These are radical and complex number questions, i need to simplify both WITH WORK, please help

In 1820  different ways a group of four people can be selected from this group of 16.

In 35 ways four women can be chosen from the group of 7 women.

The probability that all women will be chosen to attend the conference is 1.92%.

The proportion of favourable outcomes to all possible outcomes of an event is known as the probability. The number of positive outcomes for an experiment with 'n' possible outcomes can be represented by the symbol x. The probability of an event can be determined using the following formula.

To find how many different ways can a group of four people be selected from this group of 16, we will implement the combination formula.

[tex]^n C_r=\frac{n !}{r ! (n-r) !}[/tex]

Where,

nCr = number of combinations

n = total number of objects in the set

r = number of choosing objects from the set

Here, n = 16 and r = 4, substituting the values we get

[tex]^{16} C_4=\frac{16 !}{4 ! (16-4) !}[/tex]

[tex]^{16} C_4 =[/tex] 1820

Hence, in 1820  different ways a group of four people can be selected from this group of 16.

To find how many ways can four women be chosen from the group of 7 women we will implement the combination formula.

Here, n = 7 women and r  = 4 women, substituting the values we get

[tex]^7 C_4=\frac{7 !}{4 ! (7-4) !}[/tex]

[tex]^7 C_4=[/tex] 35

Thus, in 35 ways four women can be chosen from the group of 7 women.

The probability that all women will be chosen to attend the conference is

[tex]\frac{^7 C_4}{^{16}C_4}[/tex] = 35/1820

       = 0.01923076

       = 1.92%

Thus, the probability that all women will be chosen to attend the conference is 1.92%.

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Answer:

1/5

Step-by-step explanation:

Finding the unknown value in exponent form:

Prime factorize 125.

      125 = 5 * 5 * 5 = 5³

   [tex]\sf k^3 = \dfrac{1}{125}\\\\ k^3 = \left(\dfrac{1}{5}\right)^3[/tex]

As exponents are same, compare the bases,

 [tex]\sf k = \dfrac{1}{5}[/tex]

Answer:

x=1/5

Step-by-step explanation:

[tex]k^3=1/125\\[/tex]

[tex](k^3)^\frac{1}{3} =(\frac{1}{125} )^\frac{1}{3}[/tex]

 [tex]k^3^\frac{1}{3} =\frac{1}{125^\frac{1}{3}}[/tex]

[tex]k=\frac{1}{5}[/tex]

Hope this Helps :)

For the first function, the coordinates of A are (0, 1).

The equation of circle B is (x -4)^2 + y^2 = 25

And the circle intercepts the x-axis at:

(9, 0) and (-1, 0)

We have the equation:

y = a^x

And we know that A is the y-intercept of that equation, remember that the y-intercept is the point such that x = 0, so the y-coordinate will e:

y = a^0 = 1

So the y-intercept (point A)  is the point (0, 1).

We start with the circle:

x^2 + y^2 = 25

And we apply a translation of 4 units to the right, so we write this as:

(x - 4)^2 + y^2  = 25

c) The circle intercepts the x-axis when y = 0, then:

(x - 4)^2 + 0^2 = 25

x - 4 = ±√25

x - 4 = ±5

x = 4 ± 5

Then the two points where the circle intercepts the x-axis are:

(9, 0) and (-1, 0)

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The weight of the twelve people on the elevator is 1,825 pounds.

And the weight of the thirteen person is given by the inequality:

x ≤ 175

We have an elevator with 12 people in it, such that the weights of these 12 people are:

175, 140, 135, 155, 170, 190, 125, 160, 150, 150, 130, 145

To find the total weight we just need to add these numbers, we will get:

175 + 140 + 135 + 155 + 170 + 190 + 125 + 160 + 150 + 150 + 130 + 145 = 1,825

So the 12 people in the elevator have a total weight of 1,825 pounds.

Now, the weight limit is 2,000 pounds.

So if we define x as te weight of the 13 th person, we can write the inequality:

1,825 + x ≤ 2,000

x ≤ 2,000 - 1,825

x ≤ 175

So the person can weight at mos 175 pounds.

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Answer:

For example, 7 is a divisor of 84 because 84 ÷ 7 is an even division. However, that also means that 7 × (a number) = 84, so 7 is a factor of 84.

The amount by which an apple is more expensive than a pear is; D: 4p

We are told that  5 apples and 3 pears costs 8p more than 3 apples and 5 pears.

Let the cost of apples be x and let the cost of pears be y. Thus, the equation that represents the sentence is;

5x + 3y = 3x + 5y + 8

Rearrange to get;

5x - 3x + 3y - 5y = 8

2x - 2y = 8

divide both sides by 2 to get;

x - y = 4

Thus;

x = 4 + y

Which means it costs 4p more

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If a cave explorer is at an elevation of −32 feet and the explorer starts moving at a rate of −6 feet per minute. it will take, 9 in minutes for the explorer to reach an elevation deeper than −140 feet.

Elevation of feet =  −32 feet.

Feet per minute =  −6 feet per minute

Elevation deeper than  feet = −140 feet

Let x  represent the time for reach the desired height

Inequality

-32 - 6x = ≤ -140

Substract 32 from both side

12x ≤ 140 -32

12x  ≤ 108

Divide both side by 12x

x ≤ 108/12

x ≤ 9

Therefore we can conclude that the explorer will have to use 9 minutes to get to the elevation.

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Answer:

1.5 hour

Step-by-step explanation:

since 1 hour =70km . Then x hour =105 ÷70=1.5 hour

Answer:

3.26 time 102

Step-by-step explanation:

Because a square of 10 is 100

3.26 x 100 = 326

We know that the decimal move 2 spots to the right

So the answer is 3.26 x 102

The equation of the line that has a slope of -3 and passes through the point (5, -1) is 3x + y = 14.

What is slope ?

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.

We know the slope point form,

y - y1 = m( x - x1 )

Where x1 and y1 atre the coordinates of the points and m is the slope.

Putting thew values from the question:

y - (-1) = -3 ( x - 5)

=> y  + 1 = -3x + 15

=> 3x + y = 14

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Answer: $13,713.75

Step-by-step explanation: 10% of $13,250 = $1,325 (the raise given)

$13,250 - $1,325 = $11,925 (original salary)

15% of $11,925 = $1,788.75

$11,925 + $1,788.75 = $13,713.75

Answer:

0.86

Step-by-step explanation:

Move the decimal point one place to the right

The constant of the proportionality is 5.

Constant of proportionality:

The word constant of proportionality refers the ratio that relates two given values in what is known as a proportional relationship.

Given,

Greg has to find the area of a rectangle. The area can be determined by the equation A=5I, where A is area and I is the length of rectangle.

Here we need to find the constant of proportionality.

Through the given question we know that the area of the rectangle is

A = 5l

Here A represents the area of the rectangle

and the letter "l" denotes the length of the rectangle.

While we compare these with the standard form,

y = mx

Here m represents the constant of proportionality.

While in the given equation the place of m in standard equation number 5 is presented.

Therefore, 5 is the constant of proportionality.

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Option (B) Yes, it is proportional because the ratios for miles per hour are all equivalent to 1.25 miles per hour is correct.

It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.

It is given that:

A group of hikers tracked how long it took to hike a 10-mile trail. They hiked 2.5 miles in 2 hours, 7.5 miles in 6 hours, and 8.75 miles in 7 hours.

From the data given:

Ratio = distance/time

2.5 / 2 = 1.25 miles per hour

7.5 / 6 = 1.25 miles per hour

8.75 / 7 = 1.25 miles per hour

Thus, option (B) Yes, it is proportional because the ratios for miles per hour are all equivalent to 1.25 miles per hour is correct.

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Answer:

x = 27

Step-by-step explanation:

AOB is a straight angle = 180°

the 3 angles on it therefore sum to 180° , that is

36 + 90 + 2x = 180

126 + 2x = 180 ( subtract 126 from both sides )

2x = 54 ( divide both sides by 2 )

x = 27

No. there is no rigid transformation taking Rectangle A to Rectangle B. See the explanation below.

The type of transformation that is taking place in the attached image from Rectangle A to Rectangle B is a non-rigid transformation. This is is because A rigid transformation (or isometry) is a transformation that DOES NOT change the size or shape of a geometric figure.

As it is easily observed, rectangle A is no longer the same shape and size as B. This means that the change or transformation that has occurred is non-rigid.

It is to be noted that dilation is a transformation that keeps the figure's geometry and orientation but alters its size. A dilation's scale factor is the factor by which each linear measure of the figure (such as a side length) is multiplied.

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[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{"d" proportional to }t^2}{ {\Large \begin{array}{llll} d=kt^2 \end{array}}}\qquad \textit{we also know that} \begin{cases} d=80\\ t=4 \end{cases}\implies 80=k(4)^2 \\\\\\ \cfrac{80}{4^2}=k\implies 5=k\hspace{15em}\boxed{d=5t^2} \\\\\\ \textit{when t = 8, what is "d"?}\qquad d=5(8)^2\implies d=640~in[/tex]

nswer:

Explanation:

) We want to start by drawoing a Venn diagram

We call the set of the married people M and the set of the full-time workers F

We have the Venn diagram represented as follows:

b) We want to get the probability that an employee works full time and is married

We have that as:

P(full-time) OR P(married) -P(Full time and married)

P(full time) = 70/110

P(married) = 60/110

P(full time and married) = 35/110 (since half of the full-time workers are married)

Thus, we have:

:

c) The probability that an employee works full time or is not married

Mathematically, we have that as:

P(full time) OR P(not married) -P(full time and not married)

P(not married) = 1 - P(married)

:

Answer:

Step-by-step explanation: $3.02

3 pounds difference

Answer:

77/12

Step-by-step explanation:

3 3/4 + 2 2/3

15/4+8/3

45/12+32/12

77/12

I just checked it for you. yes it can

Answer:60°

Step-by-step explanation:the whole thing equals 180° since it is a straight line. 30°+90°=120°   180°-120°=60°

note that parallel lines have equal gradients.

give the line 2x+3y =5 write it in the form y=mx+c first so that you can be able to know its gradient. Mind you getting the gradient of the given line means finding the gradient of the new equation because they are equal as stated above.

[tex]2x + 3y = 5 \\ 3y =5 - 2x \\ \frac{3y}{3} = \frac{5}{3} - \frac{2x}{3} \\ y = \frac{5}{3} - \frac{2}{3} x[/tex]

FROM THE GIVEN EQUATION WE CAN NOW SEE THAT THE GRADIENT IS

[tex] - \frac{2}{3} [/tex]

Meaning the gradient of the new EQUATION sknce it is parallel to the given one will be

[tex]m = - \frac{2}{3} [/tex]

also.

given the points we can substitute to get the value of the unknown c.

[tex] - 1= - \frac{2}{3} (3) + c \\ - 1 = -2 + c \\ c = - 1 + 2 \\ c = 1[/tex]

[tex]y = - \frac{2}{3} x + 1[/tex]

Value of x is 28.5 and y is 14.

An angle is a figure in Euclidean geometry made up of two rays that share a terminal and are referred to as the angle's sides and vertices, respectively. Angles created when two rays are in the plane where the rays are located. The intersection of two planes also creates angles. We refer to these as dihedral angles.

Given Data

a = 2x + 3y

b = 4x - y

c = 3x + 2y

∠b = 100° ( corresponding angle)

4x - y = 100

4x - 100 = y

∠a = ∠b ( alternate angle)

2x + 3y = 4x - y

Equating values of y

2x + 3(4x - 100) = 4x - 4x + 100

2x + 12x - 300 = 100

14x = 400

x = [tex]\frac{400}{14}[/tex]

x = 28.5

For the values of y,

4(28.5) -100

114 -100

14

Value of x is 28.5 and y is 14.

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Answer: 9.73

Step-by-step explanation:

the five at the end indicates rounding up so the answer for the 2 decimal places is 9.73.

Answer:

9.73

Rule #1: If the last digit in 9.725 is less than 5, then remove the last digit.

Rule #2: If the last digit in 9.725 is 5 or more and the second to the last digit in 9.725 is less than 9, then remove the last digit and add 1 to the second to the last digit.

Rule #3: If the last digit in 9.725 is 5 or more and the second to the last digit in 9.725 is 9, and the third to the last digit is less than 9, then remove the last digit, make the second to last digit 0, and add 1 to the number to the third to the last digit.

Rule #4: If the last digit in 9.725 is 5 or more and the second to the last digit is 9, and the third to the last digit is 9, then add 1 to the number on the left side of the decimal point and make the right side of the decimal point 00.

When rounding 9.725 to two decimal places we use Rule #2. Therefore, the answer to "What is 9.725 rounded to 2 decimal places?" is:

1. First we find the product of 3 and 6. Product=addition

3+6=8

8 is the product of 3 and 6.

2. Now we find the difference between 8 and the square root of 36.

The square root of 36 is 6. (6x6=36)

8-6=2.

3. Now we must divide 36 by 2.

36/2=18.

ANSWER= 18

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these are a bit complicated, but i hope that helped!! the tricky part is breaking it up and trying to find which goes first.- || much love! <33

Dividing 36 by the difference between product of 3 and 6 and the square root of 36 gives 3.

The problem asks us to divide 36 by the difference between the product of 3 and 6 and the square root of 36.

First, we need to find the product of 3 and 6, which is 18.

Then, we need to find the square root of 36, which is 6.

So, the difference between the product of 3 and 6 and the square root of 36 is 18 - 6 = 12.

Therefore, we need to divide 36 by 12.

We can do this by performing long division, or by using the calculator.

The answer is 3.

Here is the long division solution:

36 / 12 = 3

Here is the calculator solution:

36 / 12 = 3

Therefore, the answer to the problem is 3.

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Answer: HL

Step-by-step explanation: the diagram compares the two sides, or legs, and the hypotenuse.

NO. Your friend is incorrect because the solution to the system of equations on the graph is: (4, 3).

The solution to a system of linear equations is the coordinates of the point where the two lines of the linear equations intersect.

The x-coordinate and the y-coordinate of this point lie on each of the lines of the linear equations. This means that, both values of x and y are a solution to each of the linear equation given.

Therefore, the solution to a system of linear equations is usually represented as (x, y) and not just as a single value of x.

The system of linear equations that is graphed above shows that both lines intersect at (4, 3), that is, when x = 4, the value of y = 3.

However, your friend only stated the value of x = 4, as the solution to the system of linear equations that is represented on the graph.

Therefore, your friend is wrong.

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