Answer:
I can confirm d
Step-by-step explanation:
Hen evaluated (Negative 2) squared as
What is an Expression?An expression is a number, a variable, or a combination of numbers and variables and operation symbols
How to solve it?Hen evaluated the expression below. 2 (12 minus 14) squared minus (negative 5)+12=2 (negative 2) squared minus (negative 5) + 12 =2(negative 4) minus (negative 5) +12= negative 8+ 5+12=9. What was hen's error? He did not multiply 2 and 12 first. Hen evaluated Minus (negative 5) as 5. He was added and subtracted before multiplying. Hen evaluated (Negative 2) squared as
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Using the critical value rule, if a two-sided null hypothesis cannot be rejected for a single mean at a given significance level, then the corresponding one-sided null hypothesis (i.e., the same sample size, the same standard deviation, and the same mean) will ______________ be rejected at the same significance level.
Answer:
If the null hypothesis is failed to be rejected in a two-sided test, we are not sure if a one-sided test will reject or not the null hypothesis, at the same significance level.
Step-by-step explanation:
When we performed a two-sided test and the null hypothesis failed to be rejected, when we perform a one-sided test we may reject or not the null hypothesis.
For instance, we have a 5% significance level test, where the test statistic is z=1.8.
For a two-sided test the critical values for α=5% are zc=±1.960. In this situation, the null hypothesis failed to be rejected.
But if we perform a one-sided test with the same significance level, we have a critical value z=1.645 and the conclusion is that the null hypothesis is rejected.
Then, if the null hypothesis is failed to be rejected in a two-sided test, we are not sure if a one-sided test will reject or not the null hypothesis, at the same significance level.
We are only sure that if a two-sided test rejects the null hypothesis, a one-side test with same significance level will always reject the null hypothesis.
An aquarium in the shape of a right rectangular prism is 12.5 inches long, 6 inches wide and 8 inches high. What is the total amount of water needed, to the nearest cubic inch, to fill 90% of the aquarium with water?
Answer:
The total amount of water needed is 540 cubic inches.
Step-by-step explanation:
A cubic prism has three dimension. Lenght l, width w and height h.
It's volume is:
[tex]V = l*w*h[/tex]
In this question:
[tex]l = 12.5, w = 6, h = 8[/tex]
Dimensions in inches, so the volume will be in cubic inches.
[tex]V = 12.5*6*8 = 600[/tex]
The volume is 600 cubic inches.
What is the total amount of water needed, to the nearest cubic inch, to fill 90% of the aquarium with water?
This is 90% of 600. So
0.9*600 = 540
The total amount of water needed is 540 cubic inches.
Imagine that 55% of the 800 students participate in music instead of 60%. How could
you use the idea of halves with the bar model to find 55% of 800?
Answer:
Step-by-step explanation:
Your utility company charges 11 cents per kilowatt-hour of electricity. Complete parts (a) and (b) below. a. What is the daily cost of keeping lit a 75-watt light bulb for 12 hours each day? b. How much will you save in a year if you replace the bulb with an LED bulb that provides the same amount of light using only 20 watts of power?
Answer:
a. 9.9 cents
b. 26.5 dollars
Step-by-step explanation:
The first thing they mention to us is the cost of energy 11 cents / kwh
a) In the first point they ask us to calculate the daily cost of keeping the flashlight on for 12 hours, they tell us that it consumes 75 watts per hour, but this value must be passed to kW because the cost is given in kWh
to pass it, it would be: 75 watt * 1 kw / 1000 watt = 0.075 kw,
the formula to apply would be like this:
Daily cost = flashlight cost * time * energy cost
we all know them so we replace:
Daily cost = 0.075 kw * 12 h * 11 cents / kwh = 9.9 cents
b) Now, to know the annual savings, we must calculate the difference between the expense of the normal flashlight and the LED, let's calculate the daily cost of the LED, like this:
20 watt * 1 kw / 1000 watt = 0.02 kw
Daily cost = 0.02 kw * 12 h * 11 cents / kwh = 2.64 cents
Now by calculating the difference we multiply by 365 which are the days of a year.
Savings / year = (9.9 - 2.64) * 365 = 2649.9 cents = 26.5 dollars.
What value of x is in the solution set of 2(3x - 1) = 4x - 6?
-10
-5
OOO
A line passes through the point (-4,6) and has a slope of -5. Write an equation in point-slope form for this line.
Answer:
hope this helps you
Help please. help please. Below please
Answer:
x = 30pitch = 7Step-by-step explanation:
If you draw a horizontal line through the shaded triangle such that it intersects the left vertex, you see that it bisects the 60° angle at that vertex. The measure of x is the same as the measure of either half of that bisected angle, so is 30°.
The pitch associated in the table with an angle of 30° is 7.
x = 30pitch = 7Please answer this question !! Thank you !! Will give brainliest !!
Answer:
m = 1/4
Step-by-step explanation:
We want to get the equation in slope intercept form
y = mx+b where m is the slope and b is the y intercept
x -4y +3 =0
Add 4y to each side
x -4y+3 +4y = 0+4y
x-3 = 4y
Divide each side by 4
1/4x -3/4 =y
the slope is 1/4 and the y intercept is -3/4
Aaron is a biologist who wants to determine the growth rate of a strain of bacteria. Aaron places 1450 bacteria into a controlled environment and waits 6 hours. When Aaron checks 6 hours later, there are now 3592 bacteria. What is the hourly growth rate of the bacteria?
Answer:
Roughly 15% hourly rate.
Step-by-step explanation:
This is an exponential function that relates to natural growth.
Use the formula A = P*e^(rt)
I have attached the work to your problem.
Please see the attachment below.
I hope this helps!
The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. 1. Suppose a sample of 955 tenth graders is drawn. Of the students sampled, 812 read above the eighth grade level. Using the data, estimate the proportion of tenth graders reading at or below the eighth grade level. 2. Suppose a sample of 955 tenth graders is drawn. Of the students sampled, 812 read above the eighth grade level. Using the data, construct the 90% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level.
Answer:
The estimation for the proportion of tenth graders reading at or below the eighth grade level is given by:
[tex] \hat p =\frac{955-812}{955}= 0.150[/tex]
[tex]0.150 - 1.64 \sqrt{\frac{0.150(1-0.150)}{955}}=0.131[/tex]
[tex]0.150 + 1.64 \sqrt{\frac{0.150(1-0.150)}{955}}=0.169[/tex]
And the 90% confidence interval would be given (0.131;0.169).
Step-by-step explanation:
We have the following info given:
[tex]n= 955[/tex] represent the sampel size slected
[tex] x = 812[/tex] number of students who read above the eighth grade level
The estimation for the proportion of tenth graders reading at or below the eighth grade level is given by:
[tex] \hat p =\frac{955-812}{955}= 0.150[/tex]
The confidence interval for the proportion would be given by this formula
[tex]\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
For the 90% confidence interval the significance is [tex]\alpha=1-0.9=0.1[/tex] and [tex]\alpha/2=0.05[/tex], with that value we can find the quantile required for the interval in the normal standard distribution and we got.
[tex]z_{\alpha/2}=1.64[/tex]
And replacing into the confidence interval formula we got:
[tex]0.150 - 1.64 \sqrt{\frac{0.150(1-0.150)}{955}}=0.131[/tex]
[tex]0.150 + 1.64 \sqrt{\frac{0.150(1-0.150)}{955}}=0.169[/tex]
And the 90% confidence interval would be given (0.131;0.169).
Joe is considering pursuing an MBA degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 25 percent for University A and 40 percent for University B. What is the probability that Joe will be accepted at one, and only one, university
Answer:
The probability that Joe will be accepted at one, and only one, university is 0.45 or 45%.
Step-by-step explanation:
We are given that Joe is considering pursuing an MBA degree. He has applied to two different universities.
The acceptance rate for applicants with similar qualifications is 25 percent for University A and 40 percent for University B.
Let the probability that Joe will be accepted for University A = P(A) = 0.25
Probability that Joe will be accepted for University B = P(B) = 0.40
Now, Probability that Joe will be accepted at one, and only one, university is given by ;
Accepted for University A but not for University B + Accepted for University B but not for University A
= [P(A) [tex]\times[/tex] (1 - P(B))] + [P(B) [tex]\times[/tex] (1 - P(A))]
= (0.25 [tex]\times[/tex] 0.60) + (0.40 [tex]\times[/tex] 0.75)
= 0.15 + 0.30 = 0.45
Hence, the probability that Joe will be accepted at one, and only one, university is 0.45.
The probability that Joe will be accepted at one, and only one, university is 0.45 or 45%.
The calculation is as follows:Let us assume the probability that Joe will be accepted for University A = P(A) = 0.25
Now
Probability that Joe will be accepted for University B = P(B) = 0.40
Now,
= Accepted for University A but not for University B + Accepted for University B but not for University A
= [P(A) (1 - P(B))] + [P(B) (1 - P(A))]
= (0.25 0.60) + (0.40 0.75)
= 0.15 + 0.30
= 0.45
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Customers arrive at a service facility according to a Poisson process of rate λ customers/hour. Let X(t) be the number of customers that have arrived up to time t. Let W1,W2,... be the successive arrival times of the customers.
(a) Determine the conditional mean E[W1|X(t)=2].
(b) Determine the conditional mean E[W3|X(t)=5].
(c) Determine the conditional probability density function for W2, given that X(t)=5.
Answer:
Step-by-step explanation:
Given that:
X(t) = be the number of customers that have arrived up to time t.
[tex]W_1,W_2[/tex]... = the successive arrival times of the customers.
(a)
Then; we can Determine the conditional mean E[W1|X(t)=2] as follows;
[tex]E(W_!|X(t)=2) = \int\limits^t_0 {X} ( \dfrac{d}{dx}P(X(s) \geq 1 |X(t) =2))[/tex]
[tex]= 1- P (X(s) \leq 0|X(t) = 2) \\ \\ = 1 - \dfrac{P(X(s) \leq 0 , X(t) =2) }{P(X(t) =2)}[/tex]
[tex]= 1 - \dfrac{P(X(s) \leq 0 , 1 \leq X(t)) - X(s) \leq 5 ) }{P(X(t) = 2)}[/tex]
[tex]= 1 - \dfrac{P(X(s) \leq 0 ,P((3 \eq X(t)) - X(s) \leq 5 ) }{P(X(t) = 2)}[/tex]
Now [tex]P(X(s) \leq 0) = P(X(s) = 0)[/tex]
(b) We can Determine the conditional mean E[W3|X(t)=5] as follows;
[tex]E(W_1|X(t) =2 ) = \int\limits^t_0 X (\dfrac{d}{dx}P(X(s) \geq 3 |X(t) =5 )) \\ \\ = 1- P (X(s) \leq 2 | X (t) = 5 ) \\ \\ = 1 - \dfrac{P (X(s) \leq 2, X(t) = 5 }{P(X(t) = 5)} \\ \\ = 1 - \dfrac{P (X(s) \LEQ 2, 3 (t) - X(s) \leq 5 )}{P(X(t) = 2)}[/tex]
Now; [tex]P (X(s) \leq 2 ) = P(X(s) = 0 ) + P(X(s) = 1) + P(X(s) = 2)[/tex]
(c) Determine the conditional probability density function for W2, given that X(t)=5.
So ; the conditional probability density function of [tex]W_2[/tex] given that X(t)=5 is:
[tex]f_{W_2|X(t)=5}}= (W_2|X(t) = 5) \\ \\ =\dfrac{d}{ds}P(W_2 \leq s | X(t) =5 ) \\ \\ = \dfrac{d}{ds}P(X(s) \geq 2 | X(t) = 5)[/tex]
a study shows that, over the course of a lifetime, the average salary of college graduates is greater than the salary of people with only a high school diploma. The results were published claiming that graduating from college ensures you will make more money of the course of you lifetime. What is the problem with reporting results this way?
Answer:
Answer: The word "ensures" implies that it is certain.
In the case of the study, they simply found that the average salary is greater for college graduates. This doesn't mean that in every case the college graduate makes more money.
The problem is the word "ensures". Our study doesn't show certainty only a general pattern.
Step-by-step explanation:
Given the graph below, which of the following statements is true?
On a coordinate plane, a graph shows an image with three connected lines. The first line has a negative slope and goes from (negative 5, 6) to (negative 2, 0), the second line has a positive slope and goes from (negative 2, 0) to (2, 2), and the third line has a negative slope going from (2, 2) through (4, negative 2).
Answer: D.
The graph does not represent a one-to-one function because the y-values between 0 and 2 are paired with multiple x-values.
Step-by-step explanation:
Looking at the graph included in the answer, the graph is connected between four points.
It starts with a negative slope, then changes to a positive slope after (-2, 0), and then changes back to a negative slope after (2, 2).
To answer this, first we need to know what a one-to-one function is.
A one-to-one function is any function that only has one x-coordinate for every y-coordinate. If a function has two x-coordinates for one y-coordinate (for example, (5, 4) and (10, 4)), then the function is not one-to-one.
An example of a one-to-one function is the graph of y = x.
There is only one x-coordinate for every y-coordinate on the graph.
You can use the "horizontal line" test to determine whether a function is one-to-one. If a horizontal line is placed anywhere on a graph and intersects the function more than once, the function is not one-to-one
For the function given:
When a horizontal line is placed at "y = 1", it intersects the function three times. This means that the function IS NOT one-to-one.
Choice D is correct.
The coordinates between y = 0 and y = 2 are paired with multiple x-values, and this correctly explains why the function is not one-to-one.
Answer:
Step-by-step explanation:
which expression is equivalent to (x^1/2y^-1/4z)^-2?
Answer:
y^1/2/xz^2 option 3
Step-by-step explanation:
(x^1/2 y^-1/4 z)^-2= x^(-1/2*2) y^(1/4*2) z^-2= x^-1 y^1/2 z^-2= y^1/2/xz^2
Answer: C y^1/2/xz^2
Step-by-step explanation:
I checked with my calculator.
Data collected over an extended period of time show that women college soccer players have a relatively high rate of concussions, often with life-changing consequences. See Stanford Star Retires and Concussions Derail Promising Careers. For collegiate women soccer players the concussion rate is .63 per 1,000 participation hours (practice and game participation hours), for collegiate men soccer players the concussion rate is .41 per 1,000 participation hours (the concussion rate in college football is .61 per 1,000 participation hours). Use the Poisson distribution to answer the following questions.
a. What is the probability that the men's team experiences 2 or more concussions? (Use 3 decimal places).
b. What is the probability that the women's team experiences 2 or more concussions? (Use 3 decimal places).
The probability that the women's team experiences 2 or more concussions is 0.0013.
We are given that;
The concussion rate = 0.63 per 1,000 participation hours
Now,
The Poisson distribution is used to model the number of events occurring in a fixed interval of time or space when these events occur with a known average rate and independently of the time since the last event.
The probability mass function of the Poisson distribution is given by:
[tex]$P(X=k)=\frac{\lambda^k e^{-\lambda}}{k!}$[/tex]
where X is the number of events occurring in the interval, k is a non-negative integer, and λ is the average rate of events per interval.
a. For collegiate men soccer players, the concussion rate is .41 per 1,000 participation hours.
Therefore, the average number of concussions per hour is λ = 0.41/1000 = 0.00041.
Let X be the number of concussions experienced by the men's team in an hour. Then X follows a Poisson distribution with parameter λ = 0.00041. We want to find P(X ≥ 2). Using the Poisson distribution formula,
[tex]$P(X \geq 2) = 1 - P(X < 2) = 1 - P(X = 0) - P(X = 1)$$= 1 - \frac{0.00041^0 e^{-0.00041}}{0!} - \frac{0.00041^1 e^{-0.00041}}{1!}$$= 1 - e^{-0.00041}(1 + 0.00041)$$\approx \boxed{0.0002}$[/tex]
b. For collegiate women soccer players, the concussion rate is .63 per 1,000 participation hours.
Therefore, the average number of concussions per hour is λ = 0.63/1000 = 0.00063.
Let Y be the number of concussions experienced by the women's team in an hour. Then Y follows a Poisson distribution with parameter λ = 0.00063. We want to find P(Y ≥ 2). Using the Poisson distribution formula,
[tex]$P(Y \geq 2) = 1 - P(Y < 2) = 1 - P(Y = 0) - P(Y = 1)$$= 1 - \frac{0.00063^0 e^{-0.00063}}{0!} - \frac{0.00063^1 e^{-0.00063}}{1!}$[/tex]
[tex]$= 1 - e^{-0.00063}(1 + 0.00063)$[/tex]
[tex]$\approx \boxed{0.0013}$[/tex]
Therefore, by poisson distribution formula answer will be 0.0013.
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Assume that you live in a simple economy in which only three goods are produced and traded: Cashews, pecans and almonds. Suppose that on January 1st 2105, cashews sold for $12.50 per pound, pecans were $4.00 per pound, and almonds were $5.50 per pound. At the end of the year you discover that the cashew crop was lower than expected and that cashew prices had increased to $17.00 per pound, but pecan prices stayed at $4.00 and almond prices has actually fallen to $3.00. Can you say what happened to the overall "price level"? How might you construct a measure of the "change in price level"? What additional information might you need to construct your measure?
Answer:
Step-by-step explanation:
The information given in the question can be represent in a table format for better understanding with the additional columns as follows:
Items Weights Q₀ Prices P₀ Prices P₁ P₀Q₀ P₁Q₀
Cashew 1 $12.50 $17.00 $12.50 $17.00
Pecans 1 $4.00 $4.00 $4.00 $4.00
Almonds 1 $5.50 $3.00 $5.50 $3.00
Total $22 $24
Can you say what happened to the overall "price level"?
The changes in overall price level can be a result of a condition termed as inflation rate
How might you construct a measure of the "change in price level"?
To construct a measure of the change in price level; we need to determine the consumer price index (CPI).
The consumer price index can be determined by using the relation:
[tex]=\mathbf{\dfrac{Sum \ of \ P_1Q_0}{Sum \ of \ P_oQ_o}*100 }[/tex]
[tex]= \mathbf{\dfrac{24}{22}*100 }[/tex]
= 109.0%
consumer price index (CPI) is 109.0% ; This implies that there is a 9.9% inflation in the economy.
A light bulb consumes 15300 watt-hours in 4 days and 6 hours . How many watt-hours does it consume per day?
Answer:
3600
Step-by-step explanation:
It consumes 3600 watt hours per day. Steps are included below.
We know that there is 24 hours in a day so we times 24 by the consumes watt hours that is 15300. So 24 times 15300. After that we need to time 4 times 24+6 = the answer that is 3600. That how you get the answer.
Steps:
1: 24*15300/(4*24+6)=3600
Answer: 3600 watt hours per day
Hope this helps.
Answer:
3,600
Step-by-step explanation:
In the question, there is energy consumption and a rate but not in an easy way.
In order to find out how much watt-hours the light bulb consumes per day, the easiest way is to multiply by the hour to find out how much it uses in a day.
In 4 days and 6 hours there are 102 hours.
[tex]4 \times 24 = 96[/tex]
[tex]96 + 6 = 102[/tex]The hours for 4 days...
[tex]96 + 6 = 102[/tex]
4 days plus 6 hours. The total time...
Now make the watt-hours usage an hourly rate...
[tex]15300 + 102 = 150[/tex]
150 watts/hour...
Take the hourly rate and multiply it by 24 (number of hours in a day) to find out how many watt-hours the lightbulb uses in a day...
[tex]150 \times 24 = 3600[/tex]
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Teah was selling candy bars for a fundraiser. She spent $25 on a box of candy bars and sold each candy bar for $2.50. Her profit was $75. Teah wrote the equation 2.5c - 25 = 75 for this situation, and she found c = 40. Which statement is true about the solution c = 40?
A) The solution c = 40 is the number of candy bars Teah sold.
B) The solution c = 40 is the profit in dollars Teah made from each candy bar.
C) The solution c = 40 is the amount in dollars that Teah spent on a box.
D) The solution c = 40 is the selling cost of a box of candy bars, in dollars.
E) The solution c = 40 is the selling cost of each candy bar, in dollars.
Answer:
A
Step-by-step explanation:
You can substitute 40 into c, work out the equation and you'll get $75 as the profit. Each candy bar is $2.5 so c would be the number of candy bars she sold.
The diagram shown represents a garden. The scale is 2/3 centimeters for every 3 1/2 meters. Each square in the drawing measures 1cm by 1cm. Find the actual length, width and area of the garden based upon the given drawing.
Answer:
Length = [tex]\frac{189}{4}\ m[/tex]
Width = 21 m
Area of garden = 992.25 [tex]m^{2}[/tex]
Step-by-step explanation:
Side of square = 1 cm
As per the given question figure, we can see that there are 11 square across the length of rectangular garden.
But the garden includes only 9 squares, the corner squares are not in the garden.
So, length of garden = 9 [tex]\times[/tex] 1 = 9 cm
Using the scaling given in the question,
[tex]\dfrac{2}{3}\ cm = 3\dfrac{1}{2}\ m\\[/tex][tex]\Rightarrow \dfrac{2}{3}\ cm = \dfrac{7}{2}\ m[/tex]
[tex]1 cm = \dfrac{\dfrac{7}{2}}{\dfrac{2}{3}} \ m \Rightarrow \dfrac{21}{4}\ m[/tex]
So, length of garden = [tex]\dfrac{21}{4} \times 9 \Rightarrow \dfrac{189}{4}\ m[/tex]
-------------
And, similarly width contains 4 squares, (Corner squares are excluded)
Width of garden = [tex]\dfrac{21}{4} \times 4 \Rightarrow 21\ m[/tex]
-------------
Area of garden = Length [tex]\times[/tex] Width
[tex]\Rightarrow \dfrac{189}{4} \times 21\\\Rightarrow \dfrac{3969}{4}\\\Rightarrow 992.25\ m^{2}[/tex]
Work out the value of 102 - 43
Give your answer as a power of 6.
Answer:
1.9730677676839334 or 1.97 (rounded)
Step-by-step explanation:
102-43=59
Which of the following could represent the graph of f(x)=x^4+x^3-8x^2-12x
Answer:
Plot f(x)=x^4+x^3-8x^2-12x
Step-by-step explanation:
Sample Response: Distance is a function of time. The constant rate of change is 64. Write
the equation Y=64x + 22. Substitute 4 in for x to get 278 miles,
Compare your response to the sample response above. Did your explanation
include that distance is a function of time?
include that the constant rate of change, or slope, is 64?
include the equation y = 64x + 22?
say to substitute 4 in for x to get 278 miles?
Answer:
Yes the explanation satisfy the questions stated.
See below for explanation
Step-by-step explanation:
From the question, distance is said to be a function of time and the constant rate of change is 64.
y = 64x + 22
The above is in the form of a Linear equation:
y = mx + c
Where y = dependent variable (distance)
x = independent variable (time)
m = slope = distance/time
c = constant = 22
m = constant rate of change = 64
If x (time) = 4
y (distance) = 278 miles
y = 64(4) + 22
y = 256 + 22
y = 256 + 22
y = 278 miles
Answer:
nclude that distance is a function of time?
include that the constant rate of change, or slope, is 64?
include the equation y = 64x + 22?
say to substitute 4 in for x to get 278 miles?
Step-by-step explanation:
A shopper at a local supermarket spent the following amounts in her last eight trips to the store: $32.92 $14.14 $30.80 $28.34 $75.58 $36.33 $33.51 $22.94 The amount spent of________ is most likely an outlier.
Answer:
$75.58
The amount spent of $75.58 is most likely an outlier
Step-by-step explanation:
An outliers are unusual values in a dataset, they are data values that are extremely higher or extremely lower when compared to the other values in a data (data points that are far from other data points)
For the case above, give a dataset;
$32.92 $14.14 $30.80 $28.34 $75.58 $36.33 $33.51 $22.94
$75.58 is extremely far from other value. So $75.58 is an outlier in the given dataset.
With a height of 68 in, Nelson was the shortest president of a particular club in the past century. The club presidents of the past century have a mean height of 70.7 in and a standard deviation of 2.3 in. a. What is the positive difference between Nelson's height and the mean? b. How many standard deviations is that [the difference found in part (a)]? c. Convert Nelson's height to a z score. d. If we consider "usual" heights to be those that convert to z scores between minus2 and 2, is Nelson's height usual or unusual?
Answer:
a. The positive difference between Nelson's height and the population mean is: [tex] \\ \lvert 68-70.7 \rvert = \lvert 70.7-68 \rvert\;in = 2.7\;in[/tex].
b. The difference found in part (a) is 1.174 standard deviations from the mean (without taking into account if the height is above or below the mean).
c. Nelson's z-score: [tex] \\ z = -1.1739 \approx -1.174[/tex] (Nelson's height is below the population's mean 1.174 standard deviations units).
d. Nelson's height is usual since [tex] \\ -2 < -1.174 < 2[/tex].
Step-by-step explanation:
The key concept to answer this question is the z-score. A z-score "tells us" the distance from the population's mean of a raw score in standard deviation units. A positive value for a z-score indicates that the raw score is above the population mean, whereas a negative value tells us that the raw score is below the population mean. The formula to obtain this z-score is as follows:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]
Where
[tex] \\ z[/tex] is the z-score.
[tex] \\ \mu[/tex] is the population mean.
[tex] \\ \sigma[/tex] is the population standard deviation.
From the question, we have that:
Nelson's height is 68 in. In this case, the raw score is 68 in [tex] \\ x = 68[/tex] in.[tex] \\ \mu = 70.7[/tex]in.[tex] \\ \sigma = 2.3[/tex]in.With all this information, we are ready to answer the next questions:
a. What is the positive difference between Nelson's height and the mean?
The positive difference between Nelson's height and the population mean is (taking the absolute value for this difference):
[tex] \\ \lvert 68-70.7 \rvert = \lvert 70.7-68 \rvert\;in = 2.7\;in[/tex].
That is, the positive difference is 2.7 in.
b. How many standard deviations is that [the difference found in part (a)]?
To find how many standard deviations is that, we need to divide that difference by the population standard deviation. That is:
[tex] \\ \frac{2.7\;in}{2.3\;in} \approx 1.1739 \approx 1.174[/tex]
In words, the difference found in part (a) is 1.174 standard deviations from the mean. Notice that we are not taking into account here if the raw score, x, is below or above the mean.
c. Convert Nelson's height to a z score.
Using formula [1], we have
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]
[tex] \\ z = \frac{68\;in - 70.7\;in}{2.3\;in}[/tex]
[tex] \\ z = \frac{-2.7\;in}{2.3\;in}[/tex]
[tex] \\ z = -1.1739 \approx -1.174[/tex]
This z-score "tells us" that Nelson's height is 1.174 standard deviations below the population mean (notice the negative symbol in the above result), i.e., Nelson's height is below the mean for heights in the club presidents of the past century 1.174 standard deviations units.
d. If we consider "usual" heights to be those that convert to z scores between minus2 and 2, is Nelson's height usual or unusual?
Carefully looking at Nelson's height, we notice that it is between those z-scores, because:
[tex] \\ -2 < z_{Nelson} < 2[/tex]
[tex] \\ -2 < -1.174 < 2[/tex]
Then, Nelson's height is usual according to that statement.
There were 227 Kindergarteners who wanted a sticker. Stickers came in
books of 25. How many books of stickers did the school need to buy?
a) 25 books of stickers
b)10 books of stickers
c) 9books of stickers
d) 5 books of stickers
On Monday, Richard worked for 4 hours and earned $36. On Tuesday, Richard worked for 6 hours and earned $54. On Wednesday, Richard worked for 5 hours and earned $45.
Answer:
Richard works for $9 per hour
Step-by-step explanation:
Answer:
The answer is proportional. He makes 9$ an hour
Step-by-step explanation:
Your welcome
1
TIN
10
Which inequality represents the same ages?
The inequality graphed below represents the ages, a, of
players on a baseball team
10 11 12 13 14 15 16 17 18 19 20
0 12
0 12 sa < 18
0 12 >as 18
12 a < 18
Answer: the last 1/ 12 a < 18
Step-by-step explanation:
A randomized controlled study was designed to test whether regular drinking of cranberry juice can prevent the recurrence of urinary tract infections (UTIs) in women. 150150 women with a urinary tract infection were treated with an antibiotic and then randomly assigned to one of three groups. One group drank cranberry juice concentrate daily for six months; another group took a drink containing Lactobacillus, a lactose‑fermenting bacterium thought to help inhibit the growth of UTI‑causing bacteria, daily for six months; the last group served as the control group and drank neither cranberry juice nor Lactobacillus drinks for six months. After six months, the number of women in each group with recurring symptomatic urinary tract infection (defined as one or more new infections) was recorded. Here are the results.
Outcome
Treatment Recurring UTI No new UTI Total
Cranberry juice 8 42 50
Lactobacilllus 19 30 49
Control 18 32 50
1. Compute the chi-square statistic, degrees of freedom, and find the p-value for this test.
2. Range of the p-value (to three decimal places): < p-value <
Answer:
1. The chi-squared statistic = 10.36
The degrees of freedom = 17
The p-value for the test = 0.89
2. The range of the p-value from the Chi squared table = 0.75 < p-value < 0.90
Step-by-step explanation:
1. The Chi squared test is given as follows;
[tex]\chi ^{2} = \sum \dfrac{\left (Observed - Expected \right )^{2}}{Expected }[/tex]
Therefore,
UTI No UTI % Total
Cranberry juice 8 42 84 50
Lactobacillus 19 30 61 49
Control 18 30 60 50
The chi-squared statistic is given as follows;
[tex]\chi ^{2} = \dfrac{\left (8- 18\right )^{2}}{18} + \dfrac{\left (42 - 30\right )^{2}}{30} = 10.36[/tex]
The chi-squared statistic = 10.36
The degrees of freedom, df = 18 - 1 = 17 since the all of the expected count have a minimum value of 18
With the aid of the calculator we find the p value as p as follows;
[tex]p = 0.9 - \dfrac{10.36 - 10.085}{12.972 - 10.085} \times (0.9 - 0.75)[/tex]
The p-value for the test = 0.89
2. The range of the p-value from the Chi squared table is given as follows;
0.75 < p-value < 0.90.
What is the value of y???? I NEED ANSWERS!!!! Please and thank you!!!
Answer:68
Step-by-step explanation:
angle sum property
56+y+y-12=180
44+2y=180
2y=180-44=136
y=136/2
=68
VERIFICATION :56+68+56
=180
Y =112°
remember the sum of angles in a triangle equals 180°
EDIT : previous answer is right, i messed up with the sign
