Answer:
The 90% confidence interval for the mean amount spent on the children's birthday gift is between $45.77 and $48.23.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 18 - 1 = 17
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 17 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.7396
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 1.7396\frac{3}{\sqrt{18}} = 1.23[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 47 - 1.23 = $45.77
The upper end of the interval is the sample mean added to M. So it is 47 + 1.23 = $48.23
The 90% confidence interval for the mean amount spent on the children's birthday gift is between $45.77 and $48.23.
Kristian spends 45% of his $72 on a computer game. Calculate the price of the computer game
Answer:
$32.40
Step-by-step explanation:
45% = 0.45
72(0.45) = 32.4
Based on the amount Kristian had and the percentage spent on the game, the price of the game is $32.40.
What is the Price of the Game?The price of the game can be found as:
= Amount Kristian has x Percentage spent on game
Solving gives:
= 45% x 72
= $32.40
In conclusion, the price of the game is $32.40.
Find out more about percentages at https://brainly.com/question/11570843
WILL MARK BRIANLIST IF GOTTEN RIGHT!!!
Answer:
55
Step-by-step explanation:
The angle is 1/2 of the arc
Two rectangular prisms have the same volume.the first prism has a length of 10 meters a width of 6 meters and a height of 2 meters. The second prism has a length of 6 meters and a width of 4 meters
Answer:
height of second rectangular prism is 5 meters
Step-by-step explanation:
Given that cos A 165 and sin B = 72, and that angles A and B are both in
Quadrant I, find the exact value of sin(A + B), in simplest radical form.
Given:
[tex]\cos A=\dfrac{4}{\sqrt{65}}[/tex]
[tex]\sin B=\dfrac{1}{\sqrt{2}}[/tex]
A and B both lies in I quadrant.
To find:
The value of [tex]\sin (A+B)[/tex].
Solution:
We know that, all trigonometric ratios are positive in first quadrant.
[tex]sin^2\theta +\cos^2\theta =1[/tex]
Using this we get
[tex]\sin^2A +\cos^2A =1[/tex]
[tex]\sin^2A +\left(\dfrac{4}{\sqrt{65}}\right)^2 =1[/tex]
[tex]\sin^2A +\dfrac{16}{65}=1[/tex]
[tex]\sin^2A =1-\dfrac{16}{65}[/tex]
Taking square root on both sides, we get
[tex]\sin A =\sqrt{\dfrac{65-16}{65}}[/tex] [Only positive because A lies in I quadrant]
[tex]\sin A =\sqrt{\dfrac{49}{65}}[/tex]
[tex]\sin A =\dfrac{7}{\sqrt{65}}[/tex]
Similarly,
[tex]\sin^2B +\cos^2B =1[/tex]
[tex]\left(\dfrac{1}{\sqrt{2}}\right)^2 +\cos^2B =1[/tex]
[tex]\dfrac{1}{2}+\cos^2B =1[/tex]
[tex]\cos^2B =1-\dfrac{1}{2}[/tex]
Taking square root on both sides, we get
[tex]\cos B =\sqrt{\dfrac{2-1}{2}}[/tex] [Only positive because B lies in I quadrant]
[tex]\cos B =\sqrt{\dfrac{1}{2}}[/tex]
[tex]\cos B =\dfrac{1}{\sqrt{2}}[/tex]
Now,
[tex]\sin (A+B)=\sin A\cos B+\cos A\sin B[/tex]
[tex]\sin (A+B)=\dfrac{7}{\sqrt{65}}\times \dfrac{1}{\sqrt{2}}+\dfrac{4}{\sqrt{65}}\times \dfrac{1}{\sqrt{2}}[/tex]
[tex]\sin (A+B)=\dfrac{7}{\sqrt{130}}+\dfrac{4}{\sqrt{130}}[/tex]
[tex]\sin (A+B)=\dfrac{11}{\sqrt{130}}[/tex]
Therefore, the exact value of [tex]\sin (A+B)[/tex] is [tex]\dfrac{11}{\sqrt{130}}[/tex].
Comcast Corporation is the largest cable television company, the second largest Internet service provider, and the fourth largest telephone service provider in the United States. Generally known for quality and reliable service, the company periodically experiences unexpected service interruptions. On January 14, 2009, such an interruption occurred for the Comcast customers living in southwest Florida. When customers called the Comcast office, a recorded message told them that the company was aware of the service outage and that it was anticipated that service would be restored in two hours. Assume that two hours is the mean time to do the repair and that the repair time has an exponential probability distribution.
a. What is the probability that the cable service will be repaired in one hour or less?
b. What is the probability that the repair will take between one hour and two hours?
c. For a customer who calls the Comcast office at 1:00 P.M., what is the probability that the cable service will not be repaired by 5:00 P.M.?
Answer:
wow that
Step-by-step explanation:
a lot
Determine the amplitude or period as requested . Amplitude of y = - 1/5 * sin x a - 1/5 1/5 b 5 d. pi/5
Answer:
The amplitude is 1/5
Step-by-step explanation:
Given
[tex]y = -\frac{1}{5}\sin(x)[/tex]
Required
Determine the amplitude
The general cosine function is:
[tex]y = A\sin(k(x + c)) +d[/tex]
Where
[tex]Amplitude = |A|[/tex]
Compare [tex]y = A\sin(k(x + c)) +d[/tex] and [tex]y = -\frac{1}{5}\sin(x)[/tex]
[tex]A = -\frac{1}{5}[/tex]
So:
[tex]Amplitude = |-\frac{1}{5}|[/tex]
[tex]Amplitude = \frac{1}{5}[/tex]
The diameter of a circular plate is 12 inches. What is the area of the plate? Round your answer to the nearest tenth of a square inch.
Answer:
Plate Area = PI * radius^2
Plate Area = 3.14159 * 6 * 6
Plate Area = 113.09724 square inches
Plate Area = 113.1 square inches (rounded)
Step-by-step explanation:
Two methods are proposed for testing a shipment of five items (call them A, B, C, D, and 13). In method 1, an inspector randomly samples two of the five items and tests to see whether either item is defective. In method 2, an inspector randomly samples one item and tests it; the remaining four items are sent to a second inspector who randomly samples one item and tests it. Suppose that only item A is defective in the shipment.
a. What is the probability that item A will be dis-covered by method 1?
b. What is the probability that item A will be dis-covered by method 2?
c. What general statement can you make regarding the effectiveness .of the two methods? Can your statement be extended to methods involving samples of more than two items?
Answer:
a-The probability that item A is discovered as a defective item by method 1 is 0.4
b. The probability that item A is discovered as a defective item by method 2 is 0.4
c-As the probability of detecting A as a defective item is same for the two methods, thus it can be stated that each of the methods is equally effective.
Step-by-step explanation:
a-
The first method where the inspector chooses two of the five items randomly, so the total pairs are as given below:
[tex]N_{total}=n(S_{total})\\N_{total}=n(\{AB,AC,AD,AE,BC,BD,BE,CD,CE,DE\})\\[/tex]
As the total experiments in the overall space is 10 so [tex]N_{total}[/tex] is 10.
As A comes in 4 of these experiments, thus the value of [tex]N_{A}[/tex] is 4.
So the Probability of A is given as
[tex]P(A)=\dfrac{N_{A}}{N_{total}}\\P(A)=\dfrac{4}{10}\\P(A)=0.4[/tex]
The probability that item A is discovered as a defective item by method 1 is 0.4.
b-
Now in order to find the probability of finding item A as defective by method 2, first consider the probability of not finding item A as defective.
This is given as
[tex]P(A)=1-P(A)'[/tex]
Here P(A)' is given as
[tex]P(A)'=P(A)'_{1^{st}}\times P(A)'_{2^{nd}}[/tex]
Here
P(A)'_1st is the probability that the first inspector fails to detect A as a defective item which is given as
[tex]P(A)'_{1^{st}}=1-\dfrac{1}{N_{total\ items}}[/tex]
Here N_total items is 5. so the equation becomes
[tex]P(A)'_{1^{st}}=1-\dfrac{1}{N_{total\ items}}\\P(A)'_{1^{st}}=1-\dfrac{1}{5}\\P(A)'_{1^{st}}=\dfrac{5-1}{5}\\P(A)'_{1^{st}}=\dfrac{4}{5}[/tex]
Similarly
P(A)'_2nd is the probability that the second inspector fails to detect A as a defective item which is given as
[tex]P(A)'_{2^{nd}}=1-\dfrac{1}{N_{total\ items}}[/tex]
Here N_total items is 4 as 1 item has already been checked. so the equation becomes
[tex]P(A)'_{2^{nd}}=1-\dfrac{1}{N_{total\ items}}\\P(A)'_{2^{nd}}=1-\dfrac{1}{4}\\P(A)'_{2^{nd}}=\dfrac{4-1}{4}\\P(A)'_{2^{nd}}=\dfrac{3}{4}[/tex]
So the main equation becomes
[tex]P(A)=1-P(A)'\\P(A)=1-(P(A)'_{1^{st}}\times P(A)'_{2^{nd}})[/tex]
Substituting the values give
[tex]P(A)=1-(P(A)'_{1^{st}}\times P(A)'_{2^{nd}})\\P(A)=1-(\dfrac{4}{5}\times \dfrac{3}{4})\\P(A)=1-\dfrac{3}{5}\\P(A)=\dfrac{5-3}{5}\\P(A)=\dfrac{2}{5}\\P(A)=0.4[/tex]
The probability that item A is discovered as a defective item by method 2 is 0.4.
c-
As evident from the above, that the value of probabilities for both the methods is same therefore the overall effectiveness of each of the methods is same.
The set of ordered pairs {(1,19), (2,23), (3,23), (4,29), (5,31)}
represents the number of tickets sold for a fundraiser. The x-coordinates
represent the day and the y-coordinates represent the number of tickets
sold on that day.
a) Which mapping diagram represents the relation?
Answer:
D
Step-by-step explanation:
1) remember that x indicates the independent variable, while y the dependent variable
2) remember that the first diagram represents the values of x, while the second the values of y
Mapping diagram A represent the number of tickets sold on that day. Therefore, option A is the correct answer.
The given set of ordered pairs are {(1,19), (2,23), (3,23), (4,29), (5,31)}.
What are relations in Math?In math, a relation defines the relationship between sets of values of ordered pairs. The set of elements in the first set are called domain which is related to the set of the element in another set, which is called range.
A mapping diagram consists of two parallel columns. The first column represents the domain of a function [tex]f[/tex], and the other column for its range. Lines or arrows are drawn from domain to range, to represent the relation between any two elements.
Diagram A represents the given ordered pair
Mapping diagram A represent the number of tickets sold on that day. Therefore, option A is the correct answer.
Learn more about the relations here:
https://brainly.com/question/6241820.
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A sphere has a radius of 5. What is its diameter?
Answer:
D=10
Step-by-step explanation:
Diameter of a Sphere
D = 2 r
D=2(5)
D=10
Answer:
Diameter = 10
Diameter - is the full thing
Radius - Is only half of the diameter.
Step-by-step explanation:
The picture will explain it to you visually
In 2001, gas cost $1.85 per gallon. In 2008, the price was
220% higher than in 2001.
What was the cost of gas per gallon in 2008?
Find the value of x. help please if you understand
KM and NP are parallel lines.
Which angles are alternate exterior angles?
Answer:
<MLJ and <NOQ
Step-by-step explanation:
Alternate exterior angles are angles that lie outside of the two parallel lines that are cut across by the transversal line, and are also alternating each other along the transversal
Considering the image and the options given, <MLJ and <NOQ are exterior angles that alternate each other. Therefore, they are alternate exterior angles.
What is the solution to the to system equations in the graph?
Answer:
b
Step-by-step explanation:
The solution for system of two equations is simply the intersection of the two functions. Hence (b) is the answer
Identify the solutions of the graph. Only put one number in each blank.
___________ ___________
Answers: -2 and 2
Explanation:
The solutions to a graph are the same as the roots, zeros, or x intercepts. The x intercept is the location of the curve where it crosses or touches the x axis. In this case, it does so when x = -2 and x = 2.
Write the following expression in standard form by expanding and collecting like
terms.
(6g- 27) = 3
Answer:
6g-27=3
6g=30 add 27 on both sides
g=5 divide by 6
final answer is 5
hope this helps
have a good day :)
Step-by-step explanation:
Can somebody please help me with this whoever answers first gets a thanks and no rush but can you please be quick
Answer:
Bookstore to pet store: Down 6 units
Bookstore to Ice cream shop: Down 1 unit, 5 units to the left
Ice cream shop to pet store: Down 5 units, 5 units to the right
Sorry if this is wrong the image is a little blurry
VWXY is a parallelogram. Find the value of n.
Help meeee
Answer:
3.5
Step-by-step explanation:
n+7=3n
7=2n
n=3.5
Answer:
n=7/2
Step-by-step explanation:
n+7=3n
-n -n
7=2n
/2 /2
7/2=n
A:Consecutive interior angles
B:Vertical angles
C:Alternate exterior angles
D:Corresponding angles
Answer:
D: corresponding angle
hope it helps.
Answer:
corresponding angles
Step-by-step explanation:
hope it is helpful ><
PLS HELLP PLS PLS
Aarons bedroom measures. feet by 14 feet by 8 feet. how many cubic feet of space does the room contain? round ur answer to the nearest hundredth
Answer:
it would be 100 rounded because 14x8=112 and 112 is rounded to 100 to the nearest hundreth. Please subscribe to Amiredagoat Yt
Step-by-step explanation:
The probability that Joanne has eggs for breakfast and goes to school by car is 0.4. The probability that she goes to school by car on any day is 0.5. What is the probability that Joanne has had eggs for breakfast if she went to school by car?
A) .1
B) .2
C) .4
D) .5
E) .8
Answer:
A
Step-by-step explanation:
Can you help me worth 16 points if your help me all the way
Step-by-step explanation:
120=2/5t
120×5/2=t
t=600/2
t=300
hope it helps u
In Mr. Thompson's first period class, there are 6 students with blue eyes, 8 students with brown eyes,
5 students with grey eyes, and 1 student with hazel eyes. If Mr. Thompson selects one student
randomly, what color eyes is the student most likely to have?
Answer:
blue
Step-by-step explanation:
There the most common eyes in the class?
Answer:the student would most likely have blue eyes
Step-by-step explanation:
8/20
6/20
5/20
1/20
WHAT IS THE ANSWER PLSS
Answer: X≥6
Step-by-step explanation:
x/-2≤-3
x≥-3(-2)
X≥6
pls helpppp im so stuckk
ahhhhhgggg
Answer:
hmm easy peesy
3x+6= 21
21-6=3x
15=3x
5 = X
meet my dog; (Frankie the sleeping beauty )
Answer:
x = 5
Step-by-step explanation:
Expand:
Use distributive property:
3x + 6 = 21
3x = 15
x = 5
Divide:
(x + 2) = 21/3
x + 2 = 7
x = 5
Check your work:
3(5 + 2) = 21
15 + 6 = 21
21 = 21
Correct
23. Find the value of B.
24.Find the value of x.
7 1/2 x 4 1/3 x 3 3/5
Answer:
answer: 117
Hope this helps!
Answer:
117
Step-by-step explanation:
Convert mixed numbers to improper fractions:
7 1/2 = 15/2
4 1/3 = 13/3
3 3/5 = 18/5
15/2 x 13/3 x 18/5
Multiply and cross-cancel:
18/2 x 13/1
Multiply again:
117/1 = 117
The number of guppies that a fish tank can safely hold depends on its volume. A fish tank should have a volume of 576 cubic inches to safely hold 3 guppies. How many guppies can a fish tank that is 24 inches long, 12 inches wide, and 16 inches high safely hold? It can safely hold ___ guppies.
What is the value of x?
Answer:
91.5
Step-by-step explanation:
I did the math. Add up all the numbers and then, divide the result by two to get 91.5
Need some help on this question
Answer:
9.We know that
6 × 3 = 2 × x
18 = 2x
x = 9