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 675 and 900 hours.
525 600 675 750 825 900 975
P = [?]%
Hint: use the 68 - 95 - 99.7 rule.
Enter

The Commutative Property of Addition is the mathematical principle at play here. we can see that  [tex]2 + 2 = 4[/tex]  and [tex]4 + 4 = 8[/tex]  , and this is due to the Commutative and Associative Properties of Addition.

The math property at work here is the Commutative Property of Addition. This property states that the order of the numbers being added does not affect the sum. In other words, a + b = b + a.

So, in the case of   [tex]2 + 2 = 4[/tex] and  [tex]4 + 4 = 8[/tex]  , we can apply the Commutative Property of Addition to rearrange the numbers being added:

[tex]2 + 2 = 4[/tex]

[tex]4 + 4 = 4 + (2 + 2)[/tex]

Then, we can use the Associative Property of Addition, which states that the grouping of the numbers being added does not affect the sum. In other words, ([tex]a + b) + c = a + (b + c).[/tex]

Applying this property to  [tex]4 + (2 + 2)[/tex] , we get:

[tex]4 + (2 + 2) = (4 + 2) + 2 = 6 + 2 = 8[/tex]

Therefore, we can see that  [tex]2 + 2 = 4[/tex]  and [tex]4 + 4 = 8[/tex]  , and this is due to the Commutative and Associative Properties of Addition.

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Both equations are true when x = 1 and y = 1, so the solution is correct.

What are system of equations ?

A system of equations is a set of two or more equations that are to be solved simultaneously. The equations in the system share common variables, and the solution to the system is a set of values for those variables that satisfy all of the equations in the system.
To solve this system, we need to find the values of x and y that satisfy both equations at the same time. This means that any solution we find must work in both equations simultaneously.

According to the question:
To solve the system:

x + y = 2 ...(1)

x - y = 0 ...(2)

We can add equations (1) and (2) to eliminate y:

(x + y) + (x - y) = 2 + 0

2x = 2

x = 1

Substituting x = 1 into equation (1):

1 + y = 2

y = 1

Therefore, the solution to the system is x = 1 and y = 1. We can check the solution by substituting the values into both equations

x + y = 2

1 + 1 = 2 (true)

x - y = 0

1 - 1 = 0 (true)

Both equations are true when x = 1 and y = 1, so the solution is correct.

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You're right about the answer

Answer: a

Step-by-step explanation:

Answer is: 90 ft

Step-by-step explanation:

You multiply the width, height, and length to find the volume.

Cause of its shape.

Hope this helps! :)

Have a good day.

The value of x= 4.

This is the boundary or contour length of a 2D geometric shape.

Depending on their size, multiple shapes may have the same circumference. For example, imagine a triangle made up of wires of length L.

The same wire can be used to create a square if all sides are the same length.

The length covered by the perimeter of the shape is called the perimeter. Therefore, the units of circumference are the same as the units of length.

As we can say, the surroundings are one-dimensional. As a result, you can measure in meters, kilometers, millimeters, etc.

Inches, feet, yards, and miles are other globally recognized units of circumference measurement.

According to our question-

cos(60)= x/8

x=1/2*8

x=4

Hence, The value of x= 4.

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Answer:

It's y = 3x + 1 :)

Answer:

Step-by-step explanation:

To find x + 1/x, we need to first find the value of x.

Given, x = 2-√3

To simplify x + 1/x, we need to find the value of 1/x.

1/x = 1/(2-√3)

Multiplying the numerator and denominator by the conjugate of the denominator, we get:

1/x = (2+√3)/(2-√3)(2+√3)

1/x = (2+√3)/(4-3)

1/x = 2+√3

Now, substituting the values of x and 1/x, we get:

x + 1/x = (2-√3) + (2+√3)

x + 1/x = 4

Therefore, the answer is option a) 4.

Answer:

140inch^2

Step-by-step explanation:

5×8=40inch^2

4^2×π= 16π

4^2×π=16π

16π+16π=32π

40+32π=140.53096491487

rounded to the nearest 10th= 140inch^2

The answer is 140m squared

The value of the unknown sides and angles are;

<B = 65 degrees

b = 27

c= 13

In the triangle, Using the SOHCAHTOA rule,

such that

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

From the diagram shown, we have that;

sin C = c/30

sin 25 = c/30

find the value and cross multiply, we get;

c = 12. 67

< B = 180 - sum of angle A and C

<B = 180 - 115

subtract the values

<B = 65 degrees

The value of side b

sin B = b/30

sin 65 = b/30

b = 27. 19

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Answer:

-x - 12

Step-by-step explanation:

x- (-12) = x+12. The opposite of x+12 = -x-12. The answer is therefore -x -12, NOT x + 12.

Answer:

the equation's intervals are (0;+∞)

Step-by-step explanation:

Replace x with -12:

-12 - (-12) = -12 + 12 = 0

With -12 this equation is equal to zero, but since x > -12, that means we have to replace x with numbers that are greater that -12 (-11; -10; etc.)

And since there are open intervals ( > ), we do not count the zero.

Answer:

7a^2(a^4 + 4)(a^4 - 4)

Step-by-step explanation:

To simplify 7a^10 - 112a^2, we need to find the greatest common factor (GCF) of the two terms and factor it out.

The GCF of 7a^10 and 112a^2 is 7a^2.

So, we can factor out 7a^2 from both terms, which gives:

7a^2(a^8 - 16)

Now, we can further simplify the expression by noticing that a^8 - 16 is a difference of squares. We can write it as:

a^8 - 16 = (a^4)^2 - 4^2 = (a^4 + 4)(a^4 - 4)

Therefore, the fully simplified expression is:

7a^2(a^4 + 4)(a^4 - 4)

(1/4)(1x^2y + 32)

Substituting x = 8, y = 3, and z = 5/3:

(1/4)(1(8)^2(3) + 32) = (1/4)(192 + 32) = (1/4)(224) = 56

Therefore, the value of the expression is 56.

The equation for the line passing through the point (4, 1) and perpendicular to 2x - 3y = 6 is y = (-3/2)x + 7.

A mathematical statement known as an equation consists of two algebraic expressions separated by equal signs (=) on either side.

It demonstrates the equality of the relationship between the printed statements on the left and right.

Left side equals right side in all formulas.

To find the values of unknowable variables, which stand in for unknowable quantities, you can solve equations.

A statement is not an equation if it lacks the equals sign.

When two expressions have the same value, a mathematical statement known as an equation will include the symbol "equal to" between them.

y = mx + b

1 = (-3/2) 4 + b

1 = -6 + b

1 + 6 = b

7 = b

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Answer:

BC = 62

Step-by-step explanation:

There are 3 triangles total in the figure shown, one large triangle, and two smaller triangles created by the segment BC. Now, look at triangle ACD and see that is a scaled version of common right triangle.

Some common right triangles are 3-4-5, 5-12-13, and 7-24-25. You may be able to see a pattern here where the square of the smallest side length is equal to the sum of the other two side lengths. Triangle ACD happens to be a scaled form of a 5-12-13 triangle. The triangle is scaled by a factor of 3. So the respective side length of AD is 12 * 3 = 36.

Now look at triangle ABD. We have two of the three side lengths.

AD = 36

AB = 85

We want to find BC, so we will use the pythagorean theorem, with (x + 15) to represent the length of BD.

35² + (x + 15)² = 85²

1225 + (x + 15)² = 7225

(x + 15)² = 6000

x + 15 = ±√6000

x = -15 ± √6000

Our equation provides two answers, but the negative value doesn't make sense because length can't be negative, so use the positive length for this application.

x = -15 + √6000

x = 62.4596

Rounded to the nearest whole number, the length of BC is 62.

the area of the larger sector is approximately 7.11 m².

How to solve and what does circle mean?

To find the area of the larger sector with radius 8m and central angle 40°, we can use the formula:

Area of sector = (central angle/360) x πr²2

Plugging in the given values, we get:

Area of sector = (40/360) x π(8)²2

Area of sector = (1/9) x 64π

Area of sector = 7.11 m² (rounded to the nearest hundredth)

Therefore, the area of the larger sector is approximately 7.11 m².

A circle is a closed two-dimensional geometric shape consisting of all points that are at the same distance from a fixed point called the center. The distance from the center to any point on the circle is called the radius, and twice the radius is called the diameter. The circumference of a circle is the distance around its edge, and the area of a circle is the space enclosed within its edge.

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The starting balance of investment depending on the equation [tex]y = 32000 * (1.035)^{x}[/tex] is $32000.

The equation is [tex]y = 32000 * (1.035)^{x}[/tex] where x represents the number of years since the investment started and y represents the total balance after x years.

To find the value starting balance of the investment we need to put x = 0,

since this represents the initial balance at the start of the investment:

[tex]y = 32000 * (1.035)^{x}[/tex]

put x = 0

[tex]y = 32000 * (1.035)^{0} \\y = 32000[/tex]

Therefore, the starting balance of the investment is $32,000.

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The starting balance of the investment is $32,000, since the initial investment is not multiplied by any factor in the given equation.

Investment refers to the process of allocating resources, such as money or time, to a particular venture or asset with the expectation of generating a return on investment (ROI) in the future. An investment can be made in various forms, including stocks, bonds, real estate, commodities, and mutual funds.

Investing involves taking calculated risks in order to earn a profit or generate income. The level of risk and potential reward associated with an investment depends on various factors, such as the nature of the investment, the economic conditions, and the performance of the particular asset or venture.

There are many different investment strategies and approaches, such as value investing, growth investing, dividend investing, and index investing. Each strategy involves a different approach to selecting and managing investments, depending on the investor's goals, risk tolerance, and investment horizon.

The starting balance of the investment is $32,000, since the initial investment is not multiplied by any factor in the given equation.

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Answer:

[tex]( - 28 \infty )[/tex]

Step-by-step explanation:

We have already found the solution to the inequality, but since we want to represent the solution in interval notation, we have changed it.

hopefully this helps! :)

The probability that a given person drank between 40 and 45 glasses of water is 13.5%.

What is Probability ?

Probability can be defined as ratio of number of favourable outcomes and total number outcomes.

between 40 and 45 glasses of water.

First, we need to standardize the values of 40 and 45 using the z-score formula:

z1 = (40 - 50) / 5 = -2

z2 = (45 - 50) / 5 = -1

Next, we look up the area under the standard normal distribution curve between z = -2 and z = -1. We can use a standard normal distribution table or a calculator to find this area, which is approximately 0.135.

Therefore, the probability that a given person drank between 40 and 45 glasses of water is 13.5%.

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Answer:

A (-6, -4),(-3,-3)

Step-by-step explanation:

Formula for slope of a line is y2-y1/x2-x1

If you plug each equation in:

-3-(-4)/-3-(-6)=1/3

1/3 is the perpendicular slope of -3

Answer:

-6x + 6y = 6 (Equation 1)

-6x + 3y = -12 (Equation 2)

We can use the method of elimination, which involves adding or subtracting the equations to eliminate one of the variables.

In this case, we can start by multiplying Equation 2 by 2 to eliminate the x variable:

-6x + 6y = 6 (Equation 1)

-12x + 6y = -24 (Equation 2 multiplied by 2)

Now we can subtract Equation 1 from Equation 2:

-12x + 6y = -24 (Equation 2 multiplied by 2)

-(-6x + 6y = 6) (Equation 1, with the opposite sign)

-6x = -30

Simplifying this expression, we get:

x = 5

Now we can substitute this value of x into either Equation 1 or Equation 2 to solve for y. Let's use Equation 1:

-6x + 6y = 6

-6(5) + 6y = 6

-30 + 6y = 6

6y = 36

y = 6

Therefore, the solution to the system of equations is x = 5 and y = 6, or (5, 6) in coordinate form.

Step-by-step explanation:

To enable Riley to save up to buy a new television priced $1,200.17, and since he already has $200.34 saved and earns $76.91 per week at her job, she needs to work for 13 more weeks.

To determine the number of weeks Riley has to work to earn enough to buy the new television, we apply the mathematical operations of subtraction and division.

Subtraction and division are two of the four basic mathematical operations, including addition and multiplication.

The total amount that Riley requires = $1,200.17

The amount of savings Riley already has = $200.34

The remaining amount that Riley needs to earn = $999.83 ($1,200.17 - $200.34)

Riley's earnings per week = $76.91

The number of weeks Riley needs to work to save enough money = 13 weeks ($999.83 ÷ $76.91)

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Questions:

1. 6 is not more than z.

2. The value of w is at least 12

3. Josiah plans to complete his 50 minutes of Mappers practice in 5 days and split the practice up evenly. Which inequality can he use to decide how many minutes he must complete each day?

4. Amy has $35.75 for her visit to the zoo. She must pay $7.25 for admission and wants to feed as many animals as she can. Food for the animals costs $1.25 each. What inequality represents the largest number of animal food that Amy can buy?

5. Jacob spent $40 on supplies to make 100 shirts for a baseball team fundraiser. Solve the inequality to help him decode how much to charge for each shirt to make a profit of more than $350.

100t-40 is greater than 350

Answers:

1. 6 is less than or equal to z (2nd option)

2. w is greater than or equal to 12 (1st option)

3. 5x is greater than or equal to 50 (1st option)

4. 1.25x + 7.25 is less than or equal to 35.75 (4th option)

5. t is great than 39 (3rd option)

The length and width of the new poster are 240 cm and 288 cm, respectively.

To find the length and breadth of the enlarged poster, we need to multiply the original dimensions by the enlargement ratio.

Let's first find the common ratio between the original poster and the enlarged poster:

Common ratio = Enlarged size / Original size

Common ratio = 5/3

Now, we can find the dimensions of the enlarged/New poster:

Length of enlarged poster = Length of original poster x Common ratio

Length of enlarged poster = 150 cm × 5/3

Length of enlarged poster = 250 cm

Breadth of enlarged poster = Breadth of original poster x Common ratio

Breadth of enlarged poster = 180 cm × 5/3

Breadth of enlarged poster = 300 cm

Therefore, the the dimensions of the new poster is 250cm by 300cm.

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Answer:

they have equal shape calculate the number

The solution of the given problem of unitary method comes out to be beam's maximum bending moment is 180 Nm.

Here,

=> RA - wL = 0

=> wL = 40 N/m x 2 m = 80 N, where RA =

=> RBv - RA = 0 (sum of forces in the vertical direction)

=> RBh = 0 (sum of forces in the horizontal direction) (sum of forces in the horizontal direction)

To solve for RBv, we obtain:

=> 80 N = RBv = RA

Hence, the responses at support points A and B are as follows:

=> RA = 80 N (vertical response at A) (vertical reaction at A)

=> RBv = 80 N (vertical response at B) (vertical reaction at B)

=> RBh = 0 N (horizontal reaction at B) (horizontal reaction at B)

=> M = 80 N x 2 m - 40 N/m x (2 m)2/2 - 500 Nm

=> -180 Nm, where MB = RA x L - wL2/2 -

Keep in mind that the bending moment is opposite the applied moment, as shown by the negative sign.

Thus, at point B, the beam's maximum bending moment is 180 Nm.

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The first five terms of the recursive sequence an = an-1 + 7, where a1 = 5 can be found by applying the recursive formula multiple times.

A recursive formula is a mathematical expression that uses a sequence of previously defined terms to define each successive term. This type of formula is commonly used to define sequences and can be used to define functions as well. The recursive formula is based on the idea of self-similarity, which means that each successive term is defined in terms of the one before it.