Because each roll has six possible even values (2, 4, 6, 8, 10, and 12) and only five possible odd values (3, 5, 7, 9, and 11), the dice should show even values more often than odd values. Do you agree with this statement? Explain.

The average time in hours from when a machine breaks until it is fixed is approximately 11.3 hours.

Given,

Benny's arcade has five video game machines

The average time between failures = 34 hours

The maintenance engineer can repair a machine in about = 13 hours

The failure time and repair times are both exponentially distributed

The formula for the mean of an exponential distribution is mean = 1/λ where λ is the rate parameter of the distribution.

In this problem, the rate parameter of both the failure time and repair time is the reciprocal of their respective averages. Therefore,

λ_f = 1/34λ_r = 1/13

Now, let's find the average time from when a machine breaks until it is fixed using the fact that the sum of two independent exponential distributions with rate parameters λ1 and λ2 is itself an exponential distribution with rate parameter λ1+λ2.

So, the rate parameter for the time from when a machine breaks until it is fixed is λ_f+λ_r = 1/34+1/13

= 0.0885 hours⁻¹ (approximately)

Hence, the average time from when a machine breaks until it is fixed is mean = 1/λ= 1/0.0885 ≈ 11.3 hours (approximately).

Therefore, the average time in hours from when a machine breaks until it is fixed is approximately 11.3 hours.

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The radical form of the given expression \((3^\frac{2}{3})^\frac{1}{6}\) is \(\sqrt[9]{3}\). So the option B is correct.

The given expression is \((3^\frac{2}{3})^\frac{1}{6}\).

We have to express the given expression with a rational exponent as a radical expression.

As we can see that in the given expression have two power.

We firstly solve their power.

We using the Law of Power of a Power.

In this law, if any variable have a two power as \((a^m)^n\) so their have multiplication relation between their power.

So \((a^m)^n=a^{mn}\)

Now we solving the given expression using that rule.

The expression is \((3^\frac{2}{3})^\frac{1}{6}\).

Simplifying the power first.

\((3^\frac{2}{3})^\frac{1}{6}=(3)^{\frac{2}{3}\times\frac{1}{6}}\)

Now simplifying

\((3^\frac{2}{3})^\frac{1}{6}=(3)^{\frac{2}{18}}\)

\((3^\frac{2}{3})^\frac{1}{6}=(3)^{\frac{1}{9}\)

Since the power is \(\frac{1}{9}\) which means variable \(3\) have in radical.

Now expressing the simplified variable in the form of radical and the power of radical should be \(9\).

\((3^\frac{2}{3})^\frac{1}{6}=\sqrt[9]{3}\)

Hence, the radical form of the given expression \((3^\frac{2}{3})^\frac{1}{6}\) is \(\sqrt[9]{3}\). So the option B is correct.

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Answer:

positive    +

negative   -

zero          0

hope this help

Answer: y= (5/7)x+2

Step-by-step explanation: use y2-y1/x2-x1 to find slope/m. The y-int/b is (0,2). Y=Mx+b and now y= (5/7)x+2

Answer:

1408

What you have to do is 645 + 763 = 1408 that's how you doing I think so and sorry if I did it wrong

A linear system with 3 equations and 4 variables by representing it with an augmented matrix and bringing the matrix to reduced row-echelon form can be solved.

A mathematical representation of a system based on the application of a linear operator is known as a "linear system" in systems theory. Ordinarily, compared to nonlinear systems, linear systems display much simpler features and properties. The automatic control theory, signal processing, and telecommunications all heavily rely on linear systems as a mathematical abstraction or idealisation.

Linear systems, for instance, are frequently used to model the propagation medium for wireless communication systems. An operator, H, that converts an input, x(t), into an output, y(t), a kind of black box description, can be used to describe a general deterministic system.

The superposition principle, or alternatively both the additivity and homogeneity properties, must be satisfied by a system to be considered linear, and only then.

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Answer:

a = 6, b = 6√2, c = 2√3, d = 6

Step-by-step explanation:

Applying,

sin60° = a/4√3

Therefore,

a = sin60°×4√3

a = (√3/2)(4√3)

a = 3×2

a = 6

Also,

cos60 = c/4√3

c = cos60×4√3

c = 0.5×4√3

c = 2√3

also,

tan45 = a/d

d = a/tan45

d = 6/(1)

d = 6

Also,

sin45 = a/b

b = a/sin45

b = 6/(1/√2)

b = 6√2

Answer:

Approximate solution is 541.

Step-by-step explanation:

y' = 2xy, Δx = 0.4.

Make a table:

x       y            y'            y' Δx + y

1        2           4             4*0.4 +  2 = 3.6   <---this is the new y value.

1.4    3.6        10.08      7.632

1.8    7.632    27.48     18.624

2.2  18.624   81.95      51.70

2.6  51.70    268.85   159.24

3     159.24  955.44    541.4

The coefficients obtained by the student may be less efficient and have larger standard errors compared to the professor's regression.

If the student enters each observation twice, resulting in a sample size of 100 instead of the original 50, the assumption of independent observations is violated in Ordinary Least Squares (OLS) regression. The OLS assumption assumes that the observations are independent, meaning that the value of one observation does not depend on the value of another observation.

In this case, the student's dataset contains repeated observations, which introduces dependence between observations. This violation of the independence assumption can lead to biased and inconsistent parameter estimates in the regression analysis.

Regarding the slope coefficients, if the student runs a regression using the duplicated data, the estimated coefficients may be different from the professor's regression. The duplication of observations inflates the sample size, potentially affecting the precision and accuracy of the estimates.

However, the direction and overall relationship between the variables may still be captured by the student's regression, although the estimates may not be as reliable.

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Answer:

B) 34°

Step-by-step explanation:

Answer:

B) 34°

Step-by-step explanation:

∠B = 180° - 144°

∠B = 36°

∠D = 180° - (110° + 36°)

∠D = 180° - 146°

∠D = 34°

The cost of 1 kilogram of pears is $5.70.

The cost of 1 kilogram of pears can be found by using the given information and setting up an equation. First, let's repeat the question: "1 kilogram of pears cost as much as 1.5 kilograms of apples. Alex paid $34.20 for 4 kilograms of pears and 3 kilograms for apples. How much did 1 kilogram of pears cost?"

Let's assign variables to the unknowns:

- P = cost of 1 kilogram of pears

- A = cost of 1 kilogram of apples

From the question, we know that:

- 1P = 1.5A - 4P + 3A = 34.20

Now, we can use substitution to solve for P.

1. Substitute 1.5A for P in the second equation: 4(1.5A) + 3A = 34.20

2. Simplify: 6A + 3A = 34.20

3. Combine like terms: 9A = 34.20

4. Solve for A: A = 34.20/9 A = 3.8

5. Substitute 3.8 for A in the first equation: 1P = 1.5(3.8)

6. Solve for P: P = 5.7

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Answer:

his gives us that Chris is walking 69 feet per minute faster than Heidi.

Step-by-step explanation:

1 mile is equal to 5,280 feet, we can multiply 3 by 5,280 to find that Heidi is walking 15,840 feet per hour.

Next, we need to convert both speeds to feet per minute. Since there are 60 minutes in an hour, we can divide both speeds by 60 to convert them to feet per minute. This gives us that Heidi is walking 264 feet per minute and Chris is walking 333 feet per minute.

Finally, to find out how much faster Chris is walking than Heidi, we can subtract Heidi's speed in feet per minute from Chris's speed in feet per minute.

Step-by-step explanation:

2 basic objects are combined to this figure.

a prism or box of 20×8×18

a diagonally cut box (so, triangle shaped) of 8×18 base area and 10 being the triangle Hypotenuse.

the volume of the box is easy :

20×8×18 = 2,880

for the triangle-shaped half-box we need to get the height (the third leg of the side triangle).

we get this by Pythagoras

Hypotenuse² = leg1² + leg2²

10² = 8² + height²

100 = 64 = height²

36 = height²

height = 6

so, the area of a side triangle is

8×6/2 = 8×3 = 24

and the volume of the half-box is

24 × 18 = 432

so, the total volume of the figure is

2,880 + 432 = 3,312

To find the possible values of k, we need to calculate the determinant of matrix D and set it equal to 1024.

Given matrix D:

D = | k 0 0 |

| 3 k² k³ |

| 0 kª k³ kº |

| k k k |

| 0 0 0 |

| k¹⁰ |

The determinant of D can be calculated by expanding along the first row or the first column. Let's expand along the first row:

det(D) = k(det | k³ k k |

| 0 k³ kº |

| 0 0 k¹⁰ |)

- 0(det | 3 k² k³ |

| 0 kª k³ |

| k k k |)

+ 0(det | 3 k² k³ |

| k k k |

| k k k |)

Simplifying further, we have:

det(D) = k(det | k³ k k |

| 0 k³ kº |

| 0 0 k¹⁰ |)

Now, we can calculate the determinant of the 3x3 submatrix:

det | k³ k k |

| 0 k³ kº |

| 0 0 k¹⁰ |

This determinant can be found by expanding along the first row or the first column. Expanding along the first row gives us:

det = k(k³(kº) - 0(k)) - 0(0(k¹⁰)) = k⁴kº = k⁴+kº

Now, we can set det(D) equal to 1024 and solve for k:

k⁴+kº = 1024

Since we are looking for all possible values of k, we need to solve this equation for k. However, solving this equation may require numerical methods or approximations, as it is a quartic equation.

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Answer:

11/8 or 1.375

Step-by-step explanation:

2 3/4 => 11/4

1/2 x 11/4 = 11/8

Answer:

10.5

Step-by-step explanation:

Break the problem down into small parts:

2 to the power of 3= 8

8+7+6=

15+6=21

21/2

21 divided by 2 is 10.5

Hope this helps!

A) The 96% confidence interval for the proportion of defective items in the whole shipment is (0.064, 0.176).

B) We have sufficient evidence to disprove the manufacturer's claim at the 15% level of significance, but not at the 4% level.

a) The point estimate for the proportion of defective items in the whole shipment is 0.12 (24/200). Using a 96% confidence level and the normal distribution, the margin of error is 0.056. Therefore, the 96% confidence interval for the proportion of defective items in the whole shipment is (0.064, 0.176).

b) The null hypothesis is that the true proportion of defective items in the shipment is at most 0.1, while the alternative hypothesis is that it is greater than 0.1. Using the sample proportion of 0.12, the test statistic is z = (0.12-0.1)/√(0.1*0.9/200) = 1.33.

At the 4% level of significance, the critical value for a one-tailed test is 1.645. Since 1.33 < 1.645, we fail to reject the null hypothesis. At the 15% level of significance, the critical value for a one-tailed test is 1.036. Since 1.33 > 1.036, we reject the null hypothesis in favor of the alternative hypothesis at the 15% level of significance.

Therefore, we have sufficient evidence to disprove the manufacturer's claim at the 15% level of significance, but not at the 4% level.

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The Root Test is inconclusive and we cannot determine whether the series converges or diverges using this test alone.

To determine whether the series is convergent or divergent, we can use the Root Test. The Root Test states that if the limit of the nth root of the absolute value of the nth term of a series approaches a value less than 1, then the series converges absolutely. If the limit approaches a value greater than 1 or infinity, then the series diverges.

Using the Root Test on the given series, we have:

lim(n→∞) (|n^2 + 45n^2 + 7|)^(1/n)
= lim(n→∞) [(n^2 + 45n^2 + 7)^(1/n)]
= lim(n→∞) [(n^2(1 + 45/n^2) + 7/n^2)^(1/n)]
= lim(n→∞) [(n^(2/n))(1 + 45/n^2 + 7/n^2)^(1/n)]
= 1 * lim(n→∞) [(1 + 45/n^2 + 7/n^2)^(1/n)]

Since the limit of the expression in the brackets is 1, the overall limit is also 1. Therefore, the Root Test is inconclusive and we cannot determine whether the series converges or diverges using this test alone.

However, we can use other tests such as the Ratio Test or the Comparison Test to determine convergence or divergence.

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The child advocate collects data by randomly selecting 4 out of the 25 state orphanages. In each of the four selected orphanages, the child advocate surveys every child.

This approach allows the child advocate to obtain information from a representative sample of children in state orphanages. By surveying every child in the selected orphanages, the child advocate ensures that no child is excluded from the data collection process. This method provides a comprehensive understanding of the experiences, needs, and concerns of the children in the four chosen orphanages.

By collecting data in this manner, the child advocate can gather valuable insights that can inform policies and interventions to improve the well-being and support for children in state orphanages.

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Therefore, one rotation (360 degrees) takes 0.5 seconds.

To determine how long one rotation takes in seconds, we can use the formula:

Time = 60 seconds / Cadence

In this case, the cadence is given as 120 rotations per minute (rpm), so we can substitute the value into the formula:

Time = 60 seconds / 120 rpm

Simplifying the equation:

Time = 0.5 seconds / rotation

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Answer:

B. m-3=m+3

Step-by-step explanation:

Because the others have a solution such as 0 and -1.

And That would eliminate D

Answer:

122

Step-by-step explanation:

180 degrees is in a triangle

180- 45-15= 122

thats how you get your answer

. you subtract the two points from 180 to get the missing point

- AKIA

Answer:

3

Step-by-step explanation:

We have to find the smallest possible factor of 15 and multiple of 3.

The smallest factor of any positive integer is 1.

The smallest multiple of any positive integer is the integer itself. So the smallest multiple of 3 would be 3 itself.

\(1 * 3 = 3\)

And 3 is the answer.

Four special two digit numbers exist: 1, 2, 145, and 40585.

A special two-digit number is one in which the original two-digit number is equal to the sum of the number's digits plus the product of its digits. Take the number's initial and last digits out, then add and multiply each digit independently. After that, multiply the two-digit number by the sum and product of its digits and then compare the result to the original value. If they match, it qualifies as a special two-digit number; otherwise, it does not.

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Answer:

Step-by-step explanation:

a=0.5

The value of θ from the trigonometric relation is given by θ = ( π/6 ) + 2πn and θ = ( 5π/6 ) + 2πn

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 trigonometric relation be represented as A

Now , the equation will be

sin θ = 1/2   be equation (1)

On simplifying the equation , we get

The values of θ where sin θ is 1/2 are 30° and 150°

So , the multiples of 30° and 150° of sin will also result in 1/2

Now , the radian form of θ is given by

sin θ = 1/2  ,  when θ = ( π/6 ) + 2πn and θ = ( 5π/6 ) + 2πn

Hence , the trigonometric relation is solved

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To evaluate (6.7 * 10⁻¹⁶) - (8.2 * 10⁻¹⁷), Celia should Subtract the numbers to get the difference.

Step 1: Make the powers of 10 the same To make the powers of 10 the same, adjust the second number, which is 8.2 × 10⁻¹⁷, to have the same power of 10 as the first number, which is 6.7 × 10⁻¹⁶.

Since 10⁻¹⁷ is a smaller power of 10 than 10⁻¹⁶, we must multiply the numerator and denominator of 8.2 × 10⁻¹⁷ by 10 to obtain an equivalent value that has the same power of 10 as the first number. Therefore, we get;8.2 × 10⁻¹⁷ = (8.2 × 10⁻¹⁷) × (10 / 10)

= 82 × 10⁻¹⁸.

Step 2: Subtract the numbers Now that we have the same power of 10 in both numbers, we can subtract them. 6.7 × 10⁻¹⁶ - 82 × 10⁻¹⁸ = 6.7 × 10⁻¹⁶ - 0.0082 × 10⁻¹⁶ = 6.6918 × 10⁻¹⁶.

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