Explain why subtracting a positive number is the same as adding its inverse.

To test the claim that the new production method has lengths with a standard deviation different from 3.5 cm, a hypothesis test is conducted at the 0.10 significance level. A random sample of 17 steel rods is taken, resulting in a sample standard deviation of 4.5 cm.

To test the claim, a hypothesis test is conducted using the sample data. The null hypothesis (H0) states that the standard deviation of the new production method is equal to 3.5 cm, while the alternative hypothesis (H1) states that it is different from 3.5 cm.

The test statistic used for comparing standard deviations is the F-test. However, since the sample size is small (n = 17), the sample standard deviation is used instead.

At the 0.10 significance level, a critical value is determined based on the degrees of freedom, which is n - 1. The critical value is compared to the test statistic calculated using the sample standard deviation.

If the test statistic falls within the rejection region (beyond the critical value), the null hypothesis is rejected, indicating that the standard deviation of the new production method is different from 3.5 cm. If the test statistic does not fall within the rejection region, there is not enough evidence to reject the null hypothesis, and it can be concluded that the standard deviation of the new method is not significantly different from 3.5 cm.

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Answer:

154.5 cm2

Step-by-step explanation:

height=3

lenght=8.5

breadth=4.5

the ans is 154.5 cm2

Answer:

Option 1 is a linear function.

The margin of error for a 95% confidence interval in the first sample is approximately 0.595 cups. The margin of error (ME) for a confidence interval is calculated using the formula:

ME = z * (standard deviation / √n)

where z is the z-score corresponding to the desired confidence level, standard deviation is the population standard deviation, and n is the sample size.

In the first sample, we have a sample size of 68, a mean of 2.37 cups, and a known standard deviation of 2.4 cups. For a 95% confidence level, the corresponding z-score is approximately 1.96.

ME = 1.96 * (2.4 / √68)

  ≈ 1.96 * (2.4 / 8.246)

  ≈ 1.96 * 0.291

  ≈ 0.595

Therefore, the margin of error for a 95% confidence interval in the first sample is approximately 0.595 cups.

(b) Similarly, in the second sample, we have a sample size of 16, a mean of 4.7 cups, and a standard deviation of 2.5 cups.

ME = 1.96 * (2.5 / √16)

  ≈ 1.96 * (2.5 / 4)

  ≈ 1.96 * 0.625

  ≈ 1.225

Therefore, the margin of error for a 95% confidence interval in the second sample is approximately 1.23 cups.

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Answer:

25h + 12

Explanation:

21h -10h + 14h + 16 -9 +5  ( group term )

25h + 12                             ( simplified )

Answer:

\(25h+12\)

Step-by-step explanation:

To do this, we need to combine like terms:

\(21h-10h+14h+16-9+5\)

Combine terms that have "h" with each other.

\(11h+14h+16-9+5\)

\(25h+16-9+5\)

Now, combine the rest of the terms that don't have "h".

\(25h+7+5\)

\(25h+12\)

Given the system of equations:

we can solve it using elimination by directly adding both equations to get the following:

now that we have that x=3, we can find y using this value on any of the two equations:

therefore, the solution of the system is (3,0)

The $1314^\text{th}$ digit past the decimal point is 2.

To find the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$, we can use long division to compute the decimal expansion of the fraction.

The long division of $\frac{5}{14}$ is as follows:

```

0.35    <-- Quotient

-----

14 | 5.00

   4.2    <-- Subtract: 5 - (14 * 0.3)

   -----

     80   <-- Bring down the 0

     70    <-- Subtract: 80 - (14 * 5)

     -----

     100   <-- Bring down the 0

      98    <-- Subtract: 100 - (14 * 7)

      -----

       20   <-- Bring down the 0

       14    <-- Subtract: 20 - (14 * 1)

       -----

        60   <-- Bring down the 0

        56    <-- Subtract: 60 - (14 * 4)

        -----

         40   <-- Bring down the 0

         28    <-- Subtract: 40 - (14 * 2)

         -----

         120   <-- Bring down the 0

         112    <-- Subtract: 120 - (14 * 8)

         -----

           80   <-- Bring down the 0

           70    <-- Subtract: 80 - (14 * 5)

           -----

           ...

```

We can see that the decimal expansion of $\frac{5}{14}$ is a repeating decimal pattern with a repeating block of digits 285714. Therefore, the $1314^\text{th}$ digit past the decimal point is the same as the $1314 \mod 6 = 0^\text{th}$ digit in the repeating block.

Since $1314 \mod 6 = 0$, the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$ is the first digit of the repeating block, which is 2.

So, the $1314^\text{th}$ digit past the decimal point is 2.

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We can first consider the number of ways the two people who sit together can be chosen. There are 4 ways to choose the pair of people who sit together (i.e., person 1 and 2, person 2 and 3, person 3 and 4, or person 1 and 4).

Once we have chosen the pair of people who sit together, we can treat them as a single entity, reducing the problem to arranging three entities (two individuals and one pair) in a row. There are 3! = 6 ways to arrange these three entities.

Finally, the pair of people who sit together can be arranged in two ways (i.e., left to right or right to left) within their pair.

Therefore, the total number of different ways four people can sit in a row at the opera if two of them sit together is 4 x 6 x 2 = 48.

Answer: factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly. The other factors of 12 are 1, 2, 4, and 12.

Step-by-step explanation:

Todd use to save $500 in less than 16 weeks and have $20 extra in Plan C.

In plan A,

    Plans for saving = $500

  Amount of saving each week = $20

∴ Number of weeks needed to make goal = (500 ÷ 20) (by using division)

                                                                       = 25

In plan B,

    Plans for saving = $500

   Amount of saving each week = $30

∴ Number of weeks needed to make goal = (500 ÷ 30) (by using division)

                                                                       = 17

In plan C,

    Plans for saving = $500

   Amount of saving each week = $40

∴ Number of weeks needed to make goal = (500 ÷ 40) (by using division)

                                                                       = 13

In plan D,

    Plans for saving = $500

   Amount of saving each week = $50

∴ Number of weeks needed to make goal = (500 ÷ 50) (by using division)

                                                                       = 10

So, Todd use to save $500 in less than 16 weeks and have $20 extra in Plan C.

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Answer:

\(5\sqrt{2}\)

Step-by-step explanation:

Answer:

the answer is 1+ (-13)= -12

The best measure of variability is the standard deviation.

Player A is the most consistent, with an IQR of 1.5.

Standard deviation is defined as the square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean.

The table shows the number of goals made by two hockey players.

Player A:

2, 3, 1, 3, 2, 2, 1, 3, 6

Using  a statistics calculator, we have:

Mean = 2.56

S.D. = 1.51

Player B:

1, 4, 5, 1, 2, 4, 5, 5, 11

S.D. = 3.03

The best measure of variability is the standard deviation.

Player A is the most consistent, with an IQR of 1.5.

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Based on the empirical rule, the probability that the hedge fund returns over 50% next year is approximately 5%.

The empirical rule, also known as the 68-95-99.7 rule, is a statistical guideline that applies to a normal distribution (also called a bell curve). It states that for a normal distribution:

Approximately 68% of the data falls within one standard deviation of the average.

Approximately 95% of the data falls within two standard deviations of the average.

Approximately 99.7% of the data falls within three standard deviations of the average.

In this case, we know the average return of the hedge fund is 26% per year, and the standard deviation is 12%. We want to approximate the probability that the fund returns over 50% next year.

To do this, we need to determine how many standard deviations away from the average 50% falls. This can be calculated using the formula:

Z = (X - μ) / σ

Where:

Z is the number of standard deviations away from the average.

X is the value we want to find the probability for (50% in this case).

μ is the average return of the hedge fund (26% per year in this case).

σ is the standard deviation (12% in this case).

Let's calculate the Z-value for 50% return:

Z = (50 - 26) / 12

Z ≈ 24 / 12

Z = 2

Now that we have the Z-value, we can refer to the empirical rule to estimate the probability. According to the rule, approximately 95% of the data falls within two standard deviations of the average. This means that there is a 95% chance that the hedge fund's return will fall within the range of (μ - 2σ) to (μ + 2σ).

In our case, the range is (26 - 2 * 12) to (26 + 2 * 12), which simplifies to 2 to 50.

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The descriptive statistics of the variables tota The mean of total_cases represents the average number of reported COVID-19 cases, while the mean of total_deaths represents the average number of reported COVID-19 deaths.

The measures of dispersion, such as standard deviation, indicate the spread or variability of the data points around the mean.

The mean of total_cases reveals the average magnitude of the spread of COVID-19 cases. A higher mean suggests a larger overall impact of the virus. The standard deviation quantifies the degree of variation in the total_cases data. A higher standard deviation indicates a wider range of reported cases, implying greater heterogeneity or inconsistency in the number of cases across different regions or time periods.

Skewness measures the asymmetry of the distribution. Positive skewness indicates a longer right tail, suggesting that there may be a few regions or time periods with exceptionally high case numbers. Kurtosis measures the shape of the distribution. Positive kurtosis indicates a distribution with heavier tails and a sharper peak, which implies the presence of outliers or extreme values in the data.

Similarly, the mean of total_deaths provides an average estimate of the severity of the COVID-19 outbreak. A higher mean indicates a greater number of deaths attributed to the virus. The standard deviation of total_deaths indicates the variability or dispersion of the death toll across different regions or time periods. Skewness and kurtosis for total_deaths provide insights into the shape and potential outliers in the distribution of death counts.

The means of total_cases and total_deaths offer average estimates of the impact and severity of COVID-19. The standard deviations indicate the variability or spread of the data, while skewness and kurtosis provide information about the shape and potential outliers in the distributions of the variables. These descriptive statistics help us understand the overall patterns and characteristics of COVID-19 cases and deaths.

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Answer:

69 - 52 = g

(g = 17)

Step-by-step explanation:

69 [total students] - 52 [no role] = g [those who got in]

69 - 52 = g            {simplify/combine like terms}

17 = g

g = 17

So, 17 students will be in the play

(could also be modeled as 52 + g = 69)

(this is because the only possibility for each student is to either not get in, or get in. So, if we add these two values up, we get the total number of students who auditioned).

(if you want to model the equation as such:

52 + g = 69

- 52          -52   {subtract 52 from both sides to isolate g}

g = 17)

The length of the side opposite the 60° angle in a triangle with angles of 45° and 75° and a known side length of 6 is approximately 5.196 units.

In a triangle, the sum of all angles is always 180°. Since we know two angles of the triangle, 45° and 75°, we can find the third angle by subtracting their sum from 180°:

180° - (45° + 75°) = 60°.

The triangle now has angles of 45°, 75°, and 60°.

We know the length of the side opposite the 45° angle is 6 units. To find the length of the side opposite the 60° angle, we can use the Law of Sines.

The Law of Sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides.

Applying this law, we have:

6/sin(45°) = x/sin(60°),

Solving for x, we find

x ≈ 5.196 units.

Therefore, the length of the side opposite the 60° angle is approximately 5.196 units.

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Answer:

They're not promise

Step-by-step explanation:

I did it on the calculator

I hope this helps youuu

Have a good day <3

Answer:The answer to the first one is 3.75 and for the second one it is 0.875

Step-by-step explanation:

hope it helps

Answer:

76.1

Step-by-step explanation:

x = FD

7/33.3 = 16/x

7x = 532.8

x ≈ 76.1

The specific range depends on the material properties and the energy levels involved.

The minimum and maximum frequencies for the acoustic and optic modes depend on the specific system or material under consideration. However, I can provide some general information.

Acoustic Mode:

The acoustic mode refers to the propagation of sound waves or vibrations in a material. In a solid, the acoustic mode can have different types, such as longitudinal and transverse modes.

The minimum frequency for the acoustic mode is typically determined by the size and physical properties of the material. In general, it can be close to zero for macroscopic objects or materials with low elasticity.

The maximum frequency for the acoustic mode depends on factors such as the speed of sound in the material and the characteristic dimensions of the system. It can range from a few kilohertz to several gigahertz.

Optic Mode:

The optic mode is related to the interaction of light with a material. It typically refers to the vibrations of charged particles (such as electrons) in a solid or the oscillations of electric or magnetic fields associated with photons.

The minimum frequency for the optic mode is typically determined by the energy gap between electronic states in the material. For example, in a semiconductor, the minimum frequency is usually in the infrared range.

The maximum frequency for the optic mode is not strictly defined, as it can extend into the terahertz, infrared, visible, ultraviolet, X-ray, and even gamma-ray regions. The specific range depends on the material properties and the energy levels involved.

It's important to note that these frequency ranges are general guidelines and can vary depending on the specific system or material being studied.

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The correct statements about these elements are as follows: Water is not a good conductor and Iron is a transition metal

This is option C and D

Water is a poor conductor of electricity. It is considered to be a non-conductor or insulator because it does not readily allow the flow of electric current. However, it does have a small amount of conductivity due to the presence of dissolved ions. D. Iron is a transition metal: This statement is also correct. Iron is indeed a transition metal.

Transition metals are found in the middle of the periodic table, between the main group elements on the left and the metals on the right. They exhibit a wide range of chemical properties and have partially filled d orbitals. Iron is a particularly well-known transition metal and is commonly used in various applications, such as in construction, manufacturing, and as a component in steel.

So, the correct answer is C and D

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The probability of both rice and carrots being served with dinner is 23.4%.

The probability of Alvin's mother serving rice with dinner can be expressed using the formula P(Rice) = 0.78. This means that the probability of Alvin's mother serving rice with dinner is 78%. The probability of Alvin's mother serving carrots with dinner can be expressed using the formula P(Carrots) = 0.30. This means that the probability of Alvin's mother serving carrots with dinner is 30%. To calculate the combined probability of both rice and carrots being served with dinner, we can use the formula P(Rice and Carrots) = P(Rice) * P(Carrots) = 0.78 * 0.30 = 0.2340. This means that the probability of both rice and carrots being served with dinner is 23.4%.

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Answer:

-----------------

Find each area and then find their difference.

The difference is:

Answer:

the circumstance is 56.55

Answer:

Step-by-step explanation:

I'm going to walk through this analytically, so I will have to assign some variables to angles that are not marked. Pay close attention so you can follow the logic.

The angle at the top left next to and to the left of 40 will be "x", and the one to the right of 40 will be "y". Because that angle is a right angle, then we know that

x + y + 40 = 90 and

x + y = 50.

We also know that, by the Triangle Angle-Sum Theorem, the 2 triangles that contain alpha and beta will add up to equal 360, 180 apiece. So now we have:

x + 90 + α + y + 90 + β = 360.

Let's regroup a bit:

x + y + α + β + 90 + 90 = 360 and

(x + y) + α + β + 180 = 360.

But we know from above that x + y = 50, so

50 + α + β + 180 = 360 and

230 + α + β = 360 and

α + β = 130. There you go!

Answer:

α + β = 130

Step-by-step explanation:

∠ A = ∠ C = 90°

The sum of the 3 angles in a triangle = 180°

vertex angle at D inside the Δ = 180 - (90 + α ) ← Δ on left

vertex angle at D inside the Δ = 180 - (90 + β ) ← Δ on right

∠ ADC = 90° thus

180 - (90 + α) + 180 - (90 + β) + 40 = 90

180 - 90 - α + 180 - 90 - β + 40 = 90, that is

220 - α - β = 90 (add α and β to both sides )

220 = 90 + α + β (subtract 90 from both sides )

130 = α + β

A. To save for her payout annuity with an ordinary annuity set up thirty years before her retirement, Holly Krech must make a monthly payment of $175.97.

B. If she sets up the ordinary annuity twenty years before her retirement, Holly Krech must make a monthly payment of $432.00.

To calculate the monthly payment for an ordinary annuity set up thirty years before retirement, we can use the formula for the present value of an ordinary annuity. Given the deposit amount of $218,437.048 and the total amount received from the annuity of $432,000, and solving for the monthly payment, we find that Holly must make a monthly payment of $175.97.

For an ordinary annuity set up twenty years before retirement, we use the same formula for present value. With the deposit amount and total amount received unchanged, we solve for the monthly payment, which comes out to be $432.00.

It's important to note that the monthly payment increases when the annuity is set up closer to the retirement date. This is due to the shorter time period available for saving, resulting in a higher required contribution to reach the desired payout amount.

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Answer:15m

Step-by-step explanation:

The volume of a cylinder= πr^2h

Radius=9m

Volume=3818

Height=?

3818=22/7 x 9^2 x h

26726=22 x 81 xh

26726=1782h

H = 14.9

Height= 15m

If there is something that is not clear, let me know