Instructions: Solve the following real world problem.
You and your sister are selling cookies to help raise money for
your field trip. You start out with $24 and sells each bag of
cookies, c, for $3. Your sister doesn't start out with any money but
sells her bags of cookies for $5 each. How many bags of cookies
must they sell in order for them to raise the same amount of
money?

The Average Minute to Clean up a Car is 0.7794.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The equation of the graph is y=0.7794x-1435.5.

When we compare the equation with the standard form of equation y=mx+b.

The m will be 0.7794 which means slope is 0.7794.

Hence,  0.7794 is the Average Minute to Clean up a Car.

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Answer: 2a^4b^3

Step-by-step explanation: Divide the base like normal. Subtract the exponents.

a6 - a2 = a4

b4 - b = b3

A single variable will always equal to 1 so b will be its own exponent.

After divide the solution is,

⇒ 2a⁴b³

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

Divide 10a⁶b⁴ by 5a²b.

Hence, We get;

⇒ 10a⁶b⁴ / 5a²b.

⇒ 2a⁶⁻² b⁴⁻¹

⇒ 2a⁴b³

Thus, After divide the solution is,

⇒ 2a⁴b³

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The expected value of each grab bag is $1.67 for two pairs of lined gloves, $9.87 for one pair of lined gloves and one pair of knit gloves, and $16.80 for two pairs of knit gloves.  the total profit made from selling all 60 grab bags is $149.40.

For the 2 bags that have two pairs of lined gloves, the total cost is:

2 pairs * $25/pair = $50

Total gloves = 4

For the 16 bags that have one pair of lined gloves and one pair of knit gloves, the total cost is:

1 pair lined gloves * $25/pair + 1 pair knit gloves * $12/pair = $37

Total gloves = 4

For the 42 bags that have two pairs of knit gloves, the total cost is:

2 pairs * $12/pair = $24

Total gloves = 4

The probability of selecting a bag with two pairs of lined gloves is:

2/60 = 1/30

The probability of selecting a bag with one pair of lined gloves and one pair of knit gloves is:

16/60 = 4/15

The probability of selecting a bag with two pairs of knit gloves is:

42/60 = 7/10

The expected value of a bag with two pairs of lined gloves is:

(1/30) * $50 + (0) * $37 + (0) * $24 = $1.67

The expected value of a bag with one pair of lined gloves and one pair of knit gloves is:

(4/15) * $37 + (0) * $50 + (0) * $24 = $9.87

The expected value of a bag with two pairs of knit gloves is:

(7/10) * $24 + (0) * $50 + (0) * $37 = $16.80

The total cost of the gloves used to make the grab bags is:

2 bags * $50/bag + 16 bags * $37/bag + 42 bags * $24/bag = $1,650

The total revenue from selling all 60 grab bags is:

60 bags * $29.99/bag = $1,799.40

Therefore, the total profit is:

$1,799.40 - $1,650 = $149.40

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Answer:

[tex]x=-3,x=-3,x=7[/tex]

Step-by-step explanation:

[tex]We\ know\ that\ the\ roots\ of\ an\ equation\ are\ its\ intercepts\ cut\ on\ the\ x-axis.\\We\ can\ observe\ that\ the\ graph\ of\ y=f(x)\ cuts\ the\ x\ axis\ at\ the\ point (7,0)\\ and\ touches\ the\ x-axis\ at\ (-3,0).\\[/tex]

[tex]Hence,\\The\ curve\ represents\ a\ cubic\ polynomial\ with\ double\ roots\ (-3,0),(-3,0)\\ as\ well\ as\ a\ distinct\ root:\ (7,0)[/tex]

Option A. No, this is not possible. Since A and B are not mutually exclusive events, we have P(A ∩ B) = P(A) + P(B) - P(A ∪ B), where P(A ∪ B) is the probability that the selected student has either a Visa or a MasterCard.

Since 0.5 > 1 - P(A ∪ B) = P(A') ∩ P(B'), we must have P(A') ∩ P(B') < 0, which is impossible.

B. The probability that the selected student has at least one of these two types of cards is given by P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 0.7 + 0.4 - 0.3 = 0.8.

C. The probability that the selected student has neither type of card is given by P(A' ∩ B') = 1 - P(A ∪ B) = 1 - 0.8 = 0.2.

D. The probability of the event A ∩ B' is given by P(A ∩ B') = P(A) - P(A ∩ B) = 0.7 - 0.3 = 0.4.

E. The probability that the selected student has exactly one of the two types of cards is given by P((A ∩ B') ∪ (A' ∩ B)) = P(A ∩ B') + P(A' ∩ B) = 0.4 + 0.1 = 0.5.

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Answer:

y=67

z=113
x=67

Step-by-step explanation:

opposite angles are parallel in a rhombus and they all equal 360

The variable y does not vary directly with x is wrong since when x increases by 1 unit y increases by 1/2 unit for all real x.

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

here, we have,

Given that line passes through (0,0) and (2,1)

(Note that any two points are sufficient to determine the equation of the line)

The slope = change in y/change in x

                 = (1-0)/(2-0)

                 = 1/2

Hence answers are:

Variable y varies directly with x. (if x increases y also increases and vice versa)

The constant of variation = slope of line = 1/2

The constant of variation is 2 is wrong since slope = 1/2

The variable y does not vary directly with x is wrong since when x increases by 1 unit y increases by 1/2 unit for all real x.

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1. The ratio of the shaded area to the area of the whole figure is 3/8 and the ratio of the shaded area to the unshaded area is 3/5.

2. The value of AC/CD. CD/BD, and BD/BC is 8/5, 5/2 and 10/7 respectively.

A ratio is a comparison of two quantities, and it can be expressed in different ways, such as a fraction, a decimal, or a percentage. In this case, we will explore how to find ratios of areas in geometric figures.

Firstly, let's consider the rectangle on the right. To find the ratio of the shaded area to the area of the whole figure, we need to calculate both of these values. The shaded area is a rectangle with dimensions 6 by 2, which means its area is 6 x 2 = 12 square units.

The whole figure is a rectangle with dimensions 8 by 4, so its area is

=> 8 x 4 = 32 square units.

Therefore, the ratio of the shaded area to the area of the whole figure is 12/32, which simplifies to 3/8.

To find the ratio of the shaded area to the unshaded area, we need to subtract the shaded area from the whole area. The unshaded area is a rectangle with dimensions 8 by 2, so its area is

=> 8 x 2 = 16 square units.

Subtracting the shaded area from the whole area gives us

=> 32 - 12 = 20 square units for the unshaded area.

Thus, the ratio of the shaded area to the unshaded area is 12/20, which simplifies to 3/5.

Moving on to the second question, we need to use the figure below to find three ratios: AC/CD, CD/BD, and BD/BC.

Let's start with the first ratio, AC/CD. We know that AC is 8 units long and CD is 5 units long, so

=> AC/CD is 8/5.

Next, CD/BD. We know that BD is 10 units long, so to find CD/BD, we need to subtract the length of AC from the length of BD. AC is 8 units long, so

BD - AC = 10 - 8 = 2 units.

Therefore, CD/BD is 5/2.

Finally, BD/BC. We know that BC is 12 units long, so to find BD/BC, we need to subtract the length of CD from the length of BC. CD is 5 units long, so

=> BC - CD = 12 - 5 = 7 units.

Therefore, BD/BC is 10/7.

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Answer:-17

Step-by-step explanation:

b=7,then

b^2=49

square root of 49-4*3*2=-17

Answer: Let's call the length of the cake "l" and the width of the cake "w". The total area of the cake would be l * w.

Half of the cake is frosted with vanilla icing, so the area of the vanilla half would be (l * w) / 2.

And 2/3 of the vanilla half is to be covered with sprinkles, so the area covered with sprinkles would be (l * w) / 2 * 2/3 = (l * w) / 3.

The other half of the cake is frosted with chocolate icing, so the area of the chocolate half would be (l * w) / 2.

And 1/4 of the chocolate half is to be covered with sprinkles, so the area covered with sprinkles would be (l * w) / 2 * 1/4 = (l * w) / 4.

So, the total area of the cake covered with sprinkles would be (l * w) / 3 + (l * w) / 4.

Step-by-step explanation:

The interest rate that can explain how $4081 grew to $8404.54 in 21 years with annual compounding is option (a) 3.5%, rounded to the nearest tenth.

The interest rate and the compounding frequency determine the growth of the initial amount over time. In this problem, we need to find the interest rate that can explain how an initial amount grew to a specific amount over a certain number of years.

The problem asks us to find the interest rate that can explain how an initial amount of $4081 grew to $8404.54 in 21 years with annual compounding. We can use the formula for compound interest to solve this problem:

[tex]A = P(1 + r/n)^{nt}[/tex]

where A is the future value of the investment, P is the initial amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, we know that P = $4081, A = $8404.54, n = 1 (annual compounding), and t = 21. We need to find the value of r that makes the equation true.

We can rearrange the formula to solve for r:

[tex]r = n[(A/P)^{1/nt} - 1][/tex]

Substituting the known values, we get:

[tex]r = 1[(8404.54/4081)^{1/(1*21)} - 1][/tex]

r = 0.0353 or 3.53%

This means that if the initial amount was invested with an annual interest rate of 3.5%, it would have grown to the given future value after 21 years.

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Answer: The rate of change for Miquel's position in the race can be calculated by his speed, which is 18 kilometers per hour. So, his rate of change is 18 kilometers per hour. This means that for every hour that passes, Miquel will have covered 18 kilometers in the race.

Step-by-step explanation:

The total weight in the bag is given as follows:

8.2 pounds.

The total weight is obtained applying the proportions in the context of the problem.

From the table, the weight of each equipment is given as follows:

Hence the total weight of a bag with 4 balls, 2 gloves, and 2 bats is given as follows:

4 x 0.35 + 2 x 0.77 + 2 x 2.63 = 8.2 pounds.

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x int = 15

y int = -10

y intercept can be found bt setting X to 0

x intercept can be found by setting Y to 0

2(0) - 3y = 30 --> -3y = 30 --> y = -10

2x - 3(0) = 30 --> 2x = 30 --> x = 15

alternatively, y int is "b" in eq. y = mx + b

-3y = 30 -2×

y = -10 + (2/3)x

y = (2/3)x - 10

b = -10

Answer:

[tex]x=\dfrac{1}{2},\;\;x=1,\;\;x=-\dfrac{4}{3}[/tex]

Step-by-step explanation:

Given polynomial function:

[tex]f(x) = 6x^3-x^2-9x+4[/tex]

If (2x - 1) is a factor of the given function, then 2x - 1 = 0.

Therefore:

[tex]\implies 2x-1=0[/tex]

[tex]\implies x=\dfrac{1}{2}[/tex]

To divide the given function by the factor (2x - 1), we can perform synthetic division.

As the leading coefficient of the divisor is not 1, divide the dividend and divisor by the leading coefficient of the divisor (2):

[tex]\textsf{Dividend}: \quad 3x^3-\dfrac{1}{2}x^2-\dfrac{9}{2}x+2[/tex]

[tex]\textsf{Divisor}: \quad \left(x-\dfrac{1}{2}\right)[/tex]

Perform Synthetic Division

Place ¹/₂ in the division box.

Write the coefficients of the dividend in descending order.

(Note: As no terms are missing, we do not need to use any zeros to fill in missing terms).

[tex]\begin{array}{c|crrr}\vphantom{\dfrac12}\frac{1}{2} & 3 & -\frac{1}{2}& -\frac{9}{2} & 2\\\cline{1-1}\end{array}[/tex]

Bring the leading coefficient straight down:

[tex]\begin{array}{c|crrr}\vphantom{\dfrac12}\frac{1}{2} & 3 & -\frac{1}{2}& -\frac{9}{2} & 2\\\cline{1-1}&\downarrow&&&\\\cline{2-5}&3\end{array}[/tex]

Multiply the number you brought down with the number in the division box and put the result in the next column (under the -¹/₂ ):

[tex]\begin{array}{c|crrr}\vphantom{\dfrac12}\frac{1}{2} & 3 & -\frac{1}{2}& -\frac{9}{2} & 2\\\cline{1-1}\vphantom{\dfrac12}&\downarrow&\frac{3}{2}&&\\\cline{2-5}&3\end{array}[/tex]

Add the two numbers together and put the result in the bottom row:

[tex]\begin{array}{c|crrr}\vphantom{\dfrac12}\frac{1}{2} & 3 & -\frac{1}{2}& -\frac{9}{2} & 2\\\cline{1-1}\vphantom{\dfrac12}&\downarrow&-\frac{3}{2}&&\\\cline{2-5}&3&1\end{array}[/tex]

Repeat:

[tex]\begin{array}{c|crrr}\vphantom{\dfrac12}\frac{1}{2} & 3 & -\frac{1}{2}& -\frac{9}{2} & 2\\\cline{1-1}\vphantom{\dfrac12}&\downarrow&-\frac{3}{2}&\frac{1}{2}&\\\cline{2-5}&3&1&-4\end{array}[/tex]

[tex]\begin{array}{c|crrr}\vphantom{\dfrac12}\frac{1}{2} & 3 & -\frac{1}{2}& -\frac{9}{2} & 2\\\cline{1-1}\vphantom{\dfrac12}&\downarrow&-\frac{3}{2}&\frac{1}{2}&-2\\\cline{2-5}&3&1&-4&0\end{array}[/tex]

The bottom row (except the last number) gives the coefficients of the quotient. The degree of the quotient is one less than that of the dividend.

The last number in the bottom row is the remainder.

Therefore, the factored function after synthetic division is:

[tex]f(x)=(2x-1)(3x^2+x-4)[/tex]

The quadratic factor can be factored further:

[tex]\implies 3x^2+4x-3x-4[/tex]

[tex]\implies x(3x+4)-1(3x+4)[/tex]

[tex]\implies (x-1)(3x+4)[/tex]

Therefore, the fully factored function is:

[tex]f(x)=(2x-1)(x-1)(3x+4)[/tex]

To find the roots of the function, set each factor to zero and solve for x:

[tex]2x-1=0 \implies x=\dfrac{1}{2}[/tex]

[tex]x-1=0 \implies x=1[/tex]

[tex]3x+4=0 \implies x=-\dfrac{4}{3}[/tex]

Therefore, the roots of the given function are:

[tex]x=\dfrac{1}{2},\;\;x=1,\;\;x=-\dfrac{4}{3}[/tex]

Answer:

What is X?

Step-by-step explanation:

4 multiplied by X + 8 =Ps

The total amount spend is 391.88

The noun discount refers to an amount or percentage deducted from the normal selling price of something.

If 14 bag of mix cement are bought and and every third bag is discounted

no of bag on discount = 14/3 = 4 remainder 2

therefore 4 bags will be on discount

discount on a bag = 3.88× 75/100

= 291/100 = 2.91

therefore each bag on discount will cost = 3.88 - 2.91

= 0.97

for 4 bags = 0.97 ×4 = 3.88

for remaining 10 bags = 3.88 × 10

= 388

therefore the total amount = 388+3.88

= $391.88

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The measure of the angle B is found to be 184 degrees.

The angles given in question:

line AB || DC

∠B = 9x + 2

∠C = 5x - 4

So,

∠B + ∠C = 180 ( co interior angles )

9x + 2 + 5x - 4 = 180

9x  - 2 = 180

9x = 180 + 2

x = 182/9

Then,

∠B = 9x + 2

∠B = 9*182/9 + 2

∠B = 182 + 2

∠B = 184

Thus, the measure of the angle B is found to be 184 degrees.

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The diagram of the correct question is attached.

The surface area of the ramp is 3672 in².

Option A is the correct answer.

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

The ramp consists of three rectangular surfaces and two triangles.

Now,

Triangle.

Base = 48 in

Height = 14 in

Area of a triangle.

= 1/2 x base x height

= 1/2 x 48 x 14

= 48 x 7

= 336 in²

Rectangle.

Since the back and the bottom rectangle are not included.

Front rectangle.

Length = 50 in

Width = 60 in

Area = 50 x 60

Area = 3000 in²

Now,

The surface area of the ramp.

= 300 + 2 (336)

= 3000 + 672

= 3672 in²

Thus,

The surface area of the ramp is 3672 in².

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Answer:

-1

Step-by-step explanation:

1. Plug the numbers into the equation

      6-12/6

2. Solve.

  6-12=-6

  -6/6=-1

Answer:

4

Step-by-step explanation:

A= 6

C= 12

6-12÷6

With BIDMAS the order becomes:

6-(12÷6) —> 6-2 = 4

The function [tex]\lim_{x \to 0} \frac{1 - \sqrt[3]{x^2 + 1}}{x^2}[/tex] has a limit

From the question, we have the following parameters that can be used in our computation:

[tex]\lim_{x \to 0} \frac{1 - \sqrt[3]{x^2 + 1}}{x^2}[/tex]

Substitute 0 for x in the above expression

So, we have the following representation

[tex]\lim_{x \to 0} \frac{1 - \sqrt[3]{x^2 + 1}}{x^2} = \frac{1 - \sqrt[3]{0^2 + 1}}{0^2}[/tex]

Evaluate the expression

[tex]\lim_{x \to 0} \frac{1 - \sqrt[3]{x^2 + 1}}{x^2}=\infty[/tex]

This means that the limit of the expression is to infinity

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The system of equations has one solution, which is (2, 3).

To find the solution to a graphed system of equations, you need to find the points where the graphs of the two equations intersect. These points represent the coordinates of the solution, which are the values of x and y that make both equations true simultaneously.

The system of equations as shown in the graph has one solution, which is: (2, 3). This is because the liens intersect at the point (2, 3).

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Answer:

See below for answers and explanations

Step-by-step explanation:

Part A

[tex]x^2+4x+4\\\rightarrow x^2+2x+2x+4\\\rightarrow x(x+2)+2(x+2)\\\rightarrow (x+2)(x+2)[/tex]

Part B

[tex]x^2-12x+27\\\rightarrow x^2-9x-3x+27\\\rightarrow x(x-9)-3(x-9)\\\rightarrow (x-3)(x-9)[/tex]

Part C

[tex]x^2-x-42\\\rightarrow x^2+6x-7x-42\\\rightarrow x(x+6)-7(x+6)\\\rightarrow (x-7)(x+6)[/tex]

Part D

[tex]x^2+8x-9\\\rightarrow x^2+9x-x-9\\\rightarrow x(x+9)-1(x+9)\\\rightarrow (x-1)(x+9)[/tex]

The inequality changes if both sides of the expressions are switched or multiplied by a negative sign

Inequalities are expressions not separated by an equal sign.

From the given inequalities

For -10.5 < 3e

3e > -10.5

e > -10.5/3

This shows that the sign changes

For b/6≤ 7

b ≤ 6(7)

b≤ 42

The inequality sign does not change.

For the inequality -4.5c > 9

4.5c < -9
c < -9/4.5

c < -2

The inequality sign changes.

For the inequality -21/5 ≤  -5/2 d

21/5 ≥ 5/2d

5/2d≤ 21/5

d ≤42/25

The inequality sign does not change

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The answer that makes the comparison statements true, The sum is more than 17. So Option B is correct.

Addition is a basic mathematical operation that combines two or more numbers to give a total or sum. It is one of the four elementary arithmetic operations, along with subtraction, multiplication, and division.

The equation 14+17=n represents the total number of cans Danica collected at the end of the first week, where n is the number of cans Danica collected.

We can solve for n by adding 14 and 17, which gives us:

n = 14 + 17 = 31

Therefore, Danica collected 31 cans at the end of the first week.

To make the comparison statements true:

The sum is more than 17:

This statement is true, since the sum of 14 and 17 is 31, which is greater than 17.

The sum will be 14:

This statement is false, since the sum of 14 and 17 is 31, not 14.

The sum will be 17:

This statement is false, since the sum of 14 and 17 is 31, not 17.

So, the correct answer is: The sum is greater than 17.

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For complete question image is attached:

Answer:

first 2 pairs

Step-by-step explanation:

[tex]\frac{6}{100}[/tex] = 6 ÷ 100 = 0.06 ← equivalent

[tex]\frac{7}{10}[/tex] = 7 ÷ 10 = 0.7 ← equivalent

[tex]\frac{5}{10}[/tex] = 5 ÷ 10 = 0.5 ≠ 0.05

[tex]\frac{32}{100}[/tex] = 32 ÷ 100 = 0.32 ≠ 3.2

Answer:

2:5

Step-by-step explanation:

We know

There are 9 girls and 6 boys taking golf lessons.

So, there are a total of 15 taking a golf lesson.

Write the ratio that compares the number of girls taking golf lessons to the total number of students taking golf lessons.

The ratio is

6:15 = 2:5

So, the ratio is  2:5

Answer: c[tex]\leq[/tex]-17/4

Step-by-step explanation:

-8c+13[tex]\geq[/tex]47

-8c[tex]\geq[/tex]47-13

-8c[tex]\geq[/tex]34

c[tex]\leq[/tex] -17/4 or -4 1/4

The mode of the data 20,26,16,22,20,30,22,20,26

From the question, we have the following parameters that can be used in our computation:

20,26,16,22,20,30,22,20,26

The mode of a dataset is the data element that has the highest frequency

Using the above as a guide, we have the following:

20 has the highest frequency of 3

Hence, the mode is 3

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The value of the range is 33

From the question, we have the following parameters that can be used in our computation:

61, 61, 63, 64, 65, 66, 66, 66, 67, 68, 70, 70, 70, 71, 71, 72, 74, 74, 74, 75, 75, 75, 76, 76, 77, 78, 78, 79, 79, 94

To find the range of a set of numbers, we need to subtract the smallest number from the largest number.

In this set of numbers:

The smallest number is 61 and the largest number is 94.

Therefore, the range of this set of numbers is:

94 - 61 = 33

Hence, the range of the given set of numbers is 33.

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