Answers
To change the subject you need to isolate the variable, for example the first two equations solved for t are:
t = √b/at = √(n - m)How to change the subject of a formula?Let's look at the first equations:
at² = b
We can change the subject to t. To do so, we just need to isolate the variable t in one of the sides.
if we divide both sides by a we will get:
t² = b/a
Now apply the square root in both sides:
t = √b/a
For the second equation:
t² + m = n
Now subtract m in both sides:
t² = n - m
Now again, apply the square root in both sides:
t = √(n - m)
And so on, that is how you can change the subject.
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Related Questions
8.
x 0/1
A sno-cone machine priced at $13 is on sale for 20% off. The sales tax rate is 6.75%. What is
the price of the sno-cone machine after the discount and sales tax?
Answers
Answer:
$11.10
Step-by-step explanation:
To calculate the price of the sno-cone machine after discount and sales tax, we need to first calculate the discount and then add sales tax.
The sno-cone machine is priced at $13 and is on sale for 20% off. To calculate the discount, we can multiply the original price by the discount rate:
Discount = Original Price x Discount Rate
Discount = $13 x 0.20
Discount = $2.60
Therefore, the discount is $2.60.
The sale price of the sno-cone machine after discount can be calculated by subtracting the discount from the original price:
Sale Price = Original Price - Discount
Sale Price = $13 - $2.60
Sale Price = $10.40
Therefore, the sale price of the sno-cone machine after discount is $10.40.
To calculate the sales tax, we can multiply the sale price by the sales tax rate:
Sales Tax = Sale Price x Sales Tax Rate
Sales Tax = $10.40 x 0.0675
Sales Tax = $0.70
Therefore, the sales tax is $0.70.
Finally, to calculate the final price of the sno-cone machine after discount and sales tax, we can add the sale price and sales tax:
Final Price = Sale Price + Sales Tax
Final Price = $10.40 + $0.70
Final Price = $11.10
Therefore, the final price of the sno-cone machine after discount and sales tax is $11.10 1.
I hope this helps!
Can anyone help with question 9 and please don’t mind the black pencil covering
Answers
The amount of all angles within every quadrilateral adds up to a cumulative 360°.
How to justify the claimAll triangles exhibit angles that total 180°, and since the diagonal is shared between both of these triangles, we shall add up their angles only once when totaling the quadrilateral.
Consequently, the sum of all four angles in the quadrilateral is twice the angle degree of one triangle plus 180° (for the connecting diagonal), which equates to:
(180°) + 180° = 360°
Therefore, the amount of all angles within every quadrilateral adds up to a cumulative 360°.
This justification holds true for all types of quadrilaterals, for instance the one illustrated in the representation at the right, due to it being divided into two parts through the extention of a diagonal.
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The sampling distribution of difference between two proportions is approximated by a a. t distribution with n1 n2 degrees of freedom b. t distribution with n1 n2 2 degrees of freedom c. normal distribution d. t distribution with n1 n2-1 degrees of freedom
Answers
The correct answer is (c) normal distribution.
How to find sampling distribution of difference between two proportions?When comparing two proportions, the difference between them can be calculated, and its sampling distribution can be approximated by a normal distribution when the sample sizes are sufficiently large.
The mean of the sampling distribution is the difference between the true population proportions, and the standard deviation of the sampling distribution is calculated as:
[tex]sqrt[(p1*(1-p1)/n1) + (p2*(1-p2)/n2)][/tex]
where p1 and p2 are the population proportions, and n1 and n2 are the sample sizes.
Therefore, the sampling distribution of the difference between two proportions is approximated by a normal distribution with mean (p1-p2) and standard deviation given by the above formula.
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Goofy's fast food center wishes to know the proportion of people in its city that will purchase its products. Suppose the true population proportion is 0.04. Of 238 are sampled, what is the probability that the sample proportion will differ from the population proportion by less than 0.03
Answers
The probability that the sample proportion will differ from the population proportion by less than 0.03 is 62%
To calculate the probability that the sample proportion will differ from the population proportion by less than 0.03, we first need to calculate the standard error of the sample proportion. The formula for the standard error is:
SE = [tex]\sqrt{[p(1-p)/n]}[/tex]
Where p is the population proportion (0.04), and n is the sample size (238). Plugging in these values, we get:
SE = [tex]\sqrt{[0.04(1-0.04)/238]}[/tex] = 0.028
Next, we need to calculate the margin of error, which is given by:
ME = z*SE
Where z is the z-score that corresponds to the desired level of confidence. Let's assume we want a 95% confidence level, which corresponds to a z-score of 1.96. Plugging in these values, we get:
ME = 1.96*0.028 = 0.055
Finally, we can calculate the probability that the sample proportion will differ from the population proportion by less than 0.03 by subtracting the margin of error from both sides of the true proportion (0.04) and adding it back on:
0.04 - 0.055 < p < 0.04 + 0.055
Simplifying, we get:
-0.015 < p - 0.04 < 0.015
Dividing by the standard error, we get:
-0.535 < z < 0.535
Looking up these z-scores in a standard normal distribution table, we find that the probability of getting a sample proportion within 0.03 of the population proportion is approximately 0.62, or 62%. This means that there is a 62% chance that the sample proportion will be within 0.03 of the population proportion if we were to sample 238 people from the city.
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How does the standard deviation of the population affect the width of the confidence interval for the population mean
Answers
The standard deviation of the population affects the width of the confidence interval for the population mean. A larger standard deviation results in a wider confidence interval, while a smaller standard deviation results in a narrower confidence interval.
The standard deviation of the population plays a crucial role in determining the width of the confidence interval for the population mean. The formula for the confidence interval for the population mean is:
CI = X ± Z × (σ / sqrt(n))
where:
CI is the confidence interval
X is the sample mean
Z is the Z-score corresponding to the desired level of confidence
σ is the standard deviation of the population
n is the sample size
As you can see from the formula, the width of the confidence interval is directly proportional to the standard deviation of the population. The larger the standard deviation, the wider the confidence interval. This means that if the standard deviation of the population is large, then we need a larger sample size or a lower confidence level to obtain a narrower confidence interval. On the other hand, if the standard deviation of the population is small, we can obtain a narrower confidence interval with a smaller sample size or a higher confidence level.
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The normal density curve is symmetric about Group of answer choices An inflection point Its mean The horizontal axis A point located one standard deviation from the mean
Answers
The normal density curve is symmetric about its mean, with the highest point at the "mean."
The normal density curve is a continuous probability distribution that is widely used in statistics.
It is symmetric about its mean, which is a measure of central tendency. This means that half of the observations fall below the mean, and half fall above it. The curve is bell-shaped, with the highest point at the mean, and it becomes increasingly flatter as it moves away from the mean. The horizontal axis represents the range of possible values for the variable being measured, and the area under the curve represents the probability of observing a given value. An inflection point is a point where the curve changes direction, from concave upwards to concave downwards or vice versa. It is located one standard deviation away from the mean, and it marks the point where the curve begins to flatten. This point is important because it is used to define the standard deviation, which is a measure of how spread out the observations are from the mean. The standard deviation is used to calculate probabilities and to compare different sets of data.In summary, the normal density curve is symmetric about its mean, with the highest point at the mean. The curve is bell-shaped and becomes increasingly flatter as it moves away from the mean. An inflection point is located one standard deviation away from the mean and marks the point where the curve begins to flatten.Know more about the continuous probability distribution
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Complete the statement. 6 – 6 = 6 + , or
Answers
6 - 6 = 6 - 6 is the correct statement.
To complete the statement 6 - 6 = 6 + x, we need to find the value of x that makes the statement true.
Simplifying the left-hand side of the equation, we have:
6 - 6 = 0
On the right-hand side, we have:
6 + x
To make the statement true, we need to find the value of x that satisfies:
0 = 6 + x
We can solve for x by subtracting 6 from both sides:
0 - 6 = 6 + x - 6
-6 = x
Therefore, the completed statement is:
6 - 6 = 6 - 6
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Suppose that in a class of 10 stat majors and 10 engineers, 5 students are randomly chosen to present work at the board. What is the probability that exactly 4 of the students selected to present are stat majors
Answers
The probability that exactly 4 of the students selected to present are stat majors is 0.219, or about 22%.
The total number of ways to choose 5 students from a class of 20 is:
C(20,5) = (20!)/[(5!)(15!)] = 15504
To find the probability that exactly 4 of the students selected are stat majors, we need to count the number of ways to choose 4 stat majors and 1 engineer, and divide by the total number of ways to choose 5 students:
[C(10,4) * C(10,1)] / C(20,5) = [(10!)/[(4!)(6!)]] * [(10!)/[(1!)(9!)]] / [(20!)/[(5!)(15!)]] = 0.219
Therefore, the probability that exactly 4 of the students selected to present are stat majors is 0.219, or about 22%.
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Please helppppp now asappppppp
Answers
Answer: A
Step-by-step explanation:
A rancher wishes to fence in a rectangular corral enclosing 1300 square yards and must divide it in half with a fence down the middle. If the perimeter fence costs $5 per yard and the fence down the middle costs $3 per yard, determine the dimensions of the corral so that the fencing cost will be as small as possible.'
Answers
The dimensions of the corral that will minimize the cost of the fencing are x = 4 yards (width) and y = 325 yards (length).
To begin solving this problem, we need to use the given information to set up an equation that represents the cost of the fencing. Let's start by defining the dimensions of the rectangular corral. We can use x to represent the width and y to represent the length.
Since the area of the corral is 1300 square yards, we know that:
xy = 1300
Now, let's think about the fencing. We need to divide the corral in half with a fence down the middle, which means we have two equal sections with a width of x/2. The length of each section is still y.
To find the perimeter of each section, we add up all the sides. For the top and bottom, we have two lengths of y and two widths of x/2. For the sides, we have two lengths of x/2 and two widths of y. This gives us a perimeter of:
2y + x + 2x + 2y = 4y + 2x
Since we have two sections, the total perimeter is:
2(4y + 2x) = 8y + 4x
We can now set up an equation for the cost of the fencing:
Cost = (8y + 4x)($5) + (x)($3)
The first part of the equation represents the cost of the perimeter fence, while the second part represents the cost of the fence down the middle.
Now, we want to find the dimensions of the corral that will minimize the cost of the fencing. To do this, we can use calculus. We take the derivative of the cost equation with respect to x and set it equal to zero:
dCost/dx = 20y + 3 = 0
Solving for y, we get:
y = -3/20
Since we can't have a negative length, this solution is not valid. However, we can find the minimum cost by plugging in the value of y that makes the derivative equal to zero into the original equation for the cost of the fencing. This gives us:
Cost = (8y + 4x)($5) + (x)($3)
Cost = (8(-3/20) + 4x)($5) + (x)($3)
Cost = (-(12/5) + 4x)($5) + (x)($3)
Cost = -24x + 3x^2 + 3900
To minimize the cost, we take the derivative with respect to x and set it equal to zero:
dCost/dx = -24 + 6x = 0
x = 4
Plugging this value of x back into the equation for the cost of the fencing gives us:
Cost = -24(4) + 3(4^2) + 3900
Cost = $3892
Therefore, the dimensions of the corral that will minimize the cost of the fencing are x = 4 yards (width) and y = 325 yards (length).
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Moses is twice as old as Methuselah was when Methuselah was one-third as old as Moses will be when Moses is as old as Methuselah is now. If the difference of their ages is 666, how old is Methuselah
Answers
Moses is currently 3996 years old.
Let's denote Methuselah's current age as "M" and Moses's current age as "M2".
"Moses is twice as old as Methuselah was when Methuselah was one-third as old as Moses will be when Moses is as old as Methuselah is now." This can be written as:
M2 = 2 × (M - (1/3) × M2)
We can simplify this equation by multiplying both sides by 3:
3 × M2 = 6 × (M - (1/3) × M2)
3 × M2 = 6M - 2 × M2
5 × M2 = 6M
"If the difference of their ages is 666" can be written as:
M2 - M = 666
We can use equation (5) to substitute for M2 in equation (6):
5 × M2 = 6M
5 × (M + 666) = 6M
5M + 3330 = 6M
M = 3330
Therefore, Methuselah is currently 3330 years old. We can use equation (6) to find Moses's current age:
M2 - M = 666
M2 - 3330 = 666
M2 = 3996
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-31÷(-30)+(-1) what is the answer to dis
Answers
Using the order, we can evaluate the expression, the answer is 0.
To evaluate this expression, we need to follow the order of operations, which is a set of rules that dictate the order in which mathematical operations should be performed. The order of operations is:
1. Perform any calculations inside parentheses first.
2. Exponents (ie powers and square roots, etc.)
3. Multiplication and Division (from left to right)
4. Addition and Subtraction (from left to right)
Using this order, we can evaluate the expression as follows:
-31÷(-30)+(-1)
= 1 + (-1) [since -31 ÷ (-30) = 1]
= 0
Therefore, the answer is 0.
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If $1.00 U.S. bought $1.40 Canadian dollars in 2006 and in 2010 it bought $1.00 Canadian dollar, then;
Answers
The statements are inconsistent and cannot both be true.
How to compare the exchange rates between USD and CAD in 2006 and 2010?To answer this question, we need to compare the exchange rate between the US dollar (USD) and the Canadian dollar (CAD) in 2006 and 2010.
In 2006, 1.00 USD bought 1.40 CAD. This can be expressed as:
1 USD = 1.40 CAD
In 2010, 1.00 USD bought 1.00 CAD. This can be expressed as:
1 USD = 1.00 CAD
To compare the two exchange rates, we can set them equal to each other and solve for CAD:
1 USD = 1.40 CAD
1 USD = 1.00 CAD
Setting the two equations equal to each other, we get:
1.40 CAD = 1.00 CAD
Subtracting 1.00 CAD from both sides, we get:
0.40 CAD = 0
This is a contradiction, which means that there is no consistent exchange rate that can explain both statements.
Therefore, the statements are inconsistent and cannot both be true.
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A bus comes to a station once every 10 minutes and waits at the station for 3 minutes. Assume that you arrive at the station at a random time. Express the probability as a decimal. Find the probability that you will have to wait more than 6 minutes to board a bus.
Answers
The time between buses is 10 minutes and the bus waits at the station for 3 minutes, so the time between the departure of one bus and the departure of the next bus is 10 + 3 = 13 minutes.
Since you arrive at a random time, the time you have to wait for the next bus can be any number from 0 to 13 minutes, with each value between 0 and 13 being equally likely.
The probability that you will have to wait more than 6 minutes to board a bus is the probability that you arrive at the station between 0 and 7 minutes after a bus has left.
This is because if you arrive at the station more than 7 minutes after a bus has left, you will have to wait less than 6 minutes for the next bus to arrival time.
The probability that you arrive at the station between 0 and 7 minutes after a bus has left is 7/13, or approximately 0.538.
Therefore, the probability that you will have to wait more than 6 minutes to board a bus is approximately 0.462 (1 - 0.538).
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a manufacturer plans to make a cylindrical water tak to hold 2000L of water what must be the height if he uses a readius of 500 cm
Answers
The height of the cylindrical water tank should be approximately 8.04 meters to hold 2000L of water with a radius of 500 cm.
The formula to calculate the volume of a cylinder is:
V = π[tex]r^2h[/tex]
where V is the volume, r is the radius, and h is the height.
We know that the manufacturer plans to make a cylindrical water tank that can hold 2000L of water. We also know that the radius of the tank is 500 cm.
First, we need to convert the volume from liters to cubic centimeters ([tex]cm^3[/tex]) because the units of radius and height are in centimeters:
2000L = 2,000,000[tex]cm^3[/tex]
Substituting these values into the formula, we get:
2,000,000 = π[tex](500)^2[/tex]h
Solving for h, we get:
h = 2,000,000 / (π[tex](500)^2[/tex])
h ≈ 8.04 cm
Therefore, the height of the cylindrical water tank should be approximately 8.04 meters to hold 2000L of water with a radius of 500 cm.
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rol depending on your answer. Match each equation on the left with its solution on the right. No answer on the right will be used twice. 5x + 2(x − 1) = 6(x+1) +x All real numbers 5x + 2(x − 1) = 6(x – 1) − x 5x + 2(x − 3) = 6(x − 1) − x 5x + 2(x – 3) = 6(x − 1) +x x = 0) X = = 2 No solution
Answers
The solutions to the equations are
5x + 2(x − 1) = 6(x+1) + x ---- No solution5x + 2(x − 1) = 6(x – 1) − x ----- x = -15x + 2(x − 3) = 6(x − 1) − x --- x = 05x + 2(x – 3) = 6(x − 1) +x ---- All real numbersCalculating the solutions to the equationsFrom the question, we have the following parameters that can be used in our computation:
Set of linear equations
Next, we solve the equations as follows:
5x + 2(x − 1) = 6(x+1) + x
This gives
5x + 2x - 2 = 6x + 6 + x
Evaluate the like terms
-2 = 6 ---- No solution
Next, we have
5x + 2(x − 1) = 6(x – 1) − x
This gives
5x + 2x - 2 = 6x - 6 - x
Evaluate the like terms
2x = -2
Divide
x = -1
Next, we have
5x + 2(x − 3) = 6(x − 1) − x
This gives
5x + 2x - 6 = 6x - 6 - x
Evaluate the like terms
2x = 0
Divide
x = 0
Lastly, we have
5x + 2(x – 3) = 6(x − 1) +x
This gives
5x + 2x - 6 = 6x - 6 + x
Evaluate the like terms
0 = 0 ---- All real numbers
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4. Researchers measured the sugared-beverage consumption and obesity of the same children for twoyears. They found that when these children added one sugared drink a day to their diet, their risk ofobesity increased 60%. Which quasi-experimental design did they use
Answers
The researchers monitored the same children's consumption of sugar-sweetened beverages and obesity over the course of two years using a longitudinal quasi-experimental methodology.
The researchers used a longitudinal quasi-experimental design in this study, as they measured the same children's sugared-beverage consumption and obesity for two years.
This design allows the researchers to observe changes over time and make causal inferences about the relationship between the variables.
By comparing the same group of children's obesity rates before and after the addition of one sugared drink per day, the researchers were able to establish a causal link between the consumption of sugared drinks and increased risk of obesity.
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Find the critical numbers of the function and describe the behavior of f at these numbers. (List your answers in increasing order.)
f(x) = x6(x - 2)5
At ____ the function has ---localmax/localmin/ or neither--
At _____the function has ---localmax/localmin/ or neither--
At ______ the function has ---localmax/localmin/ or neither--
Answers
The critical numbers are 0 and 2, and the behavior of f at these numbers is At x = 0, the function has a local minimum.
At x = 2, the function has neither a local maximum nor a local minimum.
To find the critical numbers, we need to take the derivative of the function and set it equal to zero:
f'(x) = 6x^5(x-2)^5 + x^6(5)(x-2)^4(1) = 0
Simplifying this equation, we get:
x(x-2)^4(6x^4 + 5x^2(x-2)) = 0
The critical numbers are where the derivative equals zero, which are x = 0 and x = 2.
To describe the behavior of f at these critical numbers, we need to examine the sign of the derivative around each critical number. If the derivative is positive to the left and negative to the right of a critical number, then the function has a local maximum at that point. If the derivative is negative to the left and positive to the right, then the function has a local minimum at that point. If the derivative does not change sign at a critical number, then the function has neither a local maximum nor a local minimum at that point.
Let's examine each critical number:
At x = 0, we can see that the factor x is negative to the left of 0 and positive to the right of 0. The factor (x-2)^4 is positive everywhere. The factor 6x^4 + 5x^2(x-2) is positive at x = 0 (since the x^2 term is zero), which means the derivative is positive to the left and right of x = 0. Therefore, f has a local minimum at x = 0.
At x = 2, we can see that the factor (x-2)^4 is zero at x = 2, which means the derivative is zero at x = 2. To determine whether f has a local maximum or minimum at x = 2, we need to examine the sign of the derivative on either side of 2. If we plug in a value slightly less than 2 (e.g. x = 1.9), we get a positive derivative. If we plug in a value slightly greater than 2 (e.g. x = 2.1), we also get a positive derivative. Therefore, f has neither a local maximum nor a local minimum at x = 2.
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Which sentence(s) are the correct interpretation sentences for the TV problem above. Check all sentence that would be correct. A total of 500 TVs can be sold if the price is set at $190. When the price for the TV is $190, there are 500 TVs sold. A total of 190 TVs can be sold if the price is set at $500. When the price for the TV is $500, there are 190 TVs sold.
Answers
The correct interpretation sentences for the TV problem above are:- A total of 500 TVs can be sold if the price is set at $190.
- When the price for the TV is $190, there are 500 TVs sold.
The other sentence "A total of 190 TVs can be sold if the price is set at $500. When the price for the TV is $500, there are 190 TVs sold" is not correct as it has the price and the quantity of TVs sold reversed.
In interpretation, it is important to pay attention to the context and the logic of the problem to ensure that the sentence accurately reflects the information provided. In this case, the correct interpretation sentences reflect the relationship between the price and the quantity of TVs sold. These sentences help to clarify the information and provide a clear understanding of the problem.
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Problem
There are 888 employees on The Game Shop's sales team. Last month, they sold a total of ggg games. One of the sales team members, Chris, sold 171717 fewer games than what the team averaged per employee.
How many games did Chris sell?
Write your answer as an expression.
Answers
There are 888 employees on The Game Shop's sales team. Last month, they sold a total of ggg games. Chris sold 171717 fewer games than the team averaged per employee, so the number of games he sold can be expressed as: (ggg/888) - 171717.
To find the average number of games sold per employee, we divide the total number of games sold by the total number of employees.
The problem gives us the total number of employees, which is 888, and the total number of games sold, which is ggg. So, the average number of games sold per employee is:
ggg games ÷ 888 employees = ggg/888 games per employee
Next, we're told that Chris sold 171717 fewer games than the team averaged per employee.
This means that the number of games he sold is equal to the average number of games sold per employee minus 171717.
Thus, the expression for the number of games Chris sold is: (ggg/888) - 171717.
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Lisa bought a treadmill for $925. She made a 20% down payment and financed the rest over 18 months. Find the monthly payment if the interest rate was 11%.
Answers
The monthly payment if the interest rate was 11% will be $45.63.
The remaining amount is calculated as,
P = (1 - 0.20) x $925
P = 0.80 x $925
P = $740
The monthly payment is calculated as,
MP = [$740 + ($740 x 0.11)] / 18
MP = $821.4 / 18
MP = $45.63
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The monthly payment is $49.69.
We have,
The amount of the down payment is:
0.20 x $925 = $185
So the amount financed is:
$925 - $185 = $740
Using the formula for the monthly payment on a loan:
= (Pr(1+r)^n) / ((1+r)^n - 1)
where:
P = principal or amount financed = $740
r = monthly interest rate = 11%/12 = 0.0091667
n = total number of payments = 18
Plugging in the values, we get:
Monthly payment
= ($7400.0091667 x (1+0.0091667)^18) / ((1 + 0.0091667)^18 - 1)
= $49.69 (rounded to the nearest cent)
Therefore,
The monthly payment is $49.69.
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You roll a pair of dice three times. What is the probability that you will roll double ones (snake eyes) or double sixes (box cars) at least once
Answers
The probability of rolling double ones or double sixes at least once in three rolls is 1 - 0.701 = 0.299, or approximately 29.9%.
There are a total of 6 x 6 = 36 possible outcomes when rolling a pair of dice, assuming the dice are fair and unbiased.
The probability of rolling double ones or double sixes on any one roll is 2/36 = 1/18. So, the probability of NOT rolling double ones or double sixes on any one roll is 1 - 1/18 = 17/18.
The probability of not rolling double ones or double sixes on all three rolls is [tex](17/18) \times (17/18) \times (17/18) = (17/18)^3 = 0.701.[/tex]
Therefore, the probability of rolling double ones or double sixes at least once in three rolls is 1 - 0.701 = 0.299, or approximately 29.9%.
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ana knows that the grade levels are equally distributed across the school of 1,200 students. She would like to use a chi-square test to see if the proportion of individuals in each class at the movie are also equally distributed. How many seniors would be expected at the event
Answers
Thus, Ana would expect 300 seniors at the movie event if the grade levels are equally represented.
Based on the given information, Ana wants to use a chi-square test to see if the proportion of individuals in each class at the movie event is equally distributed.
Since the school has 1,200 students and the grade levels are equally distributed, we can assume that each grade level has an equal share of the total number of students.
To calculate the expected number of seniors at the event, we can simply divide the total number of students by the number of grade levels.
Assuming there are four grade levels (freshmen, sophomores, juniors, and seniors), we can divide the total number of students (1,200) by 4:
1,200 students / 4 grade levels = 300 students per grade level
Therefore, Ana would expect 300 seniors at the movie event if the grade levels are equally represented. Keep in mind that the chi-square test will help her determine if there is a significant difference between the expected and observed distribution of students from each grade level at the event.
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Carol purchased one basket of fruit consisting of 4 apples and 2 oranges and another basket of fruit consisting of 3 apples and 5 oranges. Carol is to select one piece of fruit at random from each of the two baskets. What is the probability that one of the two pieces of fruit selected will be an apple and the other will be an orange
Answers
Answer:13/24
Step-by-step explanation 1. the desired probability is the sum of the probabilities of two disjoint events. In the first event, an apple is selected from the first basket and an orange is selected from the second basket; the probability of this event is (4/6)(5/8)=20/48. 2. In the second event, an orange is selected from the first basket and an apple is selected from the second basket; the probability of this event is (2/6)(3/8)=6/48. Therefore, the desired probability is 20/48+6/48=26/48=13/24.
How many $3$-digit positive integers are there whose middle digit is equal to the sum of the first and last digits
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The number of 3-digit positive integers whose middle digit is equal to the sum of the first and last digits is 55 such numbers
Let's first consider the possible values for the middle digit, which is the sum of the first and last digits:
If the first digit is 1, then the middle digit can only be 2, and the last digit can be any digit from 0 to 8.
There are 9 possible numbers in this case.
If the first digit is 2, then the middle digit can be 2 or 4, and the last digit can be any digit from 0 to 6.
There are 14 possible numbers in this case.
If the first digit is 3, then the middle digit can be 2, 4, or 6, and the last digit can be any digit from 0 to 4.
There are 15 possible numbers in this case.
If the first digit is 4, then the middle digit can be 2, 4, 6, or 8, and the last digit can be any digit from 0 to 2.
There are 13 possible numbers in this case.
If the first digit is 5, then the middle digit can be 4, 6, or 8, and the last digit can only be 0.
There are 3 possible numbers in this case.
If the first digit is 6, then the middle digit can only be 6, and the last digit can only be 0.
There is only 1 possible number in this case.
In total, the number of 3-digit positive integers whose middle digit is equal to the sum of the first and last digits is:
9 + 14 + 15 + 13 + 3 + 1 = 55
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Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle B?
Enter your answer in the box.
m∠B=
°
A quadrilateral inscribed in a circle. The vertices of quadrilateral lie on the edge of the circle and are labeled as A, B, C, D. The interior angle B is labeled as left parenthesis 6 x plus 19 right parenthesis degrees. The angle D is labeled as x degrees.
Answers
The measure of angle B is m∠B = 157°
Given Quadrilateral ABCD is inscribed in a circle. That means its four vertices lie on the edge of the circle
∠B and ∠D are opposite angles in the quadrilateral ABCD
m∠B + m∠D = 180°
The opposite ∠s in a cyclic quadrilateral,
∵ m∠B = (6x + 19)°
∵ m∠D = x°
Substitute them in the rule;
(6x + 19) + x = 180
Add the like terms in the left-hand side
(6x + x) + 19 = 180
7x + 19 = 180
Subtract 19 from both sides;
7x = 161
Divide both sides by 7
x = 23
m∠B = 6(23) + 19
m∠B = 138 + 19
m∠B = 157°
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Data was collected from 32 random students on the number of hours spent studying for the final and their corresponding exam score in a statistics class. If a 99% confidence interval for resulted in (3.59, 6.96), what is the most you would expect the exam score to increase by if the student studied an extra 3 hours
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The maximum expected increase in exam score if a student studies an extra 3 hours is 4.11 points.
Since we have a 99% confidence interval, we can assume a t-distribution with 31 degrees of freedom (n-1). Using this distribution, we can find the margin of error (E) for the mean difference in exam score (µD) between students who study for an extra 3 hours and those who do not.
E = t* (s/√n), where s is the sample standard deviation and n is the sample size.
We don't have the standard deviation, but we can estimate it using the range rule of thumb, which states that the standard deviation is approximately equal to the range of the data divided by 4.
s ≈ (6.96 - 3.59) / 4 = 0.8425
Using a t-value for a 99% confidence interval and 31 degrees of freedom, we have:
t = 2.750
E = 2.750 * (0.8425/√32) ≈ 0.929
So the 99% confidence interval for the true mean difference in exam score is (3.59 - 0.929, 6.96 + 0.929) = (2.66, 7.89).
To find the maximum expected increase in exam score if a student studies an extra 3 hours, we can subtract the mean difference in exam score from the previous 32 students from the mean difference in exam score between students who study for an extra 3 hours and those who do not.
Mean difference in exam score = (6.96 - 3.59) / 32 = 0.104
Max expected increase in exam score = 0.104 + 3 = 4.11
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Which algebraic expression represents this word description?
The product of nine and the difference between a number and five
O A. 9(x - 5)
OB. 5-9x
OC. 9x-5
OD. 9(5-x)
SUAMIT
Answers
Answer:
A.
Step-by-step explanation:
1) The product is a quantity obtained by multiplication. Therefore, the equation starts like this 9( )
2) Next, the question asks about the difference, which is obtained by subtraction. Therefore, the rest of the equation looks like this: 9(x - 5)
3) Goodluck! And let me know how you did on this exam!
Find the foci of the ellipse whose major axis has endpoints $(0,0)$ and $(13,0)$ and whose minor axis has length 12. Enter your answer as a list of ordered pairs separated by commas.
Answers
The foci of the ellipse are (4, 0) and (9, 0).
To find the foci of the ellipse, we first need to determine its standard form equation and identify the values of the major and minor axes. Given the endpoints of the major axis are (0,0) and (13,0), we can determine that the length of the major axis (2a) is 13 units. Thus, a = 6.5 units.
The minor axis has a length of 12 units, so the length of the minor axis (2b) is 12 units. Therefore, b = 6 units.
Next, we will find the value of c, which is the distance from the center of the ellipse to each focus. Using the relationship [tex]c^2 = a^2 - b^2[/tex], we get:
[tex]c^2 = (6.5)^2 - (6)^2[/tex]
[tex]c^2 = 42.25 - 36[/tex]
[tex]c^2 = 6.25[/tex]
c = √6.25
c ≈ 2.5 units
Now, we have all the necessary information to find the foci of the ellipse. Since the major axis is along the x-axis, the foci will be located at a distance of c units to the left and right of the center (which is the midpoint of the major axis). The center of the ellipse is (6.5, 0), so the foci will be at (6.5 - 2.5, 0) and (6.5 + 2.5, 0), which are (4, 0) and (9, 0).
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When we use a confidence interval to reach a conclusion about the population mean, we are applying a type of reasoning or logic called ___________.
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When we use a confidence interval to reach a conclusion about the population mean, we are applying a type of reasoning or logic called inferential statistics.
Inferential statistics involves using sample data to make inferences about a larger population. In the case of a confidence interval for the population mean, we use a sample mean and standard deviation to estimate the true population mean, and then we use the confidence interval to quantify our uncertainty about this estimate.
The confidence interval gives us a range of values within which we can be confident that the true population mean lies. The level of confidence chosen for the interval determines the width of the interval and the probability that the true population mean lies within it.
Inferential statistics plays a crucial role in making decisions based on sample data when it is not feasible or practical to collect data from the entire population.
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