Gary had a 40% discount for new tires. The sale price of a tire was $96.25. What was the original price of the tire? Round to the nearest cent

Answer:

1) B. -2 hours per person

2) C. 3.60 per pound

Step-by-step explanation:

1)

We can make a slope triangle connecting the points (4, 12) and (10,0)

We get -12/6, or -2 as our slope & final answer

2)

You can do x/y to find the unit rate for this one, or in this case 18/5 = 3.6

Answer:

Step-by-step explanation:

Answer:

2√5

Step-by-step explanation:

√125-√45​

5√5 - 3√5........simplify

2√5....................combine like terms

125 √45

125 √45= √25 x /9 × 5 = 5√√5 - 3√5=2

125 √45= √25 x /9 × 5 = 5√√5 - 3√5=2hope it helps u

The given expression is a simplified algebraic equation: (1/2) * a^2 - 3b + 2c. It represents a combination of variables a, b, and c with their respective coefficients.

Utilizing symbols and operations, an algebraic equation illustrates the equivalence or inequivalence of two expressions. These generated expressions may hold variables that have varying values.

The premise centered around calculus is to arrive at a solution by acquiring the correct value(s) of these variable(s), ultimately fulfilling the outlined specification in the problem. Algebraic equations can range from uncomplicated linear problems to elaborate polynomials and trigonometric functions.

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In the given problem, random samples of four different models of cars were selected and the gas mileage of each car was measured. The results are shown below:21 226 22 725 21
Given that,The null hypothesis H0: All the population means are equal. The alternative hypothesis H1: At least one population mean is different from the others .

To find the hypothesis test, we will use the one-way ANOVA test. We calculate the grand mean (X-bar) and the sum of squares between and within to obtain the F-test statistic. Let's find out the sample size (n), the total number of samples (N), the degree of freedom within (dfw), and the degree of freedom between (dfb).
Sample size (n) = 4 Number of samples (N) = n × 4 = 16 Degree of freedom between (dfb) = n - 1 = 4 - 1 = 3 Degree of freedom within (dfw) = N - n = 16 - 4 = 12 Total sum of squares (SST) = ∑(X - X-bar)2
From the given data, we have X-bar = (21 + 22 + 26 + 25) / 4 = 23.5
So, SST = (21 - 23.5)2 + (22 - 23.5)2 + (26 - 23.5)2 + (25 - 23.5)2 = 31.5 + 2.5 + 4.5 + 1.5 = 40.0The sum of squares between (SSB) is calculated as:SSB = n ∑(X-bar - X)2
For the given data,SSB = 4[(23.5 - 21)2 + (23.5 - 22)2 + (23.5 - 26)2 + (23.5 - 25)2] = 4[5.25 + 2.25 + 7.25 + 3.25] = 72.0 The sum of squares within (SSW) is calculated as:SSW = SST - SSB = 40.0 - 72.0 = -32.0
The mean square between (MSB) and mean square within (MSW) are calculated as:MSB = SSB / dfb = 72 / 3 = 24.0MSW = SSW / dfw = -32 / 12 = -2.6667
The F-statistic is then calculated as:F = MSB / MSW = 24 / (-2.6667) = -9.0
Since we are testing whether at least one population mean is different, we will use the F-test statistic to test the null hypothesis. If the p-value is less than the significance level, we will reject the null hypothesis. However, the calculated F-statistic is negative, and we only consider the positive F-values. Therefore, we take the absolute value of the F-statistic as:F = |-9.0| = 9.0The p-value corresponding to the F-statistic is less than 0.01. Since it is less than the significance level (α = 0.05), we reject the null hypothesis. Therefore, we can conclude that at least one of the population means is different from the others.

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Answer:

jjjjjjjjjjjjjjjjjjjjjjjjjjjjj

Step-by-step explanation:

There are 120 different ways that a student can choose major requirement courses from these four areas.

In order to solve this problem, we need to use the concept of combinations. A combination is a selection of items from a set, without regard to the order in which they are chosen. The formula for the number of combinations of n objects taken r at a time is:

C(n,r) = n! / (r! * (n-r)!)

where n! means n factorial, which is the product of all positive integers up to n. For example, 5! = 5 * 4 * 3 * 2 * 1 = 120.

To solve this problem, we need to choose one course from each of the four areas: algebra, analysis, statistics, and geometry. The number of choices in each area are:

4 algebra courses

3 analysis courses

5 statistics courses

2 geometry courses

To find the total number of ways to choose one course from each area, we can use the multiplication rule of counting. This states that if there are n1 ways to do the first task, n2 ways to do the second task, and so on up to nk ways to do the kth task, then there are n1 * n2 * ... * nk ways to do all k tasks together.

In this case, there are 4 ways to choose an algebra course, 3 ways to choose an analysis course, 5 ways to choose a statistics course, and 2 ways to choose a geometry course. Therefore, the total number of ways to choose one course from each area is:

4 * 3 * 5 * 2 = 120

Thus, there are 120 different ways that a student can choose major requirement courses from these four areas.

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The measure of arc BC is 720 times the measure of angle BAC.

Given that AC is the diameter of the circle and AB is a chord with a length of 16 units, we need to find BC (the length of the other chord) and mBC (the measure of angle BAC).

To find BC, we can use the property of chords in a circle. If two chords intersect within a circle, the products of their segments are equal. In this case, since AB = BC = 16 units, the product of their segments will be:

AB * BC = AC * CE

16 * BC = 2 * r * CE (AC is the diameter, so its length is twice the radius)

Since the area of the circle is given as 289 square units, we can find the radius (r) using the formula for the area of a circle:

Area = π * r^2

289 = π * r^2

r^2 = 289 / π

r = √(289 / π)

Now, we can substitute the known values into the equation for the product of the segments:

16 * BC = 2 * √(289 / π) * CEBC = (√(289 / π) * CE) / 8

To find mBC, we can use the properties of angles in a circle. The angle subtended by an arc at the center of a circle is double the angle subtended by the same arc at any point on the circumference. Since AC is a diameter, angle BAC is a right angle. Therefore, mBC will be half the measure of the arc BC.

mBC = 0.5 * m(arc BC)

To find the measure of the arc BC, we need to find its length. The length of an arc is determined by the ratio of the arc angle to the total angle of the circle (360 degrees). Since mBC is half the arc angle, we can write:

arc BC = (mBC / 0.5) * 360

arc BC = 720 * mBC

Therefore, the length of the arc BC equals 720 times the length of the angle BAC.

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Answer:

3/4n + 10 = 16

Step-by-step explanation:

3/4 of a number is 3/4 multiplied by a number (3/4n); increased by 10 is the sum of ten and 3/4n; Sixteen is what 3/4n + 10 equals :)

Answer:

c

Step-by-step explanation:

increase in 15% therefore 1.15% of principal amount

$27355 times 1.15= $31458.25

$31458.25 times 1.15=$36,176.8975

$36,176.8975 times 1.15= $41603.53563

round all answers to the nearest dollar and you get

$31, 458, $36, 177, $41,604

so answer c

Answer:

Option (1)

Step-by-step explanation:

Let the number of adult tickets sold = x

And the number of child tickets sold = y

Cost of adult tickets sold = $8x

And the cost of child tickets sold = $4y

If the theater company needs to earn at least $1280,

8x + 4y ≥ 1280

2x + y ≥ 320 ---------(1)

Since community center has a capacity of 240 people,

x + y ≤ 240 ----------(2)

By graphing these inequalities with the help of a graphing tool,

Shaded area above the solid line will be represented by inequality (1) (red line)

And the shaded area below the line will be the represented by inequality (2) (blue line)

Common area of both the shaded regions will represent the solution area .

Option (1) will be the answer.

Answer:

37/200

Step-by-step explanation:

Event/Sample Space = .185 = 18.5%

Answer:

Step-by-step explanation:

If 37 people out of 200 people opened an e-mail, you can write it as 37/200.

The number above the bar is the numerator: 37

The number below the bar is the denominator: 200

Divide the numerator by the denominator to get fraction's value:

Val = 37 ÷ 200

Val = 0.185

To calculate the percent value:

0.185 =  (Calculate fraction's value.)

0.185 × 100/100 =  

(0.185 × 100)/100 =  (Multiply that number by 100.)

18.5/100 =

18.5%;  (Add the percent sign % to it.)

So that's how you get 18.5%

Answer:

\(r = \sqrt{ {(6 - 2)}^{2} + {(1 - ( - 3))}^{2} } \)

\(r = \sqrt{ {4}^{2} + {4}^{2} } = \sqrt{16 + 16} = \sqrt{32} \)

So the equation of the circle is

\( {(x - 2)}^{2} + {(y + 3)}^{2} = 32\)

To determine the number of gallons of paint needed to cover office 143, we need to know the square footage of the office.

Once we have that information, we can divide the square footage by the coverage rate per gallon to calculate the required amount of paint.

Let's assume the square footage of office 143 is 800 square feet.

Number of gallons needed = Square footage / Coverage rate per gallon

Number of gallons needed = 800 square feet / 50 square feet per gallon

Number of gallons needed = 16 gallons

Therefore, you would need approximately 16 gallons of paint to cover office 143, assuming each gallon covers 50 square feet.

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Answer:

the ratio is 17/323 equals 19, therefore there would be 19 players per team.

Answer: The Number is 24.

Step-by-step explanation:
1) Set unknown number to a variable (I'm going to do x).
2) Set up equation: 5x = 120.

3) Simplify by dividing both sides by 5: 5x/5 = 120/5 = 24.

The Length of third side of the triangle is 4x +5

What is the Triangle?

A triangle is a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is called angle sum property of triangle.

How to determine the length of the third side of the Triangle?

The given parameters are:

Length of the first side = 3x+2

Length of the second side =7x-4

Perimeter of the triangle =14x+3

Now, The perimeter is the sum of the sides of lengths

So, we have

Perimeter = sum of the sides of lengths

According to the question:

14x+3 =3x+2 +7x -4 + third side

Evaluate the like terms

14x-10x = -2 -3

third side = 4x + 5

Hence, The length of the third side of the triangle is 4x+5

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The solution to the system of inequalities is option C: (1, 1). The system of inequalities typically consists of multiple equations with inequality signs. However, the given options are not in the form of inequalities.

In the given system of inequalities, option d) satisfies all the given conditions. Let's analyze the system of inequalities and understand why option d) is the solution.

The inequalities are not explicitly mentioned, so we'll assume a general form. Let's consider two inequalities:

x > 0

y > x + 2

In option d), we have x = 2 and y = 4.

For the first inequality, x = 2 satisfies the condition x > 0 since 2 is greater than 0.

For the second inequality, y = 4 satisfies the condition y > x + 2. When we substitute x = 2 into the inequality, we get 4 > 2 + 2, which is true.

Therefore, option d) 2,4 satisfies both inequalities and is the solution to the given system.

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Answer:

x=-6

Step-by-step explanation:

First you have to add 4 to both sides

3x - 4 + 4 = 2x - 10 + 4

Then you simplify it

3x + 2x - 6

Subtract 2x from both sides

3x - 2x = 2x - 6 - 2x

Simplify

x = -6

Answer:D.x=-6

Step-by-step explanation: Subtract 2x from both sides.(3x-4-2x=2x-10-2x)-->x-4=-10. 2nd step Add 4 to both sides then it would be(x-4+4=-10+4)--> -10+4=x=-6

To find the minimum score of the top 2.5% of students, we need to calculate the z-score corresponding to the 97.5th percentile and then convert it back to the original SAT score scale.

First, let's calculate the z-score using the formula:

z = (x - μ) / σ

where x is the SAT score, μ is the mean (1175), and σ is the standard deviation (120).

To find the z-score corresponding to the 97.5th percentile, we need to find the z-score value that leaves 2.5% in the tail of the distribution (to the right).

Using a standard normal distribution table or a statistical calculator, we find that the z-score corresponding to the 97.5th percentile is approximately 1.96.

Now we can solve for x (the SAT score) in the z-score formula:

1.96 = (x - 1175) / 120

Multiply both sides by 120:

1.96 * 120 = x - 1175

235.2 = x - 1175

Add 1175 to both sides:

235.2 + 1175 = x

1410.2 = x

Therefore, the minimum score of the top 2.5% of students is approximately 1410.

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Answer:

c

Step-by-step explanation:

The point in the form (1, y, z) that is equivalent to the given points is (1, 3/5, 3/5).

To find all the points in the form (1, y, z) that are equivalent to the points (2, -1, 0) and (0, -2, 1), we can use the concept of vector equivalence.

Let's consider the vector from (1, y, z) to (2, -1, 0). This vector is (2-1, -1-y, 0-z) = (1, -1-y, -z).

Similarly, the vector from (1, y, z) to (0, -2, 1) is (0-1, -2-y, 1-z) = (-1, -2-y, 1-z).

Since these two vectors are equivalent, we can set them equal to each other:

(1, -1-y, -z) = (-1, -2-y, 1-z)

Simplifying this equation, we get:

y - z = 0

2y + 3z = 3

Therefore, all points in the form (1, y, z) that are equivalent to the given points are given by the equations:

y = z

2y + 3z = 3

Solving this system of equations, we get:

y = 3/5

z = 3/5

So the point in the form (1, y, z) that is equivalent to the given points is (1, 3/5, 3/5).

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The system of equations that models the given situation are;

y = 10x + 35

y = 5x + 35

Let x denote the number of years since 2010

Let y denote the total members

The linear equation in slope intercept form is expressed as;

y = mx + b

where;

m is the slope or unit rate

b is the y-intercept or initial value

For the swim team, since  the team increased by an average of 10 members per year, then;

Slope = 10

In 2010, they had 5 members and so; y-intercept = 35

Thus, the equation is; y = 10x + 35

For the chorus team, we can deduce that;

Slope = 5 members per year

In 2010, they had 35 members and so; y-intercept = 35

Thus, the equation is; y = 5x + 35

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Complete question is;

Central High School had five members on their swim team in 2010. Over the next several years, the team increased by an average of 10 members per year. The same school had 35 members in their chorus in 2010. The chorus saw an increase of 5 members per year. Write a system of equations to model this situation, where x represents the number of years since 2010.

(a) The area of triangle F is 4 times the area of triangle G.

(b) The area of triangle B is 1/4 times the area of triangle G.

(c) The area of triangle F is 16 times the area of triangle B.

(d) The area of triangle H is 1/9 times the area of triangle F.

(e) The area of triangle H is 4/9 times the area of triangle G.

(f) The area of triangle B is 9/16 times the area of triangle H.

(a) Triangle G and Triangle F

Consider triangle F,

The height of the triangle is 8.

The base of the triangle is 6.

The hypotenuse of the triangle is 10.

Area of ΔF = ( 1/2 ) × b × h = ( 1/2 ) × 6 × 8 = 24 square units.

Consider triangle G,

The height of the triangle is 4.

The base of the triangle is 3.

The hypotenuse of the triangle is 5.

Area of ΔG = ( 1/2 ) × b × h = ( 1/2 ) × 3 × 4 = 6 square units.

Therefore,

Area of ΔF = 4 × Area of ΔG

(b) Triangle G and Triangle B

Consider triangle G,

The area of the triangle is:

Area of ΔG = ( 1/2 ) × b × h = ( 1/2 ) × 3 × 4 = 6 square units.

Consider triangle B,

The height of the triangle is 2.

The base of the triangle is 3/2.

The hypotenuse of the triangle is 5/2.

Area of ΔB = ( 1/2 ) × b × h = ( 1/2 ) × 3/2 × 2 = 3/2 square units.

Now, 4 × 3/2 = 6

Therefore,

Area of ΔG = 4 × Area of ΔB

Area of ΔB = 1/4 × Area of ΔG

(c) Triangle B and Triangle F

Consider triangle B,

Area of ΔB = ( 1/2 ) × b × h = ( 1/2 ) × 3/2 × 2 = 3/2 square units.

Consider triangle F,

Area of ΔF = ( 1/2 ) × b × h = ( 1/2 ) × 6 × 8 = 24 square units.

Now, 16 × 3/2 = 24

Therefore,

Area of ΔF = 16 × Area of ΔB

(d) Triangle F and Triangle H

Consider triangle F,

Area of ΔF = ( 1/2 ) × b × h = ( 1/2 ) × 6 × 8 = 24 square units.

Consider triangle H,

The height of the triangle is 8/3.

The base of the triangle is 2.

The hypotenuse of the triangle is 10/3.

Area of ΔH = ( 1/2 ) × b × h = ( 1/2 ) × 2 × 8/3 = 8/3 square units.

Now, 9 × 8/3 = 24

Therefore,

Area of ΔF = 9 × Area of ΔH

Area of ΔH = 1/9 ×  Area of ΔF

(e) Triangle G and Triangle H

Consider triangle G,

Area of ΔG = ( 1/2 ) × b × h = ( 1/2 ) × 3 × 4 = 6 square units

Consider triangle H,

Area of ΔH = ( 1/2 ) × b × h = ( 1/2 ) × 2 × 8/3 = 8/3 square units.

Now,

9/4 × 8/3 = 6

Therefore,

Area of ΔG = 9/4 × Area of ΔH

Area of ΔH = 4/9 × Area of ΔG

(f) Triangle H and Triangle B

Consider triangle H,

Area of ΔH = ( 1/2 ) × b × h = ( 1/2 ) × 2 × 8/3 = 8/3 square units

Consider triangle B,

Area of ΔB = ( 1/2 ) × b × h = ( 1/2 ) × 3/2 × 2 = 3/2 square units

Now,

16/9 × 3/2 = 8/3

Therefore,

Area of ΔH = 16/9 × Area of ΔB

Area of ΔB = 9/16 × Area of ΔH

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Answer:

Slop= 1/2 (fraction not division just to make sure you know that ;-;)

Y intercept = ( 0,-3)

Step-by-step explanation: I can't really explain it since I did this years ago in 8th grade but just search up the step by step or watch a video about intercepts

Answer:

slope: 1/2

y-intercept: -3

Step-by-step explanation:

slope= rise over run of 2 points

(0,-3) and (6,0) are the points

We go up on the y axis 3 units

We go right on the x axis 6 units

rise/run= 3/6

3 ÷ 6= 0.5 or 1/2

y intercept: I graphed on desmos

It is the value when x= 0

Answer:

A) 32 centimeters

Step-by-step explanation:

If the rectangle has a length L and a Width W the area is
A = L x W

Perimeter
P = 2(L + W)

We can write this as
P/2 = L + W

Given area = 48, lets try some factors of 48 and also add them and multiply by 2 to get the perimeter of each configuration

48 = 1 x 48   ⇒  P = 2( 1 + 48) =  2 x 49 = 98

48 = 2 x 24  ⇒  P = 2(2 + 24) = 2 x 26 = 52

48  = 3 x 16  ⇒  P = 2(3 + 48) = 2 x 51 = 102

48 = 4 x 12   ⇒  P = 2(4 + 12) = 2 x 16 = 32

48 = 6 x 8   ⇒    P = 2(6 + 8) = 2 x 14 = 28

now compare these values to the answer choices and see which one fits

Only 32 (Answer choice A) fits

So correct answer
A) 32 centimeters

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

say what is this about the phone

(a) The angle between vectors a and b is approximately 84.55 degrees.

(b) The angle that vector b makes with the Z-axis is approximately 14.04 degrees.

(a) To find the angle between vectors a and b, we can use the dot product formula: cos(theta) = (a · b) / (|a| * |b|)

where theta is the angle between the vectors, a · b is the dot product of a and b, and |a| and |b| are the magnitudes of a and b, respectively.

Given:

a = -3i + j - 4k

b = i + 2j - 5k

Substituting the values into the formula:

cos(theta) = 19 / (sqrt(26) * sqrt(30))

theta ≈ acos(19 / (sqrt(26) * sqrt(30)))

theta ≈ 84.55 degrees

(b) The angle that vector b makes with the Z-axis can be found using the dot product formula and the fact that the Z-axis is represented by the unit vector k = 0i + 0j + 1k: cos(theta) = (b · k) / (|b| * |k|)

Calculating the dot product: b · k = (1 * 0) + (2 * 0) + (-5 * 1) = -5

Substituting the values into the formula:

cos(theta) = -5 / (sqrt(30) * 1)

theta ≈ acos(-5 / sqrt(30))

theta ≈ 14.04 degrees

Therefore, the angle between vectors a and b is approximately 84.55 degrees, and the angle that vector b makes with the Z-axis is approximately 14.04 degrees.

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