It would have cost the family an
additional $22.70 a month to purchase
disability insurance for Camila. The
family opted out of this expense.
Assuming that you had no knowledge of
Camila's impending accident, would you
have made the same decision to not
purchase disability insurance? Explain.

The top and lower sums for n =2,4, and 8 and f(x) = 2 +sin(x),0  x   are as follows:

n = 2: Upper Sum = 7.85398; Lower sum ≈ 7.85398

n = 4: Upper sum ≈ 6.43917; Lower sum ≈ 6.43917

n = 8: Upper sum ≈ 6.35258; Lower sum ≈ 6.352

It is necessary to first divide the range [0, ] into n subintervals of identical width x, where x = ( - 0)/n = /n, in order to calculate the upper and lower sums for the equations f(x) = 2 + sin(x), 0 x for n = 2, 4, and 8. The endpoints of these subintervals are:

x0 = 0, x1 = Δx, x2 = 2Δx, ..., xn-1 = (n-1)Δx, xn = π.

Then, for each subinterval [xi-1, xi], we can approximate the area under the curve by the area of a rectangle whose height is either the maximum or minimum value of f(x) on that interval. The sum of these areas' overall subintervals gives us the upper and lower sums.

For n = 2:

[0, π/2]: f(π/2) = 2 + sin(π/2) = 3

[π/2, π]: f(π) = 2 + sin(π) = 2

[0, π/2]: f(0) = 2 + sin(0) = 2

[π/2, π]: f(π/2) = 2 + sin(π/2) = 3

For n = 4:

[0, π/4]: f(π/4) = 2 + sin(π/4) ≈ 2.70711

[π/4, π/2]: f(π/2) = 2 + sin(π/2) = 3

[π/2, 3π/4]: f(3π/4) = 2 + sin(3π/4) ≈ 2.29289

[3π/4, π]: f(π) = 2 + sin(π) = 2

[0, π/4]: f(0) = 2 + sin(0) = 2

[π/4, π/2]: f(π/4) = 2 + sin(π/4) ≈ 2.70711

[π/2, 3π/4]: f(π/2) = 2 + sin(π/2) = 3

[3π/4, π]: f(3π/4) = 2 + sin(3π/4) ≈ 2.29289

For n = 8:

[0, π/8]: f(π/8) = 2 + sin(π/8) ≈ 2.25882

[π/8, π/4]: f(π/4) = 2 + sin(π/4) ≈ 2.70711

[π/4, 3π/8]: f(3π/8) = 2 + sin(3π/8) ≈ 2.96593

[3π/8, π/2]: f(π/2) = 2 + sin(π/2) = 3

[π/2, 5π/8]: f(5π/8) = 2 + sin(5π/8) ≈ 2.96593

[5π/8, 3π/4]: f(3π/4) = 2 + sin(3π/4) ≈ 2.70711

[3π/4, 7π/8]: f(7π/8) = 2 + sin(7π/8) ≈ 2.25882

[7π/8, π]: f(π) = 2 + sin(π) = 2

[0, π/8]: f(0) = 2 + sin(0) = 2

[π/8, π/4]: f(π/8) = 2 + sin(π/8) ≈ 2.25882

[π/4, 3π/8]: f(π/4) = 2 + sin(π/4) ≈ 2.70711

[3π/8, π/2]: f(3π/8) = 2 + sin(3π/8) ≈ 2.96593

[π/2, 5π/8]: f(π/2) = 2 + sin(π/2) = 3

[5π/8, 3π/4]: f(5π/8) = 2 + sin(5π/8) ≈ 2.96593

[3π/4, 7π/8]: f(3π/4) = 2 + sin(3π/4) ≈ 2.70711

[7π/8, π]: f(7π/8) = 2 + sin(7π/8) ≈ 2.25882

The complete question is:-

Unless specified, all approximating rectangles are assumed to have the same width. Evaluate the upper and lower sums for f(x) = 2 + sin(x),0 ≤ x ≤ π with n = 2, 4, and 8.

To learn more about the upper sum, refer:-

https://brainly.com/question/29636891

#SPJ1

Answer:

[tex]u = \frac{2 \sqrt{6} }{3} [/tex]

[tex]v = \frac{ \sqrt{6} }{3} [/tex]

Step-by-step explanation:

Use trigonometry:

[tex] \tan(60°) = \frac{ \sqrt{2} }{v} [/tex]

Use the property of proportion to find v:

[tex]v = \frac{ \sqrt{2} }{ \tan(60°) } = \frac{ \sqrt{2} }{ \sqrt{3} } = \frac{ \sqrt{2} \times \sqrt{3} }{ \sqrt{3} \times \sqrt{3} } = \frac{ \sqrt{6} }{3} [/tex]

Use the Pythagorean theorem to find u:

[tex] {u}^{2} = {v}^{2} + ( { \sqrt{2} )}^{2} [/tex]

[tex] {u}^{2} = ( { \frac{ \sqrt{6} }{3}) }^{2} + ( { \sqrt{2} )}^{2} = \frac{6}{9} + \frac{2}{1} = \frac{6}{9} + \frac{2 \times 9}{9} = \frac{6}{9} + \frac{18}{9} = \frac{24}{9} = \frac{8}{3} [/tex]

[tex]u > 0[/tex]

[tex]u = \sqrt{ \frac{8}{3} } = \frac{2 \sqrt{6} }{3} [/tex]

Answer:

C)  decreasing then increasing.

Step-by-step explanation:

A function is said to be increasing if the y-values increase as the x-values increase.

A function is said to be decreasing if the y-values decrease as the x-values increase.

From inspection of the given graph of y = x², we can see that for the first half of the graph, the y-values are decreasing as the x-values increase. Therefore, the function is decreasing for this part of the graph.

Similarly, for the second half of the graph, we can see that the y-values are increasing as the x-values increase. Therefore, the function is increasing for this part of the graph.

So the description of the graph of the function is:

The range, on the other hand, is affected by extreme values and may not be a good representation of the spread of the data in these cases.

What is Histogram ?

A histogram is a graphical representation of the distribution of a dataset. It is a way to display the frequency of occurrence of different values or ranges of values in a dataset.

The correct answer is IQR, because it is more robust to outliers and is not affected by extreme values like Range.

Although the question provides information about the shape of the histograms, it does not indicate whether the distributions are symmetric or skewed. Therefore, the choice of IQR over Range is not based on the shape of the data but on the fact that IQR is a more appropriate measure of variability when dealing with skewed data or data with outliers.

In general, the IQR is a better measure of variability than the range when the data is skewed or contains outliers, as it only considers the middle 50% of the data and is not affected by extreme values.

Therefore, The range, on the other hand, is affected by extreme values and may not be a good representation of the spread of the data in these cases.

To learn more about Histogram from given link.

https://brainly.com/question/16819077

#SPJ1

Answer:

1) option A

2) p > 34

Step-by-step explanation:

1)  Inequality:   7 ≤ n + 5

Subtract 5 from both sides,

                  7 - 5 ≤ n +5 - 5

                    2 ≤ n

The value of n is all values greater than or equal to 2.

So, the answer is option A.

2) Inequality:   16 + p > 50

 Solution:

             Subtract 16 from both sides,

                  16 - 16 + p > 50 - 16

                                p > 34

Answer:

825 miles

Step-by-step explanation:

275 x 3 = 825

Helping in the name of Jesus.

Answer: 15 inches

Step-by-step explanation:

An equilateral triangle has three equal sides, so if the perimeter of the triangle is 45 inches, then each side must be 45 inches divided by 3, which gives us:

45 in ÷ 3 = 15 in

Therefore, the length of each side of the flag is 15 inches.

Samantha waters her tomato plants once a week with between 15 and 60 gallons of water.

Domain refers to the set of possible values that the independent variable can take. In this case, the domain is the range of possible amounts of water that Samantha can use to water her tomato plants, which is 15 to 60 gallons.

The independent variable is the variable that is being manipulated or controlled by Samantha, which in this case is the amount of water used to water the tomato plants. So, the independent variable is "gallons of water used".

The dependent variable is the variable that is being measured or observed, which in this case is the number of tomatoes produced each week. So, the dependent variable is the "number of tomatoes produced".

Therefore, the answer is:

To learn more about dependent variables, refer:-

https://brainly.com/question/29430246

#SPJ1

Answer:

using the trigonometry identities

Cos ∅ = Adj/Hyp

where ∅ = 73°

Cos 73 = 8.6/x

X × Cos 73 = 8.6

x = 8.6/0.2923

x = 29.421 ≈ 29.4

Answer:

m∠B = 36.9 °

Step-by-step explanation:

SOH  -  CAH  -  TOA

Sine → Opposite/Hypotenuse

sin(θ) = 3/5

[tex]\theta = sin^-^1(3/5)\\[/tex]

θ = 36.86 degrees

Round to nearest tenth, so m∠B = 36.9 °

The graph represents the equation with option C, tan x/2.

A graph is a structure that resembles a collection of objects in discrete mathematics, more specifically in graph theory, in which some pairs of the objects are conceptually "related." The objects are represented by mathematical abstractions known as vertices, and each set of connected vertices is referred to as an edge.

Here,

The graph of the function tan(x/2) represents the tangent of half of the angle x in radians.

The tangent function has vertical asymptotes at odd multiples of π/2, which means that the function is undefined at those points. Therefore, the graph has vertical asymptotes at x = π/2, 3π/2, 5π/2, ....

The function also has zeros at even multiples of π, which occur when tan(x/2) = 0. This happens when x/2 = kπ where k is an integer, so x = 2kπ.

Between each pair of vertical asymptotes, the function oscillates between positive and negative infinity. The function is positive in the intervals (2kπ, (2k+1)π) and negative in the intervals ((2k-1)π, 2kπ) for all integers k.

To know more about graph,

https://brainly.com/question/29467965

#SPJ1

So the area of the living room on the scale drawing is 334128.48 square centimeters.

Area is a measure of the size of a two-dimensional surface or region, typically expressed in square units. It is the amount of space inside a flat, enclosed shape or surface, and is calculated by multiplying the length and width of the shape or surface. For example, the area of a rectangle can be calculated by multiplying its length by its width, while the area of a circle can be calculated by multiplying pi (3.14) by the square of its radius. Area is a fundamental concept in mathematics and is used in a wide range of fields, from geometry and physics to engineering and architecture.

Here,

First, we need to determine the actual dimensions of the living room. Since each 4 cm on the scale drawing is equal to 8 feet, we can set up a proportion:

4 cm : 8 feet = 12 cm : x

Solving for x, we get:

x = (12 cm x 8 feet) / 4 cm

= 24 feet

So the actual length and width of the living room are 24 feet and 24 feet, respectively.

The area of the living room is then:

Area = length x width

= 24 feet x 24 feet

= 576 square feet

Now, we need to determine the area of the living room on the scale drawing. Since the length and width of the scale drawing are both 12 cm, the area is:

Area = length x width

= 12 cm x 12 cm

= 144 square cm

Finally, we can determine the scale factor for the area by dividing the actual area by the scale area:

Scale factor = actual area / scale area

= 576 square feet / 144 square cm

Since we need the area in square centimeters, we can convert square feet to square centimeters by multiplying by 929.03:

Scale factor = (576 square feet / 144 square cm) x (929.03 square cm/square feet)

= 2324.12

Therefore, the area of the living room on the scale drawing is:

Area = scale area x scale factor

= 144 square cm x 2324.12

= 334128.48 square cm

To know more about area,

https://brainly.com/question/13194650

#SPJ1

After solving by linear programming, the business needs create 100 Type I pencils and 80 Type II pencils to increase revenue.

LINEAR PROGRAMMING: WHAT IS IT?

A mathematical method called linear programming is used to maximise a linear objective function under the restrictions of linear equality and inequality. In a mathematical model whose requirements are expressed by linear connections, it is used to identify the best result.

With linear programming, this issue can be resolved.

Please define x as the quantity of Type I pencils produced and y as the quantity of Type II pencils produced.

Profit = 3x + 5y is the formula for the goal function.

2x + 5y 660 are the restrictions (sanding constraint)

(Polishing constraint): x ≥0 y≥ 0; 6x + 3y 730

Under these limitations, we wish to maximize the profit function.

The largest profit comes when x = 100 and y = 80,

with a profit of $740, according to software that can solve linear programming issues or a graphing calculator.

Thus, the business needs create 100 Type I pencils.80pencil for type II

To know more about linear programming visit:

brainly.com/question/15417573

#SPJ1

The ratio of vegetable oil to water is  [tex]\frac{5}{8}[/tex] : 2 and the value of the ratio is 0.3125.

What is ratio?

By dividing two amounts of the same unit, it is possible to determine how much of one quantity is in the other. This is referred to as ratio in mathematics.

We are given that a particular recipe uses [tex]\frac{5}{8}[/tex] cup of vegetable oil and 2 cups of water.

So, from this, we get the ratio of vegetable oil to water as [tex]\frac{5}{8}[/tex] : 2.

Now, the value of the obtained ratio is

⇒ 0.625 : 2

⇒ 0.3125

Hence, the required solution has been obtained.

Learn more about ratio from the given link

https://brainly.com/question/12024093

#SPJ9

The equation of the line perpendicular to the given line passing through the point   [tex](-2, 3)[/tex] is  [tex]y = -3/2 x + 15/2[/tex] , which is not one of the options provided.

To find the equation of a line parallel to a given line, we need to use the fact that parallel lines have the same slope.

The given line has a slope of  [tex]2/3,[/tex]so the parallel line we're looking for will also have a slope of [tex]2/3[/tex]. Using the point-slope form of a line, we can write:

[tex]y - y_{1} = m(x - x_{1} )[/tex]

where m is the slope and [tex](x_{1} , y_{1} )[/tex] is the given point. Substituting the values we have:

[tex]y - 3 = (2/3)(x - (-2))[/tex]

[tex]y - 3 = 2/3 x + 4/3[/tex]

[tex]y = 2/3 x + 13/3[/tex]

So the equation of the line parallel to the given line passing through the point  [tex]t (-2, 3) is y = 2/3 x + 13/3[/tex], which is option A.

To find the equation of a line perpendicular to a given line, we need to use the fact that perpendicular lines have slopes that are negative reciprocals of each other.

The given line has a slope of 2/3, so the perpendicular line we're looking for will have a slope of -3/2. Using the point-slope form of a line again, we can write:

[tex]y - y_{1} = m(x - x_{1} )[/tex]

where m is the slope and  [tex](x_{1} , y_{1} )[/tex] is the given point. Substituting the values we have:

[tex]y - 3 = (-3/2)(x - (-2))[/tex]

[tex]y - 3 = -3/2 x - 9/2[/tex]

[tex]y = -3/2 x + 15/2[/tex]

Therefore,  the equation of the line perpendicular to the given line passing through the point [tex](-2, 3) is y = -3/2 x + 15/2,[/tex] which is not one of the options provided.

Learn more about perpendicular here:

brainly.com/question/29268451

#SPJ1

The linear inequality for the shaded region with slope -4 is:

[tex]y < -4x + 4[/tex]

In mathematics, a linear inequality is an inequality involving a linear function in one or more variables. It describes a region in the coordinate plane that satisfies the inequality.

In mathematics, the slope is a measure of the steepness of a line. It describes how much a line rises or falls as we move from left to right along it.

According to the given information,

To write the linear inequality for the graph passing through points (0,4) and (1,0), we need to find the equation of the line first.

The slope of the line passing through these two points is:

[tex]m = (y_{2} - y_{1} ) / (x_{2} - x_{1})[/tex]

= (0 - 4) / (1 - 0)

= -4

Using the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept, we can find the equation of the line passing through these two points:

[tex]y = -4x + 4[/tex]

Now, to write the linear inequality for this line, we need to determine which side of the line is shaded. We can use the test point (0,0) to check which side of the line contains the solutions to the inequality.

If we plug in (0,0) into the equation [tex]y = -4x + 4[/tex], we get:

0 = -4(0) + 4

0 = 4

Since 0 is not less than 4, the point (0,0) is not a solution to the inequality. Therefore, we need to shade the side of the line that does not contain the origin (0,0).

The linear inequality for the shaded region is:

[tex]y < -4x + 4[/tex]

So any point below the line [tex]y = -4x + 4[/tex]satisfies this inequality.

Tp learn more about linear inequality, visit

brainly.com/question/2419833

#SPJ1

Answer:

The answer to your question is $2.55

Step-by-step explanation:

85% × $3 = $2.55

With original price $3 and 85% off,

Final price: $0.45

Saved amount: $2.55

I hope this helps and have a wonderful day!

Answer:0.45

Step-by-step explanation:

Purchase Price:

$3

Discount:

(3 x 85)/100 = $2.55

Final Price:

3 - 2.55 = $0.45

Answer: To determine the range of input (L) over which production should take place, we need to find the point at which the marginal product of labor (MPL) is zero:

MPL = 20 - 0.4L

0 = 20 - 0.4L

0.4L = 20

L = 50

So production should take place for values of L less than or equal to 50.

To find the range of output over this range of labor, we can use the average product of labor (APL) equation:

APL = 20 - 0.2L - 320/L

Substituting L = 50, we get:

APL = 20 - 0.2(50) - 320/50

APL = 20 - 10 - 6.4

APL = 3.6

So the range of output over the range of labor from 0 to 50 is approximately 0 to 3.6 units of output.

Step-by-step explanation:

The conclusion about p using an absolute value inequality is in the range of 29.8% to 34.2%.

What is absolute value inequality?

An expression using absolute functions and inequality signs is known as an absolute value inequality.

We know that the absolute value inequality about p using an absolute value inequality is written as,

[tex]|p-\hat{p}|\leq E[/tex]

where E is the margin of error and is the sample proportion.

Now, it is given that the poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76%. Therefore, p can be written as,

[tex]|p-0.72|\leq 0.04\\(0.72-0.04)\leq p\leq (0.72+0.04)\\\\0.68 \leq p \leq 0.76[/tex]

Thus, the p is most likely to be between the range of 68% to 76%.

Similarly, the proportion of people who like dark chocolate more than milk chocolate was 32% with a margin of error of 2.2%. Therefore, p can be written as,

[tex]|p-0.32| \leq 0.022\\\\0.248 \leq p \leq 0.342[/tex]

Thus, the p is most likely to be between the range of 29.8% to 34.2%.

Hence, the conclusion about p using an absolute value inequality is in the range of 29.8% to 34.2%.

Learn more about Absolute Value Inequality:

brainly.com/question/4688732

#SPJ1

The rule for f in the desired form is: f(x) = (3x^2 + 12x + 13r(x) + 52) / (x + 4)

To rewrite the rule for f in the form f(x) = q(x) + d(r), we need to first write g(x) in terms of r(x).

We know that g(x) = r(x) / (x + 4) + 1, so we can rewrite it as:

g(x) = r(x) / (x + 4) + (x + 4) / (x + 4)

g(x) = (r(x) + x + 4) / (x + 4)

Now, we can see that f(x) is a transformation of g(x) with q(x) = 3x and d(r) = 13. So, we can write:

f(x) = q(x) + d(r)

f(x) = 3x + 13(r(x) + x + 4) / (x + 4)

f(x) = (3x(x + 4) + 13r(x) + 52) / (x + 4)

Therefore, the rule for f in the desired form is: f(x) = (3x^2 + 12x + 13r(x) + 52) / (x + 4)

Learn more about polynomials at https://brainly.com/question/1496352

#$SPJ1

Answer:27499.975

Step-by-step explanation:

Answer:

[tex]v = \frac{28\pi}{3} [/tex]

Step-by-step explanation:

First, we can find the area of the cone's base:

[tex]a(base) = \pi \times {r}^{2} = 4\pi[/tex]

Now, let's find the volume:

[tex]v = \frac{1}{3} \times a(base)\times h[/tex]

[tex]v = \frac{1}{3} \times 4\pi \times 7 = \frac{28\pi}{3} [/tex]

Answer:

Step-by-step explanation:

For question 3,

Simplified brackets -> (8+11)2-8+11

Open brackets -> 19*2-8+11

Multiply -> 38-8+11

Calculate -> 41

Solution = 41

For question 4,

Remove Brackets -> m+11+m+44

Put common numbers together -> m+n+44+11

Calculate -> m+55+n

Solution = m+55+n

-Your smart 6th grader

Answer:

Step-by-step explanation:

In the given figure, we have three circles arranged such that they touch each other. Let the centers of these circles be A, B, and C, with radii 5.4, 4.4, and 3.4, respectively.

We can see that triangle ABC is an equilateral triangle, since all sides are of equal length (the radii of the circles).

To find the angle A, we can use the law of cosines, which states that:

c^2 = a^2 + b^2 - 2ab cos(C)

where a, b, and c are the lengths of the sides of a triangle, and C is the angle opposite the side of length c.

Since triangle ABC is equilateral, we have a = b = c, and C = 60°. Therefore, we can rewrite the above equation as:

c^2 = 2a^2 - 2a^2 cos(60°)

Simplifying and solving for a, we get:

a = c / sqrt(3)

Substituting the given values, we have:

a = 4.4 / sqrt(3) ≈ 2.54

Therefore, angle A is:

A = 180° - 60° - 60° = 60°

And angle B is:

B = 180° - A = 120°

Finally, we can use the law of sines to find the length of side c:

sin(A) / a = sin(B) / b = sin(C) / c

Substituting the values we have found, we get:

sin(60°) / 2.54 = sin(120°) / c

Simplifying and solving for c, we get:

c = 2.54 / sqrt(3) / sin(120°) ≈ 3.71

Therefore, the length of side c is approximately 3.71, and angle B is 120°.

According to the given information, the absolute value of the difference between the y-intercepts of f(x) and g(x) is 0.

What is a function?

A function is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output.

To find the y-intercept of a function, we set x=0 and evaluate the function at that value.

For the function f(x) = (x + 4)2 - 3, we have:

f(0) = (0 + 4)2 - 3 = 13.

To find the y-intercept of the function g(x), we can use the given points and try to write it in the form y = ax² + bx + c, where a, b, and c are constants.

Using the given points, we can write three equations:

When x = -2, y = 17: 17 = 4a - 2b + c

When x = -1, y = 15: 15 = a - b + c

When x = 1, y = 9: 9 = a + b + c

Solving this system of equations, we get a = -1, b = 1, and c = 13. Therefore, the equation of the function g(x) is:

g(x) = -x² + x + 13.

To find the absolute value of the difference between the y-intercepts of f(x) and g(x), we can subtract the two y-intercepts and take the absolute value:

|f(0) - g(0)| = |13 - 13| = 0.

Therefore, the absolute value of the difference between the y-intercepts of f(x) and g(x) is 0.

To know more about functions visit:

brainly.com/question/29120892

#SPJ1

Answer:

The selling price of the automobile after the $500 rebate is:

$18,340 - $500 = $17,840

The markdown is the difference between the original selling price and the selling price after the rebate, expressed as a percentage of the original selling price. The markdown can be calculated as follows:

Markdown = [(Original Price - Discounted Price) / Original Price] × 100%

Markdown = [(18,340 - 17,840) / 18,340] × 100%

Markdown = (500 / 18,340) × 100%

Markdown ≈ 2.72%

Rounding to the nearest tenth of a percent, the percent markdown is approximately 2.7%.

At a 5% level of significance, we reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the percentage of vegetarians in age group 18 to 35 years is higher than 5%.

To test the hypothesis that the percentage of vegetarians is higher in the age group 18 to 35 years at a 5% level of significance, we can use a hypothesis test with the following null and alternative hypotheses:

Null hypothesis (H0): The percentage of vegetarians in the age group 18 to 35 years is equal to 5%.

Alternative hypothesis (Ha): The percentage of vegetarians in the age group 18 to 35 years is greater than 5%.

We can conduct a one-tailed z-test to test this hypothesis, using the following formula:

z = (p - P0) / sqrt(P0 * (1 - P0) / n)

where:

p is the sample proportion of vegetarians in the age group 18 to 35 years

P0 is the hypothesized proportion (5%)

n is the sample size

We will reject the null hypothesis if the calculated z-value is greater than the critical z-value corresponding to a 5% level of significance (one-tailed test).

Assuming a sample of size n = 100, if we find that 10 people in the sample identify themselves as vegetarians, then the sample proportion is:

p = 10/100 = 0.1

Using the formula above, we can calculate the z-value:

z = (0.1 - 0.05) / sqrt(0.05 * 0.95 / 100) = 1.96

The critical z-value for a one-tailed test at a 5% level of significance is 1.645 .

To learn more about z-test please click on below link        

https://brainly.com/question/30034815

#SPJ1

The 90th percentile of the distribution for the time a CD player lasts is approximately 4.674 years.

In statistics, a percentile is a measure used to indicate the value below which a given percentage of observations falls in a dataset or distribution.

For example, the 90th percentile is the value below which 90% of the observations fall, and above which only 10% of the observations fall.

Similarly, the 50th percentile (also known as the median) is the value below which 50% of the observations fall, and above which 50% of the observations fall.

Here we have

The life of Sunshine CD players is normally distributed with a mean of 4.3 years and a standard deviation of 1.1 years.

To find the 90th percentile of the distribution for the time a CD player lasts, find the value of x such that 90% of the CD players last less than x and 10% last more than x.

First, standardize the distribution by converting it to a standard normal distribution with a mean of 0 and a standard deviation of 1.

This can be done by subtracting the mean and dividing by the standard deviation:

Z = (x - μ) / σ

To find the Z-score corresponding to the 90th percentile,

We can use a standard normal distribution table or a calculator.

The Z-score corresponding to the 90th percentile is approximately 1.28.

Now we can solve for x by rearranging the standardization equation above:

=> Z = (x - μ) / σ

=> 1.28 = (x - 4.3) / 1.1

=> 1.28 * 1.1 = x - 4.3

=> x = 4.674

Therefore,

The 90th percentile of the distribution for the time a CD player lasts is approximately 4.674 years.

Learn more about Percentile of distribution

https://brainly.com/question/25151638

#SPJ1