A store sells new video games for $45 each and used video games for $14 each. Jerry is buying 3 new video games and xused video games?

Answer:

[tex]\boxed{\textbf{a}-\dfrac{3}{2}\textbf{b}}[/tex]

[tex]\boxed{10 \textbf{a}-15\textbf{b}}[/tex]

[tex]\boxed{-4 \textbf{a}+6\textbf{b}}[/tex]

[tex]\boxed{2\textbf{a}-12\textbf{b}+4\textbf{a}+3\textbf{b}}[/tex]

Step-by-step explanation:

Given vector:

[tex]\overrightarrow{\rm FG}=2 \textbf{a}-3\textbf{b}[/tex]

Two vectors are parallel if one can be written as a scalar multiple of the other.

Therefore, the following vectors are parallel to FG:

[tex]\textbf{a}-\dfrac{3}{2}\textbf{b}=\dfrac{1}{2}(2 \textbf{a}-3\textbf{b})[/tex]

[tex]10 \textbf{a}-15\textbf{b}=5(2 \textbf{a}-3\textbf{b})[/tex]

[tex]-4 \textbf{a}+6\textbf{b}=-2(2 \textbf{a}-3\textbf{b})[/tex]

[tex]2\textbf{a}-12\textbf{b}+4\textbf{a}+3\textbf{b}=6\textbf{a}-9\textbf{b}=3(2 \textbf{a}-3\textbf{b})[/tex]

In linear equation,    x = 1  is the maximum height, in feet, reached by the pebble.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                  Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

The height of the pebble over time is modeled by the equation

        y = -16x2 + 32x + 80

At the maximum height, the final velocity of the pebble is zero.

The velocity of the pebble will be obtained by taking the derivative of the given equation.

That is

                y' = dy/dx

                    = d/dx (-16x2 + 32x + 80 )

                    = -32x + 32

At the maximum height, y' = 0 .

So,

        -32x + 32 = 0

  32x = 32

    x = 32/32

    x = 1

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To calculate the total area of the cylinder, we need to use the formula for calculating surface area; SA = 2πr² + 2πrh. In this case, r is equal to 1.5 yards and h is equal to 24 yards:

SA = 2(3.14)(1.5^2) + (2)(3.14)(1.5)(24)

= 28 ft² + 144 ft²

= 172 ft²  

Therefore, we need 172/150 gallons of paint in order to cover both sides of the ilo with one coat each - approximately 1 gallon and 14 fluid ounces or about 1 3/4 gallons of paint will be needed in total

What is Surface Area?

The area is the area occupied by a flat, two-dimensional surface. It is expressed in square units. The surface area of a three-dimensional object is the space taken up by its exterior surface.

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Answer:

Step-by-step explanation:1.08%

Interest rate required in order for Kiran to end up with $9,500 is 4.55%.

Compound interest is defined as the amount of interest which has been calculated on the principal amount as well as the amount accumulated over the previous period is also included.

Given,

Principal amount = $6,600

Time in years = 8 years

Final amount = $9,500

The final amount is calculated in compound interest by the formula,

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

Here, P is the principal amount, r is the rate of interest, n is the number of  years.

Substituting in the formula,

9500 = 6600 (1 + [tex]\frac{r}{365}[/tex]) ^(365 × 8)

9500 / 6600 = (1 + [tex]\frac{r}{365}[/tex])²⁹²⁰

1.4394 = (1 + [tex]\frac{r}{365}[/tex])²⁹²⁰

1.000125 = 1 + [tex]\frac{r}{365}[/tex]

[tex]\frac{r}{365}[/tex] = 0.00125

r = 0.045531

r = 4.5531% ≈ 4.55%

Hence the interest rate to the nearest hundredth of a percent is 4.55%.

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The percent of his monthly income that will be budgeted for the utilities will be approximately 5.21%.

According to the question,

We have the following information:

Greg evaluated his spending and found that he was spending about $50 more per month on utilities than he has budgeted. He can transfer money from other categories to increase his utilities budget to $125 per month. If his total monthly income is $2,400.

Now, let's take the percent to be x.

We have the following expression:

2400*x/100 = 125

24x = 125

x = 125/24

x = 5.21%

Hence, the percent of his monthly income that will be budgeted for the utilities will be approximately 5.21%.

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False. While using the right sampling technique can increase the probability of getting sample mean values that are close to population mean values.

A population is the entire set of people in a group, whether that group is a country or a collection of people who share a certain trait. A population is the group of people from which a statistical sample is taken in statistics.

The sample mean is the mathematical average of values selected at random from the population. The population mean is a representation of the population's real mean.

It is impossible to ensure that the sample mean and population mean will be a perfect match. This is because sampling has intrinsic variability and randomness, which can cause discrepancies between the sample and the population even in studies that are carefully planned. Additionally, there could still be some variability or error in the estimates even if the sample mean is quite near to the population mean, which might have an impact on the accuracy of the findings.

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Answer: x > or = to 4 (Inequality Form), [4, infinity) (Interval Notation)

Step-by-step explanation:

Isolate the equation.

Divide each side by the factors that do not contain x.

Solve for x.

Inequality is 2x+178 >=2000. and Solution set is x>=911 i.e., the no: of cans that Shane should have collected

The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities1, is at the core of social justice theories. However, because it frequently has different meanings to different people, it is prone to misunderstanding in public discourse. However, some distinctions are shared.

Lifetime Inequality (the distribution of incomes across households or individuals over a person's lifetime), Inequality of Wealth (the distribution of wealth across households or individuals at a particular point in time), and Inequality of Opportunity (the impact on income of factors that people cannot control) are all related concepts.

Let the number of cans collected by Shane = x and the number of cans collected by Abha = y.

It is given that, Abha collected 178 cans more than Shane.

So, we have, .

Since, they both have to collect cans no less than 2000 i.e. greater than or equal to 2000.

So, the equation representing the situation is,

Shane + Abha ≥ 2000

i.e. y + x ≥ 2000

Thus, by substitution we have,

Inequality for the number of cans Shane collected is .2x+178 >=2000.

Solution set of the inequality is x>=911.

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(2) The statements and reasons in the two-column method are presented as follows;

Statement [tex]{}[/tex]                                           Reasons

1. [tex]\overline{BD}[/tex] bisects ∠ABC [tex]{}[/tex]                          1. Given

2. ∠BAD ≅ ∠BCD   [tex]{}[/tex]                            2. Given

3. ∠ABD ≅ ∠CBD    [tex]{}[/tex]                           3. Definition of angle bisector

4. [tex]\overline{BD}[/tex] ≅ [tex]\overline{DB}[/tex]    [tex]{}[/tex]                                    4. Reflexive property

5. ΔABD ≅ ΔCBD     [tex]{}[/tex]                          5. AAS congruency postulate

(3) The two-column method used to prove the congruency of triangles ΔQRS and ΔSTU, is presented as follows;

Statement       [tex]{}[/tex]                                           Reason

1. S is the midpoint of [tex]\overline{QU}[/tex]       [tex]{}[/tex]                 1. Given

2. [tex]\overline{QR}[/tex] ≅ [tex]\overline{ST}[/tex]        [tex]{}[/tex]                                       2. Given

3.  [tex]\overline{RS}[/tex] ≅ [tex]\overline{TU}[/tex]        [tex]{}[/tex]                                       3. Given  

4.  [tex]\overline{QS}[/tex] ≅ [tex]\overline{SU}[/tex]        [tex]{}[/tex]                                  4. Definition of midpoint of [tex]\overline{QU}[/tex]

5. ΔQRS ≅ ΔSTV           [tex]{}[/tex]                            5. SSS congruency postulate

The two column method consists of statements and  the associated reasons arranged sequentially side by side in a two-column tabula format.

The reasons used to prove the above statements are as follows;

Angle bisector

An angle bisector is a segment that divides an angle into  two angles of the same measure.

Reflexive property

The reflexive property of equality states that the value of an object or the measure of a dimension is equal to itself

AAS congruency postulate

AAS which is the acronym for Angle-Angle-Side  congruency, states that  if two angles and a non included side of one triangle are congruent to two angles and the non  included side of  another triangle, then  the two triangles are congruent

Midpoint of a line

The midpoint of a line is a point that divides the line into two segments of the same measure.

SSS congruency postulate

The Side-Side-Side congruency postulate states that two triangles are congruent if three sides are congruent to three sides of the other triangle

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Answer:

(-x,y)

Step-by-step explanation:

The midpoint of AC is 0.5 where A is at -2 and C is at 3 on the number line.

A number line is a line on which numbers are pointed at some intervals, it is used to show numerical operations.

Given that,

A and C are two points on number line.

A is at -2 and C is at 3

The midpoint of AC can be given by finding average of both the points,

Midpoint of AC = (-2 + 3) / 2

                          = 1 /2

                          = 0.5

The required midpoint of AC where A is at -2 and C is at 3 is 0.5.

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the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

[tex]\begin{array}{|cc|ll} \cline{1-2} \stackrel{x}{year}&\stackrel{y}{population}\\ \cline{1-2} 2010&16200\\ 2016&13824\\ \cline{1-2} \end{array}\hspace{5em} (\stackrel{x_1}{2010}~,~\stackrel{y_1}{16200})\qquad (\stackrel{x_2}{2016}~,~\stackrel{y_2}{13824}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{13824}-\stackrel{y1}{16200}}}{\underset{run} {\underset{x_2}{2016}-\underset{x_1}{2010}}} \implies \cfrac{ -2376 }{ 6 } \implies \text{\LARGE -396} ~~ \textit{per year}[/tex]

5% of the students either passed all 3, or none of the tests.

What is amount ?

Mass nouns are referred to by the word amount. Count nouns are referred to as numbers.

To illustrate the process of thinking, tets assume there are no people who passed all subjects.

40% (Maths) - 10%(+sceince) - 15% (+english) = 15% only maths

45% - 10% - 20% = 15% only science

55% - 20% - 15% = 20% only english.

That gives

15+15+20 = 50% of the students passing only one course

10+20+15 = 45% of students passing only 2 courses

… that’s 95% together …

… but we need to get to 100%; obviously.

If we assume there are X% students that passed in all 3 courses, then from the first line, we substracted this person twice: (once for +science, and once for +english). Considering we only need to substract ’m once, that’s the same as substracting twice and adding once. we get:

40% (Maths) - 10%(+sceince) - 15% (+english) + X% = 15+X % only maths

and likewise

45% - 10% - 20% + X= 15 +X % only science

55% - 20% - 15% +x X= 20 +X % only english.

Now, for the students who passed exactly 2 classes, that’s

10 - X % only maths and science

20 - X %

15 - X%

And of course, the amount of students who passed all three exams: X.

This gives us

(15+X) + (15+X) + (20+X) + (10-X) + (20 - X) + (15 - X) + X = 100

95 + X = 100

X = 5

Or, 5% of students passed all 3 tests.

edit: this answer assumes all students pass at least one test. The actual summation should be: As pointed out with the first line, if that answer is

0%, the amount of students mentioned is 95%.

The actual answer is

5% of the students either passed all 3, or none of the tests.

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The ratio of the segments formed on each transversal are equal.

  AB/CB = EF/DF

How do parallel lines work?

In terms of geometry, parallel lines are two separate lines that never cross each other and are located in the same plane. They may be vertical or horizontal.

The equation of the parallel lines are;

y = x, and y = x + 1

The point of intersection of transversal 1 and the parallel lines y, and z

(0.2, 0.2), and (0.3, 0.8)

The length of segment AB = √((0.3 - 0.2)² + (0.8 - 0.2)²) = 0.1·√(37)

The point of intersection of transversal 1 and the parallel lines x, and y

(0.3, 0.8), and (0.4, 1.4)

The length of segment CB = √((0.4 - 0.3)² + (1.4 - 0.8)²) = 0.1·√(37)

The ratio of the lengths of the line segments formed by the transversal 1, AB:CB is found as  follows;

              AB/CB = 0.1 . √37/ 0.1 . √37  = 1

The point of intersection of transversal 2 and the parallel lines y and z are;

(0.8, 0.8), and (0.7, 1.2)

The length of segment EF = √((0.7 - 0.8)² + (1.2 - 0.8)²) = 0.1·√(17)

The point of intersection of transversal 2 and the parallel lines x and y are;

(0.7, 1.2), and (0.6, 1.6)

The length of segment DE = √((0.6 - 0.7)² + (1.6 - 1.2)²) = 0.1·√17

The ratio of the lengths of the line segments formed by the transversal 2, EF:DE is found as  follows;

                EF/DF  =  0.1 . √17/ 0.1 . √17 = 1

Therefore:

The ratio of the lengths of the two line segments formed on each transversal are equal.

                AB/CB = EF/DF

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A function is a relationship between inputs where each input is related to exactly one output.

The value of f(x) at x = 5 is -23.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = -4 |x| - 3

The value of f(x) at x = 5.

f(5) = -4 |5| - 3

f(5) = -4 x 5 - 3

f(5) = -20 - 3

f(5) = -23

Thus,

The value of f(x) at x = 5 is -23.

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Answer:

The maximum value of a function can be found at its highest point, or vertex, on a graph

Step-by-step explanation:

The slopes and points are:

a) (-3/4) and the point is (4, 9)

b) (-2/3), and the point is (-4, 3)

A line with a slope a and a known point (h, k) can be written as:

y - k = a*(x - h)

So that is the slope-point form of the linear equation.

a) The first linear equation is:

y - 9 = (-3/4)*(x - 4)

Comparing this with the general line above, we can see that the slope is (-3/4) and the point is (4, 9)

b) y = 3 - 2/3 (x +4)

We can rewrite this as:

y - 3 = -(2/3)*(x + 4)

Then in this case the slope is (-2/3), and the point is (-4, 3)

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Answer: its around 25,000 during the end of august

Step-by-step explanation:

Answer:

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

Let the number be N.

If N is divided by 5 the remainder is 3:

Similarly:

We can observe N + 2 is divisible by both 5 and 6, then it can be represented as:

so

The left side is divisible by 3, then q = 3t:

The least m and t would be m = 5 and t = 7.

Then:

Proof:

y= x/2 -3 , y+3x = 12 and y = x  are determined as linear equations , while y=6/x -2 and y= 3x^3  +5 are non-linear equations.  

A linear equation is a mathematical equation that forms a constant straight line on a graph.

Non-linear equations are functional equations that form different types of curves or other non-linear shapes on a graph.

According to the slope-intercept formula of the straight line : y=mx+b

1. y=6/x - 2 ,is not satisfying the above formula of straight line , having x in the denominator, hence it is a non-linear equation.

2. y=x/2-3 , here slope(m)=1/2 and intercept(b)=-3 which are real numbers and satisfy the straight line formula , hence it is a linear equation.

3. y=-3x+12, here slope(m)=-3 and intercept(b)=12 as real numbers and satisfy the straight line graph formula , hence it is a linear equation.

4. y = 3x^3+5, here slope(m)=3x^2 which is not a real number, hence not satisfying the given formula it is a non-linear equation.

5. y = x , here slope(m)=1 and intercept(b) =0 which are real numbers and satisfy the straight line graph formula ,hence it is a linear equation.

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The cylindrical wheels covers about 9428.7 squared centimeter

This is the total area covering the entire body of the cylinder.

The formula of surface area of a cylinder is given as;

A = 2πrh + 2πr²

A = 2(22/7) × 30 × 20 + 2(22/7)×30²

A = 9428.57 cm²

The area of the wheel is 9428.7cm²

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Answer:

Step-by-step explanation:

The system of equations that to be used to calculate the number of chicken wings (x) and sliders (y) in the combination meal:

55x + 275y = 1100 and y = 8x.

A system of equations is a collection of one or more equations with multiple variables.

Let x represent each onion ring.

Allow each slider to be represented by y.

That is what we are told;

The calorie count for each onion ring is 55.

The number of calories in each slider is 275.

A combination meal of both contained 1100calories.

Thus;

The equation formed wiil be,

55x + 275y = 1100

It also shows that there are 8 more onion rings than as many sliders.

Thus;

The equation formed is,

y = 8x

Therefore the system of equations in the combination meal are as follows: 55x + 275y = 1100 and y = 8x.

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Difference in miles walked between 2 teams is 2x+12.

Team A walks total of 6*x+12 miles.

let's suppose Team A walks y1 miles

y1 = 6*x+12.

Team B walks total of 4x-7 miles

let's suppose Team B walks y2 miles

y2 = 4*x-7

Let's understand what means by difference?

One of the most crucial mathematical operations, which is obtained by removing two numbers, produces difference in mathematics. It reveals how much one number deviates from another. To determine how many numbers are between the two given numbers is the goal of finding the difference in math.

Difference in miles walked between 2 teams

=  y1-y2.

=  6x+12-(4x-7)

= 6x+12-4x+7

=2x+12

So the difference in miles walked between 2 teams is 2x+12.

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The box and whisker plot that represents the data given is option D (see attachment below).

The box and whisker plot that represents a data set will display the five-number summary of the data, which include minimum and maximum values, upper quartiles and lower quartiles, and the median of the data.

Given the data set, 6, 9, 13, 13, 18, 20, 22, 25, 26, 28, 30, 30, the five-number summary that would be displayed on the box and whisker plot include:

Minimum: 6 (at the beginning of the whisker to the left)

First Quartile: 13 (at the beginning of the edge of the box)

Median: 21 (at the middle line on the box)

Third Quartile: 27 (at the end of the edge of the box)

Maximum: 30 (at the end of the whisker to the right)

Therefor, the box and whisker plot would be the option D (see image below).

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Answer:

x= 19.5

Step-by-step explanation

sin58 = x/23

x = 23×sin58

x = 19.5

In the provided figure, the value of y is 5.5 units.

Trigonometric functions are real functions in mathematics that connect an angle of a right-angled triangle to ratios of two side lengths. They are widely utilized in all geosciences, including navigation, solid mechanics, celestial mechanics, geodesy, and many more. The values of all trigonometric functions depending on the ratio of sides of a right-angled triangle are defined as trigonometric ratios. The trigonometric ratios of any acute angle are the ratios of the sides of a right-angled triangle with respect to that acute angle.

Here,

cos 30°=b/15

b=15*cos 30°

b=13 units

since this is square so all sides are equal.

sin 30°=p/15

p=15*sin 30°

p=7.5 units

required difference=13-7.5

=5.5 units

The value of y in the given figure is 5.5 units.

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Answer:

1 cup of banana for 2 cups of flour

Step-by-step explanation:

Divide 4 cups of banana by 4 and 8 cups of flour by 4

Then you will get 1 cup of banana for 2 cups of flour

On solving the provided proportionality question we got that, U = 7.72, is rounded off nearest to tenth digit.

We must determine the ratio of the two quantities for each value supplied in order to determine if two quantities are proportionate. The proportionate link between them is evident if their proportions are equal. Their connection is not proportionate if all the ratios are out of balance.

When two quantities or variables are linearly related in mathematics, the term "proportional" is used. Both quantities increase by two times when one increases by two. Each variable decreases in proportion to the other when it falls to 1/100th of its previous value.

Here,

[tex]\frac{U}{5} = \frac{17}{11} \\\\[/tex]

[tex]U = \frac{17}{11} X 5\\[/tex]

[tex]U = \frac{85}{11}\\ U = 7.72[/tex]

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Therefore, 20 is the lowest of the four numbers.

An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion.

Integers include things like -5, 0, 1, 5, 8, 97, and 3,043. Z is a set of integers that consists of the following:

Positive, negative, and zero are all examples of integers.

The Latin word "integer" signifies "whole" or "intact." Thus, fractions and decimals are not included in integers.

According to our question-

4 numbers added together yields the product 4612 - 1.

The least of the four integers is the required information. Let N-2, N-1, N, and N + 1 be the numbers.

According to our calculations

, (N - 2)(N)(N + 1)(N - 1) = 4612 - 1 (N - 2)(N)(N + 1)(N - 1)- (4612 - 1) = 0

This results in N4 - 2N3 - N2 + 2N - 212520 = 0.:

(N + 21)(N - 22)(N2 - N + 460) = 0. N = 22 or -21 are hence potential solutions. However, the necessity for positive integers results in

N = 22 as a potential solution.

Because of this, where the four numbers are N-2, N-1, N, and N + 1, we get the following numbers:

22 -2, 22 -1, 22 + 1, which equals

20, 21, 22, and 23.

Therefore, 20 is the lowest of the four numbers.

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Answer:

medium is 5 dollars and 39 cents

large is 6 dollars and 89 cents

Step-by-step explanation:

3m + 2l = 29.95

4m + l = 28.45

3m + 2l = 29.95

8m + 2l = 56.9

-5m = -26.95

5m = 26.95

m = 5.39

3(5.39) + 2l = 29.95

16.17 + 2l = 29.95

2l = 13.78

l = 6.89