A credit card company monitors cardholder transaction habits to detect any unusual activity. Suppose that the dollar value of unusual activity for a customer in a month follows a normal distribution with mean $250 and variance $2400.
(a) What is the probability of $250 to $294 in unusual activity in a month? Round your answer to four decimal places (e.g. 98.7654) P-0.4861
(b) What is the probability of more than $294 in unusual activity in a month? Round your answer to four decimal places (e.g. 98.7654) P 0.0139
(c) Suppose that 10 customer accounts independently follow the same normal distribution. What is the probability that at least one of these customers exceeds $294 in unusual activity in a month? Round your answer to four decimal places (e.g. 98.7654)
Answer:
Step-by-step explanation:
Let x be the random variable representing the dollar value of unusual activity for a customer in a month. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = standard deviation
From the information given,
µ = 250
σ = √variance = √2400 = 48.99
a) the probability of $250 to $294 in unusual activity in a month is expressed as
P(250 ≤ x ≤ 294)
For x = 250,
z = (250 - 250)/48.99 = 0
Looking at the normal distribution table, the probability corresponding to the z score is 0.5
For x = 294
z = (294 - 250)/48.99 = 0.9
Looking at the normal distribution table, the probability corresponding to the z score is 0.8159
Therefore,
P(250 ≤ x ≤ 294) = 0.8159 - 0.5 = 0.3159
b) the probability of more than $294 in unusual activity in a month is expressed as
P(x > 294) = 1 - P(x < 294)
P(x > 294) = 1 - 0.8159 = 0.1841
c) since n = 10, the formula becomes
z = (x - µ)/(σ/n)
z = (294 - 250)/(48.99/√10) = 2.84
Looking at the normal distribution table, the probability is 0.9977
Therefore, the probability that at least one of these customers exceeds $294 in unusual activity in a month is
1 - 0.9977 = 0.0023
Jose runs a factory that makes stereo tuners. Each S100 takes 8 ounces of plastic and 4 ounces of metal. Each FS20 requires 4 ounces of plastic and 6 ounces of metal. The factory has 312 ounces of plastic, 372 ounces of metal available, with a maximum of 20 S100 that can be built each week. If each S100 generates $7 in profit, and each FS20 generates $13, how many of each of the stereo tuners should Jose have the factory make each week to make the most profit
Answer: Jose should have the factory make 50 FS20 stereo tuners and 14 S100 stereo tuners each week to make the most profit
Step-by-step explanation:
Since each S100 takes 8 ounces of plastic and 4 ounces of metal. Each FS20 requires 4 ounces of plastic and 6 ounces of metal. And the factory has 312 ounces of plastic, 372 ounces of metal available, then,
For plastic
8 ounces + 4 ounces = 12 ounces
The number of stereo tuners it can produce will be
312/12 = 26 stereo tuners
For metal
4 ounces + 6 ounces = 10 ounces
The number of stereo tuners it can produce will be
372/10 = 37.2 = 37 approximately
Since FS20 generate more profit than S100, let assume that Jose produces 50 FS20 by consuming
4 × 50 = 200 ounces of plastic
6 × 50 = 300 ounces of metal
The remaining plastic will be
312 - 200 = 112
The remaining plastic will be
372 - 300 = 72
Divide 112 by 8 in order to make S100
112/8 = 14
Also 72/4 = 18.
Therefore, Jose should have the factory make 50 FS20 stereo tuners and 14 S100 stereo tuners each week to make the most profit
Goods available for sale are $40000, beginning inventory is $16000, ending inventory is $20000, the cost of goods sold $50000, what is the inventory turnover
Answer:
2.78Step-by-step explanation:
Inventory turn over is the same as the inventory turn over ratio. Inventory turn over is defined simply as the ratio of the cost of goods that was sold (net sales) to the average inventory at the selling price.
Inventory turn over = Cost of goods/average inventory
Cost of goods sold = $50000
Average inventory = beginning of inventory + ending inventory/2
Average inventory = $16000+$20000/2
Average inventory = $36000/2
Average inventory = $18000
Inventory turn over = $50000/$18000
Inventory turn over= 2.78
g You run a regression analysis on a bivariate set of data ( n = 14 ). With ¯ x = 27.7 and ¯ y = 26.5 , you obtain the regression equation y = 0.495 x − 14.914 with a correlation coefficient of r = 0.39 . You want to predict what value (on average) for the response variable will be obtained from a value of 110 as the explanatory variable. What is the predicted response value?
Answer:
Predicted response value = 39.536
Note that this predicted response value will most likely be far from the actual response value because the correlation coefficient of the regression equation used (r = 0.39) is too far away from 1.
Step-by-step explanation:
The response variable is the dependent variable (y) whose value is obtained from the expression involving the independent variable (x).
For this question, although the correlation coefficient, r = 0.39, is far from 1, the regression equation is
y = 0.495x - 14.914
The predicted response value will be obtained from the explanatory variable and the regression equation
x = 110
y = 0.495x - 14.914
y = (0.495×110) - 14.914 = 39.536
Note that this predicted response value will most likely be far from the actual response value because the correlation coefficient of the regression equation used (r = 0.39) is too far away from 1.
Hope this Helps!!!
find the value of the expression :1/216^-2/3 + 1/256^-3/4 + 1/243^-1/5
Answer:
103
Step-by-step explanation:
A number to the power of a negative exponent, means 1 divided by that same number to the power of the positive exponent.
1/(216^(-2/3)) + 1/(256^(-3/4)) + 1/(243^(-1/5))
Break it apart into three pieces.
1/(216^(-2/3))
216^(2/3) = 36
1/(256^(-3/4))
256^(3/4) = 64
1/(243^(-1/5))
243^(1/5) = 3
So...
1/(216^(-2/3)) = 36
1/(256^(-3/4)) = 64
1/(243^(-1/5)) = 3
Add the numbers gives:
36 + 64 + 3 = 103
The manufacturer of a smart watch claims that individuals who pay attention to how many steps they take per day will inadvertently take more steps per day than individuals who pay no attention to how many steps they take per day. To investigate this claim, the manufacturer conducts a study to estimate the difference in the mean number of steps taken by those that pay attention to how many steps they take per day and those that do not. To do so, 40 volunteers are recruited. Half of the volunteers are randomly assigned to receive a smart watch and are taught how to use it to track their steps. The other half of the volunteers are given a wristband to wear, but are not informed that the wristband is tracking their steps. The volunteers are monitored for 30 days. The mean and standard deviation of the number of steps taken per day are computed for each group. Here are the data:
Payti
Do not pay itin 01 0 10 20 87 64 82 350
Which of the following is a 99% confidence interval for the difference in the mean number of steps taken by all people like these that do and do not pay attention to the number of steps they take per day using df - 192
(A) 1596 + 2.861/15802 + 23502
(B) 1596 +2.861, 15.302 – 23502
(C) 1596 +2.576,15802 + 23502
(D) 1596 + 2.576 ( 15802 + 23502) °
(E) 1596 + 2.576 ( 15892 – 23502)
Here is the correct question.
The manufacturer of a smart watch claims that individuals who pay attention to how many steps they take per day will inadvertently take more steps per day than individuals who pay no attention to how many steps they take per day. To investigate this claim, the manufacturer conducts a study to estimate the difference in the mean number of steps taken by those that pay attention to how many steps they take per day and those that do not. To do so, 40 volunteers are recruited. Half of the volunteers are randomly assigned to receive a smart watch and are taught how to use it to track their steps. The other half of the volunteers are given a wristband to wear, but are not informed that the wristband is tracking their steps. The volunteers are monitored for 30 days. The mean and standard deviation of the number of steps taken per day are computed for each group. Here are the data:
[tex]n[/tex] [tex]\bar x[/tex] [tex]S_x[/tex]
Pay attention 20 10,244 1,580
Do not pay attention 20 8.,648 2,350
Which of the following is a 99% confidence interval for the difference in the mean number of steps taken by all people like these that do and do not pay attention to the number of steps they take per day using df - 19 ?
[tex](A) \ 1596 \ \pm 2.861 \sqrt{ \dfrac{1580^2}{20} + \dfrac{2350^2}{20}} \\ \\ \\ (B) \ 1596 \ \pm 2.861 \sqrt{ \dfrac{1580^2}{20} - \dfrac{2350^2}{20}} \\ \\ \\ (C) \ 1596 \pm 2.576 \sqrt{ \dfrac{1580^2}{20} + \dfrac{2350^2}{20}} \\ \\ \\ (D) 1596 \pm 2.576 ( \dfrac{1580^2}{\sqrt{20}} + \dfrac{2350^2}{\sqrt{20}}) \\ \\ \\ (E) 1596 \pm 2.576 ( \dfrac{1580^2}{\sqrt{20}} - \dfrac{2350^2}{\sqrt{20}})[/tex]
Answer:
[tex]\mathbf{(A) \ 1596 \ \pm 2.861 \sqrt{ \dfrac{1580^2}{20} + \dfrac{2350^2}{20}}}[/tex]
Step-by-step explanation:
Given that :
significance level [tex]\alpha = \mathbf{0.01}[/tex]
From the Given data;
Using Excel with the function : TINV(0.01,19);
Critical value t* = 2.861
The margin of error can now be represented by the illustration:
Margin of error = [tex]t^* \sqrt{ \dfrac {s_1 ^2}{n_1} + \dfrac {s_2 ^2}{n_2}[/tex]
Lower Limit = [tex](\bar x_1 - \bar x_2)- (Margin \ of \ error)[/tex]
Upper Limit = [tex](\bar x_1 - \bar x_2)+ (Margin \ of \ error)[/tex]
Thus; the confidence interval for the difference in the mean number of steps taken by all people like these that do and do not pay attention to the number of steps they take per day using df - 19 is:
[tex]\mathbf{(A) \ 1596 \ \pm 2.861 \sqrt{ \dfrac{1580^2}{20} + \dfrac{2350^2}{20}}}[/tex]
Labrador Retriever weighs 48 kg after a diet and exercise program the dog weighs 43 kilograms to determine if this shows a percent increase or decrease and explain why what is the percent change of its weight a 10% B 11% C 110% D 111% please help.
Answer:
percentage change in weight ≈ 10%
Step-by-step explanation:
The dog weighed 48 kg after a diet and after an exercise program the dog had a weight of 43 kg. This means the dog loss weight since the dog weight decreased from an initial value of 48 kg to 43 kg. The decrease in weight can be calculate as
decrease in weight = original weight - new weight
original weight = 48 kg
new weight = 43 kg
decrease in weight = 48 - 43 = 5 kg
Since the weight decrease their will be a percentage decrease in weight.
% decrease = decrease in weight/original weight × 100
% decrease = 5/48 × 100
% decrease = 500/48
% decrease = 10. 42666666667
percentage change in weight ≈ 10%
3y-y please can you work it out
Given that f(x)=x^2+4x-32f(x)=x
2 +4x−32 and g(x)=x-4g(x)=x−4, find (f+g)(x)(f+g)(x) and express the result in standard form.
Answer:
So your question was not very clear but with (f+g) im guessing thats f(x)+g(x)
So first we add them x^2+4x-32 + x-4 then we will get x^2 + 5x - 36
Then we need to multiply both
(x^2+5x-36)(x^2+5x-36)
=
(x^2+5x-36)^2
The only reason im not solving it out is because it yields large numbers and you might not understand.
At the Rowlett Holiday Parade
there were a total of 51 floats. If
7 of those floats were from
sports teams, what percent
were NOT sports teams?
Answer:
[tex] p =\frac{7}{51}= 0.1372[/tex]
And then the probability that is NOT from sport temas using the complement rule is given by:
[tex] q = 1-p =1- \frac{7}{51}= 0.8627[/tex]
And if we convert that into % we got:
[tex] 0.8627 *100= 86.27\%[/tex]
Approximately 86.27% of the floats were NOT sports teams
Step-by-step explanation:
For this case we can begin finding the % of floats that were from sport tems using the Laplace definition of probability given by:
[tex]p = \frac{Possible}{Total}[/tex]
And replacing we got:
[tex] p =\frac{7}{51}= 0.1372[/tex]
And then the probability that is NOT from sport temas using the complement rule is given by:
[tex] q = 1-p =1- \frac{7}{51}= 0.8627[/tex]
And if we convert that into % we got:
[tex] 0.8627 *100= 86.27\%[/tex]
Approximately 86.27% of the floats were NOT sports teams
Directly above center court, the Yakima SunDome in Yakima, Washington, rises to its maximum height of 92 ft. The angle of elevation from justins parking spot at a Yakama sun kings home to the top of the dome is 11. To the nearest fooot how far from the center court is Justin Parked?
Answer:
473 feet.
Step-by-step explanation:
Let's look at the image below. We have that the angle of elevation from Justin parking spot is 11º and the height of the building is 92 feet and we need to know how far from the building is Justin parked, in other words, we need to find x in the image.
We can see that to find x we can use a trigonometric function (in this case is tan since we have the Opposite side (92 feet) and we need the Adjacent side (x)
Thus we have:
[tex]Tan11= \frac{92}{x} \\0.1943=\frac{92}{x}\\ x=\frac{92}{0.1943}\\ x=473.49\\x=473[/tex]
Thus, Justin is parked 473 feet away from the center court.
Simplify the given expression. Assume x doesn’t = 0. (20x^-3/10x^-1)^-2
X^4/2
X^4/4
X^2/4
Answer:
X^4
------
4
Step-by-step explanation:
The simplified expression is 1/4x²
What is a polynomial expression?Polynomial is made up of two terms, namely Poly (meaning “many”) and Nominal (meaning “terms.”). A polynomial is an expression composed of variables, constants, and exponents, combined using mathematical operations such as addition, subtraction, multiplication, and division (No division operation by a variable). Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial. For example P(x) = x²-5x+11
Given here, the expression is (20x⁻³ / 10x⁻¹)⁻² =2⁻²× x⁻²
= 1/4x²
Hence, the simplified expression is 1/4x²
Learn more about polynomial expression here:
https://brainly.com/question/11536910
#SPJ2
Borland, Inc., has a profit margin of 5.6 percent on sales of $13.6 million. If the firm has debt of $6.4 million and total assets of $9.8 million, what is the firm’s ROA?
Answer:
ROA = 7.77 percent
Step-by-step explanation:
Borland, Inc., has a profit margin of 5.6 percent on sales of $13.6 million
Thus, profit = 5.6% of $13.6 million
profit = 5.6 / 100 * $13.6 million = $0.7616 million
Profit is same as net income
Formula for ROA (return on asset) = net income/ total asset
total asset as given = $9.8 million
Thus, ROA = $0.7616/ $9.8 = 0.0777
ROA in percentage = 0.0777*100 = 7.77
Thus, ROA is 7.77 percent .
X+4 is prime. X2-9can be factored using the __formula
[tex] \purple \bold{a^2 - b^2} [/tex]
Step-by-step explanation:
X+4 is prime. X2-9can be factored using the [tex] \purple \bold{a^2 - b^2} [/tex] formula
[tex] x^2 - 9\\
=x^2 - 3^2 \\
= (x+3)(x-3)[/tex]
Answer: difference-of-squares
next one is (x+3)(x-3)(x+4)
Step-by-step explanation:
just took it on ed genuity :)
The author purchased a slot machine (Bally Model 809) and tested it by playing it 1197 times. There are 10 different categories of outcomes, including no win, win jackpot, win with three bells, and so on. When testing the claim that the observed outcomes agree with the expected frequencies, the author obtained a test statistic of x^2 = 8.185 . Use α= 0.05 significance level to test the claim that the actual outcomes agree with the expected frequencies. Does the slot machine appear to be functioning as expected?
Answer:
No the slot machine doesn't appear to function as expected.
Step-by-step explanation:
From chi-squared table , for 9 degrees of freedom and alpha 0.05,
critical value is, 3.325.
Since observed value is greater than critical value we can say that actual outcomes do not agree with the expected frequencies. The slot machine doesn't appear to function as expected.
What sequence is generated by the function f(n+1)=f(n)-2 for f(1)=10
Answer:
-3
Step-by-step explanation:
Please answer this correctly
Answer:
342 square meters
Step-by-step explanation:
Consider the length of j;
[tex]j * 9 * 9 = 405,\\j = 405 / 81,\\j = 5 meters[/tex]
Applying the volume of a rectangular prism formula length * width * height = volume, we noted that 9, 9, and j corresponded to the length, width, and height of the rectangular prism and made it equivalent to the volume. Doing so, we solved for j. Now let us solve for the surface area;
[tex]Area of 1st Face = 5 * 9 = 45,\\Area of 2nd Face = 9 * 9 = 81,\\Area of 3rd Face = 5 * 9 = 45,\\\\Surface Area = 2 * ( 45 ) + 2 * ( 81 ) + 2 * ( 45 ) = 342 square meters[/tex]
Opposite faces are equal in terms of their area, so by finding the area of 3 faces, we multiply their area each by 2 to result in the total surface area!
A box plot is shown below:
What is the median and Q1 of the data set represented on the plot?
Median = 31; Q1 = 26
Median = 30; Q1 = 26
Median = 31; Q1 = 20
Median = 30; Q1 = 20
Answer:
Step-by-step explanation:
Hello!
I didn't find the exact box plot for this exercise but I've found one that'll help you identify the required values
When constructing a box plot the box lower and upper limits are defined by the first and third quartiles and the line separating it in two represents the median.
In this case, the box is lying on the side, the first quartile is represented by the left side of the box. If you see the graphic this one corresponds to 25.
The median, as said, is represented by the line drawn inside the box, it is not necessarily in its middle but it will always be inside it.
Watching the example, the median is 33
I hope this helps!
Answer: D
Step-by-step explanation:
A steep mountain is inclined 74 degree to the horizontal and rises to a height of 3400 ft above the surrounding plain. A cable car is to be installed running to the top of the mountain from a point 890 ft out in the plain from the base of the mountain. Find the shortest length of cable needed.
Answer:
about 3878 ft
Step-by-step explanation:
Assuming that the cable is not doubled, we need to find the length of the base of the mountain i.e
3400/tan(74) = about 975 ft
Therefore, the length of the cable =
√[ 3400² + (975 + 890)²] = about 3878 ft
True or False: As the value of cos(x) approaches 1 and the value of sin(x) approaches 0, the value of tan(x) approaches infinity
Answer: False
Step-by-step explanation:
We can write tan(x) = sin(x)/cos(x)
if cos(x) tends to 1, and sin (x) tends to 0 (this happens aronund the point x = 0)
then we have:
Tan(x) = 0/1 = 0
Then the statement is false, as cos(x) approaches 1 and sin(x) approaches 0, tan(x) also approaches 0.
NEED HELP ASAP!!! a hexagon-based pyramid has a height of 54cm. The volume of the pyramid is 1080cm3. What is the area of the base?
Answer:
32
Step-by-step explanation:
What is the simplified value of the exponential expression 27 1/3 ?
1/3
1/9
3
9
Answer:
3
Step-by-step explanation:
27^1/3 = cuberoot(27) = 3
Marta recorded the temperature at 8 p.m. as 56°F and the temperature at 8 a.m. the next morning as 36°F. Marta assumed the temperature changed at a constant rate. She wrote an equation to find the number of degrees the temperature dropped each hour, h, of the night. Which equation did Marta write?
Answer: 5h/3
Step-by-step explanation:
12 hours passed, and 20 degrees dropped.
Every hour, that's 20/12 = 5/3 degrees dropped. Therefore, the equation is 5h/3.
Hope that helped,
-sirswagger21
Answer:
5h 3
Step-by-step explanation:
12 hours passed, and 20 degrees dropped.
Every hour, that's 20/12 = 5/3 degrees dropped. Therefore, the equation is 5h/3.
Hope that helped,
-sirswagger21
Only answer if you know geometry or if you know this
Answer:
SAS
Step-by-step explanation:
the angles are congruent, and the 2 pairs of sides are proportional.
200/150 is 4/3 and 320/240 is 4/3 as well.
therefore Side-Angle-Side
The following data shows the weekly amounts spent on food for a family of three in a random sample of 30 families:
40 42 46 47 47 48 52 53 53 53
54 56 57 57 57 57 58 58 58 62
62 63 63 63 63 66 67 68 72 73
1. Determine the number of classes and the class interval.
2. Group the data into a frequency distribution starting with the lowest value.
3. Draw an absolute frequency histogram using class limits.
4. Draw a relative frequency polygon for the data using midpoints.
5. Draw a cumulative frequency polygon (ogive) for the data using class limits
Answer:
1. Number of classes used are 7 with 5 class interval.
Step-by-step explanation:
Note: See the attached files for the tables and answers to questions 2, 3, 4 and 5.
how much alcohol must be added to 480grams of hand sanitizer that is 24% alcohol to make it a hand sanitizer that is 40% alcohol?
Answer:
what she/he said
Step-by-step explanation:
When planning road development, the road commission estimates the future population using the function represented in the table, where x is the time in years and f(x) is the total population. What is the significance of 160,000 in the function . Graph is x: 0, 1, 2, 3, 4, 5 f(x):160,000, 163,200, 166,464, 169,793, 173,189, 176,653
Answer:C
Step-by-step explanation:
Answer:
The answer is C
Step-by-step explanation:
Source: Dude trust me
Simplify (x2y)3. x 5y 3 x 2y 3 x 6y 3
Answer:
[tex]x^{6} y^{3}[/tex]
Step-by-step explanation:
[tex](x^2y)3[/tex]
[tex]x^{2 \times 3} \times y^3[/tex]
[tex]x^{6} \times y^3[/tex]
A company is constructing an open-top, square-based, rectangular metal tank that will have a volume of 49 cubic feet. What dimensions yield the minimum surface area? Round to the nearest tenth.
Answer:
b = 4.6 ft
h = 2.3 ft
Step-by-step explanation:
The volume of the tank is given by:
[tex]b^2*h=49[/tex]
Where 'b' is the length of the each side of the square base, and 'h' is the height of the tank.
The surface area can be written as:
[tex]A=b^2+4bh\\A=b^2+4b*({\frac{49}{b^2}})\\A=b^2+\frac{196}{b}[/tex]
The value of b for which the derivate of the expression above is zero is the value that yields the minimum surface area:
[tex]\frac{dA}{db} =0=2b-\frac{196}{b^2}\\2b^3=196\\b=4.61\ ft[/tex]
The value of h is then:
[tex]h=\frac{49}{4.61^2}\\h=2.31\ ft[/tex]
Rounded to the nearest tenth, the dimensions are b = 4.6 ft and h = 2.3 ft.
Consider the vector x: x <- c(2, 43, 27, 96, 18) Match the following outputs to the function which produces that output. Options include sort(x), order(x), rank(x) and none of these
Completed Question
Outputs to be matched to the functions are:
1,2,3,4,51,5,3,2,41, 4, 3, 5, 2 2, 18, 27, 43, 96Answer:
sort(x): 2, 18, 27, 43, 96 order(x): 1, 5, 3, 2, 4 rank(x) : 1, 4, 3, 5, 2none of these : 1, 2, 3, 4, 5Step-by-step explanation:
Given the vector x: x <- c(2, 43, 27, 96, 18)
Sort
In R, the sort(x) function is used to arrange the entries in ascending or descending order. By default, R will sort the vector in ascending order.
Therefore, the output that matches the sort function is:
sort(x): 2, 18, 27, 43, 96
Rank
The rank function returns a vector with the "rank" of each value.
x <- c(2, 43, 27, 96, 18)
2 has a rank of 143 has a rank of 427 has a rank of 396 has a rank of 518 has a rank of 2Therefore, the output of rank(x) is: 1, 4, 3, 5, 2
Order
When the function is sorted, the order function gives the previous location of each of the element of the vector.
Using the sort(x) function, we obtain: 2, 18, 27, 43, 96
In the vector: x <- c(2, 43, 27, 96, 18)
2 was in the 1st position18 was in the 5th position27 was in the 3rd position43 was in the 2nd position96 was in the 4th positionTherefore, the output of order(x) is: 1, 5, 3, 2, 4
