you sold two different types of wrapping paper for your band fund-raiser. One type sold for $6 a roll and the other for $8 a roll. You collected a total of $92 for the 14 rolls you sold. How many of each type of wrapping paper did you sell?

[tex]2(a+b)=p\qquad\text{divide both sides by 2}\\\\a+b=\dfrac{p}{2}\qquad\text{subtract a from both sides}\\\\\boxed{b=\dfrac{p}{2}-a}\\\\or\\\\2(a+b)=p\qquad\text{use distributive property}\\\\2a+2b=p\qquad\text{subtract 2a from both sides}\\\\2b=p-2a\qquad\text{divide both sides by 2}\\\\\boxed{b=\dfrac{p-2a}{2}}[/tex]

Answer:

97/100

Step-by-step explanation:

9/10 = 90/100

90/100 + 7/100 = 97/100

Answer:

The expression represents

[tex]a\geq\frac{1}{4}\times (10^{-2})[/tex] and solution is   [tex]a \geq 0.0025[/tex]  

Step-by-step explanation:

Given : Expression represents a number one fourth as great as [tex]10^{-2}[/tex]

To find : What is the expression?

Solution :

Let the number be 'a'.

According to question,

A number one fourth as great as [tex]10^{-2}[/tex]

i.e.  [tex]a\geq \frac{1}{4}\times (10^{-2})[/tex]

Now, we solve the expression

[tex]a \geq \frac{1}{4}\times\frac{1}{100}[/tex]

[tex]a \geq\frac{1}{400}[/tex]

[tex]a \geq 0.0025[/tex]

Therefore, The expression represents

[tex]a\geq\frac{1}{4}\times (10^{-2})[/tex] and solution is   [tex]a \geq 0.0025[/tex]

Answer:

40

Step-by-step explanation:

5+1 3/8n=60

Subtract 5

1 3/8n=55

11/8n=55

8/11(55/1)  

n=40

Answer:

y = [tex]\frac{1}{2}[/tex] x + 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + b ( m is the slope and b the y-intercept )

here m = [tex]\frac{1}{2}[/tex] and b = 4, hence

y = [tex]\frac{1}{2}[/tex] x + 4 ← equation of line

Answer:

where is the question?

Answer:

Consider the following cases

Case 1: In n first gear,  an automobile's engine runs about three times as fast as the drive shaft.

So, if Speed of Engine = 1,850 r.p.m

Then Speed of Drive Shaft  [tex]=\frac{1850}{3}=616.67[/tex] r.p.m

Case 2 : In second gear, the engine does not have to run as fast; usually it runs about 1.6 times faster than the drive shaft.

 So, if Speed of Engine = 1,850 r.p.m

Then Speed of Drive Shaft  [tex]=\frac{1850}{1.6}=1156.25[/tex] r.p.m

Case 3:  Finally, in third, or high gear, the engine runs at the same speed as the drive shaft.

So, if Speed of Engine = 1,850 r.p.m

Then Speed of Drive Shaft is also equal to 1,850 r.p.m

Answer:

He paid $6,000 in taxes.

Step-by-step explanation:

His final amount after taxes is $24000.  In order to obtain this number we had to tax 20% of the total (Note that 100%-20%=80%).  In other words if he was taxed 20% he took home 80% of what he was paid.  Therefore mathematically we have:

[tex]0.8A_{pre-tax}=A_{taxed}[/tex]

Since we know he was left with $24000 after taxes then:

[tex]0.8A_{pre-tax}=24000\\\\\frac{0.8A_{pre-tax}}{0.8}=\frac{24000}{0.8}\\\\A_{pre-tax}=\frac{24000}{0.8}\\\\A_{pre-tax}=30000[/tex]

So originally he had $30,000.  So how much did he pay in taxes? We can calculate the difference of both pretax and after tax and we get:

$30,000 - $24,000= $6,000 taxed

Answer:

x = .140741

Step-by-step explanation:

0.7(3x−0.2)=0.3(0.8−2x)

Distribute

.7 * 3x - .7*.2 = .3*.8 - .3 * 2x

2.1x - .14 = .24 - .6x

Add .6x to each side

2.1x +.6x -.14 = .24 -.6x+.6x

2.7x -.14 = .24

Add .14 to each side

2.7x -.14+.14 = .24+.14

2.7x = .38

Divide by 2.7 on each side

2.7x/2.7 = .38/2.7

x = .140741

Answer:

y-2 = 2/3(x-8)

Step-by-step explanation:

We have the line 6x-9y = -7

Let's rewrite it in the form y=mx+b

6x-9y = -7

Subtract 6x from each side

6x-6x-9y = -7 -6x

-9y = -6x-7

Divide by -9

-9y/-9 = -6x/-9 -7/-9

y = 2/3 x + 7/9

The slope is 2/3

If the line is parallel, the slope will be the same so the slope will be 2/3

We have the slope and a point (8,2) on the new line, so we can use the point slope form of a line

y-y1 = m(x-x1)

y-2 = 2/3(x-8)

Answer: -2,0,2,4,6

The solution of the inequality is x<1

Step-by-step explanation:

Answer:

x < 1

Step-by-step explanation:

2x < 2

Divide 2 on both sides

x < 1

------------------------------------------------------------------------

Table: (I think)

-2 , 0 , 2 , 4 , 6

Answer:

2/25 chance for both.

Step-by-step explanation:

There is a total of 25 students = 25 as my denominator.

11 + 12 = 23.

25 -23 = 2

Therefore my numerator is 2.

----> 2/25

Answer:

r= -5 , r= 17

Step-by-step explanation:

5|-6+r|=55

solve for 'r'

First we isolate absolute function

We divide both sides by 5

|-6+r| = 11

for absolute function we consider two cases, one with positive and one with negative. Now we make two equations

-6+r = 11   or -6+r = -11

Now solve both equations

-6 + r= 11

Add 6 on both sides

so , r= 17

-6 + r= -11

add 6 on both sides , so r= -5

Answer: B - 3/40

Step-by-step explanation: in order to find their difference, set up their common denominators equally, resulting in them having 5/40 and 8/40. subtract and you will get 3/40 as your final answer.

The equation[tex]x^5 - y^5 = (x - y)(x^4 + x^3y + x^2y^2 + xy^3 + y^4)[/tex]  is a representation of the Difference of Powers formula in algebra. This formula can be proven accurate by expanding the expression on the right hand side and simplifying.

Your question essentially asks about the proof of a formula in algebra known as the Difference of Powers. This formula is applied when you have a difference of two terms, each raised to the same power.

Let us prove[tex]x^5 - y^5 = (x - y)(x^4 + x^3y + x^2y^2 + xy^3 + y^4):[/tex]

This demonstrates that the original formula you asked about is accurate.

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Answer:

55 + 14 sqrt(6)

Step-by-step explanation:

(7+√6)(7+√6)

We can figure out this problem by FOILing

First : 7*7 = 49

Outer: 7* sqrt(6) = 7 sqrt(6)

Inner:  7* sqrt(6) = 7 sqrt(6)

Last: sqrt(6) * sqrt(6) = 6

Add these together

49+ 7 sqrt(6)+ 7 sqrt(6)+6

55 + 14 sqrt(6)

Answer:

(1,3)

Step-by-step explanation:

From the graph, determine the coordinates of the point of intersection of the two.  They are x=1 and y=3:  (1,3)

This is the last of the four given possible answers.

Answer:

(1,3)

Step-by-step explanation:

The solution to a system of equations that is graphed is where the two graphs intersect.  The two lines intersection at 1, 3.  We can check this by putting them into the equation

y = 3x

3 = 3*1

True

y =x+2

3 = 1+2

3=3

True

This is the solution to the system of equations

Answer:

y = 5x + 25

Explaination:

To get the equation of a line, first get the slope of the line.

Slope = (change in y)/(change in x)

          = (60-30)/(7-1)

          = 30/6

            = 5

Now use one point in the line (4,45) and a general point (x,y).

Slope = (change in y)/(change in x)

    5 = (y - 45)/(x - 4)

    5(x - 4) = (y - 45)

  5x - 20 = y - 45

y = 5x -20 + 45

[tex]\mathbb{ANSWER:}[/tex]

Refer to the attachment to view the answer.

Answer:

4/5x + y = -2

Step-by-step explanation:

Answer:

4x+5y=-10

Step-by-step explanation:

We have to arrange [tex]y=\frac{-4}{5}x-2[/tex] in the standard form using integers.

The standard form of the equation of a line is represented as Ax+By=C, where A,B,C are integers and A≥0.

Therefore, multiplying the given equation by 5 on the both sides, we have,

[tex]5y=-4x-10[/tex]

On rearranging,we get,

[tex]4x+5y=-10[/tex]

Which is the required standard form using integers.

The maximum number of trees the student can plant per row is 10. This is found by identifying the greatest common divisor of the total number of apple trees and peach trees he has which is 10.

To solve this problem, you need to find the greatest common divisor of 50 (the number of apple trees) and 30 (the number of peach trees). The greatest common divisor is the highest number that can divide both numbers without a remainder.

Both 50 and 30 can be divided by 10 without any remainder, but they can't be divided evenly by any number higher than 10. Therefore, 10 is the greatest common divisor of 50 and 30.

In this context, being able to divide the number of trees evenly means that you can plant the same number of each type of tree in each row. So, given the total numbers of apple and peach trees, the maximum number of trees you can plant per row is 10.

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To determine the maximum number of trees that can be planted per row when planting 50 apple trees and 30 peach trees with uniformity, calculate the greatest common divisor (GCD) of the two quantities, which is 10. This means the maximum number of trees per row that can evenly divide both 50 and 30 is 10 trees per row.

The question involves finding the maximum number of trees that can be planted per row when planting 50 apple trees and 30 peach trees with the same number and type of trees per row. To find this number, we need to determine the greatest common divisor (GCD) of the two quantities, which will tell us the largest number of trees that can uniformly fit into each row for both types of trees.

First, list the factors of 50 (1, 2, 5, 10, 25, 50) and the factors of 30 (1, 2, 3, 5, 6, 10, 15, 30).

Find the largest factor that appears in both lists. In this case, it is 10.

The maximum number of trees per row that can evenly divide both 50 and 30 is 10 trees per row.

Therefore, you can plant up to 10 trees per row for a neat and organized orchard layout.

M and O are congruent

N, M and O are similar

M and N are similar because the sides of M are proportional to sides of N:

[tex]\dfrac{2}{4}=\dfrac{1}{2}[/tex]

Two figures are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

[tex]3rs-5cr-15cs+25c^2=r(3s-5c)-5c(3s-5c)\\\\=(3s-5c)(r-5c)\\\\Answer:\ \boxed{3rs-5cr-15cs+25c^2=(3s-5c)(r-5c)}[/tex]

Answer:

D

Step-by-step explanation: 1/3 x 3 = 1/9 same with 2/3

Answer:

B is the one here as well

Answer:

X=28

Step-by-step explanation:

3x-8=2x+20. So x=28

Answer:

0.707 to nearest thousandth

Step-by-step explanation:

People who go at least 2 times a month = 219 + 180 + 96

= 495

So the required probability = 495 / 700

= 0.707 14

Answer:

42 miles

Step-by-step explanation:

She drove 35% of 120 miles.

To find a percent of a number, multiply the percent by  the number.

35% of 120 miles =

= 35% * 120 miles

= 0.35 * 120

= 42

Answer:

x=12

Step-by-step explanation:

Solve for x:

(3 (x/6 + 16))/4 = (3 ((4 + 3/8) x - 21))/7

Put 4 + 3/8 over the common denominator 8. 4 + 3/8 = (8×4)/8 + 3/8:

(3 (x/6 + 16))/4 = (3 ((8×4)/8 + 3/8 x - 21))/7

8×4 = 32:

(3 (x/6 + 16))/4 = (3 ((32/8 + 3/8) x - 21))/7

32/8 + 3/8 = (32 + 3)/8:

(3 (x/6 + 16))/4 = (3 ((32 + 3)/8 x - 21))/7

32 + 3 = 35:

(3 (x/6 + 16))/4 = (3 ((35 x)/8 - 21))/7

Put each term in x/6 + 16 over the common denominator 6: x/6 + 16 = x/6 + 96/6:

3/4 x/6 + 96/6 = (3 ((35 x)/8 - 21))/7

x/6 + 96/6 = (x + 96)/6:

3/4 (x + 96)/6 = (3 ((35 x)/8 - 21))/7

3/6 = 3/(3×2) = 1/2:

(x + 96)/(2×4) = (3 ((35 x)/8 - 21))/7

Put each term in (35 x)/8 - 21 over the common denominator 8: (35 x)/8 - 21 = (35 x)/8 - 168/8:

(x + 96)/(2×4) = 3/7 (35 x)/8 - 168/8

(35 x)/8 - 168/8 = (35 x - 168)/8:

(x + 96)/(2×4) = 3/7 (35 x - 168)/8

2×4 = 8:

(x + 96)/8 = (3 (35 x - 168))/(8×7)

8×7 = 56:

(x + 96)/8 = (3 (35 x - 168))/56

Multiply both sides by 56:

(56 (x + 96))/8 = (56×3 (35 x - 168))/56

56/8 = (8×7)/8 = 7:

7 (x + 96) = (56×3 (35 x - 168))/56

(56×3 (35 x - 168))/56 = 56/56×3 (35 x - 168) = 3 (35 x - 168):

7 (x + 96) = 3 (35 x - 168)

Expand out terms of the left hand side:

7 x + 672 = 3 (35 x - 168)

Expand out terms of the right hand side:

7 x + 672 = 105 x - 504

Subtract 105 x from both sides:

(7 x - 105 x) + 672 = (105 x - 105 x) - 504

7 x - 105 x = -98 x:

-98 x + 672 = (105 x - 105 x) - 504

105 x - 105 x = 0:

672 - 98 x = -504

Subtract 672 from both sides:

(672 - 672) - 98 x = -672 - 504

672 - 672 = 0:

-98 x = -672 - 504

-672 - 504 = -1176:

-98 x = -1176

Divide both sides of -98 x = -1176 by -98:

(-98 x)/(-98) = (-1176)/(-98)

(-98)/(-98) = 1:

x = (-1176)/(-98)

The gcd of -1176 and -98 is -98, so (-1176)/(-98) = (-98×12)/(-98×1) = (-98)/(-98)×12 = 12:

Answer:  x = 12

Answer:

4/113

Step-by-step explanation:

1/28 for non leap years and 1/29 for leap years

However if u put those together it would be 4/113 overall

This is because every 4 years there are 113 days in February and 4 of those days will be the 28th.

Final answer:

The probability of someone being born on February 28th given that they were born in February is 1/28, assuming a non-leap year scenario.

Explanation:

The student is asking about the probability of being born on February 28th, given that they were born in February. Given that February usually has 28 days, except for leap years when it has 29 days, to find this probability, we consider a non-leap year scenario.

The total number of possible birth dates in February, in a non-leap year, is 28. Since being born on any given day in February is equally likely, the probability of being born on February 28th is simply 1 divided by the number of days in February.

Therefore, the probability is:
P(born on Feb. 28) = 1/28

Answer:

Step-by-step explanation:

35 x .08 = $2.80

35 + 2.80 = 37.80

Answer:

T = 0.08 × 35

Step-by-step explanation:

The cost of a jacket = $35

The tax rate on the jacket = 8% =  [tex]\frac{8}{100}[/tex]

                                           = 0.08

The expression to find the cost of the tax on the jacket would be

T = 0.08 × 35