A group consists of men and women. people are selected to attend a conference.
a. In how many ways can people be selected from this group of ​?

Answer:

To solve the inequality 40(7−5x)<7−25(8x+2), we can start by distributing the 40 on the left side and the -25 on the right side:

280 - 200x < 7 - 200x - 50

Next, we can combine like terms on both sides:

230 - 200x < -200x - 43

Now, we can add 200x to both sides:

230 < -43

This is a false statement, which means that there is no solution to the inequality. Therefore, the inequality 40(7−5x)<7−25(8x+2) is false for all values of x.

Answer:

(-4,8)

Step-by-step explanation:

The combination of existing functions is not limited to function composition. Another method is to do addition, subtraction, multiplication, and division on the functions using standard algebraic operations.

In mathematics, the process of "function composition" combines two functions, f and g, to produce h = g f, where h(x) = g(f(x)).

Function composition is the process of combining two functions to produce a third function.

Simply using the first function's output as the input for the second function is how it works.

The function g is applied in this operation on the outcome of applying the function f to x.

In other words, the functions f: X Y and g: Y Z are combined to create a function that maps x in domain X to g(f(x)) in codomain Z. If z were a function of y and y were a function of x, it seems sensible that z would be a function of x.

The final composite function is denoted by the notation (g f)(x) = g(f(x)) for all x in X, and is represented by the notation g f: X Z. [nb 1]

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Using the probability, we can find that when a single card is drawn from the deck, the probability of not drawing a king is 12/13.

The ability to occur is known as probability. The occurrence of random events is the subject of this branch of mathematics. The value is expressed as a number between 0 and 1. Probability has been introduced in mathematics to predict how likely events are to occur.

Here the total number of cards in a deck is 52.

There are four jacks, four queens, and four kings in a deck of 52 cards. Twelve face cards follow.

If we choose one of the king cards here, then:

Probability of drawing a king will be:

P = 4/52

= 1/13

Now, we have to find the probability of not drawing a king, so:

Probability = 1 - 1/13

= 13-1/13

=12/13

Therefore, when a single card is drawn from the deck, the probability of not drawing a king is 12/13.

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Answer:

Option C

Step-by-step explanation:

f(x) can be factorised and re-written as (2x+3)(x-2)

g(x) can be re-written as (x+2)(x-2)

On dividing f(x) by g(x): (x-2) cancels out

Quotient: (2x+3)/(x+2)

Answer: -20

Step-by-step explanation:

The formula is written as -2 - (-8) + (-14) + 2. Using the following addition and subtraction rules for integers will allow us to simplify this expression:

1.  To add two integers with the same sign, we add their absolute values and then assign the common sign to the sum.

2.  To add two integers with different signs, we find the difference   between their absolute values and assign the sign of the integer with the greater absolute value to the sum.

3.  To subtract an integer, we add its opposite.

Using these rules, we can simplify the given expression as follows:

-2 - (-8) + (-14) + 2

= -2 + 8 - 14 + 2      (using rule 3 for the second term)

= -6 - 14              (combining like terms)

= -20

Therefore, the value of the expression is -20.

Hence, -12×[tex]\frac{1}{2}[/tex]×13 this expression is used  Commutative property to make it easier to evaluate -12×13×[tex]\frac{1}{2}[/tex] .

According to mathematics, an arithmetic operation is commutative if switching the operands positions has no effect on the computation's outcome.

When two numbers A and B are provided, the commutative property of the numbers formula is as follows:

A+B=B+A

A×B=B×A

A-B≠B-A

A÷B≠B÷A

According to the commutative property formula, the outcome is unaffected by the sequence in which two integers are added or multiplied. However, the order of the integers matters for subtracting and dividing any two real numbers, thus it cannot be altered.

The commutativity property is used to get

-12×13×[tex]\frac{1}{2}[/tex] = -12×[tex]\frac{1}{2}[/tex]×13

such that the evaluation becomes easier, which is to get 12×[tex]\frac{1}{2}[/tex]=6.

The commutativity property is used as follows:

-12×(13×[tex]\frac{1}{2}[/tex])=-12×([tex]\frac{1}{2}[/tex]×13).

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The area of the shaded region is 83.3% of the area of the sector ONQ.

First, let's find the area of the sector ONQ:

The formula for area of a sector is;

Area of sector = (angle/360) x πr²

In this case, the angle of the sector ONQ is 120 degrees (since AOB is an equilateral triangle and each angle of an equilateral triangle is 60 degrees). So;

Area of sector ONQ = (120/360) x π(11²)

= 127.2 cm²

Next, we need to find the area of the equilateral triangle AOB:

The formula for area of an equilateral triangle is;

Area of equilateral triangle = (√3/4) x s²

where s is length of a side of the triangle.

In this case, s =7 cm, so;

Area of equilateral triangle AOB = (√3/4) x (7²) = 21.2 cm²

Now we can find the area of the shaded region (which is the area of sector ONQ minus the area of triangle AOB);

Area of shaded region = Area of sector ONQ - Area of equilateral triangle AOB

= 127.2 - 21.2

= 106 cm²

Finally, we can express the area of the shaded region as a percentage of the area of sector ONQ;

Percentage = (Area of shaded region / Area of sector ONQ) x 100%

= (106 / 127.2) x 100%

= 83.3%

Therefore, the area of the shaded region is 83.3%

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--The given question is incomplete, the complete question is

"ONQ is a sector of a circle with centre O and radius 11 cm. A is the point on ON and B is the point on OQ such that AOB is an equilateral triangle of side 7 cm. Calculate the area of the shaded region as a percentage of the area of the sector ONQ. Give your answer correct to 1 decimal place.​"--

Answer:

width = 16 in

height = 24 in

depth = 32  in

Step-by-step explanation:

Volume = height x width x depth = hwd

h = 1.5w

d = 2w

V = (1.5w)(w)(2w) = 12,288

V = 3w³ = 12,288

w³ = 12,288/3 = 4096

w = ∛4096 = 16

h = 1.5(16) = 24

d = 2(16) = 32

Answer:

Based on the description, Rhett's drawing of his house is a rectangular prism. A rectangular prism is a three-dimensional figure that has six faces, where each face is a rectangle. In a rectangular prism, opposite faces are congruent and parallel, and adjacent faces meet at right angles.

The angle measure of RUT is m∠RUT = 33°.

The diameter of an arc within a circle is equal to the diameter of the central angle that subtends the arc.

Therefore, if we know the length of an arc, we may calculate the length of its corresponding central angle.

In this case, we are given that the measure of the minor arc RT is 66°.

We need to find the measure of angle RUT.

We achieve this by taking use of the fact that an inscribed angle's measure is half that of its equivalent central angle.

Since angle RUT is an inscribed angle that intercepts arc RT, we have:

m∠RUT = 1/2 × m/RT

m∠RUT = 1/2 × 66°

m∠RUT = 33°.

Therefore, the measure of angle RUT is 33°.

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Answer:

Genotype: 100% rr
phenotype: 100% white

Step-by-step explanation:

since there are no dominant genes the cross will definitely be a rr genotype

The expression of the given statement is 2y - 3  = -1

Expressions are mathematical statements that comprise either numbers, variables, or both and at least two terms associated by an operator. The operations of mathematics include multiplication, division, addition, and subtraction.

A phrase is considered a mathematical expression if it contains at least two numbers or variables and one or more mathematical operations. Let's look at how expressions are written.

The expression of the given statement is 2y - 3  = 4.

Here, let the unknown number = y

Now, product of y and 2 =  2 times  y   =   2y

Also, three less than the product   =  Product - 3

So, three less than the product  of 3 and y =  2 y - 3

Now, this above expression is equivalent to -1.

⇒2 y - 3  = -1

Hence the expression of the given statement is 2y - 3  = -1

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The sentence "Three less than the product of 2 and a number is 4" can be translated into the equation: 2x - 3 = 4

A mathematical statement that demonstrates the equivalence of two expressions is known as an equation.

It has two sides that are divided by the equals sign (=).

Variables, constants, coefficients, operators, and functions can all be used in the expressions on either side of the equation.

Here, x represents the unknown number that we are trying to solve for. The expression "the product of 2 and a number" is represented by 2x, and "three less than" is represented by the subtraction of 3 from that product. This expression is set equal to 4, which is the result given in the original sentence.

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The statements that are true include the following:

B. It is the ceiling function.

D. Any decimal or fraction round to the least integer that is greater than x.

In Mathematics, a piecewise-defined function can be defined as a type of function that is defined by two (2) or more mathematical expressions over a specific domain.

Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. By critically observing the graph of the given piecewise-defined function, we can reasonably infer and logically deduce that it is the ceiling function (least integer function) because it comprises the smallest integer that cannot be smaller than x i.e it assigns a decimal or fraction to the next integer;

x = 1.3 ≈ 2

x = 9 ≈ 9

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Out of 220 students, 44 would like dogs more than cats.

How to find the number of students who like dogs more than cats?

First, we know that 20 students like dogs and 12 like cats, so there are 20 - 12 = 8 more students who like dogs than cats.

We also know that there are 40 students in total, so the percentage of students who like dogs more than cats is 8/40 = 0.2.

To find the number of students who would like dogs more than cats among 220 students, we can use the same percentage:

We know that there are 220 students in total, so the number of students who would like dogs more than cats is 0.2 × 220 = 44.

Therefore, out of 220 students, 44 would like dogs more than cats.

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Answer:

B(x) appears to be an exponential function because the population increases at a constant rate over time. This can be seen by observing that the population roughly triples with each passing year, indicating that the function is of the form B(x) = ab^x, where a is the initial population and b is the growth factor. To confirm this, we can calculate the growth factor by dividing the population at each successive year by the population in the previous year. For example, we have:

b = B(1)/B(0) = 6/2 = 3

b = B(2)/B(1) = 18/6 = 3

b = B(3)/B(2) = 54/18 = 3

and so on.

M(x) appears to be a quadratic function because the population growth rate is not constant, but rather increases over time. This can be seen by observing that the rate of increase in the population growth appears to accelerate as time goes on, suggesting that the function is of the form M(x) = ax^2 + bx + c, where a, b, and c are constants. To confirm this, we can plot the data and observe that the graph has a parabolic shape.

S(x) also appears to be a quadratic function for similar reasons to M(x), where the population growth rate increases over time.

From the given data, the function S(x) appears to be the same type as W(x) because both are quadratic functions. Both functions appear to have an increasing rate of growth over time.

Step-by-step explanation:

The data presented shows the growth of the Javanese gibbon population on three different islands over time.

Data trends must be analyzed to determine the type of function that is modeling population growth. A common way to do this is to plot the data points and observe the shape of the curve. However, since the table only contains data, you can analyze trends by looking at the differences between consecutive terms.

To do this, we can calculate the first difference and the second difference in the population data.

The first difference:

- Swing: 40 - 30 = 10, 50 - 40 = 10, 60 - 50 = 10

Example: 60 - 50 = 10, 75 - 60 = 15, 90 - 75 = 15

- Salavati: 80 - 60 = 20, 100 - 80 = 20, 120 - 100 = 20

The second difference:

- Batanta: 10 - 10 = 0, 10 - 10 = 0

- Example: 15 - 10 = 5, 15 - 15 = 0

- Salavati: 20 - 20 = 0, 20 - 20 = 0

The first difference is constant for each island and shows a linear relationship between time and population growth. Also, the second difference is zero, indicating a constant rate of change.

Therefore, we can conclude that the population growth modeling function is a linear function that can be written as

M(x) = mx + b

where x is the time in years, m is the slope (population growth rate), and b is the y-intercept (initial population).

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The volume of the rectangular prism is  234 cm³

The formula for calculating the volume of a rectangular prism is expressed with the equation

V = Bh

Such that the parameters are enumerated as;

From the information given, we have that;

Substitute the values into the equation

Volume = 36(6.5)

multiply the values, and expand the bracket, we get;

Volume= 234 cm³

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The answer  is ,  the total number of positive integers less than 1000 with a digit sum of 4 is 35 - 20 = 15.

An integer is a whole number that can be positive, negative, or zero, but does not have any fractional or decimal parts. Integers can be represented on the number line, with zero at the center and positive integers to the right and negative integers to the left.

We  use technique called "stars and bars" to solve this problem.

Using this approach, the number of positive integers less than 1000 with a digit sum of 4 is equal to the number of ways to arrange 4 stars and 3 bars. We can choose the positions of the bars in 7 ways (i.e., there are 7 places where we can place a bar), so the total number of such arrangements is 7 choose 3 (i.e., we choose 3 places for the bars out of the 7 possible places), which is:

7 choose 3 = 7! / (3! * (7-3)!) = 35

Note that we need to subtract the number of solutions that have 0 as the first digit, since we are only looking for positive integers. We can choose the positions of the bars in 6 ways (i.e., we cannot place a bar before the first star), so the number of such arrangements is 6 choose 3, which is:

6 choose 3 = 6! / (3! * (6-3)!) = 20

Therefore, the total number of positive integers less than 1000 with a digit sum of 4 is 35 - 20 = 15.

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If Thabang worked for three hours and Ndivhu worked for two hours, then the total number of hours worked is five. To determine the amount Thabang will receive if they decided to share their money according to hours, we need to calculate the proportion of the total hours that Thabang worked and multiply that by the total amount of money earned.

Thabang worked for three out of five hours, which is 3/5 or 0.6 of the total time. To find out how much money he should receive, we can multiply this fraction by the total amount earned:

0.6 x R400 = R240

Therefore, Thabang should receive R240 if they decide to split the money based on hours worked.

The function that is represented by the graph is y = - [tex]\frac{1}{x}[/tex] + 1, Option C.

Graph functions are mathematical functions that are plotted on a graph, with the input values on the horizontal axis and the corresponding output values on the vertical axis.

They are a visual representation of how the output values of the function change as the input values change.

The function is y = -(1/x) + 1 might be identifies as transformation of the reciprocal function y = 1/x.

we can start by identifying any coordinated we see for both curved lines.
The first curved line has (-1, 2)

The second curved line has (1, 0)

We can cross check if we can find y using the function y = - [tex]\frac{1}{x}[/tex] + 1,

x = -1  therefore

y = (-1/(-1)) + 1 = 2. 2 matches matches the y coordinate (-1, 2).

x = 1 therefore,

y = (-1/1) + 1 = 0. 0 matches the y coordinate (1, 0).

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The average speed of the Moon's orbit is  593,21 km/h

The average speed is defined as the quotient between distance and time, here we know that:

distance = 384,400 km

time = 27 days = 27*(24 hours)= 648 hours.

Then the average speed will be:

S = 384,400 km/648h

S = 593,21 km/h

That is the average speed of the Moon's orbit.

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The 95 percent confidence interval for the true mean metal thickness is [0.290351, 0.290649] (rounded to 4 decimal places).

Confidence level is a statistical phrase that reflects the degree of confidence or reliability associated with an estimated parameter (such as a mean or percentage) generated from a sample of data. It is frequently stated as a percentage and shows the likelihood that the real population parameter falls within a certain confidence range.

Given :

Sample mean ([tex]\mu[/tex]) = 0.2905 mm

Sample size (n) = 59

Standard deviation (σ) = 0.000586 mm

Critical value for 95% confidence level = 1.96 (rounded to two decimal places)

Now,

[tex]\text{Standard error (SE)}= \sigma /\sqrt(n)\\\\SE = 0.000586 / \sqrt(59) = 0.00007613 \;\text{(rounded to 5 decimal places)}[/tex]

Now, for confidence interval;

[tex]\text {Confidence Interval }= \mu \pm Critical \;Value * SE[/tex]

[tex]\text{Confidence Interval} = 0.2905 \pm 1.96 * 0.00007613}\\\\\text{Confidence Interval} = 0.2905 \pm 0.000149 \text{ (rounded to 6 decimal places)}[/tex]

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The median would be a better measure to use for his homework grades.

What is the median?

The midway number in a set of data is known as the median. The data should first be arranged and ranked from smallest to greatest. Divide the total number of observations by two to get the midway value. The value in that location is the median if there are an odd number of observations; otherwise, round the number up.

Here, we have

Given: In his history class, Han's homework scores are:

100 100 100 100 95 100 90 100 0

The history teacher uses the mean to calculate the grade for homework.

We have to write an argument for Han.

Median would objectively fair better as a way to calculate grades. The median value doesn't rely on all of the assets that make up the dataset, unlike the mean method would.

The mean sum up every asset, which can lead to it being unreliable. The median, however, is the middle-most value within a list of numbers, which would make it a more accurate method of grading.

Overall, it would make the most sense for Han's history teacher to use the median method for grading homework.

Hence, the median would be a better measure to use for his homework grades.

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instead, they either involve random selection or selection for certain expressions jobs.

It is possible to multiply, divide, add, or subtract in mathematics. The following is how an expression is put together: Number, expression, and mathematical operator The components of a mathematical expression (such as addition, subtraction, multiplication or division, etc.) include numbers, variables, and functions. It is possible to contrast expressions and phrases. An expression, often known as an algebraic expression, is any mathematical statement that contains variables, numbers, and an arithmetic operation between them. For instance, the word m in the given equation is separated from the terms 4m and 5 by the arithmetic symbol +, as does the variable m in the expression 4m + 5.

The first choice is a combination since it entails picking four students from a group to serve in particular committee positions without respect to their order. The other choices don't include picking a group of people without taking into account their rank or position within the group; instead, they either involve random selection or selection for certain jobs.

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Part 1) The variables are y, the total cost (dependent variable), and x the charge per day (independent variable).

Part B) A linear equation in a slope-intercept form representing the cost of the campsite is y = 15 + 20x.

A linear equation is an algebraic equation.

A linear equation is written in the form of y = mx+b, where y is the dependent variable, m is the slope and b is the y-intercept or a constant.

The fixed rental fee to reserve the camping site, b = $15

The charge per day (slope), m = $20

Let the number of days the site is rented = x

Total cost, y = 15 + 20x.

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The square root of the surd expression 4 - 2√5 does not exist

Given that

4-2root5

Express properly

So, we have

4 - 2√5

The root can be expressed as

(√a - √b)

So, we have

(√a - √b)² = 4 - 2√5

Expand

So, we have

a - 2√ab + b = 4 - 2√5

By comparison, we have

a + b = 4

ab = 5

When solved graphically, the system has no solution

Hence, the surd expression has no square root

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The United States senate passes a bill that increases

the federal income tax rate, which then pays for the service would most likely provide the revenue to pay for this new public service.

What is revenue?

Revenue means money received in the ordinary course of business and is calculated by multiplying the average selling price by the number of items sold. This is the total amount of money from which other costs and expenses are subtracted to calculate net income.

The definition of revenue says it is the total amount of money received from a business, such as sales. This is also called sales in the income statement. This is a top-line figure because it appears first on the company's income statement. There are two types of income i.e. operating income and non-operating income.

Here, the most likely way to generate revenue to pay for a new national water pollution abatement plan is for the United States Senate to pass a bill that raises the federal income tax rate that would then pay for the service. This is because it directly increases the funds available to the federal government, which can then be allocated to a new public service. Other options, such as homeowners paying higher property taxes or states raising sales taxes, may not generate enough revenue or may not be directly related to the new public service. Furthermore, selling clean water to other countries may not be sustainable or ethical to fund a public service.

So, The United States senate passes a bill that increases the federal income tax rate, which then pays for the service would most likely provide the revenue to pay for this new public service.

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