Tests show that the lives of light bulbs are
normally distributed with a mean of 750 hours
and a standard deviation of 75 hours. Find
the probability that a randomly selected light
bulb will last between 750 and 900 hours.
675 750 825 900 975
P = [? ]%
Hint: use the 68 - 95 - 99.7 rule.
525 600
Enter

The statement "we number the vertices counterclockwise 0, 1, ..., n − 1, and number the axes of symmetry counterclockwise, 0, 1, ..., n − 1" is likely referring to a specific mathematical context, such as a polygon or a regular solid.

In this context, "numbering the vertices counterclockwise" means that the vertices (or corners) of the shape are given labels or numbers in a particular order, moving counterclockwise around the shape. For example, in a triangle, the vertices might be labeled as 0, 1, and 2, in counterclockwise order around the triangle.

Similarly, "numbering the axes of symmetry counterclockwise" means that the axes of symmetry (or lines of reflection) in the shape are also given labels or numbers in a particular order, moving counterclockwise around the shape. For example, in a regular pentagon, there are 5 axes of symmetry that can be labeled as 0, 1, 2, 3, and 4 in counterclockwise order around the pentagon.

By establishing this numbering convention, mathematicians and scientists can more easily communicate about the properties and characteristics of the shape or object, and can refer to specific vertices or axes of symmetry in a standardized way.

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Answer:120 degrees

Step-by-step explanation:

2pi = 360 degrees

pi = 180 degrees

2pi/3 = 120 degrees

The result is, [tex]\dfrac{dy}{dx} = x \times ln\dfrac{x}{(x+3)} + 2x\times ln\dfrac{x}{(x+3)} - \dfrac{(3x^2)}{(x+3)^2}[/tex].

The derivative of a function is a measure of how much the function changes as its input (often time or space) changes. More specifically, the derivative is the instantaneous rate of change of the function at a particular point.

To find the derivative of y = x^2ln(x/(x+3)), we use the product rule and the chain rule.

y = x^2 * ln(x/(x+3))

[tex]y' = 2x \times ln\dfrac{x}{(x+3)} + x^2 \times \dfrac{d}{dx}ln\dfrac{x}{(x+3)}[/tex]

To find the derivative of ln(x/(x+3)), we use the quotient rule:

[tex]\dfrac{d}{dx} ln\dfrac{x}{(x+3)} = \dfrac{1}{\dfrac{x}{(x+3)}} \times \dfrac{d}{dx}\dfrac{x}{(x+3)} - \dfrac{1}{\dfrac{x+3}{x}} \times \dfrac{d}{dx}\dfrac{(x+3)}{x}[/tex]

= [(x+3)/(x^2)] - [x/(x+3)^2]

= (x^2 + 3x - x^2)/(x^2(x+3)^2)

= 3(x+1)/(x^2(x+3)^2)

Substituting this back into the original equation, we get:

y' = 2x * ln(x/(x+3)) + x^2 * [3(x+1)/(x^2(x+3)^2)]

= 2x * ln(x/(x+3)) + 3(x+1)/(x+3)^2

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The width and length of the rectangle will be -1 units and 3 units, respectively.

Let W be the rectangle's width and L its length.

The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be

[tex]\text{Area of the rectangle = L x W square units}[/tex]

The width of a square shape is 4 units less than the length. The region of the square shape is 12 square units. Then the equations are given below.

[tex]W = L - 4[/tex]              ...1

[tex]L \times W = 12[/tex]           ...2

From equations 1 and 2, then we have

[tex]L \times (L - 4) = 12[/tex]

[tex]L^2 - 4L = 12[/tex]

[tex]L^2 - 4L - 12 = 0[/tex]

[tex]L^2 - 3L + 4L - 12 = 0[/tex]

[tex]L(L - 3) + 4(L - 3) = 0[/tex]

[tex](L - 3)(L + 4) = 0[/tex]

[tex]L = 3, -4[/tex]

Then the width of the rectangle is given as,

[tex]W = 3 - 4[/tex]

[tex]W = -1 \ \text{units}[/tex]

The width and length of the rectangular shape will be -1 units and 3 units, separately.

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a) The probability that the sample mean breaking strength for a random sample of 40 rivets is between 9,850 and 10,150 is equal to 0.8903.

b) No, because n should be greater than 30 in order to apply the central limit theorem. So, right choice for answer is option (b).

The normal distribution forms a bell shaped curve. The parameter of normal distribution is [tex]\mu[/tex] and [tex]\sigma ^2 [/tex]. It is a continuous distribution. Now, Mean value of breaking strength of a rivet = 9,950

Standard deviations = 502

Let's X be variable denotes breaking strength of a rivet.

a) Now, a random sample is choosen from X such that, Sample size, n = 40. By using central limit theorem, sample mean follows approximately normal distribution with mean 9950 and standard deviations = 502/√40 = 79.3732 that is [tex]\bar X \: \tilde \: \: N( 9950, ( 79.3732)²)[/tex]

[tex]P( 9,850 < \bar X < 10,150 ) = P( \bar X < 10,150) -

P( \bar X < 9,850) \\ [/tex]

= [tex] P(\frac{\bar X - \mu }{\sigma} < \frac{10,150 - 9950}{79.3732} )- P(\frac{\bar X - \mu }{\sigma} < \frac{10,150 - 9850}{79.3732}) \\ [/tex]

= P( Z < 2.52 ) - P( Z < -1.26)

= 0.9941 - 0.1038

= 0.8903

b) If sample size,n is 15 instead of 40, then the probability requested in part (a) will not be calculated from the provide information. Because, for applying central limit theorem we have sample size must be grater than 30. So, option(b) is correct.

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the statement that "as x decreases, f(x) increases" is not true for an exponential decay function.

An exponent, also known as a power or index, is a mathematical operation that indicates how many times a number (the base) is multiplied by itself.

When graphed, an exponential decay function shows that

as x increases

f(x) approaches 0

but as x decreases

f(x) also approaches 0.

The function decreases from left to right, meaning that as x increases, f(x) decreases towards 0. However, it does not increase as x decreases.

In general, an exponential decay function can be represented as f(x) = a ×e⁻ᵇˣ, where a and b are constants. As x gets larger and larger, the exponential term e⁻ᵇˣ approaches 0, which causes the overall function value f(x) to approach 0 as well. As x gets smaller and smaller, the exponential term e⁻ᵇˣ becomes larger, but the function value f(x) still approaches 0.

Therefore, the statement that "as x decreases, f(x) increases" is not true for an exponential decay function.

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The present value of 350,000 due after 10 years, compounded annually at an interest rate of 8% per year, is approximately 157,456.41, while the present value of 350,000 due after 10 years, compounded continuously at an interest rate of 8% per year, is approximately 147,252.13.

i. To find the present value of 350,000 due after 10 years, compounded annually at an interest rate of 8% per year, we can use the formula:

[tex]PV = FV / (1 + r)^n[/tex]

where PV is the present value, FV is the future value, r is the interest rate, and n is the number of periods.

Substituting the given values, we get:

PV = 350,000 / (1 + 0.08)^10

PV ≈ 157,456.41

Therefore, the present value of 350,000 due after 10 years, compounded annually at an interest rate of 8% per year, is approximately 157,456.41.

ii. To find the present value of 350,000 due after 10 years, compounded continuously at an interest rate of 8% per year, we can use the formula:

[tex]PV = FV / e^(r * n)[/tex]

where e is the mathematical constant approximately equal to 2.71828.

Substituting the given values, we get:

[tex]PV = 350,000 / e^(0.08 * 10)[/tex]

PV ≈ 147,252.13

Therefore, the present value of 350,000 due after 10 years, compounded continuously at an interest rate of 8% per year, is approximately 147,252.13.

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11 is the value of x in this polygon.

What exactly is a polygon in mathematics?

A closed, two-dimensional, flat, closed polygon is a shape that is constrained by geometry and has straight sides. Its sides don't curve inward at all.

                               Another term for a polygon's sides is its polygonal edges. The points where two sides converge are known as a polygon's vertices (or corners).

2x - 4/6  = 9/3

(2x - 4)3  = 6 * 9

 2x - 4 = 54/3

   2x - 4 = 18

     2x = 18 + 4

       2x = 22

          x = 11

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Answer-

answer marked on the picture

Step-by-step explanation:

angle 1 and 55 is not vertical angles thus is the wrong answer

angle 2 can be determined with the given info by subtracting the other two angles to 180

Angle 2 not equal to 125 as the angles are not supplementary from each other

Anna should pay N$289,711.85 in two and a half years from now to meet her obligation.

An interest rate is the rate at which a borrower pays to a lender for the use of borrowed money. It is expressed as a percentage of the principal amount borrowed and is typically calculated on an annual basis.

To solve this problem, we can use the formula for the future value of an annuity:

FV = [tex]P * [(1 + r)^n - 1]/r[/tex]

Where FV is the future value of the annuity, P is the periodic payment, r is the interest rate per period, and n is the total number of periods.

We know that Anna borrowed N$20,000 at 5% for three and a half years, which is equivalent to 42 months. The periodic payment, P, is the sum of N$2,000 and N$5,000, which is N$7,000.

First, we can calculate the future value of the annuity after 42 months:

FV = 7,000 * [(1 + 0.05/12)[tex]^42[/tex] - 1]/(0.05/12)

FV = 7,000 * 56.3743

FV = N$394,120.10

Since Anna wants to pay N$8,000 on maturity, she will need to pay N$386,120.10 at the end of the 42 months to meet her obligation.

Now we can calculate how much Anna should pay in two and a half years from now, which is equivalent to 30 months:

[tex]PV = FV / (1 + r)^n[/tex]

PV = 386,120.10 / (1 + 0.05/12)[tex]^30[/tex]

PV = N$289,711.85

Therefore, Anna should pay N$289,711.85 in two and a half years from now to meet her obligation.

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Answer:

Step-by-step explanation:

By answering the presented question, we may conclude that Option D is false because function addition is not commutative in general.

In mathematics, a function seems to be a link between two sets of numbers in which each member of the first set (known as the domain) corresponds to a specific member of the second set (called the range). In other words, a function takes input from one collection and creates output from another. The variable x has frequently been used to represent inputs, whereas the variable y has been used to represent outputs. A formula or a graph can be used to represent a function. For example, the formula y = 2x + 1 depicts a functional form in which each value of x generates a unique value of y.

The correct statement about functions is:

C. If f is a function, then f(2 + h) = f(2) + f(2 + h) (h)

This is known as the additivity property or the additivity rule. It indicates that evaluating a function at a total of two values is equivalent to evaluating the function at each value individually and then adding the results. This is true for a wide range of functions, including linear and polynomial functions.

Option A is false since the order of function composition matters in general.

Option B is false because matrix multiplication is not always defined unless the matrices' dimensions are compatible.

Option D is false because function addition is not commutative in general.

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The price that maximizes revenue is $10 per ticket, which will bring in $1,500,000 in revenue. 60,000 people will attend at that price.

Price is the amount of money that is required to purchase or obtain a good or service. It is a numerical value that is assigned to a particular product or service and is used to indicate its value in the market. The price of a product or service is determined by a variety of factors, including the cost of production, supply and demand, competition, and market conditions.

In the given question,

To maximize revenue, we need to find the price per ticket that will bring in the greatest total revenue. Let's start by figuring out how many people will attend at various price points:

At $20 per ticket, 40,000 people attend.

At $15 per ticket, 50,000 people attend.

At $10 per ticket, 60,000 people attend.

At $5 per ticket, 70,000 people attend.

Now we can calculate the total revenue at each price point:

At $20 per ticket, revenue is 40,000 × $20 + 40,000 × $5 = $1,000,000.

At $15 per ticket, revenue is 50,000 × $15 + 50,000 × $5 = $1,250,000.

At $10 per ticket, revenue is 60,000 × $10 + 60,000 × $5 = $1,500,000.

At $5 per ticket, revenue is 70,000 × $5 + 70,000 × $5 = $700,000.

From these calculations, we can see that the price that maximizes revenue is $10 per ticket, which will bring in $1,500,000 in revenue. 60,000 people will attend at that price.

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Step-by-step explanation:

To find the inverse of an equation, we need to switch the roles of the dependent variable and the independent variable. In other words, if we have an equation of the form y = f(x), we need to rewrite it as x = f^{-1}(y), where f^{-1}(y) is the inverse function of f.

Once we have found the inverse equation, we can perform the original steps of the inverse equation by plugging in the output of the inverse function into the original equation.

For example, let's say we have the equation y = 2x + 3. To find the inverse equation, we first switch the roles of x and y to get:

x = 2y + 3

Next, we solve for y in terms of x:

x - 3 = 2y

(y = x - 3)/2

So the inverse equation is y = (x - 3)/2.

To perform the original steps of the inverse equation, we can plug the output of the inverse function, (x - 3)/2, into the original equation, y = 2x + 3:

y = 2((x - 3)/2) + 3

y = x - 3 + 3

y = x

We have arrived back at the independent variable, x, so the inverse and original steps have canceled each other out, as expected.

Answer:

Step-by-step explanation:

1+8×6091+689+8×879+68×9+7​

We need to do the multiplications first

1+(8×6091)+689+(8×879)+(68×9)+7​=

1+(48728)+689+(7032)+(612)+7​

Now we add all of them up

48729 + 7721 + 619 =

57069

Answer is 57069

The two axes should be perpendicular, so the angle betwen them is 90°, and the y-axis is 150° above the horizontal.

If we have a coordinate axis, the two axis should be perpendicular between them, this means that the angle between the positive x-axis and the positive y-axis should always be 90°.

Now, what should be the direction of the positive y axis?

We know that the positive x-axis is 60° above the horizontal, and the angle between the two axes is 90°, then the positive y axis is at:

60° + 90° = 150°

The positive y-axis is at 150° above the horizontal line.

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Answer:

g(0)= -1/3

g(-1)=0

g(1)=-1

g(2)=-3

g(3)=∞

Step-by-step explanation:

g(0)= -1/3

g(-1)=0

g(1)=-1

g(2)=-3

g(3)=∞

According to the given information, divide in Scientific Notation, you must divide the co-efficients and subtract the powers of 10.

What is Scientific Notation?

Scientific notation, also known as standard form or exponential notation, is a way of expressing numbers that are either very large or very small, using powers of 10. In scientific notation, a number is expressed in the form:

a x 10ⁿ

where "a" is a number between 1 and 10 (usually a decimal), and "n" is an integer (positive or negative) that represents the power of 10 by which the number is multiplied.

To add (or subtract) in Scientific Notation, you must have the same power of 10. Then you can add (or subtract) the co-efficients and keep the power of 10.

To multiply in Scientific Notation, you must multiply the co-efficients and add the powers of 10.

To divide in Scientific Notation, you must divide the co-efficients and subtract the powers of 10.

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Using the formula for lines intersecting in a circle, we get the value of x to be = 32.5cm.

A diameter is a line segment that traverses a circle by going through its centre.

The radius is twice as long as the diameter.  A chord is a segment that does not have to pass through the centre and has endpoints on the circle.

We know that in a circle when lines are intersecting each other than the lines divided are in the formula:

a × b = c × d

Here,

13 × 20 = 8 × x

⇒ x = 260/8

⇒ x = 32.5cm.

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Answer:

D

Step-by-step explanation:

A=LW

A=L(36)

Divide by 36

L=A/36

(L=X)

:)

The calculated resolved part of vector p (6i-3j+9k) in the direction of a is 2i + 2j - k.

Given that

p = (6i-3j+9k)

a =  (2i+2j-k)​

To find the resolved part of the vector p in the direction of a, we can use the following formula:

r = (p · a) / |a|

where · denotes the dot product and |a| denotes the magnitude of vector a.

First, we need to calculate the magnitude of vector a:

|a| = √(2² + 2² + (-1)²)

|a| = √(4 + 4 + 1)

|a| = √9

|a| = 3

Next, we need to calculate the dot product p · a:

p · a = (6i - 3j + 9k) · (2i + 2j - k)

= 12i + 12j - 6k - 6i - 6j + 3k

= 6i + 6j - 3k

Finally, we can calculate the resolved part of p in the direction of a:

r = (p · a) / |a|

= (6i + 6j - 3k) / 3

= 2i + 2j - k

Therefore, the resolved part of vector p in the direction of a is 2i + 2j - k.

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Answer:

Step-by-step explanation:The number of hours Jin reads in 20 days is 39.8 hours.

The expression for the given situation is 0.75d + 1.24d.

What is an expression?

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

In the given expression 0.75d + 1.24d, d is number of days.

Substitute d=20 in 0.75d + 1.24d, we get

0.75(20) + 1.24(20)

15+24.8

=39.8 hours

Hence, the number of hours Jin reads in 20 days is 39.8 hours

Answer:

Step-by-step explanation:

y=x23 so the dt is moved to perticlulate the dy

C. (4, 4), (-2, 2), (7, 1), (-7, 2)

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y.[1] The set X is called the domain of the function[2] and the set Y is called the codomain of the function

if the probability of observing 4 or fewer years with 5 hurricanes is much lower (e.g., less than 5%), then we might conclude that the Poisson distribution does not work well for this particular scenario.

a. The probability of observing 5 hurricanes in a year can be calculated using the Poisson distribution formula:

[tex]P(X=5) = (e^(-λ) * λ^5) / 5![/tex]

where λ is the mean number of hurricanes per year. In this case [tex], λ = 7.7[/tex] . Thus,

[tex]P(X=5) = (e^(-7.7) * 7.7^5) / 5! = 0.0834[/tex]   (rounded to four decimal places)

Therefore, the probability of observing 5 hurricanes in a year is approximately  [tex]0.0834[/tex] or   [tex]8.34[/tex] %.

b. The number of hurricanes in a 45-year period follows a Poisson distribution with mean [tex]λ = 7.7 \times 45 = 346.5[/tex] . The expected number of years with 5 hurricanes in a 45-year period is then:

[tex]E(X) = λ = 346.5[/tex]

Therefore, we expect about [tex]346.5/45 ≈ 7.7[/tex] % or 8 years out of 45 to have 5 hurricanes.

c. If in a recent period of 45 years, only 4 years had 5 hurricanes, we can compare this to the expected number of years with 5 hurricanes based on the Poisson distribution. Using the same mean λ = 346.5, we can calculate the probability of observing 4 or fewer years with 5 hurricanes in a 45-year period:

[tex]P(X ≤ 4) = Σ(i=0 to 4) [(e^(-λ) * λ^i) / i!] ≈ 0.2088[/tex]

This means that there is about a 20.88% chance of observing 4 or fewer years with 5 hurricanes in a 45-year period, based on the Poisson distribution with [tex]λ = 346.5[/tex]  .

Therefore,  This is not a very low probability, so the observed 4 years with 5 hurricanes in the recent [tex]45[/tex]  -year period is not necessarily inconsistent with the Poisson distribution.

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a) Let x, y, and z be the selling price of one cabbage, one orange, and one mango, respectively.

From the given data, we can write three simultaneous equations:

Monday: 55x + 100y + 95z = 1625

Tuesday: 60x + 120y + 80z = 1580

Wednesday: 75x + 150y + 120z = 2175

b) To find the selling price of each item, we need to solve the system of equations. We can use any method of solving systems of equations, such as substitution or elimination. Here, we will use the elimination method.

Multiplying the first equation by 6, the second equation by -5, and the third equation by 3, we get:

Monday: 330x + 600y + 570z = 9750

Tuesday: -300x - 600y - 400z = -7900

Wednesday: 225x + 450y + 360z = 6525

Adding all three equations, we get:

255x + 450y + 530z = 8385

Dividing both sides by 5, we get:

51x + 90y + 106z = 1677

Now we can use this equation and any of the original equations to solve for one of the variables. Let's use the first equation:

55x + 100y + 95z = 1625

Multiplying both sides by 106 and subtracting 530 times the first equation from it, we get:

76x + 45z = 43

Solving for x, we get:

x = (43 - 45z)/76

Now we can substitute this value of x into any of the previous equations to solve for y and z. Let's use the third equation:

75x + 150y + 120z = 2175

Substituting x, we get:

75[(43-45z)/76] + 150y + 120z = 2175

Simplifying, we get:

43z/2 - 375/2 + 150y = 825

Solving for y, we get:

y = (825 - 43z/2 + 375/2)/150

Now we can substitute the values of x and y into any of the previous equations to solve for z. Let's use the second equation:

60x + 120y + 80z = 1580

Substituting x and y, we get:

60[(43-45z)/76] + 120[(825-43z/2+375/2)/150] + 80z = 1580

Simplifying, we get:

z = 4.6

Substituting z into the equation for y, we get:

y = 3.45

Substituting z and y into the equation for x, we get:

x = 1.5

Therefore, the selling price for one cabbage is sh. 1.5, for one orange is sh. 3.45, and for one mango is sh. 4.6.

c) The profit that James Kamau made on each of the three days and his total profits:

To calculate the profit, we need to subtract the cost of the items from the revenue generated by selling them.

On Monday:

Cost of cabbages = 55 x 3 = 165 shillings

Cost of oranges = 100 x 2 = 200 shillings

Cost of mangoes = 95 x 6 = 570 shillings

Total cost = 935 shillings

Revenue = 1625 shillings

Profit = Revenue - Cost = 1625 - 935 = 690 shillings

On Tuesday:

Cost of cabbages = 60 x 3 = 180 shillings

Cost of oranges = 120 x 2 = 240 shillings

Cost of mangoes = 80 x 6 = 480 shillings

Total cost = 900 shillings

Revenue = 1580 shillings

Profit = Revenue - Cost = 1580 - 900 = 680 shillings

On Wednesday:

Cost of cabbages = 75 x 3 = 225 shillings

Cost of oranges = 150 x 2 = 300 shillings

Cost of mangoes = 120 x 6 = 720 shillings

Total cost = 1245 shillings

Revenue = 2175 shillings

Profit = Revenue - Cost = 2175 - 1245 = 930 shillings

Total profit over three days:

Profit on Monday + Profit on Tuesday + Profit on Wednesday = 690 + 680 + 930 = 2300 shillings

Therefore, James Kamau made a profit of 690 shillings on Monday, 680 shillings on Tuesday and 930 shillings on Wednesday, with a total profit of 2300 shillings over the three days.