Marc commutes to work on his bicycle, which has tires that measure 26 inches in diameter. A device on his bike informs him that one tire completed 388 full rotations between the time he left his house and the time he arrived at work. Rounded to the nearest inch, how far did Marc bike between his home and work.
A. 10,088 in.
B. 15,846 in.
C. 31,692 in.
D. 63,385 in.

Answer:

The sides length x of each square windowpane is [tex]10\ in[/tex]

Step-by-step explanation:

we know that

[tex]924\ in^{2}=(6+3x+6)(6+x+6)\\ \\924=(12+3x)(12+x)\\ \\924=144+12x+36x+3x^{2}\\ \\ 3x^{2}+48x- 780=0[/tex]

Solve the quadratic equation

using a graphing tool

The solution is [tex]x=10\ in[/tex]

see the attached figure

Answer:

10 inches is the side length of each square windowpane.

Step-by-step explanation:

Length of the single window plane = x

Width of the single window plane = x

On combining all the windows pane ,length becomes , l= 3x

On combining all the windows pane ,width becomes , b= x

Length of the frame = L = 6 + 3x+ 6 = 12 + 3x

Width of the frame = B = 6 + x+ 6 = 12 + x

Area of the frame, A = L × B = [tex](12+3x)\times (12+x)[/tex]

Given sum of combined area of the 3 windowpanes and frame = [tex]924 inch^2[/tex]

[tex]a + A=924[/tex]

[tex](12+3x)\times (12+x)=924[/tex]

[tex]144+48x+3x^2=924[/tex]

[tex]3x^2+48x-780=[/tex]

[tex]x^2+16x-260=0[/tex]

[tex]x^2+26x-10x-260=0[/tex]

[tex]x(x+26)-10(x+26)=0[/tex]

[tex](x+260)(x-10)=0[/tex]

x = 10 (accept)

x  = -26 (reject)

10 inches is the side length of each square windowpane.

Answer with explanation:

We will use [tex]\frac{28}{36}[/tex] rule here, to prove that, the statement given is Incorrect,which is you can afford to pay a maximum of 1/2 of your monthly income for rent.

[tex]\frac{28}{36}[/tex] rule, states that,you can use , 28% of gross monthly Income for Housing expenses, and 36 % of your gross monthly income is used for Debt purposes.

→→[tex]\frac{1}{2}[/tex] of monthly income =50 % of Monthly Income

we can use ,only 28% of Monthly income for rent Purpose.

False Statement

Answer:

Option D. (6, 2)

Step-by-step explanation:

we know that

The formula to calculate the midpoint between two points is equal to

[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]

substitute

[tex]M(\frac{3+9}{2},\frac{-1+5}{2})[/tex]

[tex]M(\frac{12}{2},\frac{4}{2})[/tex]

[tex]M(6,2)[/tex]

Answer:  a) x = {-3, 3, -3i, 3i}

               b) x = {-√5, √5}

               c) x = {-√3, √3, -i√2, i√2}

Step-by-step explanation:

[tex]a)\ x^4-81=0\\\\(x^2-9)(x^2+9)=0\\\\x^2=9\quad and\quad x^2=-9\\\\x=\pm 3\quad and\quad x=\pm3i[/tex]

[tex]b)\ x^4+10x^2+25=0\\\\(x^2+5)^2=0\\\\x^2=-5\\\\x=\pm i\sqrt5[/tex]

[tex]c)\ x^4-x^2-6=0\\\\(x^2-3)(x^2+2)=0\\\\x^2-3=0\quad and\quad x^2+2=0\\\\x^2=3\qquad and\quad x^2=-2\\\\x=\pm\sqrt3\quad and\quad x=\pm i\sqrt2[/tex]

No picture

Step-by-step explanation:

Answer:

The attached picture is the requested graph

Step-by-step explanation:

The system

[tex]y=\frac{3}{2}x-1\\ y= \frac{1}{2}x+3[/tex]

Has the following solution

x = 4 and y = 5 , which serves us to plot the desire graph, both function are lines and they intercept in (4,5)

Answer: A

Step-by-step explanation:

♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫

➷ 2x-3y=3

First:

Add -2y to both sides

-3y=-2x+3

Next:

Divide both sides by -3

y= 2/3x - 1

The answer

y= 2/3x - 1

✽

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

TROLLER

Answer:

[tex]\large\boxed{4n^5+3.5n^5+(-2.1n^5)=5.4n^5}[/tex]

Step-by-step explanation:

[tex]4n^5+3.5n^5+(-2.1n^5)=4n^5+3.5n^5-2.1n^5\qquad\text{combine like terms}\\\\=(4+3.5-2.1)n^5=5.4n^5[/tex]

Answer:

Step-by-step explanation:

"y/3"  is the symbolic representation of "an unknown number, y, divided by 3."

Note that all terms in 8xy − 9x2 y − 5x + 6, except for the 6, involve a variable, either x or y.  6 is the constant term.

Answer:

x = -14

Step-by-step explanation:

x/2 = -7

Multiply each side by 2 to get the x by itself

x = -7 * 2

x = -14

The answer would be x= -14

The answer is 3 units up

Divide the first number by the second number for each ratio:

A. 1 to 4 = 1/4 = 0.25 = 25%

B. 4 to 1 = 4/1 = 4 = 400%

C. 2 to 5 = 2/5 = 0.4 = 40%

The answer is C.

An equivalent ratio to 40% is 2 to 5, which is option C. The percentage is simplified by dividing it by the greatest common divisor to find its simplest ratio form.

To find a ratio equivalent to 40%, we first understand that percentages are a way of expressing a ratio where the second term is 100. Therefore, 40% is the same as saying 40 out of 100 or 40/100.

Next, we simplify this fraction to its lowest terms. Dividing both numerator and denominator by their greatest common divisor, which is 20 in this case, gives us 2/5. Thus, the ratio equivalent to 40% in its simplest form is 2 to 5, which corresponds to option C.

If we were to check the other options given, A (1 to 4) and B (4 to 1) are equivalent to 25% and 400% respectively, while D (5 to 2) is equivalent to 250%. Hence, these are not correct.

To illustrate the concept, let's consider an example. If the scale dimension is 4 cm, then to find the actual dimension using the proportion 1:2=4:x, we would cross-multiply to find x, which would be 8 cm, showing how ratios can be used to find corresponding values.

Answer:

Jadzia finished 80% of her homework.

Answer:

960

Step-by-step explanation:

10 x 8 x 4 x 3

Hope This Helped

Regards Jaygtgajm11

Disclaimer: The number of cities in Asia will be 8 and not 888.

Elyse can choose from 960 different combinations of cities.

The different ways in which objects from a set can be picked, often without replacement, to produce subsets are known as permutations and combinations. When the order of selection is a factor, this selection of subsets is termed a permutation; when order is not a factor, it is called a combination.

We are given 4 continents, with a number of cities to choose from for Elyse to visit.

The table is like this:

Continent                          Number of cities

Europe                                           10

Asia                                                8

Africa                                              4

Australia                                         3

We use permutations and combinations to find the number of combinations Elyse will have to choose from.

We can say that for every 10 cities in Europe, she can choose any of the 8 cities in Asia. Similarly, for every 8 cities in Asia, she can choose any of the 4 cities in Africa. And similar is the case for Africa and Australia.

∴ Elyse can choose from a combination of 10*8*4*3 cities,

or, Elyse can choose from a combination of 960 cities.

Learn more about permutations and combinations at

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Answer:

Your question is the answer

Step-by-step explanation:

None of the terms can be simplified further

t=100

p=3000

t 1/2 = 20

Try inserting the numbers in the half-life formula.

Answer:

93.75 gm.

Step-by-step explanation:

We have been given that an element has half life of about 20 days. We are asked to find the amount of 3000 gm sample left after 100 days.

We will use half-life formula to solve our given problem.

[tex]A=a\cdot (\frac{1}{2})^{\frac{t}{h}}[/tex], where,

A = Amount left after t units of time,

t = Time,

a = Initial amount,

h = Half-life.

Upon substituting our given values in above formula, we will get:

[tex]A=3000\cdot (\frac{1}{2})^{\frac{100}{20}}[/tex]

[tex]A=3000\cdot (0.5)^{5}[/tex]

[tex]A=3000\cdot 0.03125[/tex]

[tex]A=93.75[/tex]

Therefore, 93.75 gm of sample is left after 100 days.

Answer:

The option B (4 5/8,-2 3/4)  = (4.6 , -2.75) will be the coordinates belonging in the box.

Step-by-step explanation:

A.(4 3/4,-3 3/4) = (4.75,-3.75)

B.(4 5/8,-2 3/4)  = (4.6 , -2.75)

C.(4 1/4,-5 1/2)  = (4.25, -5.5)

D.(4 1/8,-2 3/5) = (4.125, -2.6)

The first point of line segment is: (5.5, -4.25)

second will be (4.75,-3.75)

third will be (4.6 , -2.75)

fourth will be (4.125, -2.6)

and fifth is  (3.75,-1.25)

The option C is not correct i.e not included in line segment.

The option B will be the coordinates belonging in the box.

I think the answer is C because the question says in one row there are 100 seats so with a total of 100 seats there is a row.

Answer:

D

Step-by-step explanation:

The answer is D because 100 divided by 10 = 10. Hope this helps! ☺

The weight of cargo of the truck is represented by;

w ≤ 2,000

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The cargo of the truck weighs at most 2,000 pounds.

Since, The weight of a cargo is at most 2,000 pounds.

Hence, The weight of cargo is less than or equal to 2,000.

Thus, The weight of cargo of the truck is represented by;

w ≤ 2,000

Learn more about the inequality visit:

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The weight of the cargo truck is given as w ≤ 2,000

Now it is given that cargo of the truck weighs at most 2,000 pounds.

Let 'w' be the symbol used to represent the weight of the cargo

Thus according to given information, the weight of the cargo can be less than or equal to 2000 pounds

Now a relation by which we can compare two or more mathematical expression is called an inequality.

Thus, the weight of cargo of the truck is represented using inequality as :

[tex]w\leq 2000[/tex]

This is the required answer.

Answer:

[tex]4-i[/tex]

Step-by-step explanation:

The distance of a complex number

[tex]z=a+bi[/tex]

from the origin is given by:

[tex]|z|=\sqrt{(a-0)^2+(b-0)^2}[/tex]

[tex]|z|=\sqrt{a^2+b^2}[/tex]

The length of  [tex]2+15i[/tex] is;

[tex]=\sqrt{2^2+15^2}[/tex]

[tex]=\sqrt{4+225}[/tex]

[tex]=\sqrt{229}[/tex]

The length of  [tex]17+i[/tex] is;

[tex]=\sqrt{17^2+1^2}[/tex]

[tex]=\sqrt{289+1}[/tex]

[tex]=\sqrt{290}[/tex]

The length of  [tex]20-3i[/tex] is;

[tex]=\sqrt{20^2+3^2}[/tex]

[tex]=\sqrt{400+9}[/tex]

[tex]=\sqrt{409}[/tex]

The length of  [tex]4-i[/tex] is;

[tex]=\sqrt{4^2+1^2}[/tex]

[tex]=\sqrt{16+1}[/tex]

[tex]=\sqrt{17}[/tex]

The correct choice is D

Answer:

Because when you square 8 or -8, you will still end up at 64

8 x 8 = 64

(-8) x (-8) = 64

Step-by-step explanation:

Ok so the square root of 64 is both positive and negative 8 because :

8^2= 64 but at the same time:

(-8)^2=64 because - to the power of two becomes positive so it has two answers because both 8 and -8 to the power of 2 is 64

Answer:

Option A

Step-by-step explanation:

We are given that a height is labeled on the triangle in given figure.

We have to find the  that segment which shows the base that correspond to the given height of the triangle

We know that base is that side of triangle on which height is perpendicular.

In the given figure, Height is perpendicular to side A.

Therefore, side A represent the base of triangle.

Hence, line segments A shows base that corresponds to the given height of the triangle.

Option A is true.

Answer:

[tex]h=(x^{4}+4x^{3}+8x+4)/(x^{3}+3x^{2}+8)[/tex]

Step-by-step explanation:

Let

h------> the height of the prism

we know that

The volume of the prism is equal to

[tex]V=Bh[/tex]

where

B is the area of the base

h is the height of the prism

In this problem we have

[tex]V=x^{4}+4x^{3}+8x+4[/tex]

[tex]B=x^{3}+3x^{2}+8[/tex]

substitute and solve for h

[tex]x^{4}+4x^{3}+8x+4=(x^{3}+3x^{2}+8)h[/tex]

[tex]h=(x^{4}+4x^{3}+8x+4)/(x^{3}+3x^{2}+8)[/tex]

Answer:

2.87

Step-by-step explanation:

2x^2-7=9

2x^2=9+7

2x^2/2=16/2

(square root)x^2=(square root)8

x=2.87

I used this method because I don't know any other method.

Answer:

Sample Response:  I would use the square root property of equality. Because there is no x term, I would just add and divide to get x^2 by itself.  Then I would take the square root.

2x^2 - 7 = 9

2x^2 - 7 + 7 = 9 + 7

2x^2 = 16

2x^2/2 = 16/2

x^2 = 8  (square root of 8 would be square root of 4*2 = 2*square root of 2

x = +/- 2*square root of 2

Answer:

The correct one is b nice you chose the right one!

Step-by-step explanation:

Answer:

25/12 - pounds more vegetables

Step-by-step explanation:

first we need to put these variables into like terms

36/12 - 3

8/12 - 2/3

3/12 - 1/4

add the last two up and subtract from the first and you get how much you need left over

Tim already has 11/12 pounds of vegetables. He requires Problem Solving for an additional 2 1/12 pounds of vegetables to reach the desired 3 pounds for his soup recipe. Therefore, option B is the correct answer.

The problem is asking about the amount of vegetables Tim needs to add to reach a total of 3 pounds for his soup. Given, he already has 2/3 pound of carrots and 1/4 pound of celery, he already has a combined total of 2/3 + 1/4 = 11/12 pounds of vegetables.

Now, we need to find out how many more pounds of vegetables he needs to reach 3 pounds. To do this, subtract the weight of the vegetables he has from the total weight required: 3 pounds - 11/12 pounds = 25/12 or 2 1/12 pounds.

So, Tim needs to add an additional 2 1/12 pounds of vegetables for his soup. Looking at the options given, Tim should choose option B) 1 1/12 pounds of zucchini.

Learn more about Problem Solving here:

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The probable question may be:

Tim is preparing a vegetable soup recipe that requires a total of 3 pounds of vegetables. Currently, he has 2/3 pound of carrots and 1/4 pound of celery. To make exactly 3 pounds of vegetables, what additional amount of vegetables should Tim add to his existing ingredients?

Additional Information:

  Tim needs 3 pounds of vegetables in total.

  He already has 2/3 pound of carrots.

  He also has 1/4 pound of celery.

Options for Tim to add to his existing ingredients to make a total of 3 pounds:

A) 5/12 pound of broccoli

B) 1 1/12 pounds of zucchini

C) 2/3 pound of spinach

D) 3/4 pound of tomatoes

Answer:

Step-by-step explanation:

So you want to start by multiplying so 5×8 = 40 , 5×1=5 , 2×3=6, 7×3=21 , now you take all that and add it together 40+5+6+21

Which your answer is 72

Answer:

[tex]\large\boxed{q=4P+4r}[/tex]

Step-by-step explanation:

[tex]\dfrac{q}{4}-r=P\qquad\text{muliply both sides by 4}\\\\4\!\!\!\!\diagup^1\cdot\dfrac{q}{4\!\!\!\!\diagup_1}-4r=4P\\\\q-4r=4P\qquad\text{add}\ 4r\ \text{to both sides}\\\\q=4P+4r[/tex]

First one is #2

Second one is #1

I'm positive about this

Answer:

53

Step-by-step explanation:

median is right in the middle of the other numbers.

Answer:

The median is 80

Step-by-step explanation:

To find the median we should arrange the given data set in ascending or descending  order. If there are even number of items in the given data set we have to take the average of central terms.

To find the median

It is given a data set,

98, 102, 53, 80, 22

Arrange them in ascending order

22, 53, 80, 98, 102

To find the middle term, From the set of data we get median is 80

22, 53, 80, 98, 102