A basketball player stands near the middle of the court and throws the ball toward the basket.
The path of the ball is a parabola. The ball leaves the player's hands at a height of 6 feet above the ground. The
ball travels to a maximum height of 12 feet when it is a horizontal distance of 18 feet from the player's hands.
Write a function to represent the height of the ball in terms of its distance from the player's hands?

Answers

Answer 1

Answer:

A function to represent the height of the ball in terms of its distance from the player's hands is \(y=\frac{-1}{54}(x-18)^2+12\)

Step-by-step explanation:

General equation of parabola in vertex form \(y= a(x-h)^2+k\)

y represents the height

x represents horizontal distance

(h,k) is the coordinates of vertex of parabola

We are given that The  ball travels to a maximum height of 12 feet when it is a horizontal distance of 18 feet from the player's hands.

So,(h,k)=(18,12)

Substitute the value in equation

\(y=a(x-18)^2+12\)  ---1

The ball leaves the player's hands at a height of 6 feet above the ground and the distance at this time is 0

So, y = 6

So,\(6=a(0-18)^2+12\)

6=324a+12

-6=324a

\(\frac{-6}{324}=a\)

\(\frac{-1}{54}=a\)

Substitute the value in 1

So,\(y=\frac{-1}{54}(x-18)^2+12\)

Hence a function to represent the height of the ball in terms of its distance from the player's hands is \(y=\frac{-1}{54}(x-18)^2+12\)


Related Questions

find fourier transform f(x)=1\|x|

Answers

Answer:

Step-by-step explanation:

Using historical records, the personnel manager of a plant has determined the probability of XX, the number of employees absent per day. It isX 0 1 2 3 4 5 6 7P(X) 0.0046 0.0248 0.3098 0.3399 0.219 0.0798 0.019 0.0031Find the following probabilities.A. P(2≤X≤5)P(2≤X≤5)Probability =B. P(X>5)P(X>5)Probability =C. P(X<4)P(X<4)Probability =

Answers

The probability in each case is:

A. P(2≤X≤5) = 0.5945 (0.3098 + 0.3399 + 0.219) B. P(X>5) = 0.019 (0.0798 + 0.019) C. P(X<4) = 0.3614 (0.0046 + 0.0248 + 0.3098 + 0.3399)

The probabilities provided are the probabilities of each value of X. For example,

P(X=0) is 0.0046, which means that there is a 0.0046 probability that exactly 0 employees will be absent per day.

Similarly,

P(X=1) is 0.0248, which means that there is a 0.0248 probability that exactly 1 employee will be absent per day. P(X=2) is 0.3098, which means that there is a 0.3098 probability that exactly 2 employees will be absent per day, and so on.

When finding probabilities for a range of X values, you need to add up the individual probabilities of all the values in the range. For example, if you are looking for

P(2≤X≤5), then you need to add the individual probabilities for X = 2, 3, 4, and 5, which is 0.3098 + 0.3399 + 0.219 + 0.0798 = 0.5945. Similarly, if you are looking for P(X>5), then you need to add the individual probabilities for X = 6 and 7, which is 0.019 + 0.0031 = 0.0221. Finally, if you are looking for P(X<4), then you need to add the individual probabilities for X = 0, 1, 2, and 3, which is 0.0046 + 0.0248 + 0.3098 + 0.3399 = 0.3614.

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45% of 81.21 is a number between?

45% of 81.21 is a number between?

Answers

Answer:

4 and 40

Step-by-step explanation:

the answer is 36

45/100 multiplied by 81.21

Ms. Thomspon needs 15/2 yards of red fabric and 7 1/2 yards of silver fabric. which comparison is true.

Answers

Step-by-step explanation:

To compare the two amounts of fabric, we need to express them with a common denominator:

15/2 = 30/4

7 1/2 = 15/2

Now we can compare the two amounts:

30/4 > 15/2

This is true because 30/4 is equal to 7.5 yards, which is greater than 7.5 yards (or 15/2 yards) of silver fabric.

Therefore, Ms. Thompson needs more red fabric than silver fabric.

If the demand equation is
Q + 4 P = 60
fi nd a general expression for the price elasticity of demand in terms of P . For what value
of P is demand unit elastic?

Answers

The general expression for the price elasticity of demand in terms of P is E = - (P / (15 - P)).

The value of P that makes the demand to be unit elastic would be 7.5.

Price elasticity of demand

The price elasticity of demand is given by the formula:

E = (%ΔQ / %ΔP) * (P/Q)

We can solve the demand equation for Q in terms of P as:

Q = 60 - 4P

Taking the derivative of Q with respect to P, we get:

dQ/dP = -4

We can now express the percentage change in Q as a function of the percentage change in P:

%ΔQ / %ΔP = (ΔQ / Q) / (ΔP / P) = (-4P/Q) / (P/Q) = -4

Substituting this expression into the formula for price elasticity of demand, we get:

E = (%ΔQ / %ΔP) * (P/Q) = -4 * (P / (60 - 4P))E = - (P / (15 - P))

To find the value of P for which demand is unit elastic, we need to set the absolute value of the price elasticity of demand equal to 1. So we have:

|E| = 1(P / (15 - P)) = 1P = 7.5

In other words, the value of P for which demand is unit elastic is 7.5.

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if you were to flip the coin 15, how many times will the coin land on tails based on experimental probability? jordan flipped a count of 45 times.His result are below: heads: 24 tails: 21

Answers

Answer:

It will land 7.5 times on tails, which is rounded up to 8 times

Step-by-step explanation:

there are 2 possibilities, heads or tails

so you divide 15 in 2 and get 7.5

The coin will land 7 times tail based on the experimental probability.

What is Probability?

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

When the coin tossed 45 times.

Head= 24, tail = 21

So, fraction of appearing tail will be

= 21 / 45

= 0.466667

Now, if the coin tossed 15 times then the coin land on tails

= 15 x 0.466667

= 7

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A car is traveling at a rate of 30 meters per second. What is the car's rate in kilometers per hour? How many kilometers will the car travel in 5 hours? Do not
round your answers.

Answers

The speed of the car is 108 kilometers per hour and the distance covered in 5 hours is 540 kilometers.

What is the speed of the car in kilometers per hour and distance covered after 5 hours?

Speed is simply referred to as distance traveled per unit time.

It is expressed as;

Speed = Distance ÷ time.

Given that the car is traveling at a rate of 30 meters per second.

First, convert the car's speed from meters per second to kilometers per hour using the conversion factor.

1 kilometer = 1000 meters

1 hour = 3600 seconds

Hence;

Speed = 30m/s = ( 30 × 3600/1000 )kmh

Speed = 108 kmh

Next, the distance covered in 5 hours will be:

Speed = Distance / time

Distance = speed × time

Distance = 108 kmh × 5 h

Distance = 540 km

Therefore, the disatnce covered is 540 kilometers.

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In the figure, d || m. What is the value of x?
I WILL MARK BRAINLIEST!!
|
———— | ————
(2x - 20°)|
| 86°
———— | ———-
|

In the figure, d || m. What is the value of x?I WILL MARK BRAINLIEST!! | | (2x - 20)| | 86 | - |

Answers

Answer: 53

Step-by-step explanation:

2x-20=86 [alternate interior angles theorem]2x=106 [add 20 to both sides]x = 53 [divide both sides by 2]

Un profesor de Enseñanza Básica le indica a sus alumnos que escojan tres dígitos
diferentes del conjunto {1, 2, 3, 4, 5} y formen números mixtos colocando los dígitos
en el casillero . También les recuerda que la parte fraccionaria tiene que ser
menor que 1, por ejemplo
2
3
5
. ¿Cuál es la diferencia entre el mayor y el menor de los
números mixtos que se pueden formar?

Answers

Enseñanza Básica is the term used to describe the first level of education in the Chilean education system, which includes the first to eighth grades. A teacher of Enseñanza Básica asked his students to choose three-digit mixed numbers that can be formed.

A mixed number is a number that has both a whole number and a fraction component. To form three-digit mixed numbers, we need to have a whole number that is less than 100 and a proper fraction that has a denominator less than or equal to 99. Here are some examples:123 4/567 2/8109 1/2382 3/47There are a total of 900 three-digit numbers that can be formed using digits 1 to 9 without repetition. To find the number of three-digit mixed numbers that can be formed, we need to count the number of ways we can choose a proper fraction with a denominator less than or equal to 99. There are 99 possible denominators, and for each denominator, there are 98 possible numerators (excluding 0 and the denominator itself). Therefore, the total number of three-digit mixed numbers that can be formed is:900 x 99 x 98 = 8,334,600There are 8,334,600 three-digit mixed numbers that can be formed using digits 1 to 9 without repetition.

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The difference between the greatest and the least mixed numbers is 9.87 - 6.0789 ≈ 3.7911.

How to solve

The three digits different from {1, 2, 3, 4, 5} can be chosen from {0, 6, 7, 8, 9}.

The greatest mixed number is formed by placing the largest digit as the whole number and the remaining two digits as the fraction in descending order, i.e., 9 87/100 or 9.87.

The smallest mixed number is formed by placing the smallest non-zero digit as the whole number and the remaining two digits as the fraction in ascending order, i.e., 6 07/90 or 6.0789.

The difference between the greatest and the least mixed numbers is 9.87 - 6.0789 ≈ 3.7911.

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The Question in English

A Basic Education teacher tells his students to choose three digits

different from the set {1, 2, 3, 4, 5} and form mixed numbers by placing the digits

in the locker It also reminds them that the fractional part has to be

less than 1, for example

2

3

5

. What is the difference between the greatest and the least of the

mixed numbers that can be formed?

Can someone help me, please? I will give 80 points for answering.

Match the representations that have the same proportional relationship as the situations described.







Answer:
Situation 1:
Situation 2:
Situation 3:

Can someone help me, please? I will give 80 points for answering.Match the representations that have

Answers

The equivalent proportional relationships in this problem are given as follows:

A, B and E.C and G.D and F.

Proportional relationships

In a proportional relationship, the output variable y is obtained from the multiplication of the input variable x and the constant of proportionality k, by the rule presented as follows:

y = kx.

Proportional relationships are said to be the same when they have the same constant of proportionality k.

For each relationship in this problem, the constants are given as follows:

Relationship A: k = 6.Relationship B: k = 6 (same as A).Relationship C: k = 5.5Relationship D: k = 35.Relationship E: k = 6 (same as A).Relationship F: k = 35. (same as D).Relationship G: k = 5.5 (same as C).

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Help! Can some one explain Jessica has her hair styled and wants to tip her hair stylist 18%. Write an
equation that could be used to calculate the tip, y, for a bill of x dollars.

Answers

Answer:

y = .18x

Step-by-step explanation:

The tip is going to be 18% of what she payed, and this says that x is what she payed. That means you can write it as:

tip = 18% of bill

y = 18% of x

18% of x an be written as .18x in decimal, so:

y = .18x

house designer uses computer-aided drawings to illustrate new houses. She likes to show her drawings to clients on a large screen. She often uses the zoom-in function to enlarge the drawings so that clients can see certain features better.
Each click of the zoom-in button results in a 10 percent increase in the size of a drawing.
(a) On a certain drawing of a house, the width of the front door is 3 inches on screen, using the default settings. Make a table of values to show the width of the door on screen after each of the first four clicks of the zoom-in button. These values should be accurate to the thousandths place.
(b) Write an algebraic rule for the function that will give the display size of the door for any number of clicks.
c) To show clients a detail on the front door, she needs to zoom in so the door is approximately 3 feet wide on screen. How many clicks of the zoom-in button will be needed to make this enlargement? Explain how you got your answer.
d) Suppose one click of the zoom-out button results in a 10 percent decrease in the size of the drawing. How many clicks of the zoom-out button would it take to transform the display of the door from 3 feet wide back to a width of approximately 3 inches?
Explain how you got your answer.

house designer uses computer-aided drawings to illustrate new houses. She likes to show her drawings
house designer uses computer-aided drawings to illustrate new houses. She likes to show her drawings

Answers

(a) Clicks Width of Door (inches)

1 3.3

2 3.63

3 3.99

4 4.39
(b) The function is y = 3  (1.1)ˣ.

(c) It would take about 15 clicks of the zoom-in button to make the door approximately 3 feet wide on the screen.

(d) It would take about 12 clicks of the zoom-out button to transform the display of the door from 3 feet wide back to a width of approximately 3 inches.

(a)

Clicks Width of Door (inches)

1 3.3

2 3.63

3 3.99

4 4.39

(b) Let x be the number of clicks and y be the width of the door on the screen. Then, we can write the algebraic rule as:

y = 3  (1.1)ˣ

(c) To make the door approximately 3 feet wide on screen, we need to convert 3 feet to inches, which is 36 inches. Then, we need to solve for x in the equation:

3 (1.1)ˣ = 36

Dividing both sides by 3, we get:

(1.1)ˣ = 12

Taking the logarithm of both sides (with base 1.1), we get:

x = log(12) / log(1.1) ≈ 14.7

So, it would take about 15 clicks of the zoom-in button to make the door approximately 3 feet wide on the screen.

(d) To transform the display of the door from 3 feet wide back to a width of approximately 3 inches, we need to find the number of clicks of the zoom-out button that will result in a width of approximately 3 inches. We can use the same formula as before, but with the initial width of 36 inches (since we are zooming out):

36 (0.9)ˣ = 3

Dividing both sides by 36, we get:

(0.9)ˣ = 1/12

Taking the logarithm of both sides (with base 0.9), we get:

x = log(1/12) / log(0.9) ≈ 11.5

So, it would take about 12 clicks of the zoom-out button to transform the display of the door from 3 feet wide back to a width of approximately 3 inches.

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Nelson lands 4650 on 2% interest rate. He plans to pay this after 2 months. What will the total principal and interest payment be?

Answers

The total principal and interest payment that Nelson will have to pay after 2 months is $4665.50.

To calculate the total principal and interest payment, we need to determine the interest amount and add it to the principal.

First, let's find the interest amount:

Interest = Principal x Interest Rate x Time

Given:

Principal = $4650

Interest Rate = 2% per year

Time = 2 months

Since the interest rate is given on an annual basis, we need to convert the time from months to years. There are 12 months in a year, so 2 months is equivalent to 2/12 = 1/6 years.

Interest = $4650 x 0.02 x (1/6) = $15.50

Now, we can calculate the total principal and interest payment:

Total Payment = Principal + Interest

Total Payment = $4650 + $15.50 = $4665.50

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En un cuadrado de 10 cm por 10 cm pinta de
forma creativa el 30 % de su área y encuentra
la fracción correspondiente.​

Answers

El área del cuadrado de 10 cm por 10 cm es:

10 cm x 10 cm = 100 cm²

Para encontrar el 30% del área del cuadrado, multiplicamos el área por 0.3:

100 cm² x 0.3 = 30 cm²

Por lo tanto, el área que se debe pintar de forma creativa es de 30 cm².

La fracción correspondiente se obtiene dividiendo el área que se debe pintar por el área total del cuadrado:

30 cm² / 100 cm² = 3/10

Por lo tanto, la fracción correspondiente es 3/10.

?????????? WHAT ??????????

?????????? WHAT ??????????

Answers

The area of square’s formula is length x length= answer^(2)
Or
Length^(2) = answer
Don’t forget to add the unit
?????????? WHAT ??????????

Answer:

Side of the square (a) = 3½ = 7/2 m

Area of the square

= a²

= (7/2)²

= 49/4

= 12.25 m²

Hope it helps ⚜

The graph below shows the line y=[x]. If the line y=|x|*2 were graphed on the same grid, hc would it compare to the line shown in the graph below. ​

Answers

The graph of the function y = 2|x| is a vertical stretch by a factor of 2 of the parent function y = |x|.

How to identify the transformation?

The functions for this problem are defined as follows:

Parent function: y = |x|.Transformed function: y = 2|x|.

When a function is multiplied by 2, we have that it is vertically stretched by a factor of 2.

Hence the graph of the function y = 2|x| is a vertical stretch by a factor of 2 of the parent function y = |x|.

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Chay is buying mulch for the zoo's summer flower beds. She has enough in her budget to purchase 55 bags of mulch. If there are 20 flower beds, how many bags of mulch can be used in each flower bed?

Answers

Chay can use 3 bags of mulch per flower bed.

Chay is buying mulch for the zoo's summer flower beds. She has enough in her budget to purchase 55 bags of mulch. If there are 20 flower beds, how many bags of mulch can be used in each flower bed?The number of bags of mulch that can be used in each flower bed can be found by dividing the total number of bags of mulch by the number of flower beds, as given by the problem.Let X be the number of bags of mulch used in each flower bed. Then, the following equation can be written:Total number of bags of mulch = X × number of flower beds (20)Or, 55 = 20XDividing both sides of the equation by 20, we get: X = 55/20X = 2.75.Therefore, Chay can use 2.75 bags of mulch in each flower bed. However, since we cannot have a fraction of a bag of mulch, she would have to round up to 3 bags of mulch per flower bed to ensure each flower bed has enough mulch.

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number of apples (x) 3 5 8 11 cost (y) $2.37 $3.95 $6.32 $8.69 assume the cost of apples is a linear function of the number of apples purchased. part a write a linear equation that describes the cost of apples, y , in dollars, as a linear function of the number of apples purchased, x .

Answers

The linear equation which  describes the cost of apples, y , in dollars, as a linear function of the number of apples purchased x is ,

m = y2 - y1 / x2 - x1.

where the given values are ,

3=x1 , 5=x2, 2.37=y1 ,3.95=y2

Therefore,

m = 3.95 - 2.37 / 5 - 3

=1.58 / 2

0.79

and then ,

y - 2.37 = 0.79( x - 3 )

y=0.79x

A mathematical equation can be defined in a variety of ways. In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal.

3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. In mathematics, the most basic and simple algebraic equations consist of one or more variables.

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Carns Company is considering eliminating its Small Tools Division, which reported a loss for the prior year of $205,000 as shown below. Segment Income (Loss) Sales $ 1,430,000 Variable costs 1,295,000 Contribution margin 135,000 Fixed costs 340,000 Income (loss) $ (205,000) If the Small Tools Division is dropped, all of its variable costs are avoidable, and $119,000 of its fixed costs are avoidable. The impact on Carns’s income from eliminating the Small Tools Division would be: Multiple Choice

Answers

The impact on Carns Company's income from eliminating the Small Tools Division would be a decrease of $1,209,000.

To determine the impact on Carns Company's income from eliminating the Small Tools Division, we need to consider the avoidable costs associated with the division.

The avoidable costs include all of the variable costs of the division and a portion of the fixed costs that are specifically related to the Small Tools Division. In this case, the variable costs of the division are $1,295,000, and $119,000 of the fixed costs are avoidable.

To calculate the impact on income, we subtract the avoidable costs from the loss reported by the division:

Impact on income = Loss - Avoidable costs

Impact on income = $205,000 - ($1,295,000 + $119,000)

Impact on income = $205,000 - $1,414,000

Impact on income = -$1,209,000

The negative sign indicates a decrease in income.

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Help! This is timed!

Help! This is timed!

Answers

Answer: 5 ft i think so

Use the Pythagorean theorem

Help! This is timed!

Oliver and Chen both write down a number. Oliver says, my number has 8 hundreds and Chen's number only has 3 hundreds my number must be bigger. Oliver is not correct. explain why

Answers

Oliver's number is bigger than that of Chen.

What are hundreds in a number?

It is a number equal to 10 times 10.

Given is that Oliver and Chen both write down a number. Oliver says, my number has 8 hundreds and Chen's number only has 3 hundreds, my number must be bigger.

Oliver number can be written as follows -

8 x 10 x 10

Chens number can be written as follows -

3 x 10 x 10

It can be concluded that Oliver's number is bigger than that of Chen.

Therefore, Oliver's number is bigger than that of Chen.

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a significant positive correlation is found between variables x and y. which of the following may be safely inferred?

Answers

It can be inferred that as one variable increases, so does the other. Additionally, a change in one variable is likely to be accompanied by a corresponding change in the other.

A significant positive correlation between two variables means that as one variable increases, the other also increases. This implies that when one variable changes, the other is likely to follow suit. For example, if Variable X increases, Variable Y is likely to increase as well. This can be interpreted as a direct relationship between the two variables. Additionally, a significant positive correlation indicates that the two variables have a strong relationship, meaning that as one variable increases or decreases, the other is likely to follow suit. This can be used to help make predictions and draw conclusions about the relationship between the two variables.

The complete question: A significant positive correlation is found between variables x and y. Which one of the following may be safely inferred? a. As x increases, y increases. b. As x increases, y decreases. c. y causes x. d. x causes y.

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I NEED HELP WITH THIS QUESTION PLEASE NO LINKS!!!
Where would the point go

I NEED HELP WITH THIS QUESTION PLEASE NO LINKS!!!Where would the point go

Answers

\( - 1 - ( - 8) \\ = - 1 + 8 \\ = 7\)

Hope it helps

ray4918 here to help

I NEED HELP WITH THIS QUESTION PLEASE NO LINKS!!!Where would the point go

Please awnser asap I will brainlist

Please awnser asap I will brainlist

Answers

Using simultaneous equation, the solution to the system of linear equations are 1223 $10 tickets, 1332 $20 tickets, and 763 $30 tickets were sold.

How many tickets of each kind has been sold?

Let's solve the problem step by step.

Let:

x = number of $10 tickets sold

y = number of $20 tickets sold

z = number of $30 tickets sold

From the given information, we can form the following equations:

Equation 1: x + y + z = 3318 (Total number of tickets sold)

Equation 2: y = x + 109 (109 more $20 tickets than $10 tickets were sold)

Equation 3: 10x + 20y + 30z = 61760 (Total sales from ticket sales)

We can use these three equations to solve for the values of x, y, and z.

First, let's substitute Equation 2 into Equation 1:

x + (x + 109) + z = 3318

2x + 109 + z = 3318

2x + z = 3209 (Equation 4)

Now, let's substitute the value of y from Equation 2 into Equation 3:

10x + 20(x + 109) + 30z = 61760

10x + 20x + 2180 + 30z = 61760

30x + 30z = 59580

x + z = 1986 (Equation 5)

We now have a system of equations (Equations 4 and 5) with two variables (x and z). We can solve this system to find the values of x and z.

Multiplying Equation 4 by 30, and Equation 5 by 2, we get:

60x + 30z = 96270 (Equation 6)

2x + 2z = 3972 (Equation 7)

Now, subtract Equation 7 from Equation 6:

(60x + 30z) - (2x + 2z) = 96270 - 3972

58x + 28z = 92298

Simplifying, we have:

29x + 14z = 46149 (Equation 8)

Now, we can solve Equations 5 and 8 simultaneously:

x + z = 1986 (Equation 5)

29x + 14z = 46149 (Equation 8)

Multiplying Equation 5 by 14, and Equation 8 by 1, we get:

14x + 14z = 27804 (Equation 9)

29x + 14z = 46149 (Equation 8)

Now, subtract Equation 9 from Equation 8:

(29x + 14z) - (14x + 14z) = 46149 - 27804

15x = 18345

Divide both sides of the equation by 15:

x = 18345 / 15

x = 1223

Substituting the value of x into Equation 5, we can find z:

1223 + z = 1986

z = 1986 - 1223

z = 763

Now that we have the values of x and z, we can substitute them back into Equation 1 to find y:

1223 + y + 763 = 3318

y + 1986 = 3318

y = 3318 - 1986

y = 1332

Therefore, the solution to the problem is:

x = 1223 (number of $10 tickets sold)

y = 1332 (number of $20 tickets sold)

z = 763 (number of $30 tickets sold)

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Can someone help me please

Can someone help me please

Answers

Answer:

A. addition property of equality

Step-by-step explanation:

To make x stand alone, "5" was added to both sides of the equation. The property that is applied here is the addition property of equality.

Adding "5" to both sides of the equation makes the equation balanced.

The answer is: A. addition property of equality

Given the following five-number summary, find Q₁.
2.9, 5.7, 10.0, 13.2, 21.1
OA. 5.7
OB. 2.9
OC. 10.0

Answers

Given the following five-number summary: 2.9, 5.7, 10.0, 13.2, 21.1, so Q₁ = 5.7. This can be solved using the concept of quartile.

What is quartile?

A kind of percentile is a quartile. The first quartile (Q₁, or the lowest quartile), which corresponds to the 25th percentile of the data, is below which 25% of the data are found. The second quartile (Q₂, or the median), which represents the 50th percentile, indicates that 50% of the data are below this quartile.

There are 5 data points, and the middle value of the lower half of the data set will represent the first quartile. So the second data value is the first quartile. So, Q₁ = 5.7

There are 5 data points, and the middle value of the upper half of the data set will represent the third quartile. The fourth data value is the third quartile. So,

Q₃ = 13.2

SO IQR will be:

= Q₃ - Q₁

= 13.7 - 5.1

= 7.5

Thus, Q₁ = 5.7

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Ramesh dan syarika ans. Ramesh takes a medical and health insurance policy with a deductible of RM1 500 per year and co-insurance of 20% of covered medical expenses. Ramesh went to the hospital for the first time for knee treatment and the medical cost was RM700, the medical cost for the second and third treatments was RM2 000 and RM1 700 respectively. The three treatments were in the same year. How much medical expenses should be borne by Ramesh and the insurance company? ​

Answers

Ramesh will bear a total medical expense of RM1,760, and the insurance company will cover RM2,900.

1. Ramesh's deductible is RM1,500 per year. This means that he is responsible for paying the first RM1,500 of medical expenses before the insurance coverage kicks in.

2. For the first treatment, the medical cost was RM700. Since this amount is less than the deductible, Ramesh will have to pay the entire RM700 out of pocket.

3. For the second treatment, the medical cost was RM2,000. Since Ramesh has already met his deductible with the first treatment, the insurance company will cover a portion of the expenses. Ramesh will be responsible for 20% of the remaining RM500 (RM2,000 - RM1,500), which amounts to RM100. The insurance company will cover the remaining 80% of RM500, which amounts to RM400.

4. For the third treatment, the medical cost was RM1,700. Again, since Ramesh has already met his deductible, the insurance company will cover a portion of the expenses. Ramesh will be responsible for 20% of the entire cost, which amounts to RM340 (20% of RM1,700). The insurance company will cover the remaining 80% of RM1,700, which amounts to RM1,360.

5. To calculate the total medical expenses borne by Ramesh, we add up the amounts he is responsible for in each treatment: RM700 + RM100 + RM340 = RM1,140.

6. The total medical expenses covered by the insurance company can be calculated by adding up the amounts they pay in each treatment: RM400 + RM1,360 = RM1,760.

7. Finally, to find the overall amount borne by Ramesh and the insurance company, we sum up the individual expenses: Ramesh's expenses + insurance company's expenses = RM1,140 + RM1,760 = RM2,900.

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what multiplies to -65 and adds to -8

Answers

Answer: The two numbers that multiply to -65 and add to -8 are -13 and 5.

Steps: Here are the steps to find two numbers that multiply to -65 and add to -8:

Write down the equation x * y = -65 where x and y are the two numbers you’re looking for.

Write down the equation x + y = -8.

Solve for one of the variables in one of the equations. For example, solving for x in the second equation gives us x = -8 - y.

Substitute this expression for x into the first equation: (-8 - y) * y = -65.

Solve this quadratic equation for y: -y^2 - 8y + 65 = 0.

Use the quadratic formula to find the values of y: y = (-(-8) +/- sqrt((-8)^2 - 4 * (-1) * 65)) / (2 * (-1)).

This gives us two possible values for y: -13 and 5.

Substitute these values back into one of the original equations to find the corresponding values of x. For example, when y = -13, we have x = -8 - (-13) = 5. When y = 5, we have x = -8 - 5 = -13.

So, the two numbers that multiply to -65 and add to -8 are -13 and 5.

NO LINKS!! Each graph represents a relation. Determine the domain and range. 2ii​

NO LINKS!! Each graph represents a relation. Determine the domain and range. 2ii

Answers

Answer:

7)  Domain:  (-∞, ∞)

    Range:  [-1, ∞)

8)  Domain:  (-∞, ∞)

    Range:  (-∞, ∞)

Step-by-step explanation:

Interval notation

( or ) : Use parentheses to indicate that the endpoint is excluded.

[ or ] : Use square brackets to indicate that the endpoint is included.

Domain & Range

The domain is the set of all possible input values (x-values).

The range is the set of all possible output values (y-values).

Question 5

From inspection of the graph, the line is continuous.

The arrows either end of the line indicate that the line continues indefinitely in those directions.

Therefore, the domain of the relation is unrestricted:  (-∞, ∞)

From inspection of the graph, the minimum y-value is y = -1.  

The end behavior of the relation is:

\(y \rightarrow + \infty, \textsf{as } x \rightarrow - \infty\)

\(y \rightarrow + \infty, \textsf{as } x \rightarrow +\infty\)

Therefore, the range of the relation is restricted:  [-1, ∞)

Question 6

From inspection of the graph, the line is continuous.

The arrows either end of the line indicate that the line continues indefinitely in those directions.

Therefore, the domain of the relation is unrestricted:  (-∞, ∞)

The end behavior of the function is:

\(y \rightarrow + \infty, \textsf{as } x \rightarrow - \infty\)

\(y \rightarrow -\infty, \textsf{as } x \rightarrow +\infty\)

Therefore, the domain of the relation is unrestricted:  (-∞, ∞)

A number line going from negative 3 to positive 5. A closed circle is at 2. Everything to the right of the circle is shaded. Which inequality is graphed? 2 < x 2 > x 2 Less-than-or-equal-to x 2 Greater-than-or-equal-to x

Answers

Answer:

2 Less-than-or-equal-to x

Step-by-step explanation:

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