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The probability is approximately 0.9167 or 91.67%.

To find the probability that the sum of two dice numbers does not exceed 10, we need to determine the favorable outcomes (sums less than or equal to 10) and the total possible outcomes when rolling two dice.

There are 36 possible outcomes when rolling two dice because each die has six faces (1, 2, 3, 4, 5, and 6), and the total number of outcomes is obtained by multiplying the number of outcomes for each die (6 * 6 = 36).

Now let's determine the favorable outcomes (sums less than or equal to 10):

When the sum is 2: There is only one combination (1 + 1).

When the sum is 3: There are two combinations (1 + 2 and 2 + 1).

When the sum is 4: There are three combinations (1 + 3, 2 + 2, and 3 + 1).

When the sum is 5: There are four combinations (1 + 4, 2 + 3, 3 + 2, and 4 + 1).

When the sum is 6: There are five combinations (1 + 5, 2 + 4, 3 + 3, 4 + 2, and 5 + 1).

When the sum is 7: There are six combinations (1 + 6, 2 + 5, 3 + 4, 4 + 3, 5 + 2, and 6 + 1).

When the sum is 8: There are five combinations (2 + 6, 3 + 5, 4 + 4, 5 + 3, and 6 + 2).

When the sum is 9: There are four combinations (3 + 6, 4 + 5, 5 + 4, and 6 + 3).

When the sum is 10: There are three combinations (4 + 6, 5 + 5, and 6 + 4).

Adding up the favorable outcomes, we get: 1 + 2 + 3 + 4 + 5 + 6 + 5 + 4 + 3 = 33.

Therefore, the probability that the sum of the two dice numbers does not exceed 10 is given by:

Probability = Favorable outcomes / Total outcomes = 33 / 36 = 11/12 ≈ 0.9167.

So, the probability is approximately 0.9167 or 91.67%.

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The correct decision in a hypothesis test when the data produces a t-statistic that is in the critical region is to reject the null hypothesis.

This is because a t-statics in the critical region indicates that the differences between the sample mean and the population mean are statistically significant. This means that the data indicates that the null hypothesis is wrong and that the alternative hypothesis is true. In a hypothesis test, the null hypothesis is what the researcher is trying to disprove. It is the general statement that suggests that there is no difference between the sample mean and the population mean. The alternative hypothesis is what the researcher is attempting to prove. It suggests that there is a difference between the sample mean and the population mean. Therefore, when the data produces a t-statistic that is in the critical region, it indicates that the alternative hypothesis is true. When a t-statistic is in the critical region, it means that the result is statistically significant. This means that the differences between the sample mean and the population mean are unlikely to have occurred by chance and that the alternative hypothesis is likely to be true. Therefore, when the data produces a t-statistic that is in the critical region, the correct decision is to reject the null hypothesis and accept the alternative hypothesis.

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The integral of 2x / (5(5 - 4x²)¹/²) with respect to x simplifies to (1/5) * arcsin(2x/5) + C, where C is the constant of integration.

To solve the integral, we can start by simplifying the denominator. Notice that we have (5 - 4x²)¹/², which can be written as √(5 - 4x²).

Now, let's proceed with the integration step by step:

Multiply the numerator and denominator by √(5 - 4x²) to rationalize the denominator:

∫(2x / (5(5 - 4x²)¹/²)) dx = ∫(2x√(5 - 4x²) / (5(5 - 4x²))) dx

Separate the terms and simplify the integral:

∫(2x√(5 - 4x²) / (5(5 - 4x²))) dx = (2/5) ∫(x / √(5 - 4x²)) dx

Perform a substitution by letting u = 5 - 4x²:

Differentiate u with respect to x: du/dx = -8x

Rearrange to solve for dx: dx = -(1/8x) du

Substituting the values, the integral becomes:

(2/5) ∫(x / √u) (-1/8x) du

= -(1/40) ∫(1 / √u) du

Integrate the expression:

-(1/40) ∫(1 / √u) du = -(1/40) * 2√u + C

= -(1/20)√(5 - 4x²) + C

Simplify the expression:

-(1/20)√(5 - 4x²) + C = (1/20)√(4x² - 5) + C

Therefore, the final result is (1/20)√(4x² - 5) + C, where C is the constant of integration.

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Answer:

0.9333=9333 / 10000

Step-by-step explanation:

Rewrite the decimal number as a fraction with 1 in the denominator

0.9333=0.9333 / 1

Multiply to remove 4 decimal places. Here, you multiply top and bottom by 104 = 10000

0.9333 / 1   ×   10000 / 10000  =  9333 / 10000

In conclusion,

0.9333  =  9333 / 10000

To model the consumption of Coca-Cola in Russia, a logistic model can be used. With an initial average consumption of 2 servings in 1993 and a doubling time of 2 years, the model can predict when the average consumption reached 50 servings per year.

A logistic model describes the growth of a population or a quantity that initially grows exponentially but eventually reaches a saturation point. The logistic model is given by the formula P(t) = K / (1 + e^(-r(t - t0))), where P(t) represents the quantity at time t, K is the saturation point, r is the growth rate, and t0 is the time at which the growth starts.

In this case, the initial consumption in 1993 is 2 servings, and the saturation point is 100 servings per year. The doubling time of 2 years corresponds to a growth rate of r = ln(2) / 2. Plugging these values into the logistic model, we can solve for t when P(t) equals 50.

To find the approximate year when the average consumption reached 50 servings per year, we round the value of t to the nearest year.

By using the logistic model with the given parameters, we can predict that the average consumption of Coca-Cola in Russia reached 50 servings per year approximately [insert predicted year] to the nearest year.

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Answer:

1/10

0.1

Step-by-step explanation:

Answer:

C. 59

Step-by-step explanation:

Hello There!

Remember the angles in a triangle add up to equal 180

So if we want to find a missing angle we subtract the given angles ( in this case 65 and 56) from 180

So missing angle = 180 - 65 - 56

180 - 65 = 115

115 - 56 = 59

So we can conclude that the missing angle has a measure of 59 degrees

Answer:

C: 59

Step-by-step explanation: His explanation is correct, I did it myself.

Kay deposited (c)$93.44  in cash and coins.

Money or coins that are legal tender can be used to pay for goods, debts, or services. Additionally, as stated by a corporation, it occasionally includes the worth of assets that can be quickly converted into cash. In its physical form, cash is another name for money. Bank accounts and marketable securities, such as government bonds and banker's acceptances, are typically included in the definition of "cash" in a business context.

We proceed from the whole backward. The amount deducted for cash received is first added back,

498.01+213.51 = 711.52

Each cheque that was deposited is then subtracted:

711.52-40.25 = 671.27

671.27-57.68 = 613.59

613.59-520.15 = 93.44

She started with (c) $93.44 in cash and coins.

Correct Question :

How much did kay deposit in cash and coins? a. $404.57 b. $213.51 c. $93.44 d. $284.50

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The extraction efficiency of liquid-liquid extraction (LLE) depends on the hydrophobicity (D) of the chemical to be extracted and the number of extractions. In this case, a water sample contaminated with PCB is being extracted using methylene chloride, with a partition coefficient (D) of 25.

To calculate the extraction efficiency, we need to consider two scenarios: one extraction with 30 mL of methylene chloride and three extractions with 10 mL each. The total volume of the water sample is 100 mL.

1. One extraction with 30 mL of methylene chloride:
  - The volume of methylene chloride used is 30 mL.
  - The extraction efficiency can be calculated using the formula:
    Extraction Efficiency = (Volume of Chemical Extracted / Total Volume of Chemical in the Water Sample) * 100
  - Volume of PCB extracted = D * Volume of Methylene Chloride used = 25 * 30 mL = 750 mL
  - Extraction Efficiency = (750 mL / 100 mL) * 100 = 750%

2. Three extractions with 10 mL each:
  - The volume of methylene chloride used in each extraction is 10 mL.
  - In each extraction, the volume of PCB extracted is given by D * Volume of Methylene Chloride used = 25 * 10 mL = 250 mL.
  - Total volume of PCB extracted in three extractions = 250 mL * 3 = 750 mL.
  - Extraction Efficiency = (750 mL / 100 mL) * 100 = 750%

Both methods of extraction, one with 30 mL and three with 10 mL each, result in the same extraction efficiency of 750%. Therefore, both methods are equally effective in extracting the PCB from the water sample.

In summary, the extraction efficiency depends on the hydrophobicity of the chemical and the number of extractions. In this case, both methods of extraction yield the same efficiency, indicating that the choice between one extraction with 30 mL or three extractions with 10 mL each does not affect the overall efficiency.

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The probability that if a random person is chosen from the group of lawyers, the person will be a liar is 38/45, or 0.84.

As a fraction: The probability is given as 38/45, which means that out of 45 people chosen randomly from the group of lawyers, 38 of them are expected to be liars.

As a decimal: To express the probability as a decimal, we divide the numerator (38) by the denominator (45):

38 ÷ 45 ≈ 0.8444444444444444

Rounded to two decimal places, this would be approximately 0.84.

As a percentage: To express the probability as a percentage, we multiply the decimal form by 100:

0.8444444444444444 * 100 ≈ 84.44%

Rounded to two decimal places, this would also be approximately 84.44%.

So, the probability that if a random person is chosen from the group of lawyers, the person will be a liar can be expressed as 38/45 as a fraction, approximately 0.84 as a decimal, or approximately 84.44% as a percentage.

This can be expressed as a fraction, decimal, or percentage, whichever is more helpful.

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The equation y + 9 = 2(x + 6) can be as y  = 2x + 3 written in Slope-Intercept form: y = mx + b.

We have been given a linear equation of x and y in the form of,

y + 9 = 2(x + 6)

To write this equation in the slope-intercept form i.e.

y = mx + b

we will have to rearrange the given linear equation

So,

y + 9 = 2(x + 6)

y + 9 = 2x + 12

Subtracting 9 both sides we get,

y  = 2x + 3

The equation obtained above is in the slope-intercept form

So, if we compare we find that the slope of the line is 2 and its intercept is 3.

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When graphing an exponential function, a T-chart is commonly used to determine the values. The correct answer is option A.

The T-chart employs positive real numbers since this is the most typical form of exponential function.

Exponential functions are utilized to represent processes that increase or decrease exponentially, as well as to model phenomena in many different disciplines, including science, economics, and engineering.

The exponential function can be represented by the following equation:

\(y=a^x\), where a is the base, x is the exponent, and y is the outcome.

When a is a positive number greater than one, the function is called exponential growth, while when a is a fraction between 0 and 1, the function is called exponential decay.

The T-chart is used to determine the values to use in the graph and connect the dots as required. Positive real numbers are used as the values in the T-chart in order to effectively graph the exponential function.

Therefore, the correct answer is option A.

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Answer:

x = -5

Step-by-step explanation:

Step 1: Write equation

-2x + 8 = 18

Step 2: Solve for x

Step 3: Check

Plug in x to verify it's a solution.

-2(-5) + 8 = 18

10 + 8 = 18

18 = 18

Answer:

x = -5

Step-by-step explanation:

-2x + 8 = 18

Subtract 8 from each side

-2x + 8-8 = 18-8

-2x = 10

Divide each side by -2

-2x/-2 = 10/-2

x = -5

Answer:

polynomial means more than 3 equation and trinomial means 3 equation

Data

Option 1

• $1000.50 per year until you are 21.

Option 2

• $1 this year, $2 next year, and so on, doubling the amount until 21.

Procedure

• Option 1

• Option 2

Based on these equations, we would need to know the year that she would start giving us money and if the account had some money previously, as it would be added as a constant.

For example, if we had already $800, then we would have to add as follows:

Answer: we would have to know if the account had some money previously.

Answer:

The card removed was number '4'.

Step-by-step explanation:

9+8= 17

17+6= 23

23+1=24

You then must divide 24 by 4:

24/4 = 6

Therefore the card removed must have been 4.

I hope that helped and I hope it is correct lol.

Find the circumference and area of a circle with a radius of 11 inches.

Answer:

69.12

Answer:

Step-by-step explanation:

Function given by the table represents a linear function.

a). Since, slope of a linear function passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is,

Slope = \(\frac{y_2-y_1}{x_2-x_1}\)

Slope of the linear function passing through two points (0, -5) and (2, 1) will be,

Slope = \(\frac{1+5}{2-0}=3\)

b). Let the equation of the function is,

y = mx + b

Where m = slope of the function

b = y-intercept

Here slope of the function 'm' = 3

y-intercept of he function = -5 [y-value of the function at x = 0]

Therefore, the function is,

y = 3x - 5

a) The 90% confidence interval for the population proportion is approximately (0.7777, 0.8423).

b) The 95% confidence interval for the population proportion is approximately (0.7737, 0.8463).

To calculate the confidence intervals for the population proportion, we can use the formula:

Confidence Interval = sample proportion ± margin of error

The margin of error can be calculated using the formula:

Margin of Error = critical value * standard error

where the critical value is determined based on the desired confidence level and the standard error is calculated as:

Standard Error = \(\sqrt{((p * (1 - p)) / n)}\)

Given that the sample proportion (p) is 0.81 and the sample size (n) is 500, we can calculate the confidence intervals.

a. 90% Confidence Interval:

To find the critical value for a 90% confidence interval, we need to determine the z-score associated with the desired confidence level. The z-score can be found using a standard normal distribution table or calculator. For a 90% confidence level, the critical value is approximately 1.645.

Margin of Error = \(1.645 * \sqrt{(0.81 * (1 - 0.81)) / 500)}\)

≈ 0.0323

Confidence Interval = 0.81 ± 0.0323

≈ (0.7777, 0.8423)

Therefore, the 90% confidence interval for the population proportion is approximately (0.7777, 0.8423).

b. 95% Confidence Interval:

For a 95% confidence level, the critical value is approximately 1.96.

Margin of Error = \(1.96 * \sqrt{(0.81 * (1 - 0.81)) / 500)}\)

≈ 0.0363

Confidence Interval = 0.81 ± 0.0363

≈ (0.7737, 0.8463)

Thus, the 95% confidence interval for the population proportion is approximately (0.7737, 0.8463).

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To calculate the duration of the shift, you need to subtract the clock-in time from the clock-out time.

In this case, the shift worker clocked in at 1730 hours (5:30 PM) and clocked out at 0330 hours (3:30 AM). However, since the clock is based on a 24-hour format, it's necessary to consider that the clock-out time of 0330 hours actually refers to the next day.

To calculate the duration of the shift, you can perform the following steps:

1. Calculate the duration until midnight (0000 hours) on the same day:

  - The time between 1730 hours and 0000 hours is 6 hours and 30 minutes (1730 - 0000 = 6:30 PM to 12:00 AM).

2. Calculate the duration from midnight (0000 hours) to the clock-out time:

  - The time between 0000 hours and 0330 hours is 3 hours and 30 minutes (12:00 AM to 3:30 AM).

3. Add the durations from step 1 and step 2 to find the total duration of the shift:

  - 6 hours and 30 minutes + 3 hours and 30 minutes = 10 hours.

Therefore, the duration of the shift was 10 hours.

The time study is 8 hours, the observed time is approximately 17.14 minutes, and the standard time is approximately 2.28 hours.

To solve the given problem, we can follow these steps:

1. Time study:

  First, we calculate the number of cycles using the formula: Number of cycles = Total time ÷ Cycle time.

  Given that the total time is 8 hours (8 × 60 = 480 minutes) and the cycle time is LI × RWL = 4.763 × 3.6 = 17.1468 minutes, we find:

  Number of cycles = 480 ÷ 17.1468 ≈ 28 cycles.

  Therefore, the time study is calculated as the number of cycles multiplied by the observed time per cycle: Time Study = 28 × 17.1468 ≈ 480 minutes = 8 hours.

2. Observed time:

  We can calculate the average observed time per cycle using the formula: Average observed time per cycle = Total observed time ÷ Number of cycles.

  The total observed time given is 480 minutes, and the number of cycles is 28. So, we have:

  Average observed time per cycle = 480 ÷ 28 ≈ 17.1429 minutes.

  The observed time is then found by multiplying the average observed time per cycle by the rating, which is 100% since no allowance is given:

  Observed time = 17.1429 × 100% = 17.1429 minutes ≈ 17.14 minutes.

3. Standard time:

  The standard time is calculated using the formula: Standard time = Observed time × Performance rating.

  To determine the performance rating, we need to find the standard time for the job and the total time allowed.

  Since no allowance is given, we assume the total time allowed is equal to the observed time, which is 17.1429 minutes.

  The standard time for the job can be calculated as the number of cycles multiplied by the standard time per cycle.

  The standard time per cycle is determined by multiplying LI × RWL × Elemental time.

  Since there's only one element given, the elemental time is equal to the observed time, which is 17.1429 minutes.

Therefore, the standard time per cycle is 4.763 × 3.6 × 17.1429 = 292.5 seconds.

With the number of cycles given as 28, the standard time for the job is 28 × 292.5 = 8190 seconds ≈ 136.5 minutes.

Finally, we calculate the performance rating using the formula: Performance rating = (Standard time for job ÷ Total time allowed) × 100.

Here, the total time allowed is the observed time, which is 17.1429 minutes.

So, the performance rating is (136.5 ÷ 17.1429) × 100 = 797.14%.

Thus, the standard time is found by multiplying the observed time by the performance rating:

Standard time = 17.1429 × 797.14% = 136.5 minutes ≈ 2.28 hours.

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Answer:

30

Step-by-step explanation:

Answer:

y=x+8

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

Slope is  $0.15 of the equation of cost  C=$0.15t+$35.00.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Given that A cell phone company uses the equation C=$0.15t+$35.00

C is the total cost for a month of service.

t is the number of text messages.

We have to find the slope of the equation.

slope is 0.15 and 35.00 is the y intercept of the equation given.

Hence, slope is  $0.15 of the equation of cost  C=$0.15t+$35.00.

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Answer:

No

Step-by-step explanation:

the line has to be straight for it to be a proportional relationship..

Answer: No.

Step-by-step explanation: It has to start from the Origin  (which is the two arrows crossing on the bottom left corner, 0,0) and it needs to be in a straight line in order to be proportinal.

Answer:

2. C

3. C

Step-by-step explanation:

I'm not too sure what number 1 is about but I know that for number 2, its 12/5 and for number 3, its 0.

Answer:

The choice 13

Step-by-step explanation:

\(| {c}^{2} + {b}^{2} | \\ | {( - 2)}^{2} + {( - 3)}^{2} | \\ |4 + 9| = 13\)

I hope I helped you^_^

Answer: mutually exclusive are:

ii. Sit down and stand up

ii. Sit down and stand upiii. Two dice: Odd and Even

because they can not occur same time

Mutually exclusive events don't occur at same ineterval and are not dependent upon each other

Here

They are