A random sample of size 64 is to be used to test the null hypothesis that for a certian age group
the mean score on an achievement test (the mean of a normal population with sigma square (variance)variancesigma square= 256) is
less than or equal to 40 against the alternative that it is greater than 40. If the null hypothesis
is to be rejected if and only if the mean of the random sample exceeds 43.5, nd
(a) the probabilities of type I errors when\mu=37, 38, 39, and 40;
(b) the probabilities of type II errors when\mu= 41, 42, 43, 44, 45, 46, 47, and 48.
Also plot the power function of this test criterion.

77 is the value of Q in linear equation.

What in mathematics is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.  

                                   Equations with power 1 variables are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

P ∝ 1/Q

PQ = K

AT P= 11

Q = 28

11 * 28 = K

K = 308

AT P = 4

4Q = 308

Q = 77

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Answer:

d(0) = -3

Step-by-step explanation:

d(x) = -x + -3                           d(0)

d(0) = 0 - 3

d(0) = -3

So, the answer is d(0) = -3

Answer:

2 9/14

Step-by-step explanation:

The  standard deviation of the sampling distribution of the sample mean for the given sample size is equal  to 3.1623°F.

For the normally distributed data,

Mean of the population distribution 'μ' = 59F

Population standard deviation 'σ' = 10°F

Sample size 'n' = 10

Formula for the standard deviation of the sampling distribution of the sample mean (also known as the standard error of the mean) is equal to ,

= σ / √(n)

Substitute the value to get the standard deviation of the sampling distribution of the sample mean we get,

= 10°F / √(10)

= 3.1623°F

Therefore, the standard deviation of the sampling distribution of the sample mean for all possible random samples of size 10 from this population is approximately 3.1623°F.

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The fraction and ratio that complete the equations in its simplest term is 5/6k and 2 : 9 respectively.

h : k = 5 : 6

h/k = 5/6

cross product

h × 6 = k × 5

6h = 5k

divide both sides by 6

h = 5/6k

Then,

2x = 9y

2/9 = x/y

2 : 9 = x : y

Ultimately, the simplest form of fraction and ratio which completes the equation is 5/6k and 2:9.

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It is true that Jayden's solution is incorrect. It is false that Jayden added inside the parentheses before dividing.

It is false that Jayden substituted the wrong value for a. It is true that Jayden divided 14 by 2 and then added 1. 5. Jayden added inside the parentheses before multiplying. ​

1) The correct solution is

Given,

a ÷ (2 + 1. 5)

Substituting the value of a which is 14

= 14 ÷ (2 + 1. 5)

= 14 ÷ 3.5

= 4

2) As there is no term which needs to be divided so, the second statement is false.

3) Jayden didn't substitute the wrong value of a he just solved the given expression without considering the bracket and divided the 14 which is the value of a by 2.

4) Jyaden divided 14 by 2 and then added 1. 5. Jayden added inside the parentheses before multiplying. ​

i.e. a ÷ (2 + 1. 5)

14 ÷ 2 + 1. 5

7+1.5

8.5

This is the way Jayden solved the equation due to which he arrived at the wrong solution.

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The Correct question is as below

Jayden evaluated the expression a ÷ (2 + 1.5) for a = 14. He said that the answer was 8.5. Choose True or False for each statement.

1. Jayden's solution is incorrect.

2. Jayden added in the parentheses before dividing.

3. Jayden substituted the wrong value for a.

4. Jayden divided 14 by 2 and added 1.5

$4

Multiply 80 by 0.05 to get the answer of $4

Answer:

4 (insert the currency needed)

Step-by-step explanation:

To find our answer we have to find 5% of Kate's wages and to do this we have to do 5 divided by 100. Then that answer is multiplied by 80!

This means she has to put £4 into her savings!

Hope this helps, have a lovely day! :)

Answer:

120

Step-by-step explanation:

20 percent of 600 is 120 so he will get 120

Answer:calculate the cube root of a cube's volume.

Step-by-step explanation:

The probability of all will fail is the lowest.

The given problem states that a missile guidance system has seven fail-safe components, and the probability of each failing is 0.2. The given variable is binomial. We need to find the following probabilities:

(a) Exactly two will fail.

(b) More than two will fail.

(c) All will fail.

(d) Compare the answers for parts a, b, and c, and explain why these results are reasonable.

(a) Exactly two will fail.

The probability of exactly two will fail is given by;

P(exactly two will fail) = (7C2) × (0.2)2 × (0.8)5
= 21 × 0.04 × 0.32768
= 0.2713

Therefore, the probability of exactly two will fail is 0.2713.

(b) More than two will fail.

The probability of more than two will fail is given by;

P(more than two will fail) = P(X > 2)
= 1 - P(X ≤ 2)
= 1 - (P(X = 0) + P(X = 1) + P(X = 2))
= 1 - [(7C0) × (0.2)0 × (0.8)7 + (7C1) × (0.2)1 × (0.8)6 + (7C2) × (0.2)2 × (0.8)5]
= 1 - (0.8)7 × [1 + 7 × 0.2 + 21 × (0.2)2]
= 1 - 0.2097152 × 3.848
= 0.1967

Therefore, the probability of more than two will fail is 0.1967.

(c) All will fail.

The probability of all will fail is given by;

P(all will fail) = P(X = 7) = (7C7) × (0.2)7 × (0.8)0
= 0.00002

Therefore, the probability of all will fail is 0.00002.

(d) Compare the answers for parts a, b, and c, and explain why these results are reasonable.

The probability of exactly two will fail is the highest probability, followed by the probability of more than two will fail. And, the probability of all will fail is the lowest probability. These results are reasonable since the more the number of components that fail, the less likely it is to happen. Therefore, it is reasonable that the probability of exactly two will fail is higher than the probability of more than two will fail, and the probability of all will fail is the lowest.

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A student attempts a 10-question multiple-choice test where each question presents four options, and the student makes random guesses for each answer. So the probability of (a) P(5)= 0.058 and (b) P(More than 3)= 0.093.

Part 1: Calculation of probability of getting 5 questions correct

(a) P(5)The formula used to find the probability of getting a certain number of questions correct is:

P(k) = (nCk)pk(q(n−k))

Where, n = total number of questions

(10)k = number of questions that are answered correctly

p = probability of getting any question right = 1/4

q = probability of getting any question wrong = 3/4

P(5) = P(k = 5) = (10C5)(1/4)5(3/4)5= 252 × 0.0009765625 × 0.2373046875≈ 0.058

Part 2: Calculation of probability of getting more than 3 questions correct

(b) P(More than 3) = P(k > 3) = P(k = 4) + P(k = 5) + P(k = 6) + P(k = 7) + P(k = 8) + P(k = 9) + P(k = 10)

P(k = 4) = [tex]10\choose4[/tex](1/4)4(3/4)6 = 210 × 0.00390625 × 0.31640625 ≈ 0.02

P(k = 5) = [tex]10\choose5[/tex](1/4)5(3/4)5 = 252 × 0.0009765625 × 0.2373046875 ≈ 0.058

P(k = 6) = [tex]10\choose6[/tex](1/4)6(3/4)4 = 210 × 0.0002441406 × 0.31640625 ≈ 0.012

P(k = 7) = [tex]10\choose7[/tex](1/4)7(3/4)3 = 120 × 0.00006103516 × 0.421875 ≈ 0.002

P(k = 8) = [tex]10\choose8[/tex](1/4)8(3/4)2 = 45 × 0.00001525878 × 0.5625 ≈ 0.001

P(k = 9) = [tex]10\choose9[/tex](1/4)9(3/4)1 = 10 × 0.000003814697 × 0.75 ≈ 0.000

P(k = 10) = [tex]10\choose10[/tex](1/4)10(3/4)0 = 1 × 0.0000009536743 × 1 ≈ 0

P(More than 3) = 0.020 + 0.058 + 0.012 + 0.002 + 0.001 + 0.000 + 0≈ 0.093

Therefore, the probabilities of the given situations are: P(5) ≈ 0.058, P(More than 3) ≈ 0.093.

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Answer:

To calculate the distance between each pair of points given, we can use the distance formula which is derived from the Pythagorean theorem. The formula is:

distance = square root of [(x2 - x1)^2 + (y2 - y1)^2]

Using this formula, we can calculate the following distances:

a. Distance between M and P = 13 units

b. Distance between A and B = 5 units

c. Distance between C and D = 10 units

In attempts to reduce greenhouse gas emissions and the effects of climate change, these sources must be taken into account.

A mathematical equation is a claim that two expressions are equal, typically represented with an equal sign (=) between them. The terms "left hand side" (LHS) and "right hand side" (RHS) of the equation, respectively, refer to the expressions on either side of the equal sign. Equations are a common tool for problem solving because they may be used to depict relationships between variables or quantities and to determine the value(s) of the unknown variable(s) that satisfies the equation. For instance, the link between the variables x and the integers 2, 5, and 11 is represented by the equation 2x + 5 = 11. Finding the value of x that makes the left and right sides of the equation equal is necessary to solve this equation.

given

A) Rice farming operations release methane into the atmosphere.

B) Methane is created when cows break down cellulose anaerobically.

E) Methane is released into the atmosphere when landfill material decomposes anaerobically.

Any of the aforementioned behaviours would raise the atmospheric methane concentrations and may have an impact on climate change globally.

Methane is a greenhouse gas that causes the atmosphere of the Earth to warm.

It is produced by both natural and artificial processes. Examples of human activities that contribute to methane emissions into the atmosphere include the production of rice, cattle digestion, and landfill decomposition.

In attempts to reduce greenhouse gas emissions and the effects of climate change, these sources must be taken into account.

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Answer: 7 dollars 18 cents.

Step-by-step explanation:

The correct option that expresses the form of the given argument is "d. if c then f."Explanation:In the given argument, it is stated that if cell phone companies screen text messages, then freedom of speech is threatened.

But as cell phone companies do not screen text messages, so freedom of speech is not threatened. This is a conditional argument, and it can be expressed in the form of a hypothetical syllogism.

The hypothetical syllogism is a syllogism that has a conditional statement in its premises. It is also called a chain argument or transitive argument. The form of the hypothetical syllogism is "If A, then B. If B, then C.

Therefore, if A, then C."In the given argument, it can be expressed in the form of the hypothetical syllogism as follows:If cell phone companies screen text messages, then freedom of speech is threatened. If freedom of speech is threatened, then cell phone companies screen text messages. Therefore, if cell phone companies do not screen text messages, then freedom of speech is not threatened.This can also be represented as "if C then F."Therefore, the correct option that expresses the form of the given argument is "d. if c then f."

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The Riemann sum is:Σ(3-xᵢₖ*yᵢₖ²)ΔA, where i=1,2 and k=1,2,3.

We can create a Riemann sum to estimate the value of the double integral ∬R (3-xy²) dA over the rectangular region R=[0, 4]×[-1, 2] by subdividing [0, 4] into m=2 intervals and [-1, 2] into n=3 intervals. Then we can evaluate the function at the upper left corner of each subrectangle, multiply by the area of the rectangle, and sum all the results.

The width of each subinterval in the x-direction is Δx=(4-0)/2=2, and the width of each subinterval in the y-direction is Δy=(2-(-1))/3=1. The area of each subrectangle is ΔA=ΔxΔy=2*1=2.

Therefore, the Riemann sum is:

Σ(3-xᵢₖ*yᵢₖ²)ΔA, where i=1,2 and k=1,2,3.

Evaluating the function at the upper left corner of each subrectangle, we get:

(3-0*(-1)²)2 + (3-20²)2 + (3-21²)2 + (3-41²)*2 = 2 + 6 + 2 + (-22) = -12.

Thus, the estimate for the double integral is -12.

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Answer: 38 I think if it's not right I'm sorry I'm bad at math that's like the only thing I suck at

Step-by-step explanation:

Answer: The total number of students is the sum of the number of students who have vanilla and those who have chocolate:

Total = 25 + (68 - 25) = 43

The ratio of the number of students who have vanilla to the total number of students is:

Vanilla : Total = 25 : 43

This ratio cannot be simplified any further because 25 and 43 do not have any common factors other than 1. Therefore, the ratio of the number of students who have vanilla to the total number of students is:

25 : 43

Step-by-step explanation:

Answer:

The profit made is given by the difference between the total revenue and the total production cost:

P = R - C

Substituting the given expressions for R and C, we get:

P = 33.70N - (750 + 16.95N)

Simplifying:

P = 16.75N - 750

Therefore, the equation relating P to N is P = 16.75N - 750

The following is the recursive formula for the arithmetic sequence in this issue:

c(1) = -16.

c(n) = c(n - 1) - 17.

An arithmetic sequence is a series of numbers where each term is obtained by adding a fixed constant, known as the common difference, to the previous term. For example, in the sequence 2, 5, 8, 11, 14, 17, each term is obtained by adding 3 to the previous term.

The formula for finding the nth term of an arithmetic sequence is: a(n) = a(1) + (n-1)d, where a(1) is the first term, d is the common difference, and n is the term number. For example, to find the 10th term of the sequence 2, 5, 8, 11, 14, 17, we would use the formula a(10) = 2 + (10-1)3 = 29. Arithmetic sequences have many practical applications, such as in finance, where they can be used to calculate the interest earned on an investment over time.

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We know that the product of lengths of the same chord is equal to the product of the other chord intersecting it.. So;

[tex] \purple{ \mathfrak{x \times 6 = 12 \times 5}}[/tex]

[tex] \large \purple{ \mathfrak{x = \frac{12 \times 5}{6}}}[/tex]

[tex] \large \purple{ \mathfrak{x = \frac{ \cancel{12} \times 5}{ \cancel6}}}[/tex]

[tex] \large \purple{ \mathfrak{x = 2 \times 5}}[/tex]

[tex] \large \boxed{ \red{ \mathfrak{x =10}}}[/tex]

If an Estate dealer sells houses and makes a commission of GHc3750 for the first house sold and receives GHc500 increase in commission for each additional house sold, for reaching a total commission of GHc6500, she must have sold 6.5 houses.

The number of houses the estate dealer sold to reach a total commission of GHc6500 can be determined using the mathematical operations of subtraction, division, and addition.

The total commission received = GHc6,500

The commission for the first house = GHc3,750

The commission for the remaining houses sold = GHc2,750 (GHc6,500 - GHc3,750)

The commission for additional sale of each house = GHc500

The number of additional houses sold = 5.5 (GHc2,750/GHc500)

The total number of houses sold = 6.5 (5.5 + 1 or the first house)

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The lower limit of a 90% confidence interval for the average difference in the number of days the temperature was above 90 degrees between 1948 and 2018 is -22.8 days and the upper limit is 28.6 days.

The margin of error for the 90% confidence interval is 25.4 days.

The 90% confidence interval does provide evidence that the number of 90-degree days increased globally comparing 1948 to 2018.

The 99% confidence interval also provides evidence that the number of 90-degree days increased globally comparing 1948 to 2018.

If the mean difference and standard deviation stay relatively constant, decreasing the degrees of freedom would make it harder to conclude that there are more days above 90 degrees in 2018 versus 1948 globally.

Lowering the confidence level would also make it harder to conclude that there are more days above 90 degrees in 2018 versus 1948 globally.

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Answer:

1/2 or .5

Step-by-step explanation:

If y is inversely proportional to the square of x, we can express this relationship using the formula:

y = k/x^2

where k is a constant of proportionality. We are told that y = 8 for a particular value of x, so we can substitute these values into the equation:

8 = k/x^2

To find the value of k, we can solve for it:

k = 8x^2

Now we are asked to find the new value of y when x increases by 300%. This means that the new value of x will be 4 times the original value (since an increase of 300% means an increase by a factor of 3, and we need to add the original value to get the new value). So we can substitute 4x for x in our equation:

y = k/(4x)^2 = k/16x^2

We already know the value of k, so we can substitute it in and simplify:

y = (8x^2)/(16x^2) = 1/2

Therefore, the new value of y is 1/2 when x increases by 300%.

In order to make the same amount of money, they would have to each sell 5 bicycles. They would both make $500

To find the number of bicycles they would need to sell to make the same amount of money,

We can set Jim's and Tom's weekly earnings equal to each other and solve for the number of bicycles:

250 + 50x = 400 + 20x

30x = 150

x = 5

So they would need to sell 5 bicycles to make the same amount of money.

To find out how much money they would make for selling 5 bicycles, we can substitute x = 5 into either equation.

Let's use Jim's equation:

250 + 50(5) = 500

So they would make $500 for selling 5 bicycles.

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Answer: 50x - 27

Step-by-step explanation:

To find the 8th term of the arithmetic sequence, we need to first find the common difference between consecutive terms:

Common difference (d) = second term - first term

d = (8x - 3) - (x + 1)

d = 7x - 4

Now, we can use the formula to find the nth term of an arithmetic sequence:

an = a1 + (n - 1)d

where a1 is the first term, d is the common difference, and n is the term number we want to find.

Plugging in the values, we get:

a8 = (x + 1) + (8 - 1)(7x - 4)

a8 = x + 1 + 7(7x - 4)

a8 = x + 1 + 49x - 28

a8 = 50x - 27

Therefore, the 8th term of the arithmetic sequence x + 1, 8x - 3, 15x - 7 is 50x - 27.

Answer: 240 miles in 2 hours

Step-by-step explanation:

we know the car is traveling 60 km per half hour (30 minutes)

so to find km per hour, multiply both by 2.

the rate of speed is 120 miles per 60 minutes (1 hour)

multiply 120 mph by the 2 hours given = 240 miles in 2 hours

Answer:

240 km in 2 hours

Step-by-step explanation:

If the car travels 60 km in 30 minutes, then its speed can be calculated as follows:

Speed = distance ÷ time

Speed = 60 km ÷ (30 minutes ÷ 60) = 120 km/hour

Since the car is traveling at a constant speed, we can use the formula:

Distance = Speed × Time

To find how far the car will travel in 2 hours, we can substitute the values we have found:

Distance = Speed × Time

Distance = 120 km/hour × 2 hours

Distance = 240 km

Therefore, the car will travel 240 km in 2 hours if it continues at the same constant speed.