identify the system of linear equations from the tables of values given below.

a. Decision rule: Reject the null hypothesis if the calculated z-value is less than or equal to -1.28. b. Calculated z-value: -1.8892. c. Conclusion: Reject the null hypothesis, indicating evidence that the population mean is less than 128.

To complete parts (a) through (c), we need to perform a hypothesis test for the given hypotheses

H0: μ = 128 (null hypothesis)

HA: μ ≤ 128 (alternative hypothesis)

Given: X= 119 (sample mean)

σ = 27 (population standard deviation)

n = 46 (sample size)

α = 0.10 (significance level)

a. The decision rule is to reject the null hypothesis if the calculated value of the test statistic is less than or equal to the critical value(s) of the test statistic. Since the alternative hypothesis is one-sided (μ ≤ 128), we will use a one-sample z-test and compare the calculated z-value with the critical z-value.

To find the critical z-value, we need to determine the z-value corresponding to the significance level α = 0.10. Looking up the critical value in the standard normal distribution table, we find that the critical z-value is -1.28 (rounded to two decimal places).

b. The calculated value of the test statistic, in this case, is the z-value. We can calculate the z-value using the formula

z = (X - μ) / (σ / √n)

Substituting the given values:

z = (119 - 128) / (27 / √46) ≈ -1.8892 (rounded to two decimal places)

c. The conclusion is based on comparing the calculated value of the test statistic with the critical value. Since the calculated z-value of -1.8892 is less than the critical z-value of -1.28, we have enough evidence to reject the null hypothesis. Therefore, we conclude that the population mean is less than 128.

The conclusion statement in part (c) is inconsistent with the given alternative hypothesis and should be revised accordingly.

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The purpose of using prefix in the metric system is to properly sale the basis of the unit so large numeric values can be used effectively.

If the metric system is not properly prefixed it can lead to various inconsistencies in the the numeric values. for example if you go to a computer store and you do not know the scale like (kb, mb, gb, tb) you will get quite confused about what is the sales representative saying

Consider you went to a store to get sugar and you do not know the metric system say(gram, kg, mg) you would not know how much sugar you need directly by taking it in your hands.

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Answer:

5 wall and 1 desk

Step-by-step explanation:

5 x 6$ = 30$
1 x 7$ = 7

30 + 7 = 37, which is the total price

Answer:

I believe it is rational depending on the question of course

Answer: C. Rational Numbers

Step-by-step explanation:

Gradpoint.

The optimal point values for x1, x2, λ, and μ (Lagrange multipliers) in the given problem are:

x1 = 1

x2 = 1

λ = -4

μ = 2

To solve the optimization problem using the Lagrange multipliers technique, we first construct the Lagrangian function L(x1, x2, λ) by incorporating the equality constraint:

L(x1, x2, λ) = f(x1, x2) - λ(g(x1, x2))

Where f(x1, x2) is the objective function, g(x1, x2) is the equality constraint, and λ is the Lagrange multiplier.

In this case, the objective function is f(x1, x2) = 2x1^2 - 2x1x2 + 2x2 - 6x1 + 6, and the equality constraint is g(x1, x2) = x1 + x2 - 2.

The Lagrangian function becomes:

L(x1, x2, λ) = 2x1^2 - 2x1x2 + 2x2 - 6x1 + 6 - λ(x1 + x2 - 2)

To find the optimal values, we need to find the critical points by taking partial derivatives of L with respect to x1, x2, and λ and setting them equal to zero. Solving these equations simultaneously, we get:

∂L/∂x1 = 4x1 - 2x2 - 6 - λ = 0

∂L/∂x2 = -2x1 + 2 + λ = 0

∂L/∂λ = -(x1 + x2 - 2) = 0

Solving these equations, we find x1 = 1, x2 = 1, and λ = -4. Substituting these values into the equality constraint, we can solve for μ:

x1 + x2 - 2 = 1 + 1 - 2 = 0

Therefore, μ = 2.

The optimal point values for the variables in the optimization problem are x1 = 1, x2 = 1, λ = -4, and μ = 2. The Lagrange multipliers λ and μ represent the rates of change of the objective function and the equality constraint, respectively, with respect to the variables. They provide insights into the sensitivity of the objective function to changes in the constraints and can indicate the impact of relaxing or tightening the constraints on the optimal solution. In this case, the Lagrange multiplier λ of -4 indicates that a small increase in the equality constraint (x1 + x2 - 2) would result in a decrease in the objective function value. The Lagrange multiplier μ of 2 indicates the shadow price or the marginal cost of satisfying the equality constraint.

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The value of 6x is 102.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

x=51/3

For 6x put x= 51/3 we get

6x = 6 x 51/3

6x = 2 x 51

6x = 102

Or, \(x^6\) = \((51/3)^6\)

\(x^6\) = 17,596,287,801 / 531,441

Hence, the value of 6x = 102.

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The addition equation to represent Jackson's net change in money is x + (-y) = 4.63

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Jackson receives 4.63 as his change at the grocery store. He places it into a charity donation jar at the register.

WE need to Write an addition equation to represent Jackson's net change in money.

Given that :

The change received = 4.63

The Net change in money :

Let initial amount before purchase is represented by  x

The Cost of item purchased = y (negative as it is incurred)

The Net change in money:

Initial amount + cost of item purchased = change received

x + (-y) = 4.63

Therefore, an addition equation to represent Jackson's net change in money is x + (-y) = 4.63

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Answer:

243

Step-by-step explanation:

im so happy

The probability that a second scientist will detect two errors in seven calculations randomly checked from 500, with a 0.05 error rate, is approximately 4.09%.

This problem can be solved using the binomial probability formula:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

where P(X=k) is the probability of getting k successes (detecting errors), n is the number of trials (7 calculations checked by the second scientist), k is the number of successes (2 errors detected), p is the probability of success in one trial (detecting an error in one calculation), n choose k is the number of ways to choose k successes from n trials, calculated as n! / (k! * (n-k)!).

In this case, n = 7 and k = 2. To find p, we need to know the proportion of errors in the 500 calculations made by the first scientist:

p = number of errors / total number of calculations

p = 25 / 500

p = 0.05

So the probability of detecting two errors in seven calculations checked by the second scientist is:

P(X=2) = (7 choose 2) * 0.05^2 * 0.95^5

P(X=2) = (21) * 0.0025 * 0.7737809375

P(X=2) = 0.0409

Therefore, the probability that the second scientist detects two errors is approximately 0.0409 or 4.09%.

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Answer:

For a give event with outcomes:

{x₁, x₂, ..., xₙ}

Each with probabilities:

{p₁, p₂, ..., pₙ}

The expected value is:

Ev = x₁*p₁ + ... + xₙ*pₙ

Here we have the outcomes and probabilities:

win $1, with a probability 20%/100% = 0.2

win $2, with a probability 25%/100% = 0.25

win $5, with a probability of 35%/100% = 0.35

do not win, with a probability of 20%/100% = 0.2

Then the expected value of the game is:

Ev = $1*0.2 + $2*0.25 + $5*0.35 + $0*0.2 = $2.45

And if we know that the game costs $2, then the expected value is:

Ev = $2.45 - $2 = $0.45

The expected value is  $0.45

If the cyclist rode for 1 hour at the same average speed, she would have ridden 17.4 miles.

To find the average speed of a cyclist, you can divide the total distance covered by the total time taken. In this case, the cyclist rode for 3.5 hours and completed a distance of 60.9 miles, giving an average speed of 60.9 miles ÷ 3.5 hours = 17.4 miles per hour. This average speed is constant, meaning that the cyclist would have traveled the same distance in 1 hour as she did in 3.5 hours if she kept the same pace.

Therefore, if the cyclist rode for 1 hour at the same average speed, she would have ridden 17.4 miles. This calculation is important for cyclists and other athletes as it helps them to determine their speed and track their progress over time.

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Answer:

y = 5

Step-by-step explanation:

All angles must add up to 90° as you can see the right angle symbol, this means:

51 + 9y - 6 = 90

51 - 6 + 9y = 90

45 + 9y = 90

Subtract 45 from both sides of the equation to isolate the 9y:

45 + 9y - 45 = 90 - 45

9y = 45

Divide both sides by 9:

\(\frac{9y}{9} = \frac{45}{9}\)

y = 5

Hope this helps!

Answer:

Step-by-step explanation:

9x+3y

Answer:

9x+3y

Step-by-step explanation:

As per the given sample size, the shape of the population distribution when conducting t test is approximately normal.

Sampling.

in statistics, sampling refers the statistical procedure that is concerned with the selection of the individual observation; it helps us to make statistical inferences about the population.

Given,

Here we have the sample size is 81.

Now, we need to find the shape of the population distribution when conducting the t test.

Let us consider you are the manager of a restaurant for a fast-food franchise. And in last month, the mean waiting time at the drive-through window for branches in your geographical region, as measured from the time a customer places an order until the time the customer receives the order, was 3.9 minutes.

Now, you are selecting a random sample of 81 orders.

As per the sample size, the sample mean waiting time is 3.72 minutes, with a sample standard deviation of 0.8 minute.

Now, we complete parts (a) and (b) below.

a. here at the 0.01 level of significance, is there evidence that the population mean waiting time is different from 3.9 minutes.

And state the null and alternative hypotheses.

H0: μ▼ H1: μ ▼

So, H0 is sufficient insufficient evidence to conclude that the population mean waiting time is different from 3.9 minutes .

b. According to the sample size is 81,

The shpe of the population distribution when conducting t test is approximately normal. As in the t test is appropriate for a large sample size.

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Answer:2/5

Step-by-step explanation:

1.The formula for the volume of a right circular cylinder is V = πr^2h, where r is the radius of the base and h is the height of the cylinder.

We are given that the base diameter is 20cm, so the radius is half of that, which is 10cm.

Therefore, the volume of the cylinder is:

V = πr^2h

V = π(10cm)^2(5cm)

V = π(100cm^2)(5cm)

V = 500π cm^3

Hence, the volume of the cylinder is 500π cubic centimeters.

2.We are given that the height of the cylinder is 22 1/4 and the diameter is 2 2/5 times its height. First, we need to find the radius of the base.

The diameter of the base is 2 2/5 times the height, so we can write:

d = (12/5)h

Substituting in the given value of h, we get:

d = (12/5)(22 1/4) = 54.4 cm

Therefore, the radius of the base is:

r = d/2 = 27.2 cm

Now, we can use the formula for the volume of a cylinder:

V = πr^2h

Substituting in the values of r and h, we get:

V = π(27.2cm)^2(22 1/4 cm)

V ≈ 50,873.36 cm^3

Rounding to the nearest hundredth, we get:

V ≈ 50,873.36 cm^3 ≈ 50,873.35 cm^3

Hence, the volume of the cylinder is approximately 50,873.35 cubic centimeters.

Answer:

6/5 or 1 1/5

Step-by-step explanation:

Make a common denominator: 1/2 is equal to 5/10

7/10+5/10=12/10

12/10 simplified is 6/5

Answer:

\( - \frac{5 + 5 \sqrt{3} }{2} \)

Option A is the correct option.

Solution,

Multiply and divide by its conjugate.

\( \frac{5}{1 - \sqrt{3} } \times \frac{1 + \sqrt{3} }{1 + \sqrt{3} } \\ = \frac{5(1 + \sqrt{3)} }{(1 - \sqrt{3} )(1 + \sqrt{3)} } \\ = \frac{5 + 5 \sqrt{3} }{ {(1)}^{2} - { (\sqrt{3}) }^{2} } \\ = \frac{5 + 5 \sqrt{3} }{1 - 3} \\ = \frac{5 + 5 \sqrt{3} }{ - 2} \\ = - \frac{5 + 5 \sqrt{3} }{2} \)

hope this helps...

Good luck on your assignment..

Answer:

0

Step-by-step explanation:

.21 is closer to 0 than to 1

After rounding to the nearest whole number, we get;

⇒ 0

We have to given that;

A number is,

⇒ 0.21

And, Round 0.21 to the nearest whole number.

Since, We know that;

Whole numbers are defined from 0 to infinity.

Here, Number is, 0.21

Which is written as,

⇒ 0 < 0.21 < 1

Hence, 0.21 is closer to 0.

So, After rounding to the nearest whole number, we get;

⇒ 0

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Hello there. To graph this function, the best way is to find two points that are into the line and then pass a line through them.

Since the image of a line is all the real numbers, we can pick any point for x and find y that satisfy it.

Starting with x = 0, we have that f(0) = -3 * 0 + 4 = 4.

So the point (0, 4) is in the line.

Now, making x = 1, we have that f(1) = -3 * 1 + 4 = -3 + 4 = 1

So the point (1, 1) is in the line.

Graphing the function, we have:

This is the graph of this function.

Answer:480

Step-by-step explanation: (pemdas) hope this helps

111.6 can be written as 111 and 6 tenths when expressed in whole numbers.

To convert 111.6 into a whole number, you'll need to round it to the nearest integer. To do this, follow these steps:

1. Identify the decimal part of the number: In this case, it's 0.6.
2. Determine if the decimal part is greater than or equal to 0.5. If it is, round up. If not, round down. Since 0.6 is greater than or equal to 0.5, you'll round up.
3. Add 1 to the whole number part (if rounding up) or leave it as is (if rounding down). In this case, you'll add 1 to 111, which gives you 112.

So, when converting 111.6 into a whole number, you'll get 112.

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The correct conclusion is C.Reject the null hypothesis.

A hypothesis is an educated guess or proposed explanation for a phenomenon or observation that can be tested through further investigation or experimentation. It is a tentative statement that can be either supported or refuted by evidence.

Conclusion refers to the final part of something, typically a written piece, where the main points or arguments are summarized and a final decision or opinion is presented. It is often used to bring closure to a discussion or to provide a final statement on a topic.

The correct conclusion is C.

In hypothesis testing, the alpha (significance level) is the threshold used to determine whether the null hypothesis should be rejected or not. If the p-value (observed significance level) is less than the alpha, it means that the observed data is unlikely to have occurred by chance alone. In this case, the p-value is 0.001, which is less than the alpha of 0.025, so the correct conclusion is to reject the null hypothesis.

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The employee's yearly salary is calculated as $37,440 using the arithmetic operations.  

The employee earns $18 per hour and works 40 hours per week. To calculate the weekly salary, we multiply the hourly wage by the number of hours worked:

Weekly salary = Hourly wage × Hours worked per week

Weekly salary = $18/hour × 40 hours/week = $720

Next, to calculate the yearly salary, we use the multiplication operation the weekly salary by the number of weeks in a year:

Yearly salary = Weekly salary × Weeks in a year

Yearly salary = $720/week × 52 weeks/year = $37,440

Therefore, the employee's yearly salary is $37,440. This calculation assumes a 40-hour work week and 52 weeks in a year. It's important to note that this calculation does not account for overtime pay or any other additional benefits or deductions that may affect the employee's total annual income.

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Since 2k2 + 5k + 4 is an integer, it follows that n2 + 3n + 5 is odd.

Direct proof of the statement (in order):

Let T be even. By the definition of even, there exists an integer k such that T = 2k.

Let n be odd. By the definition of odd, there exists an integer k such that n = 2k + 1.

It follows thatn

2 + 3n + 5 = (2k + 1)2 + 3(2k + 1) + 5

= 4k2 + 10k + 9

= 2(2k2 + 5k + 4) + 1.

Since 2k2 + 5k + 4 is an integer, it follows that n2 + 3n + 5 is odd.

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A. 6^12 . 2^3

This is correct

Answer:

A

Step-by-step explanation:

You would multiply the exponents. So for the first one 4x3=12, which is why it is 6^12

Answer:

Neither

Step-by-step explanation:

Neither is a perfect square

1^2 = 1

2^2 = 4

3^2 = 9

4^2 = 16

5^2 = 25

These are perfect squares

Answer:

Step-by-step explanation:

neither 20 nor 24 is perfect square.

\(1 \times 1 = 1 \\ 2 \times 2 = 4 \\ 3 \times 3 = 9 \\ 4 \times 4 = 16 \\ 5 \times 5 = 25 \\ 6 \times 6 = 36 \\ 7 \times 7 = 49 \\ 8 \times 8 = 64 \\ 9 \times 9 = 81 \\ 10 \times 10 = 100\)

These are perfect square.

hope this helps

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