with an average, you add everything up and then divide the total by the number of items you are adding. this gives every number equal weight in the average. but what if you want to weight one item more than others? you will use a weighted average. this can be used, for example, to determine your grade in a class. follow these steps to find the weighted average in the problem below. first, convert each percentage to a decimal. then, multiply each percentage in decimal form by its respective grade. and lastly, add everything up to find the weighted average. for example, emily received a 67 on her first economics exam, which counts for 20% of her grade; an 84 on her second exam, which counts for 30% of her grade; and a 78 on her third exam, which counts for 50% of her grade. what is her weighted average in the class?

Answer:

b

Step-by-step explanation:

The inverse of the function will be x=(4y-2)/(y+2) where x is the inverse of the function given in i.

What is a function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).

There are several types of functions in math. Some important types are:

Injective function or One to one function: When there is mapping for a range for each domain between two sets.

Surjective functions or Onto function: When there is more than one element mapped from domain to range.

Polynomial function: The function which consists of polynomials.

Inverse Functions: The function which can invert another function.In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x.

Now,

As given

f(x)=2(x+1)/4-x

from here x will be inverse of the function

Therefore

y(4-x)=2x+2

4y-yx=2x+2

4y-2=x(y+2)

x=(4y-2)/(y+2)

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Answer:

To graph the inequality y ≤ x - 2 on the axes, you would:

Plot the line y = x - 2 on the graph. The line will be a straight line passing through the point (-2,0) and has a slope of 1.

Determine the direction of the inequality symbol. Since it is a less-than-or-equal-to symbol, we will shade the region that is less than or equal to the line.

Shade the region that is less than or equal to the line in the graph. In this case, the region above the line y = x - 2.

The line is solid, it's not dotted.

Note: The graph will be a straight line that is tilted towards the top right of the coordinate axes, the region above the line will be shaded.

Step-by-step explanation:

Answer:

1750 BOOKS

Step-by-step explanation:

Answer:

There were a total of 14 books on Friday and 2396 on Saturday to find the total amount sold on both days you will add the two together.

1,461 + 2,396 = 3,857

A. There were a total of 3, 857 books sold on both days.

To find how many more books were sold on Saturday than Friday, youn will subtract.

2,396 - 1,461 = 935

B. 835 more books were sold on Saturday than Friday.

Step-by-step explanation:

Hope it helps! =D

Answer:

No

Step-by-step explanation:

It could only represent large colleges, not all colleges.  Sampling requires similar characteristics to represent the entire population of testing.

A linear equation - y = 5x -7 is a slant line with intercepts for linear equations. A vertical line is x = 2. A line that runs through the origin is y = 3/4x.

A slant line with intercepts is y = 1/2x + 3. A horizontal line is y = 9. The line x = -1 runs vertically.

A direct condition is one that has a level of 1 as its most extreme worth. As a result, there is no variable in a linear equation with an exponent greater than 1. The graph of a linear equation will always be straight.

This line is not horizontal or vertical when the equation is graphed; rather, it is slant.

Additionally, this line does not traverse the origin. As a result, this equation has intercepts and slant lines.

Since there is no y-intercept in this equation, it will be a vertical line that runs parallel to the y-axis.

Additionally, this line does not traverse the origin. As a result, this equation has a line that runs vertically.

This line is not horizontal or vertical when the equation is graphed; rather, it is slant.

Additionally, this line actually traverses the origin. As a result, the origin of this equation is traversed by slant lines.

This line is not horizontal or vertical when the equation is graphed; rather, it is slant.

Additionally, this line does not traverse the origin. This equation is therefore a slant line with intercepts.

Since there is no x-intercept in this equation, it will be a horizontal line that runs parallel to the x-axis.

Additionally, this line does not traverse the origin. As a result, there is a horizontal line in this equation.

Since there is no y-intercept in this equation, it will be a vertical line that runs parallel to the y-axis.

Additionally, this line does not traverse the origin. As a result, this equation has a line that runs vertically.

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Step-by-step explanation:

Σ^n=1 -144 (1/2)n-1

This is a finite geometric series with n

=4, a₁-144, and r = 2.

S = a₁ (1-r") / (1 − r)

S-144 (1 - (1/2)) / (1 - 1/2)

S=-270

If you wanted to find the infinite sum (n

= ∞0)

:S = a₁ / (1 − r)

S-144/(1-1/2)

S=-288

Absolute value function f(x) = | x + 3 | written in piece wise function includes the piece  given by option B . x + 3, x > -3.

Function f(x) is represented as absolute value function:

f(x) = | x + 3 |

Absolute function is always positive when the included variable is greater than zero.

| x + 3 |  > 0

⇒ ( x + 3 ) > 0

Subtract three from both the sides we get,

⇒ x + 3 - 3 > 0 - 3

⇒ x > -3

Here piecewise function incudes the piece :

x + 3,  x > -3.

Therefore, the absolute function f(x) = | x + 3 | includes the piece after written in piecewise function form is equal to option B. x + 3,  x > -3.

The above question is incomplete , the complete question is:

Select the correct answer.

Consider this absolute value function.

f(x) = | x + 3 |

If function f is written as a piecewise function, which piece will it include?

A. x + 3, x > 3

B. x + 3, x > -3

C. -x + 3, x < -3

D. -x - 3, x < 3

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The evaluation of the equation to find the value of n in the rational function [tex]\frac{1}{n^2} + \frac{1}{n} = \frac{1}{2\cdot n^2}[/tex] is; n = -1/2

A rational function is a function that contains rational fractions, such that the dividend and the divisor are polynomial expressions.

2) The specified rational equation or function can be presented as follows;

The above equation consists of rational expressions. The expressions can be resolved by collecting like terms as follows;

The like terms are terms that can be resolved by simple addition or subtraction.

1/n = 1/(2·n²) - 1/(n²) = (1 - 2)/(2·n²) = -1/(2·n²)

1/n = -1/(2·n²)

Multiplying both sides by n, we get;

(1/n) × n = (-1/(2·n²)) × n

(1/n) × n = 1 = (-1/(2·n))

1 = (-1/(2·n))

Multiplying both sides by n, we get;

1 × n = (-1/(2·n)) × n

n = -1/2

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The unit cost of an apple and a pear are $1.27 and $1. 98 respectively.

Algebraic expressions are defined as expressions that comprises of variables, factors, constants, terms and coefficients.

They are also made up of arithmetic operations like;

From the information given, we have that;

Let the apples be x

Let the pears by y

2x + 3y = 2.40

5x - 3y = 6.5

Let's solve the simultaneous equation

-1(2x + 3y = 2.40)

-2x - 3y = -2. 40

5x - 3y = 6.5

-2x - 5x = -2. 40 - 6.5

-7x = -8.9

x = $1.27

substitute the value for y

-2y -5(1.27) = -2.40

y = $1. 98

Hence, the values are $1.27 and $1. 98

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The perimeter of a rectangle measuring 4.1263cm long and 2.8315cm is 13.9 cm

from the question, we have the following parameters that can be used in our computation:

Length = 4.1263 cm

Width = 2.8315 cm

The perimeter of a rectangle can be calculated using tge following equation

Perimeter = 2 x (Length + Width)

substitute the known values in the above equation, so, we have the following representation

Perimeter = 2 x (4.1263 + 2.8315)

Evaluate

Perimeter = 13.9156

Approximate

Perimeter = 13.9 to 3 significant figures

Perimeter = 13.916 to 3 decimal places

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The answer to each question are:

a). probability of an insect of this type surviving its first day is 0.8

b). probability of an insect of this type surviving it's first three days is 0.512.

c). probability of an insect of this type dying on its fourth day is 0.2.

d). If 200 insects of this type are being studied in a laboratory, 102 to be alive after the third day.

What is the probability?

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are.

a). The probability that an insect of this type survives its first day is 1 - 0.2 = 0.8.

b). The probability that an insect of this type survives it's first three days is 0.8 * 0.8 * 0.8 = 0.512.

c). The probability that an insect of this type dies on its fourth day is 0.2.

d). The expected number of days that an insect of this type would survive is not determinable with the information given.

e). If 200 insects of this type are being studied in a laboratory, you would expect approximately 200 * 0.512 = 102.24 to be alive after the third day. Round down to 102 insects.

Hence, The answer to each question is:

a). probability of an insect of this type surviving its first day is 0.8

b). probability of an insect of this type surviving it's first three days is 0.512.

c). probability of an insect of this type dying on its fourth day is 0.2.

d). If 200 insects of this type are being studied in a laboratory, 102 to be alive after the third day.

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The solution of the given equation is 1.6. It has been represented and solved as a real-world problem below.

The given equation is = - 20 + 2x5 = 4

We can rewrite this equation as = - 4 + 2x5 = 20

Let us suppose that person A has x number of bananas that they have taken out from a stock full of bananas. They continue taking x number of bananas two more times. They then stop and see that person B has already taken 4 bananas from the stock. We can write this equation as -

= 4 + 2x

Person A saw knew that there were 20 bananas in total. So, we can write it as -

= 4 + 2x = 20

Person A then resumed and took x number of bananas again 5 more times. We can rewrite this as -

= 4 + 2x5 = 20

Solving this equation, we get -

= 4 + 10x = 20

= 10x = 20-4 = 16

= x = 16/10

= x = 1.6

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Answer:

give me brainlist please

Step-by-step explanation:

We can use the formula for conditional probability and the formula for the probability of the union of events to find P(C).

Using the formula for conditional probability, we can find P(A|B) = P(A n B) / P(B) = 0.05 / 0.26 = 0.192

Using the formula for conditional probability again, we can find P(A|C) = P(A n C) / P(C) = 0.05 / P(C)

Since A and C are independent events, we know that P(A|C) = P(A), so we can write:

0.05 / P(C) = 0.24

Solving for P(C) we get P(C) = 0.05/0.24 = 0.208

Alternatively, we can use the formula for the probability of the union of events:

P(A u B u C) = P(A) + P(B) + P(C) - P(A n B) - P(A n C) - P(B n C) + P(A n B n C)

We know that P(A u B u C) = 1 - P((A u B u C)^/) = 1 - 0.33 = 0.67

and we know the values of P(A), P(B), P(A n B), P(A n C), P(B n C), P(A n B n C)

We can substitute these values into the above equation to find P(C)

P(C) = 0.67 - 0.24 - 0.26 + 0.05 + 0.05 + 0.05 - 0.02 = 0.208

So P(C) = 0.208

Statistical risk refers to the likelihood of an adverse event occurring, as determined through statistical analysis. This can include events such as financial loss, injury, or death. It is typically measured using probability, which is a value between 0 and 1 that represents the likelihood of an event occurring.

For example, in finance, the risk of an investment is often measured by the standard deviation of the returns over time. In healthcare, the risk of a particular treatment or procedure is often measured by the rate of complications or adverse events.

The board game you described, where the goal is to conquer the world, does not involve statistical risk. It is a game of strategy, and the outcome is determined by the players' decisions and actions, rather than by chance.

The long-run probability of making a particular kind of mistake is an example of statistical risk. For example, if a pilot has a history of making landing errors, we can use statistical analysis to determine the probability that they will make a similar mistake in the future.

The probability that a single flip of a coin will come up 'tails' is also an example of statistical risk. In this case, the probability of the coin landing tails is 0.5 or 50%.

In summary, Statistical risk is the likelihood of an adverse event occurring, as determined through statistical analysis. It is measured using probability, and it is used to understand and manage the risk in various fields such as finance, healthcare, and engineering.

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The largest exterior angle of hexagone is 108°.

Given that exterior angle of a hexagon are x, 3x, 4x, 5x, 8x and 9x.

Exterior angles are those that run parallel to a polygon’s inner angles but are located outside of polygon.

We know that sum of exterior angle of any polygon is 360°.

So, sum of exterior angle of hexagon will be 360°.

x + 3x + 4x + 5x + 8x + 9x = 360°

30x = 360°

x = 360° / 30

x = 12°

Now the largest angle = 9 * 12 = 108°

Therefore, the largest angle of hexagon is 108°.

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A. On the sixth day, the plant grows to 64 times its original height.

B. On the nth day, the plant would  [tex]2^n[/tex] time its original height.

A. From the given condition we can that the growth of the plant shows a geometric progression with a first term of 2 and a common ratio of 2.

On the first day, the plant grows to [tex]2^1[/tex] = 2 times its original height.

On the second day, the plant grows to [tex]2^2[/tex] = 4 times its original height.

Similarly, on the sixth day, the plant grows to [tex]2^6[/tex] = 64 times its original height.

B. The nth term of the progression can be calculated by multiplying the first term by the common ratio raised to the power of n-1.

In this case, the first term is 2 and the common ratio is 2. So the nth term is [tex]2 * 2^{n-1} = 2^n[/tex]

Hence, on the nth day, the plant grows to [tex]2^n[/tex] times its original height.

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The negative values, zero and the positive numbers lesser than 12 and equal to twelve are solutions of inequality.

A relationship between two expressions or values that are not equal to each other is called 'inequality.

We need to find the solutions for the inequality k≤12

k lesser than or equal to twelve.

Which means the solution of the inequality are the values which are lesser than or equal to 12.

The solution of the inequality k≤12 is (-∞, 12]

All the negative values, zero and the positive numbers lesser than 12 and equal to twelve are solutions of inequality.

Hence,  the negative values, zero and the positive numbers lesser than 12 and equal to twelve are solutions of inequality.

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A conversion of this equation in standard form to slope-intercept is y = 4x/5 - 3.

In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:

y = mx + c

Where:

Based on the information provided about the line, it is represented by this equation;

8x + 10y = -30

Making y the subject of formula in the above equation, we have the following:

10y = 8x - 30

y = 8x/10 - 30/10

y = 4x/5 - 3

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Answer:

Multiply all of the terms of each polynomial and then combine like terms. Example: Multiply: ( 2 x 2 + x − 3 ) ( x 2 − 2 x + 5 ) . Solution: Multiply each term of the first trinomial by each term of the second trinomial and then combine like terms.

After reflection over the x-axis the ordered pair is at (-4, 7).

When two different media come together at an interface, a wavefront might change direction so that it returns to the first medium, which is known as reflection.

When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the x-axis is (x, -y).

Here,

The reflection of point (-4, 7) across the x-axis is (-4, -7).

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The sum between the functions:

f(x) = 3x² - 2x + 6

g(x) = 7x - 4

is (f + g)(x) = 3x² + 5x + 2

Here we have two functions which are:

f(x) = 3x² - 2x + 6

g(x) = 7x - 4

And we want to add these to get f + g,  so we only need to add the two functions, we will get:

f(x) + g(x) = (3x² - 2x + 6) + (7x - 4)

Grouping like terms we will get:

(3x² - 2x + 6) + (7x - 4) = (3x²) + (-2x + 7x) + (6 - 4)

And now we can simplify that to get:

(3x²) + (-2x + 7x) + (6 - 4) = 3x² + 5x + 2

The sum is:

(f + g)(x) = 3x² + 5x + 2

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Answer:

Slope is 3.5

There is a proportional relationship between the variables x and y

The other statements are false.

The slope is 3.5, not 7

A linear relationship is the same a proportional relationship so statement 4 is always false

The graph does pass through (0, 0)

Step-by-step explanation:

Consider the first 2 pairs of coordinates, (2, 7) and (6, 21);

The increase in x is from 2 to 6, i.e. an addition of 4, the increase in y is from 7 to 21, i.e. an addition of 14;

Now consider the the 2nd and 3rd pairs of coordinates, (6, 21) and (8, 28);

The increase in x is from 6 to 8, i.e. an addition of 2, the increase in y is from 21 to 28, i.e. an addition of 7;

So, with the first 2 pairs of coordinates, an increase of 4 in x resulted in an increase of 14 in y and with the second 2 pairs of coordinates, an increase of 2 in x resulted in an increase of 7 in y, i.e. (+4, +14) and (+2, + 7);

2 × (+2, +7) = (+4, 14)

Or:

(+4, +14) ÷ 2 = (+2, +7)

This means a line from the 1st point to the 2nd point and a line from the 2nd point to the 3rd point will have the same gradient:

To find the slope simple, find the increase in y resulting from an increase of 1 in x, so:

(+2, +7) ÷ 2 = (+1, +3.5)

The gradient (or slope) is 3.5;

If there is a line with a fixed gradient that passes through all the points, then the relationship is proportional, also linear;

This is the case for this question;

If we follow the pattern backwards as well, so the point:

(2, 7) - (+2, +7) = (0,0)

This means (0,0) lies on the line.

(0,0), (2, 7), (4, 14), (6, 21), (8, 28), (10, 35), (12, 42), (14, 49), etc.

All these points would lie on the line, just add 2 to x, add 7 to y;

You would find the same points plus others by the rule, add 1 to x, add 3.5 to y.

The total distance from the starting point is 7.21 miles

Now, According to the question:

The movements are represented as:

[tex]N_1= 1miles\\E_1= 2miles\\\\N_2 =3 miles\\\\E_2 = 4miles[/tex]

To find the distance from the starting point.

First, calculate the total distance towards North.

[tex]N = N_1+N_2[/tex]

N = 1 + 3

N = 4 miles

Next, calculate the total distance towards East

[tex]E = E_1+E_2[/tex]

E = 2 + 4

E = 6 miles

The total distance from the starting point is calculated using Pythagoras theorem.

[tex]D^2=N^2+E^2[/tex]

[tex]D^2[/tex] = [tex]4^2+6^2[/tex]

[tex]D^2[/tex] = 16 + 36

[tex]D^2 =[/tex] 52

[tex]D = \sqrt{52}[/tex]

D = 7.21

Hence, The total distance from the starting point is 7.21 miles

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Answer:

C

Step-by-step explanation:

The procedure that cannot be used are:

A. Knowing that 3² + 4² = 5², draw any two sides with a right angle between them. The third side will fit to form a right triangle.

B.

Knowing that 3 + 4 > 5, draw the 3 cm side and the 4 cm side with a right angle between them. The 5 cm side will fit to form a right triangle.

C.

Knowing that 3 + 5 > 6, draw the 3 cm side and the 5 cm side with a right angle between them. The 6 cm side will fit to form a right triangle.

The Pythagorean theorem states that the result obtained by squaring the value of the hypotenuse of a right angled triangle is equal to the sum of the squares of the values other two sides of the triangle.

The hypotenuse of a a given triangle is usually longer that the other two sides.

Therefore, the correct procedure when lengths such as 3 cm, 4 cm, 5 cm, and 6 cm should be knowing that 3² + 4² = 5², draw the 3 cm side and the 4 cm side with a right angle between them. The 5 cm side will fit to form a right triangle.

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8) The Length of major arc MQN is; ⁵/₄πr

Length of minor arc MPN is; ³/₄πr

9) Length of major arc HJK is; ¹³/₁₅πr

Length of minor arc MPN is; ⁴/₁₅πr

The formula that is used to find the length of an arc is;

L = (θ/360) * 2πr

where;

L is length of arc

θ is central angle

r is radius

8) We are not given the radius and as such;

Length of major arc MQN = (225/360) * 2πr

= ⁵/₄πr

Length of minor arc MPN = ((360 - 225)/360) * 2πr

= ³/₄πr

9) Length of major arc HJK = (312/360) * 2πr

= ¹³/₁₅πr

Length of minor arc MPN = ((360 - 312)/360) * 2πr

= ⁴/₁₅πr

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The factorization of the given expression is p(4p-12q+qp).

The factorization method uses basic factorization formula to reduce any algebraic or quadratic equation into its simpler form, where the equations are represented as the product of factors instead of expanding the brackets. The factors of any equation can be an integer, a variable, or an algebraic expression itself.

The given expression is 4p²-12pq+qp².

Group and factor out the greatest common factor (GCF), then combine.

Here, the greatest common factor of the terms is p

Now, p(4p-12q+qp)

Therefor, the factorization of the given expression is p(4p-12q+qp).

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The given graph is represented by the following inequalities (C) y ≤ 2x − 2, y > −x + 3.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.

The majority of the time, size comparisons between two numbers on the number line are made.

If an inequality matching y > -ax + b is solved, area A will be shaded above a dashed line with a negative slope.

Such inequality exists between Options A and C.

The solution of an inequality that fits y ax + b will be below a solid line with a positive slope where region B is shaded (for some positive a).

The only option with the correct inequality symbol is Choice C.

We discover that choice C matches the graph when we closely examine it.

Region A matches y > -x+3 because the line with a negative slope has a slope of -1 and a y-intercept of 3.

Region B corresponds to y 2x -2 because the line with a positive slope has a slope of +2 and a y-intercept of -2.

Therefore, the given graph is represented by the following inequalities (C) y ≤ 2x − 2, y > −x + 3.

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Correct question:

In the graph, the area above f(x) is shaded and labeled A, the area below g(x) is shaded and labeled B, and the area where f(x) and g(x) have shading in common is labeled AB.

Graph of two intersecting lines. The line g of x is solid, and goes through the points 0, negative 2 and 1, 0 and is shaded in below the line. The other line f of x is dashed, and goes through the points 0, 3, 3, 0 and is shaded in above the line.

The graph represents which system of inequalities?

Group of answer choices

a. y > 2x − 3

y > −x − 3

b. y < 2x − 2

y < −x + 3

c. y ≤ 2x − 2

y > −x + 3

d. None of the above