Can someone help me out with these problems and show work please !!

The method to use is Combination

Combination is a way or method of selecting items from a collection without a defined order or manner.

The formula for finding Combination is given as;

Combination = n!/ r!(n -r)!

n = 135

r = 2

Combination = 135!/ 2!(135 - 2)!

Thus, the method to use is Combination

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Answer:

The circle is a round shape that has a total angle of 360 degrees. If a circle is divided into 6 equal parts, the measure of the angles between spokes is 12 degrees.

Step-by-step explanation:

to find the angle

360/30=12

the angle is 12 degrees

I hope this helps and have a good day!

The value of expression is 18.

A modulus function is a function that determines a number or variable's absolute value.  A function with absolute values is another name for it. This function's result is always positive. let's suppose if you want to find modulus of -2 then you will get 2 as the answer.

now according to question

4|a|+8-a at a=-2

here a is negative that means modulus will give us positive value.

put a =-2 in the expression and get the answer. modulus of -2 will give us +2

so

=4(2)+8-(-2)

=8+8-(-2)

=8+8+2

=18

hence the answer is 18.

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Using the given table:

a) the average rate of change is 32.5 jobs/year.

b) the average rate of change is 12.5 jobs/year.

For a function f(x), the average rate of change on an interval [a, b] is:

[tex]\frac{f(b) - f(a)}{b - a}[/tex]

a) The average rate of change between 1997 and 1999 is:

[tex]A = \frac{695 - 630}{1999 - 1997} = 32.5[/tex]

So the average rate of change is 32.5 jobs/year.

b) Now the interval is 1999 to 2001.

The rate this time is:

[tex]A ' = \frac{720 - 695}{2001 - 1999} = 12.5[/tex]

So the average rate of change is 12.5 jobs/year.

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For finding the given literal equation is necessary to apply the power 2 on both sides of the given equation and after that you should rewrite the equation as a function of the variable m .

There are different power rules, see some them:

1. Multiplication with the same base: you should repeat the base and  add the exponents.

2. Division with the same base: you should repeat the base and  subctract the exponents.

3.Power. For this rule, you should repeat the base and multiply the exponents.

4. Zero Exponent. When you have an exponent equals to zero, the result must be 1.

The question gives: [tex]t=2\pi *\sqrt{\frac{m}{k}}[/tex] and from the previous equation, you should find [tex]m=\frac{kt^2}{4\pi ^2}[/tex].

STEP 1 - Applying the power 2 on both sides of the equation [tex]t=2\pi *\sqrt{\frac{m}{k}}[/tex].

[tex]t=2\pi *\sqrt{\frac{m}{k}}\\ \\ t^2=(2\pi *\sqrt{\frac{m}{k}})^2\\ \\ t^2=4\pi ^2*\frac{m}{k}[/tex]

STEP 2 - Rewriting the equation  [tex]t^2=4\pi ^2*\frac{m}{k}[/tex]  as a function of the variable m .

[tex]t^2=4\pi ^2*\frac{m}{k}\\ \\ t^2k=4\pi ^2m\\ \\ m=\frac{kt^2}{4\pi ^2}[/tex]

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Answer:

1. divide both sides of the equation by 2pi

2. square both sides of the equation

3. use the rule to simplify a fraction to a power

4. multiply both sides of the equation by k

Step-by-step explanation:

edg '22

Answer:

(x + 6)(x - 2) = x² + 4x - 12

(x + 2)(x - 8) = x² - 6x - 16

(x + 6)(x - 6) = x² - 36

(x - 5)(x - 1) = x² - 6x + 5

(x - 4)(x - 10) = x² - 14x + 40

(x + 2)(x + 5) = x² + 7x + 10

Step-by-step explanation:

Use FOIL.

(x + 6)(x - 2) =

F - first: x × x = x²

O - outer: -2 × x = -2x

I - inner: 6 × x = 6x

L - last: 6 × -2 = -12

(x + 6)(x - 2) = x² - 2x + 6x - 12

Now, combine like terms.

(x + 6)(x - 2) = x² + 4x - 12

(x + 2)(x - 8) = x² - 6x - 16

(x + 6)(x - 6) = x² - 36

(x - 5)(x - 1) = x² - 6x + 5

(x - 4)(x - 10) = x² - 14x + 40

(x + 2)(x + 5) = x² + 7x + 10

Answer:

It is stretched taller by a factor of 2.

A type of sampling in which individuals to be interviewed are selected based on their proportion or quota in the general population being polled is known as public opinion.

What is sampling type of public opinion ?

A survey that measures the entire target population is called a census. A sample refers to a group or section of a population from which information is to be obtained. Survey samples can be broadly divided into two types: probability samples and super samples.

The collective opinion of large segment of the population on an issue, candidate or public policy on which the public may be much divided and lake a consensus.

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Trapezoid

[tex]A=\frac{1}{2}(3.5)(6+8)=24.5[/tex]

Parallelogram

[tex]A=(3.5)(6)=21[/tex]

Rhombus

[tex]A=\frac{1}{2}(7 \cdot 2)=7[/tex]

Red Area

[tex]2(21)+2(24.5)=91[/tex]

White Area

[tex]2(21)+2(24.5)=91[/tex]

The circular area surrounding the design is an existing rock bed are 24.5, 21, 27, 91 and 91 ft sq.

That quadrilateral in which opposite sides are parallel is called a parallelogram.

Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.

It is given the bases of the trapezoids are 6 ft and 8 ft,

The heights of the trapezoid and the parallelogram are 3.5 ft each, and the horizontal distances between the left and right vertices of each rhombus is 2 ft.

Trapezoid

Area = 1/2(3.5)(6 + 8)

Area = 24.5

Parallelogram

Area = 1/2(3.5)(6)

Area = 21

Rhombus

Area = 1/2(7)(2)

Area = 7

Red Area

Area = 2(21) + 2(2.4)

Area = 91

White Area

Area = 2(21) + 2(2.4)

Area = 91

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Answer:

58%

Step-by-step explanation:

47/81 x 100%

≈ 58%

Hope it helps : )

The probability of a student taking a math class or a physics class is [tex]0.85[/tex] when the probability of a student taking a math class is [tex]0.70[/tex], the probability of taking a physics class is [tex]0.30[/tex], and the probability of taking a math class and a physics class is [tex]0.15[/tex]

How can we find the probability of taking math class or a physics class ?

Given in the question probability of the student taking class

[tex]p(M)=0.70\\p(P)=0.30\\p( M and P)=0.15[/tex]

So we use the probability union intersection formula

[tex]p(M or P)=p(M)+p(P)-p(M and P)[/tex]

Substitute the values

[tex]p(M or P)=0.7+0.3-0.15\\=0.85[/tex]

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The area of the semicircle = 8π

A semicircle is formed when the panel passing through the center touches both ends of the circle. Therefore, if you connect two semicircles, you get a circle

If you cut them in half or divide the circumference of the circle by 2, you will get a semi-circle. Area of ​​semicircle The area of ​​the semicircle is half the area of ​​the circle. Because the area of ​​the circle is πr2. Therefore, the area of ​​the semicircle is 1/2 (πr2). Where r is the radius. The value of π is 3.14 or 22/7.

Semi-circular area = 1/2 (πr2)

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By the inclusion/exclusion principle,

[tex]P(A\cup B) = P(A) + P(B) - P(A\cap B)[/tex]

[tex]P(A\cup B) = \dfrac23 + \dfrac45 - \dfrac35[/tex]

[tex]P(A\cup B) = \dfrac{10}{15} + \dfrac{12}{15} - \dfrac9{15}[/tex]

[tex]P(A\cup B) = \boxed{\dfrac{11}{15}}[/tex]

The value of √(7 * 23 - 1)/8 is 4.47, the values of a, b and c are -14/11, -10/11 and 3, respectively and the area of the shape is 5√5 + 5 square meters

The question goes thus:

If √5 = 2.236, evaluate √(7 * 23 - 1)/8

We have:

√(7 * 23 - 1)/8

Evaluate the product of 7 and 23

√(7 * 23 - 1)/8 = √(161 - 1)/8

Evaluate the difference of 161 and 1

√(7 * 23 - 1)/8 = √160/8

Evaluate the quotient of 160 and 8

√(7 * 23 - 1)/8 = √20

Express 20 as the product 4 and 5

√(7 * 23 - 1)/8 = √(4 * 5)

Expand the product

√(7 * 23 - 1)/8 = √4 * √5

Express √4 as 2

√(7 * 23 - 1)/8 = 2 * √5

Substitute √5 = 2.236

√(7 * 23 - 1)/8 = 2 * 2.236

Evaluate the product

√(7 * 23 - 1)/8 = 4.472

Approximate

√(7 * 23 - 1)/8 = 4.47

Hence, the value of √(7 * 23 - 1)/8 is 4.47

The expression is given as:

(3√2 + 5√6)/(3√2 - 5√6)

Rationalize the above expression

(3√2 + 5√6)/(3√2 - 5√6) * (3√2 + 5√6)/(3√2 + 5√6)

Evaluate the product

(3√2 + 5√6)²/((3√2)² - (5√6)²)

Simplify the denominator

(3√2 + 5√6)²/(18 - 150)

This gives

[(3√2)² + (5√6)² + 2 *(3√2) * (5√6)]/(-132)

Simplify the numerator

[168 + 120√3]/(-132)

Simplify the fraction

-14/11 - 10√3/11

Hence, the values of a, b and c are -14/11, -10/11 and 3, respectively

The area is calculated as:

A = 1/2 * (Sum of parallel bases) * Height

So, we have:

A = 1/2 * (4 + 3√5 + 6 - √5) * √5

Evaluate the like terms

A = 1/2 * (10 + 2√5) * √5

Evaluate the product

A = (5 + √5) * √5

Evaluate the product

A = 5√5 + 5

Hence, the area of the shape is 5√5 + 5 square meters

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Answer: 100

Step-by-step explanation:

The angles with measure 100° and x° are vertical angles, which are two opposite angles made from two intersecting lines. These vertical angles are always the same measure.

Hence, both x and 100 have the same measure.

Answer:

Step-by-step explanation:

hello :

|x – 5| + 2 < 20  means :  |x – 5| + 2-2 < 20-2

|x – 5|  < 18

-18< x - 5 < 18

-18+5< x - 5+5 < 18+5

-13< x< 23   ( solutions)

The vertex form of the function is f(x) = -2(x-4)^2 + 2

The standard vertex form of a function is expressed according to the expression;

f(x) = a(x-h)^2+k

where

a is a constant = -2

(h, k) is the vertex = (4, 2)

Substitute

f(x) = -2(x-4))^2+2

f(x) = -2(x-4)^2 + 2

Hence the vertex form of the function is f(x) = -2(x-4)^2 + 2

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Option D. The most appropriate comparison for the spread is that the interquartile range for town A, 15 degrees is less than that of B.

The inter quartile is solved as Q3 - Q1

This is seen as

For Town A,

30 - 15 = 15 degrees

For town B

40 - 20 = 20 degrees.

Hence we can see that 15 is less than 20, so town A is less than town B. The answer is option D.

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The definition of the piecewise function is given as follows:

A piecewise function is a function that has different definitions, depending on the input.

Researching this problem on the internet, for x equal or greater than -3 and less than -1, the function is a line with a slope of 1 that goes through (-3,0), hence the definition is found as follows:

y = x + b

0 = -3 + b

b = 3

Then:

[tex]f(x) = x + 3, -3 \leq x < 1[/tex].

For x between -1 and 1, inclusive, the function is constant at 5, hence the definition is:

[tex]f(x) = 5, -1 \leq x \leq 1[/tex].

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The recursive formula of the geometric sequence is [tex]b(1) = -0.25[/tex], [tex]b(n) = b(n-1)\cdot 8[/tex]

The sequence is given as:

[tex]-0.25\,,-2\,,-16\,,-128,..[/tex]

The first term of the above sequence is

[tex]b(1) = -0.25[/tex]

Calculate the common ratio using

r = b(2)/b(1)

So, we have:

r = -2/-0.25

Evaluate

r = 8

So, we have:

[tex]b(n) = b(n-1)\cdot 8[/tex]

Hence, the recursive formula of the geometric sequence is [tex]b(1) = -0.25[/tex], [tex]b(n) = b(n-1)\cdot 8[/tex]

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Complete question

Complete the recursive formula of the geometric sequence

[tex]-0.25\,,-2\,,-16\,,-128,..[/tex]

[tex]b(1) =[/tex]

[tex]b(n) = b(n-1)\cdot[/tex]

Based on the given scenario, the kind of sequence explained is an arithmetic sequence

First term, a = 19

Second term, a + d

28 = 19 + d

28 - 19 = d

9 = d

Third term, a + 2d

= 19 + 2(9)

= 19 + 18

= 37

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Answer:

150 [tex]m^{2}[/tex]

Step-by-step explanation:

Consider the figure as an isosceles triangle and a rectangle combined.

ISOSCELES TRIANGLE

[tex]A = \frac{1}{2} bh[/tex]

[tex]A = \frac{1}{2} *15*12[/tex]

A = 90

RECTANGLE

[tex]A=lw[/tex]

[tex]A = 5*12[/tex]

[tex]A = 60[/tex]

60 + 90 = 150

Answer:

150m

Step-by-step explanation:

break up the polygon into a triangle and a rectangle.

Triangle:

to find the height of the triangle, subtract 5 from 20

height = 15m     base = 12m

[tex]area=\frac{1}{2}bh\\ A=\frac{1}{2} (12)(15)\\A=6(15)\\A=90m[/tex]

rectangle:

[tex]A=bh\\A=12(5)\\A=60m[/tex]

Add both areas together:

[tex]90+60=150m[/tex]

Answer:

20 % are red

Step-by-step explanation:

I THINK this is what you mean:

24 blue + 6 red = 30 blocks total

6 red / 30 total = 6/30 = .2   = 20 %

Answer:

9.09 years

Step-by-step explanation:

Use the simple interest formula

A=P(1+rt)

18000=9000(1+.11*t), solve for t

t = 9.0909

The  accounting principle she would use to value the assets of the company at their original cost is historical cost accounting.

Historical cost accounting is an accounting method for recording the value of fixed assets under US GAAP where the value of an asset on a balance sheet is equal to the cost of acquiring the asset.

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Answer:

5 cm

Step-by-step explanation:

When two chords are equidistant from the center of the circle, the two chords have equal length. Therefore, the length of chord AB, 4x - 6, is equal to the length of chord CD, 6x - 12.

4x - 6 = 6x - 12

6 = 2x

x = 3

Now that we know x = 3, we can substitute the value back into the original expression, 4x - 6, to find the length of chord AB.

AB = 4x - 6 = 4*3 - 6 = 12 - 6 = 6 cm

When measuring the distance between a line and a point, we create a segment through the point perpendicular to the line. In Geometry, we also learn that the perpendicular bisector of a chord in a circle contains the center of the circle.

In this case, the gray line perpendicularly bisects segment AB. PX is 4 cm long and AX is 3 cm long (because AX is half the length of AB). Notice that triangle AXP is a right triangle, so we can use Pythagorean Theorem to find AP.

[tex]AP^{2} = AX^{2} +PX^{2}[/tex]

[tex]AP = \sqrt{3^{2} +4^{2} }[/tex]

[tex]AP =\sqrt{9+16}[/tex]

[tex]AP = \sqrt{25}[/tex]

[tex]AP = 5[/tex]

Answer: 36

Step-by-step explanation:

If 5/6 = 180

lets find what 1/6 equals

To do this lets divide 180 by 5 to find 1/6

[tex]\frac{180}{5} =36[/tex]

Therefore, 1/6 = 36

We know 180/5 will give us the answer because 180 is already 5/6 of the total; dividing by 5 will give us 1/6 of the total. Ex: if we had 4/6 of the total, we would divide by 4 to find 1/6.

Anyways, we can check our answer by doing:

36*5 = 216 then taking 5/6 of 216, which should equal 180

[tex]216*\frac{5}{6} =180[/tex]

Therefore, we know 36 is the correct answer

Answer:

2400 mm^2.

Step-by-step explanation:

The ratio of their areas = ratio of the squares of their sides.

So x / 7350 = 40^2 / 70^2   where x is area of smaller hexagon.

x = 7350 * 40^2 / 70^2

= 2400 mm^2.

The area of the smaller hexagon is found to be 2,400 mm², given the two hexagons are similar. Hence, 4th option is the right choice.

The areas of two similar figures are in the ratio which is equal to the square of the ratio of their corresponding sides.

If we have two figures A and B, and they are similar, then we can say that:

(Area of A)/(Area of B) = {(Side of A)/(Side of B)}².

In the question, we are informed that the two hexagons are similar in shape.

We are asked to find the area of the smaller hexagon, given the larger hexagon has an area of 7350 mm².

As the two hexagons are similar, we can show that:

(Area of the smaller hexagon)/(Area of the larger hexagon) = {(Side of the smaller hexagon)/(Side of the larger hexagon)}².

The side of the smaller hexagon is given to be 40mm, whereas the corresponding side of the larger hexagon is given to be 70 mm.

Thus, we can show that:

(Area of the smaller hexagon)/7350 = {40/70}²,

or, Area of the smaller hexagon = (16/49)*7350 = 16*150 mm² = 2400 mm².

Thus, the area of the smaller hexagon is found to be 2,400 mm², given the two hexagons are similar. Hence, 4th option is the right choice.

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