

f(2) = 4

For n = 3,

f(3) = f(3 - 1) - 2

f(3) = f(2) - 2

f(3) = 4 - 2

f(3) = 2

For n = 4,

f(4) = f(4 - 1) - 2

f(4) = f(3) - 2

f(4) = 2 - 2

f(4) = 0

For n = 5,

f(5) = f(5 - 1) - 2

f(5) = f(4) - 2

f(5) = 0 - 2

f(5) = -2

For n = 6,

f(6) = f(6 - 1) - 2

f(6) = f(5) - 2

f(6) = -2 - 2

f(6) = -4

Therefore, the value of function f(n) = f(n - 1) - 2, at n = 6 is f(6) = -4

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Find the vertex of the quadratic function f(x)=(x+3)2−4

Answers

The vertex form of the quadratic equation is y + 4 = (x + 3)² and the vertex of the parabola is (h, k) = (- 3, - 4).

How to find the vertex of the parabola from the expression of a quadratic equation

Herein we find the expression of a quadratic equation in vertex form, whose definition is shown below:

4 · p · (y - k) = (x - h)² (1)

Where:

h, k - Coordinates of the vertex.

p - Distance from the vertex to the focus.

Then, the vertex form of the quadratic equation is y + 4 = (x + 3)² and the vertex of the parabola is (h, k) = (- 3, - 4).

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Find all the solutions to the equation 4x3 + 16x2 + 28x = 0. 0, negative 4 + 2 i StartRoot 3 EndRoot, negative 4 negative 2 i StartRoot 3 EndRoot 0, 4 + 2 i StartRoot 3 EndRoot, 4 minus 2 i StartRoot 3 EndRoot 0, negative 2 + i StartRoot 3 EndRoot, negative 2 minus i StartRoot 3 EndRoot 0, 2 + StartRoot 3 EndRoot, 2 minus i StartRoot 3 EndRoot

Answers

The required solution to the equation 4x^3 + 16x^2 + 28x = 0 is 0, -2 + i√3, -2 - i√3

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .

Now the given equation is,

4x^3 + 16x^2 + 28x = 0

Taking x common we get,

x(4x^2 + 16x + 28) = 0

So, we get

x = 0

And 4x^2 + 16x + 28 = 0

or, x^2 + 4x + 7 = 0

Thus from the above equation is of the form

ax^2 + bx + c = 0

where, a = 1, b = 4 and c = 7

Therefore solution of the above equation is given as,

x = [-b ± √(b^2 - 4ac)] / 2a

Putting the values we get,

x = [-4 ± √(4^2 - 4*1*7)] / 2*1

so, x = [-4 ± √(16 - 28)] / 2

x = [-4 ± √(- 12)] / 2

x = [-4 ± 2√(- 3)] / 2

or, x = [-2 ± √(- 3)]

Since √-1 = i

∴ √(- 3) = i√3

Thus,

x = -2 ± i√3

So, the required values of x are 0, -2 + i√3, -2 - i√3.

Thus, the required solution to the equation 4x^3 + 16x^2 + 28x = 0 is 0, -2 + i√3, -2 - i√3.

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14. Jennifer and Francine are running a race where Francine runs the race far faster than Jennifer.
It takes Jennifer just five seconds less than twice Francine's time to finish. If their combined
total time is 86 seconds and frepresents the amount of time it takes Francine to finish, then
which of the following equations models this situation?
(1) ƒ+2(ƒ-5)=86
(3) ƒ+2ƒ-5=86
(2) 2ƒ-5=86
(4) 2f-5=43

Answers

The answer is (2) 2f-5=86; I hope- :\

Given q = √(5p²-1)²-2 find p in terms of q.

Answers

Answer:

[tex]\sf p =\sqrt{\dfrac{q+3}{5}}[/tex]

Step-by-step explanation:

To find p in terms of q, we have to isolate p.

[tex]\sf \sqrt{(5p^2 - 1)^2}-2 = q\\\\[/tex]

5p² - 1 - 2 = q

5p² - 3 = q

Add 3 to both sides,

5p² = q + 3

Divide both sides by 5,

[tex]\sf p^2 = \dfrac{q+3}{5}\\\\\text{Take square root,}\\\\p =\sqrt{\dfrac{q+3}{5}}[/tex]

Express the given function

Answers

Answer:

f(x) = [tex]{\displaystyle {\sqrt[8]{x}}}[/tex]

Step-by-step explanation:

If we let
[tex]g(x) = x^2 - 3\\\\\rm Then \;f(g(x) \;also \;written\; as\; (f\;\circ \rm \;g) \;is\; f(x^2 - 3)\\\\For\; this \;to \;be\; \sqrt[8]{x^2-3} , \\\\\rm f(x) \;has\;to\;be\;\sqrt[8]{x}[/tex]

Mathematics in the modern world

Answers

Answer:

Mathematics shaping the modern world.

PLEASE HELP in the figure below, what is the value of x? Show all work

Answers

Answer:

x=19

Step-by-step explanation:

All of the angles add up to 180 degrees since it is a straight angle. So, the equation is:

3x+7+90+x+7=180

You combine like terms:

4x+104=180

Then you subtract on both sides:

4x=76

Then you divide by 4 on both sides:

x=19

please help with this! i am stuck

Answers

The required simplification of the given expression [tex]=\lim_{x \to \infty} \frac{x^2-4x +4}{x^2-4}[/tex] is 1.

Given that,
To determine the simplified value of the expression [tex]=\lim_{x \to \infty} \frac{x^2-4x +4}{x^2-4}[/tex].

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Given expression,
[tex]=\lim_{x \to \infty} \frac{x^2-4x +4}{x^2-4}[/tex]
[tex]=\lim_{x \to \infty} \frac{x^2(1-4/x +4/x^2)}{x^2(1-4/x^2)}[/tex]
Now put limits, so 1 / x², 1 / x becomes zero so,
= 1

Thus, the required simplification of the given expression is 1.

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3. Jerry purchased two cans of paint. He used 6/4 of it. How much did Jerry have
used in decimal?
A. 6.40
B. 4.60
C. 1.50
D. 0.67

Answers

The amount used in decimal is 1.50

How to determine the amount used?

The given parameters are

Cans = 2

Amount used = 6/4

The amount used in decimal is calculated as:

Amount used = 6/4

Divide 6 by 4

So, we have

Amount used = 1.50

Hence, the amount used in decimal is 1.50

Answers

1.76, 4.98-3.22 4.98 is Jill’s money and 3.22 is marks

Answer: Answer choice 'B'

Step-by-step explanation:

4.00 + 0.75 + 0.40 + 0.03 = $5.18. This is Jill's amount.

3.00 + 0.40 + 0.02 = $3.42. This is Mark's amount.

To find out how much more money Jill has in comparison to how much mark has, we need to subtract Jill's money by Mark's money ($5.18 - $3.42)

if done correctly, your answer should be $1.76 (answer 'B')

K
Convert the angle to a decimal in degrees.
16°43'27"

Answers

The value of the angle 16°43'27"is approximately 16.724167 degrees.

A plane angle is measured in degrees, with the letter ° typically used to indicate that one full rotation is equal to 360 degrees.

The radian is the SI unit for measuring angles.1 degree = [tex]\frac{\pi}{180}[/tex] radiansA complete rotation around a circle is 180°.A degree is a narrow enough angle for many practical tasks where full degrees are enough for precision. In those instances when this is not the case, such as in astronomy or for geographic coordinates (latitude and longitude), degree measurements may be expressed in decimal degrees.

To convert a degree from minutes and seconds to decimal we must know the relation between degree and minutes and seconds.

1 degree=60 minutes.

1 minute = 60 seconds.

The given angle is 16°43'27"

27 seconds = 27 ÷ 60 minutes = 0.45 minutes = 0.45 ÷ 60 degree =0.0075 degree

43 minutes= 43 ÷ 60 degree = 0.71666666..

Total angle in decimal = 16+0.71666666+0.0075 =16.7241666...

Therefore required angle ≈ 16.7241667 degrees.

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Solve these questions
1) x +2x + x = 68
2) x+y+3y= 45
3) x+y-4z= -32
4) x+y+z= ?
5) -x + 8x= 63
6) 4x+3x-x=42
Same questions as the pic

Answers

Answer:

here is the answers

Step-by-step explanation:

sample:

1. 4x = 68

x = 68/4

x = 17

Solution :

1) x + 2x + x = 68

>> 4x = 68

>> x = 68 / 4

>> x = 17

2) x + y + 3y = 45

>> x + 4y = 45

>> 17 + 4y = 45

>> 4y = 45 - 17

>> 4y = 28

>> y = 28 / 4

>> y = 7

3) x + y - 4z = -32

>> 17 + 7 - 4z = -32

>> 24 - 4z = -32

>> -4z = -32 - 24

>> -4z = -56

>> z = 56 / 4

>> z = 14

4) x + y + z = ?

>> 17 + 7 + 14

>> 24 + 14

>> 38

5) -x + 8x = 63

>> 7x = 63

>> x = 63 / 7

>> x = 9

6) 4x + 3x - x = 42

>> 7x - x = 42

>> 6x = 42

>> x = 42 / 6

>> x = 7

The cost to rent a storage unit is different for two storage companies. Stack n’ Store charges $150 per month, plus a non refundable deposit of $175. Smart Storage charges $185 each month with no deposit. Complete the table showing the total cost for each company during the first six months and use it to answer the questions.

Lee plans to store clothes for four months. Which company offers the better deal?

After how many months is the total cost the same at both storage companies?

Answers

Month Cost at Stack n’ Store Cost at Smart Storage

1 $325 $185

2 $475 $370

3 $625 $555

4 $775 $740

5 $925 $925

6 $1075 $1100

The company that offers the better deal is Smart Storage.

After 5 months the cost would be the same at both storage companies.

What are the total costs?

The equation that represent the total cost of renting at Stack n’ Store is:

Total cost = non refundable deposit + charge per month

Total cost in the first month : $175 x ($150 x 1 ) = $325

Total cost in the second month : $175 x ($150 x 2 ) = $475

Total cost in the third month : $175 x ($150 x 3 ) = $625

Total cost in the fourth month : $175 x ($150 x 4) = $775

Total cost in the fifth month : $175 x ($150 x 5) = $925

Total cost in the sixth month : $175 x ($150 x 6) = $1075

The equation that represent the total cost of renting at Smart Storage is:

Total cost = cost per month x number of months

Total cost in the first month : $185 x 1 = $185

Total cost in the second month : $185 x 2 = $370

Total cost in the third month : $185 x 3 = $555

Total cost in the fourth month : $185 x 4 = $740

Total cost in the fifth month : $185 x 5 = $925

Total cost in the sixth month : $185 x 6 = $1,110

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using associative property

(y+12)+28

Answers

y+(12+28)

Associative Property of addition states: a+(b+c)=(a+b)+c.

Find the slope P=(-4,-1) Q=(-3,-3)

Answers

The slope of P=(-4,-1) Q=(-3,-3) is -2.

Given,

P=(-4,-1)

Q=(-3,-3)

The slope between two points P=(x₁, y₁)

Q=(x₂ ,y₂)

slope = (y₂-y₁)/(x₂-x₁)

So slope between P=(-4,-1) Q=(-3,-3) is

[(-3)-(-1) ]/ [(-3)-(-4)]

=-2/1

=-2

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line may be used to compute the slope of any line. The ratio of "vertical change" to "horizontal change" between two separate locations on a line is calculated using the slope of a line formula.

The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line. Finding the slope between two separate locations and calculating the slope of a line are related tasks. In general, we require the values of any two separate coordinates of a line in order to determine its slope.

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In August 2006, a report was issued about an Internet poll conducted on behalf of the Oxygen Television Network. The survey included 1400 women and 700 men, aged 15 to 49. The following is part of a press release about the findings.
"Apparently if it's a gadget, women gotta have it, according to a survey done by Oxygen Media, an American cable network owned and operated by women. The Women's Watch: Girls Gone Wired survey released in August indicates that 77 per cent of women fancy a new plasma TV over a diamond solitaire necklace, 78 per cent would rather have a sleek new cell phone than shoes, and 86 per cent would prefer a new digital video camera over designer footwear."
What can be said about these poll results?

Answers

Answer:

Results of the Assembly elections in five States are indeed a shot in the arm for the Bharatiya Janata Party (BJP), which won in all four States where it was in power. The Hindu editorial captures the broad trends that emerge out of these results. Prime Minister Narendra Modi has said these results have sealed the outcome of the 2024 Lok Sabha elections too in the BJP’s favour. He said people have rejected caste and dynastic politics.

The total attendance at a science museum is modeled by the function f(x)=17,371(1.041)x. If the initial total attendance (that is, the total attendance when x=0) was measured January 1, 2013, what was the initial total attendance?

Answers

The initial total attendance at a science museum is modeled by the function f(x)=17,371(1.041)x will be 17371.

How to calculate the value?

It should be noted that from the information, the total attendance at a science museum is modeled by the function

In this case, the total attendance when x=0 will be:

f(x) = 17,371(1.041)x.

f(x) = 17,371(1.041^0)

= 17371 × 1

= 17371

Therefore, the total attendance when x = 0 will be 17371.

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Help asap please!! I don’t understand

Answers

Answer: 2+[tex]\frac{6x-2}{x(x-3)}[/tex] ==> x[tex]\neq[/tex]0, x[tex]\neq[/tex]3

Step-by-step explanation:

f(x)=2x^2-2

g(x)=x^2-3x

(f/g)(x)=

[tex]\frac{2x^2-2}{x^2-3x}[/tex]=

[tex]\frac{2x^2-6x+6x-2}{x^2-3x}[/tex]=

2+[tex]\frac{6x-2}{x^2-3x}[/tex]=2+[tex]\frac{6x-2}{x(x-3)}[/tex] ==> x[tex]\neq[/tex]0, x[tex]\neq[/tex]3

2.
If a train travels between two cities in 3 hours at an average speed of 65 miles per hour, how long
would it take at an average speed of 80 miles per hour?

Answers

Answer:

At 65mph the car traveled 195 miles in 3hrs.

So divide 195 miles by 80mph to get 2.4375 hrs

At 65mph the car traveled 195 miles in 3hrs.

Find the area of the shaded region. Help please!

Answers

[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=10\\ \theta =85 \end{cases}\implies \begin{array}{llll} A=\cfrac{(85)\pi (10)^2}{360} \\\\\\ A=\cfrac{425\pi }{18}\implies A\approx 74.18~cm^2 \end{array}[/tex]

Quantitative Reasoning :')

Answers

Answer:

Step-by-step explanation:

more taking a shower you use almost 3 gallons per a shower

HELP 50 POINTS (see image attached)
5
1
2
8
-2

Answers

The value of the function f(3) is 1

How to determine the value of f(3)?

The graph represents the given parameter

The value of f(3) implies that we calculate the value of the function when x = 3

From the graph, we have

f(x) = 1, when x = 3

This means that

f(3) = 1

The above is calculated by substituting 3 for x in the equation f(x) = 1

Hence, the value of f(3) is 1