21. Brian wants to purchase a piece of fabric
that is between 49 and 53 inches long.
He can choose between three pieces of
fabric. Choice A is 4 3/4 feet long. Choice
B is 4 1/2 feet long. Choice C is 4 1/3 feet
long. Which piece of fabric should Brian
purchase?
(Show WORK!!)

John sold 18 adults tickets and 9 children tickets.

Step-by-step explanation:

Given,

Cost of adult ticket = $6.50

Cost of children ticket = $4.50

Total collected = $157.50

Let,

Number of adult tickets sold = x

Number of children tickets sold = y

According to given statement;

6.50x+4.50y=157.50    Eqn 1

he sells twice as many adult tickets as children’s tickets.

x=2y     Eqn 2

Putting value of x from Eqn 2 in Eqn 1

[tex]6.50(2y)+4.50y=157.50\\13y+4.50y=157.50\\17.50y=157.50[/tex]

Dividing both sides by 17.50

[tex]\frac{17.50y}{17.50}=\frac{157.50}{17.50}\\y=9[/tex]

Putting y=9 in Eqn 2

[tex]x=2(9)\\x=18[/tex]

John sold 18 adults tickets and 9 children tickets.

Keywords: linear equation, substitution method

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Option 4

f(x) = -x is an odd function

Solution:

A function is odd if and only if f(–x) = –f(x)

Option 1

[tex]f(x) = x^3 + 5x^2 + x[/tex]

Substitute x = -x in above equation

[tex]f(-x) = (-x)^3 + 5(-x)^2 + (-x)[/tex]

Cubes always involve multiplying a number by itself three times, so if the number is negative the cube will always be negative

Ans squaring results in positive

[tex]f(-x) = -x^3 + 5x -x[/tex]  --- eqn 1

[tex]-f(x) = -(x^3 + 5x^2 + x)\\\\-f(x) = -x^3 - 5x^2 - x[/tex]  ---- eqn 2

Comparing eqn 1 and eqn 2,

[tex]f(-x) \neq -f(x)[/tex]

Therefore not an odd function

Option 2

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

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

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

Therefore,

[tex]f(-x) \neq -f(x)[/tex]

Therefore not an odd function

Option 3

[tex]f(x) = x^2 + x\\\\f(-x) = (-x)^2 + (-x)\\\\f(-x) = x^2 - x[/tex]

[tex]-f(x) = -(x^2 + x) = -x^2 - x[/tex]

[tex]f(-x) \neq -f(x)[/tex]

Therefore not an odd function

Option 4

[tex]f(x) = -x\\\\f(-x) = -(-x) = x[/tex]

[tex]-f(x) = -(-x) = x[/tex]

[tex]f(-x) = -f(x)[/tex]

Thus option 4 is correct and it is an odd function

Answer:

D

Step-by-step explanation:

just took test on edge

The median is found by ordering the numbers and choosing the middle one (or the average of the two middle ones in the case of an even set). Tanya's mistake was not ordering the numbers before choosing the median. Thus, the correct median for the provided list is 31.5.

In mathematics, the median is the middle number in a sorted, ascending or descending, list of numbers. It can be found by arranging all the numbers from smallest to greatest. If there is an odd number of observations, the median is the middle number. If there is an even number of observations, the median is the average of the two middle numbers.

So, here is the mistake in Tanya's method: She didn't arrange the numbers in order from smallest to largest before choosing the middle number. This is why 37 is not the correct median.

Now, let's find the correct median for the provided list of numbers: 20, 29, 30, 31, 32, 33, 34, 37. Since it's an even number of observations, we take the average of the two middle numbers, which are 31 and 32. Hence, the median of the numbers in the list is (31+32)/2 = 31.5.

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(a) Tanya's mistake is that she did not first arrange the numbers in ascending (or descending) order.

(b) The median of the numbers in the list is 31.5.

a) Tanya's mistake is that she did not first arrange the numbers in ascending (or descending) order. The median is the middle number in a sorted list of numbers. If the list has an odd number of elements, the median is the middle element. If the list has an even number of elements, the median is the average of the two middle numbers. Tanya needs to sort the numbers before finding the median.

b) Sort the numbers in ascending order, so the list will become.

[tex]\[ 20, 29, 30, 31, 32, 33, 34, 37 \][/tex]

Determine the median:

  Since there are 8 numbers (an even number of elements), the median will be the average of the 4th and 5th numbers in the sorted list.

  - The 4th number is 31.

  - The 5th number is 32.

[tex]\[ \text{Median} = \frac{31 + 32}{2} = \frac{63}{2} = 31.5 \][/tex]

Therefore, the median of the numbers in the list is 31.5.

Answer:

73

Step-by-step explanation:

Givens

d = 3

Equation 7d^2 + 10 = ?

Solution

7*3*3 + 10                

7*9 + 10

63 + 10 = 73

Answer:

Graph 3 represents the solution to the system of equations.

Step-by-step explanation:

The given two linear equations of x and y are

y = 3x + 2 ........ (1) and  

10x + 2y = 20 .......... (2)

Now, to solve those two equations let substitute the value of y from equation (1) to the equation (2).

Hence, 10x + 2(3x + 2) = 20

⇒ 16x = 16

⇒ x = 1  

And from equation (1), y = 3x + 2 = 5  

Therefore, the solution of the system of equations (1) and (2) are (1,5).

Therefore, graph 3 represents the solution to the system of equations. (Answer)

Answer:

29,025 is the answer

Step-by-step explanation:

9,675 × 3

The number of people who visited Hank's website last month is found by dividing the total visitors this month (9,675 people) by 3, resulting in 3,225 visitors last month.

The student is faced with a mathematics problem involving division with whole numbers. The problem states that the number of people who visited Hank's website this month is three times the number of visitors from the previous month. Given that we know the number of visitors this month is 9,675, we can find out the number of visitors from the previous month by dividing this number by three.

So, the calculation is:

9675 people (this month) ÷ 3

From this calculation, we can determine that 3,225 people visited Hank's website last month.

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Answer:

Step-by-step explanation:

Sin (π - x ) = Sin x = m

Answer:

[tex]\large\boxed{y+1=3(x-1)}\\\\\boxed{y=3x-4}[/tex]

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

(x₁, y₁) - a point on a line

We have

[tex]m=3,\ (1,\ -1)\to x_1=1,\ y_1=-1[/tex]

Substitute:

[tex]y-(-1)=3(x-1)\\\\\boxed{y+1=3(x-1)}[/tex]

Convert to the slope-intercept form

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

[tex]y+1=3(x-1)[/tex]            use the distributive property

[tex]y+1=3x-3[/tex]             subtract 1 from both sides

[tex]\boxed{y=3x-4}[/tex]

Answer:

Grover has $24, Percy has $31 and Annabeth has $19.

Step-by-step explanation:

Create equations to represent the situation.

let a be Annabeth

let g be Grover

let p be Percy

a + g = 43      Together, Annabeth and Grover have $43

g + p = 55    If Grover and Percy combine their money, they have $55

p = g + 7        Percy has $7 more than Grover

See if any of the equations can be combined. For example, we know p is g+7.

Substitute p for g+7 in an equation that has the variable p.

g + p = 55

g + g + 7 = 55    Combine like terms (g)

2g + 7 = 55   Start isolating g. Subtract 7 from both sides

2g = 55 - 7

2g = 48     Divide both sides by 2

g = 48/2    

g = 24         Money Grover has

Use the equation p = g + 7. Find "p" by substituting g for 24.

p = g + 7

p = 24 + 7   Add

p = 31    Money Percy has

Substitute g for 24 in the last equation, a + g = 43, to find a.

a + g = 43

a + 24 = 43    Subtract 24 from both sides

a = 43 - 24

a = 19     Money Annabeth has

Therefore Grover has $24, Percy has $31 and Annabeth has $19.

Answer:

Grover has $24, Percy has $31 and Annabeth has $19.

Create equations to represent the situation.

let a be Annabeth

let g be Grover

let p be Percy

a + g = 43      Together, Annabeth and Grover have $43

g + p = 55    If Grover and Percy combine their money, they have $55

p = g + 7        Percy has $7 more than Grover

See if any of the equations can be combined. For example, we know p is g+7.

Substitute p for g+7 in an equation that has the variable p.

g + p = 55

g + g + 7 = 55    Combine like terms (g)

2g + 7 = 55   Start isolating g. Subtract 7 from both sides

2g = 55 - 7

2g = 48     Divide both sides by 2

g = 48/2    

g = 24         Money Grover has

Use the equation p = g + 7. Find "p" by substituting g for 24.

p = g + 7

p = 24 + 7   Add

p = 31    Money Percy has

Substitute g for 24 in the last equation, a + g = 43, to find a.

a + g = 43

a + 24 = 43    Subtract 24 from both sides

a = 43 - 24

a = 19     Money Annabeth has

Therefore Grover has $24, Percy has $31 and Annabeth has $19.

Answer:

there are 1,440 minutes in 24 hrs a day

Step-by-step explanation:

Now thank me and rate me

Hope your year has been going great !!

The answer is 1440 if im correct

Answer:

7 kg

Step-by-step explanation:

F=35*2=m*10

70=10m

7=m

The mass of the second object is 7 kg

First, we make the following representations

[tex]F \to[/tex] Force

[tex]a \to[/tex] acceleration

[tex]m \to[/tex] mass

The formula of force is:

[tex]F = m * a[/tex]

Since force is constant, then:

[tex]m_1 =2kg[/tex]    [tex]a_1 = 35m/s^2[/tex] --- subset 1 represents the first object

[tex]m_2 = ??[/tex]       [tex]a_2 = 10m/s^2[/tex] --- subset 2 represents the second object

We are to calculate the mass of the second object

A constant force means:

[tex]m_1 * a_1 = m_2 * a_2[/tex]

Make m2 the subject

[tex]m_2 = \frac{m_1 * a_1}{a_2}[/tex]

Substitute known values

[tex]m_2 = \frac{2kg * 35m/s^2}{10m/s^2}[/tex]

[tex]m_2 = \frac{2kg * 35}{10}[/tex]

[tex]m_2 = \frac{70kg}{10}[/tex]

[tex]m_2 =7kg[/tex]

Hence, the mass of the second object is 7kg

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Answer:

50 rooms with kitchen facilities and 100 rooms without kitchen facilities

Step-by-step explanation:

Let the rooms without kitchen facilities be x and those with kitchen facilities be y

Form set of equations

Since the total rooms are 15, then the first equation is

x+y=150

Therefore, x=150-y

Considering the cost of rooms and what was collected, then

80x+100y=13000

Substituting x with 150-y then

80(150-y)+100y=13000

12000-80y+100y=13000

20y=1000

[tex]y=\frac {1000}{20}=50 rooms[/tex]

Therefore, x=150-y=150-50=100 rooms

Therefore, there are 50 rooms with kitchen facilities and 100 rooms without kitchen facilities

Answer:

3x-2y^2-2

Step-by-step explanation:

3x-(2y^2+2)=3x-2y^2-2

Answer:

28.5 inches.

Step-by-step explanation:

Given: Measurement of diagonal= 36 inch.

           Height= 22 inches

Picture attached to show the measurement.

As the screen of televison is measured by diagonal of screen.

∴ Hypotenous= diagonal of screen, which is 36 inches.

Now, using pythagorean theoram to find length of television screen.

[tex]hypotenous^{2} = opposite^{2}+adjacent^{2}[/tex]

∴ [tex]36^{2} = 22^{2} + adjacent^{2}[/tex]

Here adjacent is the length of television.

⇒[tex]1296= 484+ length^{2}[/tex]

Subtracting both side by 484.

⇒[tex]length^{2} = 812[/tex]

Taking square root on both side

remember: [tex]\sqrt{a^{2} } = a[/tex]

∴ [tex]length= \sqrt{812}= 28.495 \approx 28.5[/tex]

Hence, length of televison screen is 28.5 inches.

The width of a television screen can be calculated using the Pythagorean theorem. Given a diagonal of 36 inches and height of 22 inches, the approximate length of the screen is 30 inches.

To solve this problem, we will use the Pythagorean theorem which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This principle can be written as a^2 + b^2 = c^2 where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.

In the case of a television screen, the diagonal (from one corner to the opposite corner) is the hypotenuse. Given the height of the TV screen as 22 inches (one of the sides of the right triangle), and the diagonal as 36 inches (the hypotenuse), the length (the other side of the right triangle) can be found using the formula.

Let's rearrange the formula to solve for the length (b): b = sqrt(c^2 - a^2). Substitute the given measurements into the formula: length = sqrt(36^2 - 22^2), or approximately 30 inches.

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Answer:

yassar

Step-by-step explanation:

Answer:

The answer is 40

Step-by-step explanation:

First, since roger has 3 times as many grapes as Marissa. do 10 times 3. The answer is 30. Roger has 30 grapes. The question is asking how much they have all together. Add 30 plus 10 and the answer that you will get is 40. The answer is 40

Answer:

Step-by-step explanation:

Total money raised = 658 + 95.60 = $ 753.60

donated to each charity = 753.60/12 = $62.80

Answer:

Move right by 4 units and down by 9 units

Step-by-step explanation:

The vertex of the parabolic function f(x) = x² is at (0,0)

Now, the parabolic function g(x) = - 8x + x² + 7 can be rearranged to vertex form.

g(x) = x² - 8x + 16 + 7 - 16

⇒ g(x) = (x - 4)² - 9

⇒ (x - 4)² = (y + 9) {If y = g(x)}

Therefore, the vertex of the parabolic function g(x) is at (4,-9).

Therefore, we have to move right by 4 units and down by 9 units to reach from vertex of f(x) to vertex of g(x). (Answer)

Using translation concepts, it is found that the translation that maps f(x) into g(x) is described by: right 4, down 9

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, function f(x) is defined by:

f(x) = x².

Function g(x) is defined by:

g(x) = x² - 8x + 7

Completing the squares, we have that g(x) can be written as:

g(x) = (x - 4)² - 9

Hence, the correct translation is:

right 4, down 9

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The question is a college-level mathematics problem involving taking the third derivative of the function f(x) = 2x/(x^2 - 1). The process requires the application of quotient rule and chain rule of differentiation.

The student question involves calculating the third derivative of the function f(x) = 2x/(x2 - 1). This function is a rational function and can be differentiated using the quotient rule and chain rule of differentiation. Let's proceed with the derivative calculations.

First, we should recall that the function can be rewritten as:

f(x) = 2x/(x2 - 1) = 2x/[(x - 1)(x + 1)]

Now we can calculate the derivatives. For the first derivative f'(x), we use the quotient rule:

f'(x) = [(x2 - 1)(2) - (2x)(2x)]/(x2 - 1)2

For the second derivative f''(x), we differentiate f'(x) again:

f''(x) = Derivative of f'(x) with respect to x

The third derivative f'''(x) is then the derivative of f''(x). Calculations for the second and third derivatives can be a bit complex and lengthy, and it is necessary to apply the quotient rule and product rule carefully.

Through this process, we will arrive at the third derivative, f'''(x), which is what the question asks for.

Answer:

Step-by-step explanation:

Total fruits T= 5+7 = 12

No. Of apple n(A) = 5

No. Of peaches n(P) = 7

P(A) 1st = n(A)/T = 5/12

P(P) 2nd = n(p)/(T-1) = 7/11

: P(A and P) = 5/12 × 7/11

= 35/132

Answer:

[tex]A=65.97\ cm^2[/tex]

Step-by-step explanation:

The complete question is

The shaded region is the area outside the smaller circle and inside the larger circle

we know that

The area of the shaded region is equal to subtract the area of the smaller circle from the area of the larger circle

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

so

The area of the shaded region is

[tex]A=\pi [r_1^2-r_2^2][/tex]

where

[tex]r_1=12.5/2=6.25\ cm[/tex] ---> radius of the larger circle (is half the diameter)

[tex]r_2=8.5/2=4.25\ cm[/tex] ---> radius of the smaller circle (is half the diameter)

assume

[tex]\pi =3.1416[/tex]

substitute

[tex]A=3.1416[(6.25)^2-(4.25)^2][/tex]

[tex]A=65.97\ cm^2[/tex]

Answer:

1/8x___________=7/8 the answer is 6

Step-by-step Explanation:

Before heading towards the solution, you need to make sure how multiple and factors are related to each other.

The multiple of a number could be obtained by multiply it with another number.

For example, the first five multiples of 12 are 12, 24, 36, 48 and 60

Factors are the numbers that are multiplied to get a given number.

For example,

The factors of 12 are 1, 2, 3, 4, 6 and 12.

As division and multiplication can be used to find factors and multiples.

For example a whole number is a multiple of its factors.

Let w = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20} be the set of even wholes numbers from 2 to 20.

As 2 is a factor of 20 because 20 ÷ 2 = 4

20 is a multiple of 2 because 2 X 10 = 20

So, in the same way, the equation 8 X 5 = 40 can be used to determine how factors and multiples are related.

Let the equation be

                                    8 X 5 = 40

8 is a factor of 40 because 8 X 5 = 40

40 is a multiple of 8 because 40 ÷ 5 = 8

So, this is how factors and multiples are related to each other.

Keywords: factors, multiples, division, multiplication

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2.615

Step-by-step explanation:

22 divided by 8

the average snowfall per hour is 2.75 inch.

Division is the process of splitting a number or an amount into equal parts.

here, given that,

A snowstorm dumped 22 inches of snow in 8 hours.

i.e. per hour = 22/8

                    =2.76

hence,  the average snowfall per hour is 2.75 inch.

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Answer:

$7.50

Step-by-step explanation:

10 divided by 4 = $2.50

so, $2.50 x 3 = $7.50

Answer:

$7.5 Dollars

Step-by-step explanation:

The cost of 4 bottles is $10. So, 1 bottle is going to be $2.50 (division)

Now, to find the cost of 3 water-bottles, we have to multiply.

$2.50 * 3 = $7.50.

So, the answer to this question is  3 bottles = $7.50

(Hope this helps!)

Answer:

[tex]\int \ln (x+1) \, dx=x\cdot \ln (x+1)-x+\ln (x+1)+C[/tex]

Step-by-step explanation:

Use integration by parts formula:

[tex]\int u \, dv=uv-\int v \, du[/tex]

For the integral

[tex]\int \ln(x+1) \, dx,[/tex]

[tex]u=\ln (x+1)\\ \\dv=dx,[/tex]

then

[tex]du=d(\ln (x+1))=\dfrac{1}{x+1}\ dx\\ \\v=x[/tex]

and

[tex]\int \ln(x+1) \, dx\\ \\=x\cdot \ln (x+1)-\int x\cdot \dfrac{1}{x+1} \, dx\\ \\= x\cdot \ln (x+1)-\int \dfrac{x+1-1}{x+1} \, dx\\ \\=x\cdot \ln (x+1)-\int \left(1-\dfrac{1}{x+1}\right) \, dx\\ \\=x\cdot \ln (x+1)-\int \, dx +\int \dfrac{1}{x+1} \, dx\\ \\=x\cdot \ln (x+1)-x+\ln (x+1)+C[/tex]

Answer:

The correct answer is C. 15 ¹⁵√x⁵y³

Correct question and statement:

Express 15x^1/3 y^1/5 using a radical, as it is written in the graph attached.

Step-by-step explanation:

15x^1/3 y^1/5

15 * (x^1/3 y^1/5)

For multiplying two fractional exponents with different bases, we need to equal the denominator of the fractional exponents.

Therefore, we have:

1/3 * 5/5 = 5/15 ⇒ 1/5 * 3/3 = 3/15

15 * (x^5/15 y^3/15)

Now we can express the fractional exponents as an only radical, this way:

x^a/b = ᵇ√xᵃ

15 * ¹⁵√x⁵y³

The correct answer is C. 15 ¹⁵√x⁵y³

Answer:

y = 25.

Step-by-step explanation:

PQ and RQ and SQ are congruent so

x + 10 = 2x - 5

15 = x.

So PQ = 15 + 10 = 25.

But PQ = RQ  = y, so

y = 25.