what is the probability that the person selected drives a truck exercises four or more times per week?

To find the distance traveled by a particle with position (x, y) as t varies in the given time interval, we need to calculate the length of the path traced by the particle. We can evaluate this integral using a substitution method or a numerical approach to find the exact distance traveled by the particle in the given time interval.

The position functions are x = 3sin^2(t) and y = 3cos^2(t) in the interval 0 ≤ t ≤ 5.

Find the derivatives of the position functions with respect to t.
dx/dt = d(3sin^2(t))/dt = 6sin(t)cos(t)
dy/dt = d(3cos^2(t))/dt = -6sin(t)cos(t)

Calculate the magnitude of the velocity vector.
|v| = sqrt((dx/dt)^2 + (dy/dt)^2) = sqrt((6sin(t)cos(t))^2 + (-6sin(t)cos(t))^2)

Simplify the expression.
|v| = sqrt(36sin^2(t)cos^2(t) + 36sin^2(t)cos^2(t)) = sqrt(72sin^2(t)cos^2(t))

Integrate |v| over the interval [0, 5] to find the distance traveled.
Distance traveled = ∫|v| dt from 0 to 5 = ∫(sqrt(72sin^2(t)cos^2(t))) dt from 0 to 5

Now, you can evaluate this integral using a substitution method or a numerical approach to find the exact distance traveled by the particle in the given time interval.

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Answer:

B. 60L

Step-by-step explanation:

30L = 1hr

2hrs= 30×2= 60L

Answer:

B

Step-by-step explanation:

The average value of  the function f on the interval \(∫1(3f(x) + 2x)dx\) is 56.

The average value of the function f on the interval 1 ≤ x ≤ 4 is 8 To Find: The value of\(∫1(3f(x) + 2x)dx\)  Approach: We know that if the average value of the function f on the interval [a,b] is given by Avg.

value of \(f = (1/(b-a)) ∫baf(x)dx\)  Then, \(∫baf(x)dx = Avg. value of f * (b-a)\)Formula Used: \(∫baf(x)dx = Avg. value of f * (b-a)\)

The average value of the function f on the interval 1 ≤ x ≤ 4 is 8Therefore, Avg. value of \(f = (1/(4-1)) ∫41f(x)dx⇒ Avg.alue of f = (1/3) ∫41f(x)dx\)Multiplying both sides by (3),

we ge\(t∫41f(x)dx = 3 * 8 = 24\)  Using the formula, we get\(∫1(3f(x) + 2x)dx= 3∫1f(x)dx + 2∫1xdx⇒ 3 * 24 + 2[(1/2) * (1)^2] - 2[(1/2) * (4)^2]⇒ 72 - 16⇒ 56\)

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The probability that the flip results in a head is given as Pr[H] = 23. Therefore, the probability that the flip results in a tail is Pr[T] = 1 - Pr[H] = 1 - 23 = 13.

Let A be the event that a white marble is selected. We need to find the conditional probability Pr[H|A], i.e., the probability that the flip resulted in a head given that a white marble was selected.

Using Bayes' theorem, we have:

Pr[H|A] = (Pr[A|H]*Pr[H]) / Pr[A]

Pr[A|H] is the probability of selecting a white marble given that the flip resulted in a head. This is given by (9/25), since there are 9 white marbles out of 25 in the first urn.

Pr[A] is the total probability of selecting a white marble, which can be found using the law of total probability:

Pr[A] = Pr[A|H]*Pr[H] + Pr[A|T]*Pr[T]

= (9/25)*0.23 + (1/11)*0.13

= 0.0888 + 0.0118

= 0.1006

Pr[A|T] is the probability of selecting a white marble given that the flip resulted in a tail. This is given by (1/11), since there is only 1 white marble out of 11 in the second urn.

Therefore,

Pr[H|A] = (9/25 * 0.23) / 0.1006 = 0.6508

Hence, the probability that the flip resulted in a head given that a white marble was selected is 0.6508 (or approximately 0.65).

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The 90% confidence interval for the proportion of district residents in favor of starting the school day 15 minutes later is (0.392, 0.548). The true proportion is estimated to lie within this interval with 90% confidence.

To calculate the 90% confidence interval for the true proportion of district residents who are in favor of starting the school day 15 minutes later, we can use the following formula:

CI = p ± z*(√(p*(1-p)/n))

where:

CI: confidence interval

p: proportion of residents in favor of starting the day later

z: z- score based on the confidence level (90% in this case)

n: sample size

First, we need to calculate the sample proportion:

p = 94/200 = 0.47

Next, we need to find the z- score corresponding to the 90% confidence level. Since we want a two-tailed test, we need to find the z- score that cuts off 5% of the area in each tail of the standard normal distribution. Using a z-table, we find that the z- score is 1.645.

Substituting the values into the formula, we get:

CI = 0.47 ± 1.645*(√(0.47*(1-0.47)/200))

Simplifying this expression gives:

CI = 0.47 ± 0.078

Therefore, the 90% confidence interval for the true proportion of district residents who are in favor of starting the school day 15 minutes later is (0.392, 0.548). We can be 90% confident that the true proportion lies within this interval.

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The circumference of the circle is 26.38 inches and the area of the circle is 55.39 square inches, both rounded to the nearest hundredth.

The diameter of a circle is the distance across the circle passing through its center. In this problem, the diameter of the circle is given as 8.4 inches. We can use the formula for the circumference and the area of a circle in terms of its diameter to find the solutions.

First, we can find the radius of the circle by dividing the diameter by 2. So, the radius is 8.4/2 = 4.2 inches.

To find the circumference of the circle, we can use the formula:

C = πd

where d is the diameter. Substituting the value of d = 8.4 inches and π = 3.14, we get:

C = 3.14 x 8.4 = 26.376

Therefore, the circumference of the circle is 26.38 inches (rounded to the nearest hundredth).

To find the area of the circle, we can use the formula:

A = πr²

where r is the radius. Substituting the value of r = 4.2 inches and π = 3.14, we get:

A = 3.14 x (4.2)² = 55.3896

Therefore, the area of the circle is 55.39 square inches (rounded to the nearest hundredth).

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As the percentages of dropouts are different there is sufficient evidence that the dropout rate at this school is different from the state level.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, In recent years, 3% of Ohio high school seniors drop out last year.

On the other hand Podunk, high school had 30 dropouts from their total enrollment of 600 students which is,

= (30/600)×100%.

= 5%.

So, there is sufficient evidence that the dropout rate at this school is different from the state level.

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The approximate number of students with Scores between 68 and 83 is 98.Answer: a. 98

The five-number summary for scores on a statistics exam is: 35, 68, 77, 83 and 97. In all, 196 students took this exam About how many students had scores between 68 and 83?

The five-number summary consists of the minimum value, the first quartile, the median, the third quartile, and the maximum value.

The interquartile range is the difference between the third and first quartiles. Interquartile range (IQR) = Q3 – Q1, where Q3 is the third quartile and Q1 is the first quartile. The 5-number summary for scores on a statistics exam is given below:

Minimum value = 35

First quartile Q1 = 68

Median = 77

Third quartile Q3 = 83

Maximum value = 97

The interval 68–83 is the range between Q1 and Q3.

Thus, it is the interquartile range.

The interquartile range is calculated as follows:IQR = Q3 – Q1 = 83 – 68 = 15

The interquartile range of the scores between 68 and 83 is 15. Therefore, the number of students with scores between 68 and 83 is roughly half of the total number of students. 196/2 = 98.

Thus, the approximate number of students with scores between 68 and 83 is 98.Answer: a. 98

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Answer:

2

Step-by-step explanation:

The easiest way to explain slope is the units up between each point on the line, divided by the units across. For this graph:

(-5,-6) and (0,4)

(y2 - y1) / (x2-x1)

4-(-6) = 4+6 = 10

0-(-5) = 0+5 = 5

10/5 = 2

Hope this helped!

Answer:

answer below

Step-by-step explanation:

Antarctica ( average temperature in 1960 Fahrenheit) = -11

Khartoum, Sudan ( change from 1960 to 2014 Fahrenheit) = 2

Greenland ( change from 1960 to 2014 Fahrenheit) = 3

To determine if the observed data supports the geneticist's claim, we should use the Chi-square test for goodness of fit. .

This test will help we compare the observed frequencies of the four species in your sample with the expected frequencies based on the ratio 1:3:3:9.

1. Calculate the expected frequencies based on the ratio 1:3:3:9.
  Total ratio = 1+3+3+9 = 16
  Expected frequency of Species 1 = (1/16) * 4000 = 250
  Expected frequency of Species 2 = (3/16) * 4000 = 750
  Expected frequency of Species 3 = (3/16) * 4000 = 750
  Expected frequency of Species 4 = (9/16) * 4000 = 2250
2. Compute the Chi-square statistic using the formula:
  χ² = Σ [(Observed - Expected)² / Expected]
  χ² = (226-250)²/250 + (764-750)²/750 + (733-750)²/750 + (2277-2250)²/2250
  χ² = 2.304 + 0.2667 + 0.3067 + 0.3244
  χ² = 3.202
3. Determine the degrees of freedom (df) using the formula:
  df = Number of categories - 1
  df = 4 - 1 = 3
4. Choose a significance level (usually 0.05) and compare the calculated χ² value to the critical value from the Chi-square distribution table.  

5. If the calculated χ² value is less than or equal to the critical value, you cannot reject the null hypothesis, meaning the observed data is consistent with the geneticist's claim.

If the calculated χ² value is greater than the critical value, you can reject the null hypothesis, meaning the observed data does not support the geneticist's claim.

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Since segment AD bisects angle BAC, the value of x is equal to 14.6.

In Mathematics, an angle bisector can be defined as a type of line, ray, or segment, that bisects or divides a line segment exactly into two (2) equal angles.

By applying the angle bisector theorem to this triangle (ΔABC), we have:

AB/BD = AC/DC

19/x = 17/(20 - x)

17x = 19(20 - x)

17x = 380 - 19x

19x + 17x = 380

26x = 380

x = 380/26

x = 14.6.

In conclusion, we can reasonably infer and logically deduce that the value of x in triangle ABC is 14.6.

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The Fion invested $24,000 in the savings account, $11,000 in the time deposit, and $7,000 in bonds.

Fion invested a total of $42,000 across three different accounts: savings, time deposit, and bonds. Let's represent the amounts invested in each account with variables. We'll use S for the savings account, T for the time deposit, and B for the bonds.

According to the given information, the total annual interest earned by Fion was $2,600. We can write this as an equation:

We also know that the interest from the savings account was $200 less than the total interest from the other two investments. Mathematically, this can be expressed as:

To solve this system of equations, we can use matrices. First, let's represent the coefficients of the variables in matrix form:

| 0.05   0.07   0.09 |   | S |   | 2600   |

| 0.05   0      0    | x | T | = | -200   |

| 0      0.07   0    |   | B |   | 0      |

By solving this matrix equation, we can find the values of S, T, and B, which represent the amounts invested in each account.

Using matrix operations, we find:

S = $24,000, T = $11,000, and B = $7,000.

Fion invested $24,000 in the savings account, $11,000 in the time deposit, and $7,000 in bonds.

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Answer: 7 is B

8 is G

9 is C

10 is F

Step-by-step explanation:

Answer:

that is your answer hope this helps u

Answer:

41

Step-by-step explanation:

5 integers with an average of 44

⇒ sum of the integers = 5 x 44 = 220

The median is the middle number when the numbers are put in order of smallest to largest.  So the integers are:  x  x  50  x  x

The modal integer is the one that occurs most frequently, so if the mode is 52, then at least 2 of the integer are 52.  Since the median is 50, the integers are:  x x 50 52 52

Therefore, the remaining two integers are less than 50.

The range is the difference between the largest integer and the smallest integer.  As we know that the largest integer is 52 and the range is 27, then the smallest integer is 52 - 27 = 25

25 x 50 52 52

To find the last unknown integer :

⇒ sum of the integers = 25 + 50 + 52 + 52 + x = 220

⇒ x = 41

Therefore, the integers are:

25, 41, 50, 52, 52

Answer:

  use the actual dimensions on your drawing

Step-by-step explanation:

"Full scale" simply means you use the actual object dimensions on your drawing of it.

If you don't know the meaning of "plan view", "front elevation", or "side elevation," you may need to consult your curriculum materials or any of numerous references on mechanical drawing.

For this object, I would say a "front elevation" is the view from the point marked "Y". A "side elevation" is the view from the point marked "X". A plan view is the view from above.

__

If you draw, on paper, patterns for cutting out the pieces that make up the object, you will be well on your way to making the required drawings. For example, the face ABCPEF would represent the front elevation. (The only thing added on the drawing of it is a dashed line representing hidden line RQ 1 cm below line AB.)

The side elevation is the shape of AQHGF on top of the shape EMLD. On your drawing of it, the line for EM is the same line as the line representing FG.

The top (plan) view is the shape CPNK with lines in the appropriate places to represent the edges EM, FG, and RQ.

__

Orthogonal views of an object like this are different from the kind of drawing you would make if you were trying to make a "net" for folding or calculating surface area. A net has every face actual size. Here, every face is represented the way it would be seen from a given direction. Slanted faces never show up actual size.

Using properties of exponents, the simplified expression for 5³ x 5^(-5) is given by:

A. 1/(5²).

The exponent property applied to multiply the terms with the same base but different exponents is that we keep the bases and then add the exponents.

For this problem, the expression is given as follows:

5³ x 5^(-5)

Hence:

Adding the exponents, we have that:

3 + (- 5) = 3 - 5 = -2.

Hence the simplified expression is:

5³ x 5^(-5) = 5^(-2).

When a number has a negative exponent, we can move it to the denominator, then the exponent becomes positive, hence:

5^(-2) = (1/5)² = 1/5² = 1/25.

Meaning that option A is correct.

The expression in this problem is 5³ x 5^(-5), and the correct options are given by the image at the end of the answer.

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Answer:

2m²

Step-by-step explanation:

radius = circumference ÷ ( Pi ×2)

r = 15 ÷ ( 3.14 × 2)

= 2.388535032

rounded off = 2m²

a. When evaluating a model, we use R2 as a parameter for performance assessment.

b. If model A has a higher MAPE but model B has a higher R2, we choose the model with the higher R2 for better overall performance.

c. For accuracy measures, we typically use MAPE (Mean Absolute Percentage Error) due to its interpretability and ability to capture relative errors.

When evaluating a model's performance, it is crucial to choose the appropriate parameters to assess its accuracy and reliability. In the case of MAPE (Mean Absolute Percentage Error) and R2 (Coefficient of Determination), the choice between them depends on the specific evaluation goals.

The R2 parameter is commonly used for evaluating models because it measures the proportion of the dependent variable's variance that can be explained by the independent variables. R2 provides insights into how well the model fits the data and captures the relationship between the input features and the target variable. Therefore, R2 is a suitable parameter to use when evaluating a model.

When comparing two models, if model A has a higher MAPE but model B has a higher R2, it is advisable to choose the model with the higher R2 value. This is because R2 indicates the proportion of variance explained, suggesting that model B performs better in capturing the underlying patterns and predicting the target variable.

Although model A may have a lower relative error (MAPE), it is crucial to prioritize the model's ability to explain and predict the target variable accurately.

Among MAPE, MAD (Mean Absolute Deviation), and MSD (Mean Squared Deviation), MAPE is commonly preferred as a parameter for accuracy measures. MAPE calculates the average percentage difference between the predicted and actual values, making it interpretable and easily understandable.

It captures relative errors and enables comparisons across different scales and datasets. MAD and MSD, on the other hand, measure absolute and squared errors, respectively, but they do not account for the relative magnitude of the errors. Hence, MAPE is a more suitable parameter for accuracy measures.

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Answer:

Opposite angles are equal, all add to 360:

10x-7=83

10x=90

X=9

Z = (360-(83*2))

Z = 97

Answer:-6s-2r

Step-by-step explanation:

you must add all like terms in this case S -4-3 is -7. -7+1=-6.
-6s-2r

Answer:

-6r - 2s

Step-by-step explanation:

Given expression,

→ -4r + s - 2r - 3s

Let's simplify the expression,

→ -4r + s - 2r - 3s

→ (-4r - 2r) + (s - 3s)

→ -6r + (-2s)

→ -6r - 2s

Hence, the answer is -6r - 2s.

Answer:

.4

Step-by-step explanation:

Camile shaded 18/30 of a model.

Thus the unshaded portion of the model is:

30 - 18 = 12

12/30

12/30 = 0.4

Answer:

5c + 2

Step-by-step explanation:

you first of all group like terms together

2c + 3c + 6 -4

5c + 2

Answer:

9

Step-by-step explanation:

1. First, we need to set up an equation to find the value of x and then the length of EF.

2. We know that DG is equal to 33, so we can add all the three sections it's cut into altogether to get 33. Therefore, we get an equation of: \(3x - 28 + 3x - 30 + x = 33\)

3. (Solving for x)

Step 1: Simplify both sides of the equation.

Step 2: Add 58 to both sides.

Step 3: Divide both sides by 7.

4. Now that we know x is equal to 13, we can plug that value in for the expression 3x - 30.

Therefore, the length of EF is 9.

The central angle of a dodecagon is 30°, the value of each internal angle is 150°, and the sum of internal angles is 1800°. For a hexadecagon, the central angle is 22.5°, the value of each internal angle is 157.5°, and the sum of internal angles is 2520°.

a) Dodecagon:

A dodecagon is a polygon with 12 sides. To calculate the central angle of a dodecagon, we use the formula:

Central Angle = 360° / Number of sides

Central Angle = 360° / 12 = 30°

Since a dodecagon has 12 equal sides, each internal angle can be calculated using the formula:

Internal Angle = (Number of sides - 2) * 180° / Number of sides

Internal Angle = (12 - 2) * 180° / 12 = 150°

The sum of the internal angles of a dodecagon can be calculated by multiplying the number of sides by the value of each internal angle:

Sum of Internal Angles = Number of sides * Internal Angle

Sum of Internal Angles = 12 * 150° = 1800°

b) Hexadecagon:

A hexadecagon is a polygon with 16 sides. Using the same formulas as above, we can calculate its central angle and internal angles.

Central Angle = 360° / 16 = 22.5°

Internal Angle = (16 - 2) * 180° / 16 = 157.5°

Sum of Internal Angles = 16 * 157.5° = 2520°

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Answer:

Step-by-step explanation:

No because √2 and 3i come in pairs. The four roots are ±√2, 3i and -3i. The 5 guarantees that there are at least 5 roots to this equation. This is a good question to know the answer to. It looks like something that could be put on a test.