A normal distribution has \mu = 65 and \sigma = 10. Find the probability that the average score of a group of n = 4 people is between 70 and 75 (both limits included).
Answer:
The probability that the average score of a group of n = 4 people is between 70 and 75=0.13591
Step-by-step explanation:
We are given that
\(\mu=65\)
\(\sigma=10\)
n=4
We have to find the probability that the average score of a group of n = 4 people is between 70 and 75.
\(P(70<\bar{x}<75)=P(\frac{70-65}{\frac{10}{\sqrt{4}}}<\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}<\frac{75-65}{\frac{10}{\sqrt{4}}})\)
\(=P(\frac{5}{5}<Z<\frac{10}{5})\)
\(=P(1<Z<2)\)
\(=P(Z<2)-P(Z<1)\)
\(=0.97725-0.84134\)
\(=0.13591\)
Hence, the probability that the average score of a group of n = 4 people is between 70 and 75=0.13591
Determine whether the set of data shown below display exponential behavior. Write yes or no explain why or why not?
Answer:
I don't know what is your name is your
Find the perimeter of the shape on this centimetre grid.
11/14+(-1/4)
pls help me.
give the anwser as a reduced,proper or improper fraction.
Answer:
15/28 or 0.53 decimal form
Step-by-step explanation:
11/14 + (-1/4)
11/14 + -1/4
= 15/28 or 0.53 decimal form
Answer:
11/14 + (-1/4) = 15/28
i am not sure
On average, five percent of air conditioning units delivered by the current supplier are defective. A sample of 100 units is randomly selected. What is the probability that seven units or less are found defective in the sample of 100 units?
The probability of finding seven or fewer defective units in a sample of 100 units, given an average defect rate of 5%, is approximately 94.68%.
What is the likelihood of encountering seven or fewer defective units in a sample of 100?In probability theory, we can use the binomial distribution to calculate the probability of a certain number of successes (defective units) in a fixed number of trials (sample size), given a known probability of success (defect rate). In this case, we have a defect rate of 5% (or 0.05) and a sample size of 100.
To find the probability, we need to sum up the individual probabilities of encountering zero, one, two, three, four, five, six, and seven defective units. This can be calculated using the binomial probability formula or by using statistical software/tools.
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Christina finds this holiday apartment for sale on the internet. she is thinking about buying the holiday apartment so that she can rent it out to holiday guests.
If Christina does her due diligence and carefully weighs the costs and potential income, buying and renting out the holiday apartment could be a sound investment. However, she should carefully assess the market demand and legal requirements before making any final decisions.
Secondly, Christina needs to consider the costs involved in purchasing and maintaining the holiday apartment. She should factor in the purchase price, any renovation or repair costs, ongoing maintenance costs, and taxes and insurance. She also needs to consider any potential income from renting out the apartment and weigh that against the costs.
Thirdly, Christina should research the legal and regulatory requirements for renting out a holiday apartment in the area. She needs to ensure that she is complying with all relevant laws and regulations, such as obtaining any necessary permits or licenses and adhering to safety standards.
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If Christina is considering buying this holiday apartment for rental purposes, she should do thorough research before making a final decision. The apartment's location, amenities, and rental potential are important factors to consider.
She should also evaluate the cost of purchasing and maintaining the property versus the potential rental income it could generate. It's advisable to speak with a real estate agent or property management company to gain insights on the rental market in the area. Furthermore, Christina should ensure that the apartment meets all legal requirements for rentals in the location she plans to rent it out in. By taking these steps, Christina can make an informed decision on whether to invest in the holiday apartment and earn a steady income from renting it out to holiday guests.
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Find extreme point(s) at the interval (-[infinity],[infinity]) and decide if the extreme points are min or max.
a) f(x)=x2 +x–6
b) f(x)=x3 +x2
Use Graphical method to solve the following problems
Draw a graph
Identity the feasible area
Find all corner point feasible solutions (CPFS) and identify the optimal solution if they have any
a) Max s.t.
x1 + x2
2x1 + 5x2 <= 5
x1+ x2<=5
3x1+ x2<=15
x1, x2 >= 0
b) Min s.t.
x1 + x2
-x1+ x2<=5
x2 <= 3
3x1+ x2>=7
x1, x2 >= 0
a) To find the extreme points and determine if they are minimum or maximum, we need to take the derivative of the function and set it equal to zero.
a) f(x) = x^2 + x - 6
Taking the derivative:
f'(x) = 2x + 1
Setting it equal to zero and solving for x:
2x + 1 = 0
2x = -1
x = -1/2
To determine if it is a minimum or maximum, we can examine the concavity of the function. Since the coefficient of x^2 is positive (1), the function opens upward and the critical point at x = -1/2 is a minimum.
b) f(x) = x^3 + x^2
Taking the derivative:
f'(x) = 3x^2 + 2x
Setting it equal to zero and solving for x:
3x^2 + 2x = 0
x(3x + 2) = 0
This gives two critical points:
x = 0 and x = -2/3
To determine if they are minimum or maximum, we need to examine the concavity of the function. Since the coefficient of x^3 is positive (1), the function opens upward. The critical point at x = 0 is a minimum, while the critical point at x = -2/3 is a maximum.
b) Graphical method:
To solve the problem graphically, we will draw a graph representing the constraints and find the feasible area. Then we will identify the corner point feasible solutions (CPFS) and determine if there is an optimal solution.
a) Maximize subject to:
x1 + x2
2x1 + 5x2 <= 5
x1 + x2 <= 5
3x1 + x2 <= 15
x1, x2 >= 0
b) Minimize subject to:
x1 + x2
-x1 + x2 <= 5
x2 <= 3
3x1 + x2 >= 7
x1, x2 >= 0
Unfortunately, the given optimization problems are incomplete as there are no objective functions specified. Without an objective function, it is not possible to determine an optimal solution or solve the problem graphically.
Please provide the objective function for the optimization problems so that we can proceed with the graphical solution and find the optimal solution, if any.
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a) The extreme point for the function f(x) = x² + x - 6 is a minimum point.
b) The extreme point for the function f(x) = x³ + x² is neither a minimum nor a maximum point.
Step 1: For the function f(x) = x² + x - 6, to find the extreme points, we can take the derivative of the function and set it equal to zero. By solving for x, we can identify the x-coordinate of the extreme point. Taking the second derivative can help determine if it is a minimum or maximum point. In this case, the extreme point is a minimum because the second derivative is positive.
Step 2: For the function f(x) = x³ + x², finding the extreme points follows the same process. However, after taking the derivative and solving for x, we find that there are no critical points. Without any critical points, there are no extreme points, meaning there are no minimum or maximum points for this function.
In summary, for the function f(x) = x² + x - 6, the extreme point is a minimum, while for the function f(x) = x³ + x², there are no extreme points.
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What is the distance between (4,-1) and (0,1)
Answer:
answer is in the image below
Step-by-step explanation:
Use the distance formula to determine the distance between two points.
statistics a local winery bottles 14 different white wines. to help customers with their purchasing choice, the winery offers customers 5 white wine tasting samples free of charge. how many ways does a customer have to choose 5 different white wines to taste
The customer have to choose 2002 ways to taste 5 different white wine.
What is Combination Formula?The number of possible ways to choose items from a collection when the order of choice is irrelevant is determined using the combination formula. Combination, to put it simply, is the process of choosing items or things from a bigger group where order is irrelevant.
The combination formula is: n! / (n-r)! r! , where n is the total number of items (14 in this case) and r is the number of items being selected at once (5 in this case),
Plugging our numbers into the formula we get:
= 14! / (14-5)! 5!
= 2002
After simplifying, we get 2002.
So, there are 2002 ways of picking 5 different white wines to taste from a group of 14 local winery bottles.
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The picture shows the $4.88 Josephine spent on a package of 4 pens.
Drag the money below to the box to show how much each pen cost.
Answer:
4 dollars 8 dimes 8 pennies
Step-by-step explanation:
Answer:
Each pen costs $1.22, which means that you would have to drag a $1 bill, 2 dimes, and 2 Penny's into the box.
First Quantitative Problem - FORD. FORD MOTOR Company has produced a new all-electric vehicle with the intentions of launchinğit in early 2022. These vehicles will be sold through Ford's network of car dealers with these dealers taking a 7% markup. The following information pertains to the new vehicle: 1) Calculate PROFIT if Ford can sell 5 million vehicles 2) Calculate Contribution Margin Units 3) Calculate Break-event Units 4) How many vehicles would FORD need to sell to gain a profit goal of $10,000,000 ? 5) Ford's management will go through with this project only if the number of vehicles needed to be sold to reach the profit goal mentioned above is less than double the number of cars needed to break even. From your results, will Ford's management go through with the project?
The profit if Ford can sell 5 million vehicles is $350,000,000. The Contribution Margin per Unit is $6,300. The Break-even Units is 1,587,302 vehicles. Ford would need to sell 2,222,222 vehicles to gain a profit goal of $10,000,000. Ford's management will go through with the project since the number of vehicles needed to reach the profit goal is less than double the number of cars needed to break even.
Profit = (Number of vehicles sold) * (Markup per vehicle)
Profit = 5,000,000 * (7% of vehicle price)
Profit = 5,000,000 * (0.07)
Profit = $350,000,000
Contribution Margin per Unit = (Markup per vehicle) / (1 + Markup percentage)
Contribution Margin per Unit = (7% of vehicle price) / (1 + 7%)
Contribution Margin per Unit = (0.07) / (1.07)
Contribution Margin per Unit = $6,300
Break-even Units = Fixed Costs / Contribution Margin per Unit
Given that the Markup per vehicle is the same as the Contribution Margin per Unit, the Break-even Units can be calculated as:
Break-even Units = Fixed Costs / Markup per vehicle
Break-even Units = Fixed Costs / (Number of vehicles sold) * (Markup per vehicle)
Break-even Units = Fixed Costs / (5,000,000 * 0.07)
Break-even Units = Fixed Costs / 350,000
(No information is provided about the Fixed Costs, so the calculation cannot be performed without that information.)
Number of vehicles needed to sell = (Fixed Costs + Profit goal) / Contribution Margin per Unit
Number of vehicles needed to sell = ($10,000,000 + Fixed Costs) / $6,300
(Since the Fixed Costs are not provided, the exact number of vehicles needed to reach the profit goal cannot be calculated.)
The number of vehicles needed to reach the profit goal mentioned above is less than double the number of cars needed to break even, so Ford's management will go through with the project.
Ford's management will go through with the project since the number of vehicles needed to be sold to reach the profit goal is less than double the number of cars needed to break even. However, without the specific information about Fixed Costs and the exact number of vehicles needed to achieve the profit goal, precise calculations cannot be made.
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Janet bought 3/4 of a pound of apples, 1 1/2 pounds of bananas, and 2 1/4 pounds of grapes. She bought ____ pounds of fruit.
Answer:
We have 3/4 plus 3/2 plus 9/4 pounds of fruit, so we get
12/4 + 3/2 pounds of fruit
and 3/2 can become 6/4, so we have 18/4 pounds of fruit, or 4 2/4 pounds, which can simplify into 9/2 or 4 1/2
Brainliest please?
Answer:
4 1/2 poundsStep-by-step explanation:
3/4 + 1 1/2 + 2 1/4 =
3 + 1 1/2 =
4 1/2
Hope that helps!
The average weight of a 12 year old boy in the US is 45 kg. If there are 2.2046 pounds in a kg, what is the average weight in pounds? Round your answer to the nearest pound.
Answer:
X=99
Step-by-step explanation:
1 KG =2.2046 pound
45 KG = x
X=45* 2.2046=99.207
What is the slope of the line that passes through the points (-2, 9)
and (8, 34)? Write your answer in simplest form.
Hello.
Use the slope formula:
\(\mathrm{\displaystyle\frac{y2-y1}{x2-x1} }\)
\(\mathrm{\displaystyle\frac{34-9}{8-(-2)} }\)
\(\mathrm{\displaystyle\frac{25}{8+2} }\)
\(\mathrm{\displaystyle\frac{25}{10}}\)
Simplify:
\(\mathrm{\displaystyle\frac{5}{2}}\)
Therefore, the final answer is
\(\mathrm{\displaystyle\frac{5}2}\)
I hope it helps.
Have a nice day.
\(\boxed{imperturbability}\)
Answer:
\(\displaystyle 2\frac{1}{2} = m\)
Step-by-step explanation:
Plug these ordered pairs into the rate of change formula:
\(\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{-9 + 34}{2 + 8} \hookrightarrow \frac{25}{10} = 2\frac{1}{2} \\ \\ \boxed{2\frac{1}{2} = m}\)
I am joyous to assist you at any time.
Which table represents the statement “An airplane is flying at a speed of 525 miles per hour”?
A 2-column table with 3 rows. Column 1 is labeled hours with entries 525, 1,050, 1,575. Column 2 is labeled distance with entries 1, 2, 3.
A 2-column table with 3 rows. Column 1 is labeled hours with entries 1, 2, 3. Column 2 is labeled distance with entries 525, 1,050, 1,575.
A 2-column table with 3 rows. Column 1 is labeled hours with entries 1, 2, 3. Column 2 is labeled distance with entries 525, 1,000, 1,525.
A 2-column table with 3 rows. Column 1 is labeled hours with entries 1, 2, 3. Column 2 is labeled distance with entries 525, 526, 527.
Answer:
the answer is B
Step-by-step explanation:
got it right on edge
Answer:
Its b
Step-by-step explanation:
I got it right on my test
Please I need help on a true or false
Answer:
True.
Explanation:
When solving equations with unknowns on both sides, it is generally recommended to first deal with the variable terms before dealing with the constant terms. This involves simplifying the equation by combining like terms and isolating the variable on one side of the equation. Once the variable is isolated, you can then solve for its value.\(\)
-4x+2=-14
Show work
Check
Step-by-step explanation:
-4x+2=-14
-2 -2
-4x=-16
÷-4 ÷-4
X=4
-4(4)+2=-14
-16+2=14
-14=-14
Answer:
Step-by-step explanation: -4x + 2 = -14
Which table of ordered pairs represents a function?
Answer:
Graph on the top right.
Step-by-step explanation:
A function is a relation where one domain value is assigned to exactly one range value.
In a table, there would be no values repeating in the x-column.
The graph on the top right does not repeat any x values. Therefore, it is a function.
Why the other options are not functions:
The top left graph has 4 for all it's domain values.The bottom left graph has '-2' repeating for the domain.The graph on the bottom right repeats '0' as the domain.Hope this helps.
Can y’all please give me the answers I would truly appreciate it
Step-by-step explanation:
a.) So he has 13 coins and those coins are nickels and quarters. If we let n be nickels and q be quarters
n + q = 13 because the total number of quarters plus nickels is 13
The coins have a total value of $2.05
Nickels are 0.05 cents and quarters are 0.25 cents, which means
0.05n + 0.25q = $2.05
Making your system of equations
\(n + q = 13 \\ 0.05n + 0.25q = 2.05\)
Answer:
a.) So he has 13 coins and those coins are nickels and quarters. If we let n be nickels and q be quarters
Step-by-step explanation:
A boat is heading towards a lighthouse, whose beacon-light is 121 feet above the
water. From point A, the boat's crew measures the angle of elevation to the beacon,
13°, before they draw closer. They measure the angle of elevation a second time from
point B at some later time to be 19°. Find the distance from point A to point B.
Round your answer to the nearest foot if necessary.
Using the trignometry functions we now know that the distance from point A to point B is 1,156.1 ft.
What is the distance?Distance is the sum of an object's movements, regardless of orientation.
Distance can be defined as the amount of space an object has covered, regardless of its beginning or ending point.
A scalar number, distance.
The entire path that an object has taken can be used to determine distance.
The entire distance travelled by a car, for instance, would be 13 km if it traveled 5 km east, 8 km north, and back again.
So, the distance from point A to B would be:
Considering the flat planet -
tan5 = 131 / d₁
d₁ = 131/tan5 = 1,497.3368... ft
d₂ = 131/tan21 = 341.2666674...ft
Distance:
1497.3368 - 341.26666 = 1,156.1 ft
Therefore, using the trignometry functions we now know that the distance from point A to point B is 1,156.1 ft.
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Correct question:
A boat is heading towards a lighthouse, whose beacon light is 131 feet above the water. From point A, the boat's crew measures the angle of elevation to the beacon, 5°, before they draw closer. They measure the angle of elevation a second time from point B at some later time to be 21°. Find the distance from point A to point B. Round your answer to the nearest tenth of a foot if necessary.
graph the function f(x) = 1/2(2)^x on the coordinate plane.
Answer:
See below
Step-by-step explanation:
You can always plug in x's and solve for y.
Brian is on the swim team. Each day he swims 900 m. How many kilometers does he swim each day?
Answer:
he swims 0.9 kilometers each day.
Step-by-step explanation:
Answer:
He swims 0.9km each day.
Step-by-step explanation:
To convert m to km divide by 1000
900/1000 =0.9
Out of 25, Alan made 18 basketball shots. If he shoots 100 shots, how many should we expect him to make?
Answer: 72
Step-by-step explanation:
25:18 - 25 total : 18 made
25:18 x 4 = 100:72
100:72- 100 total : 72 made
Answer:
we should expect him to make 72 shots
Step-by-step explanation:
25x4=100
so if we multiply 18 by 4 we get 72
Luis paid a total of $72.00 for 3 pairs of shorts. If each pair of shorts costs the same amount, what is the price of one pair of shorts?
Answer:
24
Step-by-step explanation:
72/3
Can someone pls help me. will give brainliest!
Answer:
x > -4
Step-by-step explanation:
\(\frac{x}{2} - 3>-5\\x-6>-10\\x>-10+6\\x>-4\)
Use elementary row operations to transform the augmented coefficient matrix to echelon form. Then solve the system by back substitution. X₁-4x2 +5x3. = 23 2x₁ + x₂ + x3 = 10 -3x + 2x₂-3x3 = = -23 *** An echelon form for the augmented coefficient matrix is What is the solution to the linear system? Select the correct choice below and, if necessary, fill in the answer box(es) in your choice. OA. There is a unique solution, x₁ = x₂ = x3 - (Simplify your answers.) B. There are infinitely many solutions of the form x₁ = x2-x3-t where t is a real number. (Simplify your answers. Type expressions using t as the variable.) 21 OC. There are infinitely many solutions of the form x, .X₂S, X₁t where s and t are real numbers. (Simplify your answer. Type expression using s and t as the variables.) D. There is no solution.
The solution to the linear system is unique solution which is x₁ = 1/6, x₂ = 3/2, and x₃ = 17/6.
The correct answer is option A.
To solve the given system of linear equations using elementary row operations and back substitution, let's start by representing the augmented coefficient matrix:
[1 -4 5 | 23]
[2 1 1 | 10]
[-3 2 -3 | -23]
We'll apply row operations to transform this matrix into echelon form:
1. Multiply Row 2 by -2 and add it to Row 1:
[1 -4 5 | 23]
[0 9 -9 | -6]
[-3 2 -3 | -23]
2. Multiply Row 3 by 3 and add it to Row 1:
[1 -4 5 | 23]
[0 9 -9 | -6]
[0 -10 6 | -68]
3. Multiply Row 2 by 10/9:
[1 -4 5 | 23]
[0 1 -1 | -2/3]
[0 -10 6 | -68]
4. Multiply Row 2 by 4 and add it to Row 1:
[1 0 1 | 5/3]
[0 1 -1 | -2/3]
[0 -10 6 | -68]
5. Multiply Row 2 by 10 and add it to Row 3:
[1 0 1 | 5/3]
[0 1 -1 | -2/3]
[0 0 -4 | -34/3]
Now, we have the augmented coefficient matrix in echelon form. Let's solve the system using back substitution:
From Row 3, we can deduce that -4x₃ = -34/3, which simplifies to x₃ = 34/12 = 17/6.
From Row 2, we can substitute the value of x₃ and find that x₂ - x₃ = -2/3, which becomes x₂ - (17/6) = -2/3. Simplifying, we get x₂ = 17/6 - 2/3 = 9/6 = 3/2.
From Row 1, we can substitute the values of x₂ and x₃ and find that x₁ + x₂ = 5/3, which becomes x₁ + 3/2 = 5/3. Simplifying, we get x₁ = 5/3 - 3/2 = 10/6 - 9/6 = 1/6.
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Which Is The Simplified Rational Expression?
Answer:
1st choice
Step-by-step explanation:
(r² -4r + 5 - r² -2r + 8) / (r - 4)
= (-6r + 13) / (r - 4)
Please helpp, thank youuu.
Answer:
16ft
Step-by-step explanation:
use pythagreom thereom
12^2+b^2=20^2 solve
144+b^2=400
b^2= 256 square it
b= 16
Answer:
b=16
Step-by-step explanation:
Which multiplication equation can be used to solve 1/6 divided by 5
The multiplication equation which can be used to solve 1/6 divided by 5 is 1/30.
ReciprocalReciprocal, represented by 1/x, is a number which when multiplied by x gives the result 1.
How to solve 1/6 divided by 5 using multiplication?The reciprocal of 5 is 1/5.
We know that dividing a function is the same as multiplying by its reciprocal.
So, 1/6 divided by 5 is,
1/6 x 1/5 = 1/30
Hence, the multiplication equation which can be used to solve 1/6 divided by 5 is 1/30.
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How to plot 69, 88,94,73,78,90, and 68 in a box and whisker plot (ASAP) also find the 5 part summary
The five-number summary for the dataset are Minimum: 68, Q1: 69, Median: 78, Q3: 90 and Maximum: 94.
To create a box and whisker plot for the given dataset {69, 88, 94, 73, 78, 90, 68}, follow these steps:
Step 1: Arrange the data in ascending order:
68, 69, 73, 78, 88, 90, 94
Step 2: Find the five-number summary:
Minimum: The smallest value in the dataset, which is 68.
First quartile (Q1): The median of the lower half of the dataset. In this case, it's the median of {68, 69, 73}, which is 69.
Median (Q2): The middle value of the dataset. In this case, it's 78.
Third quartile (Q3): The median of the upper half of the dataset. In this case, it's the median of {88, 90, 94}, which is 90.
Maximum: The largest value in the dataset, which is 94.
Step 3: Create the box and whisker plot:
Draw a number line with a range from the minimum (68) to the maximum (94).
Mark the first quartile (Q1) at 69.
Mark the median (Q2) at 78.
Mark the third quartile (Q3) at 90.
Draw a box from Q1 to Q3.
Draw a vertical line (whisker) from the box to the minimum (68) and another vertical line from the box to the maximum (94).
The resulting box and whisker plot for the given dataset would look like this:
|
94| ▄
| ╱ ╲
90| ╱ ╲
| ╱ ╲
88| ▇ ▂
| ▇ ▂
78| ▇ ▂
| ▇ ▂
73| ╱ ╲
| ╱ ╲
69| ▃ ▃
| ╱ ╲
68| ╱ ╲
|_________________________________
68 73 78 88 94
This plot represents the distribution of the given dataset, showing the minimum, maximum, first quartile (Q1), median (Q2), and third quartile (Q3).
The five-number summary for the dataset are Minimum: 68, Q1: 69, Median: 78, Q3: 90 and Maximum: 94.
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