find the average rate of hange for the function f(x)=2 cos(x^2) on the interval [1,3]

Answer: The probability of the spinner landing on yellow is 6/10 or 3/5, which can also be expressed as 0.6 or 60%.

Answer:

70 miles

Step-by-step explanation:

Subtracting ten minutes from the elapsed time 94 minutes tells us that the travel (at constant average speed) took 84 minutes.  We convert 84 minutes to 84/60 hour.

distance = rate•time = 50 mi/hr (84/60 hour) = 50(1.4) = 70 miles

The required slopes are:

(a) slope = 4

(b) slope = 6/7

(c) slope =  -3

(d) slope = 4

(e) slope = -5/2

We know that,

When a line passing through (x₁, y₁) and (x₂, y₂)

Then  the slope of the line be,

slope (m) = (y₂ - y₁) / (x₂ - x₁)

Using this formula, calculate the slope for each given points

a. (9, 10) and (7, 2)

⇒ slope (m) = (2 - 10) / (7 - 9)

                    = -8/-2 = 4

So, the slope is 4.

b. (-8, -11) and (-1, -5)

⇒ slope (m) = (-5 - (-11)) / (-1 - (-8))

                    = 6/7

So, the slope is 6/7.

c. (5, -6) and (2, 3)

⇒ slope (m) = (3 - (-6)) / (2 - 5)

                    = 9/-3

                    = -3

So, the slope is -3.

d. (6, 3) and (5, -1)

⇒ slope (m) = (-1 - 3) / (5 - 6)

                    = -4/-1

                    = 4

So, the slope is 4.

e. (4, 7) and (6, 2)

⇒ slope (m) = (2 - 7) / (6 - 4)

                    = -5/2

So, the slope is -5/2.

Therefore, the slope of the line that joins (-8, -11) and (-1, -5) is 6/7.

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In logic, the term statement is variously understood to mean either: a meaningful declarative sentence that is true or false, or a proposition. Which is the assertion that is made by a true or false declarative sentence.
a. is insufficient. Both truth values are possible.b. is insufficient. Both truth values are possible.c. is insufficient. Both truth values are possible.d. is sufficient. The statement is true. The logarithm of a positive number less than 1 is negative.e. is sufficient. The statement is false. The logarithm of 0 is undefined.f. is sufficient. The statement is false. The logarithm of a negative number is undefined.

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Answer: Yes.

Step-by-step explanation: With a triangle, the hypotenuse, or the longest side, would be on the bottom.  The legs, or the other two sides, pretty much build off of that hypotenuse, which makes it a right triangle.

Have a great day! :)

Answer:

f^(-1)(x) = e^(x/3)

Step-by-step explanation:

1.  Replace 'f(x)' by 'y:'  y = 3ln x

2. Interchange x and y:  x = 3ln y => x/3 = ln y

3. Solve for y:  

   e^(x/3) = y

4.  Replace this 'y' with 'f^(-1)(x)'

    Then f^(-1)(x) = e^(x/3)

The probability of getting 3 is P(A) = 1/216. The probability that sum being 3 is 1 / 216.

When three dice are thrown simultaneously, the probability that the sum is 3 is 1/216. A dice can show a minimum of one and a maximum of six dots, for a total of six sides, giving it a total of 6 * 6 * 6 = 216 possible outcomes.

:When three dice are thrown simultaneously, the probability that the sum is 3 is 1/216. The probability can be calculated as follows:

Let A be the event that the sum is 3. The number of ways to get 3 is 1, i.e., (1, 1, 1). The total number of possible outcomes is 6³,

since each die can have 6 possible outcomes.

Therefore, the probability of getting 3 is P(A) = 1/216.

In conclusion, the probability that sum being 3 is 1 / 216.

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To simplify

First of all, Octavia error can be spotted from the correct steps below

Step1: Expand the expression

Step2: Collect like terms

Step 3: Simplify by using exponents laws

Step 4: Combine the terms.

The value is

Her error was that she didn't apply the exponents' law properly.

One of the laws she violated was

Her mistake was that she did

So she missed it from our step 1 above

Answer:

7<x-5

12<x

x>12

Step-by-step explanation:

The value of length PB is 2cm

Similar triangles have the same corresponding angle measures and proportional side lengths. This means that the corresponding angles of similar triangles are equal.

And also the ratio of corresponding sides of similar triangles are equal.

Therefore ;

3/9 = PB/ 6

represent PB by x

3/9 = x/6

18 = 9x

divide both by 9

x = 18/9

x = 2cm

Therefore the value of length PB is 2

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The correct explanation for preferring the mean over the median as a measure of center is option 3: The mean is the same as the median for symmetric data.

The mean over the median as a measure of center is that the mean takes into account all values in a data set, making it more representative of the data as a whole. On the other hand, the median only considers the middle value(s), and is less sensitive to outliers. This means that extreme values in a data set have less impact on the median than they do on the mean. However, if the data set is skewed or has outliers that significantly affect the mean, the median may be a better measure of central tendency. In summary, the choice between the mean and the median depends on the characteristics of the data set being analyzed and the research question being asked.
In symmetric data, the mean and median provide the same central value, giving an accurate representation of the data's center. However, it's important to note that the mean is more sensitive to outliers than the median, which might affect its accuracy in skewed data sets.

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Answer:

5

Step-by-step explanation:

Since the two lines are parallel, they must have the same slope. This means that the slope of green line must be 5 just like the red line. You can also use the slope formula (rise/run) or change in y divided by change in x.

Answer:

15 kg, 22.5 kg, 52.5 kg

Step-by-step explanation:

Let the common multiplier of the given ratios be x. Therefore, weights of each bag would be 2x, 3x and 7x

According to the given information:

\(2x + 3x + 7x = 90 \\ 12x = 90 \\ x = \frac{90}{12} \\ x = 7.5 \: \\ \implies \\ 2x = 2 \times 7.5 = 15 \: kg \\ 3x = 3 \times 7.5 = 22.5 \: kg \\ 7x = 7 \times 7.5 = 52.5 \: kg\)

Hence the weight of sand in bag would be 15 kg, 22.5 kg and 52.5 kg

Answer:

B

Step-by-step explanation:

Answer:

Expression is equivalent to (x^1/4 y^16)^1/2 is x^1/8 y^8

Answer:

36

Step-by-step explanation:

21+15 is 36 so there for u just add 15 to 21 giving you 36

Answer:

40%

Step-by-step explanation:

Step-by-step explanation:

12x7 + 2x7 = 84 + 14 = 98

sa=98

For the  image, its surface area  is mathematically given as

x= 98cm^2

The surface area of a three-dimensional object is the amount of space that covers the exterior of the object.

In conclusion, calculating the individual surfaces we have

x=12x7 + 2x7 = 84 + 14

x= 98cm^2

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Answer:

question 9

= –12

while question 11=, x= –72

Step-by-step explanation:

question 9=

u= –16+4= –12

question 11=

cross multiplication

x = -36 multiplied by 2 =

-72

I HOPE THIS HELPED IF WRONG IM SORRY

Answer: 42 I think

Step-by-step explanation:

I did 6 times 7

Answer:

6/5

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(\dfrac{3}{5}\)   ÷ \(\dfrac{1}{2}\)

\(=\dfrac{3}{5}*\dfrac{2}{1}\\\\=\dfrac{6}{5}\\\\\\=1\dfrac{1}{5}\)

To rank the steps involved in transforming one couple to another couple in a parallel plane, here is the correct order:

Identify the initial couple and the desired final couple.

Determine the translation vector that will move the initial couple to the desired final couple.

Translate the initial couple using the determined translation vector. This will shift the entire couple in the parallel plane.

Verify that the translation has successfully moved the initial couple to the desired final couple.

If necessary, make any additional adjustments or transformations to align the initial and final couples precisely in the parallel plane.

Confirm that the final couple is now in the desired position and orientation relative to the initial couple, maintaining the parallelism of the plane.

By following these steps in order, you can effectively transform one couple to another in a parallel plane.

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Answer:

x · 8 - 3

Step-by-step explanation:

Answer:

8x-3

3 is being taken from 8 and a number. 8 and the number are being multiplied together

The ordered pairs which make the open sentence true are:

An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an algebraic expression based on any of the following arguments:

For this exercise, you should evaluate each of the given expressions to determine which inequalities is true when the ordered pairs are substituted. This ultimately implies that, you would have to substitute the ordered pairs into each of the given algebraic expressions and then evaluate.

When ordered pairs = (3, 6), we have:

3x + y < 14

3(3) + 6 < 14

9 + 6 < 14

15 < 14 (False).

When ordered pairs = (7, -7), we have:

3x + y < 14

3(7) + (-7) < 14

21 - 7 < 14

14 < 14 (False).

When ordered pairs = (6, 0), we have:

3x + y < 14

3(6) + 0 < 14

18 - 0 < 14

18 < 14 (False).

When ordered pairs = (-1, 6), we have:

3x + y < 14

3(-1) + 6 < 14

-3 + 6 < 14

3 < 14 (True).

When ordered pairs = (4, -1), we have:

3x + y < 14

3(4) + (-1) < 14

12 - 1 < 14

11 < 14 (True).

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An equation in slope-intercept form to represent this linear function is y = 65x + 40.

The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.

The slope, m, is a measure of how steep a line is. Sometimes, the gradient of a line is referred to as its slope. A line's y-intercept, ab, denotes the y-coordinate of the location where the line's graph crosses the y-axis.

Let the fee per month = x.

Given that, A membership at Rocky Heights Climbing Gym costs $65 per month plus a $40 initial fee.

y = 65x + 40.

Hence, an equation in slope-intercept form to represent this linear function is y = 65x + 40.

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Answer: 160 yd³

Step-by-step explanation:

Volume for a rectangular prism is bhl

a triangular prism is half that

so V= 1/2(bhl)

      = (1/2)(5)(8)(8)

      =160 yd³

The term "normally distributed error term with mean of zero" refers to the residual errors in a statistical model that follow a normal distribution with an average (mean) value of zero.

In statistics, when we use a model to represent data, there is often some variability or discrepancy between the predicted values of the model and the actual observed values. This discrepancy is captured by the error term, which represents the unexplained variation in the data.

A normally distributed error term with a mean of zero means that, on average, the errors have no bias or systematic tendency to be positive or negative. This means that the model is not consistently overestimating or underestimating the true values.

To illustrate this concept, let's consider a simple example. Suppose we have a linear regression model that predicts the exam scores of students based on the number of hours they studied. The error term in this model represents the difference between the predicted scores and the actual scores.

If the error term is normally distributed with a mean of zero, it implies that, on average, the predicted scores will be equal to the actual scores. However, individual predictions may still deviate from the true values due to random fluctuations.

In practical terms, a normally distributed error term with a mean of zero is desirable because it indicates that the model is unbiased and does not systematically under- or over-predict the outcomes. This assumption is often made in statistical analyses to ensure the validity of the results and to make appropriate inferences.

In summary, a normally distributed error term with a mean of zero implies that the errors in a statistical model have no systematic bias and follow a normal distribution. This assumption is important in many statistical analyses and helps to ensure the accuracy and reliability of the model's predictions.

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The probability that the fan will not be able to watch all 8 new episodes in one sitting can be determined by calculating the probability that the mean duration of the new episodes is greater than 45 minutes.

Using the Central Limit Theorem, we know that the distribution of the sample means will be approximately normal, regardless of the distribution of the individual episode durations, as long as the sample size is sufficiently large.

In this case, the mean episode duration is normally distributed with a mean of 47 minutes and a standard deviation of 6 minutes. Since we are interested in the mean duration of 8 new episodes, we can use the properties of the normal distribution to calculate the probability.

First, we need to find the standard deviation of the mean duration of the 8 episodes, also known as the standard error of the mean (SE). The SE can be calculated by dividing the standard deviation of the individual episodes by the square root of the sample size:

SE = σ / sqrt(n) = 6 / sqrt(8) ≈ 2.1213

Next, we can use the properties of the normal distribution to calculate the probability that the mean duration is greater than 45 minutes. We standardize the value of 45 minutes using the mean and SE:

Z = (45 - 47) / 2.1213 ≈ -0.9428

Using a standard normal distribution table or a calculator, we can find the probability corresponding to the Z-score of -0.9428. This probability represents the likelihood that the mean duration of the 8 episodes is greater than 45 minutes.

Therefore, the probability that the fan will not be able to watch all 8 new episodes in one sitting is approximately the probability corresponding to the Z-score of -0.9428, rounded to four decimal places.

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Step-by-step explanation:

If the simple interest rate is 4% per year, then the interest earned each year is calculated by multiplying the principal amount by the interest rate.

The interest earned in one year is:

Interest = Principal x Rate = $6000 x 0.04 = $240

After four years, the total interest earned is:

Total Interest = Interest x Time = $240 x 4 = $960

Therefore, the total amount Mr. Khan can withdraw after four years is:

Withdrawal Amount = Principal + Total Interest = $6000 + $960 = $6960

Answer:

If the simple interest rate was 4% per year, we can use the formula for simple interest to calculate the amount of interest Mr. Khan earned on his $6000 deposit:

Simple interest = P * r * t

Where P is the principal (the initial amount deposited), r is the interest rate (as a decimal), and t is the time (in years).

In this case, P = $6000, r = 0.04, and t = 4. Substituting these values into the formula, we get:

Simple interest = $6000 * 0.04 * 4 = $960

The total amount Mr. Khan can withdraw after four years is the sum of his initial deposit and the interest earned:

Total amount = Principal + Interest

Total amount = $6000 + $960 = $6960

Therefore, Mr. Khan can withdraw $6960 from his bank account after four years if the simple interest rate was 4% per year.

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Answer:

x = -3

Step-by-step explanation:

3(x - 6) + 6 = 5x - 6

Distribute;

3x - 18 + 6 = 5x - 6

3x - 12 = 5x - 6

Subtract 5x from both sides;

-2x - 12 = -6

Add 12 to both sides;

-2x = 6

Divide both sides by -2

x = -3

Answer:

x=-9

Step-by-step explanation:

3x-18+6=5x-6 distribute

3x-18=5x  cancel out 6es

-18=2x subtract 3x

x=-9 divide by 2

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