Answers
The expected value is the summary of the product between each element and its probability.
In this case, we have to multiply the number of dollars in each area with the probability of happening. It's important to note that there are 8 portions inside the circle because each of them has 45°.
According to the given diagram $160 represents one slice, $80 represents one slice, and -$40 represents 6 slices.
Having said that, we can express the expected value as follows.
\(\begin{gathered} E=160\cdot(\frac{1}{8})+80\cdot(\frac{1}{8})-40\cdot(\frac{6}{8}) \\ E=\frac{160}{8}+\frac{80}{8}-\frac{240}{8}=20+10-60=-30 \end{gathered}\)Therefore, the expected value is -30 which means you most likely will lose $30 if you play.Related Questions
Tristan is a salesperson who sells computers at an electronics store. He makes a base pay amount each day and then is paid a commission as a percentage of the total dollar amount the company makes from his sales that day. Let
P
P represent Tristan's total pay on a day on which he sells
x
x dollars worth of computers. The table below has select values showing the linear relationship between
x
x and
P
.
P. Determine the percentage commission Tristan makes on his daily sales.
Answers
Answer:
\(m = 1.5\%\)
Step-by-step explanation:
Given
The attached table
Required
Determine his percentage commission
To do this, we need to calculate the slope (m) of the table as follows:
\(m = \frac{P_2 - P_1}{x_2 - x_1}\)
Where
\((x_1,P_1) = (7000,165)\)
\((x_2,P_2) = (7500,172.5)\)
\(m = \frac{P_2 - P_1}{x_2 - x_1}\) becomes
\(m = \frac{172.5 - 165}{7500- 7000}\)
\(m = \frac{7.5}{500}\)
\(m = 0.015\)
Convert to percentage
\(m = 0.015 * 100\%\)
\(m = 1.5\%\)
Hence, his percentage commission is 1.5%
Find three rational numbers between 2 and 3
Answers
2.5: This rational number is obtained by taking the average of 2.25 and 2.75. It lies closer to 3 than to 2.
2.75: This rational number is obtained by taking the average of 2.5 and 3. It lies closer to 3 than to 2.
Answer:
Step-by-step explanation:
\(\frac{15}{7} or \frac{26}{9}\)
Takuya traded New Zealand dollars for Japanese yen at an exchange rate of 1 New Zealand dollar = 62.8792 Japanese yen. He gave the exchanger a total of $3800 and was charged a flat fee of $70. Approximately how many Chinese yen does Takuya have
Answers
Takuya will have approximately 234,539.416 yen after conversion from New Zealand dollars.
We are given that: Takuya traded the New Zealand dollars for the Japanese yen.
So, it means that it used conversion to convert one currency into the another.
Now, we have:
1 New Zealand dollar = 62.8792 Japanese yen.
Also, Takuya has a total of $ 3800 dollars.
But $ 70 fee has also to be paid for the exchange.
So, the dollars left will be:
= $ 3800 - $ 70
= $ 3730
Converting them to Japanese yen by multiplication:
$ 3730 = 3730 × 62.8792 yen
= 234,539.416 yen.
Therefore, we get that, Takuya will have approximately 234,539.416 yen after conversion from New Zealand dollars.
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Given the following definitions: U = {1, 2, 3, 4, 5, 6, 7} A = {1, 2, 4, 5} B = {1, 3, 5, 7} How many elements are in A ∪ B' ? Your Answer:
Answers
Consequently, there are 5 elements in A B'.
Given the following definitions:
U = {1, 2, 3, 4, 5, 6, 7}A = {1, 2, 4, 5}B = {1, 3, 5, 7}
The complement of a set B is the set of all elements that belong to the universal set U but not to B.
A’ = {x | x ∈ U and x ∉ A} = {3, 6, 7}B’ = {x | x ∈ U and x ∉ B} = {2, 4, 6}
The union of sets A and B is the set of all elements that belong to set A or set B, or both.
A ∪ B = {x | x ∈ A or x ∈ B}
= {1, 2, 3, 4, 5, 7}A ∪ B'
= {x | x ∈ A or x ∈ B’}
= {1, 2, 4, 5, 6}
Therefore, the number of elements in A ∪ B' is 5.
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To purchase $14,500 worth of restaurant equipment for her business, Debra made a down payment of $1300 and took out a business loan for the rest. After 2 years of paying monthly payments of $585.04, she finally paid off the loan.
(a) What was the total amount Debra ended up paying for the equipment (including the down payment and monthly payments)?
(b) How much interest did Debra pay on the loan?
Answers
The total amount Debra ended up paying for the equipment was $28,541.60 and the amount of interest Debra paid on the loan was $14,041.60
(a) To find the total amount Debra ended up paying for the equipment (including the down payment and monthly payments), we need to add the down payment to the total amount of the loan, and then add the total amount of the monthly payments made over the two years.
Total amount of the loan = $14,500 - $1,300 (down payment) = $13,200
Total amount paid = Down payment + Total amount of the loan + Total amount of monthly payments
Total amount paid = $1,300 + $13,200 + ($585.04 x 24) [since there are 24 monthly payments in 2 years]
Total amount paid = $1,300 + $13,200 + $14,041.60
Total amount paid = $28,541.60
Therefore, the total amount Debra ended up paying for the equipment (including the down payment and monthly payments) was $28,541.60.
(b) To find the amount of interest paid on the loan, we need to subtract the total amount borrowed from the total amount paid, and then subtract the down payment. This will give us the total amount of interest paid over the two years.
Total interest paid = Total amount paid - Total amount borrowed - Down payment
Total interest paid = $28,541.60 - $13,200 - $1,300
Total interest paid = $14,041.60
Therefore, the amount of interest Debra paid on the loan was $14,041.60.
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Covert, how many lb. If = 3,200 oz
Answers
Answer:
200 lbs.
Step-by-step explanation:
Divide mass value by 16 to convert oz to lbs.
3,200/16=200
PLEASE HELP
The table of values represents an exponential function.
What is the y-coordinate of -3f(x-1) when x = 0
Enter your answer in the box.
SEE PHOTO
Answers
The y-coordinate of -3f(x-1) when x = 0 is -63
What is the y-coordinate of -3f(x-1) when x = 0From the question, we have the following parameters that can be used in our computation:
The table of values
So, we have
-3f(x - 1)
When x = 0, we have
y = -3f(0 - 1)
This gives
y = -3f(-1)
From the table, we have
y = -3 * 21
Evaluate
y = -63
Hence, the y-coordinate is -63
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Each pound of potatoes costs $1 20 The total cost, in dollars,
is given by the function c(p) = 1.2p.
Pound 1. 2. 3. 4.
Cost in dollars
Common difference
Answers
Answer:
$1.2
Step-by-step explanation:
Given the total cost, in dollars, given by the function c(p) = 1.2p.
If p = 1
c(1) = 1.2(1)
c(1) = $1.2
If p = 2
c(2) = 1.2(2)
c(2) = $2.4
If p = 3
c(3) = 1.2(3)
c(3) = $3.6
If p = 4
c(4) = 1.2(4)
c(4) = $4.8
Common difference = c2 - c1 = c3 - c2 = c4 - c3
Common difference = 2.4 - 1.2 = 3.6 - 2.4 = 4.8 - 3.6 = 1.2
Hence the common difference is $1.2
Part B. Hector said there will be 55 gallon of water in the pool after 11 minutes. Explain how Hector could have found his answer.
Answers
simplify -5^2-2^4
and it just says to make it 20 words long
Answers
Answer:
9 because all you have to do is put number by number in the calculator
Please anyone that can help me
Answers
Answer:
\(|\frac{x}{y} |\)
Step-by-step explanation:
Pre-SolvingWe are given the following expression: \(\sqrt\frac{x^3y^5}{xy^7}\), where x > 0 and y > 0.
We want to simplify it.
To do that, we can first simplify what is under the radical, then take the square root of what is left.
Recall that when simplifying exponents, we don't want any negative or non-integer radicals left.
SolvingTo simplify what is under the radical, we can remember the rule where \(\frac{a^n}{a^m} = a^{n-m}\).
So, that means that \(\frac{x^3}{x} = x^2\) and \(\frac{y^5}{y^7} = y^{-2}\) .
Under the radical, we now have:
\(\sqrt{x^2y^{-2}}\)
Now, we take the square root of both exponents to get:
\(|xy^{-1}|\)
The reason why we need the absolute value signs is because we know that x > 0 and y > 0, but when we take the square root of of \(x^2\) and \(y^{-2}\) , the values of x and y can be either positive or negative, so by taking the absolute value, we ensure that the value is positive.
However, we aren't done yet; remember that we don't want any radicals to be negative, and the integer of y is negative.
Recall that if \(a^{-n}\), that is equal to \(\frac{1}{a^n}\).
So, by using that,
\(|x * \frac{1}{y} |\)
This can be simplified to:
\(|\frac{x}{y} |\)
Tina pet sits to earn extra money. She charges a flat service fee of $20, plus $15 per day. If one of her customers spent less than $125, which of the following inequalities could be used to solve for x, the number of days the customer paid for pet sitting?
Answers
Therefore, **x < 7** is the inequality that may be utilized to find x
What is inequality?A mathematical statement known as an inequality compares two expressions using an inequality sign, such as (less than), > (greater than), or (less than or equal to).
For instance, the inequality x + 2 5 signifies that "x + 2 is less than 5".
Let x represent how many days the client paid for pet sitting.
$15 per day plus a $20 fixed service fee equals the total cost of pet sitting.
We are aware that the customer's purchase was under $125. Consequently, we can write:
20 + 15x < 125
Putting this disparity simply:
15x < 105
x < 7
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A check cashing service found that approximately 5% of all checks submitted to the service were fraudulent. After instituting a check-verification system to reduce its losses, the service found that only 45 checks out of a random sample of 1124 were fraudulent. Does this sample provide sufficient evidence at the .01 significance level that the check verification system is effective
Answers
Answer:
Pvalue of the test is 0.0618 > 0.01, which means that this sample does not provide sufficient evidence at the .01 significance level that the check verification system is effective.
Step-by-step explanation:
A check cashing service found that approximately 5% of all checks submitted to the service were fraudulent.
This means that the null hypothesis is:
\(H_{0}: p = 0.05\)
Test if the check verification system is effective:
If it is effective, the proportion will decrease, so we are going to test if after the change the proportion is lower than 0.05, that is:
\(H_{a}: p < 0.05\)
The test statistic is:
\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)
In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, \(\sigma\) is the standard deviation and n is the size of the sample.
0.05 is tested at the null hypothesis:
This means that
\(\mu = 0.05\)
\(\sigma = \sqrt{0.05*0.95}\)
After instituting a check-verification system to reduce its losses, the service found that only 45 checks out of a random sample of 1124 were fraudulent.
This means that \(n = 1124, X = \frac{45}{1124} = 0.04\)
Value of the test statistic:
\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)
\(z = \frac{0.04 - 0.05}{\frac{\sqrt{0.05*0.95}}{\sqrt{1124}}}\)
\(z = -1.54\)
Pvalue of the test and decision:
Probability of finding a sample proportion lower than 0.04, which is the pvalue of z = -1.54.
Looking at the z-table, z = -1.54 has a pvalue of 0.0618.
Pvalue of the test is 0.0618 > 0.01, which means that this sample does not provide sufficient evidence at the .01 significance level that the check verification system is effective.
A bakery has 2 machines that bake bread. The first machine can make 50 loaves each hour. The second machine can make 75 loaves each hour.
Let h= the number of hours both machines have been making bread. Which THREE of the following expressions can be used to represent the number of loaves of bread that are made in h hours
Answer choices:
A.50h + 75h
B.50 (h+ 25h)
C. 50 + 75h.
D.25h
E. 125h
F.(50 + 75)
Answers
Answer:
A
Step-by-step explanation:
E can also be an answer since 50h +75h =125h but not a equation.
Answer:
Answers A and E are correct.
Step-by-step explanation:
None of the others are correct
Answer F could be corrected by multiplying by h
(50 + 75)h
Assume that we want to estimate the mean IQ score for the population of statistics students. How many statistics students must be randomly selected for IQ tests if we want 95% confidence that the sample mean is within 3 IQ points of the population mean? The Standard Deviation is 15.
Answers
Answer:
97 students must be randomly selected for IQ tests.
Step-by-step explanation:
We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:
\(\alpha = \frac{1 - 0.95}{2} = 0.025\)
Now, we have to find z in the Z-table as such z has a p-value of \(1 - \alpha\).
That is z with a pvalue of \(1 - 0.025 = 0.975\), so Z = 1.96.
Now, find the margin of error M as such
\(M = z\frac{\sigma}{\sqrt{n}}\)
In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.
The Standard Deviation is 15.
This means that \(\sigma = 15\)
How many statistics students must be randomly selected for IQ tests if we want 95% confidence that the sample mean is within 3 IQ points of the population mean?
This is n for which M = 3. So
\(M = z\frac{\sigma}{\sqrt{n}}\)
\(3 = 1.96\frac{15}{\sqrt{n}}\)
\(3\sqrt{n} = 1.96*15\)
Simplifying both sides by 3
\(\sqrt{n} = 1.96*5\)
\((\sqrt{n})^2 = (1.96*5)^2\)
\(n = 96.04\)
Rounding up(as with a sample size of 96 the margin of error will be slightly above 3):
97 students must be randomly selected for IQ tests.
Your friend Brianna is considering getting a credit card. She is going to use the credit card to help build her credit. The credit card she is considering has an APR of 24.99%. It also has a yearly fee of $150.00, but it does offer 1% cash back on most purchases. She asks you for your advice. Use CER to answer the question: Should Brianna get the credit card?
Answers
Based on this evidence and reasoning, it is reasonable to conclude that Brianna should get the credit card, as long as she uses it responsibly and pays off her balance in full every month to avoid paying interest charges.
What is percent?Percent, denoted by the symbol "%", is a way of expressing a fraction or ratio as a portion of 100. It is commonly used in everyday life to express a part of a whole or to compare quantities. Percentages can be used in various contexts, such as in finance to calculate interest rates, in statistics to represent data, and in everyday life to express discounts, tax rates, and tips. It is important to understand percentages to make informed decisions and to effectively communicate information.
Here,
CER stands for Claim, Evidence, and Reasoning, which is a framework for presenting a persuasive argument. Using this framework, we can evaluate whether Brianna should get the credit card in question:
Claim: Brianna should get the credit card.
Evidence:
The credit card has an APR of 24.99%, which is high compared to other credit cards.
The credit card has a yearly fee of $150.00.
The credit card offers 1% cash back on most purchases.
Reasoning:
While the APR and yearly fee are high, Brianna can still benefit from using the credit card to build her credit.
The 1% cash back on most purchases can help offset the cost of the yearly fee and the interest charges if she pays off her balance in full every month.
By using the credit card, such as making payments on time and not carrying a high balance, Brianna can establish a positive credit history, which can help her in the future when she wants to apply for loans or other credit cards.
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how much hours and minutes are there between 9:30am and 1:50 pm.
Answers
Answer: 4 Hours and 20 Minutes
Step-by-step explanation:
find the measure of all the missing angles
Answers
Answer:
a = 70 . b = 55 . c = 25
Step-by-step explanation:
c = 25 (vertically opposite)
100 + 25 = 125
180 - 125 = 55
b = 55
180 - 110 = 70
a = 70
B = 55 degrees as a angles on a straight line equal 180 degrees
C = 25 degrees as opposite angles are equal
Kevin said that if you triple his age the result will be 1 less than his mother age Graph
Answers
Answer:
Let's use "K" to represent Kevin's current age, and "M" to represent his mother's current age.
According to the problem, if you triple Kevin's age, the result is 1 less than his mother's age:
3K = M - 1
We can simplify this equation by adding 1 to both sides:
3K + 1 = M
This equation tells us that if we add 1 to three times Kevin's age, we get his mother's age. We can use this equation to solve for Kevin's age if we know his mother's age, or we can use it to solve for his mother's age if we know Kevin's age.
On a coordinate plane, a point is 4 units to the left and 1 unit down.
For the point shown:
The x-coordinate is
.
The y-coordinate is
.
The point is in quadrant
.
.
Answers
The point has an x-coordinate of -4 and a y-coorindate of -1, and it is on the third quadrant.
In which quadrant is the point?First, remember that for a point (x, y):
if x >0, y > 0, then the point is in quadrant I.if x <0, y > 0, then the point is in quadrant II.if x < 0, y < 0, then the point is in quadrant III.if x >0, y < 0, then the point is in quadrant IV.For the point that is 4 units to the lefft and 1 unit down (of the origin) it is written as:
(-4, -1)
Then we can see that this point is on the quadrant III.
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I Need help asap PLS HURRY
Answers
️️️️️
You substitute -2 into
️️️️️makes it 4(-2) + 10
Which would be ️️️️️️to -8+10
️️️️️️= 2
how can you tell whether or not a figure is a scaled copy of another figure?
Answers
Answer:
If they are divisible by the numbers in the original shape, then try and see if the others sides of the scaled copy are scaled by the same factor. If they are, then they are a scaled copy.
Step-by-step explanation:
the values f(x) of a function f can be made arbitrarily large by taking x sufficiently close to 1 but not equal to 1. which of the following statements must be true?
Answers
The following statements which must be true is \(\lim_{x \to \1} _1\) f ( x ) = ∞.
Given :
the values f ( x ) of a function f can be made arbitrarily large by taking x sufficiently close to 1 but not equal to 1.
Function :
In simple words, a function is a relationship between inputs where each input is related to exactly one output.
Every function has a domain and a co - domain.
x sufficiently close to 1 means x → 1
but x ≠ 1.
so function = \(\lim_{x \to \1} _1\) f ( x ) = ∞
Therefore the following statements which must be true is \(\lim_{x \to \1} _1\) f ( x ) = ∞.
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PLS HELP WILL IVE BRAINLIST
Answers
Answer:
inches: 0 and 7
Step-by-step explanation:
because you are subtracting by 1
Calculate the coefficient of determination for the following data set. Round your answer to three decimal places. ACT Scores and College GPAs ACT Score, x College GPA, y 16 1.85 18 2.20 24 2.80 25 3.50 34 4.00 27 3.18 29 3.90 25 2.90 30 4.00 21 2.60 17 2.50 21 3.65 28 3.10 31 3.72 35 3.24 18 2.30 17 1.70 26 3.10 28 3.50 23 2.76
Answers
Answer:
n=20 \( \sum x = 493, \sum y = 60.5, \sum xy= 1553.01, \sum x^2 =12775, \sum y^2 =192.021\)
And in order to calculate the correlation coefficient we can use this formula:
\(r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}\)
\(r=\frac{20(1553.01)-(493)(60.5)}{\sqrt{[20(12775) -(493)^2][20(192.021) -(60.5)^2]}}=0.8237\)
And then the determination coeffcient would be:
\( r^2 = 0.8237^2= 0.6785 \approx 0.679\)
Step-by-step explanation:
College GPAs ACT Score, x
16 18 24 25 34 27 29 25 30 21 17 21 28 31 35 18 17 26 28 23
College GPA, y
1.85 2.20 2.80 3.50 4.00 3.18 3.90 2.90 4.00 2.60 2.50 3.65 3.10 3.72 3.24 2.30 1.70 3.10 3.50 2.76
From the info given we can calculate the following sums:
n=20 \( \sum x = 493, \sum y = 60.5, \sum xy= 1553.01, \sum x^2 =12775, \sum y^2 =192.021\)
And in order to calculate the correlation coefficient we can use this formula:
\(r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}\)
\(r=\frac{20(1553.01)-(493)(60.5)}{\sqrt{[20(12775) -(493)^2][20(192.021) -(60.5)^2]}}=0.8237\)
And then the determination coeffcient would be:
\( r^2 = 0.8237^2= 0.6785 \approx 0.679\)
HELPPP ME PRECAL CLASS
Answers
the answer is g(x)= (x+6).
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
from the given , we get,
f(x)=x^4
and, f(g(x))= (x+6)^4
hence, the answer is g(x)= (x+6).
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A $525,000 adjustable rate mortgage is expected to have the following payments:
Year Interest Rate Monthly Payment
1–5 4% $2,506.43
6–15 6% $3,059.46
16–25 8% $3,464.78
26–30 10% $3,630.65
A fixed-rate mortgage in the same amount is offered with an interest rate of 4.65%.
What is the difference in the total cost between the two mortgages, rounded to the nearest dollar?
A spreadsheet was used to calculate the correct answer. Your answer may vary slightly depending on the technology used.
$176,580
$878,626
$158,184
$394,911
Answers
Since the adjustable-rate mortgage is more expensive than the fixed-rate mortgage, the answer is $158,184 rounded to the nearest dollar.
To calculate the total cost of the adjustable-rate mortgage, we need to add up all the payments for the 30-year term:
Total cost = 5 years of payments at 4% + 10 years of payments at 6% + 10 years of payments at 8% + 5 years of payments at 10%
Total cost = (5 x 12 x $2,506.43) + (10 x 12 x $3,059.46) + (10 x 12 x $3,464.78) + (5 x 12 x $3,630.65)
Total cost = $150,385.80 + $367,135.20 + $415,773.60 + $217,839.00
Total cost = $1,151,133.60
To calculate the total cost of the fixed-rate mortgage, we can use a mortgage calculator or formula:
Total cost = Monthly payment x Number of payments
Total cost = $2,763.35 x 360
Total cost = $993,606
The difference in total cost between the two mortgages is:
Difference = Fixed-rate mortgage cost - Adjustable-rate mortgage cost
Difference = $993,606 - $1,151,133.60
Difference = -$157,527.60
Thus, the answer is $158,184 rounded to the nearest dollar. Therefore, the correct option is C.
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Find the length of side AB. Round to the nearest hundredth inch.
Answers
The value of length of side AB is,
⇒ AB = 5 units
We have to given that;
The figure is shown a trapezoid.
Hence, By using Pythagoras theorem we get;
⇒ AB² = 4² + (5.25 - 2.25)²
⇒ AB² = 16 + 3²
⇒ AB² = 16 + 9
⇒ AB² = 25
⇒ AB = √25
⇒ AB = 5 units
Therefore, The value of length of AB is,
⇒ AB = 5 units
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The difference between the circumference and the diameter of a circle is 90cm. Find the radius
Answers
Answer:
Step-by-step explanation:
Circumference is 2πr - 2r = 90cm
2r(π-1)=90
divide both sides by (π-1)
2r = 90/(π-1)
2r = 42.024...
r = 21.012399 cm
Find the sum of 4x2 + 3x + 2 and 7x2 + 7x + 3.
Answers
Answer:
27 + 10x
you combine like terms