The number of cars Gary sold each month was 12, 5, 9, 11, 14, and 10.
What was Gary's median number of sales per month?
Ο
10.2
Ο
10.5
Ο
Ο

We can use the kinematic equation:

h = vi*t + 0.5*a*t^2

where h is the initial height, vi is the initial velocity, a is the acceleration due to gravity (9.8 m/s^2 or 32 ft/s^2), and t is the time.

Since we want to find the time it takes for the ball to hit the ground, we can set h = 0 and solve for t:

0 = 23*t - 0.5*32*t^2 + 3.5

0 = -16t^2 + 23t + 3.5

Using the quadratic formula, we get:

t = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = -16, b = 23, and c = 3.5.

t = (-23 ± sqrt(23^2 - 4*(-16)*3.5)) / 2*(-16)

t = (-23 ± sqrt(529)) / (-32)

t = (-23 ± 23) / (-32)

t = 0.125 s or 1.438 s

Since we are looking for the time it takes for the ball to hit the ground, we only want the positive solution:

t = 1.438 s

Therefore, Barbara has about 1.438 seconds before the ball hits the ground.

Final answer:

Barbara has approximately 1.43 seconds before the volleyball served by Sharon with an upward velocity of 23 ft/s and from a height of 3.5 ft hits the ground.

Explanation:

To determine how long Barbara has before the volleyball hits the ground, we need to use the kinematic equations for projectile motion, assuming the ball is moving under the influence of gravity alone. Since Sharon serves the volleyball with an upward velocity of 23 ft/s and the initial height is 3.5 ft, we can use the following kinematic equation:

[tex]s = ut + (1/2)at^2[/tex]

Where:

s is the displacement (which is -3.5 ft because the ball is falling to the ground, hence the negative sign)

u is the initial velocity (23 ft/s upwards, hence positive)

a is the acceleration due to gravity ( [tex]-32 ft/s^2[/tex], negative because it is directed downward)

t is the time

Plugging in the values we get:

[tex]-3.5 = 23t - (1/2)(32)t^2[/tex]

This is a quadratic equation in the form of  [tex]at^2 + bt + c = 0[/tex] , where a = -16, b = 23, and c = -3.5. We can solve for t using the quadratic formula [tex]t = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}[/tex]. After calculating, we find that t is approximately 1.43 seconds. However, since time cannot be negative, we take the positive value which is the time it takes for the ball to hit the ground.

Therefore, Barbara has approximately 1.46 seconds before the volleyball hits the ground.

The solution of the expression of 13 and three-fourths + x = 7 and one-fourth equation is x = [tex]6\frac{1}{2}[/tex]

To solve this equation, we need to find the value of x (unknown variable) in the given equation:

13 and three-fourths + x = 7 and one-fourth

First, we need to convert the mixed numbers to improper fractions.

13 and three-fourths = [tex]13 + \frac{3}{4} = 13\frac{3}{4}[/tex]

7 and one-fourth = [tex]7 + \frac{1}{4} = 7 \frac{1}{4}[/tex]

Now, the equation becomes:

[tex]13\frac{3}{4} + x =7\frac{1}{4}\\ x = 13\frac{3}{4} - 7\frac{1}{4}\\\\x = 6\frac{1}{2}[/tex]

Answer:

-120

Step-by-step explanation:

-60/1/2 = -60/1 x 2

= -120/1

= -120

Answer:

I don't know how to explain the math, but I know the answer is 115 women for every 100 men.

Answer:

  about 115 women

Step-by-step explanation:

You need to raise the value on the left side of the ratio by a factor of 100/87. Multiply both numbers by that factor, and you get ...

  (100/87)(87) : (100/87)(100)

  = 100 : (10,000/87) = 100 : 114.9425...

  ≈ 100 : 115

There are about 115 women for each 100 men.

Answer:

For the given question,the equation of the asked line would be same as that of the line parallel to it but the only difference would be in the constant part.

Step-by-step explanation:

the equtions of the lines (variable parts) would be the same but the constant part will be different according to the point known on the particular line.

The integers are 52 and 53

Solution:

Consecutive numbers are numbers that follow each other in order. They have a difference of 1 between every two numbers

Let the two consecutive integers be x and x + 1

Given that, sum of two consecutive integers is 105

Therefore,

x + x + 1 = 105

Combine the like terms

2x + 1 = 105

2x = 105 - 1

2x = 104

Divide both sides of equation by 2

x = 52

Thus, another integer = x + 1 = 52 + 1 = 53

Thus the integers are 52 and 53

Answer:

52,53

Step-by-step explanation:

The answer is true.

Step-by-step explanation:

To find the points all lie on the same line, we need to substitute the points in the equation of the line, to determine if the values on both sides of the equation are equal.

Substituting the point [tex](6,13)[/tex] in the equation of the line, we get,

[tex]\begin{aligned}y &=\frac{4}{3} x+5 \\13 &=\frac{4}{3}(6)+5 \\&=4(2)+5 \\&=8+5 \\13 &=13\end{aligned}[/tex]

Thus, the values on both sides are equal. The point [tex](6,13)[/tex] lie on the same line.

Substituting the point [tex](21,33)[/tex] in the equation of the line, we get,

[tex]\begin{aligned}y &=\frac{4}{3} x+5 \\33 &=\frac{4}{3}(21)+5 \\&=4(7)+5 \\&=28+5 \\33 &=33\end{aligned}[/tex]

Thus, the values on both sides are equal. The point [tex](21,33)[/tex] lie on the same line.

Substituting the point [tex](99,137)[/tex] in the equation of the line, we get,

[tex]\begin{aligned}y &=\frac{4}{3} x+5 \\137 &=\frac{4}{3}(99)+5 \\&=4(33)+5 \\&=132+5 \\137 &=137\end{aligned}[/tex]

Thus, the values on both sides are equal. The point [tex](99,137)[/tex] lie on the same line.

Thus, all the three points lie on the same plane.

Hence, the answer is true.

All three points (6 , 13), (21 , 33), and (99 , 137) lie on the line y = [tex]\frac{4}{3}[/tex]x + 5. Thus, the statement is True, all three points make the equation true. Option 3 is the correct answer.

To determine whether the points (6,13), (21,33), and (99,137) all lie on the line y = [tex]\frac{4}{3}[/tex]x + 5, we need to substitute the x-values of each point into the equation and see if the corresponding y-values match.

1. For the point (6,13):

Substitute x = 6 into the equation.

⇒ y = ([tex]\frac{4}{3}[/tex]) × 6 + 5

⇒ y = 8 + 5

⇒ y = 13

Since the y-value matches, the point (6,13) is on the line.

2. For the point (21,33):

Substitute x = 21 into the equation.

⇒ y = ([tex]\frac{4}{3}[/tex]) × 21 + 5

⇒ y = 28 + 5

⇒ y = 33

Since the y-value matches, the point (21,33) is on the line.

3. For the point (99,137):

Substitute x = 99 into the equation.

⇒ y = ([tex]\frac{4}{3}[/tex]) × 99 + 5

⇒ y = 132 + 5

⇒ y = 137

Since the y-value matches, the point (99,137) is on the line.

All three points satisfy the equation y = [tex]\frac{4}{3}[/tex]x + 5. Therefore, the statement is True: all three points make the equation true option (3).

Complete question:

True or False:

The points (6,13), (21,33) and (99,137) all lie on the same line. The equation of the line is y = [tex]\frac{4}{3}[/tex]x + 5.

Select the correct explanation.

The value of the 5 in 50.8 is 1,000 times the value of the 5 in 18.35 ⇒ 1st answer

Step-by-step explanation:

Let us revise some important notes in a number:

∵ The number is 50.8

∵ 5 is in the tens place

∴ The place value of 5 is 10

∵ The number is 18.35

∵ 5 is in the hundredths place

∴ The place value of 5 is 0.01

Let us compare between the places value of 5 in the two numbers

Let x the number which multiplying by the hundredth digit to give the ten digit

∵ 10 = x × 0.01

∴ 10 = 0.01 x

- Divide both sides by 0.01

∴ 1,000 = x

∵ 5 × 10 = 0.05 × 1000

∴ 50 = 50

∴ The value of 5 in 50.8 = 1,000 × the value of 5 in 18.35

The value of the 5 in 50.8 is 1,000 times the value of the 5 in 18.35

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Answer:

Step-by-step explanation:

let

x = kg of mocha beans

y = kg of java beans

so

(1)   x + y = 50

(2)   20x + 15y = 18(50)

solve by substitution (or whatever method you prefer):

(x, y) = (30, 20)

The diameter of a circle with a circumference of 15 meters, using 3 for pi, is 5 meters.

To determine the diameter of a circle when given its circumference and using 3 as the approximation for pi, you can use the formula for the circumference of a circle, which is C = πd, where C is the circumference and d is the diameter. Since we're using 3 for pi (π), when C = 15 meters, the formula becomes 15 = 3d. To find the diameter, divide both sides of the equation by 3, giving us d = 15 / 3, which equals 5 meters.

Answer:

d. The second angle is 116, and the third angle is 29°

Step-by-step explanation:

second unknown angle be x

the other unknown angle = 4*x = 4x

x+ 4x + 35 = 180  {sum of all angles of triangle}

5x = 180-35 = 145

x = 145/5

x = 29

the other unknown angle = 4x = 4*29 = 116

Answer:

A. x+3y =4

A. 3x-y=5

B. x+2y-z =8

B. X-Y+22 =0

B. 2X-3Y+Z =1

Step-by-step explanation:

To determine which linear systems have unique solutions, calculate the determinant of the coefficient matrix for each system.

In order to determine which of the given linear systems have unique solutions, we need to use the determinant of the coefficient matrix.

To do this, we need to calculate the determinant of the 3x3 coefficient matrix for each system:

System 1:
0x + 3y = 4
3x - y = 5
x + 2y - z = 8

Determinant = (0) (-1) (-2) + (3)(1)(1) + (1)(3)(1) - (3)(-1)(1) - (1)(3)(-2) - (0)(2)(1) = 18

Since the determinant is non-zero (18), System 1 has a unique solution.

Similarly, we can calculate the determinants for the other systems to determine their solutions.

System 2: determinant = -88

System 3: determinant = -48

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Answer:

The simplified expression to the given expression is [tex]\frac{4x^6}{y^2}[/tex]

Therefore [tex]\frac{4(2x^3y^4)^4}{2(2x^2y^6)^3}=\frac{4x^6}{y^2}[/tex]

Step-by-step explanation:

Given fractional expression is [tex]\frac{4(2x^3y^4)^4}{2(2x^2y^6)^3}[/tex]

To simplify the given expression as below :

[tex]\frac{4(2x^3y^4)^4}{2(2x^2y^6)^3}[/tex]

[tex]=\frac{2(2x^3y^4)^4}{(2x^2y^6)^3}[/tex]

[tex]=\frac{2[(2)^4(x^3)^4(y^4)^4]}{(2)^3(x^2)^3(y^6)^3}[/tex]  ( using the property [tex](a^m)^n=a^{mn}[/tex])

[tex]=\frac{2[(2)^4(x^{12})(y^{16})]}{(2)^3(x^6)(y^{18})}[/tex]

[tex]=2[(2)^4(x^{12})(y^{16})](2)^{-3}(x^{-6})(y^{-18})[/tex]  (  ( using the property [tex]a^m=\frac{1}{a^{-m}}[/tex] )

[tex]=2[2^{4-3}x^{12-6}y^{16-18}][/tex]( using the property [tex]a^m.a^n=a^{m+n}[/tex] )

[tex]=2[2^1x^6y^{-2}][/tex]

[tex]=\frac{4x^6}{y^2}[/tex] ( using the property [tex]a^m=\frac{1}{a^{-m}}[/tex] )

Therefore the simplified expression is [tex]\frac{4x^6}{y^2}[/tex]

Therefore [tex]\frac{4(2x^3y^4)^4}{2(2x^2y^6)^3}=\frac{4x^6}{y^2}[/tex]

There are 11,375 ounces are still in the bucket ⇒ (not in the choices)

Step-by-step explanation:

An art teacher is cleaning up her room at the end of the week

We need to find how many ounces of blue paint are still in the bucket

∵ The jars have 212 ounces, 825 ounces, and 11110 ounces of blue paint

∵ She combines all of them in an empty bucket

- Add them to find the quantity of the blue paint in the bucket

∴ The bucket contains = 212 + 825 + 11110

∴ The bucket contains = 12,147 ounces

∵ This bucket is then used to fill one can with 414 ounces of

   the paint and another can with 358 ounces

- Add them to find the quantity that used from the bucket

∵ She used = 414 + 358 = 772

∴ 772 ounces is used to fill the two cans

To find how many ounces of the blue paint are still in the bucket subtract from the total amount of paint in the bucked the amount used to fill the two cans

∵ The remainder paint in the bucket = 12,147 - 772

∴ The remainder paint in the bucket = 11,375 ounces

There are 11,375 ounces are still in the bucket

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Answer: For every 5 quarts of blue, you should have 3 quarts of yellow. Since you have 25 quarts of blue in the mix (5*5), there should be 3*5 or 15 quarts of yellow. As there are only 9, you need to add 6 quarts of yellow to get the proper ratio of blue to yellow.

Step-by-step explanation:

Final answer:

To create the specific shade of green glaze, one must adjust the existing mix of 25 quarts blue and 9 quarts yellow to reach a 5:3 blue to yellow ratio. The calculation shows that an additional 6 quarts of yellow glaze are needed to achieve the desired shade.

Explanation:

To achieve the specific shade of green glaze, which is made of 5 parts blue to 3 parts yellow, we must adjust the current mixture of 25 quarts blue glaze and 9 quarts yellow glaze. We first determine the ratio of blue to yellow glaze in the current mixture:

25 quarts blue / 9 quarts yellow = approximately 2.78 parts blue to 1 part yellow.

To achieve the desired 5:3 ratio, the blue glaze needs to be reduced or the yellow glaze needs to be increased. Since removing material can be difficult, we focus on adding yellow glaze. Using the proportion method:

5 parts blue / 3 parts yellow = 25 parts blue / x parts yellow

We cross-multiply and solve for x, the amount of yellow glaze needed:

5x = 75 → x = 15

Therefore, we would need 15 parts of yellow glaze to match 25 parts of blue glaze. Since we already have 9 parts (quarts) of yellow glaze, we need to add:

15 - 9 = 6 quarts of yellow glaze.

Finally, add 6 more quarts of yellow glaze to achieve the specific shade of green glaze.

Answer:

60%

Step-by-step explanation:

To find the percentage of successful basketball shots, divide the number of made shots by the total number shots taken, then multiply by 100. In Hakeem's case, his shooting percentage is approximately 61%.

This is a question about calculating a percentage, which is a basic concept in Mathematics. Percentages are a way of expressing a number or proportion as a fraction of 100. In this case, Hakeem made 17 out of 28 basketball shots. This can be expressed as a fraction – 17/28. To convert this fraction into a percentage, you simply multiply it by 100.

Here is the calculation: (17 / 28) * 100 = 60.71. Therefore, Hakeem made approximately 61% of his basketball shots.

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Tree casts a shadow 30 feet long. A MHS student standing near the tree casts a shadow 9 feet long. The  student is 6 feet tall. What is the height of the tree? Show all work

Answer:

Option D

The height of tree is 20 feet tall

Solution:

From given question,

Shadow of tree = 30 feet

Height of tree = ?

Height of student = 6 feet

Shadow of student = 9 feet

We have to find the height of tree

We can solve the sum by proportion

[tex]\frac{\text{height of tree}}{\text{shadow of tree}} = \frac{\text{height of student}}{\text{shadow of tree}}[/tex]

This forms a proportion and we can solve the sum by cross multiplying

[tex]\frac{\text{height of tree}}{30} = \frac{6}{9}\\\\\text{height of tree} = 30 \times \frac{6}{9} = 30 \times \frac{2}{3}\\\\\text{ height of tree } = 10 \times 2 = 20[/tex]

Thus height of tree is 20 feet tall

Answer:

A. 30

Step-by-step explanation:

The answer is 30 because x= 12 so that means that x-2 is 10 because x is 12, so since its in parenthesizes that means you do that part of the problem first. So, after we have 10 we will do times 3 since the 3 is also there and it says what is the value. So, therefore the answer is A. 30.

Answer:

steps in attached picture

Step-by-step explanation:

Answer:

Therefore the value of 'y' is,

[tex]y=3[/tex]

Step-by-step explanation:

Given:

[tex]10y-50=-20[/tex]

To Find:

y= ?

Solution:

[tex]10y-50=-20[/tex]    ........Given

Step 1. Adding 50 to both the side we get

[tex]10y-50+50=-20+50\\10y=30[/tex]

Step 2. Dividing by 10 on both the side we get

[tex]\dfrac{10y}{10}=\dfrac{30}{10}\\\\y=3[/tex]

Therefore the value of 'y' is,

[tex]y=3[/tex]

Let [tex]\( x \)[/tex] be the number of CDs. The equation representing the statement "1 more than twice as many CDs is 17" is [tex]\( 2x + 1 = 17 \).[/tex]

Let's break down the statement into a mathematical expression. "Twice as many CDs" is represented by [tex]\( 2x \)[/tex]. Adding "1 more than" to this gives [tex]\( 2x + 1 \)[/tex]. Finally, the statement "is 17" translates to [tex]\( 2x + 1 = 17 \),[/tex] creating the equation that represents the given information.

The complete question is: Explain the statement "1 more than twice as many CDs is 17"

Answer:

B. {1, 2, 3, 4}.

Step-by-step explanation:

The domain is the set of x values.

The domain of the function represented by the given table, with the corresponding values of x and y being (1, 2), (2, 4), (3, 3), and (4, 2), is  Option B)  {1, 2, 3, 4}.

The domain of a function consists of all possible input values (x-values) for which there are corresponding output values (y-values). In the given table, we see the following pairs of values: (1, 2), (2, 4), (3, 3), and (4, 2).

These x-values are explicitly provided in the table, and they are 1, 2, 3, and 4. Therefore, the domain of the function, based on the data in the table, is {1, 2, 3, 4}.

This means that for this specific function, you can input any of these four values into the function, and there are corresponding y-values for each of them. Any other values not listed in the table, such as decimals or negative numbers, are not part of the domain for this function because they do not have corresponding y-values in the given data.

In summary, the domain of the function represented by the table is the Option B). set {1, 2, 3, 4}, which includes the x-values provided in the table.

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The question is worded a bit strangely (in my opinion anyway), but I think your teacher wants you to describe how exponents work.

Let's say we had the expression [tex]5^3[/tex]

The base is 5 as its the bottom most value (think of something like the base of a tree or building). The exponent is 3.

The exponent of 3 tells the reader to multiply the base 5 by itself 3 times like so

[tex]5^3 = 5*5*5 = 125[/tex]

With larger exponents, it becomes more tedious to write out all the repeated multiplications, which is why many calculators have an exponent button to save time.

An exponent signifies how many times a base is multiplied by itself. The expression "5 squared" (5²) means 5 x 5 = 25. Similarly, "5 cubed" (5³) means 5 x 5 x 5 = 125. This concept of exponentiation is essential in mathematics for representing repeated multiplication of a number.

An exponent indicates the number of times a base is multiplied by itself. For example, the exponent "2" in the expression "5²" means that the base "5" is multiplied by itself, resulting in 5 x 5 = 25. This is also known as squaring a number. Similarly, an exponent of "3" denotes cubing, which means the base is multiplied by itself three times. For instance, 5³ equals 5 x 5 x 5, which equals 125.

It's also important to understand that when we talk about exponents, we are often referring to powers. If the base is "b" and the exponent is "n", then the expression can be written as bn, indicating a chain of multiplications of "b", "n" times. For instance, witnessing an expression like (10²)³, we multiply the exponents to get a new exponent (2 x 3 = 6), resulting in 10⁶.

The concept of exponents is a foundational element in various mathematical operations and is crucial for understanding more complex mathematical concepts.

Answer:

7/1

Step-by-step explanation:

simplify top and bottom by 3

72 rr rvmfklm;vrmfkvfdmlmv;m,fd;vmfd;lvmfl;v fek;

s(t(-5)) First find t(-5), since you know x = -5, substitute/plug in -5 for x in t(x) = 5x - 4

t(x) = 5x - 4

t(-5) = 5(-5) - 4

t(-5) = -25 - 4

t(-5) = -29

s(t(-5)) plug in -29 for t(-5)

s(-29) = -3(-29) - 2 (- times a - equals a positive)

s(-29) = 87 - 2

s(-29) = 85

Your answer is 85

Answer:

$812.5

Step-by-step explanation:

Given: Ethan need to save at least $500.

          He has saved so far $175

          Ethan hope to use two-fifths of his next paycheck to cover the remaining amount.

Lets assume Ethan´s paycheck amount be "x"

First finding the remaining amount to be covered.

Remaining amount= [tex]\$ 500 - \$ 175= \$ 325[/tex]

∴ The remaining amount to be covered is $325.

As given, Ethan hope to use two-fifths of his next paycheck to cover the remaining amount.

Now, using the inequality to find the amount of paycheck.

⇒ [tex]x\times \frac{2}{5} \geq \$ 325[/tex]

multiplying both side by 5

⇒ [tex]x\times 2\geq 325\times 5[/tex]

divinding both side 2

⇒ [tex]x\geq \frac{1625}{2}[/tex]

∴ [tex]x\geq \$ 812.5[/tex]

Hence, Ethan must make at least $812.5 in his paycheck to cover his remaining anount to buy dirt bike.

Answer:

Step-by-step explanation:

3x = 39.....so instead of just subbing in all ur answer choices....just solve for x

3x = 39...divide both sides by 3, cancelling out the 3 on the left side

x = 39/3

x = 13 <=====

Answer:

1/10 the value is 100% right!

Step-by-step explanation: