An operation manager at an electronics company wants to test their amplifiers. The design engineer claims they have a mean output of 364
watts with a standard deviation of 12
watts.

What is the probability that the mean amplifier output would differ from the population mean by more than 0.9
watts in a sample of 52
amplifiers if the claim is true? Round your answer to four decimal places.

Length is 33.33 feet and width is 25 feet are dimensions should

be used so that the enclosed area will be a maximum.

The area of Rectangle is length times of width

Given that, a rancher has 200 feet of fencing to enclose two adjacent rectangular corrals of the same dimensions.

Here, the dimensions of the rectangles are the same.

The width of the two rectangles is W=2W+2W=4W

The length of the two rectangles is L=L+L+L=3L

Because the adjacent side has a common length.

3L+4W=200

3L=200-4W

Divide both sides by 3

L=(200-4W)/3

Let us form an equation using the area of rectangle formula:

A=2LW

=2(200-4W)/3.W

A=400-8W²/3

Let us differentiate to get the area to be maximized dA/dW=0

1/3×(400-8W²)=0

1/3(400-16W)=0

400-16W=0

400=16W

Divide both sides by 16

W=25

The width is 25 feet.

Substitute W value in equation to get L value:

L=200-4×25/3

=200-100/3

=100/3

=33.33

The length is 33.33 feet.

Now let us find the maximum area

A=2LW

=2×33.33×25

=1666.66

Hence, length is 33.33 feet and width is 25 feet are dimensions should

be used so that the enclosed area will be a maximum.

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Answer:

-1/2

Step-by-step explanation:

We know

The dilation of K(-2,4) equals K'(1,-2)

To get from -2 to 1, we time -1/2

To get from 4 to -2, we time -1/2

So, the scale factor used for the dilation is -1/2

Answer:

4cm

Step-by-step explanation:

Each of the other sides of the regular decagon is (√19/4) cm long, or approximately 1.861 cm to three decimal places.

Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We can apply this theorem only in a right triangle.

Example:

The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.

Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm

We have,

A regular decagon is a polygon with ten sides of equal length and ten angles of equal measure.

To find the length of each of the other sides, we can use the fact that a regular decagon can be divided into ten congruent isosceles triangles.

The isosceles triangle can be split into two right triangles by drawing an altitude from the vertex opposite the base to the midpoint of the base.

Let's call the length of one of the equal sides of the isosceles triangle "s", and let's call the length of the altitude "h".

Then we can use the Pythagorean theorem to find the length of the other side:

s² = h² + (s/2)²

We can solve for "h" in terms of "s" as follows:

h² = s² - (s/2)²

h² = (4s²)/4 - s²/4

h² = (15s²)/16

h = (s√15)/4

Since the altitude divides the isosceles triangle into two congruent right triangles, each with a hypotenuse of "s",

We can use the Pythagorean theorem again to find the length of each of the other sides of the regular decagon:

s² = h² + (s/2)²

s² = [(s√15)/4]² + (s/2)²

s² = (15s²)/16 + (s²)/4

s² = (15s² + 4s²)/16

s^2 = (19s²)/16

s = √(19/16) s

s = (√19/4) cm

Therefore,

Each of the other sides of the regular decagon is (√19/4) cm long, or approximately 1.861 cm to three decimal places.

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Answer:

18

Step-by-step explanation:

Answer:

4:5

Step-by-step explanation:

8/10 divided by 2/2 is 4/5

The three equivalent equations are 2 + x = 5, x + 1 = 4 and -5 + x = -2. So, correct options are A, B and E.

Two equations are considered equivalent if they have the same solution set. In other words, if we solve both equations, we should get the same value for the variable.

To determine which of the given equations are equivalent, we need to solve them for x and see if they have the same solution.

Let's start with the first equation:

2 + x = 5

Subtract 2 from both sides:

x = 3

Now let's move on to the second equation:

x + 1 = 4

Subtract 1 from both sides:

x = 3

Notice that we got the same value of x for both equations, so they are equivalent.

Next, let's look at the third equation:

9 + x = 6

Subtract 9 from both sides:

x = -3

Since this value of x is different from the previous two equations, we can conclude that it is not equivalent to them.

Now, let's move on to the fourth equation:

x + (-4) = 7

Add 4 to both sides:

x = 11

This value of x is also different from the first two equations, so it is not equivalent to them.

Finally, let's look at the fifth equation:

-5 + x = -2

Add 5 to both sides:

x = 3

Notice that we got the same value of x as the first two equations, so this equation is also equivalent to them.

So, correct options are A, B and E.

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Complete question is:

Which of the following equations are equivalent? Select three options.

2 + x = 5

x + 1 = 4

9 + x = 6

x + (- 4) = 7

- 5 + x = - 2

The value of such that = k * 180, where k is an integer, is the value at which cotangent is undefinable.

Cotangent, or cot, is one of the six standard trigonometric functions. Cotangent of an angle is defined as the ratio of the adjacent side to the opposite side of a right-angled triangle.

The value of cotangent is undefined when the denominator is zero. This implies that cotangent is undefined at angles where the value of sine is zero.

Since the sine function is periodic and has a period of 360 degrees, the values of sine repeat themselves after every 360 degrees.

For this reason, cotangent is undefined at angles such that θ = k * 180, where k is an integer.

That is, cotangent is undefined at 0°, 180°, 360°, and so on. It is also important to note that cotangent is a periodic function, and its values repeat every 180 degrees.

Therefore, cotangent is undefined at 0° + k * 180°, where k is an integer.

To summarize, the value of Θ at which cotangent is undefined is such that θ = k * 180, where k is an integer.

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I assume you mean

\(\displaystyle \lim_{x\to0} \frac{\log(1+x)}{\cos(x) + e^x - 1}\)

since the limand is free of n. As x goes to 0, the numerator converges to log(1 + 0) = 0, while the denominator converges to cos(0) + e⁰ - 1 = 1, so the overall limit is

\(\displaystyle \lim_{x\to0} \frac{\log(1+x)}{\cos(x) + e^x - 1} = \frac01 = \boxed{0}\)

Step-by-step explanation:

This is a geometric series, where the first term is -5 and the common ratio is -⅔.

aₙ = -5 (-⅔)ⁿ⁻¹

Answer:

30 square inches

Step-by-step explanation:

The equation for the area of a trapezoid is: (b1 + b2) x h) / 2

(10 + 5) x 4) /2

15 x 4 = 60

60/2 = 30

30 square inches

Answer:

(a) He would need 76 feet of fencing

(b) Kevin should buy the packaged box of 90 feet of fencing for $950.

(c) How much does he save?

For every 1 feet of packaged fencing Kevin buys, he saves $1.94 naira.

Step-by-step explanation:

(a) At the outside edge of the pool is a protective fence. How many feet of fencing would be needed to surround the pool area?

From the question, we are told that the swimming pool measures:

14-1/2 feet wide and 23-1/2 feet long.

Perimeter of a fence = 2(L + W)

= 2( 14-1/2 + 23-1/2)feet

= 76 feet

This means he need 76 feet of fencing.

(b) Kevin discovers that he can buy a packaged box of 90 feet of fencing for $950 or he can buy cut-to-order fencing that costs $12.40 per foot. Which type of fencing should he buy?

If : For cut to order fencing

1 foot = $12.40

76 feet =

Cross Multiply

= 76feet × $12.40/1 foot

= $942.4

This means that the cut to order fencing would cost him $942.40

The packaged box of fencing cost $950 for 90 feet of fencing. This is cheaper than the cut to order fencing and he would have extra feet of fencing(14 feet) .

Therefore, Kevin should buy the packaged box of 90 feet of fencing for $950.

How much money does he save?

For the cut to order box

1 feet = $12.40

For the packaged fence,

90 feet = $950

1 feet = x

= 950/90

= $10.555555556

≈ $10.56

Hence, 1 feet of packaged fence = $10.56

Subtracting $10.56 from $12.40

= $12.40 - $10.56

=$ 1.94

Therefore, for every 1 feet of packaged fencing Kevin buys, he saves $1.94 naira.

This means:

1 feet (packaged fence) = $10.56

76 feet = x

= 76 × $10.56

= $802.56

Answer:

The graph of IxI is:

y = x for values of x ≥ 0

y = -x for values of x ≤ 0

Then you will see a "V", with the arms pointing up and the vertex in the point (0, 0)

(Something like in the image, but with the arms pointing upside instead of downside)

The actual graph is:

Answer:

D. 286.5 in.^2

Step-by-step explanation:

3 X 7.5+ 3 X 11.5 + 3 X 7.5+ 11.5 X 3 + 7.5 X 11.5 + 7.5 X 11.5=

22.5 + 34.5 + 22.5 + 34.5 + 86.25 + 86.25=

total surface area= 286.5 in.^2

The graph shows two functions, f(x) and g(x). So, the statements that describe the resulting graph h(x) is point (-2,2) is on h(x)

A graph is described as the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

In the question above, we have two functions f(x)=x²-2 and g(x)=x²+2 by adding the function we will get the combined function.

The graph that the function is varying from the coordinates (-2,2) is seen on the attached graph.

Therefore, we can conclude that the graph shows two functions, f(x) and g(x). So point (-2,2) is on h(x)

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The expression for the area of frame is 4x² + 24x + 35

Area of rectangle is the region occupied by a rectangle within its four sides or boundaries. The area of a rectangle depends on its sides.

Here, Old length of photograph = 5 inch

          Old width of photograph = 7 inch

Now, length of new photograph = (5 + 2x) inch

        width of new photograph = (7 + 2x) inch

Now, Area of frame with new dimension = Length X breadth

                                                                     = (5+2x) X (7+2x)

                                                                     = 5(7+2x) + 2x(7+2x)

                                                                    = 35 + 10x + 14x + 4x²

                                                                    = 4x² + 24x + 35

Thus, the expression for the area of frame is 4x² + 24x + 35.

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a) y = 756

b) x = 5

y is directly proportional to x

y α x

y = kx

y = 216 when x = 2

Substitute the values of x and y into the equation y = kx to get the constant of proportionality, k.

y = kx

216 = k x 2

k = 216 / 2

k = 108

y = 108x

a) Find y when x = 7

y = 108x

y = 108(7)

y = 756

b) Find x when y = 540

y = 108x

540 = 108x

x = 540/108

x = 5

1. Simplifying the exponent (a⁵a⁹)⁻⁵/a⁻¹⁵ = a⁻⁵⁵

2. Simplifying the exponent  [(m⁻³m⁻⁷)/(m⁻⁴)⁻³]⁵ = m⁻¹⁰

Exponents are powers to which a number is raised.

1. Given the exponential expression, (a⁵a⁹)⁻⁵/a⁻¹⁵, we desire to simplify the expression. We proceed as follows

Since we have  (a⁵a⁹)⁻⁵/a⁻¹⁵

Using the multiplication law of exponents which is xᵃ x xᵇ = xᵃ⁺ᵇ, the numerator becomes

(a⁵a⁹)⁻⁵/a⁻¹⁵ =  (a⁵⁺⁹)⁻⁵/a⁻¹⁵

=  (a¹⁴)⁻⁵/a⁻¹⁵

Also, using the factor law (xᵃ)ᵇ = xᵃᵇ, we have that

 (a¹⁴)⁻⁵/a⁻¹⁵ = (a¹⁴×⁻⁵)/a⁻¹⁵

=  (a⁻⁷⁰)/a⁻¹⁵

Now using the division law of exponents, we have xᵃ/xᵇ = xᵃ⁻ᵇ

So,   (a⁻⁷⁰)/a⁻¹⁵ = a⁻⁷⁰ ⁻⁽⁻¹⁵⁾

= a⁻⁷⁰⁺¹⁵

= a⁻⁵⁵

So, (a⁵a⁹)⁻⁵/a⁻¹⁵ = a⁻⁵⁵

2. Given the exponential expression, [(m⁻³m⁻⁷)/(m⁻⁴)⁻³]⁵, we desire to simplify the expression. We proceed as follows

Since we have [(m⁻³m⁻⁷)/(m⁻⁴)⁻³]⁵

Using the multiplication law of exponents which is xᵃ x xᵇ = xᵃ⁺ᵇ, the numerator becomes

[(m⁻³m⁻⁷)/(m⁻⁴)⁻³]⁵ = [(m⁻³⁺⁽⁻⁷⁾)/(m⁻⁴)⁻³]⁵

= [(m⁻³⁻⁷)/(m⁻⁴)⁻³]⁵

= [(m⁻¹⁰)/(m⁻⁴)⁻³]⁵

Also, using the factor law (xᵃ)ᵇ = xᵃᵇ, we have that

= [m⁻¹⁰/(m⁻⁴)⁻³]⁵ = [(m⁻¹⁰)/(m⁻⁴×⁽⁻³⁾)]⁵

= [(m⁻¹⁰)/m⁻¹²]⁵

Now using the division law of exponents, we have xᵃ/xᵇ = xᵃ⁻ᵇ

So, [(m⁻¹⁰)/m⁻¹²]⁵ = [m⁻¹⁰ ⁻⁽⁻¹²⁾]⁵

= [m⁻¹⁰⁺¹²]⁵

= [m⁻²]⁵

Using the factor law (xᵃ)ᵇ = xᵃᵇ, we have that

[m⁻²]⁵ = m⁻²ˣ⁵

= m⁻¹⁰

So, [(m⁻³m⁻⁷)/(m⁻⁴)⁻³]⁵ = m⁻¹⁰

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The missing values in the quantitative reasoning given are : -2, 13 and 9

Given the rule :

We can deduce that :

For the left circle :

circle = -6 - (-4) = -6 + 4 = -2

For the right circle :

circle = 11 - (-2) = 11 + 2 = 13

For the left square :

square = 13 + (-4)

square = 13 -4 = 9

Therefore, the missing values are : -2, 13 and 9

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Step-by-step explanation:

21x²-2x +1/2 = 0

x² - 2x ×21 + 1/2× 21 = 0

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You need to find the length of A F and BC first

Lets call BC --> 'x'

Lets form an equation

9 + 9 + x + x = 28

18 + 2x = 28

- 18

2x = 10

/ 2

x = 5

So now we have the length BC

We can subtract this length from the 11cm to find the vertical height of the trapezium

11 - 5 = 6

Now we have all we need to work it out.

area = (a + b) / 2 x h

area = (5 + 9) / 2 x 6

area = 42 cm^2

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Answer:

42 cm²

Step-by-step explanation:

We can see this shape is made of 2 shapes that we are familiar with which are a rectangle and a trapezium.

⇒ The first step in working out the area of the trapezium is working out the length of CB and then working out the height of trapezium. We are given that the perimeter of the rectangle is 28 cm and we know that opposite sides of a rectangle are equal so we will call the length we want to work out x

→ x + x + 9 + 9 = 28

⇒ Simplify

→ 2x + 18 = 28

⇒ Minus 18 from both sides to isolate 2x

→ 2x = 10

⇒ Divide both sides by 5 to isolate x

→ x = 5

5 cm is the length of CB, we will need to minus that from 11 to find the height of the trapezium so,

11 - 5 = 6. The height of the trapezium is 6

Now we have the height of the trapezium (6), we have the base (9) and we have the top length (5). All we do now is substitute these numbers into the trapezium formula which is

→ 0.5 × ( a + b ) × h

Where 'a' and 'b' are the parallel sides and 'h' is the height

Now we begin to substitute in the values,

→ 0.5 × ( a + b ) × h

⇒ Substitute in the values

→ 0.5 × ( 5 + 9 ) × 6

⇒ Simplify

→ 0.5 × ( 14 ) × 6

⇒ Simplify further

→ 42

The area of the trapezium is 42 cm²

Answer: See below

Step-by-step explanation:

The first is a beaker, it's used to measure liquid volume

The second is a ruler, it's used to measure length.

Last is a thermometer, it's used to measure temperature.

The simplified value of the given expression (2x^3 + 3x + 7) / (x^2 + x + 10) is: the quotient will be 2x - 2 and the remainder will be -15x + 27.

Let us solve the given algebraic expression by the long division method:

We are given the expression:

(2x^3 + 3x + 7) / (x^2 + x + 10)

We need to perform the division of the given algebraic expression:

x^2 + x + 10  ) 2x^3 + 3x + 7 ( 2x - 2

                       2x^3 + 2x^2 + 20x

                     -         -            -        

                         -2x^2 - 17x + 7

                         -2x^2 - 2x  - 20

                         +        +       +          

                                  -15x + 27

So,

quotient = 2x - 2

remainder =  -15x + 27

Thus, the simplified value of the given expression (2x^3 + 3x + 7) / (x^2 + x + 10) is: the quotient will be 2x - 2 and the remainder will be -15x + 27.

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Answer:

100 or A

Step-by-step explanation:

i hope this is what you were looking for ;)

Answer:

\(\frac{\sqrt{3} }{2} }\)

Step-by-step

substitute θ=30° into the expression

like this cos(30°)

and then use a calculator to calculate the expression

= \(\frac{\sqrt{3} }{2} }\)

Answer: A

Step-by-step explanation:

Answer:

Option A; He did not distribute the 2 to both components of vector u.

Step-by-step explanation:

edge 2022 :-)

Answer:

Step-by-step explanation:

\(5(x - 2) + x = 6(x -4)\)

\(6x-10=6x-24\)

\(6x-10+10=6x-24+10\)

\(6x=6x-14\)

\(6x-6x=6x-14-6x\)

\(0=-14\)

Answer:

i belive 7

Step-by-step explanation:

becuse 3+6 in one line = 9 so 2 + 7= 9

Answer:

-2

Step-by-step explanation:

Add them up: -14

Divide by how many there are: -14 / 7 = -2

Answer:

\(\frac{2}{3} + \frac{1}{5} = \frac{10}{15} +\frac{3}{15} = \frac{13}{15}\)

PLEASE BRANLIEST ANSWER IS CORRECT I CHECKED

Step-by-step explanation:

First, find the least common denominator which is 15.

\((\frac{5}{5})\frac{2}{3} + (\frac{3}{3})\frac{1}{5}\)

When we multiply by 5/5 or 3/3 we are not changing the value of the fraction, just turning the denominator into one which we can work with the other fraction's denominator.

After simplification:

\(\frac{10}{15} + \frac{3}{15}\)

Now we can add:

\(\frac{13}{15}\)

Answer:

13/15

Step-by-step explanation:

because 5 x 2=10                  3 x 1=3

              5 x 3=15                5 x 3=15

   10/15+3/15= 13/15

Floyd needs 33 matches to make a rectangle with a length of 20 matches.

To find out how many matches Floyd needs to make a rectangle with a length of 20 matches, we can observe a pattern in the given information.

From the given data, we can see that as the length of the rectangle increases by 4 matches, the number of matches used increases by 8. This means that for every additional 4 matches in length, Floyd requires 8 more matches.

Using this pattern, we can calculate the number of matches needed for a rectangle with a length of 20 matches.

First, we need to determine the number of 4-match increments in the length of 20 matches. We can do this by subtracting the starting length of 3 matches from the target length of 20 matches, which gives us 20 - 3 = 17.

Next, we divide the number of 4-match increments by 4 to determine how many times Floyd needs to add 4 matches. In this case, 17 ÷ 4 = 4 with a remainder of 1.

Since Floyd requires 8 matches for each 4-match increment, we multiply the number of increments by 8, which gives us 4 × 8 = 32 matches.

Finally, we add the remaining matches (1 match in this case) to the total, resulting in 32 + 1 = 33 matches needed to reach a length of 20 matches.

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