Neil will be able to receive Olga's weather updates for a distance of 10 miles on the road.
What is equation?Equation is a mathematical statement that expresses the equality of two expressions. It is usually written using symbols, such as '=', '<', '>', '+', and '-'. Equations can be used to describe, model, and solve real-world problems. They can also be used to predict the behavior of a system or to find unknown values.
To calculate the approximate number of miles Neil will be able to receive Olga's weather updates, a quadratic equation can be used. The equation is as follows:
A = (x - 15)²+ (y - 15)² <= 100
where A is the area of a circle with a radius of 10 miles, centered at the ranger station, and (x,y) is the position of Neil's car on the road. The equation represents the area that is within the range of Olga's walkie-talkie, which is the area where Neil's car can receive Olga's weather updates.
To solve for x and y, we can use the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is equal to the square root of (x2 - x1)² + (y2 - y1)². Since we know the starting and ending points of Neil's road, we can use this formula to solve for x and y:
x = Square root of [ (10 - 15)² + (20 - 15)² ] = 10
y = Square root of [ (10 - 15)² + (10 - 15)² ] = 5
Substituting these values into the equation above, we get A = (10 - 15)² + (5 - 15)²= 100, which is Olga's walkie-talkie range. Therefore, Neil will be able to receive Olga's weather updates for a distance of 10 miles on the road.
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suppose that alpha and omega have identically sized working-age populations but that total annual hours of work are much greater in alpha than in omega. what are two possible reasons for this difference?
If workers in Alpha are more productive than those in Omega, they may be able to accomplish more work in the same amount of time, resulting in more total annual hours of work in Alpha. This could be due to a variety of factors, such as differences in technology, education levels, or infrastructure.
There could be several reasons why the total annual hours of work are much greater in Alpha than in Omega, even though both countries have identically sized working-age populations. Here are two possible reasons:
Differences in labor force participation: It is possible that a larger proportion of the working-age population in Alpha is participating in the labor force than in Omega. Labor force participation refers to the percentage of the working-age population that is either employed or actively seeking employment. If more people in Alpha are working or looking for work, then the total annual hours of work would be higher in Alpha than in Omega.
Differences in productivity: Another possible reason for the difference in total annual hours of work is differences in productivity levels between Alpha and Omega. Even if both countries have the same number of people in their working-age population, the productivity of those workers can vary significantly. If workers in Alpha are more productive than those in Omega, they may be able to accomplish more work in the same amount of time, resulting in more total annual hours of work in Alpha. This could be due to a variety of factors, such as differences in technology, education levels, or infrastructure.
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HELP! Georgie took 275 mg of medicine for her cold in the first hour she got home from work. In each subsequent hour, the amount of
medicine in her body is 91% of the amount from the previous hour.
What is the explicit rule for the amount of medicine remaining in her body in the nth hour and approximately how much medicine
would remain in the 8th hour?
Round to two decimal places.
Drag and drop the answers into the boxes to match the situation.
Explicit rule
Amount of medicine, in mg, during the 8th hour.
Answer:
here is the ananswer
Step-by-step explanation:
red go to red and black to black
the equations 6x + 5y = 28 and 10x + 14y = 58 represent the cost for lunch and dinner for a family eating out on vacation. if x is the number of adults and y is the number of children, how many adults are in the family?
There are 3 adults in the family by using the method of substitution and elimination.
What is Substitution?Substitution is a method used in mathematics to replace one or more variables in an equation or expression with a value or expression that is equivalent to the variable(s). This is done in order to simplify an equation or expression or to solve for a variable.
What is Elimination?Elimination is a method used in mathematics to solve a system of equations by eliminating one variable. This method involves manipulating the equations in such a way that one of the variables is eliminated, leaving a simpler equation with only one variable that can be solved easily.
In the given question,
Here's how we can solve for x, the number of adults:
Multiply the first equation by 2 to get rid of the coefficient of x in the second equation:
12x + 10y = 56
10x + 14y = 58
Subtract the first equation from the second equation to eliminate y:
10x + 14y - (12x + 10y) = 58 - 56
-2x + 4y = 2
Divide both sides by -2 to isolate x:
x - 2y = -1
x = 2y - 1
Substitute x = 2y - 1 into one of the original equations (let's use the first one) and solve for y:
6x + 5y = 28
6(2y - 1) + 5y = 28
12y - 6 + 5y = 28
17y = 34
y = 2
Substitute y = 2 into the equation x = 2y - 1 to solve for x:
x = 2(2) - 1
x = 3
Therefore, there are 3 adults in the family.
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The length in inches of each side of a square is given by the expression x 2 . the area of the square can be represented by (x 2)2−16=0 when the area is 16 square inches. what is the value of x?
The value of x is 2 inches.
We are given that the area of the square is 16 square inches and can be represented by the expression,
(x+2)^2 - 16 = 0
We can simplify this equation by expanding the square,
x^2 + 4x + 4 - 16 = 0
x^2 + 4x - 12 = 0
Now we can use the quadratic formula to solve for x
x = (-b ± sqrt(b^2 - 4ac)) / 2a
Where a = 1, b = 4, and c = -12.
Plugging in these values, we get
x = (-4 ± sqrt(4^2 - 4(1)(-12))) / 2(1)
x = (-4 ± sqrt(16 + 48)) / 2
x = (-4 ± sqrt(64)) / 2
x = (-4 ± 8) / 2
We get two solutions,
x = (-4 + 8) / 2 = 2
x = (-4 - 8) / 2 = -6
Since we are dealing with the length of a side of a square, we can eliminate the negative solution and conclude that the value of x is 2 inches.
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The given question is incomplete, the complete question is:
The length in inches of each side of a square is given by the expression x + 2 . the area of the square can be represented by (x+2)^2−16=0 when the area is 16 square inches. what is the value of x?
5
6
of the employees in a company are male.
7
8
of the male employees wear spectacles.
What fraction of the employees are males who wear spectacles?
Answer:
If 5/6 of the employees in a company are male, then the fraction of male employees in the company is:
5/6
If 7/8 of the male employees wear spectacles, then the fraction of male employees who wear spectacles is:
7/8
To find the fraction of employees who are males and wear spectacles, we need to multiply the fractions:
(5/6) x (7/8) = 35/48
Therefore, the fraction of employees who are males and wear spectacles is 35/48.
what is the center od dilation type ( Number, number)
the center of dilation for the triangle is (0,0)
Define center of dilationThe center of dilation is a point in a plane about which a dilation, a type of transformation, is performed. A dilation is a transformation that changes the size of a geometric figure, while preserving its shape and orientation. The center of dilation is the fixed point that serves as the reference for the scaling or shrinking of the figure.
In a dilation, each point of the original figure is moved away from or towards the center of dilation, by a certain factor called the scale factor.
The coordinate of yellow triangle and scaled triangle both passes through center of axes.
So, the center of dilation is (0,0).
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a lawn sprinkler sprays water 7 feet in every direction as it rotates. what is the area of the watered lawn? use 3.14 for π and be sure to put the correct unit of measure.
If a lawn sprinkler sprays water 7 feet in every direction as it rotates, the area of the watered lawn is approximately 153.94 square feet.
Assuming the sprinkler is placed at the center of the lawn, the area of the watered lawn can be found by calculating the area of a circle with a radius of 7 feet. The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.
Plugging in the given value of the radius, we get:
A = π(7 feet)^2
A = 153.94 square feet (rounded to two decimal places)
It's important to include the correct unit of measure, which is square feet in this case, to avoid confusion.
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Can the segment form a triangle? Why or why not?
A. 6 + 5 is not greater than twelve
B. Yes 6+5 is equal to twelve
C. No 6+5 is not equal to 12
D. Yes 6+5 equals less than twelve
Answer: b
Step-by-step explanation:
a reasonable abstraction for a car includes: group of answer choices an engine number of miles driven driving car color
Answer:
Of the given options, "an engine" is the most reasonable abstraction for a car.
An engine is a fundamental component of a car that powers its movement, and it is present in almost all cars. The number of miles driven and the driving car color are characteristics of a specific car rather than abstractions of a car itself. For example, a car can still be considered a car even if it has not been driven any miles yet or if it has no color at all.
Therefore, an engine is a more reasonable abstraction for a car as it captures an essential feature of a car that is present in all cars.
The solution is, D. Driving, a reasonable abstraction for a car includes. Driving is an action or behavior associated with a car, as it involves operating or using the car to travel from one place to another. It is an essential aspect of the car's purpose and function.
Here, we have,
we know that,
An engine is a machine designed to convert fuel into mechanical energy that can be used to power other machines or devices. In the context of automobiles, an engine is the primary source of power that drives the vehicle. It typically operates by burning fuel in a combustion chamber to generate high-pressure gases that drive a piston, which in turn rotates a crankshaft that ultimately powers the car's wheels.
Car color and number of miles driven are characteristics or properties of a car, while an engine is a component that helps to power the car. Driving, on the other hand, is an action or behavior associated with a car, as it refers to the act of operating or using the car to travel from one place to another.
Therefore, driving is a reasonable abstraction for a car, as it captures an essential aspect of the car's purpose and function.
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A right triangle has a leg of 9 cm and a hypotenuse of 18 cm.
What is the length of the other leg?
Round to the nearest tenth.
Answer:
Using the Pythagorean theorem, we know that:
a^2 + b^2 = c^2
where a and b are the legs of the right triangle, and c is the hypotenuse.
We can plug in the values given:
9^2 + b^2 = 18^2
Simplifying:
81 + b^2 = 324
b^2 = 243
b = sqrt(243) = 15.6 (rounded to the nearest tenth)
Therefore, the length of the other leg is approximately 15.6 cm.
Step-by-step explanation:
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a frozen food company uses a machine that packages okra in six ounce portions. a sample of 54 54 packages of okra has a variance of 0.44 0.44 . construct the 98% 98 % confidence interval to estimate the variance of the weights of the packages prepared by the machine. round your answers to two decimal places.
The confidence interval for variance is (0.29,0.58)
A family of continuous probability distributions is known as the chi-square (X2) distribution. They are frequently employed in hypothesis tests, such as the chi-square test of independence and the goodness of fit test.
The parameter k, which stands for the degrees of freedom, determines the shape of a chi-square distribution.
The distribution of real-world observations rarely has a chi-square shape. Chi-square distributions are primarily used for testing hypotheses rather than for modeling actual distributions.
Since we have given that the sample size n= 54,
variance = 0.44
we need to find a 98% confidence interval to estimate the variance.
So, we will use Chi-square distribution,
For this, we will find
df=n-1 = 54-1 = 53,
the interval would be,
[tex]\frac{(n-1)s^2}{X^2_{\alpha/2}} < \sigma^2 < \frac{(n-1)s^2}{X^2_{1-\alpha/2}}\\\\\alpha=1-0.98=0.02\\\\\alpha/2=0.02/2=0.01\\X^2_{0.01,53}=79.84\\Similarly\\\\1-\alpha/2=0.99\\\\X_{1-\alpha/2}^2,df=X^2_{0.99,53}=40.308\\\\So,\\\frac{53*0.44}{79.84} < \sigma^2 < \frac{53*0.44}{40.308}\\\\0.29 < \sigma^2 < 0.58[/tex]
Hence the confidence interval is (0.29,0.58)
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On a certain hot summers day, 402 people used the public swimming pool. The daily prices are 1. 50$ for children and 2. 00$ for adults. The receipts for admission totaled 648. 50$. How many children and how many adults swam at the public pool that day?
From the given information provided, there were 311 children who swam at the pool that day.
Let's use C to represent the number of children who swam at the pool and A to represent the number of adults who swam at the pool.
From the problem, we know that:
C + A = 402 (Equation 1) (The total number of people who used the pool was 402)
1.50C + 2.00A = 648.50 (Equation 2) (The total receipts from admission were $648.50)
To solve for C and A, we need to eliminate one of the variables. We can do this by multiplying Equation 1 by 1.50, which will give us:
1.50C + 1.50A = 603 (Equation 3)
Now we can subtract Equation 3 from Equation 2 to eliminate C:
2.00A - 1.50A = 648.50 - 603
0.50A = 45.50
A = 91
So there were 91 adults who swam at the pool that day. To find the number of children, we can substitute A = 91 into Equation 1:
C + 91 = 402
C = 311
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if the sun rotates once every 24.5 days at the equator, once every 24.8 days at latitude 15 degrees, and once every 34.3 days at the poles, what is the average number of days the sun takes to rotate once based on these three numbers?
Answer:
Step-by-step explanation:
To find the average number of days it takes for the sun to rotate once, we can add the three rotation periods and divide by 3:
Average rotation period = (24.5 + 24.8 + 34.3) / 3
Average rotation period = 83.6 / 3
Average rotation period = 27.87 days (rounded to two decimal places)
Therefore, the average number of days it takes for the sun to rotate once based on the given information is approximately 27.87 days.
Consider the following hypothetical survey results of 18- to 34-year-olds in a certain country, in response to the question "Are you currently living with your family.
Yes No Totals
Men 106 141 247
Women 92 161 253
Totals 198 302 500
a. Develop the joint probability table for these data and use it to answer the following questions
b. What are the marginal probabilities?
c. What is the probability of living with family given you are an 18- to 34-year-old marn in the U. S. ?
d. What is the probability of living with family given you are an 18- to 34-year-old woman in the U. S. ?
e. What is the probability of an 18- to 34-year-old in the U. S. Living with family?
f. If, in the U. S. , 49. 4% of 18-to 34-year-olds are male, do you consider this a good representative sample? Why?
After considering the following hypothetical survey results of 18- to 34-year-olds in a certain country, in response to the question "Are you currently living with your family?" we get the following probabilities.
a. The joint probability table for the given data is:
Yes No Totals
Men 0.212 0.282 0.494
Women 0.184 0.322 0.506
Totals 0.396 0.604 1
b. The marginal probabilities for living with family and not living with family are:
Yes No
Men 0.212 0.282
Women 0.184 0.322
Totals 0.396 0.604
c. The probability of living with family given you are an 18- to 34-year-old man in the U.S. is 0.212/0.396 = 0.5354 or approximately 53.54%.
d. The probability of living with family given you are an 18- to 34-year-old woman in the U.S. is 0.184/0.506 = 0.3636 or approximately 36.36%.
e. The probability of an 18- to 34-year-old in the U.S. living with family is 0.396 or 39.6%.
f. We cannot determine whether the sample is representative solely based on the percentage of males in the survey.
A good representative sample should be randomly selected to accurately reflect the population being studied. The percentage of males in the sample is relevant only if it differs significantly from the percentage of males in the population being studied.
The joint probability table was developed for the survey results of 18- to 34-year-olds on living with family. Marginal probabilities were calculated and the probability of living with the family was found for both men and women. The overall probability of living with the family was also determined. It is unclear if the sample is representative without additional information.
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10 points if someone gets it right
Tarzan loaded 4 trucks every 6 hours. At that rate, how long, in hours? will it take to load 6 trucks
What is the measure of
∠1 if
∠1 is (8x)
∘ and
∠2 is (2x - 3)
∘?
∠1 + ∠2 = 180
Substituting the given expressions for ∠1 and ∠2:
8x + (2x - 3) = 180
Simplifying and solving for x:
10x - 3 = 180
10x = 183
x = 18.3
Now we can substitute x back into the expression for ∠1 to find its measure:
∠1 = 8x = 8(18.3) = 146.4 degrees.
Therefore, if ∠1 and ∠2 add up to 180 degrees and ∠1 is given as 8x° and ∠2 is given as (2x - 3)°, then ∠1 measures 146.4 degrees
Answer:
<1=146.4
<2=34.6
Step-by-step explanation:
<1+<2=180 degrees
So,
8x+(2x-3)=180
10x-3=180
10x=183
X=18.3
subsitute:
<1=8x
<1=8(18.3)
<1=146.4
<2=2x-3
<2=2(18.3)-3
<2=34.6
5. Twenty students in Mr. Martin's class each took a survey about the number of minutes they played outside. The box
plots represent the amount of time the students spent outside playing in the summer and in the winter. Which statement is
best supported by the data?
SUMMER WINTER
30
45
60
NUMBER OF MINUTES
75
90
A. The range of number of minutes outside is the same in the
summer and in the winter.
B. The median number of minutes outside in the summer is
equal to the maximum number of minutes outside in
the winter.
C. The interquartile range for the number of minutes outside is
the same in the summer and in the winter.
D. The minimum number of minutes outside in the summer is
the same as the first quartile in the winter.
The statement "The median number of minutes outside in the summer is equal to the maximum number of minutes outside in the winter" is best supported by the data (option B).
How to find the maximum number of minutes outside?Looking at the plot;
Winter: Minimum= 0 Maximum= 60 Median= 30
Range = 60 - 0 = 60
Summer: Minimum= 20 Maximum= 90 Median= 60
Range = 90 - 20 = 70
So the median number of minutes outside in the summer is
equal to the maximum number of minutes outside in the winter.
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Missing information:
The question is incomplete and the complete question is shown in the attached image.
i hate math fr but pls help asap
Answer:
The formula for the area of a circle is A = πr^2, where r is the radius of the circle and π (pi) is a mathematical constant approximately equal to 3.14159.
If the radius of the circle is 11 inches, then we can substitute this value into the formula:
A = πr^2
A = π(11)^2
A = π(121)
So the area of the circle is 121π square inches, which is approximately 380.1327 square inches when rounded to four decimal places.
coupling tetraalkylammonium and ethylene glycol ether side chain to enable highly soluble anthraquinone-based ionic species for nonaqueous redox flow battery
Coupling tetraalkylammonium and ethylene glycol ether side chain is an effective method to enable highly soluble anthraquinone-based ionic species for nonaqueous redox flow battery. The side chains of the tetraalkylammonium are modified with the ethylene glycol ether, which is a highly polar solvent, allowing for better solubility in nonaqueous electrolyte solutions. Additionally, the ethylene glycol ether has the ability to modify the stability of the ionic species, preventing aggregation and ensuring the longevity of the battery. This increases the redox capacity and enhances the performance of the flow battery.
The ethylene glycol ether-tetraalkylammonium coupling has been proven to be an effective method for improving the solubility and stability of anthraquinone-based ionic species. For example, it has been observed that the coupling of ethylene glycol ether to anthraquinone-based ionic species enhanced the current density of the battery by more than 3 times. Furthermore, the coupling process has also been found to improve the energy efficiency and storage capacity of the nonaqueous redox flow battery.
Overall, coupling tetraalkylammonium and ethylene glycol ether side chain is an effective method for enabling highly soluble anthraquinone-based ionic species for nonaqueous redox flow battery. This process has been proven to improve the performance of the battery, including current density, energy efficiency, and storage capacity.
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the air speed of a small airplane during the first 25 seconds of takeoff and flight can be modeled as
The air speed of a small airplane during the first 25 seconds of takeoff and flight can be modeled by Newton's Second Law of Motion.
According to Newton's Second Law of Motion, the rate of change of the airplane's momentum is equal to the sum of all the forces acting on the airplane. As the plane takes off and accelerates, the thrust of the engines acting in the forward direction causes the plane's momentum to increase. This increase in momentum results in an increase in air speed. The air resistance acting against the motion of the plane is another force that affects the plane's speed. As the plane accelerates, the air resistance increases, and the plane's speed decreases.
In summary, the air speed of a small airplane during the first 25 seconds of takeoff and flight can be modeled by Newton's Second Law of Motion, where the thrust of the engines and air resistance act as forces that influence the plane's air speed.
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a laptop has a listed price of 882.99 before tax. if the sales tax rate is 6.25% , find the total cost of the laptop with sales tax included. round your answer to the nearest cent, as necessary.
The total cost of the laptop with the sales tax included is 938.18.
The total cost of the laptop with the sales tax included is the sum of the original price and the tax amount. The formula to calculate the total cost is given below:
Total Cost = Original Price + (Original Price * Sales Tax Rate)
In this case, the Original Price is 882.99 and the Sales Tax Rate is 6.25%. Therefore, the Total Cost of the laptop with the sales tax included is calculated as follows:
Total Cost = 882.99 + (882.99 * 0.0625)
Total Cost = 882.99 + 55.19
Total Cost = 938.18
Rounding to the nearest cent, the total cost of the laptop with the sales tax included is 938.18.
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Two fishermen, Ashraf and Khalid, went fishing. Ashraf caught x fish, Khalid caught y fish and in total they cau 69 fish. (a) Write down an equation in x and y. Ashraf caught 30% more fish than Khalid. (b)Write down another equation in x and y. (c)Solve your equations to find the number of fish caught by Ashraf and the number of fish caught h Khalid
The number of fish caught by Ashraf and Khalid by solving the equation formed is 39 and 30 respectively.
What is the Substitution method for solving equations?
In a system of linear equations to solve, we have N variables and N equations between them to solve. In substitution, we represent one variable in terms of another and replace it in the equation to convert it to a 1-variable equation and solve it.
a) Given, the number of fishes caught by Ashraf is "x" and by Khalid is "y".
As the total number of fish caught is 69, the equation is :
[tex]x + y = 69[/tex]
b) It is stated in the question that the number of fish caught by Ashraf i.e. x is 30% more than that caught by Khalid i.e. y.
The equation formed is :
x = 30% greater than y
[tex]= y + 30y/100[/tex]
[tex]= (100+30)y/100[/tex]
[tex]= 13y/10[/tex]
Hence, the equation is : [tex]10x = 13y[/tex]
c) Here, we have 2 equations and 2 variables. We use the substitution method to find the values of the variables :
[tex]y + 13y/10 = 69[/tex]
[tex](10+13)y/10 = 69[/tex]
[tex]23y/10 = 69[/tex]
[tex]y = 69 * 10 /23[/tex]
[tex]y = 30[/tex]
Putting the value of y in the first equation :
[tex]x + 30 = 69[/tex]
[tex]x = 39[/tex]
Hence, the number of fish caught by Ashraf is 39, and by Khalid is 30.
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Martha has read 52 pages of her book. This is
20% of the book. How many pages does the
book have?
Identify the area of the polygon with vertices P(1,2), Q(1,4), R(-1,6), and S(-3,2).
A = 16 units²
A= 10 units²
A= 6 units²
A = 14 units²
The area of the polygon with vertices P(1,2), Q(1,4), R(-1,6), and S(-3,2) is given as 10 units. Option B
How to find the areaWe can find the area of the polygon with the given vertices by dividing it into triangles and adding their areas.
One way to divide the polygon into triangles is to draw a diagonal from vertex P to vertex R. This creates two triangles, PQR and PRS.
[tex]\frac{1 }{2} ((4 - 2) + (6--4) + (-2 - - 18) + (-6 - 2)[/tex]
= 1 / 2 ( 2 + `10 + 16 - 8)
= 1 / 2 ( 20
= 10
The area of the polygon is 10 units
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Pls just say a b c or d
a lottery offers one $1000 prize, one $500 prize, and five $100 prizes. one thousand tickets are sold at $3 each. find the expectation if a person buys one ticket.
the expectation of buying one ticket is $2
Expectation if a person buys one ticket A person is interested in buying a ticket for a lottery that offers one $1000 prize, one $500 prize, and five $100 prizes. One thousand tickets are sold at $3 each. The expected return is calculated using the following formula:
Expectation = (Probability of winning Prize 1 × Value of Prize 1) + (Probability of winning Prize 2 × Value of Prize 2) + (Probability of winning Prize 3 × Value of Prize 3)To determine the expectation, we must first determine the probability of winning each of the three prizes.
Since one thousand tickets are sold and only one person can win the first prize, the probability of winning the $1000 prize is 1/1000 or 0.001. Similarly, the probability of winning the $500 prize is 1/1000 or 0.001. Since five $100 prizes are available and only one person can win each prize, the probability of winning any one of the five $100 prizes is 5/1000 or 0.005.
Therefore, the expectation is calculated as follows: Expectation = (0.001 × $1000) + (0.001 × $500) + (0.005 × $100)Expectation = $1 + $0.50 + $0.50Expectation = $2Thus, the expectation of buying one ticket is $2. This means that the average value of a ticket is $2, and a person can expect to win $2 on average by purchasing a ticket. Since the cost of a ticket is $3, the expected return is less than the cost of the ticket, and therefore, it is not a good investment from a financial standpoint.
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Use ABC to write the indicated trigonometric ratio
Sin B=
Answer:
b/c
Step-by-step explanation:
sin B = opp/hyp
sin B = b/c
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Find a point e satisfying the conclusion of the Mean Value Theorem for the function f(x) = x^-8 on the interval [1, 5].
c =
The point c satisfying the conclusion of the Mean Value Theorem for the function f(x) = x^-8 on the interval [1, 5] is: c = 1.4697
How to solve mean value theorem?The conclusion of the Mean Value Theorem says that there is a number
c in the interval (1, 5) such that:
f'(c) = (f(5) - f(1))/(5 - 1)
We are given the function f(x) = x⁻⁸
Thus:
f(1) = 1⁻⁸ = 1
f(5) = 5⁻⁸ = 0.00000256
Thus:
f'(c) = (0.00000256 - 1)/4
= -0.25
f'(c) = -8x⁻⁹
Thus:
-8c⁻⁹ = -0.25
c⁻⁹ = 0.25/8
c⁻⁹ = 0.03125
c = 0.03125^(-1/9)
c = 1.4697
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A snack stand sold hot dogs and chips at a recent game. The hot dogs cost $2. 50 and the chips cost $0. 75. After the game, they tallied 175 transactions totaling $262. 50. Represent the linear system in an augmented matrix:
1
1
175
2. 5
0. 75
262. 5
The number of hotdogs sold was
100. The number of chips sold was
The number of hot dogs is 100 while the number of snacks is 75. And it is found by using linear equation.
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are present. The variables in the previous sentence, y and x, are referred to as a "linear equation of two variables" at times.
The linear equation to solve the question will be:-
h+s= 175 ------(1)
2.50h + 0.75s = 262.50 -----(2)
From equation (1), s= 175-h -----(3)
Put qeauation (3) into (2) :-
2.50h + 0.75 = 262.50
2.50 + 0.75 (175-h) = 262.50
2.50 + 131.25 - 0.75 = 262.50
Collect like terms :-
2.50-0.75= 262.50-131.25
1.75= 131.25
h= 131.25/1.75
h= 75
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the slant height of a cone measures 26 centimeters. The height of the cone measures 24 centimeters.
What is the exact surface area of the cone?
help!!
Enter your answer in the box.
The value of the exact surface area of the cone is 360π
What is the exact surface area of the cone?To find the surface area of a cone, we need to calculate the area of the circular base and the curved lateral surface.
The radius of the circular base can be found using the Pythagorean theorem:
r = √(s^2 - h^2)
where s is the slant height and h is the height.
In this case, we have:
r = √(26^2 - 24^2)
r = 10
So, the surface area is
S = πr² + πrl
This gives
S = π * 10² + π * 10 * 26
S = 360π
Hence, the exact surface area of the cone is 360π
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