Justin is playing tennis. When serving, he stands 12 feet away from the net, which is 3 feet tall. The ball is served from a height of 7.5 feet. Justin thinks the ball travels about 21.4 feet before it hits the ground 8 feet from the net on the opposite side.
a) How far does the ball travel?
b) What assumptions did you make to solve the distance the ball travels?
c) What mathematical practice did you use to solve this problem?

Answer:

84 cm

Step-by-step explanation:

H=51+m

m=months, substitute m for 33 months

H=51+33

H=84

The plant's height will be 84 cm after 33 months

7.25 would be 7 1/4 or 29/4

The description of the graph of function g(x) is 3 units translation up

The equations of the functions are given as

f(x) = 4x + 1

g(x) = (4x + 1) + 3

Substitute f(x) = 4x + 1 in the equation g(x) = (4x + 1) + 3

So, we have

g(x) = f(x) + 3

The above rule implies that:

The function g(x) is a translation of the function f(x)

The unit of the translation is 3 and the direction of the translation is up

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It is to be noted that Option A is the most appropriate choice of origin and scale for this graph.

In mathematics, a graph is defined as a graphical representation or diagram that organizes facts or values. The graph's points frequently reflect the relationship between two or more objects.

Note that we are given the following:

Week:     2      3      4      5      6     7       8

Minutes: 300 450 600 750 900 1050 1200

The difference between two cumulative weeks is one week, while the difference between two cumulative minutes is 150.

Plotting the graph between minutes and weeks we can get the most suitable scale is

x-axis scale:  1 unit = 1 week

y-axis scale:  1 unit = 150 minutes

Assuming we extend the table to the left to reflect the origin, we'll obtain

Week     0   1      2...............8

Minutes 0   150  300..........1200

Hence, The origin ⇒ (0 weeks, 0 minutes)

From the above, therefore, the most suitable choice of origin and scale is:

x-axis scale: 1 unit = 1 week

y-axis scale: 1 unit = 150 minutes

origin:          (0 weeks, 0 minutes)

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The scale on the x-axis should be 1 unit equal to 1 week and the scale on the y- axis should be 1 unit = 150 minutes. Option A is correct.

The graph is a demonstration of curves that gives the relationship between the x and y-axis.

Here,
As observing the data, the data mentioned in the table is represents the linear relationship.
Slope of the function = 450 - 300 / 3 - 2 = 150
This implies that for 1 week there is 150 minutes on the graph of the relationship,

Thus, the scale on the x-axis should be 1 unit equal to 1 week and the scale on the y- axis should be 1 unit = 150 minutes.

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Answer:

n= 3

Step-by-step explanation:

3(n+3)= -4n+30

3n+9= -4n +30 expand

7n+9 = 30 +4n to both sides

7n = 21 -9 from both sides

n= 3 divide by 7 on both sides

Solving for n for n in the formula A = yn + y is expressed as: n = A/y - 1.

Solving for the formula for a variable, means we should make the variable the subject of the formula by isolating the variable to one side of the equation to determine its value.

Given the equation of the formula, A = yn + y, to solve for n, follow the steps below:

A = y(n + 1)

Divide both sides by y:

A/y = y(n + 1)/y [division property of equality]

A/y = n + 1

Subtract 1 from both sides:

A/y - 1 = n + 1 - 1 [subtraction property of equality]

A/y - 1 = n

n = A/y - 1

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The equation  y + 2x = 3 best represents the relationship between x and y in the graph.

We are provided with the graph shown in question. We were supposed  to find the equation of the line shown in the graph. From this graph we can clearly see that the line is passing through ( 1.5 , 0 ) and ( 0 , 3 ).

The equation of line passing through two points is given below:

[tex](y - y_{1}) = (\frac{y_{2}-y_{1} }{x_{2}-x_{1} }) (x - x_{1} )[/tex]

As the line is passing through points  ( 1.5 , 0 ) and ( 0 , 3 ) , so we can write the above equation as

( y - 0 ) = ( ( 3 - 0 )/( 0 - 1.5 ) ) ( x - 1.5 )

y = -2 ( x - 1.5 )

y = -2x + 3

y + 2x = 3

The required equation of line is y + 2x = 3 i.e., this equation best represents the relationship between x and y in the graph.

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The given vertices when plotted gives a parallelogram.

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

To solve this problem, we simply need to plot the vertices and check if the opposite sides are equal to each other.

Kindly find the attached image of the parallelogram below.

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Cost of total 12 chocolate crackle is $8.875

What is multiplication and division?

Multiplication and division are two of the basic arithmetic operations . in multiplication we find the product of two numbers. And division is splitting a number in equal given part.

We are given cost of 24 chocolate crackel

The total cost comes out to be $17.75

a) To make 12 chocolate crackle we require material of exactly half cost

Which will be $8.875

b) To make 6 chocolate crackle we will require material of exactly one fourth of the cost which will be $4.435

c) To make 36 chocolate crackle we will require material of exactly one and half cost

Which will be $26.625

d) To find the cost of one chocolate we divide the cost of 24 chocolate Crackle by 24 we get the cost of 1 chocolate crackel as $0.739

e) The cost of one chocolate crackel in cents is $74 cents

Hence, Cost of total 12 chocolate crackle is $8.875

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Answer:

- 54

Step-by-step explanation:

substitute x = 3 , y = 2 into the expression

- 6x² + y³ - 8

= - 6(3)² + 2³ - 8

= - 6(9) + 8 - 8

= - 54 + 0

= - 54

Considering the expression 4x + 12 = 64, it is found that:

A. The problem is that you purchased x fried pastry, costing $4, plus a chocolate and a soda, costing $12, and the total purchase cost was of $64.

B. The solution is x = 13.

C. The solution means that you purchased 13 fried pastry.

The expression is presented as follows:

4x + 12 = 64.

A possible context for this problem is:

The number of fried pastry purchased is the solution to the equation, calculated as follows:

4x + 12 = 64

4x = 52

x = 52/4

x = 13 -> 13 fried pastry were purchased.

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Answer:

v = 9

Step-by-step explanation:

2(3v + 8)  = 70  Distribute the 2

2(3v) + 2(8) = 70

6v + 16 = 70  Subtract 16 from both sides

6v = 54  Divide both sides by 6

v = 9

The variance of the sample means will be 0.3428.

What is Variance of sample means?

The variance of the sampling distribution of the mean is the population variance divided by the sample size.

Given that;

A uniform continuous distribution has a maximum of 14 and a minimum

of 2.

Samples of size 36 are drawn from the distribution.

Now,

The population variance = 14 - 2

                                      = 12

And, Sample size = 36

Since, The variance of the sample means is defined as;

= Population variance / Sample size

Substitute all the values, we get;

= 12 / 35

= 0.3428

Thus, The variance of the sample means will be 0.3428.

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Step-by-step explanation:

putting the value of x in -3x-4 where x is 4 so the ans is -17

The value of x, y, z is -18000/83, -30000/83, 297000/83 respectively.

This problem is solve by substitution method.

what is substitution method?

Substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.

Given,

x+y+z=3000

5x−3y=0

x−10.5y−z=0

Solve x+y+z=3000 for x.

x=−y−z+3000

Substitute −y−z+3000 for x in the second and third equation.

5(−y−z+3000)−3y=0

−y−z+3000−10.5y−z=0

Solve these equations for y and z respectively.

y=1875−5/8z

z=1500-23/4y

Substitute 1875−5/8z for y in the equation z=1500−23/4y

​z=1500−23/4(1875-5/8z)

z= 297000/83

put this value in y = 1875- 5/8z

y= -30000/83

substitute the value of y and z in equation one

x= -18000/83

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In the given right-angled triangle, the sine, cosine, and tan of the angle A are: sin A =0.88, cos A = 0.4705, tan A= 1.875

We have a right angles triangle ABC with AC as the hypotenuse and AB and AC as the other two sides.

Given, hypotenuse AC=34, side BC = 30, side AB = 16

∴From the formulae for evaluating sin, cos, and tan of an angle

sin A[tex]=\frac{opposite}{hypotenuse}= \frac{BC}{AC}=\frac{30}{34}=\frac{15}{17}=0.88[/tex]     (1)

cos A[tex]= \frac{adjacent}{hypotenuse} =\frac{16}{34}=\frac{8}{17}=0.4705[/tex]          (2)

tan A[tex]=\frac{OppositeSide}{AdjacentSide}=\frac{30}{16}=\frac{15}{8}=1.875[/tex]           (3)

Thus sin A= 0.88, cos A= 0.4705, tan A= 1.875

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The time taken for them to reach the ground is 0.305s.

What are the equations of motion?
Kinematics equations of motion define the fundamentals of an object's motion, such as its position, velocity, or acceleration over time. These three equations of motion control how an item moves in one, two, and three dimensions. It is possible to determine components like displacement(s), velocity(initial and final), time(t), and acceleration(a) using one of three equations of motion (a). The three equations of motion are as follows:
First equation: v = u + at
Second equation: s = u*t + 0.5t²
Third equation: v² = u² + 2as

Given, the initial velocity of the skydiver = 3 m/s
Height of fall for the skydiver = 1200 m
Also, after reaching ground, final velocity of the skydiver = v = 0 m/s
Let the time taken to reach the ground be = t
Therefore, using the first equation, we have
0 = 3 + (-9.81)t ⇒ t = -3/-9.81 = 0.305 s
Thus, time taken for them to reach the ground is 0.305s.

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Answer:

Tori studies 4 subjects (including Chemistry)

Step-by-step explanation:

the picture asks for similar things as your text but got other numbers.

let's do both.

first the picture :

find g(0) and one value of x for which g(x) = 0.

g(0) means that x = 0.

so, we find x = 0 on the x-axis (it is where the y-axis intersects) and then go straight up or down until we meet or intersect the function curve.

in our case we go up and intersect the curve at y = 2.

and that is the result.

y = g(x), it is a named variable for the function result, nothing else.

so,

y = g(0) = 2

to find a value of x for which g(x) = 0 means we go along the x-axis (these are all the points for which y = 0) until the x-axis intersects with the curve.

and that is here at x = -1.

now for your text :

we repeat the same principles.

but now, we need to use imaginary lines that go parallel to the x- and y-axis.

your text now calls the function h(x), but since I have no other information, I assume it is the same line function in the picture.

for which value of x is h(x) = -4 ?

remember, y is just the variable that stands for the function result.

so, we are asking for

y = h(x) = -4

imagine a horizontal line through y = -4.

where does it intercept the line h(x) ?

at that point we go straight up or down (in our case up) to the x-axis and read the x-value there : -3

so,

y = h(-3) = -4

to find h(1) we find x = 1 on the x-axis, and from there we go straight up or down (in our case up) parallel to the y-axis until we intersect the function curve.

from there we go straight left out right (in our case left) to the y-axis and read the y-value there : 4

so,

y = h(1) = 4

The error interval is 12.305 ≤ t < 12.315 (by using rounding rules)

What is rounding rules?

Round the number up if 5, 6, 7, 8, or 9 follow the number you are rounding.

Round the number down if the rounded number is followed by a 0, 1, 2, 3, or 4. for e.g, 1.205 becomes 1.21 (rounding up) and if 1.21 (round the number down) then it will be 1.2.

In this question :

- Time = 12.31 seconds

- if we consider the thousandth digit then the times of 12.305 or greater and less than 12.315 are rounded to 12.31.

Therefore, the interval is 12.305 ≤ t < 12.315.

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The average of the fraction of students on both classes who went on the field trip is; 13/20.

A fraction represents a part of a number or any number of equal parts. A fraction is a ratio of two integers called the numerator and denominator.

Given that the sum of the fraction of both students in the two classes is;

3/5 + 7/10

We know that the LCM of the denominators which are 5 and 10 is 10

Therefore, the sum of both fractions = 6/10 + 7/10 = 13/10

The average = 13/10 /2 = 13/10 x 2

The average = 13/20

Therefore, the average of the fraction of students on both classes who went on the field trip is; 13/20.

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The quotient of [tex]12\frac{3}{8}[/tex] ÷ [tex]2\frac{3}{4}[/tex] is 4 1/2.

The quotient of [tex]9\frac{2}{5}[/tex] ÷ [tex]1\frac{3}{10}[/tex] is 7 3/13

The quotient of [tex]7\frac{1}{4}[/tex] ÷ [tex]1\frac{7}{8}[/tex] is 1 13/15

The quotient of [tex]8\frac{5}{6}[/tex] ÷ [tex]2\frac{1}{4}[/tex] is3 25/27

The quotient of [tex]5\frac{4}{7}[/tex] ÷ [tex]2\frac{10}{21}[/tex] is 2 1/4

The quotient of [tex]12\frac{5}{8}[/tex] ÷ [tex]3\frac{19}{24}[/tex] is 3 30 / 91

The quotient of [tex]7\frac{5}{6}[/tex]  ÷ [tex]3\frac{1}{2}[/tex]is 2 5/21

The quotient of [tex]14\frac{2}{3}[/tex]  ÷[tex]2\frac{2}{9}[/tex]is 6 3/5

A quotient is the result of a division process. Division is the mathematical operation that is used to part a number into equal groups using another number. The sign that is used to represent division is ÷.

A mixed number is a fraction that is made up of a whole number and a proper fraction. An example of a mixed number is 1 1/2.

[tex]12\frac{3}{8}[/tex] ÷ [tex]2\frac{3}{4}[/tex]

99 / 8÷ 11/4

99 / 8 x 4/11 = 9/2 = [tex]4\frac{1}{2}[/tex]

[tex]9\frac{2}{5}[/tex] ÷ [tex]1\frac{3}{10}[/tex]

47 / 5 ÷ 13/10

47 / 5 x 10/13 = 94 / 13 = 7 3/13

[tex]7\frac{1}{4}[/tex] ÷ [tex]1\frac{7}{8}[/tex]

29 / 4 ÷ 15/8

29 / 4 x 8/15 = 58 / 15 = 1 13/15

[tex]8\frac{5}{6}[/tex] ÷ [tex]2\frac{1}{4}[/tex]

53 / 6 ÷ 9/4

53 / 6 x 4/9 = 106 / 27 = 3 25/27

[tex]5\frac{4}{7}[/tex] ÷ [tex]2\frac{10}{21}[/tex]

39 / 7  ÷ 52/21

39 / 7 x 21/52 = 117 / 52 = 2 1/4

[tex]12\frac{5}{8}[/tex] ÷ [tex]3\frac{19}{24}[/tex]

101 / 8  ÷91 / 24

101 / 8  x 24/91 = 303 / 91 = 3 30 / 91

[tex]7\frac{5}{6}[/tex]  ÷ [tex]3\frac{1}{2}[/tex]

47 / 6 ÷ 7/2

47 / 6 x 2/7 =  47 / 21 = 2 5/21

[tex]14\frac{2}{3}[/tex]  ÷[tex]2\frac{2}{9}[/tex]

44 / 3 ÷ 20/9

44 / 3 x 9/20 = 33/5 = 6 3/5

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The likelihood or probability that the population mean evidence-based reading and writing test score of 533 will be within 10 points of the sample mean test score provided by a sample of 49 test takers is 0.274.

From the given information, we have:

The population mean, μ = 533

The sample size, n = 49

The population standard deviation, σ = 100

The standard deviation for X  is:

= 100/√49 = 14.2857142857

Normal distribution with mean 533 and SD of 12.3091

P( 523 <x< 543 )

Z = 10 ÷ 14.2857142857

Z = 0.7, - 0.7

P( z < 0.7 ) - P( z < - 0.7 )

= 0.75804 - 0.48393

= 0.27411

The required probability is 0.274.

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The complete question is mentioned below:

A certain organization reported the following scores for two parts of the scholastic Aptitude test ( SAT)

Evidence-based Reading and writing: 533

Mathematics  : 527

Assume the population standard deviation for each part is σ = 100.

What is the probability a sample of 49 test takers will provide a sample mean test score within 10 points of the population mean of 533 on the Evidence-based Reading and Writing part of the test?

Answer: x = -2     y = 2

Step-by-step explanation:

There are different ways to solve systems of equations. I will set them equal to each other.

First, I have to divide 2 from both sides of the first equation, which gives

y = -4x - 6

Now I can set them equal to each other and solve for x.

-4x - 6 = 2x^2 + 4 x + 2

0 = 2x^2 + 8x + 8

Now we factor it. If you cannot see the factors right away, you can use the quadratic formula, but I see that

(2x+4)(x+2) = 2x^2 + 8x + 8 = 0

so, because (2x+4)(x+2) = 0, one (or both) of the parenthesis must equal zero.

Solve for each parenthesis.

2x+4=0  =>   2x = -4  =>   x = -2

x+2=0  =>   x = -2

As we see here, there is only one value for x. Now we can plug it into either one of the original equations. I'll do the first since there are no squares.

2y = -8(-2) -12

2y = 16 - 12

2y = 4

y = 2

Sum expressions are true and some are false.

What does a math expression mean?

a) Calculate the sum or difference =   15. 02

Check equivalency =  True

Answer: True

b)Calculate the sum or difference = 15.02

Check equivalency = False

Answer: False

c)

Calculate the sum or difference = 15.02

Check equivalency =True

Answer: True

d)

Calculate the sum or difference = 3.02+12

Calculate the sum or difference = 15.02

Check equivalency: True

Answer: True

e)

Calculate the sum or difference = 1.5 + 13.8

Calculate the sum or difference = 15.3

Check equivalency: False

Answer: False

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Solution

Let f(x) = 2x+4. If f(x) = 16, find x.

Answer:

x=6

Step-by-step explanation:

Substitute f(x)=16 into the equation:

16=2x+4

Get x by itself:

2x=12

Divide both sides by 2:

x=6

Answer:

You need to know that not a cheat

By working with the given mixed numbers, we will get that for the project they need (4 + 1/4) yards of metal.

At this point, we have two pieces that measures (1 + 1/6) yd and (3/12) yd, adding that length we get a total length:

L = (1 + 1/6) yd + (3/12) yd = (1 + 2/12) yd + 3/12yd = (1 + 5/12) yd

Now we know that we need 3 times that amount of metal for the project, then the total amount of metal that we need is:

3*L = 3*(1 + 5/12) yd = (3 + 15/12) yd

We can write this as a mixed number as:

(3 + 12/12yd + 3/12yd) = (4 + 3/12)yd = (4 + 1/4) yd

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