www.g The physical plant at the main campus of a large state university recieves daily requests to replace fluorescent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 40 and a standard deviation of 8. Using the empirical rule, what is the approximate percentage of lightbulb replacement requests numbering between 24 and 40

The formula for calculating continuous compound interest is expressed as

A = Pe^rt

where

A is the amount after t years

P is the principal or initial amount deposited

r is the interest rate

t is the number of years

e represents exponent

From the information given

P = 2300

r = 5.5/100 = 0.055

t = 5 years

Thus,

A = 2300 x e^(0.055 x 5)

A = 2300 x e^0.275

A = 3028.02

She will have $3028.02 in her account after 5 years

Answer:

DJ docks glam Kalahandi focusing more than a few days to get the latest flash player of year and a half hour or so to the following information to you soon and we are looking to

The height of the building is approximately 227 feet.

In the given question, a man wants to measure the height of a nearby building. He places a 7 ft pole in the shadow of the building so that the shadow of the pole is exactly covered by the shadow of the building.

The total length of the building's shadow is 162 ft, and the pole casts a shadow that is 5.5 ft long. We have to determine the height of the building.The given situation can be explained with the help of a diagram.

As shown in the figure above, let AB be the building and CD be the 7 ft pole. The height of the building is represented by the line segment AE, which is to be determined. Let the length of the shadow of the pole be CD and that of the building be BD.

Therefore, the length of the total shadow will be BC or CD + BD.According to the question, the shadow of the pole is exactly covered by the shadow of the building. This implies that the two triangles AEF and CDF are similar. Hence, the corresponding sides are proportional. Therefore, we have:AE/EF = CD/DF

On substituting the values from the given data, we get:

AE/(EF + 5.5) = 7/5.5.... (1)

Similarly, we can write from the given data:

BD/DF = 162/5.5.... (2)

From equations (1) and (2), we can write:

AE/(EF + 5.5) = BD/DF => AE/(EF + 5.5) = 162/5.5.... (3)

On solving the above equation for AE, we get:

AE = (7/5.5) × (162/5.5 - 5.5)≈ 226.6 ft

Therefore, the height of the building is approximately 227 feet.

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Answer:

72

Step-by-step explanation:

(a+b)h / 2

(9+15)6 / 2

24 x 6 / 2

72

I hope im right!!

Answer:

gradient = \(\frac{3}{2}\) , y- intercept = \(\frac{5}{2}\)

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the gradient and c the y- intercept )

given

2y - 3x = 5 ( add 3x to both sides )

2y = 3x + 5 ( divide through by 2 )

y = \(\frac{3}{2}\) x + \(\frac{5}{2}\) ← in slope- intercept form

with gradient m = \(\frac{3}{2}\) and y- intercept c = \(\frac{5}{2}\)

The gradient is:

The y intercept is:

Work/explanation:

Let's rearrange the equation first so that it's in slope intercept.

Our equation is

\(\bf{2y-3x=5}\)

And we should write it in \(\bf{y=mx+b}\) form. Let's go ahead and perform the required operations.

________________________

Add 3x on each side:

\(\bf{2y=5+3x}\)

\(\bf{2y=3x+5}\)

Now, divide each side by 2:

\(\bf{y=\dfrac{3}{2}x+\dfrac{5}{2}}\)

This is the equation in slope intercept.

As for the gradient, that is the number in front of x : 3/2.

As for the y intercept, that is the constant : 5/2

Hence, these are the answers.

Given:

\(A=15^\circ, C=120^\circ,b=3\).

To find:

The length of side c.

Solution:

According to the angle sum of property of a triangle, the sum of all interior angles of a triangle is 180 degrees.

\(m\angle A+m\angle B+m\angle C=180^\circ\)

\(15^\circ+m\angle B+120^\circ=180^\circ\)

\(m\angle B+135^\circ=180^\circ\)

\(m\angle B=180^\circ-135^\circ\)

\(m\angle B=45^\circ\)

According to the Law of sines,

\(\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\)

Using Law of sines, we get

\(\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\)

\(\dfrac{3}{\sin 45^\circ}=\dfrac{c}{\sin 120^\circ}\)

\(\dfrac{3}{\dfrac{1}{\sqrt{2}}}=\dfrac{c}{\dfrac{\sqrt{3}}{2}}\)

\(3\sqrt{2}\times \dfrac{\sqrt{3}}{2}=c\)

On further simplification, we get

\(\dfrac{3\sqrt{6}}{2}=c\)

\(3.674235=c\)

\(c\approx 3.7\)

Therefore, the length of side c is about 3.7 units.

Answer: \(5\sqrt 5\)

Step-by-step explanation:

Sol \(\sqrt 125\) = \(\sqrt{25.5}\)

= \(\sqrt{25}\)  x  \(\sqrt{5}\)

\(5 \sqrt{5}\)

Answer:

y=2x+35

Step-by-step explanation:

so y is what it's equal too so you put y=

then since its $2 every mile you put them next to eachother like

2x so y=2x

then there is just a plain fee of $35 so you add that to the equation which is what makes it look like

y=2x+35

Hope this helps!! :D

Answer:

 x = 7

 y = -49

Step-by-step explanation:

           y = -6x - 7 ---------------(I)

           y = -7x -------------------(II)

Substitute y = -7x  in equation (I)

          -7x = -6x  - 7

   -7x + 6x = -7

            -x   = -7    

Multiply both sides by (-1)

           \(\sf \boxed{\bf x = 7}\)

Substitute x =7 in equation (II)

       y = -7*7

       \(\sf \boxed{\bf y = -49}\)

Answer:

X = 7 Y = -49

Step-by-step explanation:

Y= -6 X -7---------(1)

Y= -7 X ------------(2)

-7 X = -6X -7

-7 X+6X = -7

- X = -7

cancelling the - sign on bothsides

X = 7

put X = 7 into equation (2)

Y = -7(7)

Y = -49

therefore, X = 7 Y= -49

(a) Chebyshev's theorem states that at least 75% of lifespan fall between 748 and 1112 hours.

(b) Chebyshev's theorem states that at least 56% of all lifetimes fall between the average lifespan minus the standard deviation and the average lifetime plus the standard deviation. Additional information, such as the mean and standard deviation of the lifespan, would be required to calculate the exact interval.

A % is a relative figure that represents the hundredth part of any amount. One percent (symbolized 1%) is one hundredth part; consequently, 100 percent denotes the complete amount and 200 percent defines twice the supplied amount. percentage. Mathematics percentile is a related topic. A percentage is a fraction of a whole represented as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent. To calculate a percentage, divide the share of the total by the total and multiply by 100.

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Answer:

here's the answer to your question

Answer:

One angle is 70 degrees and the other one is 20 degrees

Step-by-step explanation:

If two angles are complementary, that means that they both add up to 90 degrees.

You have to use algebra to solve this bc you don't have the actual numbers.

So you can use the equation...

7f + 2f = 90

Solve for f, and then substitute the f back into the equation to find the measure of each angle.

7f + 2f = 90

9f = 90

f = 10

Substituting the 10 back in

7f = 7(10) = 70

2f = 2(10) = 20

Answer: 1

Step-by-step explanation: 3-2=1

Answer:

A.

Step-by-step explanation:

Add 4:

-5x ≤ 10

Divide by -5:

x ≥ -2

Answer:

29 degrees

Step-by-step explanation:

Note how both triangles are isosceles triangles, which mean two angles will be equivalent. In the triangle with the marked angle measurement, since the total of angles in a triangle is 180, then the measurement of the unmarked angles have a sum of 180-64, which is 116. Then, as stated before, this triangle is isosceles, so the measurement of each unmarked angle is 116/2, which is 58.
Next, notice how the angle below angle x in that triangle shares a line with one of the 58 degree angles. This means that angle is 180-58, which is 122. Now, since the total of angles in a triangle is 180 and the triangle is isosceles, then angle x is (180-122)/2, which is 58/2, or 29 degrees

The graph's curve "moves to the left/right/up/down," "expands or compresses," or "reflects" when a function is transformed.

When a function is transformed, the graph's curve either "moves to the left/right/up/down," "expands or compresses," or "reflects." For instance, by simply moving the graph of the function g(x) = x² up by 3 units, the graph of the function f(x) = x² + 3 is obtained.

Given that the transformation of the coordinate is x,y ( x+2,y-3). Let the coordinate of the point be ( 2, 2 ).

The translation of the point will be:-

( 2 , 2 ) = ( 2 + 2 , 2 - 3 )

( 2 , 2 ) = ( 4 , -1 )

The graph of the translation of the point is attached with the answer below.

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Answer:

\(x=8, y=3\)

Step-by-step explanation:

Recall that if a matrix multiplication of two matrices is defined, then the number of columns of the first matrix is equivalent to the number of rows of the second matrix.

Since matrix M has (11-x) columns and matrix N has y rows, and MN is defined, so it follows:

\(y=11-x----(1)\)

Since matrix N has (y+5) columns and matrix M has x rows, and NM is defined, so it follows:

\(y+5=x----(2)\)

Substitute (1) into (2):

\(11-x+5=x\\2x=16\\\therefore x=8--(3)\)

Substitute (3) into (1):

\(y=11-8=3\)

The value of y when x = 15 is 9

If the  variable y varies directly as x, this is expressed as;

y = kx

where k is the constant of proportionality

If x = 20 when y = 12, then;

k = y/x

k = 12/20

If x = 15, then the value of y is;

y = 12/20*15

y = 9

Hence the value of y when x = 15 is 9

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Answer:

here! I hope this helps :) the answer is 13.2 or 13 1 (upon 5)

Step-by-step explanation:

3 × 4 2 (upon 5)

=3× 22 (upon 5)

=66 (upon 5)

=13 1 (upon 5)

D 231 = 46w can be used to solve for w, the number of white eggs used last week.

By using the concept of dilation factor, length of BC obtained is 3 units

What is dilation factor?

Dilation is a transformation which changes the size of a figure by a certain factor.

That factor is called the scale factor

In the figure, A'B'C'D' is the image of ABCD under dilation with a scale factor of 3

A'B'C'D' is the dilated figure

Length of B'C' = 9 units

Length of BC = \(9 \div 3\) = 3 units

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Complete Question

The figure has been attached here

The equation of the circle is given by (C) (x-3)² + (y + 4)² = 9

All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant. The radius of a circle is the separation between any point on the circle and its center.

The equation of the circle in the general form is given by the

(x-a)²+(y-b)²=r²

Where (a,b) is the co-ordinates of the center of the circle and the radius is r.

Now the center of the circle is given at (3,-4) and the radius is r.

We know that the general equation of a circle is  \({\displaystyle (x-a)^{2}+(y-b)^{2}=r^{2}}\)

Substituting the values in the equation we get:

(x-3)²+(y-(-4))²=(3)²

or, (x-3)²+(y+4)²=9

Hence the equation of the circle is (x-3)² + (y + 4)² = 9.

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Answer:

-9 - 10 = -19

Step-by-step explanation:

If both numbers are a negative, then add them together but keep the negative or minus sign

Hope this Helps!!!

Check the picture below.

Answer: $43,823.37

Step-by-step explanation:

Formula to calculate the accumulated amount earned on principal (P) at rate of interest (r) compounded daily after t years :

\(A=P(1+\dfrac{r}{365})^{365t}\)

As per given , we have

P= $ 30,700

r= 8.9 % = 0.089

t= 4 years

\(A=30700(1+\dfrac{0.089}{365})^{365(4)}\\\\=30700(1+0.0002438)^{365(4)}\\\\=30700(1.0002438)^{1460}\\\\=30700(1.42747138525)\\\\=43823.3715272\approx43823.37\)

Hence, the amount at the end of 4 years would be $43,823.37 .

Using proportional relationships, it is discovered that they will cover 32 miles overall by walking 12 laps and running 20 laps.

For the second issue, the appropriate response is:

Brown 12 10 14 30

Green 20 25 35 75

Total 32 35 49 105

What is a direct proportional relationship?

In a direct proportional connection, the output variable is determined by multiplying the input variable by the proportionality constant, k, as in the example below:

y = kx.

For the first question, we have that out of a total distance of 8 miles, they:

Walk 3/8 of the distance.

Run 5/8 of the distance.

Hence the proportional relationships for the distances are given as follows:

Walked = 3/8 x Total Distance.

Ran = 5/8 x Total Distance.

For a total distance of 32 miles, the distances walked and ran are given as follows:

Walked: 3/8 x 32 = 3 x 4 = 12 miles = 12 laps.

Ran: 5/8 x 32 = 5 x 4 = 20 miles = 20 laps.

For the second question, we have that the table has to following the given ratios of the first row to the second row, with the third row being the sum of the first two rows, hence the third table is correct.

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Answer:

x = 6

Step-by-step explanation:

This is a bit of a tricky equation, and it's what we call an exponential equation since it involves some exponents. The way we begin to solve these kinds of problems is make the base on each side of the equals sign the same. On one side, we have 9 as our base, and on the other side, we have 3 as our base. 9 = 3², so we can rewrite our equation as shown below:

(3²)⁴ˣ⁻¹⁰ = 3⁵ˣ⁻²

From there, we can use the exponent rule (xᵃ)ᵇ = xᵃᵇ to simplify the left side of the equation.

3²⁽⁴ˣ⁻¹⁰⁾ = 3⁵ˣ⁻²

3⁸ˣ⁻²⁰ = 3⁵ˣ⁻²

Since our bases are now the same, we can take just the exponents and turn it into a new equation as shown below:

8x - 20 = 5x - 2

Hopefully at this point, this problem becomes easy for you, but I'll show how I solved this new equation below in case it doesn't make sense.

8x - 20 = 5x - 2

8x - 20 - 5x = 5x - 2 - 5x

3x - 20 = -2

3x - 20 + 20 = -2 + 20

3x = 18

3x/3 = 18/3

x = 6

Hopefully that's helpful! Let me know if you need more help. :)

The sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

To translate the inequality expression "2/3y - 9 < y + 1" into a sentence, we can break it down into smaller parts:

"2/3y" represents two-thirds of a number.

"9" represents the number nine.

"y + 1" represents the number increased by one.

Now let's construct the sentence:

"Nine less than two-thirds of a number" - This refers to the expression "2/3y - 9," indicating that we have subtracted nine from two-thirds of a number.

"is less than" - This is the comparison symbol in the inequality.

"the number" - This refers to the expression "y + 1," representing the number increased by one.

Combining these parts, we form the sentence: "Nine less than two-thirds of a number is less than the number."

Hence, the correct sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

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Step-by-step explanation:

As per MBTI personality people work

based on hunches and feelings use

their imagination and get the main

idea while missing some of the facts

are intuition