The expected result for each shot is a loss of $ 12.50, so if 100 people played, Sophie would win on average about $ 1250. Lastly, Sophie should charge $ 5.77 for this value to be fair.
Since Sophie charges you $ 25 to get a chance to shoot at a target, and if you hit the bullseye, you get a $ 100 (win $ 75), and if you miss the bullseye but are within two circles of it, you get your money back, and over the course of sophies career, she finds that 5% of people hit the bullseye and 30% of people miss but are within two circles, while all other contestants miss by further and lose; to determine what is the expected amount for you to win or lose; how much money would you expect Sophie to win or lose if 100 people played the game; and what should she charge to make this game fair, the following calculations must be performed:
(75 x 5 + -25 x 65) / 100 = X (375 - 1625) / 100 = X -1250 / 100 = X -12.5 = X
375 + 65X = 0 65X = 375 X = 375/65 X = 5.77
Therefore, the expected result for each shot is a loss of $ 12.50, so if 100 people played, Sophie would win on average about $ 1250. Lastly, Sophie should charge $ 5.77 for this value to be fair.
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On the highway, a car can travel 21 miles per gallon of gas. If the car travels for 4 hours on the highway at a rate of 65 miles per hour, how many gallons of gas should the car use, to the nearest tenth of a gallon?
Answer:
5.36
Step-by-step explanation:
If the car travels for 4 hours on the highway at a rate of 65 miles per hour,12.4 gallons of gas should the car used, to the nearest tenth of a gallon.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that a car can go 21 miles per gallon of gas on a highway and that the car can travel for 4 hours at a speed of 65 miles per hour.
As a result, the distance traveled by car,
Distance = speed × time
Distance = 65 miles / hr × 4 hr
Distance = 260 miles
The number of gallons of gas the car should consume is determined by dividing the entire distance driven by the per gallon of gas as follows:
= 260 miles / 21 miles per gallon
= 12.38 gallon
The value nearest tenth of a gallon is,
=12.4 gallons
Thus, if the car travels for 4 hours on the highway at a rate of 65 miles per hour,12.4 gallons of gas should the car used, to the nearest tenth of a gallon.
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Urgent!
18. A tennis ball is launched straight upward with an initial velocity of 24.5 m/s from the edge of a cliff that is 117.6 meters above the ground. Which quadratic equation could be used to correctly determine when the ball will hit the ground:
4.9t2 + 24.5t + 117.6 = 0
-4.9t2 - 24.5t + 117.6 = 0
-4.9t2 + 24.5t - 117.6 = 0
4.9t2 + 24.5t - 117.6 = 0
-4.9t2 + 24.5t + 117.6 = 0
19. Solve the equation you chose in question 18 to determine when the ball will hit the ground. (HINT: If you don't get one of the answers listed for this question, then maybe you chose the wrong equation in #18. Use this opportunity to double check your work!)
t = 8 seconds
t = 4 seconds
t = 3 seconds
t = -3 seconds
The ball will never reach the ground.
20. Using the same equation, determine when the ball is at a height of 49 meters.
Step-by-step explanation:
18.
the last one.
-4.9t² + 24.5t + 117.6 = 0
the ball starts at 117.6 meters height. then, during the first seconds the thrust upwards is adding height, until finally, with more and more seconds passing, gravity will win with a vengeance and pulls the ball down faster and faster than any other force in any other direction.
19.
the general solution for a quadratic equation
y = ax² + bx + c
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = t
a = -4.9
b = 24.5
c = 117.6
t = (-24.5 ± sqrt(600.25 - -4×4.9×117.6))/-9.8 =
= (-24.5 ± sqrt(600.25 + 2304.96))/-9.8 =
= (-24.5 ± sqrt(2905.21))/-9.8 = (-24.5 ± 53.9)/-9.8
t1 = (-24.5 + 53.9)/-9.8 = -3
t2 = (-24.5 - 53.9)/-9.8 = 8
a negative time does not make any sense, so the real solution is : the ball reached the ground after 8 seconds.
20.
now the equation is
-4.9t² + 24.5t + 117.6 = 49
but this is quickly transformed again into a "= 0" equation :
-4.9t² + 24.5t + 68.6 = 0
t = (-24.5 ± sqrt(600.25 - -4×4.9×68.6))/-9.8 =
= (-24.5 ± sqrt(600.25 + 1344.56))/-9.8 =
= (-24.5 ± sqrt(1944.81))/-9.8 = (-24.5 ± 44.1)/-9.8
t1 = (-24.5 + 44.1)/-9.8 = -2
t2 = (-24.5 - 44.1)/-9.8 = 7
again, negative time does not make sense.
the ball will be at 49 m height after 7 seconds.
what is the scale factor of 3x + 2, 3y -1?
(will give brainliest)
21 Line is mapped onto line m by a dilation centered at the origin with a scale factor of 2. The equation of line is 3x − y = 4. Determine and state an.
A large container in the shape of a rectangular solid must have a volume of 480 m3. The bottom of the container costs $5/m2 to construct whereas the top and sides cost $3/ m2 to construct. Use Lagrange multipliers to find the dimensions of the container of this size that has the minimum cost
The dimension of the container of this size that has the minimum cost is [tex]x = \sqrt[3]{360}[/tex], [tex]y = \sqrt[3]{360}[/tex] and [tex]z =\frac{4}{3} \sqrt[3]{360}[/tex]
The given parameters are:
Volume = 480m^3Cost: $5 per square meter for the bottom, and $3 per square meter for the sides.Assume the dimensions of the container are: x, y and z.
The volume (V) would be:
[tex]V = xyz[/tex]
Substitute 480 for V
[tex]xyz =480[/tex]
And the objective cost function would be:
[tex]C =8xy + 6xz + 6yz[/tex]
Differentiate the cost function using Lagrange multipliers
[tex]8x + 6z = \lambda xz[/tex]
[tex]8y + 6z = \lambda yz[/tex]
[tex]6x + 6y = \lambda xy[/tex]
Divide equation (1) by (2)
[tex]\frac{8x + 6z}{8y + 6z} = \frac{\lambda xz}{\lambda yz}[/tex]
[tex]\frac{8x + 6z}{8y + 6z} = \frac{x}{y}[/tex]
Factor out 2
[tex]\frac{4x + 3z}{4y + 3z} = \frac{x}{y}[/tex]
Cross multiply
[tex]4xy + 3yz = 4xy + 3xz[/tex]
Evaluate the like terms
[tex]3yz = 3xz[/tex]
Divide both sides by 3z
[tex]y = x[/tex]
Divide the first equation by the third
[tex]\frac{8y + 6z}{6x + 6y} = \frac{\lambda yz}{\lambda xy}[/tex]
[tex]\frac{8y + 6z}{6x + 6y} = \frac{z}{x}[/tex]
Factor out 2
[tex]\frac{4y + 3z}{3x + 3y} = \frac{z}{x}[/tex]
Cross multiply
[tex]4xy+3xz = 3xz + 3yz[/tex]
Cancel out the common terms
[tex]4xy = 3yz[/tex]
Divide both sides by y
[tex]4x = 3z[/tex]
Make z the subject
[tex]z =\frac{4}{3}x\\[/tex]
So, we have:
[tex]y = x[/tex] and [tex]z =\frac{4}{3}x\\[/tex]
Recall that:
[tex]xyz =480[/tex]
Substitute [tex]y = x[/tex] and [tex]z =\frac{4}{3}x\\[/tex]
[tex]x \times x \times \frac 43x = 480[/tex]
So, we have:
[tex]\frac 43x^3 = 480[/tex]
Multiply both sides by 3/4
[tex]x^3 = 360[/tex]
Take the cube roots of both sides
[tex]x = \sqrt[3]{360}[/tex]
Recall that:
[tex]y = x[/tex]
So, we have:
[tex]y = \sqrt[3]{360}[/tex]
Also, we have:
[tex]z =\frac{4}{3}x\\[/tex]
So, we have:
[tex]z =\frac{4}{3} \sqrt[3]{360}[/tex]
Hence, the dimension of the container of this size that has the minimum cost is [tex]x = \sqrt[3]{360}[/tex], [tex]y = \sqrt[3]{360}[/tex] and [tex]z =\frac{4}{3} \sqrt[3]{360}[/tex]
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PLEASE HELP QUESTION IN PICTURE 15 POINTS
Jessica is wrapping a gift in a rectangular box with gift wrapping paper for a birthday party. The box is 11 inches long, 8 inches wide, and 5 inches tall. How much gift wrapping paper will she need to wrap the box
Using the surface area of a rectangular prism, it is found that she will need 366 square inches of wrapping paper to wrap the box.
He wraps the box with paper outside, hence, the amount needed is the surface area.
Surface area:The surface area of a rectangular prism of length l, width w and height h is given by:
[tex]S = 2(lw + lh + wh)[/tex]
In this problem, the dimensions of 11 inches long, 8 inches wide, and 5 inches tall mean that [tex]l = 11, w = 8, h = 5[/tex]. Hence:
[tex]S = 2[11(8) + 11(5) + 8(5)] = 366[/tex]
She will need 366 square inches of wrapping paper to wrap the box.
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A car travels 182 kilometers in 4 hours with the constant speed. how much time will it take traveling 42 kilometers
Answer:
55.38 min
Step-by-step explanation:
A car travels,
182 km ⇒ 4 hours
And we have to find the time that it takes to travel 42 km .
Lets make a equation.
Let the unknown time be x
182 km ⇒ 4 hours
42 km ⇒ x
To make easy let's km in to meters and hours in to minutes
182000 m ⇒ 240 min
42000m ⇒ x
Now use cross multiplication.
[tex]182000x=240*42000\\[/tex]
[tex]182000x=10080000[/tex]
[tex]\frac{182000x}{182000} =\frac{1008000}{182000}[/tex]
[tex]x =55.38min[/tex]
Hope this helps you.
Let me know if you have any other questions :-)
The art club in Northwestern middle school is selling candy bars as a fundraiser. each art club member....
Twenty is what percent of 25?
Answer:
80%
Step-by-step explanation:
20:25*100 =
(20*100):25 =
2000:25 = 80
Now we have: 20 is what percent of 25 = 80
Question: 20 is what percent of 25?
Percentage solution with steps:
Step 1: We make the assumption that 25 is 100% since it is our output value.
Step 2: We next represent the value we seek with $x$.
Step 3: From step 1, it follows that $100\%=25$.
Step 4: In the same vein, $x\%=20$.
Step 5: This gives us a pair of simple equations:
$100\%=25(1)$.
$x\%=20(2)$.
Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS
(left hand side) of both equations have the same unit (%); we have
$\frac{100\%}{x\%}=\frac{25}{20}$
Step 7: Taking the inverse (or reciprocal) of both sides yields
$\frac{x\%}{100\%}=\frac{20}{25}$
$\Rightarrow x=80\%$
Therefore, $20$ is $80\%$ of $25$.
Hopes This Helps :)
Find the angle measure
<ABD and <EBC are equal to each other. In order to solve for the x value, set the equations equal to each other;
4x = 2x + 40,
x = 20
Based off what angle you are trying to find, you would plug x = 20 into the equation.
Write an equation for the proportional relationship shown in the table.
Answer:
y = 14x
Step-by-step explanation:
First Way of Finding the Equation:
We can find the equation for this proportional relationship by subtracting two of the y-values from each other and then dividing that by the difference of two of the x-values. For now, I'll use the points (2, 28) and (1, 14).
[tex]\frac{28-14}{2-1} =\frac{14}{1} =14[/tex]
So, this proportional relationship has an equation of y = 14x.
Second Way of Finding the Equation:
Another way of finding the equation is to simply examine the table given. What are all the x-values multiplied by to get to their corresponding y-values? Well, one easy way of answering this question is looking at the point (1, 14) - 1 × 14 = 14, so the constant of proportionality must be 14.
From this information, we know that the equation must be y = 14x.
Hopefully that's helpful! :)
The scatter plot shows the number of minutes since several celebrities have posted a photo compared to the number of likes the photo has received. If a celebrity posted a photo 6.5 minutes ago, which is the best prediction of the number of likes it has received?
Answer:
is there a photo of a scatter plot?
Step-by-step explanation:
there were 8000 people at a festival. people bought their tickets online, by phone, or in person.based on a random sample of people at the festival, 60% bought their tickets online, 15% bought their tickets by phone, and the rest bought their tickets in person
Answer:
People who bought tickets = 100%
= 8000
People who bought their tickets in person = (100%-60%-15%) × 8000
= 2000
The number of tickets sold online is 4800, by phone is 1200, and in person is 2000.
What is the percentage?The Percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that there were 8000 people at the festival. people bought their tickets online, by phone, or in person. based on a random sample of people at the festival, 60% bought their tickets online, and 15% bought their tickets by phone.
The number of the tickets will be calculated as below:-
Total tickets = 8000
Online tickets = 60% of 8000 = 8000 x 0.6 = 4800
By phone = 15% of 8000 = 8000 x 0.15 = 1200
In-person = 25% x 8000 = 0.25 x 89000 = 2000
Therefore, the number of tickets sold online is 4800, by phone is 1200, and in person is 2000.
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If one lap takes me 11 minutes and 10 seconds how long will it take me to do 10 laps
Answer:
111 minutes and 40 sec
Step-by-step explanation:
11x10=110 minutes
10 sec x 10 = 100 seconds = 1 minute 40 sec
110 minutes+1 minute+40 seconds= 111 minutes and 40 seconds
find the measure of angle A
Answer:
60° is your answerStep-by-step explanation:
the sum of the interior angles of a triangle is 180°
180 - 70 = 110
110 = 12x + 2 + 15x
108 = 27x
108 : 27 = 4°
4 * 15 = 60° is your answer
check
15 * 4 + 12 * 4 + 2 + 70 = 180
60 + 48 + 72 = 180
the answer is good
Suppose that n is a positive number and Log10 n = q. Which expression always equals the value of Log10 n^2?
2q
Answer:
solution given:
[tex]log_{10} n=q[/tex]
now
[tex] Log_{10 }n^2=?[/tex]
by using property of logarithms
[tex]log_{a} n^p=p log_{a}n [/tex]
now
[tex] Log_{10 }n^2=2 Log_{10 }n[/tex]
=2q
since [tex]log_{10} n=q[/tex]
Step-by-step explanation:
how many solutions does the quadratic function f(x)=-x²
Answer: 4
Step-by-step explanation:
Slope = -2.000/2.000 = -1.000
x-intercept = 0/1 = 0.00000
f-intercept = 0/1 = 0.00000
x = 0
The opposite of −358 is on the
(same or opposite)
side of zero on a number line as −358. The opposite of 429is on the
(same or opposite)
side of zero on a number line as 429.
Answer:
A: Opposite
B: Same
Step-by-step explanation:
I'm not really sure, please tell me if I'm incorrect
The total bill was 56.25. how much would the bill be if 7 % tax was added
A construction crew is paving a road. The crew has already paved 1,000 square feet and can pave at a rate of 300 square feet of road per hour. The function f(x) = 300x + 1,000 represents this situation.
What is f(3), and what does it represent?
900 square feet; f(3) represents the number of additional square feet the construction crew has paved after 3 hours, not including the initial paved amount.
900 square feet;, f, (3) represents the number of additional square feet the construction crew has paved after 3 hours, not including the initial paved amount.
900 square feet; f(3) represents the total number of square feet the construction crew has paved after 3 hours.
900 square feet; , f, (3) represents the total number of square feet the construction crew has paved after 3 hours.
1,900 square feet; f(3) represents the number of additional square feet the construction crew has paved after 3 hours, not including the initial paved amount.
1,900 square feet;, f, (3) represents the number of additional square feet the construction crew has paved after 3 hours, not including the initial paved amount.
1,900 square feet; f(3) represents the total number of square feet the construction crew has paved after 3 hours.
Answer:
1,900 square feet; f(3) represents the total number of square feet the construction crew has paved after 3 hours.
The function of the construction crew is an illustration of a linear function
The value of f(3) is 1900, and f(3) represents the total number of square feet paved after working for 3 hours
The function is given as:
To calculate f(3), we substitute 3 for x
Multiply 300 and 3
Add 900 and 1000
This means that the value of f(3) is 1900.
And it represents the total number of square feet paved after working for 3 hours
1,900 square feet; f(3) represents the total number of square feet the construction crew has paved after 3 hours.
Which graph represents the solution set of the system of inequalities?
{y<2x+2x+y≥−3
Answer: the first graph (A)
Step-by-step explanation: are you actually low IQ or intellect this is the most easiest question I have ever seen I just finished this topic in my honor math class like last month in a week. BTW I am in the 9th grade
Now I got to tutor you so here you can use the process of elimination which you can see that < without the line below it means that the line is dotted and is the only one with a y-intercept of +2 is A and D are the only ligament answer now you dumc as i can't curse due to that i will get reported, so anyways go up 2 and go 1 to the right because it is 2x which is 2/1x rise/run and it is positive which means D is wrong because it has a negative slope which the only answer for this is A now get your (can't say) together and study.
Solve for X please and thank you
Answer:
x = 48
Step-by-step explanation:
Given a secant and a tangent from an external point to the circle, then
the product of the external part and the entire secant is equal to the square of the measure of the tangent , that is
2(2 + x) = 10² = 100 ( divide both sides by 2 )
2 + x = 50 ( subtract 2 from both sides )
x = 48
y varies directly as x . when x=3 , then y=12 . find y when x=20.
Answer:
Congress. would equal 80 due to x being worth 1/4 of y's total.
Find x, y, and z. Drag and drop the numbers into the boxes to show the value of each variable.
Answer:
x=186.68
y=140
z=233.34
Step-by-step explanation:
easy method to solve since you have the answers to pick from
first triangle. we have two sides 175 and 105 and we know that 175 have to be the largest number, its the hypotenuse. which means
y=140,
cannot be 233 or 186 because both greater than 175
now next triangle. x-y-z, we already know "y" and "z" needs to be the largest number so it has to be
z= 233.34 and finally
x=186. 67
help me with this pls
Answer:
Johnathan started out with 17 videogames
25-8=17
Jonita determined that the distance between her apartment and the nearest hospital was more than 1,600 meters but less than 1,900 meters. Which of the following could be a reasonable estimate for
the distance between her house and the hospital?
O 1.7 x 102 meters
O 1.8 x 103 meters
O 1.7 x 10-3 meters
O 1.8 x 10-2 meters
Answer: 1.8 x 103 meters
Step-by-step explanation:
The average of the two extremes is 1,700 meters. This would be 1.7x10^3 in scientific notation. None of the four options include this number. But three stand out as total losers. We can convert the answer options to see the difference:
O 1.7 x 102 meters = 170 meters [Loser]
O 1.8 x 103 meters = 1800 meters
O 1.7 x 10-3 meters = 0.0017 meters [Loser]
O 1.8 x 10-2 meters = 0.018 meters [Loser]
Find the commission 700 sales and 6% commmision rate
Answer: How to calculate commission. This is a very basic calculation revolving around percents. Just take sale price, multiply it by the commission ...
Step-by-step explanation:
The angle DEF has measure 75*. What type of angle is it?
Answer:
Acute angle
Step-by-step explanation:
Angles smaller than 90 degrees are acute
hope it helps :)
Given: AB IS CONGRUENT TO CD
PROVE: CD CONGRUENT TO AB
Answer:
Because of the definition of congruent
Step-by-step explanation:
This problem may sound tricky, but it's not actually that hard. We now congruent means two things are the same, so for this problem, think of it as an equal sign. (Congruent doesn't mean equal, as an equal sign denotes the relationship that two things are the same if we know the concrete value of it.) So if AB=CD, CD=AB as you can swap two sides of an equation around and get the same answer. It's like saying 2=x ∴ x=2 (The dots mean therefore in math.)
Please consider a brainliest! Thank you!
what inequality does the number line graph represent
Answer: what number line
Step-by-step explanation: