Explanation:
It depends upon the 'base" of your log. Let us say that is 10 ; we can write:
log _10( x + 7 ) = 1
using the definition of log we can write:
x + 7 =10 ^1
and:
x = 10 − 7 =3
if you have a different base use the one you got instead of 10 .
Answer:
10
Step-by-step explanation:
Generally we use the base 10 to any logarithmic function , which is known as common Base
so the base of log (x+7) is 10
Exclude leap years from the following calculations. (a) Compute the probability that a randomly selected person does not have a birthday on March 14. (b) Compute the probability that a randomly selected person does not have a birthday on the 2 nd day of a month. (c) Compute the probability that a randomly selected person does not have a birthday on the 31 st day of a month. (d) Compute the probability that a randomly selected person was not born in February.
Answer:
a) 99.73% probability that a randomly selected person does not have a birthday on March 14.
b) 96.71% probability that a randomly selected person does not have a birthday on the 2 nd day of a month.
c) 98.08% probability that a randomly selected person does not have a birthday on the 31 st day of a month.
d) 92.33% probability that a randomly selected person was not born in February.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
A non-leap year has 365 days.
(a) Compute the probability that a randomly selected person does not have a birthday on March 14.
There are 365-1 = 364 days that are not March 14. So
364/365 = 0.9973
99.73% probability that a randomly selected person does not have a birthday on March 14.
(b) Compute the probability that a randomly selected person does not have a birthday on the 2 nd day of a month.
There are 12 months, so there are 12 2nds of a month.
So
(365-12)/365 = 0.9671
96.71% probability that a randomly selected person does not have a birthday on the 2 nd day of a month.
(c) Compute the probability that a randomly selected person does not have a birthday on the 31 st day of a month.
The following months have 31 days: January, March, May, July, August, October, December.
So there are 7 31st days of a month during a year.
Then
(365-7)/365 = 0.9808
98.08% probability that a randomly selected person does not have a birthday on the 31 st day of a month.
(d) Compute the probability that a randomly selected person was not born in February.
During a non-leap year, February has 28 days. So
(365-28)/365 = 0.9233
92.33% probability that a randomly selected person was not born in February.
The probability that a person does not have a birthday on March 14, on the 2nd day of a month, on the 31st day of a month, or is not born in February is approximately 0.9973, 0.9671, 0.9808, and 0.9233 respectively. These probabilities were computed by subtracting the fraction of the year representing the specific days or month from 1. These solutions are based on a standard non-leap year of 365 days.
To solve the probability questions, we will assume a non-leap year with 365 days.
(a) Probability that a randomly selected person does not have a birthday on March 14:
There is only one day out of the year that is March 14. Therefore, the probability that a person does have a birthday on March 14 is:
P(March 14) = 1/365
Consequently, the probability that a person does not have a birthday on March 14 is:
P(Not March 14) = 1 - 1/365 = 364/365 ≈ 0.9973
(b) Probability that a randomly selected person does not have a birthday on the 2nd day of a month:
Since there are 12 months in a year, there are 12 days which fall on the 2nd day of each month.
P(2nd day) = 12/365
Therefore, the probability that a person does not have a birthday on the 2nd day of any month is:
P(Not 2nd day) = 1 - 12/365 = 353/365 ≈ 0.9671
(c) Probability that a randomly selected person does not have a birthday on the 31st day of a month:
There are only 7 months with 31 days (January, March, May, July, August, October, December).
P(31st day) = 7/365
Therefore, the probability that a person does not have a birthday on the 31st day of any month is:
P(Not 31st day) = 1 - 7/365 = 358/365 ≈ 0.9808
(d) Probability that a randomly selected person was not born in February:
February has 28 days out of the year.
P(February birthday) = 28/365
Therefore, the probability that a person was not born in February is:
P(Not February) = 1 - 28/365 = 337/365 ≈ 0.9233
Your company manufactures hot water heaters. The life spans of your product are known to be normally distributed with a mean of 13 years and a standard deviation of 1.5 years. You want to set the warranty on your product so that you do not have to replace more than 5% of the hot water heaters that you sell. How many years should you claim on your warranty
Answer:
You should claim 10.5325 years on your warranty.
Step-by-step explanation:
Problems of normally distributed samples are 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.
In this problem, we have that:
[tex]\mu = 13, \sigma = 1.5[/tex]
Want's to replace no more than 5% of the products.
This means that the warranty should be 5th percentile, that is, the value of X when Z has a pvalue of 0.05. So X when Z = -1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.645 = \frac{X - 13}{1.5}[/tex]
[tex]X - 13 = -1.645*1.5[/tex]
[tex]X = 10.5325[/tex]
You should claim 10.5325 years on your warranty.
Sharif's portfolio generated returns of 12 percent, 15 percent, −15 percent, 19 percent, and −12 percent over five years. What was his average return over this period?
3.8 percent
2.1 percent
17 percent
19 percent
Answer:
3.8 percent
Step-by-step explanation:
To find his average return over n years, we sum all of his returns, and divide by n.
In this problem:
5 years.
The sum is (12 + 15 - 15 + 19 - 12) = 19
19/5 = 3.8
So the correct answer is:
3.8 percent
Answer:
The answer is 3.82
Step-by-step explanation:
(12 + 15− 15− 12 + 19)/5 = 3.8 3.
The radius of a sphere is 6 units. A sphere has a radius of 6 units. Which expression represents the volume of the sphere, in cubic units?
Answer:
The volume of the sphere is 678.24 u³
V = ⁴⁄₃ * π * (6u)³
Step-by-step explanation:
To calculate the volume of a sphere we have to use the following formula:
V = volume
r = radius = 6 units
π = 3.14
V = ⁴⁄₃πr³
we replace with the known values
V = ⁴⁄₃ * 3.14 * (6u)³
V = 4.187 * 216 u³
V = 678.24 u³
The volume of the sphere is 678.24 u³
Which sum or difference is modeled by the algebra tiles?
Answer:
The second one is the correct answer
Step-by-step explanation:
The third one is incorrect as she stated, I tried it and got it wrong when I did the retry I put the second one and I got it correct.
Toxic Pollution: In the first year of a study, health officials discovered toxic pollutants in the soil surrounding a factory. The initial measurement was 65 parts per million (ppm) of pollutant. They returned to take similar measurements for several years afterward, and uncovered a disturbing trend. The pollutant levels in the soil surrounding the factory were growing exponentially, at a rate of 4.5% each year. Which exponential model predicts the amount of pollutant in the soil t years from the first measurement?
Answer:
The model for the pollutant levels in the soil t years from the first measurement is:
[tex]Y(t)=65e^{0.044}[/tex]
Step-by-step explanation:
We have a first measurement of 65 parts per million (ppm) of pollutant.
We also know that the pollutant levels were growing exponentially at a rate of 4.5% a year.
We can model this as:
[tex]Y(t)=Y_0e^{kt}[/tex]
The value of Y0 is the first measurement, that correspond to t=0.
[tex]Y_0=65[/tex]
The ratio for the pollutant levels for two consecutive years is 1+0.045=1.045. This can be expressed as the division between Y(t+1) and Y(t), and gives us this equation:
[tex]\dfrac{Y(t+1)}{Y(t)}=\dfrac{Y_0e^{k(t+1)}}{Y_0e^{kt}} =\dfrac{e^{k(t+1)}}{e^{kt}}=e^{k(t+1-t)}=e^k=1.045\\\\\\k=ln(1.045)\approx 0.044[/tex]
Then, we have the model for the pollutant levels in the soil t years from the first measurement:
[tex]Y(t)=65e^{0.044}[/tex]
The distance between sides of a polygon is always the same
Answer:
yes
Step-by-step explanation:
By definition, all sides are the same length, so the perimeter is simply the length of a side times the number of sides.
Since it is true that the distance between sides of a polygon are always the same.
What is a polygon?A polygon is defined as a closed figure made up of three or more line segments connected end to end
For a regular polygon of any number of sides, then the sum of its exterior angle is 360° .
Exterior angle is an measure of rotation between one extended side of the polygon with its adjacent side which is not extended. Also, regular having 'n' sides, all the exterior angles are of same measure, and therefore, their measure is (360/n)°.
When a polygon is four sided (a quadrilateral), the sum of its angles is 360°
Based on the definition, all sides are the same length, thus the perimeter is simply the length of a side times the number of sides.
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QUESTION 1 of 10: Which of the following is NOT a true statement?
a) Knowing the diferent food groups and how many servings from each group will allow you to have a balanced diet.
b) All work and no relaxation can compromise your health.
C) Technology benefits people by allowing them to avoid sore muscles.
d) Lack of sleep leads to increased risk for motor vehicle accidents.
Answer:
c
Step-by-step explanation:
cuzz im right
What is the average rate of change of h over the interval -2≤x≤2 in the equation h(x)=1/8x³-x²?
We have been given a function [tex]h(x)=\frac{1}{8}x^3-x^2[/tex]. We are asked to find the average rate of change of our given function over the interval [tex]-2\leq x\leq 2[/tex].
We will use average rate of change formula to solve our given problem.
[tex]\text{Average rate of change}=\frac{f(b)-f(a)}{b-a}[/tex]
[tex]\text{Average rate of change}=\frac{h(2)-h(-2)}{2-(-2)}[/tex]
[tex]\text{Average rate of change}=\frac{\frac{1}{8}(2)^3-2^2-(\frac{1}{8}(-2)^3-(-2)^2)}{2+2}[/tex]
[tex]\text{Average rate of change}=\frac{\frac{1}{8}(8)-4-(\frac{1}{8}(-8)-(4))}{4}[/tex]
[tex]\text{Average rate of change}=\frac{1-4-(-1-4)}{4}[/tex]
[tex]\text{Average rate of change}=\frac{-3-(-5)}{4}[/tex]
[tex]\text{Average rate of change}=\frac{-3+5}{4}[/tex]
[tex]\text{Average rate of change}=\frac{2}{4}[/tex]
[tex]\text{Average rate of change}=\frac{1}{2}[/tex]
Therefore, the average rate of change over the interval [tex]-2\leq x\leq 2[/tex] is [tex]\frac{1}{2}[/tex].
The average rate of change of h over the interval -2 ≤ x ≤ 2 in the equation h(x)=1/8x³-x² is 3/8.
Explanation:To find the average rate of change of h over the interval -2 ≤ x ≤ 2, we need to calculate the difference in the values of h at the endpoints of the interval and divide it by the change in x.
First, let's find the value of h at x = -2: h(-2) = (1/8) * (-2)^3 - (-2)^2 = -(1/2).
Next, let's find the value of h at x = 2: h(2) = (1/8) * (2)^3 - (2)^2 = 1.
The change in x is 2 - (-2) = 4. So, the average rate of change of h over the interval -2 ≤ x ≤ 2 is (1 - (-1/2))/4 = 3/8.
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Angle 1 and 2 are linear pair. If m<1=x-9 and m<2=x+47 find the measure of each angle
Answer:
m1 = 62°, m2 = 118°
Step-by-step explanation:
The definition of a linear pair of angles is a pair of angles that are adjacent and add up to 180°.
Then, we have the following equation
[tex]x-9+x+47 =180 [/tex]
Then,
[tex]2x+38=180[/tex]
Subtracting 38 on both sides
[tex] 2x = 180-38 = 142[/tex]
Dividing by two, we get x = 71. Then m1 = 71-9 = 62, m2 = 71+47=118[/tex]
helphelphelphelphelphelphelphelphelphelp
Answer:
Angle A equals Angle B so 6x-2=4x+48 ---> 2x=50 ---> x=25. From this we find that both Angles A and B are equal to 148 degrees. :)
Lauren's dog jumped 4 times as high as Cheyenne's dog. The two dogs jumped 10 feet. How high dod Lauren's dog jump
Answer:
Laurens dog: 8 feet
Cheyenne's dog: 2 feet
Step-by-step explanation:
The first step is to evaluate the question, we know that you need to find the height each dog jumped, given the sum of both combined
next, you do simple math:
4x2= 8
10-8= 2
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A huge ice glacier in the Himalayas initially covered an area of 454545 square kilometers. Because of changing weather patterns, this glacier begins to melt, and the area it covers begins to decrease exponentially.
The relationship between AAA, the area of the glacier in square kilometers, and ttt, the number of years the glacier has been melting, is modeled by the following equation.
A=45e^{-0.05t}A=45e
−0.05t
A, equals, 45, e, start superscript, minus, 0, point, 05, t, end superscript
How many years will it take for the area of the glacier to decrease to 151515 square kilometers?
Give an exact answer expressed as a natural logarithm
We have been given that a huge ice glacier in the Himalayas initially covered an area of 45 square kilo-meters. The relationship between A, the area of the glacier in square kilo-meters, and t, the number of years the glacier has been melting, is modeled by the equation [tex]A=45e^{-0.05t}[/tex].
To find the time it will take for the area of the glacier to decrease to 15 square kilo-meters, we will equate [tex]A=15[/tex] and solve for t as:
[tex]15=45e^{-0.05t}[/tex]
[tex]\frac{15}{45}=\frac{45e^{-0.05t}}{45}[/tex]
[tex]\frac{1}{3}=e^{-0.05t}[/tex]
Now we will switch sides:
[tex]e^{-0.05t}=\frac{1}{3}[/tex]
Let us take natural log on both sides of equation.
[tex]\text{ln}(e^{-0.05t})=\text{ln}(\frac{1}{3})[/tex]
Using natural log property [tex]\text{ln}(a^b)=b\cdot \text{ln}(a)[/tex], we will get:
[tex]-0.05t\cdot \text{ln}(e)=\text{ln}(\frac{1}{3})[/tex]
[tex]-0.05t\cdot (1)=\text{ln}(\frac{1}{3})[/tex]
[tex]-0.05t=\text{ln}(\frac{1}{3})[/tex]
[tex]t=\frac{\text{ln}(\frac{1}{3})}{-0.05}[/tex]
[tex]t=\frac{\text{ln}(\frac{1}{3})\cdot 100}{-0.05\cdot 100}[/tex]
[tex]t=\frac{\text{ln}(\frac{1}{3})\cdot 100}{-5}[/tex]
[tex]t=-\text{ln}(\frac{1}{3})\cdot 20[/tex]
[tex]t=-(\text{ln}(1)-\text{ln}(3))\cdot 20[/tex]
[tex]t=-(0-\text{ln}(3))\cdot 20[/tex]
[tex]t=20\text{ln}(3)[/tex]
Therefore, it will take [tex]20\text{ln}(3)[/tex] years for area of the glacier to decrease to 15 square kilo-meters.
Sera sells t-shirts at the beach. She believes the price of a t-shirt and the number of t-shirts sold are related. She has been experimenting with different prices for the
t-shirts. She has collected a data set with five pairs of
data: each consists of the price of a t-shirt and the
number of shirts sold.
The independent variable which will on on the x-axis is the price of a t-shirt.
The dependent variable which will on on the x-axis is the number of t-shirts sold.
The independent variable can be described as the variable that is used to determine the dependent variable. It is the variable that the researcher manipulates in the experiment.
The dependent variable is the variable whose value is determined in the experiment. The value of the dependent variable depends on the independent variable.
For example, assume that if the price of a shirt is $1. A person purchases 10 t shirts. If the price increases to $10, only one shirt would be sold. This means that the amount of shirts bought is dependent on the price of the t-shirt. The price of the shirt is the independent variable while the amount of shirts bought is the dependent variable.
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If you are driving at the speed of 90 km/hour. What is your speed in meter/second
Answer:
speed = 25 m/s
Step-by-step explanation:
Driving at a speed of 90 km / hour . what is the speed in meters per seconds.
converting from km to meter one have to multiply by 1000. This means 1 km is equal to 1000 meter. Converting 90 km to meter we have to multiply 90 by 1000.
90 × 1000 = 90000 meters
The time is in hours so we have to convert to seconds as required by the question.
60 minutes = 1 hour
Therefore,
1 minutes = 60 seconds
60 minutes = 3600 seconds
This means 1 hour = 3600 seconds
speed = 90000/3600
speed = 25 m/s
which number line shows the solution to 6 + (-6)
Answer
it is 0
Step-by-step explanation: you have to add 6 yto negative six so it is zero
Answer:
its is the option that shows the first line at six then 0
You work for a company in the marketing department. Your manager has tasked you with forecasting sales by month for the next year. You notice that over the past 12 months sales have consistently gone up in a linear fashion, so you decide to run a regression the company's sales history. You find that the regression equation for the data is (sales) = 128.329*(time) + 115.362. In August (time = 8) you see the actual sales quantity was 322.492. The residual is -819.502. Interpret this residual in terms of the problem.
01) The month is 819.502 months less than what we would expect.
02) The month is 819.502 months larger than what we would expect.
03) The sales is 819.502 units greater than what we would expect.
04) The sales is 819.502 units less than what we would expect.
05) The sales is 322.492 units less than what we would expect.
3Answer:
Step-by-step explanation:
Large Sample Proportion Problem. Surveys were conducted in multiple countries and respondents were asked if they felt political news was reported fairly. The data for the United States is that out of 1,000 sampled, 470 indicated yes, they felt political news was reported fairly. Suppose we want to determine if the proportion for the U.S. is below .50 for an alpha level of .05. What is conclusion of my test
Answer:
[tex]z=\frac{0.47-0.5}{\sqrt{\frac{0.5(1-0.5)}{1000}}}=-1.897[/tex]
We have aleft tailed test the p value would be:
[tex]p_v =P(z<-1.897)=0.0289[/tex]
The p value obtained is less compared to the significance level so then we have enough evidence to conclude that the true proportion is significantly lower than 0.5.
Step-by-step explanation:
Information given
n=1000 represent the random sample selected
X=470 represent the number of people who felt political news was reported fairly
[tex]\hat p=\frac{470}{1000}=0.470[/tex] estimated proportion of people who felt political news was reported fairly
[tex]p_o=0.5[/tex] is the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level
z would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
For this case we want to test if proportion for the U.S. is below .50 so then the system of hypothesis for this case are:
Null hypothesis:[tex]p \geq 0.5[/tex]
Alternative hypothesis:[tex]p < 0.5[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info provided we got:
[tex]z=\frac{0.47-0.5}{\sqrt{\frac{0.5(1-0.5)}{1000}}}=-1.897[/tex]
We have aleft tailed test the p value would be:
[tex]p_v =P(z<-1.897)=0.0289[/tex]
The p value obtained is less compared to the significance level so then we have enough evidence to conclude that the true proportion is significantly lower than 0.5.
Jackson is testing different types of planting soil to determine which type is most effective for growing strawberry bushes. He purchases two different brands of planting soil from a local store. Jackson applies brand A to an area of the yard that receives full sunlight and brand B to another area of the yard that is in partial sunlight. He waters the area with brand B daily; he waters the area with brand A every other day. At the end of the study, Jackson concludes brand A is more effective in growing strawberry bushes. Is Jackson's conclusion valid? Explain why or why not.
Answer:
The answer to this question can be described as follows:
Step-by-step explanation:
In the outcome of Jackson isn't legitimate as product A and product B were n’t considered equal in watering the plants. It is the preparation for all two to be compared, Product A with only a region of the backyard, which receives direct energy, and Product B will be maintained regularly by the very same area of the yards, that is in minimal lighting.
No, The conclusion done by Jackson's is not valid for this situation.
What is effective soiling?Effective Soiling depth is the depth of soil material which is above the layer that impedes movement of air and water and growth in plant roots.
According to outcome of Jackson that isn't legitimate as product A and product B were considered equal in watering the plants. Then it is the preparation of two to be compare with product B, Product A with only a region of the backyard, which receives direct energy, and Product B will maintained regularly very same area of the yards, that is with minimal lighting.
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Corbin recorded the amount of money spent, in dollars, on food per meal at two different restaurants. He rounded the amounts to the nearest dollar and plotted the data on the box plots below. A box plot titled Dollars Spent at Restaurant 1. The number line goes from 0 to 15. The whiskers range from 6 to 14, and the box ranges from 7 to 12. A line divides the box at 8. Dollars Spent at Restaurant 1 A box plot titled Dollars Spent at Restaurant 2. The number line goes from 0 to 16. The whiskers range from 6 to 15, and the box ranges from 8 to 12. A line divides the box at 10. Dollars Spent at Restaurant 2 Which best explains at which restaurant the average meal costs the most money? Restaurant 1, because the interquartile range of Restaurant 1 is greater Restaurant 1, because more of the graph is located to the right of the median Restaurant 2, because the median of Restaurant 2 is greater Restaurant 2, because the range of Restaurant 2 is greater
Answer:
It’s c I got a 100
Step-by-step explanation:
e d g e n u I ty
Suppose the number of prisoners held in a certain type of prison, measured in thousands, can be described by the polynomial - 2.02x + 78.47x + 744. The variable x represents the number of years since 1990, According to the polynomial, by how much did the prison population increase from 2002 to 2007?
What is the mode of the following numbers?
9,10,6,5,6
Answer:
6
Step-by-step explanation:
The mode is the number which appears most often in a set of numbers in this case that would be 6 because it appears twice
The mode of a set of values is the one that appears most frequently. In your list: 9, 10, 6, 5, 6 - the number 6 appears twice, more than any other number, making 6 the mode.
Explanation:In statistics, the mode of a set of values is the value that appears most frequently. An easy way to find the mode is to count the frequency of each number. Looking at your list of numbers: 9, 10, 6, 5, 6. The number 6 is the only number that appears more than once.
So, the mode of the given set of numbers is 6 because it appears more frequently than the other numbers.
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What is the volume of a box that is 7cm by 11cm by 13cm?
Answer:
V = 1001
Step-by-step explanation:
This is rather simple question, but I can understand not knowing how to find volume.
The volume of a rectangular prism(as specified by the way the dimensions were given) is whl, when w is width, h is height, and l is length. It does not actually matter the order, due to the Commutative Property of Multiplication, which states that is does not matter what order you multiply things.
Plugging in the numbers, we end up with 1001.
Hope this helps!
Consider the recursively defined set S: Basis Step: The unit circle is in S. Recursive Step: if x is in S, then x with a line through any diameter is in S. (a) (4 points) Prove that: is in S. (b) ( 6 points) For an element x ∈ S, define V (x) be the number of vertices (i.e. the number of intersections of lines and arcs and lines with lines), let E(x) to be the number of edges (line segments or arcs between vertices), and let F(x) be the number of faces. Prove that for any x ∈ S that F + V = E + 1. (Please use structural induction.)
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached images for the step by step explanation to the question
The volume of the cylinder is 307.9 cubic meters. Find the height. Round your answer to the nearest whole number.
In response to the question, we may say that the height of the cylinder is 6.
what is cylinder?A cylinder is a three-dimensiοnal geοmetric shape made up οf twο parallel cοngruent circular bases and a curving surface cοnnecting the twο bases. The bases οf a cylinder are always perpendicular tο its axis, which is an imaginary straight line passing thrοugh the centre οf bοth bases. The vοlume οf a cylinder is equal tο the prοduct οf its base area and height.
A cylinder's volume is computed as V = r²h,
where
"V" represents the volume,
"r" represents the radius of the base, and
"h" represents the height of the cylinder.
Thus,
307.9 = 7²h
307.9 = 49h
h = 307.9/49
h 6.283
h = 6 (rounding to the nearest whole)
Thus, The height of the cylinder is 6.
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The Census Bureau reports the average commute time for citizens of Cleveland, Ohio is 33 minutes. To see if the commute time is different in the winter, a random sample of 40 drivers were surveyed. The average commute time for the month of January was calculated to be 34.2 minutes and the population standard deviation is assumed to be 7.5 minutes. At the 0.05 level of significance, can it be concluded that the commuting times are different in the winter? What is the p-value? Use the rounded test statistic from the previous problem and round to 4 decimal places.
Answer:
We conclude that the commuting times are same in the winter.
Step-by-step explanation:
We are given that the Census Bureau reports the average commute time for citizens of Cleveland, Ohio is 33 minutes. To see if the commute time is different in the winter, a random sample of 40 drivers were surveyed.
The average commute time for the month of January was calculated to be 34.2 minutes and the population standard deviation is assumed to be 7.5 minutes.
Let [tex]\mu[/tex] = average commute time in winter.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 33 minutes {means that the commuting times are same in the winter}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 33 minutes {means that the commuting times are different in the winter}
The test statistics that would be used here One-sample z test statistics as we know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample mean commute time for the month of January = 34.2
[tex]\sigma[/tex] = population standard deviation = 7.5 minutes
n = sample of drivers = 40
So, test statistics = [tex]\frac{34.2-33}{\frac{7.5}{\sqrt{40}}}[/tex]
= 1.012
The value of z test statistics is 1.012.
Now, at 0.05 significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test. Since our test statistics lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.
Therefore, we conclude that the commuting times are same in the winter.
Also, P-value of the test statistics is given by;
P-value = P(Z > 1.012) = 1 - P(Z [tex]\leq[/tex] 1.012)
= 1 - 0.84423 = 0.1558
In circle O, AC and BD are diameters.
Circle O is shown. Line segments B D and A C are diameters. A radius is drawn to cut angle C O C into 2 equal angle measures of x. Angles A O C and B O C also have angle measure x.
What is mArc A B?
72°
108°
120°
144°
Answer:
mArc A B = 120° (C)
Step-by-step explanation:
Question:
In circle O, AC and BD are diameters.
Circle O is shown. Line segments B D and A C are diameters. A radius is drawn to cut angle D O C into 2 equal angle measures of x. Angles A O D and B O C also have angle measure x.
What is mArc A B?
a)72°
b) 108°
c) 120°
d) 144°
Solution:
Find attached the diagram of the question.
Let P be the radius drawn to cut angle D O C into 2 equal angle measures of x
From the diagram,
m Arc AOC = 180° (sum of angle in a semicircle)
∠AOD + ∠DOP + ∠COP = 180° (sum of angles on a straight line)
x° +x° + x° =180°
3x = 180
x = 180/3
x = 60°
m Arc DOB = 180° (sum of angle in a semicircle)
∠AOB + ∠AOD = 180° (sum of angles on a straight line)
∠AOB + x° = 180
∠AOB + 60° = 180°
∠AOB = 180°-60°
∠AOB = 120°
mArc A B = 120°
Answer:
c
Step-by-step explanation:
John Legend sells, on average, 115,000 songs on itunes every two weeks. Michelle did some quick math, and concluded that based on those numbers, he must sell, on average, over 9,000 songs per day. Is Michelle's conclusion true or false?
Answer: Michelle's conclusion is wrong, he sells 8214.3 songs per day
Step-by-step explanation:
Sell 115000 songs every 2 weeks
Sell 115000 songs every 14 days
Sell (a) songs for 1 day
(a) =(115000x1) ➗ 14
(a) =115000 ➗ 14
(a) =8214.3
Which functions have a maximum value greater than the maximum of the function g(x) = –(x + 3)2 – 4? Check all that apply. f(x) = –(x + 1)2 – 2 f(x) = –|x + 4| – 5 f(x) = –|2x| + 3
Answer:
A
C
D
Step-by-step explanation:
The results of a History test and Calculus test are normally distributed. The History test had a mean score of 68 with a standard deviation of 8. The Calculus test had a mean score of 70 with a standard deviation of 7.2. Joseph scored 82 on the Calculus test and Zoe scored 82 on the History test. Which student had a higher percentile rank in their class?
Answer:
Zoe, at about the 96th percentile.
Step-by-step explanation:
Problems of normally distributed samples are 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.
Zoe:
Zoe scored 82 on the History test. So X = 82.
The History test had a mean score of 68 with a standard deviation of 8. This means that [tex]\mu = 68, \sigma = 8[/tex]
Then, we find the z-score to find the percentile.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{82 - 68}{8}[/tex]
[tex]Z = 1.75[/tex]
[tex]Z = 1.75[/tex] has a pvalue of 0.9599.
So Zoe was at abouth the 96th percentile.
Joseph:
Joseph scored 82 on the Calculus test. This means that [tex]X = 82[/tex]
The Calculus test had a mean score of 70 with a standard deviation of 7.2. This means that [tex]\mu = 70, \sigma = 7.2[/tex]
Z-score
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{82 - 70}{7.2}[/tex]
[tex]Z = 1.67[/tex]
[tex]Z = 1.67[/tex] has a pvalue of 0.9525.
Joseph scored in the 95th percentile, which is below Zoe.
So the correct answer is:
Zoe, at about the 96th percentile.