Answer:
The calculated value t = 4.976 > 2.6264 at 0.01 level of significance
Null hypothesis is rejected
Alternative hypothesis is accepted
The mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012
Step-by-step explanation:
Given Mean of the population μ = $53,900
Given sample size 'n' = 100
Mean of the sample size x⁻ = 55,144
Sample standard deviation 'S' = 5200
Null hypothesis:H₀: There is no difference between the means
Alternative Hypothesis :H₁: The mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012
Test statistic
[tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }[/tex]
[tex]t = \frac{55144-53900}{\frac{5200}{\sqrt{100} } }[/tex]
t = 4.976
Degrees of freedom
ν = n-1 = 100-1 =99
t₀.₀₁ = 2.6264
The calculated value t = 4.976 > 2.6264 at 0.01 level of significance
Null hypothesis is rejected
Alternative hypothesis is accepted
Final answer:-
The mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012
Answer:
We conclude that the mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012.
Step-by-step explanation:
We are given that the Wall Street Journal reported that bachelor’s degree recipients with majors in business average starting salaries of $53,900 in 2012.
A sample of 100 business majors receiving a bachelor’s degree in 2013 showed a mean starting salary of $55,144 with a sample standard deviation of $5,200.
Let [tex]\mu[/tex] = mean starting salary for business majors in 2013.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\leq[/tex] $53,900 {means that the mean starting salary for business majors in 2013 is smaller than or equal to the mean starting salary in 2012}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > $53,900 {means that the mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012}
The test statistics that would be used here One-sample t-test statistics because we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean starting salary = $55,144
s = sample standard deviation = $5,200
n = sample of business majors = 100
So, the test statistics = [tex]\frac{55,144-53,900}{\frac{5,200}{\sqrt{100} } }[/tex] ~ [tex]t_9_9[/tex]
= 2.392
The value of t-test statistic is 2.392.
Now, at 0.01 significance level the t table gives a critical value of 2.369 at 99 degree of freedom for right-tailed test.
Since our test statistic is more than the critical value of t as 2.392 > 2.369, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012.
Simplify 8x + 10y + 9x - 3y by identifying and combining like terms. A. 17x + 13y B.24y C.17x+7 D.17x + 7y
Answer:
17x +7y
Step-by-step explanation:
8x + 10y + 9x - 3y
Combine like terms
8x+ 9x + 10y - 3y
17x +7y
8x+9x are like terms and 10y -3y are like terms
Answer:
17x + 7y
Step-by-step explanation:
8x + 10y + 9x - 3y
Rearrange.
8x + 9x + 10y - 3y
Factor out x and y.
x (8 + 9) + y (10 - 3)
Add or subtract.
x (17) + y (7)
17x + 7y
A nationwide survey of seniors by the University of Michigan reveals that almost 18.0% disapprove of daily pot smoking. If 8 seniors are selected at random, what is the probability that at least 2 disapprove of daily pot smoking.
Answer:
[tex] P(X\geq 2)=1- P(X<2)= 1-[P(X=0) +P(X=1)][/tex]
And using the probability mass function we can find the individual probabilities:
[tex]P(X=0)=(8C0)(0.18)^0 (1-0.18)^{8-0}=0.2044[/tex]
[tex]P(X=1)=(8C1)(0.18)^1 (1-0.18)^{0-1}=0.3590[/tex]
And replacing we got:
[tex] P(X\geq 2)=1 -[0.2044 +0.3590]= 0.4366[/tex]
Then the probability that at least 2 disapprove of daily pot smoking is 0.4366
Step-by-step explanation:
Let X the random variable of interest "number of seniors who disapprove of daily smoking ", on this case we now that:
[tex]X \sim Binom(n=8, p=0.18)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
And we want to find this probability:
[tex] P(X\geq 2)=1- P(X<2)= 1-[P(X=0) +P(X=1)][/tex]
And using the probability mass function we can find the individual probabilities:
[tex]P(X=0)=(8C0)(0.18)^0 (1-0.18)^{8-0}=0.2044[/tex]
[tex]P(X=1)=(8C1)(0.18)^1 (1-0.18)^{0-1}=0.3590[/tex]
And replacing we got:
[tex] P(X\geq 2)=1 -[0.2044 +0.3590]= 0.4366[/tex]
Then the probability that at least 2 disapprove of daily pot smoking is 0.4366
A researcher used the technique with 9 students and observed that they had a mean of 10.8 hours with a standard deviation of 1.5. A level of significance of 0.05 will be used to determine if the technique performs differently than the traditional method. Assume the population distribution is approximately normal. Find the value of the test statistic. Round your answer to three decimal places.
Answer:
[tex]t=\frac{10.8-11}{\frac{1.5}{\sqrt{9}}}=-0.4[/tex]
The degrees of freedom are given by:
[tex]df=n-1=9-1=8[/tex]
And the p value would be given by:
[tex]p_v =P(t_{(8)}<-0.4)=0.350[/tex]
Since the p value is higher than the the significance level of 0.05 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from the traditional methods.
Step-by-step explanation:
Assuming this first part of the problem obtained from the web: "Using traditional methods, it takes 11.0 hours to receive a basic driving license. A new license training method using Computer Aided Instruction (CAI) has been proposed"
Information given
[tex]\bar X=10.8[/tex] represent the mean height for the sample
[tex]s=1.5[/tex] represent the sample standard deviation
[tex]n=9[/tex] sample size
[tex]\mu_o =11[/tex] represent the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to check if the true mean for this case is equal to 11 or not, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 11[/tex]
Alternative hypothesis:[tex]\mu \neq 11[/tex]
The statistic would be given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{10.8-11}{\frac{1.5}{\sqrt{9}}}=-0.4[/tex]
The degrees of freedom are given by:
[tex]df=n-1=9-1=8[/tex]
And the p value would be given by:
[tex]p_v =P(t_{(8)}<-0.4)=0.350[/tex]
Since the p value is higher than the the significance level of 0.05 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from the traditional methods.
Any help would be greatly appreciated
Answer:
[tex]\boxed{\sf \ \ \ 49a^8b^6c^2 \ \ \ }[/tex]
Step-by-step explanation:
Hello,
[tex](-7a^4b^3c)^2=(-1)^27^2a^{4*2}b^{3*2}c^2=49a^8b^6c^2[/tex]
as
[tex](-1)^2=1[/tex]
Teresa's parents are getting phones that each and 64 GB of storage how many bits of storage come with each phone answer both in scientific in standard notation
Answer:
5.12 x 10¹¹ bit
Step-by-step explanation:
1GB = 8 x 10⁹ bits
so 64gb = 64 x 8 x 10⁹
= 512 x 10⁹
= 5.12 x 10¹¹ bits
scientific notation = 5.12 x 10¹¹ bits
standard Notation = 512 ,000,000,000 bits.
The graphs below have the same shape. What is the equation of the blue
graph?
Answer: b
Explanation:
The -2 outside of the parentheses means it’s at y=-2 and the -4 inside the parentheses means it’s at x= 4 because it’s always the opposite
Subtract -6 4/9-3 2/9-8 2/9
Answer:
[tex]-\frac{161}{9}=\\or\\-16\frac{8}{9}[/tex]
Step-by-step explanation:
[tex]-6\frac{4}{9}-3\frac{2}{9}-8\frac{2}{9}=\\\\-\frac{58}{9}-\frac{29}{9}-\frac{74}{9}=\\\\-\frac{161}{9}=\\\\-16\frac{8}{9}[/tex]
Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume that the population has a normal distribution. Thirty randomly selected students took the calculus final. If the sample mean was 95 and the standard deviation was 6.6, construct a 99% confidence interval for the mean score of all students.
A. 91.68
Answer:
B) 92.03 < μ < 97.97
99% confidence interval for the mean score of all students.
92.03 < μ < 97.97
Step-by-step explanation:
Step(i):-
Given sample mean (x⁻) = 95
standard deviation of the sample (s) = 6.6
Random sample size 'n' = 30
99% confidence interval for the mean score of all students.
[tex]((x^{-} - Z_{0.01} \frac{S}{\sqrt{n} } , (x^{-} + Z_{0.01} \frac{S}{\sqrt{n} })[/tex]
step(ii):-
Degrees of freedom
ν = n-1 = 30-1 =29
[tex]t_{0.01} = 2.462[/tex]
99% confidence interval for the mean score of all students.
[tex]((95 - 2.462 \frac{6.6}{\sqrt{30} } , 95 + 2.462\frac{6.6}{\sqrt{30} } )[/tex]
( 95 - 2.966 , 95 + 2.966)
(92.03 , 97.97)
Final answer:-
99% confidence interval for the mean score of all students.
92.03 < μ < 97.97
Tasha wants to take money out of the ATM for a taxi fare. She wants to do a quick estimate to see if taking $120 out of her bank account will overdraw it. She knows she had $325 in the account this morning when she checked her balance. Today she bought lunch for $19, a dress for $76, a pair of shoes for $53, and a necklace for $23. She also saw a movie with a friend for $12. Rounding each of her expenses to the nearest tens place, estimate how much money Tasha has left in her account before she goes to the ATM. Do not include the $ in your answer.
Answer:145
Step-by-step explanation: $19=20 76=80 53=50 23=20 12=10 total = 180 325-180 =145
Dylan paid a plumber $120 for 4 hours of labor. How much does the plumber charge per hour of labor? A. $15 per hour B. $30 per hour C. $116 per hour D. $480 per hour stay safe!
Answer:
Brainleist :)
Step-by-step explanation:
120 dollars for 4 hours of labor
120/4 dollars for 1 hour of labor
B) 30 dollars for 1 hour of labor
answe:
B) 30 dollars for 1 hour of labor
Step-by-step explanation:
120 dollars for 4 hours of labor
120/4 dollars for 1 hour of labor
important messagee:
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what 826,497 in standard form answer
Answer:8.2 x 10^5
Step-by-step explanation:
An individual who has automobile insurance from a certain company is randomly selected. Let Y be the number of moving violations for which the individual was cited during the last 3 years. The pmf of Y is the following.
y 0 1 2 3
p(y) 0.50 0.25 0.20 0.05
A) Compute E(Y).
B) Suppose an individual with Y violations incurs a surcharge of $110Y2. Calculate the expected amount of the surcharg.
Answer:
A. The E(Y) is 0.80
B. The expected amount of the surcharges is $165
Step-by-step explanation:
A. In order to calculate the E(Y), we would have to calculate the following formula:
E(Y)=∑yp(y)
E(Y)=(0*0.5)+(1*0.25)+(2*0.20)+(3*0.05)
E(Y)=0+0.25+0.40+0.15
E(Y)=0.80
B. In order to calculate the expected amount of the surcharges we would have to calculate the following formula:
E($110Y∧2)=110E(Y∧2)
=110∑y∧2p(y)
=110((0∧2*0.5)+(1∧2*0.25)+(2∧2*0.20)+(3∧2*0.05))
110(0+0.25+0.80+0.45)
=$165
If 1 euro is 1.07 dollars and 1 pound is 1.25 dollars how many euro is to the pound
Step-by-step explanation:
1.07×1.25
=1.3375 euros
What is the common difference of the sequence 20, 17, 14, 11, 8.... ?
Answer:
-3
Step-by-step explanation:
every sequence goes down by -3
Answer:
take away 3. the common difference is 3
Step-by-step explanation:
take away 3
A rectangle is constructed with its base on the x-axis and two of its vertices on the parabola yequals25minusxsquared. What are the dimensions of the rectangle with the maximum area? What is the area?
Answer:
The answer is "[tex]\bold{\frac{32}{3}}\\[/tex]"
Step-by-step explanation:
The rectangle should also be symmetrical to it because of the symmetry to the y-axis The pole of the y-axis. Its lower two vertices are (-x,0). it means that
and (-x,0), and (x,0). Therefore the base measurement of the rectangle is 2x. The top vertices on the parabola are as follows:
The calculation of the height of the rectangle also is clearly 16-x^2, (-x,16,-x^2) and (x,16,-x^2).
The area of the rectangle:
[tex]A(x)=(2x)(16-x^2)\\\\A(x)=32x-2x^3[/tex]
The local extremes of this function are where the first derivative is 0:
[tex]A'(x)=32-6x^2\\\\32-6x^2=0\\\\x= \pm\sqrt{\frac{32}{6}}\\\\x= \pm\frac{4\sqrt{3}}{3}\\\\[/tex]
Simply ignore the negative root because we need a positive length calculation
It wants a maximum, this we want to see if the second derivative's profit at the end is negative.
[tex]A''\frac{4\sqrt{3}}{3} = -12\frac{4\sqrt{3}}{3}<0\\\\2.\frac{4\sqrt{3}}{3}= \frac{8\sqrt{3}}{3}\\\\\vertical \ dimension\\\\16-(\frac{4\sqrt{3}}{3})^2= \frac{32}{3}[/tex]
Help me with answer B
Thank you
Answer:
193.77 < p < 1806.23
Step-by-step explanation:
You want R(p) > 2,100,000, so ...
-6p^2 +12000p > 2100000
p^2 -2000p < -350000 . . . . divide by -6
Adding (2000/2)^2 = 1000000 will "complete the square".
p^2 -2000p +1000000 < 650000 . . . . complete the square
(p -1000)^2 < 650000
-√650000 < p -1000 < √650000 . . . . take the square root
1000 -806.23 < p < 1000 +806.23 . . . .add 1000
193.77 < p < 1806.23 . . . . range of prices for desired revenue
Which is the better buy? Store A: $250 of 20% off Or Store B $280 at 25% off
Show your work
Answer:
Store A
Step-by-step explanation:
So. What we are going to want to do here is start off by having two stores obviously. And we have the sales that they have. If the discount is 20% rhat means the new price will be 80% of 250. So we take 250 x .8 = 200
If the discount is 25%, that means the new price will be 75% of what it was before hand. So we take 280 x .75 = 210. So the better price is at Store a
The percent defective for parts produced by a manufacturing process is targeted at 4%. The process is monitored daily by taking samples of sizes n = 160 units. Suppose that today’s sample contains 14 defectives. Determine a 88% confidence interval for the proportion defective for the process today. Place your LOWER limit, rounded to 3 decimal places, in the first blank. For example, 0.123 would be a legitimate answer. Place your UPPER limit, rounded to 3 decimal places, in the second blank. For example, 0.345 would be a legitimate entry.
Answer:
The 88% confidence interval for the proportion of defectives today is (0.053, 0.123)
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 160, \pi = \frac{14}{160} = 0.088[/tex]
88% confidence level
So [tex]\alpha = 0.12[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.12}{2} = 0.94[/tex], so [tex]Z = 1.555[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.088 - 1.555\sqrt{\frac{0.088*0.912}{160}} = 0.053[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.088 + 1.555\sqrt{\frac{0.088*0.912}{160}} = 0.123[/tex]
The 88% confidence interval for the proportion of defectives today is (0.053, 0.123)
A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 409 gram setting. It is believed that the machine is underfilling the bags. A 42 bag sample had a mean of 404 grams. Assume the population standard deviation is known to be 24. A level of significance of 0.01 will be used. Find the P-value of the test statistic. You may write the P-value as a range using interval notation, or as a decimal value rounded to four decimal places.
Answer:
[tex]z=\frac{404-409}{\frac{24}{\sqrt{42}}}=-1.35[/tex]
The p value for this case is given by:
[tex]p_v =P(z<-1.35)=0.0885[/tex]
For this case the p value is higher than the significance level given so we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true mean is significantly less than 409
Step-by-step explanation:
Information given
[tex]\bar X=404[/tex] represent the sample mean
[tex]\sigma=24[/tex] represent the population standard deviation
[tex]n=42[/tex] sample size
[tex]\mu_o =409[/tex] represent the value to verify
[tex]\alpha=0.01[/tex] represent the significance level for the hypothesis test.
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to verify if the true mean is less than 409, the system of hypothesis would be:
Null hypothesis:[tex]\mu \geq 409[/tex]
Alternative hypothesis:[tex]\mu < 409[/tex]
The statistic for this case is given by:
[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)
Replacing the info we got:
[tex]z=\frac{404-409}{\frac{24}{\sqrt{42}}}=-1.35[/tex]
The p value for this case is given by:
[tex]p_v =P(z<-1.35)=0.0885[/tex]
For this case the p value is higher than the significance level given so we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true mean is significantly less than 409
D
С
Micaela tried to rotate the square 180° about the origin.
Is her rotation correct? If not, explain why.
O No, she translated the figure instead of rotating it.
O No, she reflected the figure instead of rotating it.
O No, the vertices of the image and pre-image do not
correspond.
Yes, the rotation is correct.
cu
Answer:
it’s C
Step-by-step explanation:
No, the vertices of the image and pre-image do not correspond
No, the vertices of the image and pre-image do not correspond, Micaela tried to rotate the square 180° about the origin. Hence, option C is correct.
What is rotation about the origin?A figure can be rotated by 90 degrees clockwise by rotating each vertex of the figure 90 degrees clockwise about the origin.
Let's take the vertices of a square with points at (+1,+1), (-1,+1), (-1,-1), and (+1,-1), centered at the origin, can be found in the following positions after rotation:
The vertex (+1,+1) would be rotated to the point (-1,-1).The vertex (-1,+1) would be rotated to the point (+1,-1).The vertex (-1,-1) would be rotated to the point (+1,+1).The vertex (+1,-1) would be rotated to the point (-1,+1).Micaela's rotation must be accurate if it led to the same points. Her rotation is incorrect if the points are different, though.
It is impossible to tell if Micaela's rotation is accurate without more details or a diagram.
Thus, option C is correct.
For more information about rotation about the origin, click here:
https://brainly.com/question/30198965
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A video game requires at least 4 points to advance. Each solved puzzle is worth two points. Each solved riddle is worth 1 point. If x is the number of solved puzzles and y is the number of solved riddles, which graph represents the overall equation represented by this scenario (all points may not apply to the scenario)? On a coordinate plane, a solid straight line has a negative slope and goes through (0, 2) and (4, 0). Everything below the line is shaded. On a coordinate plane, a solid straight line has a negative slope and goes through (0, 2) and (4, 0). Everything above the line is shaded. On a coordinate plane, a solid straight line has a negative slope and goes through (0, 4) and (2, 0). Everything to the left of the line is shaded. On a coordinate plane, a solid straight line has a negative slope and goes through (0, 4) and (2, 0). Everything to the right of the line is shaded.
Answer:
Its D The Last Graph
Step-by-step explanation:
it just is my guy
A financial advisor is analyzing a family's estate plan. The amount of money that the family has invested in different real estate properties is normally distributed with a mean of $225,000 and a standard deviation of $50,000. Use a calculator to find how much money separates the lowest 80% of the amount invested from the highest 20% in a sampling distribution of 10 of the family's real estate holdings.
Answer:
The amount of money separating the lowest 80% of the amount invested from the highest 20% in a sampling distribution of 10 of the family's real estate holdings is $238,281.57.
Step-by-step explanation:
Let the random variable X represent the amount of money that the family has invested in different real estate properties.
The random variable X follows a Normal distribution with parameters μ = $225,000 and σ = $50,000.
It is provided that the family has invested in n = 10 different real estate properties.
Then the mean and standard deviation of amount of money that the family has invested in these 10 different real estate properties is:
[tex]\mu_{\bar x}=\mu=\$225,000\\\\\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{50000}{\sqrt{10}}=15811.39[/tex]
Now the lowest 80% of the amount invested can be represented as follows:
[tex]P(\bar X<\bar x)=0.80\\\\\Rightarrow P(Z<z)=0.80[/tex]
The value of z is 0.84.
*Use a z-table.
Compute the value of the mean amount invested as follows:
[tex]\bar x=\mu_{\bar x}+z\cdot \sigma_{\bar x}[/tex]
[tex]=225000+(0.84\times 15811.39)\\\\=225000+13281.5676\\\\=238281.5676\\\\\approx 238281.57[/tex]
Thus, the amount of money separating the lowest 80% of the amount invested from the highest 20% in a sampling distribution of 10 of the family's real estate holdings is $238,281.57.
The access code for a garage door consists of three digits. Each digit can be any number from 1 through 5, and each digit can be repeated. Complete parts (a) through (c). (a) Find the number of possible access codes. (b) What is the probability of randomly selecting the correct access code on the first try? (c) What is the probability of not selecting the correct access code on the first try? (a) Find the number of possible access codes. The number of different codes available is nothing.
Answer:
(a) 125
[tex](b) \dfrac{1}{125}[/tex]
[tex](c) \dfrac{124}{125}[/tex]
Step-by-step explanation:
We are given that access code consists of 3 digits.
Each digit can be any digit through 1 to 5 and can be repeated.
Now, this problem is equivalent to the problem that we have to find:
The number of 3 digit numbers that can be formed using the digits 1 to 5 with repetition allowed.
(a) We have 3 places here, unit's, ten's and hundred's places respectively and each of the 3 places have 5 possibilities (any digit allowed with repetition).
So, total number of access codes possible:
[tex]5\times 5 \times 5 = 125[/tex]
(b) Suppose, an access code is randomly selected, what is the probability that it will be correct.
Formula for probability of an event E can be observed as:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
Here, only 1 code is correct, so
Number of favorable cases = 1
Total number of cases = 125
So, required probability:
[tex]P(E) = \dfrac{1}{125}[/tex]
(c) Probability of not selecting the correct access code on first time:
[tex]P(\overline E) = 1-P(E)\\\Rightarrow P(\overline E) = 1-\dfrac{1}{125}\\\Rightarrow P(\overline E) = \dfrac{125-1}{125}\\\Rightarrow P(\overline E) = \dfrac{124}{125}[/tex]
So, the answers are:
(a) 125
[tex](b) \dfrac{1}{125}[/tex]
[tex](c) \dfrac{124}{125}[/tex]
The volume of a trianglular prism is 54 cubic units. What is the value of x?
3
5
7
9
Answer:
X is 3 units.
Step-by-step explanation:
Volume of prism is cross sectional area multiplied by length. So 1/2 ×2× x ×2 into 3x, which is equal to 6x^2. So, 6x^2=54. Therefore, x=3.
You are interested in estimating the the mean age of the citizens living in your community. In order to do this, you plan on constructing a confidence interval; however, you are not sure how many citizens should be included in the sample. If you want your sample estimate to be within 5 years of the actual mean with a confidence level of 97%, how many citizens should be included in your sample
Question:
You are interested in estimating the the mean age of the citizens living in your community. In order to do this, you plan on constructing a confidence interval; however, you are not sure how many citizens should be included in the sample. If you want your sample estimate to be within 5 years of the actual mean with a confidence level of 97% , how many citizens should be included in your sample? Assume that the standard deviation of the ages of all the citizens in this community is 18 years.
Answer:
61.03
Step-by-step explanation:
Given:
Standard deviation = 18
Sample estimate = 5
Confidence level = 97%
Required:
Find sample size, n.
First find the Z value. Using zscore table
Z-value at a confidence level of 97% = 2.17
To find the sample size, use the formula below:
[tex] n = (Z * \frac{\sigma}{E})^2[/tex]
[tex] n = ( 2.17 * \frac{18}{5})^2 [/tex]
[tex] n = (2.17 * 3.6)^2 [/tex]
[tex] n = (7.812)^2 [/tex]
[tex] n = 61.03 [/tex]
Sample size = 61.03
what is the answer to the equation -(-(-(-2)))
Answer:
2
Step-by-step explanation:
Since there are four negative signs, we have -1 multiplying each other 4 times, multiplying by positive 2. This is then 1 * 2, which is 2.
Answer:
+2
Step-by-step explanation:
=> -(-(-(-2))))
=> -(-(+2))
=> -(-2)
=> +2
For the dilation, DO, K = (10, 0) → (5, 0), the scale factor is equal to _____.
Answer:
[tex] \frac{1}{2} [/tex]
Step-by-step explanation:
[tex]scale \: factor = \frac{5}{10} = \frac{1}{2} \\ [/tex]
if rectangle ABCD was reflected over the y-axis, reflected over x axis, and rotated 180°, where would point A' lie?
Answer:
Option C (-4,-1) (In Quadrant III)
Step-by-step explanation:
Coordinate = (-4,1)
=> Reflecting over y-axis will make the coordinate (4,1)
=> Reflecting across x-axis will make the coordinate (4,-1)
=> Rotating 180 will make it (-4,-1)
Suppose the proportion X of surface area in a randomly selected quadrat that is covered by a certain plant has a standard beta distribution with α = 4 and β = 3.(a) Compute E(X) and V(X). (Round your answers to four decimal places.)E(X) = Correct: Your answer is correct.V(X) = Correct: Your answer is correct.(b) Compute P(X ≤ 0.5). (Round your answer to four decimal places.)
Answer:
(a) The value of E (X) is 4/7.
The value of V (X) is 3/98.
(b) The value of P (X ≤ 0.5) is 0.3438.
Step-by-step explanation:
The random variable X is defined as the proportion of surface area in a randomly selected quadrant that is covered by a certain plant.
The random variable X follows a standard beta distribution with parameters α = 4 and β = 3.
The probability density function of X is as follows:
[tex]f(x) = \frac{x^{\alpha-1}(1-x)^{\beta-1}}{B(\alpha,\beta)} ; \hspace{.3in}0 \le x \le 1;\ \alpha, \beta > 0[/tex]
Here, B (α, β) is:
[tex]B(\alpha,\beta)=\frac{(\alpha-1)!\cdot\ (\beta-1)!}{((\alpha+\beta)-1)!}[/tex]
[tex]=\frac{(4-1)!\cdot\ (3-1)!}{((4+3)-1)!}\\\\=\frac{6\times 2}{720}\\\\=\frac{1}{60}[/tex]
So, the pdf of X is:
[tex]f(x) = \frac{x^{4-1}(1-x)^{3-1}}{1/60}=60\cdot\ [x^{3}(1-x)^{2}];\ 0\leq x\leq 1[/tex]
(a)
Compute the value of E (X) as follows:
[tex]E (X)=\frac{\alpha }{\alpha +\beta }[/tex]
[tex]=\frac{4}{4+3}\\\\=\frac{4}{7}[/tex]
The value of E (X) is 4/7.
Compute the value of V (X) as follows:
[tex]V (X)=\frac{\alpha\ \cdot\ \beta}{(\alpha+\beta)^{2}\ \cdot\ (\alpha+\beta+1)}[/tex]
[tex]=\frac{4\cdot\ 3}{(4+3)^{2}\cdot\ (4+3+1)}\\\\=\frac{12}{49\times 8}\\\\=\frac{3}{98}[/tex]
The value of V (X) is 3/98.
(b)
Compute the value of P (X ≤ 0.5) as follows:
[tex]P(X\leq 0.50) = \int\limits^{0.50}_{0}{60\cdot\ [x^{3}(1-x)^{2}]} \, dx[/tex]
[tex]=60\int\limits^{0.50}_{0}{[x^{3}(1+x^{2}-2x)]} \, dx \\\\=60\int\limits^{0.50}_{0}{[x^{3}+x^{5}-2x^{4}]} \, dx \\\\=60\times [\dfrac{x^4}{4}+\dfrac{x^6}{6}-\dfrac{2x^5}{5}]\limits^{0.50}_{0}\\\\=60\times [\dfrac{x^4\left(10x^2-24x+15\right)}{60}]\limits^{0.50}_{0}\\\\=[x^4\left(10x^2-24x+15\right)]\limits^{0.50}_{0}\\\\=0.34375\\\\\approx 0.3438[/tex]
Thus, the value of P (X ≤ 0.5) is 0.3438.
Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x4 ln(x) (a) Find the interval on which f is increasing. (Enter your answer using interval notation.) Find the interval on which f is decreasing. (Enter your answer using interval notation.) (b) Find the local minimum and maximum values of f. local minimum value local maximum value (c) Find the inflection point. (x, y) = Find the interval on which f is concave up. (Enter your answer using interval notation.) Find the interval on which f is concave down. (Enter your answer using interval notation.)
Answer: (a) Interval where f is increasing: (0.78,+∞);
Interval where f is decreasing: (0,0.78);
(b) Local minimum: (0.78, - 0.09)
(c) Inflection point: (0.56,-0.06)
Interval concave up: (0.56,+∞)
Interval concave down: (0,0.56)
Step-by-step explanation:
(a) To determine the interval where function f is increasing or decreasing, first derive the function:
f'(x) = [tex]\frac{d}{dx}[/tex][[tex]x^{4}ln(x)[/tex]]
Using the product rule of derivative, which is: [u(x).v(x)]' = u'(x)v(x) + u(x).v'(x),
you have:
f'(x) = [tex]4x^{3}ln(x) + x_{4}.\frac{1}{x}[/tex]
f'(x) = [tex]4x^{3}ln(x) + x^{3}[/tex]
f'(x) = [tex]x^{3}[4ln(x) + 1][/tex]
Now, find the critical points: f'(x) = 0
[tex]x^{3}[4ln(x) + 1][/tex] = 0
[tex]x^{3} = 0[/tex]
x = 0
and
[tex]4ln(x) + 1 = 0[/tex]
[tex]ln(x) = \frac{-1}{4}[/tex]
x = [tex]e^{\frac{-1}{4} }[/tex]
x = 0.78
To determine the interval where f(x) is positive (increasing) or negative (decreasing), evaluate the function at each interval:
interval x-value f'(x) result
0<x<0.78 0.5 f'(0.5) = -0.22 decreasing
x>0.78 1 f'(1) = 1 increasing
With the table, it can be concluded that in the interval (0,0.78) the function is decreasing while in the interval (0.78, +∞), f is increasing.
Note: As it is a natural logarithm function, there are no negative x-values.
(b) A extremum point (maximum or minimum) is found where f is defined and f' changes signs. In this case:
Between 0 and 0.78, the function decreases and at point and it is defined at point 0.78;After 0.78, it increase (has a change of sign) and f is also defined;Then, x=0.78 is a point of minimum and its y-value is:
f(x) = [tex]x^{4}ln(x)[/tex]
f(0.78) = [tex]0.78^{4}ln(0.78)[/tex]
f(0.78) = - 0.092
The point of minimum is (0.78, - 0.092)
(c) To determine the inflection point (IP), calculate the second derivative of the function and solve for x:
f"(x) = [tex]\frac{d^{2}}{dx^{2}}[/tex] [[tex]x^{3}[4ln(x) + 1][/tex]]
f"(x) = [tex]3x^{2}[4ln(x) + 1] + 4x^{2}[/tex]
f"(x) = [tex]x^{2}[12ln(x) + 7][/tex]
[tex]x^{2}[12ln(x) + 7][/tex] = 0
[tex]x^{2} = 0\\x = 0[/tex]
and
[tex]12ln(x) + 7 = 0\\ln(x) = \frac{-7}{12} \\x = e^{\frac{-7}{12} }\\x = 0.56[/tex]
Substituing x in the function:
f(x) = [tex]x^{4}ln(x)[/tex]
f(0.56) = [tex]0.56^{4} ln(0.56)[/tex]
f(0.56) = - 0.06
The inflection point will be: (0.56, - 0.06)
In a function, the concave is down when f"(x) < 0 and up when f"(x) > 0, adn knowing that the critical points for that derivative are 0 and 0.56:
f"(x) = [tex]x^{2}[12ln(x) + 7][/tex]
f"(0.1) = [tex]0.1^{2}[12ln(0.1)+7][/tex]
f"(0.1) = - 0.21, i.e. Concave is DOWN.
f"(0.7) = [tex]0.7^{2}[12ln(0.7)+7][/tex]
f"(0.7) = + 1.33, i.e. Concave is UP.