Answer:
false
Step-by-step explanation:
I took the test
Answer:
I think the answer is false
USing the net below, Find the surface area of the triangular prism.
Answer:
Area of a triangle=1/2bh
>>1/2×3×6=9
Area of rectangle=L×B
=7*6=42
=7×4=28
Surface Area=2(9)+2(42)+2(28)
=18+84+56=158cm^2
What is the surface area of the triangular prism?
Answer:
The surface area of the prism is A prism=204m2Step-by-step explanation:
Area is the space that is contained in a two-dimensional figure.
Surface area is the total area of all of the sides and faces of a three-dimensional figure.
To find the surface area, the area of each face is calculated and then add these areas together.
To find the area of a rectangle, multiply the length by the width .
From the graph the length of the rectangle is 10 m and the width is 8 m. Therefore, the area of the bottom face is
From the graph the length of the rectangle is 10 m and the width is 5 m. Therefore, the area of one of the rectangular side faces is
To find the area of a triangle use the following formula where b is the base and h is the height.
From the graph the base of the triangle is 8 m and the height is 3 m. Therefore, the area of one of the triangular faces is
The surface area of the prism is the sum of the area of the bottom face, the area of the two rectangular side faces, and the area of the two triangular faces
brain liest me plshealth programs routinely study the number of days that patients stay in hospitals. in one study, a random sample of 12 men had a mean of 7.95 days and a standard deviation of 6.2 days, and a random sample of 19 women had a mean of 7.1 days and a standard deviation of 5.0 days. the sample data will be used to construct a 95 percent confidence interval to estimate the difference between men and women in the mean number of days for the length of stay at a hospital. have the conditions been met for inference with a confidence interval?
The conditions for inference with a confidence interval have been met, and we can proceed to construct a confidence interval to estimate the difference between men and women in the mean number of days.
What is confidence interval ?
A confidence interval is a range of values that is likely to contain the true value of a population parameter with a certain level of confidence.
To determine if the conditions for inference with a confidence interval have been met, we need to check the following assumptions:
Random Sampling: The sample of men and women should be random and representative of the population.Normality: The distribution of the difference between the means should be approximately normal.Independence: The two samples should be independent of each other.Since the sample sizes are greater than 30 for both men and women, we can assume normality based on the Central Limit Theorem.
Also, since the samples are selected independently and randomly, the assumption of independence is met.
Therefore, the conditions for inference with a confidence interval have been met, and we can proceed to construct a confidence interval to estimate the difference between men and women in the mean number of days for the length of stay at a hospital.
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read the story. steve is saving up for a new bike, so he gets a summer job at the sugar scoops ice cream shop. all of the money he earns from tips goes toward the new bike. a customer leaves a tip 50% of the time, and there are 5 customers in line. how likely is it that all of the customers will give steve a tip? which simulation could be used to fairly represent the situation?
There is a there is a 3.125% chance that all five customers will give Steve a tip.
How there is a 3.125% chance that all five customers will give Steve a tip?To calculate the probability of all five customers giving Steve a tip, we need to multiply the probability of one customer giving a tip (0.5) by itself five times since each customer's tip is an independent event. So, the probability is:
0.5 * 0.5 * 0.5 * 0.5 * 0.5 = 0.03125
So, there is a 3.125% chance that all five customers will give Steve a tip.
To simulate this situation, we could use a random number generator that generates either 0 or 1, with a 50% chance of each. We could then repeat this process five times and count the number of times we get five ones (representing all five customers giving a tip). We could then use the proportion of times we get five ones out of the total number of simulations to estimate the probability of all five customers giving a tip. We would want to repeat the simulation many times to get a more accurate estimate.
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describe 3 or 4 other potential sources of error that may affect your results and explain why that will change the calculated answer.
The possible sources of inaccuracy that could have an impact on your results are -
Interfaces that are incompatible.Not enough time to do the assignment.Conditions that are not tested.Define the term Experimental error?While conducting a scientific experiment, numerous errors—either systematic or random—could happen.
Errors may result from the calibration of the equipment, the preparation of the solution, or the mass- or volume-based measurements. The precision of the investigation and the recovery of the products can both be impacted by experimental mistakes. The stock solution could be diluted by the student using an inaccurate volume measurement, leading to a higher concentration over desired. For instance, the student might pipette their stock solution before dilution and accidentally add extra volume. On the other hand, if the learner adds less water than is required for dilution, the concentration will likewise be higher.Thus, more measuring is done when the bias is smaller and more measuring is done when the uncertainty is smaller.
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a study compares online instruction with a standard lecture for teaching statistics. the proper way to design such a study is:
The proper way to design a study comparing online instruction with a standard lecture for teaching statistics would be to use a randomized controlled trial.
Participants should be randomly assigned to either the online instruction group or the standard lecture group. Both groups should cover the same content and have equivalent opportunities for interaction and assessment. The effectiveness of the two methods should then be compared by measuring the performance of participants on a common set of assessments. It is also important to control for potential confounders such as prior knowledge, motivation, and learning style. By following these steps, the study can accurately determine the effectiveness of online instruction compared to the standard lecture method.
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Which interval notation represents the set of all numbers greater than or equal to -8
and less than or equal to -3?
Plz help ASAP
BRAINLIEST PERSON WHO GETS IT
Nyoko wrote these two questions.
Equation 1: 6x-5+2x = 4(2x-1) - 1
Equation 2: 3x +7 = bx+7
Part A
Nyoko says that Equation 1 has one solution. Do you agree with her? Explain your reasonings.
Part B
Can Nyoko find a value for b in Equation 2 so that the equation has no solutions? Explain Your REASONING!
a) The equation 1 has an infinite number of solutions, as both linear functions have the same slope and internet, hence Nyoko is incorrect.
b) Nyoko cannot find a value of b so that the equation has no solutions.
How to solve the equations?The equation 1 is given as follows:
6x - 5 + 2x = 4(2x - 1) - 1.
Combining the like terms and applying the distributive property, the simplified equations are given as follows:
8x - 5 = 8x - 4 - 1
8x - 5 = 8x - 5.
As they are linear functions with the same slope and intercept, the number of soltuions is of infinity.
The equation 2 is given as follows:
3x + 7 = bx + 7.
A system of linear equations will have zero solutions when:
The equations have the same slope.The equations have different intercepts.As they have the same intercept for this problem, it is not possible to attribute a value of b such that the equation will have no solution.
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Select five numbers that have 13, 2, and 3 as prime factors.
A390 B156 C897 D78 E312 F234 G598 H138
==========================================
Explanation:
Since 13, 2 and 3 are required to be prime factors, this means 13*2*3 = 26*3 = 78 must be a factor of whatever we're after.
This means that we can divide each answer choice over 78 to see which results in a whole number or not
A) 390/78 = 5 B) 156/78 = 2 C) 897/78 = 11.5 D) 78/78 = 1 E) 312/78 = 4 F) 234/78 = 3 G) 598/78 = 7.667 approximately H) 138/78 = 1.769 approximatelyWe can see that choices A, B, D, E and F result in whole numbers. Everything else is a decimal. So that's why 390, 156, 78, 312, and 234 are multiples of 78 and they are numbers that fit the requirements.
given the function w(t) = 15t - 1, w(-1/3)=?
Answer:
-6
Step-by-step explanation:
Plug in -1/3for t
W(-1/3)=15(-1/3)-1=-5-1=-6
Answer:
-6
Step-by-step explanation:
substitute -1/3 into w(t) = 15t - 1
=> w(-1/3) = 15(-1/3) - 1
=> w(-1/3) = -6
5-The endpoints of a diameter of a circle are (-7,2) and(-13,10) .(a) Write an equation of the circle in standard form.(b) Graph the circle.
For this problem, we are given the coordinates of the endpoint on the diameter of a circle. We need to write the equation in standard form and graph the circle.
To write the equation we need to know the coordinates of the center and the size of the radius. We will first find the center, which is the midpoint of the diameter:
\(\begin{gathered} x_c=\frac{-7-13}{2}=\frac{-20}{2}=-10\\ \\ y_c=\frac{2+10}{2}=\frac{12}{2}=6 \end{gathered}\)The center is located at (-10, 6). The radius is the distance between the center and one of the given points.
\(r=\sqrt{(-10+7)^2+(6-2)^2}=\sqrt{(-3)^2+4^2}=\sqrt{9+16}=\sqrt{25}=5\)The equation of the circle is:
\((x+10)^2+(y-6)^2=(5)^2\)Now we need to graph the circle, we need to find the center (-10,6) and trace the circle in a way that passes through (-7,2) and (-13, 10).
A can do a piece of work in 3 days and B in 6 days andShyam in 12 days.In how many days will they finish it when both work at it.
Answer:
Step-by-step explanation:
= 1/3 + 1/6 + 1/12 (LCM 12)
= 4/12 + 2/6 + 1/12
= 6/12
= 1/2
Therefore 1/2 = 2 days
They will all work together and finish the job in 2 days
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help pls, i’m seriously so confused ! :(
Answer:
Step-by-step explanation:
F multiplied by -2.
-2f
pls help asap if you can!!!
The statement that best proves that <XWY ≅ <ZYW is that two parallel lines are cut by a transversal, then the alternate interior angles are congruent
How to determine the statementTo determine the correct statement, we need to know the properties of a parallelogram.
These properties includes;
Opposite sides are parallel. Opposite sides are congruent. Opposite angles are congruent. Same-Side interior angles (consecutive angles) are supplementary. Each diagonal of a parallelogram separates it into two congruent triangles.The diagonals of a parallelogram bisect each other.Learn more about parallelogram at: https://brainly.com/question/10744696
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if you discovered a leaking faucet in your home , do you think it would be important to get it fixed why or why not ??
Answer:
b
Step-by-step explanation:
It is important to get a leaking faucet fixed as soon as possible to save water, money, and prevent potential problems in the future.
It is important to get a leaking faucet fixed because of the following reasons;
1. Water waste: A leaking faucet wastes a significant amount of water over time, which can contribute to higher utility bills and water shortages in drought-prone areas.
2. Cost-saving: Fixing a leaking faucet can save you money in the long run by reducing your water bill.
3. Preventing bigger issues: Ignoring a leaking faucet can lead to more serious plumbing problems down the line, which can be more expensive to fix.
4. Environmental impact: Wasting water unnecessarily has a negative impact on the environment and can contribute to water scarcity.
Overall, it is important to address a leaking faucet promptly to save water, money, and prevent potential problems in the future.
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20 POINTS GUYS
EASY WORD PROBLEM ⦁ The cylindrical Giant Ocean Tank at the New England Aquarium in Boston is 24 feet deep and has a radius of 18.8 feet. Find the volume of the tank.
⦁ Use 3.14 for pi and round your answer to the nearest tenth if necessary.
Answer:
26635.2
Step-by-step explanation:
pi18.8^2=~1109.8
1109.8*24=26635.2
An aircraft hangar is semi-cylindrical with
diameter 40 m and length 50 m. A helicopter
places a cable across the top of the hangar, and
one end is pinned to the corner at A. The cable
is then pulled tight and pinned at the opposite
corner B. Determine the length of the cable.
On solving the provided question, we can say that - the volume of the cylinder will be V = 3.14 * 20*20*50 = 62800
what is radius?The length of a circle or sphere, in more contemporary use, is the same as its radius in classical geometry, which is one of the line segments from its center to its circumference. The Latin word radius, which also refers to the spokes of a wagon wheel, gave rise to the term. The distance a circle's center is from any point on its perimeter is its radius. Usually, "R" or "r" is used to indicate it. A radius is a line segment that has one endpoint in the center and one on the circumference of a circle. Circular diameter equals radius The diameter of a circle is the segment that traverses its center and has ends that are on the circle. Diameter
volume of the cylinder -
V = \(\pi r^2h\)
r = 40/2 = 20
h = 50
V = 3.14 * 20*20*50 = 62800
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please help with this as well please
Answer:
the answer is 28 feet
Step-by-step explanation:
hdhbsn
Calculate the following double integral. I= (Your answer should be entered as an integer or a fraction. ) I= = √² (4+12ry) da dy
The value of the double integral is I = 0.
To calculate the double integral ∬ √(4+12ry) dA dy, we need to determine the limits of integration for each variable and then evaluate the integral.
Assuming the region of integration is not specified, we'll integrate over the entire xy-plane.
The integral can be rewritten as follows:
I = ∫∫ √(4 + 12ry) dA dy
Since there are no specific limits given, we'll integrate from negative infinity to positive infinity for both variables.
I = ∫(-∞ to ∞) ∫(-∞ to ∞) √(4 + 12ry) dx dy
To solve this integral, we'll integrate with respect to x first and then with respect to y.
∫(-∞ to ∞) ∫(-∞ to ∞) √(4 + 12ry) dx dy = ∫(-∞ to ∞) √(4 + 12ry) [x] dx dy
Evaluating the integral with respect to x:
∫(-∞ to ∞) √(4 + 12ry) [x] dx dy = ∫(-∞ to ∞) [x√(4 + 12ry)]|(-∞ to ∞) dy
Since the limits of integration for x are from negative infinity to positive infinity, the term [x√(4 + 12ry)] evaluates to 0. Therefore, the integral becomes:
I = ∫(-∞ to ∞) 0 dy
Integrating a constant value of 0 over the entire y-axis yields a result of 0.
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Suppose that a marginal revenue function is given by R (x)=500−12x. It is known that R(11)=474. What is the correct interpretation of this result? Select the correct answer below: a) At a production rate of 11 units, the revenue is decreasing at a rate of 474 . b) At a production rate of 11 units, the revenue is increasing at a rate of 474 . c) The total revenue generated at a production rate of 11 units is 474 . d) None of the above.
The correct interpretation is that the total revenue generated at a production rate of 11 units is $368. The Correct option is:
d) None of the above.
How We Calculated The Total Revenue Generated?The marginal revenue function R(x) represents the additional revenue generated by producing and selling one additional unit of a product. In this case, the marginal revenue function is given by R(x) = 500 - 12x.
The notation R(11) refers to evaluating the marginal revenue function at a production rate of 11 units, which means substituting x = 11 into the function. So, we have R(11) = 500 - 12(11) = 500 - 132 = 368.
The interpretation is that at a production rate of 11 units, the total revenue generated is $368.
This means that by producing and selling 11 units of the product, the company earns $368 in revenue.
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learning platforms that use algorithms to adjust the content that each student sees in order to maximize learning efficiency is called ___ learning.
Learning platforms that use algorithms to adjust the content that each student sees in order to maximize learning efficiency is called Adaptive learning
What is adaptive learning?Adaptive learning platforms utilize algorithms to tailor the learning experience for individual students based on their needs, abilities, and learning progress.
By analyzing data and feedback, adaptive learning systems can dynamically adjust the content, pace, and difficulty level to optimize learning efficiency and personalize the educational journey for each student.
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If Gabe's Soccer Ball Company is able, due to competitive pressure, to charge $60 for a new soccer ball, while one soccer ball costs $28 to make, plus $15,000 per month in overhead costs (mostly Gabe's extravagant salary) find: a. The average cost c(x) of producing each soccer ball b. Algebraically find the number of soccer balls Gabe's company must produce per month in order to break even (Profit = 0). Profit = Total Revenue – Total Cost c. Algebraically find the number of soccer balls Gabe's company must make to earn a profit of $10,000 per month. d. If Gabe took a pay cut to reduce the overhead costs to $8,000 per month, how many fewer balls would the company have to sell to break even. (There are multiple ways to get this result).
Answer:
Results are below.
Step-by-step explanation:
Giving the following information:
Selling price= $60
Unitary variable cost= $28
Fixed costs= $15,000
First, we need to calculate the average total cost:
Average cost= total cost / number of units
For example, for 1 unit and 10,000 units:
1 unit:
Average cost= 15,028/1 = 15,028
10,000 units:
Average cost= (15,000 + 28*10,000) / 10,000
Average cost= $29.5
Now, we can calculate the break-even point in units:
0= (60*x) - (28*x) - 15,000
x= number of units to break-even
0= 32x - 15,000
15,000/32= x
468.75=x
break-even point in units= 469
For the desired profit of $10,000:
10,000 = (60*x) - (28*x) - 15,000
25,000= 32x
781.25= x
Break-even point= 782 units
Finally, fixed costs dropped by $8,000:
0= 32x - 7,000
x= 7,000/32
x= 218.75
Break-even point= 219
Difference= 250 units
waterloo park posted the following schedule listing the number of hours an employee works on a given day. let b(x), t(x), r(x), and s(x) represent the number of hours worked by bill, ted, rufus, and socrates, respectively, on a given day x.
The schedule for the number of hours worked by employees at Waterloo Park is represented by the functions b(x), t(x), r(x), and s(x) for Bill, Ted, Rufus, and Socrates, respectively, on a given day x.
In the schedule, the function b(x) represents the number of hours worked by Bill on a given day x. Similarly, the function t(x) represents the number of hours worked by Ted, the function r(x) represents the number of hours worked by Rufus, and the function s(x) represents the number of hours worked by Socrates on the same given day x.
By using these functions, you can determine the specific number of hours each employee worked on any given day. For example, if you have a value for x, you can substitute it into the functions to find the corresponding number of hours worked by each employee.
It's important to note that the functions b(x), t(x), r(x), and s(x) are specific to Waterloo Park and the employees mentioned. The given schedule provides a way to track the hours worked by each employee on different days. By utilizing these functions, you can analyze and calculate the hours worked by each employee effectively.
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The tree diagram shows the number of theaters and the number of different movies being shown at each theater. How many possible movie choices are there according to the diagram?
A tree diagram is shown. Two boxes are shown with one above the other. Three lines are drawn out from each of those two boxes connecting to three boxes. (1 point)
2 choices
3 choices
6 choices
8 choices
2. Which of the following scenarios could go with the tree diagram?
A tree diagram is shown. Two boxes are shown with one above the other. Five lines are drawn out from each of those two boxes connecting to five boxes. (1 point)
three kinds of soup in four different sizes
two pairs of shoes and five colors of socks
two different CDs with six songs on each
two types of cake in two different shapes with two different types of frosting
3. Which organized list represents the outcomes for choosing gloves (G) or mittens (M) in red (R), tan (T), or black (B)? (1 point)
GR, GT, GB, MR, MT, MB
GR, GT, GB
MR, MT, MB
GR, GT, MR, MT
4. Which organized list shows the possible outcomes for flipping a coin twice? (Note: heads – H; tails – T) (1 point)
HT
HH, HT, TH, TT
HT, TH
HH, TT
5. You are creating a tree diagram that shows the possible outcomes for spinning the spinner and rolling a six-sided number cube.
A square is shown divided into four smaller equal squares. One of the smaller squares is red. One of the smaller squared is yellow. One of the smaller squares is blue, and one of the smaller squares is green. An arrow originating from the center of the large square is pointing to the red square.
Which statement is true? (1 point)
The number of outcomes for the spinner is greater than the number of outcomes for the number cube.
The number of outcomes for the spinner and the number cube are equal.
The number of outcomes for the spinner is less than the number of outcomes for the number cube.
6. How many possible outcomes are there? (1 point)
10 outcomes
16 outcomes
24 outcomes
36 outcomes
7. Find the total number of possible outcomes for four different cell phone models, each of which has three different plans. (1 point)
7 outcomes
12 outcomes
16 outcomes
24 outcomes
8. Find the total number of possible outcomes for 10 styles of running shoes, each in a men’s and women’s version. (1 point)
8 outcomes
12 outcomes
20 outcomes
100 outcomes
9. Which expression can be used to find the total number of possible outcomes for three different pairs of shorts, five different shirts, and two different pairs of shoes? (1 point)
3 times 5
3 times 7
3 + 5 + 2
3 times 5 times 2
10. A pizza shop offers 12 different pizza toppings. If the total number of possible outcomes is 36, how many different sizes of single topping pizzas do they offer? (1 point)
2 sizes
3 sizes
6 sizes
24 sizes
The answers to all parts sre whicn below.
1. Since there are two theaters each showing three different movies, the total number of possible movie choices is the product of the number of choices at each theater, which is 3 in this case. Therefore, the total number of possible movie choices is 3 x 3 = 9.
Answer: 9 choices
2. The tree diagram is most likely to go with the scenario of "two types of cake in two different shapes with two different types of frosting". The two boxes in the tree diagram represent the two types of cake, the five lines coming out of each box represent the two different shapes of cake and the two types of frosting, and the five boxes at the end of each line represent the different combinations of cake shapes and frosting types.
3. The correct organized list that represents the outcomes for choosing gloves (G) or mittens (M) in red (R), tan (T), or black (B) is:
GR, GT, GB, MR, MT, MB
4. HH, HT, TH, TT
5. There are 4 different cell phone models, each of which has 3 different plans. To find the total number of possible outcomes, we need to multiply the number of options for each choice. Using the multiplication principle, the total number of possible outcomes is:
4 (cell phone models) × 3 (plans for each model) = 12 outcomes
Therefore, the total number of possible outcomes is 12.
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Solve the following linear quadratic system of equations algebraically.
y=^2+3x-2
y+3=5x
Answer:
\(x=1\)
\(y=2\)
Step-by-step explanation:
\(y=x^2+3x-2\) , \(y+3=5x\)
Replace all occurrences of \(y\) in \(y+3=5x\) with \(x^2+3x-2.\)
\((x^2+3x-2)+3=5x\)
\(y=x^2+3x-2\)
Add \(-2\) and 3.
\(x^2+3x+1=5x\)
\(y=x^2+3x-2\)
Subtract 5x from both sides of the equation.
\(x^2+3x+1-5x=0\)
\(y=x^2+3x-2\)
Subtract 5x from 3x.
\(x^2-2x+1=0\)
\(y=x^2+3x-2\)
Rewrite 1 as \(1^2\).
\(x^2-2x+1^2=0\)
\(y=x^2+3x-2\)
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
\(2x=2\) · \(x\) · \(1\)
\(y=x^2+3x-2\)
Rewrite the polynomial.
\(x^2-2\) · \(x\) · \(1\) \(+\) \(1^2=0\)
\(y=x^2+3x-2\)
Factor using the perfect square
trinomial rule \(a^2-2ab+b^2=(a-b)^2,\)
where a = x and b = 1.
\((x-1)^2=0\)
\(y=x^2+3x-2\)
Set the \(x-1\) equal to 0.
\(x-1=0\)
\(y=x^2+3x-2\)
Add 1 to both sides of the equation.
\(x=1\)
\(y=x^2+3x-2\)
Replace all occurrences of \(x\) in
\(y=x^2+3x-2\) with 1.
\(y=(1)^2+3(1)-2\)
\(x=1\)
\(y=2\)
Which measurements could not represent the side lengths of a right triangle?
F 25 feet, 60 feet , 65 feet
G 9 feet, 12 feet, 15 feet
H 20 feet, 25 feet, 30 feet
12 feet, 35 feet, 37 feet
If someone catches me up on edge for math I will pay 100 dollars anyway you want it. Please someone help me! If interested email me at kanemagdalene at g mail.com
Solve for n.
-9 + 8n - 7n = 1 + 3n
Answer:
n = -5
Step-by-step explanation:
-9 + 8n - 7n = 1 + 3n
- 9 + n = 1 + 3n
Subtracting both sides by n (to move it from LHS to RHS):
-9 + n - n = 1 + 3n - n
-9 = 1 + 2n
Subtracting both sides by 1 (to move it from RHS to LHS):
-9 - 1 = 1 - 1 + 2n
-10 = 2n
2n = -10
Dividing both sides by 2 to make the co-efficient of n, 1:
2n/2 = -10/2
n = -5
Hope this helps and be sure to have a wonderful time ahead at Brainly! :D
Answer:
n = -5
Step-by-step explanation:
-9 + 8n - 7n = 1 + 3n
Combine like terms.
-9 + n = 1 + 3n
Subtract 3n from both sides.
-9 - 2n = 1
Add 9 to both sides.
-2n = 10
Divide both sides by -2.
n = -5.
Proof:
-9 + 8n - 7n = 1 + 3n
Substitute variable.
-9 + 8(-5) - 7(-5) = 1 + 3(-5)
Multiply 8 and -5.
-9 - 40 - 7(-5) = 1 + 3(-5)
Multiply -7 and -5.
-9 - 40 + 35 = 1 + 3(-5)
Multiply 3 and -5.
-9 - 40 + 35 = 1 - 15
Subtract 40 from -9.
-49 + 35 = 1 - 15
Add -49 and 35.
-14 = 1 - 15
Subtract 15 from 1.
-14 = -14
investment risk investors not only desire a high return on their money, but they would also like the rate of return to be stable from year to year. an investment manager invests with the goal of reducing volatility (year-to-year fluctuations in the rate of return). the following data represent the rate of return (in percent) for his mutual fund for the past 12 years. 13.8 15.9 10.0 12.4 11.3 6.6 9.6 12.4 10.3 8.7 14.9 6.7 (a) verify that the data are normally distributed by constructing a normal probability plot. (b) determine the sample standard deviation. (c) construct a 95% confidence interval for the population standard deviation of the rate of return. (d) the investment manager wants to have a population standard deviation for the rate of return below 6%. does the confidence interval validate this desire?
The normal probability plot suggests the data is approximately normally distributed. The sample standard deviation of given data is 3.13. The 95% confidence interval for the population standard deviation is (1.85, 6.28). The investment manager's desire for a population standard deviation below 6% is validated by the confidence interval.
To construct a normal probability plot, we first need to sort the data in ascending order:
6.6, 6.7, 8.7, 9.6, 10.0, 10.3, 11.3, 12.4, 12.4, 13.8, 14.9, 15.9
Then we can plot the ordered data against the expected values of a normal distribution with the same mean and standard deviation as the sample. The plot shows that the points follow a roughly straight line, which suggests that the data is roughly normally distributed.
To determine the sample standard deviation, we can use the formula:
s = sqrt[(∑(xi - x)²) / (n - 1)]
where xi is the rate of return for each year, x is the sample mean, and n is the sample size.
Sample mean:
x = (13.8 + 15.9 + 10.0 + 12.4 + 11.3 + 6.6 + 9.6 + 12.4 + 10.3 + 8.7 + 14.9 + 6.7) / 12 = 11.433
Sample standard deviation:
s = sqrt[((13.8 - 11.433)² + (15.9 - 11.433)² + ... + (6.7 - 11.433)²) / (12 - 1)]
= 3.059
Therefore, the sample standard deviation is 3.059.
To construct a 95% confidence interval for the population standard deviation of the rate of return, we can use the formula:
CI = [(n - 1) * s² / χ²(α/2, n-1), (n - 1) * s² / χ²(1-α/2, n-1)]
where n is the sample size, s is the sample standard deviation, χ² is the chi-square distribution, and α is the level of significance (1 - confidence level).
For a 95% confidence level and 11 degrees of freedom (n - 1), α = 0.05/2 = 0.025. From the chi-square distribution table with 11 degrees of freedom, we can find the critical values as follows:
χ²(0.025, 11) = 2.201 and χ²(0.975, 11) = 23.337
Plugging in the values, we get:
CI = [(12 - 1) * 3.059² / 23.337, (12 - 1) * 3.059² / 2.201]
= [1.946, 26.557]
Therefore, we can say with 95% confidence that the population standard deviation of the rate of return is between 1.946 and 26.557.
The investment manager wants to have a population standard deviation for the rate of return below 6%. The confidence interval (1.946, 26.557) does not validate this desire, as it includes values above 6%. Therefore, based on the sample data, the investment manager cannot be confident that the population standard deviation is below 6%.
To know more about confidence interval:
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Find the value of X
help asap plz
Answer:
12!! Glad I could help!!
Answer:
D) 12
Step-by-step explanation:
I would say that this is 12 because the angle x looks the same as the other shown angle.
Hope it helps!