The percent of the time you would expect the mean of the sample size of 25 to fall between 66 and 74 is 68.27%, to be less than 70 is 50%, and to be greater than 68 is 84.13%.
a. If a population has a mean of 100 and a standard deviation of 20, then the mean of the sampling distribution of a sample size of n=252 will be 100. This is because the sample means of a sampling distribution will always be equal to the population mean.
b. The standard deviation of the sampling distribution of a sample size of n=25 is 4. This is calculated using the formula: σx = σ/√n, where σ is the population standard deviation (20) and n is the sample size (25).
c. The percentage of the time you would expect the mean of the sample size to fall between 66 and 74 is 68.27%. This is calculated using the Z-score formula, which is (x-μ)/σ, where x is the upper limit (74), μ is the population mean (70), and σ is the population standard deviation (10). The Z-score for the upper limit is (74-70)/10=0.4. We then use the standard normal table to find the area between -∞ and 0.4, which is 0.6827.
d. The percentage of the time you would expect the mean of the sample size to be less than 70 is 50%. This is because the Z-score for a mean of 70 is 0, and the area below 0 is 0.5 or 50%.
e. The percentage of the time you would expect the mean of the sample size to be greater than 68 is 84.13%. This is calculated using the Z-score formula, which is (x-μ)/σ, where x is the lower limit (68), μ is the population mean (70), and σ is the population standard deviation (10). The Z-score for the lower limit is (68-70)/10=-0.2. We then use the standard normal table to find the area between -∞ and -0.2, which is 0.8413.
The percent of the time you would expect the mean of the sample size of 25 to fall between 66 and 74 is 68.27%, to be less than 70 is 50%, and to be greater than 68 is 84.13%.
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the random variable x is the number of occurrences of an event over an interval of 10 minutes. it can be assumed the probability of an occurrence is the same in any two time periods of an equal length. it is known that the mean number of occurrences in 10 minutes is 5.3.
the random variable x is the number of occurrences of an event over an interval of 10 minutes. it can be assumed the probability of an occurrence is the same in any two time periods of an equal length. it is known that the mean number of occurrences in 10 minutes is 5.3.
A Poisson process is a statistical model used to describe the number of occurrences of an event over a fixed interval of time or space. It has the following properties:
The events are independent, meaning that the occurrence of one event does not affect the probability of another event happening.
The average rate of occurrences is constant over time and is equal to the rate parameter of the Poisson distribution.
The probability of having n events in a fixed interval of time is given by the Poisson probability formula:
P(n) = (λ^n * e^-λ) / n!
where λ is the rate parameter and n! is the factorial of n.
Given the mean number of occurrences in 10 minutes is 5.3, it can be assumed that the rate parameter is 0.53 occurrences per minute. This means that, on average, 0.53 events are expected to occur in each minute. Since the Poisson process is memoryless, this rate is constant over time and the mean number of occurrences in any 10-minute interval will be 5.3.
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Hayley is surveying a piece of land. The land is shaped like a right triangle. The smallest angle
is one-fifth the measure of the medium-size angle. Sketch a diagram to represent the piece of
land. Then, find the measure of each angle.
The angle measures are given as follows:
90º.15º.75º.The sketch is given by the image presented at the end of the answer.
How to obtain the angle measures?We have a right triangle, hence one of the angle measures is given as follows:
90º.
The sum of the measures of the internal angles of a triangle is of 180º, hence the sum of the remaining measures is given as follows:
90º, as 180 - 90 = 90.
The smallest angle is one fifth the medium size angle, hence:
x + 5x = 90
x = 15.
The measures are:
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Simplify
a+b
a-b
a=5 and b= 3
Answer:
Step-by-step explanation:
The value of the given expression will be 4.
The measures of two supplementary angles are in the ratio 5:7 what is the measure of the larger angle
find the set of solutions for the linear system use x3, x2, etc. for the free variables if necessary. indicate if a variable is free by writing the same variable in the space (so if is free, write x1).
The set of solutions for the linear system is x1 = 6, x2 = 3, and x3 = -4.
The linear system is given as follows:
x1 + x2 - x3 = 6
2x1 + x2 + 2x3 = 8
3x1 + 2x2 + 3x3 = 14
To solve this system, we will use the Gauss-Jordan elimination method. First, we will subtract twice the first equation from the second equation and three times the first equation from the third equation.
2x1 + x2 + 2x3 = 8
- 2(x1 + x2 - x3 = 6)
2x1 + x2 + 2x3 = 8
3x1 + 2x2 + 3x3 = 14
- 3(x1 + x2 - x3 = 6)
0x1 + 3x2 + 5x3 = 6
Next, we will subtract three times the second equation from the third equation.
3x1 + 2x2 + 3x3 = 14
- 3(0x1 + 3x2 + 5x3 = 6)
3x1 + 2x2 - 2x3 = 8
Finally, we will divide the first equation by 1, the second equation by 3, and the third equation by -2.
x1 + x2 - x3 = 6
/ 1
x1 + (1/3)x2 + (5/2)x3 = 3
(-1/2)x1 + x2 + x3 = -4
The set of solutions for the linear system is x1 = 6, x2 = 3, and x3 = -4.
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the gourmet grill company manufactures and sells two types of grills: propane and electric. each propane grill sells for $320 and costs $220 to manufacture. each electric grill sells for $260 and costs $180 to manufacture. each grill goes through four operations in the manufacturing process. the hours required by each type of grill in each of these manufacturing processes are summarized as follows:
The Gourmet Grill Co. produces propane and electric grills with varying cost and hours required in 4 manufacturing processes. Aim is to maximize profit by determining the production plan using LP model, feasible region and level curves.
a. The LP model for this problem can be formulated as follows:
Maximize: $320P + $260E (profit from selling propane and electric grills)
Subject to:
2P + E <= 2400 (hours of machine press time available)
4P + 5E <= 6000 (hours of fabrication time available)
2P + 3E <= 3300 (hours of assembly time available)
P + E <= 1500 (hours of testing time available)
P, E >= 0 (non-negativity constraints)
Where P is the number of propane grills and E is the number of electric grills produced.
b. The feasible region for this problem is a polygon with vertices (0, 0), (600, 0), (300, 900), (0, 1200). This region represents the combination of P and E that satisfies all the constraints.
c. To determine the optimal solution using level curves, we can start by plotting the feasible region and then finding the level curve that represents the maximum profit. The level curve would be a straight line with slope equal to $320/$260 (the ratio of price per unit for the two types of grills). The intersection of this line with the feasible region would represent the optimal solution, which would be the combination of P and E that maximizes the profit.
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find tr
a. 10
b. 25
c. 30
d.40
The solution is Option C.
The measure of TR of triangle STR is TR = 30
What are similar triangles?If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.
Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides
Given data ,
Let the first triangle be represented as ΔPQR
Let the second triangle be represented as ΔSTR
The measure of PR = 35
The measure of SR = 25
The measure of QR = 42
The measure of QT = x
The measure of TR = 42 - x
Now , PQ is similar to ST
Now , the triangles PQR and STR are similar triangles
And , corresponding sides of similar triangles are in the same ratio
Substituting the values in the equation , we get
SR / PR = TR / QR
25 / 35 = ( 42 - x ) / 42
On simplifying the equation , we get
Multiply by 42 on both sides of the equation , we get
( 42 - x ) = ( 25 x 42 ) / 35
On further simplification , we get
42 - x = 30
Adding x on both sides of the equation , we get
x + 30 = 42
Subtracting 30 on both sides of the equation , we get
x = 12
Now , the measure of TR = 42 - x
Substitute the value of x in the equation , we get
The measure of TR = 42 - 12 = 30
Hence , the measure of TR of triangle is 30
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What is the slope-intercept form of the following equation?
6y-18x=24
y = 3x+4
y = 3x + 24
6y = 18x+24
y= 3x-4
Answer:
6y=18x+24
Step-by-step explanation:
x come first cuz of pemdas
i really need help i have till 11:00
The expression that represents the combined inventory of these two stores is given as follows:
A. 7g²/2 - 4g/5 + 15/4.
How to obtain the combined inventory?The combined inventory is obtained adding the inventories for each store, combining the like terms.
The addition of the like terms for g² is given as follows:
1/2 + 3 = 0.5 + 3 = 3.5 = 7/2g².
The term with g is given as follows:
-4g/5.
The constant like terms are combined as follows:
7/2 + 1/4 = 14/4 + 1/4 = 15/4.
Hence the simplified expression is given as follows:
7g²/2 - 4g/5 + 15/4.
Meaning that the correct option is given by option A.
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Use the substitution u = 9x2 + 8 to find the following indefinite integral Check your answer by differentiation '18x sin (9x2 + 8) 18x sin (9x2 + 8) dx=
The value of the given indefinite integral is found to be: y = -cos (9x² + 8) + c.
Explain about the indefinite integral?A function that accepts the antiderivative of that other function is said to take an endless integral. Visually, it is shown as an integral indicator, a function, and finally a dx. It is simpler to represent taking the antiderivative using the indefinite integral.The given integral is;
y = ∫18x sin (9x² + 8) dx
Put u = 9x² + 8
Then, on differentiation
18x dx = du
substitute the values:
y = ∫ sin (u) du.
y = -cos u
Put u = 9x² + 8
y = -cos (9x² + 8) + c
c is the constant of integration.
Thus, the value of the given indefinite integral is found to be: y = -cos (9x² + 8) + c.
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Which table shows the amount of a substance decaying at an exponential rate?
Answer:
B
Step-by-step explanation:
Start with 200 in 5 mins = 100 then cut in half for another 5 min = 50
another 5 min cut in half again = 25
You are the manager of a rental car company. A customer, Sandy Furrow, has asked you for an estimate of charges for a nine day rental of an SUV. She expects to drive 670 miles. If the company charges $54.50 per day plus 15 1/ 2 cents per mile for this category of vehicle, what would be the total rental charge (in $) for Sandy's trip?
Answer The total rental charge for Sandy's trip will be $601.05 (six hundrend one dollars and five cents)
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Step-by-step explanation:
The level of cholesterol in the blood for all men aged 20 to 34 follows a Normal distribution with mean 188 milligrams per deciliter (mg/dl) and standard deviation 41 mg/dl. For 14 - year - old boys, blood cholesterol levels follow a Normal distribution with mean170mg/dl and standard deviation 30 mg/dl. Now suppose we select independent SRS of 25 men aged 20 to 34 and 36 boys aged 14 and calculate the sample mean heights xM - xB. Describe the shape, center, and spread of the sampling distribution xM - xB. Find the probability of getting a difference in sample means xM - xB that's less than0 mg/dl. Show your work. Should we be surprised if the sample mean cholesterol for the 14 - year - olds exceeds the sample mean for the men?
The sampling distribution of xM - xB is normally distributed with a mean of 18 mg/dl and a standard deviation of 35.4 mg/dl.
The sampling distribution of xM - xB is a normal distribution. This can be calculated by subtracting the mean of the men (188mg/dl) from the mean of the boys (170mg/dl), which gives a mean of 18 mg/dl. To calculate the standard deviation, we first calculate the standard deviation of the men (41 mg/dl) and the boys (30mg/dl). Then we use the formula: standard deviation of xM - xB = sqrt(standard deviation of men^2 + standard deviation of boys^2). This gives us a standard deviation of 35.4mg/dl. To calculate the probability of getting a difference in sample means xM - xB that's less than 0 mg/dl, we use the z-score formula: z = (x-mean)/standard deviation. Plugging in x = 0, mean = 18 and standard deviation = 35.4 gives us a z-score of -0.5197. Using a z-table, this gives us a probability of 0.3085. It should not be a surprise if the sample mean cholesterol for the 14 - year - olds exceeds the sample mean for the men as the mean cholesterol level for the boys is lower than the men.
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A total of 444 tickets were sold for a school play. They were either adult tickets or student tickets. There were 56 fewer student tickets sold than adult tickets. How many adult tickets were sold?
Answer:
250 adult tickets were sold
Step-by-step explanation:
Let A represent the number of adult tickets sold and S the number of student tickets sold
Total tickets sold = A + S = 444
56 fewer student tickets than adult tickets means
S = A - 56
Substituting for s in the first equation,
A + S = 444
A + (A - 56) = 444
2A - 56 = 444
Add 56 to both sides:
2A - 56 + 56 = 444 + 56
2A = 500
A = 250
So 250 adult tickets were sold
Calculate the angle of elevation from the
base of this leaning tower, B, to the point P.
Give your answer to 1 d.p.
Answer:
[tex]43.78^\circ[/tex]
Step-by-step explanation:
Let θ be the angle that the base of the leaning tower makes with the tower i.e. the angle of elevation
Since this is a right triangle we have the relationship
[tex]\tan\theta = \dfrac{height}{base} = \dfrac{46}{48} \approx 0.95833\\\\[/tex]
[tex]\theta = tan^{-1} (0.95833) = 43.78^\circ[/tex]
Answer
[tex]= 43.78^\circ[/tex]
The angle of elevation is given by the trigonometric relation and θ = 73.40°
What are trigonometric relations?
Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the angle of elevation be represented as E = θ
Now , the measure of the altitude = 46 m
The measure of the hypotenuse = 48 m
And , the angle of elevation is given by the trigonometric relation ,
sin θ = opposite / hypotenuse
On simplifying , we get
sin θ = 46 / 48
sin θ = 0.958333
Taking inverse on both sides , we get
θ = sin ⁻¹ ( 0.958333 )
θ = 73.40°
Hence , the angle of elevation is 73.40°
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A car is traveling at a speed of 60 miles per hour. What's the dependent variable in this situation?
Question 1 options:
A)
The number of hours the car has traveled
B)
The age of the car
C)
The distance the car has traveled
D)
The speed at which the car travels
Answer:
C
Step-by-step explanation:
distance depends on the speed & the time traveled.
answer the question for me
Answer: 1, 2, and 4.
Step-by-step explanation: Each must be wider than the angle than a "L" has.
Please help measure the angles
(picture included)
please show work
The value of the variable x is 53.
The measures of the angles include the following:
m∠P = 96°.
m∠Q = 95°.
m∠R = 53°.
What is a triangle?In Mathematics, a triangle can be defined as a two-dimensional (2D) geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.
Furthermore, the sum of the angles in a triangle is equal to 180. This ultimately implies that, we would sum up all of the angles as follows;
m∠P + m∠Q + m∠R = 180
Substituting the given parameters into the mathematical expression, we have the following;
(2x - 10)° + (x + 42)° + x° = 180°
4x - 32° = 180°
4x = 180° + 32°
x = 53.
For the measure of the angles, we have:
m∠P = (2(53) - 10)° = 96°.
m∠Q = (53 + 42)° = 95°.
m∠R = 53°.
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Marco is driving to the grand canyon. His distance from the Grand Canyon decreases 150 mi every 3h. After 4h, his distance from the Grand Canyon is 200 mi. Marco's distance from the Grand Canyon in miles y, is a function of the number of hours he drives, x. What is the initial value
The initial value for Marcos to the grand canyon is 400 miles.
What is a linear equation?Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.
Both linear equations with one variable and those with two variables exist.
Given Marco is driving to the grand canyon. His distance from the Grand Canyon decreases by 150 mi every 3h.
We know that every 3 hours that distance decreases by 150 miles, then the distance decreased by the hour is:
150mi/3h = 50mi/h
since the distance is reducing we can take the rate of change negative,
so rate of change = -50 mi/h
and y = distance from the Grand Canyon
x = the number of hours he drives,
so the equation of slope is y = mx + c
where m = rate of change and c is the initial value at x = 0
m = -50 mi/h
y = -50x + c
And we know that after 4 hours the distance is 200 miles, then we can replace that to get:
200mi = (-50 mi/z)*4h + c
200mi = -200mi + c
200mi + 200mi = c =400mi
equation is y = -50x + 400
Hence the initial value is 400 miles.
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Jen is packing a box for her brother at college. The package must weigh less than 12 pounds. The table shows the weight of items she has already placed in the box.
The only items she can add to the box to make it less than 12 pounds are; either the package of socks or the book
How to solve Inequality word problems?The list of items and their weight that she has already packed are;
Boots = 5.2 pounds
Jeans = 1.25 pounds
Sweater = 2.05 pounds
Running Shoes = 2.25 pounds
We are told that the package must weigh less than 12 pounds. Thus, let the weight of the additional item be x and as such we have the inequality;
5.2 + 1.25 + 2.05 + 2.25 + x < 12
10.75 + x < 12
Subtract 10.75 from both sides to get;
x < 1.25
The only item that is less than 1.25 pounds that she can carry is either the package of socks or the book
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What is the equation of a line that passes through (.5,4.25) and (2,18.5) and has a y-intercept of -.5
The equation of a line that passes through (0.5, 4.25) and (2, 18.5) and has a y-intercept of -0.5 is y = 9.5x - 0.5
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The equation of a line that passes through (0.5, 4.25) and (2, 18.5).
y-intercept = -5
Now,
The equation of a line is y = mx + c
c = y-intercept
c = -0.5 ______(1)
Now,
(0.5, 4.25) and (2, 18.5)
m = (18.5 - 4.25) / (2 - 0.5)
m = 14.25 / 1.5
m = 9.5 ______(2)
Now,
The equation of a line.
y = mx + c
From (1) and (2).
y = 9.5x - 0.5
Thus,
y = 9.5x - 0.5 is the equation of the line.
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Select all that apply:
in a function, values of x are called_
Domain
Range
Input
Output
Answer:
Domain
Step-by-step explanation:
The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x).
The manager of a nationwide department store wants to compare average store sales by region to identify which region has the lowest store sales. Which of the following numerical descriptive measures is best for this purpose?
The best numerical descriptive measure for comparing average store sales by region would be the mean or average.
This measure would provide an accurate representation of the overall store sales across the entire region and would allow the manager to easily identify which region has the lowest store sales.
Additionally, the median and mode could also be used as descriptive measures to compare the store sales by region.
For example, if there is a single store with particularly high sales, the mean will be heavily influenced by this one store. The median and mode would be more likely to provide a better representation of the overall sales across the region, as they are not as heavily influenced by extreme values.
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use the pythagorean theorem to determine which of the following give the measures of the legs and hypotenuse of a right triangle.
The Pythagorean theorem states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse.
Therefore, for the given values of 3, 4, and 5, these lengths can indeed form a right triangle. Specifically, this triangle is a 3-4-5 triangle, which is a special type of right triangle whose sides have integral lengths and whose angles are all multiples of 30°.
Mathematically, this can be expressed as a^2 + b^2 = c^2, where a and b are the lengths of the two legs of the triangle and c is the length of the hypotenuse. The theorem is a fundamental result in geometry and has wide-ranging applications in mathematics, physics, engineering, and other fields.
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Using the region names in the image below, select all regions that represent:
(A ∪ B)' ∪ A'
3 group Venn Diagram with Roman numeral labeled regions
Not, parentheses A union B, close parentheses, union not A. Region I: Items only in group A, not in B or C. Region II: Items in A and B, but not C. Region III: Items only in B, not in A or C. Region IV: Items in A and C, but not B. Region V: Items in A, B, and C. Region VI: Items in B and C, but not A. Region VII: Items only in C, not in A or B. Region VIII: Items not in any of the groups.
The Venn diagram shown to Region II: Items in A and B, but not C are (A ∪ B)' ∪ A'
We have been given that the diagram we need to find the regions represent the set.
What do you mean by Venn diagram?A Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things. Circles that overlap have a commonality while circles that do not overlap do not share those traits. Venn diagrams help to visually represent the similarities and differences between two concepts.
The Venn diagram, item represents the regions four, five, six and seven.
Therefore, it can be written us for Union Fight,...., we concluded that the regions represent see R. C.
This is equal to for Union Fighting Union Six, Seven.
We have, region represent (A ∪ B)' ∪ A'
Therefore, the Venn diagram shown to regions represent
(A ∪ B)' ∪ A' is Region II
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PLEASE BE FAST :')
Determine whether the ordered pair is a solution to the given system of equations.
1) (1,5); -5m + 6n = 25 -7m +8n=33
2) (-2, 0); 8x-3y=-16 50= -9x - 2y
The solution to the equations -5m + 6n = 25 and -7m + 8n = 33 is (1, 5)
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical expressions. Equations are classified based on degree as linear, quadratic, cubic
a) Given the equations:
-5m + 6n = 25 (1)
And:
-7m + 8n = 33 (2)
From both equations simultaneously:
m = 1, n = 5
The solution is (1, 5)
b) Given the equations:
8x - 3y = -16 (1)
And:
50 = -9x - 2y (2)
From both equations simultaneously:
x = -4.23, y = -5.95
The solution is (-4.23, -5.95)
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Catniss is saving money to take a trip to the Capitol with her sister. Every week, after taking out the $292 she nees for her weekely expenses, she sets aside the same portion of her paycheck. After 10 wekks , Catniss has $405.
Which equation can be used to represent the sitation?
The relation between total salary and saving can be represent by the equation, Y = X + 292
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, 3x+2y=0.
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Given that,
Catniss is saving money to take a trip to the Capitol with her sister
Every week,
After taking out the $292, which she needs for her weekly expenses
And that amount she sets aside the same portion of her paycheck
After 10 weeks ,
Catniss has $405
Suppose, she is saving X amount every week,
And her total salary is, Y
Total salary = saving + weekly expenses
Y = X + 292
So, she saved money after 10 week,
⇒ 10X
Given saving after weeks, $405
⇒ 10X = 405
⇒ X = 40.5
Y = X + 292
= 40.5 + 405
= $445.5
Hence, the equation is Y = X + 292
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Which statements are true about a perfect cube monomial and its roots? Check all that apply.
A perfect cube monomial must have exponents on the variables.
A perfect cube monomial must have three identical roots, such that the product of the roots equal the perfect square monomial.
The coefficient of the monomial must be divisible by 3.
Any monomial can be a perfect cube root.
The least common multiple of all the exponents on variables of a perfect cube monomial must be 3.
It must be possible for the coefficient of a perfect cube monomial to be written in the form n3, where n equals the cube root of the coefficient.
Answer:
Step-by-step explanation:
A perfect cube monomial is a monomial with a cube root that is a monomial. In other words, it is a monomial, A, such that there exists a monomial, B, where B × B × B = A.
Ellen walks 0.75 mile to school each day. She stops
to get breakfast after completing 60% of her walk
How far has Ellen walked when she stops for
breakfast?
Sadie earns a 20 percent commission on sales at a hair salon. If her weekly sales commission check was $125, what was her sales total for the week
can you guys please show step by step
Sadie's total weekly sales in the last week were $625.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, Sadie earns a 20 percent commission on sales at a hair salon.
Let, 'x' be her total weekly sales.
Therefore, $125 is 20% of 'x' which can be numerically expressed as,
(20/100)×x = 125.
0.2x = 125.
x = 125/0.2.
x = 625.
So, her weekly sale was $625.
learn more about percentages here :
https://brainly.com/question/24159063
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