In how many ways you can put 2 books on 5 shelves so that
there is not more than one book on a shelf?

Using the sine ratio with the angle of depression, the length of the wire is 122.63m

The angle of depression is formed when the observer is higher than the object he/she is looking at. When an observer looks at an object that is situated at a distance lower than the observer, an angle is formed below the horizontal line drawn with the level of the eye of the observer and line joining object with the observer’s eye. Whereas the angle of elevation is the angle formed if a person stands on the ground and looks on the object kept above the ground at a height above the height of the person. This is the basic difference between the two angles. Both the angles are calculated by using the concept of trigonometry.

Using trigonometric ratio;

Using the sine angle ratio;

sin θ = opposite / hypothenuse

sin 58 = 104 / AC

AC = 104 / sin 58

AC = 122.63m

The length of the wire is 122.63m

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Answer:

465

Step-by-step explanation:

The sum of consecutive numbers has a formula, and it's

\(\frac{n(n+1)}{2}\).

Where n is the amount of numbers.

From 1-30, it's 30 numbers, so:

\(\frac{30(30+1)}{2} \\\\\frac{30(31)}{2} \\\\\frac{930)}{2} \\\\\\465\)

Hope this helped!

The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

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Angie decorates 8 cupcakes after putting 4 sugar flowers on each cupcake.

To find the number of cupcakes c Angie decorates, we can use the equation:4c = 32where 'c' is the number of cupcakes Angie decorates.

4 represents the number of sugar flowers Angie puts on each cupcake, and 32 is the total number of sugar flowers Angie puts on the cupcakes.

To solve this equation for c, we need to isolate c on one side of the equation. We can do this by dividing both sides of the equation by 4. This gives us:c = 8

Therefore, Angie decorates 8 cupcakes.Here's how we get to this answer:4c = 32Divide both sides by 4 to isolate c:c/4 = 32/4c = 8

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Therefore , the solution of the given problem of coordinate comes out to be the vertex's dimensions are (9/4, 9/8).

A coordinate system is a method that employs one or more values or coordinates to accurately locate points or even other mathematical objects on a space, such as Euclidean space. Coordinates, that are pairs variables of numbers, are used to locate a point or object on a double plane.

Here,

2x^2 - 9x + 9 = 0

The quadratic formula can be used to find the roots:

=> x = [-(-9) ± √((-9)^2 - 4(2)(9))] / (2*2)

=>  x = [9 ± √(9)] / 4

=>  x1 = (9 + 3) / 4 = 3

=> x2 = (9 - 3) / 4 = 3/2

The x-intercepts of the equation's curve are therefore x = 3 and x = 3/2.

We can use the following algorithm to determine the vertex's coordinates:

=>  x = -b / 2a

where b=-9 and a=2. By replacing these numbers, we obtain:

=> x = -(-9) / 2(2) = 9/4

We can change x = 9/4 into the formula f(x) = 2x2 - 9x + 9 to obtain the corresponding y-coordinate of the vertex:

f(9/4) = 2(9/4)^2 - 9(9/4) + 9 = 9/8

Therefore, the vertex's dimensions are (9/4, 9/8).

f(2) = 2(2)^2 - 9(2) + 9 = -5

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The probability that a person will purchase no more than one costume is given as follows:

93%.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

The total number of outcomes for this problem is given as follows:

187 + 228 + 29 = 444.

Only 29 people purchased more than one costume, hence the probability of at most one costume is calculated as follows:

(444 - 29)/444 = 0.93 = 93%.

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1/2 s + 3/4 s + 1/4 s + 4

((2+3+1)/4)s +4

6/4 s + 4

3/2 s + 4

Answer:

3/2 + 4

Step-by-step explanation:

1/2+3/4+1/4= 3/2s

3/2s+4

Answer:

AB =  4.9cm

Step-by-step explanation:

We know

AC is 9.1 centimeters, and BC is 4.2 centimeters.

Find AB

We take

9.1 - 4.2 = 4.9cm

So, AB = 4.9cm

The equation that represents the amount of pounds of potato that you buy is 1.15x = 3.45

The given parameters are:

Cost per pound = $1.15 per pound

Total purchase = $3.45

The equation that represents the amount of pounds of potato that you buy is

Total purchase = Cost per pound * Number of pound

Substitute the known values in the above equation

3.45 = 1.15 * x

Evaluate the product

3.45 = 1.15x

Rewrite as

1.15x = 3.45

Hence, the equation that represents the amount of pounds of potato that you buy is 1.15x = 3.45

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The value of function f (4) is,

⇒ f (4) = 19

We have to given that;

The function is,

⇒ f (x) = x² + 3

Now, WE can find the value of f (4) by substitute x = 4 in above function as,

⇒ f (x) = x² + 3

Plug x = 4;

⇒ f (4) = 4² + 3

⇒ f (4) = 16 + 3

⇒ f (4) = 19

Thus, The value of function f (4) is,

⇒ f (4) = 19

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Answer:

Step-by-step explanation:

you have a pentagon , and the sum of the angles is 540

3x-10+3x-8+5x-2+3x+1+2x+15=16x-4=540

16x-4=540

16x=544

x=544/16=34

the angle= (3x-8)=(3*34)-8=94

Answer:

40.2948

Step-by-step explanation:

area of triangle=1\2×sin125×8.5×12

=1/2×0.819×8.5×12

=40.2948

Answer:

$42.00

Step-by-step explanation:

We can represent the given information as a ratio:

% of original price : price

                          5% : $2.00

Then, we can multiply both sides of this ratio by 20 (or 100% / 5%) to get 100% of the original price, which IS the original price.

5%      :  $2.00

↓ × 20   ↓ × 20

100%  :  $40.00

Now that we know the original price, we can add $2.00 to get the new price.

$40.00 + $2.00 = $42.00

Answer:

the second one

Step-by-step explanation:

The selling price of the item at 10% marlkup is $55

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

Selling price = Cost To Store * (1 + Markup)

substitute the known values in the above equation, so, we have the following representation

Selling price = 50 * (1 + 10%)

Evaluate

Selling price = 55

Hence the selling price of the item is $55

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Answer:

  a = -5/11

Step-by-step explanation:

You want to solve the equation -1/4-a-4=7/4a-3.

The first step in solving this 3-step equation can be to add the opposite of (-a) so that the variable 'a' appears only on one side of the equation:

  -1/4 -a -4 +a = 7/4a -3 +a

  -17/4 = 11/4a -3 . . . . . . . . . . . simplify

The second step is to add the opposite of the constant (-3) so that the constant is on one side of the equation, and the variable is on the other side.

  -17/4 +3 = 11/4a -3 +3

  -5/4 = 11/4a . . . . . . . . . . simplify

The third step is to multiply by the inverse of the coefficient of the variable:

  (4/11)(-5/4) = (4/11)(11/4a)

  -5/11 = a . . . . . . . . . . . . . . . simplify

  -1/4 -(-5/11) -4 = (7/4)(-5/11) -3

  -17/4 +5/11 = -35/44 -3

  (-187 +20)/44 = (-132 -35)/44

  -167/44 = -167/44 . . . . . . answer checks OK

The given information does not provide any clear indication for determining the position that should be taken on 3/01 and 3/02. Without additional information, it is not possible to make a decision. The table only displays the closing prices of the July GBP Futures Contract on different days, and it is unclear what trading strategy or what scenario is being considered. Additional information about the goals and objectives, the market conditions, and other relevant factors would be necessary to make a decision about trading positions.

Answer:

52

Step-by-step explanation:

This is because the formula is dr

Answer:

the estimation of the size of the population after 20 hours is 10159

Step-by-step explanation:

The computation of the size of the population after 20, hours is shown below;

= 100  2^(20 by 3)

= 10159.36

If we divide 20 by 3 so it would give 6.66 that lies between 6 and 7

So the estimation of the size of the population after 20 hours is 10159

hence, the same is relevant

Answer:

The answer is "10159"

Step-by-step explanation:

Every 3 hours the population doubles, with an initial population of 100.

\(\to P(t) = 100 \times 2^{\frac{t}{3}}\)

\(P(t)= \text{The population of bacteria}\\\\ t = \text{time in hours} \\\)

when t=20

\(\to p(20)= 100 \times 2^{\frac{20}{3}} \\\)

             \(= 100 \times 101.593667\\\\ =10159.3667\)

Answer:

sorry siso don't know the answer sorry ☹☹

Answer:

B = 200

Step-by-step explanation:

Cross multiply

10(20) = 200

Answer: C) Qualitative

The response isn't a numeric value, but rather a name instead. So that's why we have qualitative data here. Specifically, it is nomimal as it deals with names or labels. The data is not ordinal as we cannot sort the labels.

Answer:

The correct answer will be 18

Step-by-step explanation:

First mutiply your object of the question which is 9 times 16 then make sure you have the right answer then divide it by 8 and 144 the answer you got, and you get 18

Answer:

awts gege masakit walangya 123456880

Answer:

4 ,-5

Step-by-step explanation:

The maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.

To find the maximum area of a Norman window with a given perimeter, we can use calculus. Let's denote the radius of the semicircle as r and the height of the rectangular window as h.The perimeter of the Norman window consists of the circumference of the semicircle and the sum of all four sides of the rectangular window. Therefore, we have the equation:

πr + 2h = 9We also know that the area of the Norman window is the sum of the area of the semicircle and the area of the rectangle, given by:

A = (πr^2)/2 + rh

To find the maximum area, we need to express the area function A in terms of a single variable. We can do this by substituting r from the perimeter equation:

r = (9 - 2h)/(π)

Now we can rewrite the area function in terms of h only:

A = (π/2) * ((9 - 2h)/(π))^2 + h * (9 - 2h)/(π)

Simplifying this equation, we get:

A = (1/2)(9h - h^2/π)

To find the maximum area, we differentiate the area function with respect to h, set it equal to zero, and solve for h:

dA/dh = 9/2 - h/π = 0

Solving this equation, we find:h = 9π/2

Substituting this value of h back into the area function, we get:

A = (1/2)(9 * 9π/2 - (9π/2)^2/π) = (81π/2 - 81π/4) = 81π/4

Therefore, the maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.

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The factored expression of 4x³ - 2x² + 8x - 4 is (2x² + 4)(2x - 1) by grouping

From the question, we have the following parameters that can be used in our computation:

4x³ - 2x² + 8x - 4

Group the expression in 2's

So, we have

(4x³ - 2x²) + (8x - 4)

Factorize each group

2x²(2x - 1) + 4(2x - 1)

So, we have

(2x² + 4)(2x - 1)

Hence, the factored expression is (2x² + 4)(2x - 1)

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9514 1404 393

Answer:

  100 ft

Step-by-step explanation:

The centroid divides each median into parts in the ratio 2 : 1. The longest part is 2/(2+1) = 2/3 of the whole length of the median.

That is, AG = 2/3AC = (2/3)(150 ft) = 100 ft.