Answer:
E(rP) = 4% + 5.50% x β(M1) + 10.92% x β(M2)
Step-by-step explanation:
let us recall from the following statement:
The two independent economic factors are M1 and M2
Th risk free rate = 4%
The standard deviation of all stocks of independent firm specific components is =49%
P = portfolios for A and B
Now,
What is the expected relationship of return-beta
The Expected return-beta relationship E(rP) = % + βp₁ + βp₂
E(rA) = 4% + 1.6 * M1 + 2.4* M2 = 39%
E(rB) = 4% + 2.3 * M1 + (-0.7)* M2 = 9%
Therefore
Solving for M1 and M2 using excel solver, we have M1 = 5.50% and M2 = 10.92%
E(rP) = 4% + 5.50% x β(M1) + 10.92% x β(M2)
The question pertains to finance and investment analysis. It emphasizes the CAPM model, which combines systematic risk measured by beta and market risk premium to calculate expected returns on portfolios. It also highlights that diversification reduces firm-specific risks.
Explanation:The question deals with the concept of portfolio return, beta coefficients, and firm-specific risk, which are important aspects of finance and investment analysis. The expected return on portfolios A and B, can be calculated using the CAPM model, which states that expected return equals the risk-free rate plus the portfolio's beta (which measures systematic risk) multiplied by the market risk premium (difference between the expected market return and the risk-free rate). To compute this, the beta coefficients need to be multiplied with their respective economic factors, and the results obtained are added together.
For portfolio A, the expected return would be calculated like this: Return = Risk-Free rate + β1*M1 + β2*M2 = 4 + (1.6 * M1) + (2.4 * M2).
For portfolio B, the calculation would be similar: Return = Risk-Free rate + β1*M1 + β2*M2 = 4 + (2.3 * M1) - (0.7 * M2). The negative beta on M2 indicates that the portfolio's return would decrease when M2 increases, hence it has an inverse relationship with the portfolio return. The independent firm-specific component would not affect the return as per the assumption that the portfolios are well diversified; diversification reduces, but not completely eliminates, the firm-specific risk.
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512 = (m + 7) ^ 3/2
It’s algebra!!!
Answer:
m = 57
Step-by-step explanation:
If we assume your equation is supposed to be ...
512 = (m +7)^(3/2)
we can raise both sides to the 2/3 power to get ...
512^(2/3) = m +7
64 = m +7
57 = m . . . . . . subtract 7
Patty is making a poster for science class. She spends. 50 minutes on each. Of 2 days. She completes 1/3 of the poster the first day and another 1/3 the next day what fraction of the poster has she completed so far?
Answer:
She has completed 2/3 of the poster
Explanation:
1/3 of the poster the first day
+
1/3 of the poster the next day
1/3 + 1/3 = 2/3
a circle with the radius of 1 cm sits inside a 11cm by 12cm rectangle.What is the area of the shaded region?
Answer:
128.86 square cm
Step-by-step explanation:
Area of shaded region = Area of rectangle - Area of circle
[tex] = 11 \times 12 - \pi {r}^{2} \\ = 132 - 3.14 \times {1}^{2} \\ = 132 - 3.14 \\ = 128.86 \: {cm}^{2} \\ [/tex]
Answer:
128.86
Step-by-step explanation:
W is less than or equal to 9 and greater than -7
Answer:
(-7, 9]
Step-by-step explanation:
Assuming you want an answer in interval notation:
W is less than or equal to 9 >> [tex]w \leq 9[/tex]
W is greater than- 7 >> [tex]-7 < w[/tex]
Combine the two >> [tex]-7 < w \leq 9[/tex]
So in interval notation, (-7, 9]
Lola is using a one-sample t-t- test for a population mean, µμ , to test the null hypothesis, H0:µ=40 mg/dLH0:μ=40 mg/dL , against the alternative hypothesis, H1:µ>40 mg/dLH1:μ>40 mg/dL . Her results are based on a simple random sample of size n=15 . The value of the one-sample t-t- statistic is t=1.457 .
If Lola requires her results to be statistically significant at significance level of a 0.10, what can she conclude and why?
a. Because the exact p-value is unknown, she cannot make a conclusion.
b. She should not reject the null hypothesis because p > 0.10.
c. She should not reject the null hypothesis because p< 0.10.
d. She should reject the null hypothesis because p< 0.10,
e. She should not reject the null hypothesis because 0.10< p < 0.05.
Answer:
d. She should reject the null hypothesis because p < 0.10.
Step-by-step explanation:
We have a t statistic, so let's solve for the P-value on our calculators. (tcdf on a TI-84 calculator is 2nd->VARS->6.)
tcdf(left bound, right bound, degrees of freedom)
Our left bound is t=1.457. Our right bound is infinity, because we're interested in the hypothesis µ>40 mg/dL. We use 999 to represent infinity in the calculator.Our degrees of freedom is n-1 = 15-1 = 14.tcdf(1.457,999,14) = .084
.084 < P-value of .10, so we reject the null hypothesis.
Lola's conclusion should be "She should reject the null hypothesis because p< 0.10". Option D is correct.
Given information:
Lola is using a one-sample t-test for a population mean, µ, to test the null hypothesis.
[tex]\mu=40[/tex]
Sample random size is, [tex]n=15[/tex].
The value of the one-sample t-statistic is [tex]t=1.457[/tex].
The left bound will be [tex]t=1.457[/tex] and the value of [tex]n-1[/tex] will be 15-1=14.
Now, use the calculator to find the value of p. The found value of p will be,
[tex]p=0.084[/tex]
So, the value of p is less than 0.1.
Therefore, Lola's conclusion should be "She should reject the null hypothesis because p< 0.10". Option D is correct.
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equation of the line through (-10,3) and (-8 -8)
Answer:
(-8-3)/(-8+10)= -11/2
y - 3 = -11/2(x+10)
y-3=-11/2x-55
y=-11/2x-52
Step-by-step explanation:
Jack bought 4 dozen eggs at k10 per dozen. 6 eggs were broken .what percent of his money goes waste?
Step-by-step explanation:
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Recall the survey you took during the first week of class. One of the questions was “do you agree that it is inappropriate to speak on a cellphone while at a restaurant?” Of the 1913 females that responded to the survey, 1729 agreed with this statement. Of the 1276 males that responded to this survey, 1111 agreed with this statement. Test to see if there is any difference between males and females with respect to how they feel about this issue. Use a significance level of .05.
State the appropriate null and alternative hypotheses.
Calculate the test statistic and report the p-value.
State your conclusion in context of the problem.
Based only on the results of the hypothesis test, would you expect a 95% confidence interval to include 0? Explain.
Calculate and interpret a 95% confidence interval for the difference between males and females.
Answer:
[tex]a) \ H_o:\hat p_f=\hat p_m\\\ \ \ H_a:\hat p_f\neq \hat p_m\\\\b) z\ test=2.925, \ p\ value(two-tail)=0.003444\\\\\\[/tex]
c) Reject H_o since there is sufficient evidence to suggest that there is difference between males and females with respect to how they feel about this issue.
d. No. Interval does not include zero
e. [tex]CI=[0.01044<(\hat p_f-\hat p_m)<0.05576[/tex]
We are 95% confident that the proportional difference lies between the [0.010444,0.05576] interval.
Step-by-step explanation:
a. The null hypothesis is that there is no difference between males and females with respect to how they feel about this issue:
[tex]H_o:p_m=p_f[/tex]
-The alternative hypothesis is that there is some difference between males and females with respect to how they feel about this issue:
[tex]H_a:p_m\neq p_f[/tex]
where [tex]p_m, \ p_f[/tex] is the proportion of males and females respectively.
b. The proportion of males and females in the study can be calculated as follows:
[tex]\hat p=\frac{x}{n}\\\\\hat p_f=\frac{1729}{1913}=0.9038\\\\\hat p_m=\frac{1111}{1276}=0.8707[/tex]
[tex]\hat p=\frac{x_f+x_m}{n_m+n_f}=\frac{1111+1729}{1276+1913}=0.8906[/tex]
#We then calculate the test statistic using the formula:
[tex]z=\frac{(\hat p_f-\hat p_m)}{\sqrt{\hat p(1-\hat p)(\frac{1}{n_f}+\frac{1}{n_m})}}\\\\\\=\frac{(0.9038-0.8707)}{\sqrt{(0.8906\times0.1094)(\frac{1}{1913}+\frac{1}{1276})}}\\\\\\=2.9250\\\\\therefore p-value=0.001722\\[/tex]
[tex]\# The \ two \ tail \ p-value \ is\\\\=0.01722\times 2\\\\=0.003444[/tex]
c. Since p<0.05:
[tex]p<0.05\\\\0.00344<0.05\\\\\therefore Reject \ H_o[/tex]
Hence, we Reject the Null Hypothesis since there is sufficient evidence to suggest that there is difference between males and females with respect to how they feel about this issue
d. The 95% confidence interval can be calculated as below:
[tex]CI=(p_f-p_m)\pm z_{\alpha/2}\sqrt{\frac{\hat p_m(1-\hat p_m)}{n_m}+\frac{\hat p_f(1-\hat p_f)}{n_f}}\\\\=(0.9038-0.8707)\pm 1.96\sqrt{0.00008823+0.000045449}\\\\=0.03310\pm 0.02266\\\\=[0.01044,0.05576][/tex]
Hence, the confidence interval does not include 0
e. The 95% confidence interval calculated from above is :
[tex]0.01044<(p_f-p_m)<0.05576[/tex]
Hence, we are 95% confident that the proportional difference will fall between the interval [tex]0.01044<(\hat p_f-\hat p_m)<0.05576[/tex]
A Rhombus with diagonal 1 equal to 5 ft and diagonal 2 equal to 8 ft
Answer:
Area = 20 ft²
Step-by-step explanation:
Area of a thrombus
½ × d1 × d2
½ × 5 × 8
20
Answer:
20 ft squared
Step-by-step explanation:
The area of a rhombus can be calculated by multiplying its diagonals by each other and then halving that product: A = [tex]\frac{1}{2} d_1d_2[/tex]
Here, we know that [tex]d_1[/tex] = 5 and [tex]d_2[/tex] = 8. So, we have the equation: A = [tex]\frac{1}{2} *5*8=(1/2)*40=20[/tex]
Thus, the area is 20 ft squared.
Hope this helps!
If ST≅SV and m∠SUT=68°, what is m∠TUV?
Answer:
136
Step-by-step explanation:
Take 68 x 2 since the side lengths are equal.
Given the properties of isosceles triangle, where congruent sides have equal opposite angles, and that the given angle ∠SUT = 68°, it implies that ∠TUV also equals 68°.
Explanation:The question involves the principles of geometry, specifically the properties of angles and congruent lines. Given that ST≅SV and m∠SUT = 68°, it means that these two line segments are equal in length and that the angle of SUT is 68 degrees.
Since ST and SV are congruent in an isosceles triangle, the angles opposite these sides are equal. Hence, the measure of ∠SUT and ∠TUV are equal. We know m∠SUT = 68°, so therefore, m∠TUV = 68°.
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Which diagram represents a cylinder with a base area equal to 50Pi square meters?
1. A cylinder with height of 50 meters and volume = 250 pi meters cubed.
2. A cylinder with height 25 meters and volume = 250 pi meters cubed.
3. A cylinder with height 5 meters and volume = 250 pi meters cubed.
Answer: C
Step-by-step explanation:
Answer:The answer Is The Third One On The Right.
Step-by-step explanation:
Multiply: (-3/10)(-2/9)
Answer:
1/15
Step-by-step explanation:
Find f such that f'(x) = 5x² + 9x - 7 and f(0) = 8.
Answer:
[tex]\frac{5}{3}x^3+\frac{9}{2}x^2-7x+8\\[/tex]
Step-by-step explanation:
Integrate your function with respect to x to get the non-differentiated form.
[tex]\int(5x^2+9x-7)dx=\frac{5}{3}x^3+\frac{9}{2}x^2-7x+c\\[/tex]
Plug in your known value of x to get your value for your constant
[tex]f(0) = 8\\ \frac{5}{3}(0^3)+\frac{9}{2}(0^2)-7(0)+c = 8 \\c=8[/tex]
This gives you your function to be
[tex]\frac{5}{3}x^3+\frac{9}{2}x^2-7x+8\\[/tex]
To find f such that f'(x) = 5x² + 9x - 7 and f(0) = 8, integrate the given function and solve for the constant of integration using the given condition. The resulting equation is f(x) = (5/3)x³ + (9/2)x² - 7x + 8.
Explanation:To find f such that f'(x) = 5x² + 9x - 7 and f(0) = 8, we need to integrate f'(x) to find the equation for f(x). Let's find the antiderivative of 5x² + 9x - 7, which is (5/3)x³ + (9/2)x² - 7x + C. To determine the value of C, we can use the given condition f(0) = 8. Substituting x = 0 into the equation, we get 8 = (5/3)(0)³ + (9/2)(0)² - 7(0) + C. Solving for C, we find that C = 8. Therefore, the equation for f(x) is f(x) = (5/3)x³ + (9/2)x² - 7x + 8.
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A manufacturer sells video games with the following cost and revenue functions (in dollars), where x is the number of games sold. Determine the interval(s) on which the profit function is increasing. Upper C (x )equals 0.17 x squared minus 0.00016 x cubed Upper R (x )equals 0.362 x squared minus 0.0002 x cubed
Answer:
Therefore profit function is increasing on the interval (0,3200)
Step-by-step explanation:
The cost function of the manufacturer C(x) is given as:
[TeX]C(x)= 0.17x^{2}-0.00016x^{3}[/TeX]
The Revenue function is also given as:
[TeX]R(x)= 0.362x^{2}-0.0002x^{3}[/TeX]
Profit=Revenue-Cost
Therefore:
P(x)=R(x)-C(x)
[TeX]= 0.362x^{2}-0.0002x^{3}-[0.17x^{2}-0.00016x^{3}][/TeX]
[TeX]= 0.362x^{2}-0.0002x^{3}-0.17x^{2}+0.00016x^{3}[/TeX]
The Profit Function, [TeX]P(x)= 0.192x^{2}-0.00004x^{3}[/TeX]
To determine the point where the function is increasing, we take the derivative and examine it's critical points.
The derivative of the profit function is:
[TeX]P^{'}(x)= 0.384x-0.00012x^{2}[/TeX]
Set the derivative equal to zero.
[TeX]0.384x-0.00012x^{2}=0[/TeX]
[TeX]x(0.384x-0.00012x)=0[/TeX]
x=0 or [TeX]0.384-0.00012x=0[/TeX]
x=0 or [TeX]0.384=0.00012x[/TeX]
x=0 or x=3200
Now let's choose 2000 and 4000 as test points.
[TeX]P^{'}(2000)= 0.384(2000)-0.00012(2000)^{2}=288[/TeX]
[TeX]P^{'}(4000)= 0.384(4000)-0.00012(4000)^{2}=-384[/TeX]
Therefore profit function is increasing on the interval (0,3200)
Answer:
The is profit function is increasing on (0, 3200).
Step-by-step explanation:
Given
C(x) = 0.17x² - 0.00016x³
R(x) = 0.362x² - 0.0002x³
The profit function is given by
P(x) = R(x) - C(x)
P(x) = (0.362x² - 0.0002x³) - (0.17x² - 0.00016x³)
P(x) = 0.362x² - 0.0002x³ - 0.17x² + 0.00016x³
P(x) = 0.192x² - 0.00004x³
The derivative of the profit function is given by
P'(x) = 0.384x - 0.00012x²
Determine the critical number of P(x) to get interval where the profit function is increasing,
Set P'(x) = 0
0.384x - 0.00012x² = 0
x(0.384 - 0.00012x) = 0
x = 0 or 0.384 - 0.00012x = 0
0.384 - 0.00012x = 0
x = 0.384/0.00012 = 3200
Therefore the is profit function is increasing on (0, 3200)
Bill Connors, a quality control manager at a Menlo Park Electronics Company, knows his company has been making surge protectors with a 10% rate of defective units. Bill decides to test 20 randomly selected surge protectors to see how many are defective. Let X represent the mumber f defective unit nth . Asminnpndenc answer the folowing :a) What type of probability distribution does X have (include the value(s) of any parameters)? b) What is the probability that more than one surge protector is defective? c) What is the probability that the number of defective surge protectors is between three and five? d) How many surge protectors would you expect to be defective? e) Find the standard deviation X.
Answer:
a) Binomial distribution, with n=20 and p=0.10.
b) P(x>1) = 0.6082
c) P(3≤X≤5) = 0.3118
d) E(X) = 2
e) σ=1.34
Step-by-step explanation:
a) As we have a constant "defective" rate for each unit, and we take a random sample of fixed size, the appropiate distribution to model this variable X is the binomial distribution.
The parameters of the binomial distribution for X are n=20 and p=0.10.
[tex]X\sim B(0.10,20)[/tex]
b) The probability of k defective surge protectors is calculated as:
[tex]P(x=k) = \binom{n}{k} p^{k}q^{n-k}[/tex]
In this case, we want to know the probability that more than one unit is defective: P(x>1). This can be calculated as:
[tex]P(x>1)=1-(P(0)+P(1))\\\\\\P(x=0) = \binom{20}{0} p^{0}q^{20}=1*1*0.1216=0.1216\\\\P(x=1) = \binom{20}{1} p^{1}q^{19}=20*0.1*0.1351=0.2702\\\\\\ P(x>1)=1-(0.1216+0.2702)=1-0.3918=0.6082[/tex]
c) We have to calculate the probability that the number of defective surge protectors is between three and five: P(3≤X≤5).
[tex]P(3\leq X\leq 5)=P(3)+P(4)+P(5)\\\\\\P(x=3) = \binom{20}{3} p^{3}q^{17}=1140*0.001*0.1668=0.1901\\\\P(x=4) = \binom{20}{4} p^{4}q^{16}=4845*0.0001*0.1853=0.0898\\\\P(x=5) = \binom{20}{5} p^{5}q^{15}=15504*0*0.2059=0.0319\\\\\\P(3\leq X\leq 5)=P(3)+P(4)+P(5)=0.1901+0.0898+0.0319=0.3118[/tex]
d) The expected number of defective surge protectors can be calculated from the mean of the binomial distribution:
[tex]E(X)=\mu_B=np=20*0.10=2[/tex]
e) The standard deviation of this binomial distribution is:
[tex]\sigma=\sqrt{np(1-p)}=\sqrt{20*0.1*0.9}=\sqrt{1.8}=1.34[/tex]
covert 4.5 yards to inches what is the answer ?
Answer:
162 inches
Step-by-step explanation:
To get the answer you would have to know how many inches are a yard. The answer is 36. So you would have to multiply 4.5 by 36.
Answer:
Conversions :
1 ft = 12 in.
3 ft = 1 yard
Step-by-step explanation:
[tex]4.5 yards (\frac{3 ft}{1 yard} ) ( \frac{12 in.}{1 ft} ) = 162[/tex]
Parallelogram ABCD is dilated to form parallelogram EFGH. Side AB is proportional to side EF. What corresponding side is proportional to segment AD? Type the answer in the box below. (2 points)
6x + 3y - 9 when x = 6, y = 9
Answer:
54
Step-by-step explanation:
6(6)+3(9)-9
=54
Answer:
54
Step-by-step explanation:
First, since it's given the x and y values, you need to plug them in.
6(6) + 3(9) - 9
36 + 27 - 9
63 - 9
54
Enter the equation that describes the line in slope-intercept form.
slope =-4, (5,6) is on the line.
Answer:
y = -4x + 26
Step-by-step explanation:
y = mx + b m: slope -4 b: y intercept
pass (5 , 6)
b = y - mx = 6 - (-4) x5 = 6 + 20 = 26
equation: y = -4x + 26
In order to estimate the mean 30-year fixed mortgage rate for a home loan in the United States, a random sample of 26 recent loans is taken. The average calculated from this sample is 7.20%. It can be assumed that 30-year fixed mortgage rates are normally distributed with a standard deviation of 0.7%. Compute 95% and 99% confidence intervals for the population mean 30-year fixed mortgage rate.
Answer:
The 95% CI is (6.93% , 7.47%)
The 99% CI is (6.85% , 7.55%)
Step-by-step explanation:
We have to estimate two confidence intervals (95% and 99%) for the population mean 30-year fixed mortgage rate.
We know that the population standard deviation is 0.7%.
The sample mean is 7.2%. The sample size is n=26.
The z-score for a 95% CI is z=1.96 and for a 99% CI is z=2.58.
The margin of error for a 95% CI is
[tex]E=z\cdot \sigma/\sqrt{n}=1.96*0.7/\sqrt{26}=1.372/5.099=0.27[/tex]
Then, the upper and lower bounds are:
[tex]LL=\bar x-z\cdot\sigma/\sqrt{n}=7.2-0.27=6.93\\\\ UL=\bar x+z\cdot\sigma/\sqrt{n} =7.2+0.27=7.47[/tex]
Then, the 95% CI is
[tex]6.93\leq x\leq 7.47[/tex]
The margin of error for a 99% CI is
[tex]E=z\cdot \sigma/\sqrt{n}=2.58*0.7/\sqrt{26}=1.806/5.099=0.35[/tex]
Then, the upper and lower bounds are:
[tex]LL=\bar x-z\cdot\sigma/\sqrt{n}=7.2-0.35=6.85\\\\ UL=\bar x+z\cdot\sigma/\sqrt{n} =7.2+0.35=7.55[/tex]
Then, the 99% CI is
[tex]6.85\leq x\leq 7.55[/tex]
Sunhee had four plastic shapes a square, a circle, and a pentagon in how many ways can she line up the four shapes of the circle cannot be next to the square
There are 12 valid arrangements for Sunhee to line up the four plastic shapes so that the circle is not next to the square.
In how many ways can Sunhee line up four plastic shapes (a square, a circle, and a pentagon) if the circle cannot be next to the square?
To solve this problem, we can count the total number of ways to arrange the shapes and then subtract the cases where the circle is next to the square.
1. Total ways to arrange the shapes:
There are 4 shapes, so there are 4! = 24 ways to arrange them.2. Cases where the circle is next to the square:Consider the circle and square together as one unit. We now have 3 units (circle and square, pentagon, and an empty spot).The circle and square can be arranged within this unit in 2! = 2 ways.The total number of ways the four shapes can be arranged with the circle next to the square is 2! × 3! = 12 ways.3. Subtract the cases where the circle is next to the square from the total:24 total ways - 12 ways = 12 ways to line up the shapes with the circle not next to the square.A project is graded on a scale of 1 to 5. If the random variable, X, is the project grade, what is the mean of the probability
distribution below?
Answer:
the mean is 3
answer choice D
Step-by-step explanation:
60/20
Hence, the correct answer is 1/5
What is a random variable?A random variable is a numerical valued variable on a defined sample space of an experiment with expressions such as X
How to solve?probability distribution of random variable X is given by,
X 1 2 3 4 5
P(X) 1/5 1/5 1/5 1/5 1/5
mean of probability distribution = [tex]\frac{\sum{P(X)}}{5}[/tex]
= 1/5
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A common design for a mountain cabin is an A-frame
cabin. A-frame cabins are fairly easy to construct and
the steeply pitched roof line is perfect for helping snow
fall to the ground during heavy winters. Determine the
angle ( between the two sides of the roof of an A-frame
cabin if the sides are both 26 feet long and the base of
the cabin is 24 feet wide.
Answer:
54.98 degrees.
Step-by-step explanation:
In the diagram, the sides of the A-Frame are lengths AB and BC. The width of the cabin is length BC. We are to determine the measure of the angle at B, i.e. the angle between the two sides of the roof.
Using Cosine Rule:
[tex]b^2=a^2+c^2-2acCos B\\Cos B=\dfrac{b^2-a^2-c^2}{-2ac} \\B=arcCos(\dfrac{b^2-a^2-c^2}{-2ac} )\\a=26, b=24, c=26\\B=arcCos(\dfrac{24^2-26^2-26^2}{-2*26*26} )\\=arcCos 0.5739\\B=54.98^0[/tex]
The angle in between the two sides of the roof is 54.98 degrees.
To find the angle between the two sides of the roof of an A-frame cabin, we can use trigonometry and the Pythagorean theorem. The angle is approximately 22.33°.
Explanation:To determine the angle between the two sides of the roof of an A-frame cabin, we can use trigonometry. Since the sides of the roof are both 26 feet long and the base of the cabin is 24 feet wide, we can consider the A-frame cabin as a right triangle. The roof line forms the hypotenuse of the triangle, and the sides of the triangle represent the rafters of the A-frame roof.
Using the Pythagorean theorem, we can find the height of the triangle (which is the distance from the base of the cabin to the point where the roof meets): h^2 = 26^2 - 12^2 = 676 - 144 = 532.
Taking the square root of both sides gives us h ≈ 23.07 feet.
Now, we can determine the angle by using trigonometric functions.
The sine function relates the opposite side (the height) to the hypotenuse (the roof line). So, sin(θ) = h / 26, where θ is the angle we want to find. Solving for θ gives us θ ≈ 22.33°.
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emily is 60 inches tall. fernando is 3/4 of emily's height and jasmine is 8/9 of fernando's height. how tall are fernanado and jasmine?
Answer:
fernando is 45 inches tall, and jasmine is 40 inches tall
Step-by-step explanatin
60 divided by 3/4 is 45, 45 divided by 8/9 is 40
Fernando is 45 inches tall, and Jasmine is 40 inches tall.
Emily is 60 inches tall. Fernando is 3/4 of Emily's height:
(60 inches x 3/4 = 45 inches).
Jasmine is 8/9 of Fernando's height:
(45 inches x 8/9 = 40 inches).
A ski resort gets an average of 2,000 customers per weekday with a standard deviation of 800 customers. Assume the underlying distribution is normal. Use an appropriate normal transformation to calculate the probability a ski resort averages more than 3,000 customers per weekday over the course of four weekdays.
Answer:
0.62% probability that a ski resort averages more than 3,000 customers per weekday over the course of four weekdays
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
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.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
[tex]\mu = 2000, \sigma = 800, n = 4, s = \frac{800}{\sqrt{4}} = 400[/tex]
Trobability a ski resort averages more than 3,000 customers per weekday over the course of four weekdays.
This is 1 subtracted by the pvalue of Z when X = 3000. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{3000 - 2000}{400}[/tex]
[tex]Z = 2.5[/tex]
[tex]Z = 2.5[/tex] has a pvalue of 0.9938
1 - 0.9938 = 0.0062
0.62% probability that a ski resort averages more than 3,000 customers per weekday over the course of four weekdays
A chemist examines 15 sedimentary samples for nitrate concentration. The mean nitrate concentration for the sample data is 0.670 cc/cubic meter with a standard deviation of 0.0616.
a. Determine the 80% confidence interval for the population mean nitrate concentration. Assume the population is approximately normal. Round your answer to three decimal places.
b. Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answer:
(a) The 80% confidence interval for the population mean nitrate concentration is (0.648, 0.692).
(b) The critical value of t that should be used in constructing the 80% confidence interval is 1.345.
Step-by-step explanation:
Let X = nitrate concentration.
The sample mean nitrate concentration is, [tex]\bar x=0.670[/tex] cc/cubic meter.
The sample standard deviation of the nitrate concentration is, [tex]s=0.0616[/tex].
It assumed that the population is approximately normal.
And since the population standard deviation is not known, we will use a t-interval.
The (1 - α)% confidence interval for population mean (μ) is:
[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}[/tex]
(a)
The critical value of t for α = 0.20 and degrees of freedom, (n - 1) = 14 is:
[tex]t_{\alpha/2, (n-1)}=t_{0.20/2, (15-1)}=t_{0.10, 14}=1.345[/tex]
*Use a t-table for the critical value.
Compute the 80% confidence interval for the population mean nitrate concentration as follows:
[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}[/tex]
[tex]=0.670\pm 1.345\times \frac{0.0616}{\sqrt{15}}[/tex]
[tex]=0.670\pm 0.022\\=(0.648, 0.692)\\[/tex]
Thus, the 80% confidence interval for the population mean nitrate concentration is (0.648, 0.692).
(b)
The critical value of t for confidence level (1 - α)% and (n - 1) degrees of freedom is:
[tex]t_{\alpha/2, (n-1)}[/tex]
The value of is:
α = 0.20
And the degrees of freedom is,
(n - 1) = 15 - 1 = 14
Compute the critical value of t for confidence level 80% and 14 degrees of freedom as follows:
[tex]t_{\alpha/2, (n-1)}=t_{0.20/2, (15-1)}[/tex]
[tex]=t_{0.10, 14}\\=1.345[/tex]
*Use a t-table for the critical value.
Thus, the critical value of t that should be used in constructing the 80% confidence interval is 1.345.
Which graph represents the solution set of the inequality Negative 14.5 less-than x?
A. A number line going from negative 15 to negative 11. An open circle is at negative 13.5. Everything to the right of the circle is shaded.
B. A number line going from negative 15 to negative 11. A closed circle is at negative 14. Everything to the right of the circle is shaded.
C. A number line going from negative 15 to negative 11. An open circle is at negative 14.5. Everything to the right of the circle is shaded.
D. A number line going from negative 15 to negative 11. A closed circle is at negative 15. Everything to the right of the circle is shaded.
The solution of the inequality -14.5 < x represents graph which is correct option C
What is inequality?
Inequality is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is not equal.
-14.5 < x
x > -14.5
A number line going from negative 15 to negative 11. An open circle is at negative 14.5. Everything to the right of the circle is shaded.
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Salim has 5 boxes of paint jars. Each box has the same number of paint jars. His teacher gives him 6 more paint jars. Now he has 41 paint jars. How many paint jars were in each box
Answer:
7 jars per box
Step-by-step explanation:
He now has 41 jars. How many did he have before his teacher gave him 6?
Well, 41-6=35. He had 35 jars before his teacher gave him more.
It says there was an equal amount of jars in each box. There are 5 boxes. Divide the total amount of jars (35) by the amount of boxes to find out how many jars are in each box.
35 jars / 5 boxes = 7 jars / box
What’s the first step to solve the equation x-6=14
To solve the equation x - 6 = 14, the first step is to isolate the variable 'x'. You do this by adding 6 to both sides of the equation, which results in x = 14 + 6. Therefore, 'x' equals 20.
Explanation:The subject of this question is Mathematics, and it is focusing on solving a basic algebraic equation: x - 6 = 14. When you are asked to solve an equation, you're figuring out what numbers you can replace the variable with to make the equation true. In this case, the variable is 'x', and your goal is to find what number 'x' stands for. The first step to solve the equation is to isolate 'x'. This means you want 'x' to stand alone on one side of the equation. To accomplish this, you need to perform the same operation on both sides of the equation to maintain equality. Here, you would add 6 to both sides of the equation (opposite of subtracting 6), which simplifies to: x = 14 + 6. So, 'x' equals 20.
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Create a cylinder with a height of 14 cm and a radius of 10 cm.
Create a cylinder with a height of 14 cm and a radius of 10 cm. What can be concluded about the cylinder’s volume when the radius is halved?
The volume is One-fourth of the original.
The volume is One-third of the original.
The volume is One-half of the original.
The volume is twice the original.
Answer:
a on edge2021
Step-by-step explanation:
The volume is One-fourth of the original.
What is a cylinder?"It is a three dimensional structure having two parallel bases joined by a curved surface, at a fixed distance."
The formula of the volume of a cylinder:V = π × r² × h, where 'r' is the radius of the circular base and 'h' is the height of the cylinder.
In the given question,
the radius of the cylinder is 10 cm, and the height is 14 cm.
⇒ r = 10 cm, h = 14 cm
The volume of the cylinder would be,
[tex]V_1=\pi\times 10^2\times 14\\\\V_1=\frac{22}{7}\times 100 \times 14\\\\V_1=4400~~cu.~cm.[/tex]
If the radius is halved, the radius becomes 5 cm.
The new volume of a cylinder would be,
[tex]V_2=\pi \times 5^2\times 14\\\\V_2=\frac{22}{7}\times 25 \times 14\\\\V_2=1100~~cu.~cm.[/tex]
The ratio between the original and the new volume of the cylinder is:
[tex]\Rightarrow \frac{1100}{4400}=\frac{1}{4}\\\\\Rightarrow V_2=\frac{1}{4}V_2[/tex]
This means, the volume is One-fourth of the original.
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