Which expressions are equivalent to 5 (one-third x + 7) minus 3 (one-half x minus 4)? Select three options.
5 and one-third x minus 3 and one-half x + 35 minus 12
One-sixth x + 47
1 and two-thirds x + 35 minus 1 and one-half x + 12
5 (one-third x) + (5) (7) minus (3) (one-half x) + (3) (4)
1 and one-third x + 35 minus 1 and one-half x minus 12

The correct answer is [tex]67\frac{9}{11}[/tex]

Write the problem in long division format,

Divide 74 by 11 to get 6,

Multiply the quotient digit (6) by the divisor 11,

Subtract 66 from 74,

Bring down the next number of the dividend,

Divide 86 by 11 to get 7,

Multiply the quotient (7) by the divisor 11,

subtract 77 from 86.

[tex]\(746 \div 11\)[/tex] equals 67 with a remainder of 9. The remainder expressed as a fraction is [tex]68\frac{2}{11}\).[/tex]

To solve the division problem 746 ÷ 11 and express the remainder as a fraction, we can perform the long division as follows:

Step 1: Divide 7 by 11, which is 0 with a remainder of 7. So, the first digit of the quotient is 0, and we bring down the next digit, which is 4, to form the dividend 74.

Step 2: Now, divide 74 by 11. The largest multiple of 11 that does not exceed 74 is 6 times 11, which is 66. The remainder is 74 - 66 = 8.

Step 3: Bring down the next digit, which is 6, to form the new dividend 86.

Step 4: Divide 86 by 11. The largest multiple of 11 that does not exceed 86 is 7 times 11, which is 77. The remainder is 86 - 77 = 9.

Step 5: Finally, bring down the last digit, which is 0, to form the new dividend 90.

Step 6: Divide 90 by 11. The largest multiple of 11 that does not exceed 90 is 8 times 11, which is 88. The remainder is 90 - 88 = 2.

Now, we have completed the long division. The quotient is 68, and the remainder is 2. To express the remainder as a fraction, we can write it as [tex]\(\frac{2}{11}\).[/tex]

So, [tex]\(746 \div 11 = 68\frac{2}{11}\).[/tex]

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Equation of the line is y = 4x + 4

Step-by-step explanation:

⇒ m = (0 - 4)/(1 - 2) = -4/-1 = 4

⇒ b = 4

⇒ y = 4x + 4

Answer:

Step-by-step explanation:

3.84 is what percent of 48

(3.84 / 48) * 100 = 0.08 * 100 = 8% tax rate

for an item that is $ 55

8% of 55 = 0.08 * 55 = $ 4.40 <=== sales tax

Answer:

can you elaborate?

Step-by-step explanation:

Answer: 0.15J

Step-by-step explanation:

Fom th question, we obtained the following information:

F = 60N

e = 5mm

We need to covert 5mm to m

1mm = 0.001m

5mm = 5 x 0.001 = 0.005m

We need to find the spring constant (K) for the spring. This is illustrated below:

K = F / e

K = 60 / 0.005 = 12000N/m

Now we can obtain the energy stored on the spring by the doing following:

Energy = 1/2 Ke^2

Energy = 1/2 x 12000 x (0.005)^2

Energy = 0.15J

Answer:

PS = 28 units.

Step-by-step explanation:

See the attached diagram.

This is a figure of rectangle with length (3y + 3) and width 4y.

Now, the perimeter of the rectangle is 2[(3y + 3) + 4y] = 2(7y + 3)

The perimeter of the rectangle is given to be 104 units.

So, 2(7y + 3) = 104

⇒ 7y + 3 = 52

⇒ 7y = 49

⇒ y = 7

Therefore, PS = 4y = 4(7) = 28 units. (Answer)

Final answer:

To calculate the amount of chemical in the pond after a very long time, multiply the rate at which the chemical flows in per hour by the number of hours that have passed.

Explanation:

To find out how much of the chemical will be in the pond after a very long time, we can first calculate the amount of chemical that flows into the pond per hour. Since 0.01 g of chemical flows in per gallon, and the rate of flow is 300 gallons per hour, the amount of chemical added per hour is 0.01 g/gal * 300 gal/hr = 3 g/hr.

Since the amount of water in the pond remains constant, the concentration of the chemical will also remain constant. Therefore, after a very long time, the amount of chemical in the pond will be the amount added per hour multiplied by the number of hours that have passed. So, if time is represented by 't', then the amount of chemical in the pond after a very long time is given by 3 g/hr * t.

Answer: [tex]\frac{A_{collage}}{15.75\ in^2}[/tex]

Step-by-step explanation:

Since you did not attach the diagram and I don't know the dimensions of the collage, I will give you a general explanation of the procedure you need to use in order to solve the exercise:

1. You need to use the formula for calculate the area of a rectangle:

[tex]A=lw[/tex]

Where "l" is the length and "w" is the width.

2. Using the formula, you must calculate the area of an small picture.

You know that its length is 4.5 inches and its width is 3.5 inches. Therefore, its area is:

[tex]A_{picture}=(4.5\ in)(3.5\ in)\\\\A_{picture}=15.75\ in^2[/tex]

3. Calculate the area of the collage using the formula:

[tex]A_{collage}=(l_{collage})(w_{collage})[/tex]

4. Finally, divide the area of the collage by the area of an small picture in order to find the number of small pictures that will fit within the collage:

[tex]\frac{A_{collage}}{15.75\ in^2}[/tex]

Answer:

C is the answer

Step-by-step explanation: I took a test

No Alan did not break even

Alan incured a loss of 6.25 %

Solution:

Given that,

Alan bought two bikes

He sold one to Beth for $300 taking a 25% loss

He also sold one to Greta for $300 making a 25% profit

When a person sells two similar items, one at a gain of say x%, and the other at a loss of x%, then the seller always incurs a loss

Which is given as:

[tex]loss\ \% = (\frac{x}{10})^2[/tex]

Here, x = 25

[tex]loss\ \% = (\frac{25}{10})^2\\\\loss\ \% = 2.5^2\\\\loss\ \% = 6.25[/tex]

Thus the loss percentage is 6.25 %

[tex]\boxed{x=\frac{4}{35}}[/tex]

Here we have the following equation:

[tex]32x + 1 = - 3x + 5[/tex]

So let's follows these steps:

Step 1: Add 3x to both sides:

[tex]32x + 1 +3x= - 3x + 5+3x \\ \\[/tex]

Step 2. Combine like terms:

[tex]32x + 3x + 1 = - 3x+3x + 5 \\ \\ 35x+1=5[/tex]

Step 3. Subtract -1 from both sides:

[tex]35x+1-1=5-1 \\ \\ 35x=4[/tex]

Step 4. Divide both sides by 35:

[tex]\frac{35}{35}x=\frac{4}{35} \\ \\ \\ \boxed{x=\frac{4}{35}}[/tex]

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Answer:

Therefore side B= 11.18  and side A=2×11.18=22.36.

Step-by-step explanation:

Given,side A is twice as long as B and C is 25.

Let side B= x

Then side A = 2x

Using Pythagorean Theorem,

A²+B²=C²

⇔(2x)²+x²=25²

⇔4x²+x²=625

⇔5x²=625

⇔x²=125

⇔x=√125

⇔x =11.18

Therefore side B= 11.18  and side A=2×11.18=22.36.

Answer:

The length of side A is 22.4 and length of side B is 11.9.

Step-by-step explanation:

Given:

If side A is twice as long as B and C is 25.

Solve by using the Pythagorean Theorem.

Now, to get the lengths of side A and side B.

As side C = 25.

Let the side B be [tex]a.[/tex]

As, given A is twice as long as B.

So, the side A be [tex]2a.[/tex]

So, we solve by using Pythagorean Theorem:

A² + B² = C²

[tex](2a)^2+(a)^2=(25)^2[/tex]

[tex]4a^2+a^2=625[/tex]

[tex]5a^2=625[/tex]

Dividing both sides by 5 we get:

[tex]a^2=125[/tex]

So, using square root on both sides we get:

[tex]a=11.18.[/tex]

Rounding to the nearest tenth B =  11.9.

Now, to get A by putting the value of [tex]a[/tex]:

[tex]2a\\=2\times 11.18\\=22.36.[/tex]

Rounding to the nearest tenth A  =  22.4.

Therefore, the length of side A is 22.4 and length of side B is 11.9.

Answer:

[tex]22 x^4y^3[/tex]

Step-by-step explanation:

[tex]11x^2y\times 2x^2y^2\\[/tex]

by multiplying

[tex]=11 \times 2 \times x^2 \timesx^2 \times y \times \times y^2\\=22 \times x^{2+2}y^{1+2}\\=22 x^4y^3[/tex]

Answer:common difference is -2

Step-by-step explanation:

Answer:common difference is -2

Step-by-step explanation:

The sequence is arithmetic if the difference between consecutive terms is constant.

Answer:

BF = 30

Step-by-step explanation:

[tex]BF=\frac{1}{2}*CE\\\\=\frac{1}{2}*60=30[/tex]

The line segment connecting the midpoint of two sides of a triangle is parallel to the third side and half the length of the that third side

Answer:

Hello, I think your answer is d/24 = 18.4/6

Hope This helps

Some number increased by two = b + 2

A variable decreased by two = x - 2

Product of an unknown value and two = 2z

Quotient of some number and two = [tex]a \div 2[/tex]

An unknown value squared = [tex]y^2[/tex]

Solution:

Some number increased by two

Let the number be "b"

Therefore, "b" is increased by two

Here, "increased" means added

Thus we get,

Some number increased by two = b + 2

A variable decreased by two

Let the number be "x"

Therefore, "x" is decreased by two

Decreased means reduced or subtraction

Thus we get,

A variable decreased by two = x - 2

Product of an unknown value and two

Let the unknown value be "z"

Product means "multiplication"

Therefore, product of "z" and 2

Product of an unknown value and two = 2z

Quotient of some number and two

Let the some number be "a"

Quotient means result of division

Quotient of some number and two = [tex]a \div 2[/tex]

An unknown value squared

Let the unknown value be "y"

Squared means multiplied by itself

An unknown value squared = [tex]y^2[/tex]

Answer

answer above is correct

Step-by-step explanation:

Answer:

x=x or it cancels out, it's one of those.

Answer:

(1,0)

Step-by-step explanation:

The given functions are:

f(x) = log₂x

and

g(x) = log₁₀x

We know that logarithm of 1 is always zero.

This means that irrespective of the base, the y-values of both functions will be equal to 0 at x=1

Therefore the point the graphs of f and g have in common is (1,0)

Answer:

B,C

(1,0)

F

Step-by-step explanation:

Answer:

Weekly income = $518

Monthly income = $2072

Rent = $621.6

Step-by-step explanation:

$14 per hour

37 hours per week

37 × 14 = $518

There is about 4 weeks in a month.

$518 × 4 = $2,072

30% of $2,072 = $621.6

Step-by-step explanation:

Kim's weekly income can be found by multiplying her hourly wage to the number of hours she works per week.

So, we have $14 * 37 = $518 weekly income.

Let's assume that Kim gets paid bi-weekly like most jobs, so she'll get paid twice a month usually, ignoring all holidays and other exceptions.

So, we have her weekly income and we are assuming she gets paid bi-weekly per month. So, we need to make her weekly income into a bi-weekly income. We just double her weekly income.

$518 * 2 = $1036 bi-weekly.

Now, we know are assuming she gets paid twice a month, so we need to double her income one more time.

$1036 * 2 = $2072 monthly income.

Now, we have her monthly income, but she can only pay 30% of it towards rent. So, we got to find out what is 30% of $2072.

There are a couple of ways to do this, but the most efficient way is to multiply $2072 by .3

So, $2072 * .3 = $621.60

She can only have $621.60 go towards rent. Hope this helps!

Answer:

Therefore x = 1 is an extraneous solution.

Step-by-step explanation:

The solution to the equation StartFraction 1 Over x minus 1 EndFraction = StartFraction x minus 2 Over 2 x squared minus 2 EndFraction

[tex]\Rightarrow \frac{1}{x - 1} = \frac{x- 2}{2x^2-2} \hspace{0.3cm} \Rightarrow \hspace{0.3cm} 2x^2 - 2 = (x-1)(x-2)[/tex]

therefore [tex]2x^2 - 2 = x^2 - 3x + 2 \hspace{0.3cm} \Rightarrow \hspace{0.3cm} x^2 + 3x - 4 = 0[/tex]

therefore [tex]x^2 + 3x - 4 = 0 \hspace{0.3cm} \Rightarrow = \hspace{0.3cm} (x-1)(x+4) = 0 \\[/tex]

therefore x = 1 and x = -4 but we can see that if we place x = 1 in the original solution then [tex]\frac{1}{x-1} = \frac{1}{1-1} = \frac{1}{0}[/tex] which is indeterminate.

Therefore x = 1 is an extraneous solution.

Answer:

C. x = 1

Step-by-step explanation:

Which solution to the equation StartFraction 1 Over x minus 1 EndFraction = StartFraction x minus 2 Over 2 x squared minus 2 EndFraction is extraneous?

x = 1 and x = –4

neither x = 1 or x = –4

x = 1

x = –4

Answer:

The commission rate is 9%

Step-by-step explanation:

We are given;

We are required to determine the commission rate;

We need to know that;

Total earnings = Monthly salary + Commission

Therefore;

Commission = Total earnings - monthly salary

                     = $1182.60 - $315

                     = $867.6

Therefore, assuming the commission rat is x %

Then;

x/100 × $9640 = $867.6

x/100 = $867.6 ÷ $9640

x/100 = 0.09

 x = 9%

Therefore, the commission rate is 9%

Answer:

0.027, [tex]\frac{1}{6}[/tex], 23%, 0.29, [tex]\frac{3}{5}[/tex]

Step-by-step explanation:

Here we have to convert the fractions and percents to decimal form, then we have to arrange them from smallest to largest.

[tex]\frac{1}{6} = 0.167[/tex]

23% = [tex]\frac{23}{100} = 0.23[/tex]

[tex]\frac{3}{5} = 0.6[/tex]

0.29

0.027

Now we have to arrange from smallest to largest.

0.027 < 0.167 < 0.23 < 0.29<0.6

From smallest to largest

0.027, [tex]\frac{1}{6}[/tex], 23%, 0.29,[tex]\frac{3}{5}[/tex]

Answer:

she lost 20 dollars

Step-by-step explanation:

she paid fpr it for 60.

she sold it for 40.

40 is less than 60.

60-40=20

Answer: She losses 20$ for want she sold

Answer: 11.636 = 12 tickets to a whole figure

Step-by-step explanation:

Let the number of adult tickets be x and y represent children tickets.

From the question;

x + y = 28 ....... equation (i)

(7.25*x) + (y*4.50) = 158

7.25x + 4.50y = 158 ........ equation (ii)

From equation (i);

x + y = 28

y = 28 - x ...... equation (iii)

Put equation (iii) into equation (ii)

7.25x + 4.50(28 - x) = 158

7.25x + 126 - 4.50x = 158

Collect like terms and subtract

2.75x = 32

x = 11.636 approximately 12 to a round number.

Put x = 11.636 into equation (i)

11.636 + y = 28

y = 28 - 11.636

y = 16.364 approximately 16 to a whole number

Final answer:

To find the number of adult tickets purchased, we can set up two equations: C + A = 28, and 4.50C + 7.25A = 159. By solving the equations, we determine that 12 adult tickets were purchased for the carnival.

Explanation:

The question asks us to determine the number of adult tickets purchased for a carnival, given the cost of children's tickets, the cost of adult tickets, and the total amount paid for a group of tickets. Let's take the number of adult tickets as A and the number of children's tickets as C. According to the given information, the admission fee for children is $4.50 and for adults is $7.25. Also, we know that 28 tickets were purchased for a total of $159.

We can set up the following system of equations based on the information provided:

C + A = 28 (since the total number of tickets is 28)

4.50C + 7.25A = 159 (this represents the total cost of all tickets)

We can solve this system of equations using substitution or elimination method. If we rearrange the first equation to get C = 28 - A and substitute it into the second equation, we get:

4.50(28 - A) + 7.25A = 159

126 - 4.50A + 7.25A = 159

2.75A = 33

A = 33 / 2.75

A = 12

Hence, the number of adult tickets purchased is 12.

Answer:

The numerator is 57 ⇒ B

The denominator is 78 ⇒ B

The value of the fraction is 73.1% ⇒ A

Step-by-step explanation:

Let us solve it step by step

∵ The loan is 12 month

∵ The numerator is after 6 month

- Put n = 1 in each bracket

∴ The numerator = {(1 + 11) + (1 + 10) + (1 + 9) + (1 + 8) + (1 + 7) + (1 + 6)}

∴ The numerator = {12 + 11 + 10 + 9 + 8 + 7}

∴ The numerator = {57}

The numerator is 57

∵ The denominator = {(n) + (n + 1) + (n + 2) + .......... + (n + 11)}

- Do the same as the numerator put n = 1

∴ The denominator = {1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12}

∴ The denominator = {78}

The denominator is 78

Now find the value of the fraction

∵ The fraction = [tex]\frac{57}{78}[/tex]

∴ Its value = 0.730769230

- Multiply it by 100%

∴ Its value = 0.730769230 × 100% = 73.0769230%

- Round it to the nearest tenth

∴ Its value = 73.1%

The value of the fraction is 73.1%

Answer:

no

Step-by-step explanation:

the line has a value which is y=7

Answer: Zero slope

Step-by-step explanation: A common mistake made by many students is to confuse what no slope is and what zero slope.

If a line has a slope of zero, it means that the line is flat or horizontal.

No slope is a vertical line or straight up and down. No slope means that we cannot describe its slope using a number because its line is vertical and it's slope is undefined. This has to do with dividing a number by 0. When you do this, you should get an error message or it should say undefined.

So, this line would have zero slope because it's flat.

Answer:

(0, 6) and (1, 2)

Step-by-step explanation:

hello :

(0, 6) and (1, 2)

put x =0 and y =6 in this system : y=x²−5x+6

y=−4x+6

you have : 6 = 0²-5(0)+6 =6  ...right

                  6 =-4(0)+6 .... right

same mhethod for:(1, 2)

The solutions are B) (0, 6) and (1, 2).

To find the solutions to the given system of equations:

y = x² − 5x + 6 and y = −4x + 6, we need to set the equations equal to each other and solve for x:

Set x² − 5x + 6 equal to −4x + 6:

x² − 5x + 6 = −4x + 6

Rearrange the equation to get:

x² − x = 0

Factor the equation:

x(x − 1) = 0

Solve for x:

x = 0 or x = 1

Substitute these values back into either original equation to find y:

When x = 0: y = −4(0) + 6 = 6 (so one solution is (0, 6)).

When x = 1: y = −4(1) + 6 = 2 (so another solution is (1, 2)).

Therefore, the solutions to the system of equations are B) (0, 6) and (1, 2)

Answer:

The total number of fliers the volunteers gave out is 1,368

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Amount of fliers the volunteers gave for a political campaign = 21/38

Remaining 612 were given out in another neighborhood

2. What is the total number of fliers they gave out?

x = Total of fliers

Let's solve for x, this way:

x - 21x/38 = 612

38x - 21x = 612 * 38 (38 is the Lowest Common Denominator)

17x = 23,256

x = 23,256/17

x = 1,368

The total number of fliers the volunteers gave out is 1,368

Answer:

The rest of the question:

Find Mean, Median, Mode, 25th Percentile, 75th Percentile, Maximum, Minimum, Range and IQR.

Let's begin by placing the data points in order from least to greatest:

32  55  66  72  72  76  77  84  88  89  89  94  97

n = 13

1) Mean sometimes called the average = the sum of the data over its number

Mean =( 32+55+66+72+72+76+77+84+88+89+89+94+97 )/13 =

         = 991/13 = 76.23 ≈ 76.2 (to the nearest tenth)

2) Median is the middle data point = 77

3) Mode is any number within a set that occurs the most often

Mode = 72 and 89

We will making a data in suitable form to find the remaining requirements:

(32  55  66  72  72  76) 77  (84  88  89  89  94  97)

4) 25th Percentile = Quartile 1 (Q1) which is the median of the first set of data

∴ 25th Percentile = (66+72)/2 = 138/2 = 69

5) 75th Percentile= Quartile 3 (Q3) which is the median of the second set of data

∴ 75th Percentile = (89+89)/2 = 89

6) Maximum = 97

7) Minimum = 32

8) Range = Maximum - Minimum = 97 - 32 = 65

9) IQR (interquartile range) = Q3 - Q1 = 89 - 69 = 20

Answer:

A) 0

B) 2

F) 10

Step-by-step explanation:

This is because these are not on the chart already and the other choices are. Each input can only have 1 output for it to be a function,

Answer:

1: a prince can use violence to keep control.

2: the safest way is to destroy them.

Answer:

For those who need this:

Step-by-step explanation:

Which text structure does Machiavelli use in this passage?

✔ cause and effect

Which signal word or words help you identify this structure?

✔ “for this reason”

How does this text structure help the author convey his central idea?

✔ It explains why destroying a state is successful.