Answer:
2.5% probability that a randomly selected book has fewer than 133 pages if the mean is 185 pages and the standard deviation is 26 pages
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 185
Standard deviation = 26
The normal distribution is symmetric, which means that 50% of the measures are above the mean and 50% are below.
What is the probability that a randomly selected book has fewer than 133 pages if the mean is 185 pages and the standard deviation is 26 pages?
133 = 185 - 2*26
So 133 is two standard deviations below the mean.
By the Empirical Rule, of the 50% of the measures below the mean, 95% are within 2 standard deviations of the mean, that is, above 133 and below 185. The other 5% is below 133
p = 0.05*0.5 = 0.025
2.5% probability that a randomly selected book has fewer than 133 pages if the mean is 185 pages and the standard deviation is 26 pages
Please answer this question !! 20 points and brainliest !!
Answer:
yes, they are parallel; the general form equation differs only in the constant.
Step-by-step explanation:
Subtract y from the first equation and multiply by 2.
y -y = 1/2x -y +3
0 = x -2y +6
x -2y +6 = 0 . . . . . put in general form
Compared to the second equation, we see the only difference is in the constant, +6 vs. -8.
This means the lines are parallel.
The function f(x) = −x2 + 16x − 60 models the daily profit, in dollars, a shop makes for selling candles, where x is the number of candles sold. Determine the vertex, and explain what it means in the context of the problem. (6, 10); The vertex represents the maximum profit. (6, 10); The vertex represents the minimum profit. (8, 4); The vertex represents the minimum profit. (8, 4); The vertex represents the maximum profit.
Answer:
A.
f is a quadratic function, which means it's graph is a parabola.
Notice that the coefficient of is negative, so the parabola opens downwards.
the x-coordinate of a parabola is always determined by the formula:
where a is coefficient of the term, and b is the coefficient of the x term.
Thus, x-coordinate of the vertex of the graph of f is :
the y-coordinate of the vertex is f(8)=-8*8+16*8-60=4.
The vertex is (8, 4).
This means that the maximum daily profit is when exactly 8 candles are sold.
B.
The x-intercepts are the values of x such that f(x)=0,
so to find these values we solve:
complete the square:
so x-8=2 or x-8=-2
the roots are x=10 and x=6, are the roots.
This means that when the shop sells exactly 6 or 10 candles, it makes no profit.
Answer: d (8, 4); The vertex represents the maximum profit.
Explanation: i got it right on the test
If 7 - y = 6, then y=
Answer:
y=1
Step-by-step explanation:
7-y=6
6+1=7
7-1=6
Hope this helps:)
Stay Safe
Answer:
y =1
Step-by-step explanation:
7 - y = 6
Subtract 7 from each side
7 - y-7 = 6 -7
-y = -1
Multiply each side by -1
-y*-1 = -1 *-1
y = 1
how to simplify 4e + 6f + 7e - f
Answer:
11e+5f
Step-by-step explanation:
Combine like terms:
4e+7e+6f-f
11e+5f
Answer:
11e +5f
Step-by-step explanation:
4e + 6f + 7e - f
Combine like terms
4e+7e +6f-f
11e +5f
Determine the least number of patties that will share equally among groups og 6, 9, 12
Answer:
72.
Step-by-step explanation:
Given a group of 6, 9 and 12.
We are to determine the least number of patties that will be shared equally among the groups.
This we do by determine the Least common multiple of the three numbers.
[tex]6=2 X 3\\9 = 3 X 3\\12 =2 X 2 X 2\\L.C.M.=2^3X3^2=72[/tex]
Therefore, the least number of patties that can be shares equally among groups of 6, 9 and 12 is 72.
True or False - the following scenario depicts an independent relationship between variables (tree growth and air quality): 20% of trees growing in a particular region are not growing to their expected height. In a particular neighborhood in that region, the Air Quality Index is labeled as "Unhealthy for Sensitive Groups" or worse 30% of the time. 10% of the trees in the region grow in this neighborhood. If you randomly measured the growth of a tree in that neighborhood, then the probability that that tree is not growing to its expected height is 33.33%.
A game is played using one die. If the die is rolled and shows 1, the player wins $5. If the die shows any number other than 1, the player wins nothing. If there is a $1 charge to play the game, what is the game’s expected value?
Answer:
1/5
Step-by-step explanation:
i had a similar question
For each roll you start with paying 2 dollars and you only with 10 dollars one out of 6 rolls (on average).
So the cost for one play is 2 dollars and your win is 10/6.
Value is -2+10/6=-1/3 dollars
So you lose 1/3 dollars on average with each game
since you have no limited rolls u put 1/5
this from another question but both same just different numbers
The product of 5 and the sum of 12 and a certain number is 10. What is the number 4
Answer:
-10
Step-by-step explanation:
5(12 + x) = 10
60 + 5x = 10
5x = -50
x = -10
Find the equation for the plane through the points Upper P0 (-2 ,2 ,-5),Q0 (1,2,-1), and Upper R0 (-1,-5,4 ).
The equation of plane is:________
Answer:
28x - 23y - 21z = 3
Step-by-step explanation:
First, we need to find two vectors in the plane as:
vector PQ = Q - P = (1, 2, -1) - (-2, 2, -5) = (3, 0, 4)
vector PR = R - P = (-1, -5, 4) - (-2 ,2 ,-5) = (1, -7, 9)
Then, we need to find a normal vector to the plane as:
PQ x RQ = ((0*9)-(4*-7), -(3*(9)-(4*1), (3*-7)-(0*1))
PQ x RQ = (28, -23, -21)
Finally, the equation of a plane is:
A(x-x0) + B(y-y0) + C(z-z0) = 0
Where (A,B,C) is a normal vector to the plane and (x0, y0, z0) is a point in the plane. So, replacing (A,B,C) by (28, -23, -21) and (x0, y0, z0) by P0(-2,2,-5), we can write the equation of the plane as:
28(x+2) - 23(y-2) - 21(z+5) = 0
Solving, we get:
28x + 56 - 23y + 46 - 21z - 105 = 0
28x - 23y - 21z - 3 = 0
28x - 23y - 21z = 3
What is the area of a rectangle that is 4 1/2 cm long and 2 5/9 cm wide? Solution: Answer: What is the area of a square that has a side of 4 3/5 cm?
Answer:
1) 23/2
2) 529/25
Step-by-step explanation:
Transformation:
[tex]4\frac{1}{2} = \frac{(2*4) + 1}{2} = \frac{9}{2}[/tex]
[tex]2\frac{5}{9} = \frac{(9*2) + 5}{9} = \frac{23}{9}[/tex]
A = [tex]\frac{9}{2} * \frac{23}{9} = \frac{23}{2}[/tex]
-----------------------------
Transformation:
[tex]4\frac{3}{5} = \frac{(5*4) + 3}{5} = \frac{23}{5}[/tex]
A = [tex](\frac{23}{5})^{2} = \frac{529}{25}[/tex]
Suppose that it costs $200 per day to search for chanterelle mushrooms at Pt. Reyes National Seashore. On an average day, the total weight of mushrooms M found at Pt. Reyes is M = 100x-x^2 pounds ,where x is the number of people mushroom hunting on that day. Chanterelles can be sold for $60 per pound. How many more people will go mushroom hunting than is socially optimal?
Answer:
For an overall profit, we need at least 97 people to go mushroom hunting.
Any number of people that is more than the socially optimal number should go mushroom hunting on any given day.
Step-by-step explanation:
The socially optimal number of people that will go mushroom hunting is the number where amount spent to go mushroom hunting equally balances the amount obtained by selling the mushrooms obtained.
If x people go mushroom hunting in a day, the total cost of hunting for that day = 200x
The amount of mushroom obtained is given as
M = (100x - x²) in pounds
The selling price of 1 pound = $60
The cost of M pounds = 60M = 60(100x - x²)
= (6000x - 60x²)
At socially optimal number,
200x = 6000x - 60x²
60x² - 6000x + 200x = 0
60x² - 5800x = 0
x(60x - 5800)
x = 0 or (60x - 5800) = 0
x = 0 or x = (5800/60) = 96.67
Socially optimal number of people = 0 or 96.67
For realistic purposes, we take the socially optimal number of people that went mushroom hunting as 96.67
Any number above this number will result in an overall profit, and any number below it results in an overall loss.
So, for an overall profit, we need at least 97 people to go mushroom hunting.
Hope this Helps!!
Answer:
48 people
Step-by-step explanation:
When allocating resources to a particular task it is important to assign optimal units of resources.
In this scenario if the people hunting mushrooms are too many they will not make profit. But an optimal number will guarantee everyone makes positive profit.
Optimal = (M÷x)Px - 200= 0
Optimal= {(100x -x^2) ÷ x} * 60 = 200
Optimal = 6000 - 60x = 200
x= 96.666~ 97 people
However to maximise profit MTB = MTC
Socially Optimal quantity = 60(100x - x^2) -200
∂(Socially Optimal amount) ÷ ∂ x= 6000 - 120x - 200
x = 48.33~ 48 people
So 48 more people go mushroom hunting than is socially optimal
You are renting a car that charges a $30 fee plus 40 cents a mile. The rate of change
is $30.
True
False
Answer:
true
is the answer
(3х^2y^3)^3 =
3x^5y^6
9х^6y^9
27x^5y^6
27x^6y^9
Answer:
27x^6y^9
Step-by-step explanation:
The outside exponent multiplies all of the inside exponents. The applicable rules of exponents are ...
(ab)^c = (a^c)(b^c)
(a^b)^c = a^(bc)
__
(3x^2y^3) = (3^3)(x^(2·3))(y^(3·3)) = 27x^6y^9
-3
n is an integer.
Write down the possible values of n.
I
Answer:
since n is an integer you substitute n with all the integers. But since that is too much you should use infinity.
n=[-∞,+∞] where -∞ is a negative infinity which stands for negative numbers and +∞ is a positive infinity where it stands for positive numbers.
an integer contains negative and positive numbers so above is the answer.
Step-by-step explanation:
Complete the following subtraction exercises.
10 – 2 =
14 – 6 =
15 – 9 =
17 – 8 =
13 – 5 =
11 – 8 =
20 – 8 =
16 – 7 =
12 – 9 =
21 – 9 =
11 – 6 =
5 – 5 =
4 – 0 =
16 – 8 =
10 – 5 =
18 – 7 =
13 – 8 =
12 – 4 =
Answer:
Below
Step-by-step explanation:
8,8,6,9,8,3,12,9,3,12,5,0,4,8,5,11,5,8. Answers are in order from the first to the last
V. Money Magazine reported that the average price of gasoline in the United States during the first quarter of 2008 was $3.46. Assume that the price reported by Money is the population mean, and the standard deviation σ is $0.15. a. What is the probability that the mean price for a sample of 30 gas stations is within $0.03 of the population mean?
Answer:
[tex] z=\frac{3.43 -3.46}{\frac{0.15}{\sqrt{30}}} = -1.095[/tex]
[tex] z=\frac{3.49 -3.46}{\frac{0.15}{\sqrt{30}}} = 1.095[/tex]
And we can find this probability using the normal standard table and we got:
[tex] P(-1.095<z<1.095) = P(z<1.095) -P(z<-1.095) =0.863 -0.137= 0.726[/tex]
Step-by-step explanation:
Let X the random variable that represent the price of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(3.46,0.15)[/tex]
Where [tex]\mu=3.46[/tex] and [tex]\sigma=0.15[/tex]
And for this case we want to find the following probability:
[tex] P(3.43 \leq \bar X \leq 3.49)[/tex]
And we can use the z score formula given by:
[tex] z=\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
If we find the z score for the limits we got:
[tex] z=\frac{3.43 -3.46}{\frac{0.15}{\sqrt{30}}} = -1.095[/tex]
[tex] z=\frac{3.49 -3.46}{\frac{0.15}{\sqrt{30}}} = 1.095[/tex]
And we can find this probability using the normal standard table and we got:
[tex] P(-1.095<z<1.095) = P(z<1.095) -P(z<-1.095) =0.863 -0.137= 0.726[/tex]
In an aquarium, there are 4 large fish and 16 small fish. Half of the small fish are blue. One fish is selected at random. Find the probability that it is a small, blue fish. Write your answer as a fraction in simplest form.
Answer:
2/5
Step-by-step explanation:
There are 20 fish, 8 of which are small and blue. Therefore, the probability of randomly selecting a small blue fish is 8/20 = 2/5.
To examine the effect of high-dose green tea extract on weight loss, researchers conducted a randomized, double-blind trial on a random sample of 115 women with obesity from Taiwan. Some of these women were randomly assigned to the main treatment group taking a high-dose green tea extract ("EGCG") daily for 12 weeks. The published abstract of this 2015 study reports that, "Significant weight loss, from 76.8 ± 11.3 kg to 75.7 ± 11.5 kg (p = 0.025), was observed in the treatment group after 12 weeks of high-dose EGCG treatment."
Which of the following inference procedures would be used to reach the quoted conclusion?
a. Z procedure for a proportion
b. Chi-square for two-way tables
c. Chi-square for goodness of fit
d. Two sample t procedure for two means
e. One sample or matched-pairs t procedure for a mean
f. ANOVA for several means
Answer:
d. Two sample t procedure for two means.
Step-by-step explanation:
The study have a treatment group, which is the group of women that are taking the high dose of green tea extract, and a control group, in order to compare. They are assigned randomly to each group.
Then, the difference fo the two sample means is calculated and a t-test is performed in order to conclude if the two populations means are significantly different.
Apparently they are significantly different, as this is the conclusion with a P-value of 0.025.
Round 5 to the nearest ten.Enter your answer in the box below.
Answer:
[tex]10[/tex]
Step-by-step explanation:
[tex]05[/tex]
If the units place is higher than 5, then add 1 to the tens place.
winnie and kevin like to create their own triathlon courses to challenge each other. last weekend, winnie created a course that included a swim of 3/4 of a mile, a bike ride of 57/4 miles and a run of 13/4 miles. how long was the course winnie created?
Many traffic experts argue that the most important factor in accidents is not the average speed of cars but the amount of variation. Suppose that the speeds of a sample of 200 cars were taken over a stretch of highway that has seen numerous accidents. Compute the standard deviation of the speeds in Excel file Q-14.xlsx.
Answer and Step-by-step explanation: Standard Deviation is the measure of how diferent a number is from the mean of the data set. It is the spread of a data set. To calculate it manually:
1) Find the mean of the data set. Mean, represented by μ, is the sum of all the values divided by the total number of elements forming the set;
2) Subtract each number with the Mean and square the result;
3) Add the differences and divide it by the total number of elements of the set;
4) Take the square root of the result and that is the Standard Deviation.
The calculations can be done by a calculator like Excel:
1) In each cell of a same column, write the data you want to know the deviation.
2) On the last cell, write: =stdev.p(A1:A10) or =stdev.s(A1:A10).
3) Press Enter. The deviation will appeared on the same cell.
The function STDEV.P is used when the data represents the entire population, whereas STDEV.S is used when the data is for a sample of the population. Inside the parenthesis, put the cells where your data is. For example, if you put your data in the column A, from cell 1 to cell 10, you write like it's written above.
Suppose an All Greens store in Sonoma, California, wants to estimate a range of advertising costs appropriate to its store. If it spends too little on advertising, it will not reach enough customers. However, it does not want to overspend on advertising for this type and size of store. At this store, x1 = 163, x2 = 2.4, x3 = 188, x5 = 6.6, and x6 = 10. Use these data to predict x4 (advertising costs) and find an 80% confidence interval for your prediction. (Use 2 decimal places.)
Answer:
The advertising cost, X₄ = 5.626 million
The 80% confidence limits for X₄ is (5.041 , 6.100)
The 80% prediction limits for X₄ is (4.048 , 7.094)
Step-by-step explanation:
Using MINITAB
The regression equation is X₄ = 4.14 + 0.0431 X₁ - 0.800 X₂ + 0.00059 X₃ - 0.661 X₅ + 0.057 X₆
Predictor Coef SE Coef T P
Constant 4.142 1.626 2.55 0.019
X₁ 0.043089 0.009466 4.55 0.000
X₂ -0.7998 0.2515 -3.18 0.005
X₃ 0.000590 0.004221 0.14 0.890
X₅ -0.6606 0.1542 -4.28 0.000
X₆ 0.0574 0.1254 0.46 0.652
S = 1.07911 R-Sq = 93.4% R-Sq(adj) = 91.8%
Analysis of Variance
Source DF SS MS F P
Regression 5 345.966 69.193 59.42 0.000
Residual Error 21 24.454 1.164
Total 26 370.420
Source DF Seq SS
X₁ 1 309.464
X₂ 1 8.699
X₃ 1 5.994
X₅ 1 21.566
X₆ 1 0.244
Unusual Observation
Obs X₁ X₄ Fit SE Fit Residual St Resid
17 398 5.500 7.714 0.641 -2.214 -2.55 R
27 400 7.000 7.366 1.025 -0.336 -1.00 X
Where R is observation with a large standardized residual.
Where X is observation whose X values give it large influence.
Predicted values for new Observations
New
Obs Fit SE Fit 80% Cl 80% Pl
1 5.571 0.400 (5.041 , 6.100) (4.048 , 7.094)
Values of Predictors for New Observations
New
Obs X₁ X₂ X₃ X₅ X₆
1 163 2.40 188 6.60 10.0
∴ The advertising cost, X₄ = 5.626 million, The 80% confidence limits for X₄ is (5.041 , 6.100), and The 80% prediction limits for X₄ is (4.048 , 7.094)
6z+10=-2
pls answer'
i willmarke brainlest
Answer:
Step-by-step explanation: 6z=-2-10
6z= -12
z=-12/6
then z= -2
Robin read somewhere that adding salt to water while heating it will raise the temperature of
the water causing it to boil faster. To test this claim, she filled 30 identical pots with one quart
of water. She randomly selected 15 of the pots and added 1 teaspoon of salt. She then placed
each pot on identical burners set to the highest setting. She measured the water temperature
In each pot after 5 minutes.
Is Robin's research method an example of an observational study experiment, or
simulation?
b
If Robin does find that there is a difference between the water temperatures in the pots
with salt compared to those without can she conclude that the salt caused the
difference in temperature?
Answer:
a. An experiment
b. No
Step-by-step explanation:
a. Robin's research method can be concluded to be an experiment because she has a testable group (pots of water with salt) and a control group (pots of water without salt).
2. Based on this alone, she cannot conclude that the salt caused the
difference in temperature because she has not set some appropriate conditions which are to be met for this test.
A cognitive psychologist would like to evaluate the claim that the omega-3 fatty acids can help improve memory in normal adult humans. One group of participants is given a large dose of fish extract containing the Omega-3 (500 mg), and a second group is given a placebo containing no Omega-3 (0 mg). The researcher asks each participant to read the front page of a local newspaper thoroughly every morning and to take their prescribed dosage (of either Omega-3 or placebo) immediately afterwards. The researcher gives each participant a memory test at the end of two weeks and records how many news items each participant remembers from the past three weeks of news. Answer the following:
A) What names would you give the independent and dependent variables;
B) Is the dependent variable discrete or continuous?
C) What scale of measurement (nominal, ordinal, interval or ratio; and continuous or discrete) is used to measure the independent variable?
D) What research method is being used (experimental or observational)? Explain why you conclude that the research method is one or the other.
Answer:
(a)
Independent Variable- Dosage of Omega-3 Fatty AcidsDependent Variable - Number of news item remembered(b)Discrete
(c)Ratio Scale and Discrete Variable
(d) Experimental Method
Step-by-step explanation:
The psychologist wants to evaluate the claim that omega-3 fatty acids can help improve memory in normal adult humans.
(a)In the study, the participants in the two groups were given fish extracts containing Omega-3 (500 mg) and no Omega-3 (0 mg).
The memory test involves measuring the number of items each participant remembers from the past three weeks of news.
Therefore:
Independent Variable- Dosage of Omega-3Dependent Variable - Number of news item remembered(b) The dependent variable is discrete since the number of news items remembered can only be whole numbers.
(c)The independent variable is in milligrams of Omega-3 where the placebo is 0 mg. This is a ratio scale since it has an absolute zero.
Since the dosage is given in multiples of 50mg, it is a discrete variable.
(d)Since the psychologist seeks to manipulate the conditions of the study by introducing Omega-3 to some of the participants and placebo to other participants, it is an experimental distribution.
Question 2 of 10
2 Points
What is the sum of the rational expressions below?
2x+3/3x+x/x+1
Answer:
5x^2+5x+3/3x^2+3x
Step-by-step explanation:
After 2 hours, there are 1,400 mL of fluids remaining in a patient’s IV. The fluids drip at a rate of 300 mL per hour. Let x be the time passed, in hours, and y be the amount of fluid left in the IV, in mL. Write a linear function that models this scenario.
Answer:
[tex] y(2) = 1400[/tex]
Using this condition we got:
[tex]1400= -300*2 +b[/tex]
And solving for b we got:
[tex] b= 1400+ 600= 2000[/tex]
So then our linear function is given by:
[tex] y = -300x +2000[/tex]
Where y is the amount of fluid left and x the number of hours ellapsing
Step-by-step explanation:
We want to set up a linear function like this one:
[tex]y = mx+b[/tex]
Where y is the amount of fluid left, m the slope and b the initial amount. From the info given we know thatm = -300. And we also have the following condition:
[tex] y(2) = 1400[/tex]
Using this condition we got:
[tex]1400= -300*2 +b[/tex]
And solving for b we got:
[tex] b= 1400+ 600= 2000[/tex]
So then our linear function is given by:
[tex] y = -300x +2000[/tex]
Where y is the amount of fluid left and x the number of hours ellapsing
You are playing a game called cornhole and let’s assume that you are reallygood at it with the winning probability is 0.8. For the following parts, find (a) the name ofthe appropriate probability distribution and correct parameters, (b) the expected value and (c) the variance of Y.
A. Y = the number of games it takes you to lose one time.
B. Y = the number of games it takes you to lose four times.
C. Y the number of times you win out of 100 games.
Answer:
Step-by-step explanation:
Given that :
The probability of winning is 0.8
i.e P(winning) = 0.8
Then P(losing) = 0.2
a) Y ~ Geometric distribution
[tex]P = P(loose) =0.2 \\ \\ \mu_{\delta} = \dfrac{1}{P}= \dfrac{1}{0.2}\\ \\ = 5.0 \\ \\ \\ \dfrac{\sigma ^2 }{\delta } = \dfrac{1-P}{P^2} \\ \\ =\dfrac{0.8}{0.04} \\ \\ = 20[/tex]
b) Y ~ Negative Binomial Distribution
[tex]P = P (loose) =0.2 \\ \\ \delta = number \ of \ loss = 4 \\ \\ \mu_{\delta} = \dfrac{\delta}{P} \\ \\ =\dfrac{4}{0.2} \\ \\ = 20 \\ \\ \\ \sigma ^2_{\delta} = \dfrac{\delta (1-P)}{P^2} \\ \\ = \dfrac{4*0.8}{0.04}\\ \\ = 80[/tex]
c) Y ~ Binomial Distribution;
n = 100 ; P = 0.8
[tex]\mu_{\delta} = nP \\ \\ = 100*0.8 \\ \\ = 80 \\ \\ \\ \sigma_{\delta}^2 = nP(1-P) \\ \\ =80*0.2 \\ \\ = 16[/tex]
How do you solve this problem? population proportion is to be estimated from a sample of 400 with a sample proportion of 0.1. Approximate the 95% confidence interval of the population proportion
Answer:
(0.0706, 0.1294)
Step-by-step explanation:
Confidence interval of a proportion is:
CI = p ± CV × SE
where p is the proportion,
CV is the critical value (z score or t score),
and SE is the standard error.
The sample is large enough to estimate as normal. For 95% confidence level, CV = z = 1.96.
Standard error for a proportion is:
SE = √(pq/n)
SE = √(0.1 × 0.9 / 400)
SE = 0.015
The confidence interval is:
CI = 0.1 ± (1.96)(0.015)
CI = (0.0706, 0.1294)
Round as needed.
Which of the functions below could have created this graph?
Answer:
i don't know if this is right or not i did to much work to put it all down but i pretty sure it's C.