Answer:
Air
Step-by-step explanation:
You can't really measure air
Answer:
Air
Step-by-step explanation:
You cannot measure air because it is invisible.
A person draws balls twice, with replacement, from a urn which contains only one red ball and one black ball. (a) (5 pt) Using the notations R and B to denote the red balls and black balls, respectively, list all the elements of the sample space S. (b) (5 pt) Which elements are in the event A that the person draws one red ball and one black? (c) (5 pt) What is P(A)?
(a) All the elements of S are : S = {RR, RB, BR, BB},
(b) Elements in event A are {RB and BR},
(c) The probability of "event-A", which is the person drawing one "red-ball" and one "black-ball", is 1/2.
Part (a) : The "sample-space" (S) consists of all possible outcomes when drawing two balls with replacement. In this case, there are four possible outcomes : S = {RR, RB, BR, BB},
Part (b) : The "event-A" represents the person drawing one red-ball and one black-ball. The elements in event A are {RB and BR},
Part (c) : To calculate the probability P(A), we need to determine the ratio of favorable outcomes (elements in A) to the total number of possible outcomes (elements in S).
P(A) can be written as : (Number of favorable outcomes)/(Total number of possible outcomes),
Substituting the values from part(a) and part(b),
We get,
P(A) = 2/4
P(A) = 1/2
Therefore, the required probability is 1/2.
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The algebra question is in the image
Answer:
B
Step-by-step explanation:
A or constant is the answer
As sales manager for Montevideo Productions, Inc., you are planning to review the prices you charge clients for television advertisement development.
You currently charge each client an hourly development fee of $2,500. With this pricing structure, the demand, measured by the number of contracts.
Montevideo signs per month, is 15 contracts. This is down 5 contracts from the figure last year, when your company charged only $2,000.
Construct a linear demand equation in the form q= ap + b where the number of contracts q is given as a function of the hourly fee p Montevideo charges for development.
Give a formula for the total revenue obtained by charging $p per hour.
The costs to Montevideo Productions are estimated as follows:
Fixed costs: $120,000 per month and Variable costs: $80,000 per contract
Express Montevideo Productions’ monthly cost as a function of the hourly production charge p.
Express Montevideo Productions’ monthly profit as a function of the
hourly development fee p and hence the price it should charge to maximize the profit.
The XYZ Clothing Company manufactures football boots for sale to
College/University bookstores, in Trinidad. Football boots are in runs of up to 500. It cost (in dollars) for a run of x football boots is:
(x) = 3,000 + 8x + 0.1x2 0 ≤ x ≤ 500
XYZ Clothing sells the football boots at $ 120 each.
(a) How many football boots does XYZ have to sell to breakeven?
(b) How many football boots does XZY have to sell to make maximum profit?
(c) On a labelled pair of axes, sketch the XYZ’s profit function. Label all important points.
(a) The number of football boots XYZ Clothing needs to sell to break even can be found by solving the quadratic equation.
(b) To maximize profit, XYZ Clothing needs to sell 1120 football boots.
(c) Plotting relevant points on a graph, we can sketch XYZ Clothing's profit function, indicating important points.
(a) To find the number of football boots XYZ Clothing needs to sell to break even, we set the profit function equal to zero:
Profit = Revenue - Cost
Since the revenue is given as $120 per football boot and the cost function is provided as C(x) = 3,000 + 8x + 0.1x^2, the profit function is:
Profit = 120x - (3,000 + 8x + 0.1x^2)
Setting the profit function equal to zero, we have:
0 = 120x - (3,000 + 8x + 0.1x^2)
Simplifying the equation, we get:
0 = 112x - 0.1x^2 - 3,000
To find the number of football boots needed to break even, we solve the quadratic equation:
0.1x^2 - 112x + 3,000 = 0
Solving this equation will give us the value of x, which represents the number of football boots XYZ Clothing needs to sell to break even.
(b) To find the number of football boots XYZ Clothing needs to sell to maximize profit, we need to determine the vertex of the profit function. The profit function is the same as in part (a):
Profit = 120x - (3,000 + 8x + 0.1x^2)
To find the vertex, we can use the formula x = -b/2a, where a = 0.1 and b = 112.
x = -(-112) / (2 * 0.1)
x = 1120
So, XYZ Clothing needs to sell 1120 football boots to maximize profit.
(c) To sketch the profit function on a pair of axes, we can plot the points that are relevant to the problem. We know that the profit function is given by:
Profit = 120x - (3,000 + 8x + 0.1x^2)
We can plot the following points:
Breakeven point: (x, 0) where x is the number of football boots needed to break even.
Maximum profit point: (1120, Profit(1120)) where Profit(1120) is the maximum profit obtained when 1120 football boots are sold.
Additionally, we can plot a few more points to get an idea of the shape of the profit function.
By connecting these points, we can sketch the profit function on the axes, indicating the relevant points and labeling them accordingly.
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Assume that a sample is used to estimate a population proportion p. Find the 99.9% confidence interval for a sample of size 176 with 118 successes. Enter your answer as an open-interval (i.e., parentheses) using decimals (not percents) accurate to three decimal places. 99.9% C.1. =
The 99.9% confidence interval for a sample of size 176 with 118 successes is (0.558, 0.778).
The formula for finding the confidence interval for a sample proportion is given as follows:
Confidence interval = sample proportion ± zα/2 * √(sample proportion * (1 - sample proportion) / n)
Where,
zα/2 is the z-value for the level of confidence α/2,
n is the sample size,
sample proportion = successes / n
Here, level of confidence, α = 99.9%, so α/2 = 0.4995. The value of zα/2 for 0.4995 can be found from the z-table or calculator and it comes out to be 3.291.
Putting all the values in the formula, we get:
Confidence interval = 0.670 ± 3.291 * √(0.670 * 0.330 / 176)
= (0.558, 0.778) (rounded to three decimal places and put in parentheses)
Thus, the 99.9% confidence interval for a sample of size 176 with 118 successes is (0.558, 0.778).
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There are 30 students in Mrs. Rodriguez’s class. 20% got an A on the test. How many students got an A?
Answer
6.
Steps
30/100×30
=6
Answer:
6
Step-by-step explanation:
There are 30 students
So,
20÷100×30=6
A worker at a computer factory can assemble 8 computers per hour. How long would it take this worker to assemble 200 computers?
A.8 h
B.20 h
C.25 h
D.200 h
To determine how long it would take for the worker to assemble 200 computers, we need to consider the rate at which the worker assembles computers and the total number of computers to be assembled.
Given that the worker can assemble 8 computers per hour, we can set up a proportion to find the time required:
8 computers / 1 hour = 200 computers / x hours
Cross-multiplying and solving for x, we get:
8x = 200
x = 200 / 8
x = 25
Therefore, it would take the worker 25 hours to assemble 200 computers. The correct answer is option (C) 25 h.
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Use a net to find the surface area of the cone to the nearest square centimeter. Use 3.14 for pie The numbers are 19cm and 8cm
Answer:
678.672cm^2
Step-by-step explanation:
Given data
A cone is described by the length and radius
l=19cm
r=8cm
The formula for the surface area of the cone is
T.S.A=πrl+πr^2
Substitute
T.S.A=3.142*8*19+3.142*8^2
T.S.A=477.584+201.088
T.S.A=678.672
Hence the surface area is
678.672cm^2
liam is making chocolate chip cookies. The recipe calls for 1 cup of sugar for every 3 cups of flour. Liam only has 2 cups of flour. How much sugar does liam use?
1/5 cups of sugar.
have a nice day
) The stem-and-leaf plot shows the ages of customers who were interviewed in a survey by a store w How many customers were older than 45? Ages of Store Customer
1 0 2 3 3 69 8
2 1 1 3 4 5 6 6 8 9
3 2 2 4 4 4 5 7
4 1 2 3 3 5 8
5 0 0 1 5 6
6 2 4 5 5
7 3
The correct answer is there are 12 customers who are older than 45.
To determine how many customers were older than 45, we need to examine the values in the stem-and-leaf plot that are greater than 45.
Looking at the plot, we can see that the stem values range from 1 to 7. However, the stem values 8 and 9 are missing, so there are no customers with ages starting from 80 to 99.
For the stem values 1, 2, 3, 4, 5, 6, and 7, we can count the number of leaf values that are greater than 5.
Stem 1: There are no leaf values greater than 5.
Stem 2: There are 3 leaf values greater than 5 (6, 6, 8).
Stem 3: There are 4 leaf values greater than 5 (6, 7).
Stem 4: There are 3 leaf values greater than 5 (8).
Stem 5: There are 2 leaf values greater than 5 (6).
Stem 6: There are 0 leaf values greater than 5.
Stem 7: There are 0 leaf values greater than 5.
Adding up the counts for each stem, we get:
0 + 3 + 4 + 3 + 2 + 0 + 0 = 12
Therefore, there are 12 customers who are older than 45.
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what is the axis of symmetry for the graph shown?
Answer:
x=2
Step-by-step explanation:
The axis of symmetry goes through the vertex and is the line that makes the image the same on one side as the other
Since this is a vertical parabola, the axis is symmetry is of the form x=
The vertex is at x=2 so the axis of symmetry is x=2
Ling measured a shopping center and made a scale drawing. The scale of the drawing was 1 millimeter: 3 meters. The actual width of the parking lot is 42 meters. How wide is the parking lot in the drawing?
Answer:
14
Step-by-step explanation:
42:?
3:1
42/3=14
42:14
3:1
can someone please help me with this question?? (no links!!!)
Answer:
960
Step-by-step explanation:
it says use 3 for pi, so you plug the values into given equation
V = 3·(4)²·20
r is 4 because it is half of 8.
Then multiply
3·16·20 = 48·20 = 960
Answer:
960 cm
Step-by-step explanation:
8/2 = 4 (radius)
3 (since we're using 3 for pi) * 4^2 * 20
3 * 16 * 20
48 * 20
= 960 cm
I hope this helps heh :)
A shipment of 5 boxes of toys weighed
34.53 pounds. Each box measures the same
weight, so what's the weight of 1 box?
Answer:
Each box weighs 6.906 pounds.
Step-by-step explanation:
We know the total weight of the boxes. We also know how many boxes we have. To find the weight of one box, we want to divide the total weight by the total number of boxes.
34.53 / 5
= 6.906
Each box weighs 6.906 pounds.
Hope this helps!
I’ll give brainless to who ever respond correctly and fast
Answer:
34cm squared
Step-by-step explanation:
Formula: 2(WL+HL+HW)
(2*5) + (1*5) + (1*2) = 10 + 5 + 2 = 17 17*2 = 34
Answer:
34
Step-by-step explanation:
2(wl+ hl+hw)
2(10+5+2)
= 34
et J2= {0, 1}. Find three functions f, g and h such that f : J2→
J2, g : J2→ J2, and h : J2→ J2, and f = g = h
There are many possible solutions, but one example in the case of three functions f, g, and h would be: f(0) = 0, f(1) = 1g(0) = 1, g(1) = 0h(0) = 0, h(1) = 1
We have the set J2 = {0,1} and we need to estimate three functions f, g, and h such that f:
J2→ J2, g: J2→ J2, and h:
J2→ J2, and f = g = h.
To do this, we can simply assign values to each element of the set J2 for each of the three functions. For example, we can let f(0) = 0 and f(1) = 1, which means that the function f maps 0 to 0 and 1 to 1. We can also let g(0) = 1 and g(1) = 0, which means that the function g maps 0 to 1 and 1 to 0.
Finally, we can let h(0) = 0 and h(1) = 1, which means that the function h maps 0 to 0 and 1 to 1. Note that all three functions have the same values for each element in J2, so we can say that f = g = h.
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The point (1, -5) is an ordered pair for which function?
ƒ( x ) = 2 x - 7
ƒ( x ) = - x + 9
ƒ( x ) = 3 x - 11
Answer:
The first one.
Step-by-step explanation:
so 1 stands for x and -5 stands for y. When you plug in 1 into the equation the answer is -5. So that order pair works with that equation.
Consider the case of equally likely transmission of multilevel signaling over AWGN channel with Variance , and mean . The signaling used is M=4 with the data rate of . The symbols are assigned the pulse values: -2v -1v +2v +1v. Develop the expression for the optimum threshold values. Write the expression of correct transmission when symbol level -2v was transmitted. Write the expression for the total probability of error. Evaluate the total probability of error when =0.40 and =0.
In multilevel signaling over an Additive White Gaussian Noise (AWGN) channel, the received signal can be represented as:
Y = X + N
where Y is the received signal, X is the transmitted signal, and N is the AWGN with zero mean and variance σ^2.
In this case, M = 4, which means we have 4 symbols: -2v, -v, +2v, +v. The pulse values assigned to these symbols are: -2v, -v, +2v, +v.
To find the optimum threshold values, we need to consider the decision regions between adjacent symbols. Let's denote the threshold values as T1, T2, and T3, corresponding to the decision boundaries between -2v and -v, -v and +2v, and +2v and +v, respectively.
For correct transmission of the symbol -2v, the received signal Y should be greater than T1 and less than or equal to T2. Mathematically, this can be expressed as:
T1 < Y ≤ T2
The probability of correct transmission for the symbol -2v can be obtained by integrating the probability density function (PDF) of the received signal Y over the region T1 < Y ≤ T2.
Now, let's find the expression for the total probability of error. The total probability of error (P_e) can be obtained by summing the probabilities of error for each symbol. In this case, we have four symbols, so the expression for P_e is:
[tex]P_e = P_error(-2v) + P_error(-v) + P_error(+2v) + P_error(+v)[/tex]
where P_error(-2v) is the probability of error for symbol -2v, P_error(-v) is the probability of error for symbol -v, and so on.
Finally, to evaluate the total probability of error when σ^2 = 0.40 and v = 0, we need more information. Specifically, we need the signal-to-noise ratio (SNR) or the value of σ^2 in order to proceed with the calculation.
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Find inverse of f(x) = 2 + 3x / x - 2
Know answer is 2x + 2 / x - 3 I just want someone to explain the steps for my revision!
Thank you.
3x+4y=-12 x-y=10 using elimination no links or download
Answer:
x = 4, y = -6
Step-by-step explanation:
Elimination Method
3x + 4y = -12 ---- (1)
x-y = 10 ---- (2)
(2) x 4:
4(x) 4(-y) = 4(10)
4x - 4y = 40 ---- (3)
(1) + (3):
3x + 4y + (4x - 4y) = -12 + 40
3x + 4y + 4x - 4y = 28
7x = 28
x = 28/7
x = 4
Sub x = 4 into (2):
(4) - y = 10
-y = 10 - 4
-y = 6
y = -6
let a be a square matrix. prove an alternate form of the polar decomposition for a: there exists a unitary matrix w and a positive semidefinite matrix p such that a = pw.
The alternate form of the polar decomposition of `A` is given by `A = PW`, where `W` is a positive semidefinite Hermitian matrix and `P` is a positive semidefinite Hermitian matrix.
Let `A` be a square matrix. Prove an alternate form of the polar decomposition for `A`.For a given square matrix `A`, the polar decomposition of `A` is a factorization of `A` into the product of a unitary matrix `U` and a positive semi-definite Hermitian matrix `P`. This polar decomposition of `A` can be given by `A = UP` or `A = PU*`, where `U` is the unitary matrix and `P` is a positive semidefinite matrix such that `P = (AA*)^(1/2)` or `P = (A*A)^(1/2)`.
The alternate form of the polar decomposition of `A` is given by `A = PW`, where `W = P^(1/2)U P^(1/2)` and `P` is a positive semidefinite matrix.Let `A = UP` be the polar decomposition of `A`, where `U` is unitary and `P` is positive semi-definite Hermitian. Then `P = A(A*)^(1/2)` and `U = P^(-1)A`. Let `W = P^(1/2)U P^(1/2)` and `W* = P^(1/2)U* P^(1/2)`. Since `U` is unitary, we have `U* = U^(-1)`. Hence `W* = P^(1/2)U^(-1) P^(1/2)`.Multiplying `UP` by `P^(1/2)`, we get `UP^(1/2) = P^(1/2)U P`. Multiplying both sides of the equation by `P^(1/2)` on the right, we get `UP^(1/2)P^(1/2) = P^(1/2)U P P^(1/2)` or `UP = P^(1/2)U P^(1/2)P^(1/2)` or `UP = P^(1/2)U P^(1/2)` or `U = P^(-1/2)W P^(1/2)`.
Substituting the value of `U` in `A = UP`, we get `A = P^(-1/2)W P^(1/2)P`. Since `P` is positive semi-definite, `P = (P^(1/2))^2` is a Hermitian matrix. Therefore, `W = P^(1/2)U P^(1/2)` is a Hermitian matrix and is positive semi-definite. Thus, we have `A = PW` where `W = P^(1/2)U P^(1/2)` is a positive semidefinite Hermitian matrix. Hence, the alternate form of the polar decomposition of `A` is given by `A = PW`, where `W` is a positive semidefinite Hermitian matrix and `P` is a positive semidefinite Hermitian matrix.
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6. Consider the trigonometric equation sin x + 2 = 0. Explain why this equation would have no solutions. [C-2]
The given trigonometric equation is sin x + 2 = 0.
It is important to note that sine values range from -1 to 1 and never exceed those bounds. Thus, it can be determined that sin x + 2 will never equal zero.This is because the lowest possible value of sine is -1, which is not equal to zero. When 2 is added to that value, the sum is still negative. Therefore, the equation sin x + 2 = 0 has no solutions.
A trigonometric equation is one that has a variable and a trigonometric function. For instance, sin x + 2 = 1 is an illustration of a mathematical condition. The equations can be as straightforward as this or more complicated than that, such as sin2 x – 2 cos x – 2 = 0.
The six mathematical capabilities are sine, secant, cosine, cosecant, digression, and cotangent. The trigonometric functions and identities are derived by referencing a right-angled triangle as a reference: Sin is the opposite side or the hypotenuse.
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Sales by Quarter A company made sales of $1,254,000 last year. Quarter 1 Quarter 2 Produced 13 more sales than in quarter 1 Quartor 3 Quarter 4 Produced 17% of total sales for the year Sales increased 100% ovor tho provious quarter. Question: Adjust the ple chart to represent the sales each quarter.
Quarter 1: $300,000Quarter 2: $300,013Quarter 3: $250,000Quarter 4: $500,000 the adjusted chart representing the Sales .
The given chart to represent the sales each quarter, we need to find out the sales of each quarter first and then represent them in the chart. Let's calculate the sales of each quarter one by one:
Sales of Quarter 1Let the sales of Quarter 1 be xSales of Quarter 2As per the given data, Quarter 2 produced 13 more sales than Quarter 1Therefore, sales of Quarter 2 = x + 13Sales of Quarter 3Let the sales of Quarter 3 be sales of Quarter 4As per the given data, Quarter 4 produced 17% of total sales for the year
therefore, 17% of $1,254,000 = (17/100) x 1,254,000= 213,180Sales of Quarter 4 = 213,180Sales increased 100% over the previous quarter
Therefore, sales of Quarter 4 = 2 x sales of Quarter 3= 2yNow, we can form the equation as follows: Total Sales = Sales of Quarter 1 + Sales of Quarter 2 + Sales of Quarter 3 + Sales of Quarter 4$1,254,000 = x + (x + 13) + y + 2y + 213,180$1,254,000 = 4x + 3y + 213,193or 4x + 3y = $1,040,807
Now, we can assume some values of x and y and then calculate the values of other variables. Let's assume x = $300,000 and y = $250,000Therefore, sales of Quarter 1 = $300,000Sales of Quarter 2 = $300,000 + $13 = $300,013Sales of Quarter 3 = $250,000Sales of Quarter 4 = 2 x $250,000 = $500,000Now, we can represent these sales in the chart as follows:
Quarter 1: $300,000Quarter 2: $300,013Quarter 3: $250,000Quarter 4: $500,000
Therefore, the adjusted chart representing the sales each quarter is shown above.
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Which number represents the probability of an event that is impossible to
occur?
Answer:
An impossible event has a probability of 0. A certain event has a probability of 1.
Please help 6th grade math please please help i will give brainliest
A cuboid made from metal plates with the dimensions x, 3x and y cm has a surface area 450 cm. Find the volume of the cuboid as a function of x.
The volume of the cuboid as a function of x is V(x) = x * 3x * y.
the volume of the cuboid as a function of x is V(x) = 675/4 - (9/4)x^2.
The surface area of the cuboid is given as 450 cm, which can be expressed as:
2(x * 3x) + 2(x * y) + 2(3x * y) = 450.
Simplifying this equation, we get:
6x^2 + 2xy + 6xy = 450,
6x^2 + 8xy = 450,
3x^2 + 4xy = 225.
Now, we need to express y in terms of x. From the given dimensions, we know that the surface area is formed by six rectangular faces of the cuboid. Therefore, the length of one face is x, the width is 3x, and the remaining face (height) is y.
To find y, we can use the equation for the surface area. Rearranging the equation above, we have:
3x^2 + 4xy = 225,
y(4x) = 225 - 3x^2,
y = (225 - 3x^2) / (4x).
Now we can substitute the value of y into the expression for the volume:
V(x) = x * 3x * [(225 - 3x^2) / (4x)].
Simplifying further:
V(x) = (3/4) * (225 - 3x^2),
V(x) = 675/4 - (9/4)x^2.
Therefore, the volume of the cuboid as a function of x is V(x) = 675/4 - (9/4)x^2.
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Rhonda and Laura are planning to watch two movies over the weekend from Laura's collection of 35 DVDs. Rhonda has two favorites among the collection. What is the probability that the girls would randomly choose those two movies to watch? Enter a fraction or round your answer to 4 decimal places, if necessary.
The probability that the girls would randomly choose their two favorite movies to watch is 0.0034.
The number of favorable outcomes is 2 (since Rhonda has two favorite movies).
Using the combination formula:
C(n, r) = n! / (r! * (n - r)!)
In this case, n = 35 (total number of movies) and r = 2 (number of movies to be chosen).
C(35, 2) = 35! / (2! x (35 - 2)!)
C(35, 2) = 35! / (2! x 33!)
= (35 x 34 x 33!) / (2! x 33!)
= (35 x 34) / 2
= 595
Therefore, there are 595 possible outcomes when choosing any two movies from Laura's collection.
Now, Probability = Favorable Outcomes / Total Outcomes
Probability = 2 / 595
Therefore, the probability that the girls would randomly choose their two favorite movies to watch is 0.0034.
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Solve for x. (log510 - log52) (log61296) = log₂(x - 5)²
The solution to the equation (log510 - log52) (log61296) = log₂(x - 5)² is x = 9. To solve the given equation, let's break it down step by step.
First, we simplify the left side of the equation using logarithmic properties. Using the property log(a) - log(b) = log(a/b), we can rewrite (log510 - log52) as log5(10/2), which simplifies to log5(5) or 1.
Next, we simplify the right side of the equation. Using the property logₐ(b²) = 2logₐ(b), we can rewrite log₂(x - 5)² as 2log₂(x - 5).
Now our equation becomes 1 * log61296 = 2log₂(x - 5).
Since log61296 is the logarithm base 6 of 1296, which is 4, we can simplify the equation further to 4 = 2log₂(x - 5).
Dividing both sides by 2, we have 2 = log₂(x - 5).
Now we can rewrite this equation in exponential form: 2² = x - 5.
Simplifying, we get 4 = x - 5.
Adding 5 to both sides, we find x = 9.
Therefore, the solution to the equation (log510 - log52) (log61296) = log₂(x - 5)² is x = 9.
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98 = x + 55 what is it????
Answer:
x = 43
Step-by-step explanation:
x = 98 - 55
x = 43
Answer:
x=43
Step-by-step explanation:
have a nice day and stay safe:)
The box-and-whisker plots below show the test scores for Mr. Scott's three math classes.
Based on this information, with which class or classes does Mr. Scott most need to review the material covered on the test?
A. third period
B. first period
C. third and fourth periods
D. fourth period
Answer:
A. Third period
Step-by-step explanation:
- hope this helped!
Answer:
3rd
Step-by-step explanation:
A simple random sample of 36 men from a normally distributed population results in a standard deviation of 64 beats per minute. The normal range of pulse rates of adults is typically given an 60 to 100 beats per minute. If the range rule of thumb is applied to that normal range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.10 significance level to test the cam that pulse rates of men have a standard deviation equal to 10 beats per minute. Complete parts (a) through (d) below a. Identify the null and attemative hypotheses. Choose the correct answer below OA H₂ 2 10 beats per minute He<10 beats per minute OB. He 10 beats per minute H: 10 beats per minute OC. He 10 beats per minute OD H10 beats per minute He 10 beats per minute H₁ #10 beats per minute b. Compute the test statistic. (Round to three decimal places as needed) c. Find the P-value P-value- (Round to four decimal places as needed.) d. State the conclusion. evidence to warrant rejection of the claim that the standard deviation of men's puise alas H. because the P-value is is equal to 10 beats per minute. the level of significance.
The conclusion is that there is evidence to warrant rejection of the claim that the standard deviation of men's pulse rates is equal to 10 beats per minute.
a. Null and alternative hypotheses Null hypothesis (H0): The standard deviation of men’s pulse rates is equal to 10 beats per minute.H0: σ = 10Alternative hypothesis (Ha): The standard deviation of men’s pulse rates is not equal to 10 beats per minute.
Ha: σ ≠ 10b. Calculation of test statistic The test statistic for the standard deviation is calculated as: \[χ^2 = \frac{(n-1)S^2}{σ^2}\]Where n = sample size, S = sample standard deviation, and σ = hypothesized standard deviation. Substituting the values, \[χ^2 = \frac{(36-1)(64)^2}{(10)^2}\] \[χ^2 = 1322.56\]
c. Calculation of P-value We can use the chi-square distribution table to find the P-value. At a significance level of 0.10 and 35 degrees of freedom (36-1), the critical values are 19.337 and 52.018.
Since the test statistic value (χ2) of 1322.56 is greater than 52.018, the P-value is less than 0.10. Therefore, we reject the null hypothesis and conclude that the standard deviation of men’s pulse rates is not equal to 10 beats per minute.
Since it is a two-tailed test, we divide the significance level by 2. The P-value for the test is P = 0.000. Therefore, the P-value is less than the level of significance (0.10).
d. Conclusion Since the P-value is less than the level of significance, we reject the null hypothesis. Hence, there is evidence to support the claim that the standard deviation of men's pulse rates is not equal to 10 beats per minute.
Therefore, the conclusion is that there is evidence to warrant rejection of the claim that the standard deviation of men's pulse rates is equal to 10 beats per minute.
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