Answer:
a) Critical value = -1.4052
Since we are checking if the mean time is less than 10 minutes, the rejection area would be
z < -1.4052
b) Option C is correct.
Reject the claim that the mean time is 10 minutes because the test statistic is smaller than the critical point.
That is, the mean time is significantly less than 10 minutes.
Step-by-Step Explanation:
a) Using z-distribution, the critical value is obtained from the confidence level at which the test is going to be performed. Since the hypothesis test tests only in one direction (checking if the claim is less than 10 minutes significantly)
P(z < Critical value) = 0.08
From the z-tables, critical value = -1.4052
Since we are checking if the mean time is less than 10 minutes, the rejection area would be
z < -1.4052
b) We first give the null and alternative hypothesis
The null hypothesis is that there isn't significant evidence to suggest that the mean time is less than 10 minutes.
And the alternative hypothesis is is that there is significant evidence to suggest that the mean time is less than 10 minutes.
To now perform this hypothesis test, we need to obtain the test statistic
Test statistic = (x - μ)/σₓ
x = sample mean = (Σx/N)
The data is
1.2, 2.8, 1.5, 19.3, 2.4, 0.7, 2.2, 0.7, 18.8, 6.1, 6, 1.7, 29.1, 2.6, 0.2, 10.2, 5.1, 0.9, 8.2
Σx = 119.7
N = Sample size = 19
x = sample mean = (119.7/19) = 6.3
μ = standard to be compared against = 10 minutes
σₓ = standard error = (σ/√N)
where N = Sample size = 19
σ = √[Σ(x - xbar)²/N]
x = each variable
xbar = mean = 6.3
N = Sample size = 19
Σ(x - xbar)² = 1122.74
σ = (√1122.74/19) = 7.687
σₓ = (7.687/√19) = 1.7635
Test statistic = (x - μ)/σₓ
Test statistic = (6.3 - 10)/1.7635
= -2.098 = -2.10
z = -2.10 and is in the rejection region, (z < -1.4052), hence, we reject the null hypothesis and the claim and say that the mean time is significantly less than 10 minutes.
The test statistic is less than the critical point, hence, we reject the null hypothesis and the claim and conclude that the mean time is less than 10 minutes.
Hope this Helps!!!
The critical value for the test based on the sampling distribution is -1.4052 and one needs to reject the claim.
How to explain the sampling distribution?From the complete information given, the descriptive statistics from the sample information has been given. The sample mean and variance are given. Therefore, the value of the test statistics from the information is -1.4052.
Also, the conclusion is to reject the claim since the test statistic is smaller than the critical point.
Therefore, the correct option is to reject the claim that the mean time is 10 minutes because the test statistic is smaller than the critical point.
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Using the data: 2, 2, 3, 3, 3, 4, 5, 6, 6, 19 What is Q1 and Q3
A. 3.5, 6.5
B. 3,6
C.2,5
D. 2,10
hi guys i have a question about order of operation 3x(-6-2)= ? i wish you answer
Answer:
[tex]-24[/tex]
Step-by-step explanation:
[tex]3 \times (-6-2)[/tex]
Solve brackets first.
[tex]3 \times (-8)[/tex]
Multiplication.
[tex]3 \times -8[/tex]
[tex]=-24[/tex]
Answer:
-24x
Step-by-step explanation:
add the stuff in the parentheses, the -2 and the -6 to get -8, then multiply the -8 to the coefficient, 3 to get -24x
Find the midpoint of the segment with the given endpoints.
(-8,9) and (- 5.8)
whats the midpoint
[tex]answer \\ = (6.5 \: 8.5) \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps[/tex]
Jessica, Miguel, and Dan sent a total of 75 text messages over their cell phones during the weekend. Dan sent 3 times as many messages as Jessica. Jessica sent 10 more messages than Miguel. How many messages did they each send?
Answer:
number of messages sent by Jessica = 17
Number of messages sent by Miguel = 7
Number of messages sent by Dan = 51
Step-by-step explanation:
Let number of messages sent by Jessica = [tex]x[/tex]
As per given statement,
Number of messages sent by Dan = [tex]3 \imes x[/tex] and
Number of messages sent by Jessica are 10 more than that of Miguel.
So, Number of messages sent by Miguel are 10 lesser than that of Jessica.
Number of messages sent by Miguel = [tex]x-10[/tex]
It is also given that,
Total number of messages sent = 75
Adding the number of messages sent by each one of them and putting them equal to 75:
[tex]x+3x+x-10=75\\\Rightarrow 5x-10=75\\\Rightarrow 5x=85\\\Rightarrow x=17[/tex]
So, number of messages sent by Jessica, [tex]x[/tex] = 17
Number of messages sent by Miguel, [tex]x-10[/tex] = 7
Number of messages sent by Dan, [tex]3x[/tex] = 3[tex]\times[/tex]17 = 51
Data was collected for a sample of organic snacks. The amount of sugar (in mg) in each snack is summarized in the histogram below. 2 4 6 8 10 12 14 amount of sugar (mg) 60 80 100 120 140 160 180 200 Frequency What is the sample size for this data set
Answer:
The sample size for the data set = 56
Step-by-step explanation:
The sample size or number of individuals (n) is gotten from a histogram by summing up the total frequencies of occurrences.
In this example, the frequencies are: 2 4 6 8 10 12 14
Therefore, the sample size (n) is calculated as follows:
n = 2 + 4 + 6 + 8 + 10 + 12 + 14 = 56
Therefore the sample size for the data set = 56
The sample size for the data set = 56
Given that,
Data was collected for a sample of organic snacks.The calculation is as follows:
= 2 + 4 + 6 + 8 + 10 + 12 + 14
= 56
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I sell hot dogs at a football game. I can make a hot dog for $0.65 and sell it for $1.00. If i sell 50 hot dogs, what is my profit? show your work
Answer:
17.50
Step-by-step explanation:
The profit on one hotdog is
1 - .65 = .35
Multiply by the number of hotdogs sold
.35 * 50 =17.50
Renee is making a scale diagram of her MP3 player. The length of her scale drawing is 8 inches, and the width is 14 inches. The actual length of the MP3 player is 4 centimeters, and the width is 7 centimeters. This is , and the scale factor is .
Answer:
2
Step-by-step explanation:
Scale Factor = [tex]\frac{AnySideOfDiagram}{AnySideOfMP3Player}[/tex]
So,
Scale Factor = [tex]\frac{8}{4} = \frac{14}{7}[/tex] = 2
So,
The scale factor is 2
Factor completely 4x2 + 20x.
Answer:
[tex]4x(x+5)[/tex]
Step-by-step explanation:
[tex]4x^2 + 20x[/tex]
The highest common factor of the expression is [tex]4x[/tex]
[tex]4x(x)+4x(5)[/tex]
[tex]4x(x+5)[/tex]
Answer:
[tex]4x(x + 5)[/tex]
Step-by-step explanation:
[tex]4 {x}^{2} + 20x \\ 4x(x + 5)[/tex]
Determine the present value P that must be invested to have the future value A at simple interest rate r after time t. A = $7000.00, r = 9.5%, t = 9 months
Answer:
$6534.42
Step-by-step explanation:
Put the given values into the simple interest formula and solve for the remaining variable.
A = P(1 +rt)
where P is the principal invested, r is the annual rate, and t is the number of years.
$7000 = P(1 +0.095(9/12)) = 1.07125P
$7000/1.07125 = P ≈ $6534.42
The value that must be invested is $6534.42.
choose the graph of y less than negative x squared plus 4x + 5
Answer:
The 1st graph
Step-by-step explanation:
The quickest and easiest way is to just graph y < x² + 4x + 5. When you do so you should be able to see your answer.
A survey of Ron’s customers showed that 2,400 of the customers buying chewing gum would buy organic chewing gum if it was placed near the register. In the first month, 1,600 out of 4,000 customers actually bought the organic gum. What was the percent error in the survey estimate of the number of people buying organic gum?
Answer:
50
Step-by-step explanation:
Answer:
50%
Step-by-step explanation:
Which would be appropriate compatible numbers to use to estimate ( 19 4 5 ) ( 4 6 ) ? Using this compatible number, what is the estimated product?
The appropriate compatible numbers to use to estimate would be 20(1/2)
estimated product is 10, took the quiz :)
Answer: 20 1/2
10
Step-by-step explanation:
Find the (a) mean, (b) median, (c) mode, and (d) midrange for the data and then (e) answer the given questions. Listed below are the highest amounts of net worth (in millions of dollars) of all celebrities.
1. What do the results tell us about the population of all celebrities?
2. Based on the nature of the amounts, what can be inferred about their precision?
250 200 185 175 165 165 150 150 150 150
Answer:
Mean = 174
Median = 165
Mode = 150
Range = 100
Mid-range= 165-150= 15
1) only few population of the celebrities have high net-worth
2) very low precision as their is a wide range in the variation of their net worth
Step-by-step explanation:
250 200 185 175 165 165 150 150 150 150
Arranged in ascending order =
150 150 150 150 165 165 175 185 200 250
Mean = (150+ 150 +150 +150 +165 +165 +175+ 185 +200 +250)/10
Mean = 1740/10
Mean = 174
Median =( 165+165)/2
Median = 165
Mode = 150
Range = 250-150
Range = 100
Mid-range= 165-150= 15
1) only few population of the celebrities have high net-worth
2) very low precision as their is a wide range in the variation of their net worth
A recent survey found that about 72.5% of all gasoline purchases at a certain service station chain are paid with a credit or debit card. If 300 gasoline purchases completed at this chain are randomly selected, find the probability that at most 210 of those purchases are paid with a credit or debit card.
Answer:
18.28% probability that at most 210 of those purchases are paid with a credit or debit card.
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]n = 300, p = 0.725[/tex]
So
[tex]\mu = E(X) = np = 300*0.725 = 217.5[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{300*0.725*0.275} = 7.7339[/tex]
Find the probability that at most 210 of those purchases are paid with a credit or debit card.
Using continuity correction, this is [tex]P(X \leq 210 + 0.5) = P(X \leq 210.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 210.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{210.5 - 217.5}{7.7339}[/tex]
[tex]Z = -0.905[/tex]
[tex]Z = -0.905[/tex] has a pvalue of 0.1828
18.28% probability that at most 210 of those purchases are paid with a credit or debit card.
I earn $20.00 in 4 hours. At this rate, how much will i earn in 28 hours (show your work)
Answer:
140$
Step-by-step explanation:
4 hours = 20
28 hours divided by 4 is 7
7 x 20 = 140
Can someone please help me ASAP
Let f be defined as shown.
What is f ^-1 (8)?
Answer:
f−1(8)= 8/f
hope i helped
-lvr
Answer:
What position did Theodore Roosevelt hold before he became president?
Step-by-step explanation:
What are the four major categories of securities? How are they evaluated?
Answer:
Cash, Bonds, Stocks and Mutual funds
Step-by-step explanation:
The four major categories of securities are:
Cash Bonds Stocks Mutual fundsThese 4 major categories are evaluated as given below:
Cash: Cash is your normal money. You can use it to buy your everyday goods and services or invest in cash in various asset classes.Bonds: Bond is debt instrument and bonds are the agreement of debt. and bonds carry coupon rate that is (interest equivalent), tenure and final capital repayment Stocks: Ownership of stock in a company. A group (or a single) share of any company is called stock. Stock means you have some stake in the company. Mutual Funds: A mutual fund is an asset basket that can hold cash, bonds, stocks, real estate, and so on. The type and structure of mutual funds will vary depending on the client's choice of the fund manager and the category of the categoryJorge is going to buy bottled water in the market. The market sells the bottles in boxes. You have two types of boxes to choose from: small bottles and large bottles. If Jorge buys a box of small bottles and a box of large bottles, he will have to pay $ 30. If you buy a box of small bottles and three boxes of large bottles, you will have to pay $ 66. How much does a box of small bottles cost?
Answer:
$12
Step-by-step explanation:
3 times the first purchase will get Jorge 3 boxes of each type for $90. That's 2 more small bottle boxes than Jorge gets for the second purchase at $66. Then those 2 small boxes cost $90 -66 = $24, or $12 for each small bottle box.
Find the volume of the cone.
Either enter an exact answer in terms of it or use 3.14 for and round your final answer to the nearest
hundredth.
The volume of the cone will be 21 cubic units.
What is the volume?Volume is defined as the space occupied by any object in the three dimensions. All three parameters are required for the volume like length, width, and height of the cube.
The formula for the volume of a cone is ⅓ r²h cubic units, where r is the radius of the circular base and h is the height of the cone.
Volume = ⅓ r²h
Volume = ⅓ x x 2² x 5
Volume = 21 cubic units
Therefore, the volume for the given shape of the cone will be 21 cubic units.
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The sum of four consecutive numbers in an A.P. is 28. The product of the
second and third numbers exceeds that of the first and last by 18. Find the
numbers.
Let x be the first number in this sequence of four. Then the next three are x + n, x + 2n, and x + 3n, because consecutive terms in an arithmetic progression differ by a fixed constant.
The sum of these four numbers is 28:
x + (x + n) + (x + 2n) + (x + 3n) = 4x + 6n = 28
or
2x + 3n = 14
The product of the second and third numbers is greater than the product of the first and last numbers by 18:
(x + n)(x + 2n) = x(x + 3n) + 18
Expanding everything on both sides gives
x² + 3nx + 2n² = x² + 3nx + 18
and terms cancel so we end up with
2n² = 18 ==> n² = 9 ==> n = 3 or n = -3
If n = 3, then
4x + 6*3 = 28 ==> 4x = 10 ==> x = 5/2
If n = -3, then
4x + 6*(-3) = 28 ==> 4x = 46 ==> x = 23/2
So we have two possible solutions, but the only difference between them is the order. If n = 3, then the four numbers are 5/2, 11/2, 17/2, and 23/2. If n = -3, then the four numbers are, again, 23/2, 17/2, 11/2, and 5/2.
If two opposite sides of a square are increased by 12 meters and the other sides are decreased by 7 meters, the area of the rectangle that is formed is 66 square meters. Find the area of the original square.
Answer:
100
Step-by-step explanation:
Let us Assume x as the original sides of the square
As we know that
Area of rectangle is
[tex]= Length \times width[/tex]
where,
Length is 12 meters
And, the width is 7 meters
Moreover, the area of the rectangle is 66 square meters
Now since the length is increased by 12 meters and the width is decreased by 7 meters
So, the equation would be
(x + 12) (x - 7) = 66
x^2 + 5x - 84 = 66
x^2 + 5x - 150 = 0
Now, we compute the factor of the above equation
(x - 10) (x + 15) = 0
We do not consider the negative root
Therefore the area of original square is
= Side^2
= 10^2
= 100
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!
Answer: x < -4 and -4 > x
x < -4 would be one of the two options.
This means that any number less than -4 is a solution.
This is shown by drawing an open dot on -4 and then
drawing an arrow to the left shows all answer less tan 4.
-4 > x would be our second option.
We can change it to say x < -4.
All I did was changed the order of numbers and switched the sign.
So x < -4 is the same as the first option.
Which of the x-values are solutions to the following inequality? 17 > x Choose all answers that apply: (A) x = 7 (B) x = 12 (C) x = 17
Answer:
7 and 12
Step-by-step explanation:
7 and 12 are ok
17 is not
hope this helps
The solution of the inequality x < 17 will be all the real numbers less than 17. Then the correct options are A and B.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The inequality is given below.
x < 17
The solution of the inequality x < 17 will be all the real numbers less than 17. Then the correct options are A and B.
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Consider the function f(x)=2|x|−3 . What is f(−3) ?
Answer:
3
Step-by-step explanation:
Hello,
[tex]f(x)=2|x|-3\\f(-3)=2|-3|-3=2*3-3=6-3=3[/tex]
Answer:
f(-3) = 3
Step-by-step explanation:
f(x)=2|x|−3
f(−3) = 2|-3| − 3
f(-3) = 2(3) - 3
f(-3) = 6 - 3
f(-3) = 3
Find the surface area of a sphere with a diameter 12 cm. Round your answer to the nearest whole number
Answer:
SA = 144π or 452 cm
Step-by-step explanation:
Surface area of a sphere: SA = 4πr²
To find r radius, we simply divide diameter by 2 to get r = 6. Now we simply plug in 6:
SA = 4π(6)²
SA = 4π36
SA = 144π or 452.389
Answer:
144pi
Step-by-step explanation:
calculator
Electromagnetic radiation is more common than you think. Radio andTV stations emit radio waves when they broadcast their programs;microwaves cook your food in a microwave oven; dentists use X raysto check your teeth. Even though they have different names anddifferent applications, these types of radiation are really all thesame thing: electromagnetic (EM) waves, that is, energy thattravels in the form of oscillating electric and magnetic fields
Consider the following:
radio waves emitted by a weather radar system to detectraindrops and ice crystals in the atmosphere to study weatherpatterns;
microwaves used in communication satellite transmissions;
infrared waves that are perceived as heat when you turn on aburner on an electric stove;
the multicolor light in a rainbow;
the ultraviolet solar radiation that reaches the surface of theearth and causes unprotected skin to burn; and
X rays used in medicine for diagnostic imaging
Answer:
a) They have different wavelengths.
b) They have different frequencies.
Step-by-step explanation:
Electromagnetic waves (EM waves) refer to waves carrying electromagnetic radiant energy which are propagated through vacuum or non-vacuum (material medium). They range from radio waves to gamma rays; they travel through space at the speed of light (about 300 million metres per second) and they are measured in photons.
The EM waves have the following characteristics:
1. They have different wavelengths
2. They have different frequencies
3. They travel at the speed of light independent of the medium of propagation (vacuum or material medium)
4. They do not require a media to be propagated
Based on the explanation above, Options a (They have different wavelengths) and b (They have different frequencies) are the correct answers
At what point will the graph of the equations 3x +y =7&
y=1 intersect?
=======================================================
Work Shown:
Substitute y = 1 into the first equation. Basically we replace every y with 1. From here we solve for x
3x+y = 7
3x+1 = 7
3x+1-1 = 7-1 .... subtracting 1 from both sides
3x = 6
3x/3 = 6/3 .... dividing both sides by 3
x = 2
We have x = 2 pair up with y = 1. The two equations intersect at (2,1)
As a check, plugging (x,y) = (2,1) into the first equation should lead to a true statement
3x+y = 7
3(2)+1 = 7
6+1 = 7
7 = 7 and it does lead to a true statement
The graph is shown below.
Evaluate (x + y)0 for x = -3 and y = 5
Answer:
0Step-by-step explanation:
[tex](x + y)0 \\ x = -3 \\y = 5\\(-3+5)0\\(2)0\\= 0[/tex]
A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of 41 feet?
Answer:
132.233 ft2
Step-by-step explanation:
Let's call the width of the rectangle 'w' and the length 'x'. So the area of the semicircle is:
[tex]A_1 = \pi*radius^2/2[/tex]
[tex]A_1 = \pi*(w/2)^2/2[/tex]
[tex]A_1 = \pi/8*w^2[/tex]
And the area of the rectangle is:
[tex]A_2 = w*x[/tex]
If the perimeter of the window is 41 feet, we have:
[tex]Perimeter = length + 2*width + \pi*radius[/tex]
[tex]41 = x + 2*w + \pi*w/2[/tex]
[tex]x = 41 - w(2 + \pi/2)[/tex]
Now, the equation for the total area of the window is:
[tex]A = A_1 + A_2 = \pi/8*w^2 + w*x[/tex]
[tex]A = \pi/8*w^2 + w*(41 - w(2 + \pi/2))[/tex]
[tex]A = (\pi/8-2 - \pi/2)*w^2 + 41w = -3.1781w^2 + 41w[/tex]
To find the maximum area, we can find the x-coordinate of the vertex of the quadratic equation:
[tex]x\_vertex = -b / 2a = -41 / (-3.1781*2) = 6.45[/tex]
So the width that gives us the maximum area of the window is 6.45 feet, and the area will be:
[tex]A = -3.1781w^2 + 41w = -3.1781*(6.45)^2 + 41*6.45 = 132.233\ ft^2[/tex]
g Of 23 fast food restaurants in the city, a total of 5 were in violation of sanitary standards, a total of 6 were in violation of safety standards, and 3 were in violation of both. If a fast food restaurant is chosen at random from these 23, what is the probability that it is in compliance of both safety and sanitary standards?
Answer:
65.22% probability that it is in compliance of both safety and sanitary standards
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Number of restaurant in compliance of both safety and sanitary standards.
First I will find those not in compliance, using a Venn's set.
Set A: Violation of sanitary standards.
Set B: Violation of safety standards.
5 were in violation of sanitary standards, a total of 6 were in violation of safety standards, and 3 were in violation of both.
This means that [tex]A = 5, B = 6, (A \cap B) = 3[/tex]
At least one:
[tex]A \cup B = A + B - (A \cap B)[/tex]
So
[tex]A \cup B = 5 + 6 - 3 = 8[/tex]
8 are in violation of at least one of these standards.
So 23-8 = 15 are in compliance of both safety and sanitary standards.
What is the probability that it is in compliance of both safety and sanitary standards?
15 out of 23
15/23 = 0.6522
65.22% probability that it is in compliance of both safety and sanitary standards
