What is the length of AC? (Giving 50 Points)​

Using the permutation formula, it is found that the people can be chosen for the roles in 6840 ways.

The order in which the people are chosen is important, as there are different roles, hence the permutation formula is used.

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this problem, 3 people will be chosen from a set of 20 people, hence the number of ways is given by:

[tex]P_{20,3} = \frac{20!}{17!} = 6840[/tex]

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Arc length = 4.28 cm.

Arc length is the distance between two points along a section of a curve.

circumference of a circle of radius r is C = 2πr,

and central angle = 360 degrees.  

circumference = 28 cm.  

28 cm =2πr

28= 2*3.14*r

28= 6.28*r

r= 4.46 cm.  

Arc length, s = r[tex]\theta[/tex]

[tex]\theta[/tex] =55 degrees,

s = 4.28 cm.

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Answer:

x = 2 or -2

Step-by-step explanation:

This is a regular hexagon

To find the value of x we will have to find the sum of interior angles first and to do that:

(n-2)*180 (n is the number of angles)

(6-2)*180 = 720 is the sum of all six angles

since this is a regular hexagon, all angles has equal measures so

720/6 = 120 now

30x^2 = 120 divide both sides by 30

x^2 = 4 find the root of both sides

x = 2 or -2

Answer:

5 oranges

Step-by-step explanation:

to solve this problem we need to make a cross-multiplication equation

2.34 is to 6 as 1.95 is to ?

? is the number of oranges that are needed to be found that were bought

2.34/6 = 1.95/?

Now we cross multiply 6 and 1.95 = 11.7

11.7/2.34 = 5

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Answer: She bought 5 oranges

Step-by-step explanation:

We need to find out how much one orange costs first, so we do:

$2.34 ÷ 6or = $0.39

Thirty-nine cents is how much one orange cost.

Now you multiply the initial value of 1 orange by 5, so:

$0.39 x 5 = $1.95, $1.95 =5 oranges

You can also do $1.95 divided by $0.39 which is 5.

(you can multiply till you find the number or divide the given number by the other divided number)

Therefore, that means Mav bought 5 oranges.

Answer: 151.2 ft²

Step-by-step explanation:

      The surface area, in this case, is the area of all the shapes given combined.

      For the rectangles:

             A = L * W

      For the triangles:

             A = [tex]\frac{L*W}{2}[/tex]

-> See attached

    Now, we will add them altogether.

54 + 54 + 27 + 16.2 = 151.2 ft²

Answer:

8.7

Step-by-step explanation:

Calculate the area of the triangle by using sine.

Area of Triangle

[tex]A = \frac{1}{2} \times \text{side} \times \text{side} \times \sin{\theta}[/tex]

θ ... included angle between the two sides

We already have two sides a and another side which is congruent to a, making it isosceles triangle. But we don't have the included angle. The angle we need is the vertex angle of the isosceles triangle. Angle B is one of the base angles (two base angles are congruent) and it measures 70°.

Recall that angles in any triangle add up to 180°.

base angle + base angle + vertex angle = 180°

70° + 70° + vertex angle = 180°

vertex angle = 40°

Now we have all the information to use the formula!

[tex]A = \frac{1}{2} \times \text{side} \times \text{side} \times \sin{\theta}[/tex]

[tex]A = \frac{1}{2} \times 5.2 \text{ cm} \times 5.2 \text{ cm} \times \sin{40^\circ}[/tex]

[tex]A = 13.52 \text{ cm}^2 \times \sin{40^\circ}[/tex]

[tex]A \approx 8.6904 \text{ cm}^2[/tex]

Rounded to 1 DP:

[tex]A = 8.7 \text{ cm}^2[/tex]

After 18.8 years, Halle account exceed $10,000 if Halle deposited $4000 into an account that earns 5% interest, each year.

It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent [tex]\rm y = a^x[/tex]

where a is a constant and a>1

We have an exponential equation:

[tex]\rm a = 4000(1+ 0.05)^t[/tex]

Plug a = $10,000

[tex]\rm 10000 = 4000(1+ 0.05)^t[/tex]

After calculating:

[tex]\rm 1.05^t= 2.5[/tex]

t = 18.78 ≈ 18.8 years

Thus, after 18.8 years, Halle account exceed $10,000 if Halle deposited $4000 into an account that earns 5% interest each year.

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Based on the given table, the maximum temperature in the year was 22°C and the minimum was -12°C. It is colder when the temperature is -7°C.

The temperatures between -7°C and 7 °C are :-6, -4, 0, 1, and 6.

During the year, the highest recorded temperature was 22°C in the month of July. The lowest temperature was -12°C in the month of Janaury.

The lower the temperature, the colder it is. This is why -7°C is colder than 7°C.

The temperatures between -7°C and 7°C are temperatures that are higher than -7°C but lower than 7°C. These are:

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Answer:

Dimensions:  125 m x 250 m

Area:  31,250 m²

Step-by-step explanation:

Given information:

First, let us assume that the land is rectangular in shape.

Let [tex]y[/tex] = length of the side opposite the river

Let [tex]x[/tex] = length of the other 2 sides of the land

Therefore, we can create two equations from the given information:

  Area of land:   [tex]A= xy[/tex]

  Perimeter of fence:   [tex]2x + y = 500[/tex]

Rearrange the equation for the perimeter of the fence to make y the subject:

[tex]\begin{aligned} \implies 2x + y & = 500\\ y & = 500-2x \end{aligned}[/tex]

Substitute this into the equation for Area:

[tex]\begin{aligned}\implies A & = xy\\& = x(500-2x)\\& = 500x-2x^2 \end{aligned}[/tex]

To find the value of x that will make the area a maximum, differentiate A with respect to x:

[tex]\begin{aligned}A & =500x-2x^2\\\implies \dfrac{dA}{dx}& =500-4x\end{aligned}[/tex]

Set it to zero and solve for x:

[tex]\begin{aligned}\dfrac{dA}{dx} & =0\\ \implies 500-4x & =0 \\ x & = 125 \end{aligned}[/tex]

Substitute the found value of x into the original equation for the perimeter and solve for y:

[tex]\begin{aligned}2x + y & = 500\\\implies 2(125)+y & = 500\\250+y & = 500\\y & = 250\end{aligned}[/tex]

Therefore, the dimensions that will give Christine the maximum area are:

125 m x 250 m (where 250 m is the side opposite the river)

The maximum area is:

[tex]\begin{aligned}\implies \sf Area_{max} & = xy\\& = 125 \cdot 250\\& = 31250\: \sf m^2 \end{aligned}[/tex]

[tex]|\Omega|=10^2=100\\|A|=2\cdot3=6\\\\P(A)=\dfrac{6}{100}=6\%[/tex]

Answer:

[tex](f+g)(x) = -8x-6[/tex]

Step-by-step explanation:

We are given the two functions:

[tex]\displaystyle f(x) = -5x - 4 \text{ and } g(x) = -3x - 2[/tex]

And we want to find:

[tex](f+g)(x)[/tex]

Recall that this is equivalent to:

[tex]\displaystyle (f+g)(x) = f(x) + g(x)[/tex]

Substitute and simplify:

[tex]\displaystyle \begin{aligned} (f+g)(x) &= (-5x-4)+(-3x-2) \\ \\ &= -8x-6 \end{aligned}[/tex]

In conclusion:

[tex](f+g)(x) = -8x-6[/tex]

Answer:

-2.6112

Step-by-step explanation:

= 0.510 (3+0.2) x -1.6

= 0.510 x 3.2 x -1.6

= -2.6112

hence answer is -2.6112.

Answer:

[tex]\text{P(green)} =\frac{45}{139}[/tex]

Step-by-step explanation:

The total number of candies is :

= 42+45+20+32

= 139

Then

we have 45 green out of 139 candies.

Then

[tex]\text{P(green)} =\frac{45}{139}[/tex]

Note : 45/139 is already simplified.

The expression w = A/l can be used to find the width of the rectangle if the area and length of the rectangle are given.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

Let's suppose the width of the rectangle is w and the length of the rectangle is l

Then, the area of rectangle(A) can be given as:

A = lw

divide by l on both the sides:

A/l  =  lw/l

A/l = w

or

w = A/l

Thus, the expression w = A/l can be used to find the width of the rectangle if the area and length of the rectangle are given.

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Answer:

C. 3rd one Fraction 10/24

Step-by-step explanation:

3/4 - 2/6 = 0.41 or = 10/24 or it could be equal to 5/12​ are 10/24, 15/36, 20/48 and 25/60 or as Decimal 0.41

Step-by-step explanation:

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Answer:

226,800

Step-by-step explanation:

Calculator

Answer:226,800

Step-by-step explanation:

Answer:

see the attachment photo!

Answer:

Step-by-step explanation:

Length=18

Width/Breadth =10

Height=2

The formula for a diagonal face of a cuboid is=√(l²+ b²)

Face diagonal=√(18²+10²)

= 20.59 to 2.d.p

The formula for the body diagonal of a cuboid is=√(l² + b² + h²)

Body diagonal=√(18² + 10² + 2²)

=20.69 to 2.d.p

Answer:

Negative 3 less-than y less-than-or-equal-to 3

Step-by-step explanation:

By looking at a coordinate plane, we can easily see the range

remember, a closed dot means includes , and an open dot means does not include

[closed dot]

(open dot)

the range is all possible y-values. so, all y values shown are

3               which it includes

to -3            which it excludes  / does not include

so, all y values are greater than -3 and less than or equal to 3

Answer: 0.388

8 continuing so draw a line over the eights.

An expression is defined as a set of numbers, variables, and mathematical operations. The coefficients for the binomial expansion of (p+q)⁶ are 1, 6, 15, and 20.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The expansion of the given binomial (p+q)⁶ can be done as shown below,

(p+q)⁶ = p⁶ + 6p⁵q + 15p⁴q² + 20p³q³ + 15p²q⁴ + 6pq⁵ + q⁶

Hence, the coefficients for the binomial expansion of (p+q)⁶ is 1, 6, 15, and 20.

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Answer:

x ≈ 8.7

Step-by-step explanation:

given 2 secants from an external point to the circle, then

the product of the external part of one secant and the entire secant is equal to the product of the external part of the other secant and the entire secant , that is

6(6 + x) = 4(4 + 18) ← distribute parenthesis on both sides

36 + 6x = 4 × 22 = 88 ( subtract 36 from both sides )

6x = 52 (divide both sides by 6 )

x ≈ 8.7 ( to the nearest tenth )

[tex] \sqrt{25 \: - \: 10 \sqrt{3} \: + \: 3} [/tex]

[tex] \sqrt{(5 \: - \: \sqrt{3} ) ^{2} } [/tex]

[tex] \boxed{ \bold{5 \: - \: \sqrt{3} }}[/tex]

The chemical need to be added to the tank is  16000 cubic cm

The volume is the total capacity of a container.

Total volume of tank = 80,000 cubic centimeters of water

Chemical volume =  5 cubic centimeters

Chemical needed = = 80,000 /5 = 16000 cubic cm is needed.

Thus,  16000 cubic cm chemical is needed.

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Answer:

Where is the expression?

Step-by-step explanation:

Please write the expression.

The statement that is true about the polygons is: the opposite angles of the rectangle are supplementary, therefore, a circle can be circumscribed about the rectangle.

An circumscribed quadrilateral is a quadrilateral whose four side lie tangent to the circumference of a circle. The opposite angles in an inscribed quadrilateral are supplementary, that is, when added together, their sum equals 180 degrees.

From the two figures given, the opposite angles of the rectangle are supplementary, therefore, a circle can be circumscribed about the rectangle. (Option D).

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Answer:

0.375x^2

Step-by-step explanation:

(-1.5x)(-0.25x)  

= (-1.5)(0.25)(x)(x)

= 0.375x^2