Answer:
80% confidence interval for the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases ([tex]\mu_1-\mu_2[/tex]) is [-9.132 , 23.332].
Step-by-step explanation:
We are given that a random sample of 7 sales receipts for mail-order sales results in a mean sale amount of $81.70 with a standard deviation of $18.75.
A random sample of 11 sales receipts for internet sales results in a mean sale amount of $74.60 with a standard deviation of $28.25.
Firstly, the Pivotal quantity for 80% confidence interval for the difference between population means is given by;
P.Q. = [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } }[/tex] ~ [tex]t__n__1-_n__2-2[/tex]
where, [tex]\bar X_1[/tex] = sample mean sales receipts for mail-order sales = $81.70
[tex]\bar X_2[/tex] = sample mean sales receipts for internet sales = $74.60
[tex]s_1[/tex] = sample standard deviation for mail-order sales = $18.75
[tex]s_2[/tex] = sample standard deviation for internet sales = $28.25
[tex]n_1[/tex] = size of sales receipts for mail-order sales = 7
[tex]n_2[/tex] = size of sales receipts for internet sales = 11
Also, [tex]s_p=\sqrt{\frac{(n_1-1)s_1^{2} +(n_2-1)s_2^{2} }{n_1+n_2-2} }[/tex] = [tex]\sqrt{\frac{(7-1)\times 18.75^{2} +(11-1)\times 28.25^{2} }{7+11-2} }[/tex] = 25.11
Here for constructing 80% confidence interval we have used Two-sample t test statistics as we don't know about population standard deviations.
So, 80% confidence interval for the difference between population means, ([tex]\mu_1-\mu_2[/tex]) is ;
P(-1.337 < [tex]t_1_6[/tex] < 1.337) = 0.80 {As the critical value of t at 16 degree
of freedom are -1.337 & 1.337 with P = 10%}
P(-1.337 < [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } }[/tex] < 1.337) = 0.80
P( [tex]-1.337 \times {s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } }[/tex] < [tex]{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}[/tex] < [tex]1.337 \times {s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } }[/tex] ) = 0.80
P( [tex](\bar X_1-\bar X_2)-1.337 \times {s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } }[/tex] < ([tex]\mu_1-\mu_2[/tex]) < [tex](\bar X_1-\bar X_2)+1.337 \times {s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } }[/tex] ) = 0.80
80% confidence interval for ([tex]\mu_1-\mu_2[/tex]) =
[ [tex](\bar X_1-\bar X_2)-1.337 \times {s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } }[/tex] , [tex](\bar X_1-\bar X_2)+1.337 \times {s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } }[/tex] ]
= [ [tex](81.70-74.60)-1.337 \times {25.11 \times \sqrt{\frac{1}{7} +\frac{1}{11} } }[/tex] , [tex](81.70-74.60)+1.337 \times {25.11 \times \sqrt{\frac{1}{7} +\frac{1}{11} } }[/tex] ]
= [-9.132 , 23.332]
Therefore, 80% confidence interval for the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases ([tex]\mu_1-\mu_2[/tex]) is [-9.132 , 23.332].
A regular deck of cards has 52 cards with 4 aces. Carl asked a friend to pick a card from the deck three times, replacing the card each time. His friend picked three aces. Which expression will give the probability of that event?
(StartFraction 4 over 52 EndFraction) (StartFraction 4 over 52 EndFraction) (StartFraction 4 over 52 EndFraction)
(StartFraction 1 over 52 EndFraction) (StartFraction 1 over 51 EndFraction) (StartFraction 1 over 50 EndFraction)
(StartFraction 4 over 52 EndFraction) (StartFraction 4 over 51 EndFraction) (StartFraction 4 over 50 EndFraction)
(StartFraction 4 over 52 EndFraction) (StartFraction 3 over 51 EndFraction) (StartFraction 2 over 50 EndFraction)
Answer:
The answer is A
Step-by-step explanation:
Edg : )
Answer:
A
Step-by-step explanation:
What’s the correct answer for this?
Answer:
A
Step-by-step explanation:
Suppose p = 6 and b = 8, so that tan x is 6/8
Then the hypotenuse is sq rt (6x6 + 8x8) = sq rt (36 + 64) = sq rt (100) = 10
So sin x = p / h = 6 / 10
And cos x = b / h = 8 / 10
So A is the answer
Answer:
A. sin x = 6/10 and cos x = 8/10.
Step-by-step explanation:
If tan x is 6/8 the opposite side to x = 6 and the adjacent side = 8.
So the hypotenuse of the triangle = √(6^2 + 8^2)
= √100
= 10.
So sin x = 6/10 and cos x = 8/10.
Mrs. McAlister wrote the equation 10t-4t+3t=8 on the board and asked students to write equivalent equations.
As we solve we generate a succession of equivalent equations.
10t - 4t + 3t = 8
9t = 8
t = 8/9
Answer:
10t-4t+3t=8
t (10-4+3)=8
t (9)=8
9t=8
t=8/9
Step-by-step explanation:
In the question stated above, the common factor amongst the numbers with the variables is t, therefore we factorise the t out of the numbers, hence leaving t outside the bracket. After we solve the equation of the simple numbers of which the product is 9. After this we already know the 9 is to be multiplied by the t to make it 9t=8. We divide both side by the 9 and get a result of t=8/9
The Hawkins Company randomly samples 10 items from every large batch before the batch is packaged and shipped. According to the contract specifications, 5 percent of the items shipped can be defective. If the inspectors find 1 or fewer defects in the sample of 10, they ship the batch without further inspection. If they find 2 or more, the entire batch is inspected.
(A) Based on this sampling plan, the probability that a batch that meets the contract requirements will be shipped without further inspection is approximately___________.
Answer:
0.9138 = 91.38%
Step-by-step explanation:
For each item, there are only two possible outcomes. Either it is defective, or it is not. The probability of an item being defective is independent of other items. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
10 items
This means that [tex]n = 10[/tex]
5 percent of the items shipped can be defective.
This means that [tex]p = 0.05[/tex]
Probability that a batch that meets the contract requirements will be shipped without further inspection
Probability of 1 or fewer defects.
So
[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{10,0}.(0.05)^{0}.(0.95)^{10} = 0.5987[/tex]
[tex]P(X = 1) = C_{10,1}.(0.05)^{1}.(0.95)^{9} = 0.3151[/tex]
[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.5987 + 0.3151 = 0.9138[/tex]
So the answer is:
0.9138 = 91.38%
Answer:
The answer is 0.9138
Step-by-step explanation:
This is a question of Binomial Probability Combination and the formula that will be used in this question is:
[tex]P(x) = nCx * p^{x} * q^{n - x}[/tex]
Where,
n ⇒ Finite sample number, here it is equal to 10p ⇒ Success, here it is equal to 5% defective or [tex]\frac{5}{100} = 0.05[/tex] q ⇒ Failure, here it is equal to (1 - p) i.e. [tex]q = 1 - \frac{5}{100} = 0.95[/tex][tex]x[/tex] ⇒ Number of defective productsNow, in order to to pass inspection and be shipped [tex]x[/tex] needs to be equal to '0' or '1'.
So,
Putting [tex]x = 0[/tex] in the formula along with the values mentioned above we get
[tex]P(0) = 10C0 * 0.05^{0} * 0.95^{10 - 0}[/tex]
[tex]P(0) = 1 * 1 * 0.5987[/tex]
[tex]P(0) = 0.5987[/tex]
Similarly,
Putting [tex]x = 1[/tex] in the formula along with the values mentioned in the bullets above we get
[tex]P(1) = 10C1 * 0.05^{1} * 0.95^{10 - 1}[/tex]
[tex]P(1) = 10 * 0.05 * 0.6302[/tex]
[tex]P(1) = 0.3151[/tex]
Now, in order to get the actual probability we need to add [tex]P(0)[/tex] and [tex]P(1)[/tex] because there is a chance that either there is no defective product or there is 1 defective in the shipped-batch from which sample was taken. Hence,
[tex]P(0) + P(1) = 0.5987 + 0.3151[/tex]
= 0.9138 (Answer)
What do you have to know before you can round a number
Answer:
if it ends in 5 then you round up but if it's less than 5 you round down
Step-by-step explanation:
You first have to locate the digit in the rounding place and this digit can be in the ones place, tens place,
hundreds place, thousands place, and so on.
After you locate the digit, look at the
digit to the right of the rounding place.
If the digit to the right of the rounding place is less than 5, we round down and if the digit is greater than or equal to 5, we round up.
You roll a number cube numbered from 1 to 6. What is the probability that the number is 3?
Answer:
1/6
Step-by-step explanation:
because there is only one number 3 there is a 1/6 chance of you getting a 3
What is more 7 9/10 or 7 4/5?
Answer:
7 9/10
Step-by-step explanation:
Fernando factored 45y^6 as (9y^3)(5y^3).
Salma factored 45y as (3y)(15y^5).
Which of them factored 45y^6 correctly?
Answer:
They both factored it correctly
Step-by-step explanation:
To find the one that was factored correctly, we expand the two of them and compare with [tex]45y^6[/tex].
Fernando
[tex](9y^3)(5y^3)[/tex]
= [tex]9 * 5 * y^3 * y^3[/tex]
= [tex]45y^6[/tex]
Salma
[tex](3y)(15y^5)[/tex]
= [tex]3 * 15 * y * y^5[/tex]
= [tex]45y^6[/tex]
As we can see, they both factored it correctly.
Answer:
both are correct in their factoring
Step-by-step explanation:
Solve equations using structure
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Let m = x2 + 3.
Which equation is equivalent to (x2 + 3)2 + 7x2 + 21 =
10 in terms of m?
Answer: [tex]9m=10[/tex] or [tex]m=\frac{10}{9}[/tex]
I don't know your options... but you can check my work below and see if any of the other options fit yours.
Step-by-step explanation:
[tex](x^2 + 3)2 + 7x^2 + 21 =10[/tex]
If [tex]x^2+3=m[/tex], we can rewrite this as;
[tex](m)2+7x^2+21=10\\2m+7x^2+21=10[/tex]
By grouping, we can factor another m.
[tex]2m+(7x^2+21)=10[/tex]
Factor a 7.
[tex]2m+7(x^2+3)=10[/tex]
Rewrite it in terms of m.
[tex]2m+7m=10[/tex]
Combine like terms;
[tex]9m=10[/tex]
Divide by 9
[tex]m=\frac{10}{9}[/tex]
877+100=__+258help me
Answer:
719 = x
Step-by-step explanation:
877+100=_x_+258
Combine like terms
977 = x+258
Subtract 258
977 -258 = x+258-258
719 = x
Which expression shows a way to find 25% of 1000?
Answer:250
Step-by-step explanation:
25% of 1000
25/100 x1000
(25 x 1000)/100
25000/100=250
1+4=5
2+5=12
3+6=21
8+11=?
Answer:40
Step-by-step explanation:
21+8=29
29+11=40
The sum of two consecutive even integers is 186. What are the two numbers?
Answer: 92 and 94
Step-by-step explanation:
x = first number
x + 2 = second number
x + x + 2 = 186
simplify
2x + 2 = 186
subtract 2 from both sides
2x = 184
divide both sides by 2
x = 92
92 + 2 = 94
The numbers are 92 and 94.
Make sure you read through the problem carefully so that you recognize that we are dealing with consecutive even integers here.
Any 2 consecutive even integers can be represented as x + x + 2.
So we can represent our integers as follows.
X ⇒ first integer
X + 2 ⇒ second integer
Since their sum is 168, our equation reads x + x + 2 = 186.
Simplifying on the left side gives us 2x + 2 = 186.
Now subtract 2 from both sides to get 2x = 184.
Now divide both sides by 2 and we find that x = 92.
If x = 92, then x + 2 will be 92 + 2 or 94.
So our two consecutive integers are 92 and 94.
Which of these quadrilaterals are rectangles?
Answer:Parallelogram, rhombus ,square
Step-by-step explanation:
14 points
At the college football game there were 48,000 people. If 77% of the
people at the game were supporters for the home team, how many
people were supporting the home team?*
11,040
36,960
62,338
36,000
Answer:
11,040 is the answer
Step-by-step explanation:
you just need to subtract
There are 36,960 people were supporting the home team.
What is the percentage?A percentage is a minimum number or ratio that is measured by a fraction of 100.
At the college football game there were 48,000 people.
If 77% of the people at the game were supporters for the home team then we need to find how many people were supporting the home team.
x/ 48000 = 77/ 100
here plugging in all our numbers gives us .
x = (77/ 100)48000
x = 36,960
Therefore, There are 36,960 people were supporting the home team.
Learn more about percentages;
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Suppose a 3x6 coefficient matrix for a system has three pivot columns. Is the system consistent? Why or why not? Choose the correct answer below. A. There is at least one row of the coefficient matrix that does not have a pivot position. This means the augmented matrix, which will have seven columns, could have a row of the form [Start 1 By 7 Matrix 1st Row 1st Column 0 2nd Column 0 3rd Column 0 4st Column 0 5st Column 0 6st Column 0 7st Column 1 EndMatrix ], so the system could be inconsistent. B. There is at least one row of the coefficient matrix that does not have a pivot position. This means the augmented matrix, which will have seven columns, must have a row of the form [Start 1 By 7 Matrix 1st Row 1st Column 0 2nd Column 0 3rd Column 0 4st Column 0 5st Column 0 6st Column 0 7st Column 1 EndMatrix ], so the system is inconsistent. C. There is a pivot position in each row of the coefficient matrix. The augmented matrix will have seven columns and will not have a row of the form [Start 1 By 7 Matrix 1st Row 1st Column 0 2nd Column 0 3rd Column 0 4st Column 0 5st Column 0 6st Column 0 7st Column 1 EndMatrix ], so the system is consiste
Answer:
Check the explanation
Step-by-step explanation:
All the 5 rows of the coefficient matrix (since it is of order 5×8) will have a pivot position. The augmented matrix obtained by adding a last column of constant terms to the 8 columns of the coefficient matrix will have nine columns and will not have a row of the form [0 0 0 0 0 0 0 0 1]. So the system is consistent.
What is the y-intercept of the graph of the function f(x) = x2 + 3x + 5?
0 (0,-5)
0 (0, -3)
O (0,3)
0 (0,5)
Answer:
(0,5)
Step-by-step explanation:
f(x) = x^2 + 3x + 5
The y intercept is when x =0
f(0) = 0 + 3*0 + 5
f(0) = 5
(0,5)
Find the area of the regular polygon.
Round your answer to the
nearest tenth if necessary.
Answer:
See Explanation
Step-by-step explanation:
The question is incomplete as the dimension of the polygon is not given.
However, I'll give a general explanation of how to calculate the area of a regular polygon.
If you follow these simple steps, you'll arrive at your answer.
The area of a polygon is calculated as thus;
A = ½(nbh)
Where A represent the area
n represents the number of sides
b represents the length of the base
h represent the height of the polygon
Take for instance, the polygon is a regular pentagon.
This means n = 5.
Also assume that the base and the height are 5cm and 7cm respectively.
This means that
Area = ½ * (5 * 5 * 7)
Area = ½ * 175
Area = 87.5cm²
Hence, the area of the polygon is 87.5cm²
how do i factor the "common factor out of each expression?" ex:
12n^6 + 27n^2 - 18
whoever answers correct/ first ill give brainliest
Answer:
Step-by-step explanation:
A "common factor" is either a constant coefficient or a variable which shows up in every term of a given algebraic expression.
Here we start with the expression 12n^6 + 27n^2 - 18. 'n' does not show up in every term and thus could not be a "common factor" of this expression. On the other hand, 12, 27 and -18 can all be divided by 3, and so 3 is a common factor.
12n^6 + 27n^2 - 18 = 3(4n^6 + 9n^2 - 6)
1) Identify the common factor (here it's 3)
2) Factor that out of the given expression: 3(4n^6 + 9n^2 - 6)
A particular paper included the accompanying data on the tar level of cigarettes smoked for a sample of male smokers who subsequently died of lung cancer.
Assume it is reasonable to regard the sample as representative of male smokers who die of lung cancer.
Is there convincing evidence that the proportion of male smoker lung cancer deaths is not the same for the four given tar level categories at the Alpha = .05 level? (Use 2 decimal places.)
Tar Level Frequency
a. 0-7 107
b. 8-14 375
c. 15-21 500
d. 22 181
x2 =
Answer:
Check the explanation
Step-by-step explanation:
[tex]H_0[/tex]:proportion of male smoker lung deaths is same for the four given tar level categories.
[tex]H_1[/tex]:proportion of male smoker lung deaths is not the same for the four given tar level categories.
Expected frequency=1177/4=294.25
Tar level Observed Freq.(O) Expected Freq.(E) (O-E)^2/E
0-7 107 294.25 120.435
8-14 375 294.25 5.643
15-21 553 294.25 227.533
>=22 183 294.25 42.061
Total= 1177 1177 395.673
Total chi square score=395.673
df=4-1=3
p-value=CHIDIST(395.673,3)<0.001
p-value<0.001,Reject null hypothesis.
There is sufficient evidence that the proportion of male smoker lung deaths is not the same for the four given tar level categories.
a square stained window is divided into four congurent traiangular sections by iron edging to represent seasons of the year. Each diagonal measures 9 inches. What is the total length of iron edging needed to create the sqaure frame and two diagnols?
Answer:
Total length of iron needed to make the square frame and two diagonals = 43.44 in (Approx)
Step-by-step explanation:
Given:
Length of diagonal = 9 in
Find:
Total length of iron needed to make the square frame and two diagonals.
Computation:
Area of square = 1/2(diagonal)²
Area of square = 1/2(9)²
Area of square = 40.5 in²
Area of square = Side × Side
40.5 in² = Side × Side
Side = 6.36 (approx)
Total length of iron needed to make the square frame and two diagonals = Permeter of square + (2 × diagonal)
⇒ (4 × 6.36) + (2 × 9)
⇒ (25.44) + (18)
⇒ 43.44 in
Total length of iron needed to make the square frame and two diagonals = 43.44 in (Approx)
The table gives a few( x,y)pairs of a line in the coordinate plane x,y 24 -8 36 1 48 10 what is the y -intercept of the line
Answer:
-26
Step-by-step explanation:
One way to answer this question is to look at what's happening to the values of x and y.
x y
24 -8
36 1
48 10
Go down the list of x values: they are increasing by 12 at each step
Go down the list of y values: they are increasing by 9 at each step.
The y-intercept of the line is the value of y when x = 0.
Think about reversing the steps (decrease x by 12 and decrease y by 10):
x y
48 10
36 1
24 -8
12 -17
0 -26 <----- the y intercept is -26.
Note: Your book or teacher may list y intercepts as points. If so, use (0, -26)
Which set of numbers is included in the solution set of the compound inequality? {–7, 5, 18, 24, 32} {–9, 7, 15, 22, 26} {16, 17, 22, 23, 24} {18, 19, 20, 21, 22}
Answer:
{-7,5,18,24,32}
Step-by-step explanation:
Let's verify all cases to determine the solution to the problem.
CASE A) we have
-9,7,15,22,26
The number 22 is not included in the solution set of the compound inequality.
CASE B) we have
-7,5,18,24,32
The number 22 is not included in the solution set of the compound inequality.
CASE C) we have
16,17,22,23,24
The number 22 is not included in the solution set of the compound inequality.
CASE D) we have
18,19,20,21,22
The numbers 19,20,21,22 are not included in the solution set of the compound inequality.
The answer to your question would be A
Classify this relation as direct, inverse, or neither:
On Sarah's 16 GB flash drive, she can fit 16 video clips of about 1 GB each, two movies of about 8 GB each, or 4000 songs of about 4 MB each.
A. Inverse; there is a constant product of 8 GB.
B. Inverse; there is a constant product of 16 GB.
C. Direct; the ratio of corresponding x- and y-values is constant.
D. Neither
Answer:
b option im not sure but
Step-by-step explanation:
1
2
5
6
7
A six-sided number cube is rolled twice.
What is the probability that the first roll is an even number and the second roll is a number greater than 4?
1
6
1
3
2
3
5
6
Answer:
1/6
Step-by-step explanation:
3/6 for even 3/6*2/6-----1/2*1/3
The box plot show the weights, in pounds, of the dogs in two different animal shelters.
Which correctly compares the ranges of the data?
• The range shelter A in 11, and the range in shelter B is 4.
• The range in shelter A is 20, and the range in shelter B is 10.
• The range in shelter A is 13, and the range in shelter B is 8.
• The range in shelter A is 22, and the range in shelter B is 18.
Answer:
The range in shelter A is 22, and the range in shelter B is 18.
Subtract 8 from 30 shelter A which gives you 22. Then subtract 10 from 28 which gives you 18 for Shelter B.
Answer:
The range in shelter A is 22, and the range in shelter B is 18.
Subtract 8 from 30 shelter A which gives you 22. Then subtract 10 from 28 which gives you 18 for Shelter B.
Step-by-step explanation:
Andre hit 46 balls at practice. He hit no fewer than 20 less than double the number of hits Jason had. Which inequality represents the situation if j represents the number of hits Jason had?
46 minus 20 less-than 2 j
2 j minus 20 less-than-or-equal-to 46
46 minus 20 less-than-or-equal-to 2 j
2 j minus 20 greater-than-or-equal-to 46
Answer:
2j -20 ≤ 46
Step-by-step explanation:
"20 less than double the number Jason [hit]" can be represented by 2j-20.
We are told that 46 is no fewer than this value, so it is greater than or equal to this value:
46 ≥ 2j -20
2j -20 ≤ 46 . . . . . swapping sides to match answer choices
Answer:
2j -20 ≤ 46
Step-by-step explanation:
A researcher developing scanners to search for hidden weapons at airports has failed to conclude that a new scanner is significantly better than the current scanner. He made his decision based on a test using alpha equals 0.025 . Would he have made the same decision at alpha equals 0.10 question mark How about alpha equals 0.01 question mark Explain.
Answer:
Yes, he would take the same decision.
Step-by-step explanation:
Consequently, because the decision is taken on the test based on the use of alpha equals 0.025, the p-value of the test must have been greater than the given amount of importance that is 0.025 since the test is not applicable to us. So, p > 0.025.
If we know that p > 0.025, that would not mean p > 0.1 as well, because we do not know with the details given he had to make the same decision for 0.1 degree of meaning.
As for the 0.01 significance point, we 're sure p > 0.01 is greater than 0.025, so the test does not matter.
HELP ME ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing. Check ALL that apply.
Answer:
the answer would be D &F
If
f(x) = -4x + 8 and
g(x) = √ x – 1, which statement is true?
Answer:
-3 is not in the domain of f°g
Step-by-step explanation:
f°g=f(g(x))
f(x) = -4(√x-1)+8
*Remember that √x-1 has to be larger than 0
since √-3-1 = √-4, -3 is not in the domain of f°g
