A group of Mathematics faculty at the local college consists of 7 women and 9 men. Four people are to be selected to go to a conference. How many different ways can a group of four people be selected from this group of 16?

In how many ways can four women be chosen from the group of 7 women?

What is the probability that all women will be chosen to attend the conference?
Enter a reduced fraction or decimal.

Answer:

m<2= 2x+6

Step-by-step explanation:

so you have +6 or six more than 2x or twice than m<1 so therefore m<2= 2x+6

Answer: linear equation

Step-by-step explanation:

because x is not squared

Answer:

p = 11

Step-by-step explanation:

This Question tests on the concept of Angle Properties.

Given from the diagram above, we can form up a equation:

4p + 7 + 90 + 3p + 6 = 180 (Sum of Angles in a Triangle)

Now we can solve for p from the equation.

[tex]4p + 7 + 90 + 3p + 6 = 180 \\ 7p + 103 = 180 \\ 7p = 180 - 103 \\ 7p = 77 \\ p = \frac{77}{7} = 11[/tex]

Answer:

11.1x²

Step-by-step explanation:

Since the isotope has only a very little amount in nature, it does not largely affect the  atomic mass of lithium.

The term isotope has to do with the atoms of the same element that do have the same atomic number but different mass numbers. The implication of this is that isotopes have the same number of protons but do not have the same number of neutrons.

Note that the average atomic mass of an atom is the weighted average of the atomic masses of all the isotopes of the compound. The isotopes that contribute greatly towards the atomic mass are those that have a larger percentage abundance.

Given that the new lithium isotope, 8Li identified  is a trace isotope, meaning that it exists in a very tiny quantity, it does not any noticeable effect on the  atomic mass of lithium.

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Step-by-step explanation:

We only combine like terms when the like terms are alike

To combine like terms, we have to add the coefficients and keep the variables the same. We add like terms to make one term. Example: 7x+3x both are like terms we can combine together and write 10x.

Answer and Explanation:

y = 5x is a line with a constant of proportionality of 5 (it goes through the origin). It goes through quadrants I and III.

See the attached image for a graph.

Answer:

216 miles

Step-by-step explanation:

so the base fee is 18.99, subtract the total (219.87) by 18.99.

219.87-18.99=200.88

200.88 divided by 0.93 (charge for each mile driven)

200.88/0.93=216

thats a lot of miles.

There are different 2,808,000 passwords possible which are the correct answer would be option (B)

A permutation is defined as a mathematical process that determines the number of different arrangements in a set of objects when the order of the sequential arrangements.

Sue picks a new password for her email that consists of 3 letters, 2 digits, and a special character (! or #) which is given in the question.

As per the given condition,

For the first letter, we have 26 options.

For the second letter, we have 25 options, because one letter is already used.

For the third letter, we have 24 options, because 2 letters are already used.

For the first digit, we have 10 options.

For the second digit, we have 9 options, because one is already used.

For the first special character (! or #), we have 2 options.

Then the total number of combinations is:

Combinations = 26×25×24×10×9×2 = 2,808,000

So if we can not repeat digits or letters, we can make 2,808,000 different passwords.

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Answer: 68.75

Step-by-step explanation: I did the math myself so it may not be correct, but it's at least very close.

Answer:

the correct answer is D:68.75

With the two solutions, the quadratic equation is x^2 - 11x + 10 = 0

From the question, we have:

Number of solutions = 2

Variable = x

Where the solutions are

1 and 10

This means that

x = 1 and x = 10

Rewrite the above solutions as

x - 1 = 0 and x - 10 = 0

Multiply the above equations

(x - 1) * (x - 10) = 0

This gives

x^2 - 11x + 10 = 0

Hence, the quadratic equation in standard form is x^2 - 11x + 10 = 0

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The value of x is 18 and the value of ∠A (interior angle) is 73°.

According to the given figure,

We have:

∠A = 6x-35°

∠B = 3x+53°

The two parallel lines have been cut by another line.

(Note that when a line divides two parallel lines then the sum of the interior angles on the same side is 180° and the alternate interior angles are equal to each other.)

So, we will have the following expression:

∠A + ∠B = 180°

(6x-35+3x+53)° = 180°

9x+18 = 180

9x = 180-18

9x = 162

x = 162/9

x = 18

Now, putting the value of x in ∠A,

∠A = 6x-35°

∠A = (6*18-35)°

∠A = (108-35)°

∠A = 73°

Hence, the value of x is 18 and the measurement of ∠A is 73°.

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When a family's ratio of income to poverty measurement is 1.05 , then the family is considered by the census bureau as rich.

The "economy food plan," which is based on the U.S. Department of Agriculture, is used as the basis for an absolute poverty indicator in the country. The World Bank also uses an absolute definition of poverty. Extreme poverty is defined as surviving on less than $1.90 USD a day.

A ratio of less than 1 generally indicates that the income is below the poverty line. When the ratio is 1, income and poverty level are equal, and when the ratio is larger than 1, income is greater than poverty level. In this case, the family is rich.

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Equation represents a line which is parallel to the line

y = 1/2x +3 with (2,5)

Since you are looking for an equation that is parallel to a line, the slope is the same: m = 1/2

Use Point-Slope equation [y-y1 = m(x-x1)]

with the given point (2,5): y-

5=1/2(x-2)

Distribute the 1/2: y-5=1/2x-1

Move the 5 to the other side to put it in y=mx+b form: y=1/2x-1+5

Answer:

y=1/2x+4

A parallel equation can be located in what way?

In the absence of an intersection, two lines are said to be parallel. Each line has the same slope. In the event that m1=m2, f(x)=m1x+b1 and g(x)=m2x+b2 are parallel. If m 1 = m 2, then f (x) = m 1 x + b1 and g (x) = m 2 x + b2 are parallel.

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The answers are subtraction, subtraction, and addition property of equality

There are 9 properties of equality, which are addition, subtraction, multiplication, division, distributive, substitution, reflexive, symmetric, and transitive. In this case, we are using the first 2. In algebra, whatever you do to one side has to be done to the other, in the case of the first problem x is being subtracted on both sides, which represents the definition of the subtraction property (If a = b, then a – c = b – c, a is the one side of the equation, b is the other side, and c is the subtraction done on both sides). The first one is the subtraction property of equality, then, and if we look at problem 2, the same thing is done (apart from that it is done with a number, which doesn't affect the property), so it is also the subtraction property.

Now the last problem seems to do the opposite, it seems to be adding instead, in this case, adding 1 on both sides. This follows the definition of the addition property of equality (If a = b, then a + c = b + c) since it is adding c (1) on both sides. So the last problem is the addition property of equality.

The value of the expression is [tex]-2x^2[/tex]-8x + 6.

Given expression:-

[tex](2x^2-5x+4)-(4x^2+3x-2)[/tex]

We have to find the value of the given expression.

We know that, while subtracting quadrating equations, we subtract like terms from like terms.

Like terms

Like terms are those that contain the same variables raised to the same power. Only the numerical coefficients are different. In an expression, only we can combine like terms.

For example : While adding (5x + 3) and (4x - 5), we will add 5x to 4x and 3 to -4 to get the answer that is 9x - 1.

Hence, we can write,

([tex]2x^2-4x^2[/tex]) + (-5x -3x) + (4 -(-2)) = [tex]-2x^2[/tex] -8x + 6.

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Using proportions, it is found that Elizabeth should order 42 mugs and 18 t-shirts.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using the unit rates, then operations such as multiplication or division are used to find the equivalent amounts.

In the context of this problem, we have to consider that:

Hence the number of mugs that she has to order is found as follows:

256/6 = 42 (rounded down, as the remainder means that the last guest to receive a mug is the 252th guest).

The number of t-shirts that she has to order is given as follows:

256/14 = 18 (also rounded down, following the same logic as the number of mugs).

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Answer:

(0,2)

Step-by-step explanation:

x  = [tex]\frac{2-2}{2}[/tex] = [tex]\frac{0}{2}[/tex] = 0  We are finding the average of the x values (2 and -2)

y = [tex]\frac{-5+9}{2}[/tex] = [tex]\frac{4}{2}[/tex] = 2  we are finding the average of the y values (-5 and 9)

The relation between x and y such that the point (x, y) is equidistant from point(2, -5) and(-2, 9) = 2x + 7y = -14

Points (2, -5) and (-2, 9).

let (x, y) be A

Let (2, -5) = (-2, 9) = B

Ax = Bx (length)

Squaring on both sides

Ax² = Bx²

By distance formula

(x - 2)² + (y +5)² = (x + 2)² + (y - 9)²

x² - 4x + 4 + y² +10y + 25 = x² + 4x + 4 + y² - 18y + 81

8x + 28y = -56

by multiplying both sides by 4

2x + 7y = -14

This is the relationship between the points (x, y) which is equidistant to A and B.

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(a) AB, BC, CD, and DA are, respectively, and long.

(b) AB, BC, CD, and DA have slopes of 0, 0, and 2, respectively.

(c) AC and BD have lengths of 8 and 72, respectively.

(d) AC and BD have slopes of 1 and 1, respectively.

A quadrilateral is a polygon having four sides, four angles, and four vertices.

There is a quadrilateral called ABCD.

The quadrilateral's vertices are A(3,5), B(7,7), C(5,3), and D. (1,1).

The side AB measures [(3-7)2 + (5-7)2] = 20.

The side BC measures [(7-5)2 + (7-3)2]. =√20 .

The side CD measures [(5-1)2 + (3-1)2] in length. = √20.

The side DA measures [(1-3)2 + (1-5)2] = 20 in length.

The diagonal AC measures [(3-5)2 + (5-3)2] = 8 in length.

The diagonal BD is [(7-1)2 + (7-1)2] in length. =√72 .

The slope of side AB is equal to 1/2 (7-5)/(7-3)

The slope of the side BC is equal to zero (7-3)/(7-3)

The side CD has a slope of (3-1)/(5-1) = 1/2.

DA's side has a slope of (5-1)/(3-1) = 2.

The sides AD and BC are parallel to one another and have the same length.

Equal in length and parallel to one another are sides AB and CD.

Each side is parallel to the side next to it.

As a result, we draw the conclusion that ABCD is a quadrilateral.

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So basically 130+90=220 and 6+8=14. And 220+14=234.

a trough has ends shaped like isosceles triangles, with width 2 m and height 5 m, and the trough is 10 m long. then the height of the water change when the water is 4 m deep is 1/8 m/min

The depth of the water is 4/5 of the depth of the trough, so the width of the surface will be 4/5 of the width of the trough:

 4/5 × 2 m = 8/5 m

Then the surface area of the water is ...

 Area = LW = (10 m)(8/5 m) = 16 m²

The rate of change of height multiplied by the area gives the rate of change of volume:

 2 m³/min = (16 m²)(h')

 h' = (2 m³/min)/(16m²) = 1/8 m/min

Hence , the height of the water change when the water is 4 m deep is 1/8 m/min

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Considering the definition of a line, x-intercept and y-intercept, the  x-intercept and y-intercept are (3, 0) and (0,6) respectively.

A linear equation o line can be expressed in the form y = mx + b

where

The point [y-intercept] is where the line crosses the y-axis, and occurs when x = 0.

The point [x-intercept] is that value of x for which the expression is equal to 0 and the line crosses the x-axis.

In this case, the line is 10x +5y=30. Expressed in the form y = mx + b, you get:

5y= 30 - 10x

y= (-10x + 30)÷5

y= -10/5x + 30/5

y= -2x +6

where:

The point [y-intercept] is represented by the value of the y-intercept b. So the point [y-intercept] is (0,6).

Being the point [intersection x] that value of x for which the expression is equal to 0 or y is equal to 0, in this case it is calculated as:

0= -2x + 6

-6= -2x

(-6)÷ (-2)= x

3=x

Finally, the point [x-intercept] is (3,0).

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Answer:

Step-by-step explanation:

9 divided by 1557

(Tell me if you mean 1557 divided by 9 lol the wording is strange :] )

See screenshot!

The nth term of the arithmetic sequence when the numbers given are 7, 4, 1, -2 is 6 - 3n.

It should be noted that an arithmetic sequence has a common difference. In this case, the values that are given include 7, 4, 1, -2.

First term = 7

The common difference between the numbers include:

= Second term - First term

= 4 - 7

= -3

The nth term will be:

= a + (n - 1)d

where a = 7

d = -3

= a + (n - 1)d

= 7 + (n - 1) -3

= 7 -3n - 1

= 6 - 3n

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The probability of selecting two lemon filled donuts in a row is 7/92.

Probability is used to determine the odds that a random event would happen. The odds that the random event happens has a probability value that lies between 0 and 1. If it is certain that the event would happen, the probability value would be 1. If it is certain that the event would not happen, the probability value is 0.

The donuts are picked without replacement because the donut are eaten as they are picked.

Probability = (number of lemon filled donuts / total number of donuts) x [(number of lemon filled donuts / total number of donuts) - 1]

(7/24) x (6/23) = 7/92

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Answer:

Similarity: Both are odd numbers

differences:  3 > 1  

Similarity: Both are Consecutive natural numbers

differences: 3 is an odd number and 4 is an even number

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Answer:4/3-2

Step-by-step explanation: