rebecca throws a fair six sided dice.
the letter in the diagram in the image attached that matches the probability of the dice landing on a number between 1 and 6 .​

Answer:

261 seconds

Step-by-step explanation:

78.2 · 1000 = 78,200

78,200/300 ≈ 261

Answer:

-1.517

Need to know:

Integral constant rule: ∫ (ax)dx = a ∫ (x)dx

Integral power rule: ∫ xⁿ = xⁿ⁺¹/(n + 1)

\(\int\limits^b_a {f(x)} \, dx = F(b) - F(a)\)

Quadratic formula: \(\frac{-b +-\sqrt{b^{2} -4ac} }{2a}\)

Step-by-step explanation:

First, we have to find the average value of f over the interval [-2, 2]

To find that, calculate the integral of 3x(x - 2)

∫ 3x(x - 2)dx = 3 ∫ x(x - 2)dx = 3 ∫ x² - 2xdx (pulled out the 3 because of the constant rule)

Use the power rule to solve the integral

3 [x²⁺¹/(2 + 1) - 2x¹⁺¹/(1 + 1)] = 3[x³/3 - 2x²/2]

Distribute the 3

3[x³/3 - 2x²/2] = x³ - 3x² = F(x)

We plug in 2 in place of x

F(2) = 2³ - 3(2)² = -4

Do the same with -2

F(-2) = (-2)³ - 3(-2)² = -20

We have to remember that  \(\int\limits^b_a {f(x)} \, dx = F(b) - F(a)\)

let a = -2    b = 2

F(2) - F(-2) = -4 - (-20) = -4 + 20 = 16

The average value of f over the given interval is 16.

Now we make it to where f(x) = 16 to find c

3x(x - 2) = 16

3x² - 6x = 16

Subtract 16 from both sides to make it equal to zero

3x² - 6x = 16

       - 16    - 16

3x² - 6x - 16 = 0

a = 3 b = -6 c = 16

Plug these numbers into the quadratic formula

\(\frac{-(-6) +-\sqrt{(-6)^{2} -4(3)(-16)} }{2(3)}\)

\(\frac{6 +-\sqrt{36 + 192} }{6}\)

\(\frac{6 +\sqrt{228} }{6}\) = -1.51661

\(\frac{6 -\sqrt{228} }{6}\) = 3.51661

-1.51661 is the only number out of the two that fits in the given interval [-2,2], so c would have to be -1.517 in order for f(c) to equal the average value of f over the given interval.

False. if you are given a graph with two shif table lines, the correct answer will always require you to move both lines.

In a graph with two shiftable lines, the correct answer may or may not require moving both lines. It depends on the specific scenario and the desired outcome or conditions that need to be met.

When working with shiftable lines, shifting refers to changing the position of the lines on the graph by adjusting their slope or intercept. The purpose of shifting the lines is often to satisfy certain criteria or align them with specific points or patterns on the graph.

In some cases, achieving the desired outcome may only require shifting one of the lines. This can happen when one line already aligns with the desired points or pattern, and the other line can remain fixed. Moving both lines may not be necessary or could result in an undesired configuration.

However, there are also situations where both lines need to be shifted to achieve the desired result. This can occur when the relationship between the lines or the positioning of the lines relative to the graph requires adjustments to both lines.

Ultimately, the key is to carefully analyze the graph, understand the relationship between the lines, and identify the specific criteria or conditions that need to be met. This analysis will guide the decision of whether one or both lines should be shifted to obtain the correct answer.

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The example on direct variation is illustrated below based on the information given.

An example will be:

When x = 2, y = 10. Find the value of y when x is 6.

In this case, this will be calculated thus:

y = kx

10 = 2k

k = 10/2

k = 5

Since y = kx.

y = 5 × 6

y = 30

The value of y is 30.

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a. To determine the most consistent results, Charles, Isabella, and Naomi should calculate the range.

b. Isabella achieved the most consistent results with the smallest range of 9, while Charles and Naomi had ranges of 18 and 33, respectively.

a) To determine who has the most consistent results, Charles, Isabella, and Naomi should calculate the range. The range measures the spread or variability of the data set and provides an indication of how dispersed the individual results are from each other.

By calculating the range, they can compare the differences between the highest and lowest scores for each person, giving them insight into the consistency of their performance.

b) To find out who achieved the most consistent results, we can calculate the range for each individual and compare the values.

For Charles: The range is the difference between the highest score (57) and the lowest score (39), which is 57 - 39 = 18.

For Isabella: The range is the difference between the highest score (71) and the lowest score (62), which is 71 - 62 = 9.

For Naomi: The range is the difference between the highest score (94) and the lowest score (61), which is 94 - 61 = 33.

Comparing the ranges, we can see that Isabella has the smallest range of 9, indicating the most consistent results among the three. Charles has a range of 18, suggesting slightly more variability in his scores. Naomi has the largest range of 33, indicating the most variation in her results.

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The center of the circle is (-7, -1) and the radius is the square root of 36, which is 6. So, correct option is D.

To find the center and radius of a circle given by its equation in the form of (x-a)² + (y-b)² = r², we need to convert the given equation to this standard form by completing the square for both x and y terms.

x² + y² + 14x + 2y + 14 = 0

(x² + 14x) + (y² + 2y) = -14

(x² + 14x + 49) + (y² + 2y + 1) = -14 + 49 + 1 // add and subtract the square of half the coefficient of x and y terms respectively

(x + 7)² + (y + 1)² = 36

Comparing with the standard form (x-a)² + (y-b)² = r², we can see that the center of the circle is (-7, -1) and the radius is the square root of 36, which is 6.

Therefore, the correct answer is option D, (-7, -1), 6 units.

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The variables are restricted to domains on which the functions are defined. If z=xey,x=u2+v2,y=u2−v2,

To find the partial derivatives of z with respect to u and v, we can use the chain rule of partial differentiation.

We have:

z = xey = x(eu2−v2)

x = u2 + v2 and y = u2 − v2

So,

∂z/∂u = ∂z/∂x * ∂x/∂u + ∂z/∂y * ∂y/∂u

= ey(u2-v2) * 2u + xe^(u^2-v^2) * 2u

= 2u(e^(u^2-v^2) + xe^(u^2-v^2))

Similarly,

∂z/∂v = ∂z/∂x * ∂x/∂v + ∂z/∂y * ∂y/∂v

= ey(u2-v2) * (-2v) + xe^(u^2-v^2) * 2v

= 2v(xe^(u^2-v^2) - ye^(u^2-v^2))

Therefore,

∂z/∂u = 2u(e^(u^2-v^2) + xe^(u^2-v^2))

∂z/∂v = 2v(xe^(u^2-v^2) - ye^(u^2-v^2))

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Answer:

henry gets 231

Step-by-step explanation:

my head

Answer:

231

Step-by-step explanation:

Let's consider that Gavin got X pounds.

Then Henry gets 3 times as much as Gavin => 3X

And Mark gets twice as much as Henry => 2 * 3X

Together they get 770, so:

X + 3X + 2*3X = 770

10X = 770  =>  X = 77

As we mentioned, Henry gets 3X, so

3X = 3 * 77 = 231

Answer:

1/5

Step-by-step explanation: You add 4+10+6 to get 20. So the probability that the spinner lands on red would be 4/20. If you need it simplified  you take 4 and divide it by 4 to get 1, then you would divide 20 by 4 to get 5. that would leave you with 1/5.

The minimum amount of candy that could be handed out is 19 pieces, and the maximum amount of candy that could be handed out is 104 pieces.

Minimum amount of candy can ve observed by selecting the least amount of candy.

The number of the least amount of candy is purple duckies, which are 19.

Number of times the game is played = 49

The minimum amount of candy, can be calculated as:

Minimum candy = 19  \(\times\)  1

Minimum candy = 19 pieces

The maximum amount of candy can be calculated as:

The number of the maximum amount of candy is 6 pink duckies, which are 6.

Number of pieces of candy per pink ducky = 3

Number of candies for remaining selections = 2

Maximum candy = (6\(\times\) 3) + (remaining selections \(\times\) 2 pieces of candy per blue ducky)

The remaining selections can be calculated as:

Remaining selections = 49 (total selections) - 6 (pink duckies) = 43 selections

Maximum candy = (6 \(\times\)3) + (43 \(\times\) 2)

                            = 18 + 86

                             = 104 pieces of candy.

So, the minimum amount of candy that could be handed out is 19 pieces, and the maximum amount of candy that could be handed out is 104 pieces.

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In a taste test comparing a generic soda to a brand name soda, the count of correct guesses among 20 tasters follows a binomial distribution with parameters n = 20 (number of trials) and p = 0.25 (probability of guessing correctly). The taste tests are conducted independently, with tasters in separate locations to avoid interaction between them during the test.

Binomial distribution: The binomial distribution is a discrete probability distribution of the number of successes in a fixed number of independent trials. P(X=k)= nCk * pk * (1-p)n-k, Where P(X=k) is the probability of getting k successes in n trials, nCk is the number of ways to get k successes in n trials, p is the probability of success, and 1 - p is the probability of failure.

So, the formula for the mean and variance of the binomial distribution is as follows: μ = npσ2 = np (1 - p).

Now, we have to find n and p. Probability of success, p is 0.25 and the number of trials, n is 20.

Thus,p = 0.25, n = 20.

So, n and p are 20 and 0.25 respectively.

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Answer:

\(Base (B) = /frac{15x² + 1 + 2}{x}\)

Step-by-step Explanation:

==>Given:

Dimensions of a rectangular prism are expressed as follow:

Volume (V) = 15x² + x + 2

Height (h) = x²

==>Required:

Expression of the Base area (B)

==>Solution:

Volume (V) = Base (B) × Height (h)

15x² + x + 2 = B × x²

Divide both sides by x²

\(\frac{15x² + x + 2}{x²} = B

\(Base (B) = /frac{15x² + 1 + 2}{x}\)

Answer: c

Step-by-step explanation:

The dimensions of the large soccer field are 361 x 295.28 feet.

To convert the dimensions of the large soccer field from meters to feet, we multiply each dimension by the conversion factor of 1 meter equals 3.281 feet.

Length conversion: The length of the soccer field is 110 meters. Multiply this by the conversion factor: 110 meters * 3.281 feet/meter = 361 feet.

Width conversion: The width of the soccer field is 90 meters. Multiply this by the conversion factor: 90 meters * 3.281 feet/meter = 295.28 feet.

Therefore, the large soccer field measures 361 feet long and 295.28 feet wide when converted to the imperial unit of feet.

By applying the conversion factor, we accurately express the field's dimensions in the desired measurement system.

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Answer:

Step-by-step explanation:

Answer:

17.72\(\frac{miles}{hr}\)

Step-by-step explanation:

If you are trying to take 26 ft/s to being miles per hour this is how you do it.

26 \(\frac{ft}{s}\) * \(\frac{mile}{5280ft}\) *\(\frac{3600s}{hr}\)

so

17.72\(\frac{miles}{hr}\)

Answer:

x = 10

Step-by-step explanation:

Given h(x) = 2x - 14 and h(x) = 6, then equating

2x - 14 = 6 ( add 14 to both sides )

2x = 20 ( divide both sides by 2 )

x = 10

The z-values for the given situations are approximate:

a. The area to the left of z is 0.1827. z = -0.90

b. The area between −z and z is 0.9830. z = 2.17

c. The area between −z and z is 0.2148. z = 0.85

d. The area to the left of z is 0.9997. z = 3.49

e. The area to the right of z is 0.6847. z= -0.48

a. For an area of 0.1827 to the left of z, the corresponding z-value can be found using a standard normal distribution table or a statistical calculator. The z-value is approximately -0.90.

b. To find the z-value for an area between -z and z equal to 0.9830, we need to find the value that corresponds to (1 - 0.9830)/2 = 0.0085 in the upper tail of the standard normal distribution. Using the table or calculator, the z-value is approximately 2.17.

c. Similarly, for an area between -z and z equal to 0.2148, we find the value that corresponds to (1 - 0.2148)/2 = 0.3926 in the upper tail. The z-value is approximately 0.85.

d. For an area of 0.9997 to the left of z, we find the value that corresponds to 0.9997 in the upper tail. The z-value is approximately 3.49.

e. To find the z-value for an area to the right of z equal to 0.6847, we find the value that corresponds to 1 - 0.6847 = 0.3153 in the upper tail. The z-value is approximately -0.48.

In summary, the z-values for the given situations are approximate:

a. -0.90

b. 2.17

c. 0.85

d. 3.49

e. -0.48

These values can be used to determine the corresponding percentiles or probabilities for the standard normal distribution. The values are typically found using standard normal distribution tables or statistical calculators that provide the cumulative probability distribution function (CDF) for the standard normal distribution.

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The value of the intercept of the regression line, b, rounded to one decimal place, is 8.1.

To find the intercept of the regression line, we need to perform linear regression analysis on the given data. The regression line is an equation of the form y = mx + b, where m is the slope and b is the intercept.

We can use a statistical software or a calculator to perform linear regression analysis. Here, we will use Microsoft Excel to find the intercept of the regression line.

First, we will create a scatter plot of the data. Then, we will add a trendline and display the equation of the trendline on the chart.

After performing linear regression analysis on the given data, we get the equation of the regression line as:

y = 1.9444x + 8.1389

Here, the intercept of the regression line is the value of b, which is 8.1389. Rounding it to one decimal place, we get the intercept as 8.1.

The intercept of the regression line is the point where the regression line intersects with the y-axis. In this context, it represents the predicted value of y when x is equal to zero. In other words, it is the starting point of the regression line.

In this example, the intercept of the regression line indicates that an employee with zero years of experience would be expected to have a salary of $8.1 thousand.

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The the equation of a line that passes through the point (2, −10) and is parallel to 14x+2y=6 is 7x + y + 8 = 0.

A straight line is just a line with no curves. So, a line that extends to both sides till infinity and has no curves is called a straight line.

The equation of a line parallel to a given line will have the same slope as the given.

The equation of a line having a slope m and passing through the point (x', y') is written as

y - y' = m (x - x').

This is called point - slope equation of a straight line.

In the given equation,

14x+2y=6

⇒ 2y = -14x + 6

⇒ y = -7x + 3

Comparing it with standard equation of a straight line; y = m x + c, the slope m of the given line = -7

Therefore equation of the line parallel to the given line and passing through point (x', y') = (2, -10) would be:

y - (-10) = -7x + 2

⇒ y + 10 = -7x + 2

⇒ 7x + y + 8 = 0

Hence the required equation of line 7x + y + 8 = 0

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Answer: its time for mathacmathists

Step-by-step explanation: i dont see it

Answer

72°

Step-by-step explanation:

\(because\ AC=AB\ therefore\ < ACB= < ABC=6x\\ And\ because\ the\ sum\ of\ the\ angles\ of\ a\ triangle\\ is\ 180\ .\\ therefore\ < ACB+ < ABC+ < CAB=180\ degrees\\ 3x+6x+6x=180\ degrees\\ 15x=180\ degrees\\ x=12\ degrees\\ < ABC=6x=6\times12\ degrees=72\ degrees\)

I hope this helps you

:)

Answer:

∠ABC = 72°

Step-by-step explanation:

When we look at the triangle carefully, we can see a bar on AC and AB. Those bars define that AC and AB are equivalent. This also means that the triangle is isosceles. Since this triangle is isosceles, the base angles of the triangle are equivalent.

⇒ AB = AC

We also know that the sum of its interior angles must be 180°.

⇒ ∠A + ∠B + ∠C = 180

Let's substitute their angle measures.

⇒ 3x + 6x + 6x = 180                                         [∠BAC = 3x; ∠ABC = ∠ACB = 6x]

Now, let's solve for x.

⇒ 3x + 6x + 6x = 180

⇒ 15x = 180

⇒ 15x/15 = 180/15

⇒ x = 12

Now, substitute the value of x into "6x" to find ∠ABC.

∠ABC = 6x

⇒ ∠ABC = 6(12)

⇒ ∠ABC = 72°

Answer:

2πr + 4a = 8

Step-by-step explanation:

Claims per year (option B) is the measure that provides the most valuable and comprehensive information for the insurance company's reevaluation of premiums.

The measure that provides the best information for the reevaluation of homeowners insurance premiums is option B: claims per year. This measure gives an overall picture of the frequency of claims filed by customers on an annual basis, allowing the insurance company to assess the risk and adjust premiums accordingly.

Option B, claims per year, provides the most comprehensive and relevant information for the insurance company's reevaluation of premiums. By analyzing the number of claims filed per year, the insurance company can determine the average rate at which claims are being made by its customers. This measure takes into account all customers and provides a general overview of the claims activity within the company.

Option A, claims per sub-division, focuses on claims within specific sub-divisions or neighborhoods. While this measure may be useful for localized risk assessment, it does not provide a holistic view of the company's overall claims activity.

Option C, claims per year per city, narrows down the analysis to claims made in specific cities. This measure may be relevant for regional risk assessment but does not capture the complete picture of the company's claims frequency.

Option D, claims per dollar value of property, relates claims to the value of insured property. While this measure may offer insights into the severity of claims, it does not provide sufficient information to determine the overall claims frequency.

Therefore, claims per year (option B) is the measure that provides the most valuable and comprehensive information for the insurance company's reevaluation of premiums.

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Answer:

The inequality to describe the problem is 15 +c >25.

We must sell more than 5 cones to make a profit

Step-by-step explanation:

From this problem,  we can see that we need to sell a number of cones (c), that when added to the 15 cones that we have already sold, the result will be greater than 25.

To set up the inequality sign, we need to, first of all, know the inequality sign that we will be using. From the preceding statement, we can see that we need to sell greater than a certain number of cones.  

This should tell us that we will be needing the greater-than sign (>).

The next step is to know the format the equation should take:

We have sold 15 cones; We need to sell c more to make it greater than 25.

This will be 15 +c >25.

The inequality to describe the problem is 15 +c >25.

from this, we can see that c > 5 cones.

We must sell more than 5 cones to make a profit

For conducting experiment based on effect of a net force , to apply net force on the object two other quantities should be measured in each trial of the experiment is given by velocity and time.

As given in the question,

To conduct a experiment based on the effect of net force applied to an object the dependable quantities are as follow:

Force = mass × acceleration

As object remain same ⇒ mass is constant as object remain same.

And there is change in the acceleration.

Acceleration depends change in velocity over total time taken.

Acceleration depends on velocity and time.

Net force also depends on velocity and time.

Two measurements need to know  while conducting trail experiments are velocity and time.

Therefore, to conduct experiment based on effect of a net force , to apply net force on the object two other quantities should be measured in each trial of the experiment is given by velocity and time.

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The equation of a line passes through the point (-6, 5) and

has a slope of 1/2 is y = (1/2)x + 8.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and equation of a line in slope-intercept form is y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

Given, A line passes through the point (-6, 5) and has a slope of 1/2.

First, we need to determine the y-intercept 'b'.

5 = (1/2)(-6) + b.

5 = - 3 + b.

b = 8.

y = (1/2)x + 8 is the required equation of the line.

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Answer:

A

Step-by-step explanation:

The given sequence is geometric. The common ratio is r=2.

If we divide each term by its previous, we would get:

r=3/6=2

r=12/6=2

r=24/12=2

Thus, r=2.

Hope this helps!

The probability that a randomly selected firm will earn between 9191 and 9797 million dollars is, 0.1879

We have to given that,

The mean income of firms in the industry for a year is 8585 million dollars with a standard deviation of 99 million dollars.

Hence, We need to standardize the values of 9191 and 9797 to a standard normal distribution with a mean of 0 and a standard deviation of 1. We can do this using the z-score formula:

z = (x - μ) / σ

where x is the value we want to standardize, μ is the mean of the distribution, and σ is the standard deviation of the distribution.

For x = 9191:

z = (9191 - 8585) / 99 = 0.61

For x = 9797:

z = (9797 - 8585) / 99 = 1.22

Now, we need to find the probability that a randomly selected firm will have an income between 9191 and 9797 million dollars.

This is equivalent to finding the area under the standard normal distribution curve between z = 0.61 and z = 1.22.

We can use a standard normal distribution table or calculator to find this probability.

For example, using a standard normal distribution table, we can find that:

P(0.61 < Z < 1.22) = 0.1879

Therefore, the probability that a randomly selected firm will earn between 9191 and 9797 million dollars is, 0.1879 or 18.79%.

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Answer:

im lost only because you made this so long

Step-by-step explanation: