The number of hours, x, Ryan rides his bike and the total number of miles, y, he rides is a lineadrelationship. Ryan has already ridden 5 miles, and he can ride at a constant rate of(12 miles per hour. Write an equation relating × hours and y miles. Then predict how many minutes will pass for Ryan to have traveled a total of 60 miles.

The roots have positive or same signs when c>0.

Note that only real numbers can be positive or negative. This concept does not apply to complex non real numbers. So first we have to make sure that the roots are real which occurs when discriminant is greater or equal to 0.

[tex]b^{2} -2ac > 0\\2^{2} -2(-1) (c) > 0\\4-2c > 0\\c > -2[/tex]

Roots of quadrant equation have Samsame sign if product of roots >0.

[tex]\frac{a}{c} > 0\\\frac{c}{-1} > 0\\c < 0[/tex]

Roots of quadratic equation have positive sign if product of roots<0.

c>0.

Combining results, we get:-

roots have positive signs when:-

c>0.

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Answer:

We are given that the point (3,w) lies on the line y = 2x + 7. This means that if we substitute x = 3 into the equation y = 2x + 7, we will get the value of y at x = 3, which is equal to w.

Substituting x = 3 into the equation y = 2x + 7, we have:

y = 2(3) + 7

y = 6 + 7

y = 13

Therefore, the value of w is 13.

Step-by-step explanation:

Answer:

y = -3x - 2

Step-by-step explanation:

To write the equation 6x + 2y = -4 in slope-intercept form, we need to solve for y.

First, we can isolate the y-term by subtracting 6x from both sides:

6x + 2y = -4

2y = -6x - 4

Next, we can divide both sides by 2 to isolate y:

2y/2 = (-6x - 4)/2

y = -3x - 2

So the slope-intercept form of the equation 6x + 2y = -4 is y = -3x - 2.

Answer:

[tex]6z \: = 6 + z \: \\ z {}^{6} = z \times z \times z \times z \times z \times z \\ [/tex]

The mathematical statement in the form of expression can be written as 15625z⁶.

An expression in mathematics is a combination of terms both constant and variable. For example, we can write the expressions as -

2x + 3y + 5

2z + y

x + 3y

Given is to find the mathematical statement -

"Difference between 6z and z to the power of 6"

We can write the given mathematical statement in the form of expression as -

(6z - z)⁶

(5z)⁶

5⁶ x z⁶

125 x 125 x z⁶

15625z⁶

Therefore, the mathematical statement in the form of expression can be written as 15625z⁶.

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Lisa's percentile rank is approximately 88%.

Percentile rank is a statistical measure that indicates the percentage of scores that fall below a particular score in a given distribution of data. It is commonly used to describe the relative position of a particular score in a set of scores.

If Lisa's score was 83 and that score was the 29th score from the top in a class of 240 scores, then her percentile rank can be calculated using the following formula:

Percentile Rank = [(Number of scores below Lisa's score) ÷ (Total number of scores)] × 100

Percentile Rank = [(240 - 29) ÷ 240] × 100

Percentile Rank = (211 ÷ 240) × 100

Percentile Rank = 0.8792 × 100

Percentile Rank ≈ 88 (rounded to the nearest whole number)

Therefore, her percentile rank is approximately 88%.

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From the given information provided, the area of the shaded region inside the circle is 22.58

The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane.

The space enclosed by the sector of a circle is called the area of the sector.

the radius of the circle is 5cm.

area of arc =  radius² × θ/2

area of the arc is =  5² × 4π/9 = 25 × 4/9 = 34.88

area of the triangle inside circle = a×b × sin(y)/2

area of triangle = 5×5 × sin(80°)/2 = 25 × 0.492

area = 12.3

area of the shaded region is = 34.88 - 12.3 = 22.58

Hence, the area of the shaded region is 22.58

Question - Find the area of the shaded region in the circle if the angle of the arc is 80 degree radius is 5cm.

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Answer:

A) k = 0.037

B) 186°F

Step-by-step explanation:

List initial (T₀) and air (Tₐ) temperature

[tex]T_0=280^\circ\\T_a=67^\circ\\[/tex]

Part A

[tex]T=T_a+(T_0-T_a)e^{-kt}\\193^\circ=67^\circ+(208^\circ-67^\circ)e^{-k(3)}\\193=67+141e^{-3k}\\126=141e^{-3k}\\\frac{126}{141}=e^{-3k}\\\ln(\frac{126}{141})=-3k\\-\frac{1}{3}\ln(\frac{126}{141})=k\\k\approx0.037[/tex]

Part B

[tex]T=T_a+(T_0-T_a)e^{-kt}\\T=67+(208-67)e^{-0.037(4.5)}\\T\approx186^\circ\text{F}[/tex]

The equation is equivalent to pq=r is option (C) q=logR p

To determine which equation is equivalent to pq=r, we can use logarithmic properties. Taking the logarithm of both sides of the equation, we get

log(pq) = log(r)

Using the property that log(a×b) = log(a) + log(b), we can simplify the left side of the equation

log(p) + log(q) = log(r)

Now, we can compare this expression to each of the answer choices

A) p = logR q

Substituting this into the equation, we get

log(p) + logR(q) = log(r)

This is not equivalent to our expression, so A is not the correct answer.

B) p = logQ r

Substituting this into the equation, we get

log(logQ r) + log(q) = log(r)

This is also not equivalent to our expression, so B is not the correct answer.

C) q = logR p

Substituting this into the equation, we get

log(p) + logR(q) = log(r)

This matches our expression, so C is the correct answer.

D) q = logP r

Substituting this into the equation, we get

log(p) + log(q) = log(logP r)

This is not equivalent to our expression, so D is not the correct answer.

Therefore, the correct option is (C)  q=logR p

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The rate of filling water in the tank is 23450t gallons per hour.

Let's assume that the time taken to fill the tank is t hours.

The volume of water filled into the tank at time t is given by the expression V(t) = 23450t.

The tank is originally empty, which means its volume = 0 gallons.

After 5 hours,

t= 5 hours

The volume of water filled in is given by [tex]V(5) = 23450 * 5= 1,17,250[/tex] gallons of water.

Therefore, 1,17,250 gallons of water are filled in the tank after 5 hours.

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The smallest number of batteries in the package for the probability to exceed 1% is a) 17. This can be calculated using the binomial distribution with parameters n=17 and b)p=0.2927 and number of batteries is c)4. (Where p is the probability from part a).

a) The probability that a battery does not reach the significant milestone after 8 hours of usage is 0.2927.

This can be calculated using the cumulative normal distribution function. The parameters are μ=7.36, σ=0.29, and x=8.

b) The probability that at least 10 batteries will last more than 7.5 hours is 0.7012.

This can be calculated using the binomial distribution with parameters n=12 and p=0.2927 (where p is the probability from part a).

c) The number of batteries should be in package is μ*4.2/7.5 = 4.

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Answer:

r = -2

Step-by-step explanation:

We can use the slope formula to find r.

m = ( y2-y1)/(x2-x1)

3 = ( 19-4)/(r- -7)

3 = 15/(r+7)

Multiply each side by (r+7).

3 ( r+7) = 15

Divide each side by 3.

r+7 = 15/3

r+7 = 5

Subtract 7 from each side.

r+7-7 = 5-7

r = -2

The Central Limit Theorem (CLT) states that as the sample size n increases, the sample mean approaches a normal distribution with a mean of μ and a standard deviation of σ/√n.

Therefore, when the number of houses in a population is unknown and a random sample of 48 houses is drawn from it, the mean for the sample sum distribution can be calculated using the CLT as follows:Mean for the sample sum distribution = nμ = 48 * 1670 = 80,160. The standard deviation for the sample sum distribution is given by:σ/√n = 140/√48 ≈ 20.20. Therefore, the sample sum distribution has a mean of 80,160 and a standard deviation of 20.20.To verify this, a histogram can be plotted in Excel using the following steps:Enter the data for the square footage of the 48 houses in column A of the Excel worksheet.Highlight column B and enter the formula =SUM(A1:A48) to sum the data in column A and store the result in column B.Highlight column C and enter the formula =B1/48 to calculate the mean for the sample sum distribution and store it in column C.Highlight column D and enter the formula =140/SQRT(48) to calculate the standard deviation for the sample sum distribution and store it in column D.Highlight columns B, C, and D, and select the Insert tab.Click on the Histogram icon under the Charts group.Select the Histogram chart type, and click OK to generate the histogram.The histogram should show a bell-shaped curve with a mean of 80,160 and a standard deviation of 20.20, indicating that the sample sum distribution is approximately normal.

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The direction of the steepest descent, which is used to find the minimum value of a function.

The necessary and sufficient condition that Aθ-b = 0 has a unique solution is: A is invertible.What is computing?Computing is a part of computer science that focuses on computer programs, including their software and hardware. It is concerned with designing algorithms to solve problems and creating software that will run these algorithms. As a result, computing is a field of study that is concerned with the process of creating algorithms and software.InvertibleAn invertible matrix is a matrix in which the determinant is not zero. An invertible matrix is also referred to as a non-singular matrix. An invertible matrix has a unique inverse. The rank of an invertible matrix is equal to its dimension. An invertible matrix can be used to solve a system of linear equations.GradientA gradient is a vector field in which the direction of the vector points to the steepest increase in a function, and the magnitude of the vector is the rate of increase in that direction. The gradient of a function is a vector field that is a derivative of the function. The gradient is used in multivariable calculus to solve optimization problems. The gradient is used to find the direction of the steepest ascent, which is used to find a maximum value of a function. It is used to find the direction of the steepest descent, which is used to find the minimum value of a function.

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Answer: 8 mangoes

Step-by-step explanation:

1. To find the total number of mangoes Peter had, add 8 and 24 which gives you 32. 8 + 24 = 32.

2. If Peter had an equal number of mangoes in each bag, and a total number of 32 mangoes, then you must divide the total number of mangoes by the number of bags, which is 4. 32 ÷ 4 = 8. Therefore, there were 8 mangoes in each bag.

Answer:

The answer  is 8 mangoes

The slope is 10 and the y-intercept is 0, making this a linear equation in the slope-intercept format.

The basic form of a linear equation is y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept. A linear equation is a mathematical equation that describes a straight line in a two-dimensional plane. Many real-world situations, such as the connection between a product's price and the number of sales, or the relationship between a person's age and height, can be modelled using linear equations.

given

Let t be the number of hours and d be the number of miles that Sebi goes. Since Sebi consistently travels at 10 mph on his bicycle, we can apply the following equation:

Distance is determined by rate and duration.

When we change the numbers, we obtain:

d = 10t

The slope is 10 and the y-intercept is 0, making this a linear equation in the slope-intercept format.

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The given functions form a fundamental set of solutions of the given system.

The solution of the given system of differential equations is shown below.a) To prove that the given functions X(1) and x(2) are the solutions of the given system of differential equations, we must substitute these functions into the given system to show that they satisfy the equations.In the given system, we have the following equations:

X_1' (t) = 2X_1 (t) - X_2 (t)
X_2' (t) = 4X_1 (t) - 2X_2 (t)

Now, let's substitute the given vector-valued functions X(1) and x(2) into the above equations and check if they satisfy these equations.

a. For X(1) = [1, 2]e^2t
Substituting X(1) into the given system, we get:

X_1' (t) = [1, 2] * 2e^2t = 2X_1 (t) - X_2 (t)
X_2' (t) = [1, 2] * 4e^2t = 4X_1 (t) - 2X_2 (t)

Therefore, the given function X(1) is a solution to the given system of differential equations.

b. To prove that X = C1x(1) + C2x(2) is also a solution of the given system for any values of C1 and C2, we need to X into the given system of equations and check if it satisfies the equations.

So, we have:

X = C_1[1, 2]e^2t + C_2[1, -1]e^-t
X_1 = C_1e^2t + C_2e^-t
X_2 = 2C_1e^2t - C_2e^-t

Differentiating X_1 and X_2 with respect to t, we get:

X_1' = 2C_1e^2t - C_2e^-t
X_2' = 4C_1e^2t + C_2e^-t

Substituting X_1 and X_2 into the given system, we get:

X_1' (t) = 2(C_1e^2t - C_2e^-t) = 2X_1 (t) - X_2 (t)
X_2' (t) = 4(C_1e^2t + C_2e^-t) = 4X_1 (t) - 2X_2 (t)

Therefore, the given function X = C1x(1) + C2x(2) is also a solution of the given system for any values of C1 and C2.

c. To show that the given functions form a fundamental set of solutions of the given system, we need to prove that they are linearly independent and that their Wronskian is non-zero.

We know that the vectors [1, 2] and [1, -1] are linearly independent, therefore the functions x(1) and x(2) are also linearly independent.

Also, the Wronskian of x(1) and x(2) is given by:

W(x1, x2) = | x1  x2 |
         | x1' x2' |

Substituting x(1) and x(2) into the above equation, we get:

W(x1, x2) = | e^2t  e^-t  |
          | 2e^2t -e^-t |

Simplifying the above equation, we get:

W(x1, x2) = 3e^(3t) ≠ 0

Therefore, the given functions form a fundamental set of solutions of the given system.

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The box plot represents the data set 2, 4, 6, 8, 10, 12 is option (a) A box-and-whisker plot. The number line goes from 1 to 10. The whiskers range from 1 to 9, and the box ranges from 3 to 8. A line divides the box at 7. 5.

A box-and-whisker plot is a graphical representation of a data set that displays the distribution of the data, as well as its quartiles and any outliers. The plot is made up of a rectangular box, which represents the middle 50% of the data, with a line in the box representing the median. Two lines, called whiskers, extend from the box to represent the range of the data outside of the box, excluding any outliers. Outliers are any values that fall outside of the whiskers.

In the given options, the box-and-whisker plot that represents the data set 2, 4, 6, 8, 10, 12 is the one that has a box ranging from 4 to 10, with a median line dividing the box at 7. This means that 50% of the data falls between 4 and 10, with the median value being 7. The whiskers range from 2 to 12, indicating that the data set has a minimum value of 2 and a maximum value of 12.

Therefore, the correct option is (a) A box-and-whisker plot. The number line goes from 0 to 12. The whiskers range from 2 to 12, and the box ranges from 4 to 10. A line divides the box at 7.

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The given question is incomplete, the complete question is:

Which box plot represents the data set 2, 4, 6, 8, 10, 12?

A box-and-whisker plot. The number line goes from 0 to 12. The whiskers range from 2 to 12, and the box ranges from 4 to 10. A line divides the box at 7.

A box-and-whisker plot. The number line goes from 0 to 12. The whiskers range from 2 to 12, and the box ranges from 4 to 8. A line divides the box at 6.

A box-and-whisker plot. The number line goes from 0 to 12. The whiskers range from 2 to 12, and the box ranges from 4 to 9. A line divides the box at 6.

A box-and-whisker plot. The number line goes from 0 to 12. The whiskers range from 2 to 12, and the box ranges from 6 to 10. A line divides the box at 8.

Answer: (B)

Correct Answer 100%! Pls, give me brainliest. Thank You!

Suppose that you wanted to predict the price of a house based on where the house was located (northeast, northwest, southeast, or southwest) as well as square footage, then the northwest indicator variable would be set to 1, and the other three indicator variables would be set to 0.

Indicator variable An indicator variable is a binary variable that indicates whether or not a specific condition or category is present. Indicator variables are typically used in statistical models to represent categorical data or conditions, and they are also known as dummy variables or binary variables.

Example suppose you want to conduct a statistical analysis to determine the impact of location and size on the price of a house. There are four possible locations: northeast, northwest, southeast, and southwest. We can use four indicator variables (one for each location) to represent this information.

For instance, if a house is in the northeast, the northeast indicator variable would be set to 1, while the other indicator variables would be set to 0. Similarly, if the house is in the northwest, the northwest indicator variable would be set to 1, and the other three indicator variables would be set to 0. We would use similar logic for the other two locations.

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The sale price including tax is $ 2390.625.

Given that,

The price of the snow machine= $ 1800

Discount percentage= 25%

Sales tax rate = 6.25%

Hence, Sale price = Price + Discount percentage of price

                              = 1800 + 25/100 × 1800

                              = 1800 + 450

                              = 2250.

Sale price including tax = Sale price + Tax rate

                                       = 2250 + 6.25/100

                                       = 2250 + 140.625

                                       = $ 2390.625.

Hence, the sale price including tax is $ 2390.625.

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The correct definition for the lines drawn to circle with centre C are:

A circle is a spherical shape without boundaries or edges.

Thus, on the basis of propertied of circle, the correct definition for the lines drawn to circle with centre C are:

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Therefore , the solution of the given problem of triangle comes out to be the angles P and Q have measurements of roughly 39.39° and 58.10°, respectively.

A polygon is a hexagon if it has over one extra segment. It's shape is a simple rectangle. Only the sides A and B can differentiate something like this arrangement from a regular triangle. Despite the exact collinearity of the borders, Euclidean geometry only produces a portion of the cube. Three edges and three angles make up a triangle.

Here,

The rule of cosines can be applied to the triangle PQR to determine the length of side PQ:

=>  PQ² = PR² + QR² - 2(PR)(QR)cos(∠PQR)

=>  PQ² = 9² + 12² - 2(9)(12)cos(62°)

=>  PQ² ≈ 110.03

=> PQ ≈ 10.49

As a result, side PQ is roughly 10.49 units long.

The rule of sines can then be used to determine the dimensions of angles P and Q:

=> sin(∠P) / PQ = sin(62°) / PR

=>  sin(∠P) / 10.49 = sin(62°) / 9

=>  sin(∠P) ≈ 0.6322

=>  ∠P ≈ 39.39°

=>  sin(∠Q) / PQ = sin(77°) / QR

=>  sin(∠Q) / 10.49 = sin(77°) / 12

=>  sin(∠Q) ≈ 0.8559

=>  ∠Q ≈ 58.10°

As a result, the angles P and Q have measurements of roughly 39.39° and 58.10°, respectively.

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Answer:

-1, 2, 5 , 8 , 11   or  2, 5, 8, 11 , 14

Step-by-step explanation:

Assume n starts from 0

a(0) = 3 (0) -1 = -1
a(1) = 3 (1) -1 = 2
a(2) = 3 (2) -1 = 5
a(3) = 3 (3) -1 = 8
a(4) = 3 (4) -1 = 11

notice If we Assume n starts from 1

a(1) = 3 (1) -1 = 2
a(2) = 3 (2) -1 = 5
a(3) = 3 (3) -1 = 8
a(4) = 3 (4) -1 = 11
a(5)= 3 (5) -1 = 14

Notice a sequence can start from any N. But the most common ones are n=0 or n=1

Answer:

Width = 17 inches

Length = 43 inches

Step-by-step explanation:

  Let the width of the rectangle = x inches

              Length = 2*width +9

                          = (2x + 9) cm

    [tex]\boxed{\bf Perimeter \ of \ rectangle = 2* (length + width)}[/tex]

        2* (length + width) = 120 inches

         2* (2x + 9 + x)       = 120

                     2* (3x + 9) = 120

Use Distributive property,

                 2 * 3x + 2*9  = 120

                         6x + 18   = 120

Subtract 18 from both sides,

                                   6x = 120 - 18

                                   6x = 102

Divide both sides by 6,

                                     x = 102 ÷ 6

                                     x = 17

Width = 17 inches

Length = 2*17 +9

           = 34 + 9

           = 43 inches

From the given information provided, the number of people having brown eyes in town is 180.

If the probability that a person in the town has brown eyes is 2/5, then we can expect that 2 out of every 5 people have brown eyes.

To find the number of people in the survey who would be expected to have brown eyes, we can use the following proportion:

(2/5) = (x/450)

where x is the number of people expected to have brown eyes.

Solving for x, we can cross-multiply:

5x = 2 × 450

5x = 900

x = 180

Therefore, the expected number of people in the survey who would have brown eyes is 180.

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The area of the parallelogram is 324 square yards.

What is a parallelogram ?

A parallelogram is a four-sided geometric shape that has two pairs of parallel sides. It isdefined by its four vertices, four sides, and two diagonals that intersect at their midpoint. The opposite sides of a parallelogram are congruent, and the opposite angles are also congruent. The adjacent angles are supplementary and add up to 180 degrees.

To find the area of a parallelogram, we need to multiply the length of the base by the height, which is the perpendicular distance from the base to the opposite side. This formula is similar to finding the area of a rectangle, where the base is one side of the rectangle and the height is the distance from that side to the opposite side.

Calculating the area of the given parallelogram :

The area of a parallelogram is  A = bh, where b is the base and h is the height.

Given the height of the parallelogram is 12 yards and the base is 27 yards. Using the formula for the area of a parallelogram, we can calculate the area as follows:

A = bh

A = 27 yards × 12 yards

A = 324 square yards

Therefore, the area of the parallelogram is 324 square yards.

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The number of distinct elements of AB = m n.

Given that G is a group with subgroups A and B of orders m and n, respectively, where m and n are prime, we need to prove that the subset of G, AB = {abla E Ab E B}, has m n distinct elements. Step-by-step. Let, G is a group with subgroups A and B of orders m and n, respectively. Since, m and n are relatively prime, then we have gcd(m, n) = 1.By Lagrange's Theorem, the order of any subgroup of G divides the order of G.

Hence, the order of G is equal to the product of the orders of A and B, i.e. |G| = |A| * |B| = m * n Let, a and a' be two distinct elements of A and b and b' be two distinct elements of B. Thus, a and a' generate distinct subgroups of G, i.e.  ≠  and b and b' generate distinct subgroups of G, i.e.  ≠ .Now, the number of distinct elements of AB = {abla E Ab E B} is equal to |A||B| since any two elements ab and a'b' of AB will be distinct if either a and a' are distinct or b and b' are distinct or both are distinct. Hence, the number of distinct elements of AB = m n.

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Answer: 50 uk pounds

Step-by-step explanation:

Step-by-step explanation:

See image below

Answer:

$56 divided by 7 hours is $8 per hour sh get payed.

Answer:

answer is 091 accc h na tu

(a) Probability that X < 0 is P(X<0) = 1/2
(b) Probability that -3.5 < X < 3.5 is given by = 1/2
(c) Probability that -5 ≤ X ≤ 6 is given by = 11/14.
(d) Let k be any number such that -7 < k < k+4 < 7 = 2/7

(a) Since the distribution is uniform, the probability of X being less than 0 is equal to the proportion of the interval (-7, 7) that lies to the left of 0. This proportion is (0 - (-7))/(7 - (-7)) ⇒ 7/14 ⇒ 1/2.

Therefore, P(X < 0) = 1/2.

(b) Following the same logic as above, the probability of X lying between -3.5 and 3.5 is equal to the proportion of the interval (-7, 7) that lies between -3.5 and 3.5. This proportion is (3.5 - (-3.5))/(7 - (-7)) ⇒ 7/14 ⇒ 1/2.

Therefore, P(-3.5 < X < 3.5) = 1/2.

(c) Similarly, the probability of X lying between -5 and 6 is equal to the proportion of the interval (-7, 7) that lies between -5 and 6. This proportion is (6 - (-5))/(7 - (-7)) ⇒ 11/14.

Therefore, P(-5 ≤ X ≤ 6) = 11/14.

(d) The interval (k, k+4) lies completely within the interval (-7, 7) if -3 < k < 3. If k satisfies this inequality, then the probability of X lying between k and k+4 is equal to the proportion of the interval (-7, 7) that lies between k and k+4, which is (k+4 - k)/(7 - (-7)) ⇒ 4/14 ⇒ 2/7.

Therefore, P(k < X < k+4) = 2/7.

To Know more about the "probability": https://brainly.com/question/23780714

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