suppose that x is a discrete random variable that takes integer values from 1 to 100 (both inclusive), and has cumulative distribution function (cdf)

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Work Shown:

[tex](f+g)(\text{x}) = f(\text{x})+g(\text{x})\\\\(f+g)(\text{x}) = (\text{x}+3)+(\text{x}^2-2)\\\\(f+g)(\text{x}) = \text{x}^2+\text{x}+1\\\\(f+g)(2) = 2^2+2+1\\\\(f+g)(2) = 4+2+1\\\\(f+g)(2) = 7\\\\[/tex]

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Another approach:

[tex]\begin{array}{lll}f(\text{x}) = \text{x}+3& & g(\text{x}) = \text{x}^2-2\\f(2) = 2+3 & \text{ and } & g(2) = 2^2-2\\f(2) = 5 & & g(2) = 2\\\end{array}\\\\\\\text{Therefore, } (f+g)(2) = f(2)+g(2) = 5+2 = 7[/tex]

Answer:

3a^2

Step-by-step explanation:

one way of answering this question is by finding the area of the whole shape, including the non-shaded shape, then taking away the area of the non-shaded shape from the whole thing, leaving you the area of the shaded shape

Step-by-step

find the area of the whole shape

2a x 2a

= 4a^2 (or 4a to the power of 2)

Now that we have the area of the whole shape, we must find the area of the non-shaded shape and take it away from 4a^2, we do this by

a x a

= a^2 (or a to the power of 2)

now we minus the non-shaded shape away from the total area

4a^2 - a^2

= 3a^2 (or 3a to the power of 2)

95% CI for the true posttreatment self-esteem score is:

(24.47, 28.73)

The formula for calculating a 95% confidence interval for the mean self-esteem score is as follows:

(standard deviation/square root of sample size) * (mean (critical value)

The standard deviation of a set of data is a measure of its spread or dispersion. It denotes the average deviation of individual values in a data set from the data set's mean.

A low standard deviation indicates that the data points are close to the mean, whereas a high standard deviation indicates that the data points are scattered across a wide range.

For a normal distribution and a 95% confidence level, the critical value is 1.96.

As a result, the 95% confidence interval for the mean posttreatment self-esteem score is as follows:

26.6 ± 1.96 * (7.4/sqrt(21)) = 26.6 ± 2.13

As a result, the 95% CI for the true posttreatment self-esteem score is:

(24.47, 28.73)

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Answer:

$400

Step-by-step explanation:

Here is my crack at it:

To find Heather's weekly salary, we can set up an equation using the information given. Let's call Heather's weekly salary "x".

According to the problem, $20 is 5% of her salary, so we can write this as an equation:

$20 = 0.05x

Now we can solve for x by dividing both sides by 0.05:

x = 400$

So Heather's weekly salary was $400.

Heather’s weekly salary would be 400$.  

If heather saved $20 a week. This was 5% of her salary. Heather’s weekly salary would be

Given, $20 = 5%

As we know, the total salary will be 100 %

If 5% = $20

then, 100% = $400 (multiplying both the sides by 20)

Thus, Heather’s weekly salary was 400$.

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Answer:

Step-by-step explanation:

The balance after 3 years can be calculated as follows:

I = P * r * t

Where:

I = interest

P = principal amount (2200)

r = interest rate (0.0295)

t = time in years (3)

So,

I = 2200 * 0.0295 * 3

I = 153.1

The final balance would be:

P + I = 2200 + 153.1

P + I = 2353.1

The final balance after 3 years is $2353.1, which is closest to option B ($2,329.80).

The area of the topper will be 24 square units.

A rectangle is a quadrilateral having four sides and the sum of the angles is 180 in the rectangle the opposite two sides are equal and parallel and the two sides are at 90-degree angles.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.

The area of the glass topper will be:-

Area = Length x Width

Area = 6 x 4

Area = 24 square units

The image of the glass topper is attached with the answer below.

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The probability that the two tallest are in the same subgroup is given as follows:

2/n².

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

In this problem, we have that:

For each student, the probability of belonging to a group is given as follows:

1/n.

Hence the probability that the two tallest are in the same subgroup is obtained as follow:

2 x 1/n x 1/n = 2/n².

The multiplication by 2 is because there are two groups.

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Cost of direct materials per equivalent unit = $0.45.

Conversion cost per equivalent unit = $0.12.

The FIFO method is the First In First Out method. It is an accounting method used for cost flow assumption purposes in the cost of goods sold calculation.

In the Bottling Department,

The cost of direct materials transferred = $27,225.

The conversion cost = $7,596.

The total equivalent units for,

Direct materials = 60,500 liters.

conversion = 63,300 liters.

By using FIFO method,

The cost  of Direct materials per equivalent unit = [tex]\frac{27,225}{60,500}[/tex]

                                                                                =$0.45

Conversion cost per equivalent unit = [tex]\frac{7596}{63,300}[/tex]

                                                            = $0.12

Hence, the cost of direct materials and conversion cost per equivalent unit is $0.45 and $0.12 respectively.

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Based on the information in the table, a graph can be created to relate the number of Supply Dolls and Demand Dolls with respect to the sale value.

To create a graph with the information in the table, we must identify what information should go on the x-axis and the y-axis. In this case, we are being asked to locate the sale value on the x axis and on the y axis we must locate the number of units supplied and demanded.

Based on this information, we can infer that at a lower sale price, more dolls are demanded, but not as many are supplied. On the contrary, when the price is higher ($4.00) more dolls are supplied but not as many are demanded. This means that the relationship is inversely proportional.

Note: This question is incomplete because there is some misinformation. Here is the complete information:

Task.

Joan King is marketing director for the BurgeRama restaurant chain. BurgerRama has decided to have a cartoon-character doll made to sell at a premium price at participating BurgerRama locations. The company can choose from several different versions of the doll that sell different prices. King's problem is to decide which selling price will best suit the needs of BurgerRama's customers and store managers. King has data from previous similar promotions to help her make a decision.

1. Use the data from the table above to plot points representing selling price and supply price on a graph. (Selling Price of Each Doll should appear on the x-axis, and Number of Dolls Per Week per Store should appear on the y-axis). Draw the line through the data points and write the word "Supply on this line.

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The shaded region in the graph represents the possible solution sets to the inequality.

Given is the inequality -

x² + 15 ≥ 23

The given inequality is -

x² + 15 ≥ 23

Refer to the graph attached.

The shaded region represents the possible solution sets to the inequality above.

Therefore, the shaded region in the graph represents the possible solution sets to the inequality.

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Answer:For part (a), the overall percentage of American voters who say the government shutdown is a "very serious problem for the country" can be calculated as follows:

P(A) = 54% (probability of being a Democrat)

P(B|A) = 80% (probability of saying the shutdown is a "very serious problem" given that the person is a Democrat)

P(A and B) = P(A) * P(B|A) = 54% * 80% = 43.2%

P(B) = 35% (probability of saying the shutdown is a "very serious problem" for Republicans)

P(A|B) = (P(A and B) / P(B)) = (43.2% / 35%) = 123.14%

P(A or B) = P(A) + P(B) - P(A and B) = 54% + 35% - 43.2% = 45.8%

Therefore, the overall percentage of American voters who say the government shutdown is a "very serious problem for the country" is 45.8%.

For part (b), the 2x2 probability table can be set up as follows:

Serious Not serious Total

Democrat 43.2% 6.8% 50%

Republican 10.5% 35.5% 46%

Total 53.7% 42.3% 100%

Step-by-step explanation:

The Maurya Empire was founded in 322 B.C. by Chandragupta Maurya, after overthrowing Dhana, the king of the Nanda dynasty. Chandragupta initiated battles to defeat and conquer the kingdoms left by Alexander the Great and gained additional lands west of the Indus River by force. He enlarged his power westward across central and western India, and by 320 B.C., the empire had fully occupied Northwestern India. Chandragupta Maurya became the first emperor to unite India into one state, under a central government.

Chandragupta Maurya was the creator of the Maurya Empire in ancient India. He established one of the largest empires on the Indian subcontinent.

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The Proof of ( x + h)² +( y + h)²  =  (a + b)² is shown below.

In geometry, two similar forms are those whose dimensions are identical or have a same ratio but the size or length of their sides differ. Examples include similar triangles, similar rectangles, and similar squares. The scale factor is another name for the common ratio. Additionally, the equivalent angles have the same magnitude.

Given:

BHC and BCA are similar

HC / BC = CA / BA    

so, h / a  =  b / ( x + y) ........... (1)

Working with your expansion

x² + h²  = a²  and

y² + h²  = b²

So, subtracting out the equal parts we are left with

2xh  + 2yh   =  2ab ..........(3)    divide through by 2

xh + yh  = ab    

h( x + y) = ab  which we can rearrange as

h / a   =  b / ( x+ y)..............(2)

Since this is equal to (1) and it's just a rearrangement of (3) adding all the other equal parts of the expansion shows that

(x² + h²) + (y² + h²) + ( 2xh + 2yh) =  a²+ b²+ 2ab

( x² + 2xh + h²) + ( y² + 2yh + h²)  =  ( a + b)²

( x + h)²   +  ( y + h)²  =  (a + b)²      

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Answer:

4^5 = 1024

Step-by-step explanation:

Let x be an even number. Then, x = 2k for some integer k. The negative of x, -x, is equal to -2k, which is also an even number. Thus, the additive inverse of an even number is an even number.

An even number is any number that can be divided by 2 without any remainder, meaning that it can be written in the form x = 2k for some integer k. The additive inverse, or negative, of an even number, x, is -x. By definition, this is equal to -2k. As -2k can still be divided by 2 without any remainder, it is also an even number.

This can also be understood by looking at the positive and negative sides of the number line. If x is an even number, then it is two units away from 0. Therefore, -x is also two units away from 0, which means it is an even number. This shows that the additive inverse of an even number is an even number.

To prove this, we can look at a specific example. Let x = 8. Then, 8 = 2x4. The negative of 8, -8, is equal to -2x4, which is still an even number. Thus, this proves that the additive inverse of an even number is an even number.

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The value for x vector is [tex]v=\left[\begin{array}{ccc}-25\\-22\end{array}\right][/tex].

What is a vector?

A vector in mathematics is a quantity that not only expresses magnitude but also motion or position of an object in relation to another point or object. Euclidean vector, geometric vector, and spatial vector are other names for it.

Given a vector v ∈ R² let (x, y) be its standard coordinates, i.e., coordinates with respect to the standard basis [tex]e_1=\left[\begin{array}{ccc}5\\-1\end{array}\right][/tex] and [tex]e_1=\left[\begin{array}{ccc}-7\\-4\end{array}\right][/tex].

The desired coordinates x, y satisfy -

v = xe1 + ye1

So, the vector v is -

[tex]v=2\left[\begin{array}{ccc}5\\-1\end{array}\right] +5\left[\begin{array}{ccc}-7\\-4\end{array}\right][/tex]

[tex]v=\left[\begin{array}{ccc}10\\-2\end{array}\right] +\left[\begin{array}{ccc}-35\\-20\end{array}\right][/tex]

[tex]v=\left[\begin{array}{ccc}-25\\-22\end{array}\right][/tex]

Therefore, the matrix is [tex]v=\left[\begin{array}{ccc}-25\\-22\end{array}\right][/tex].

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Answer:

Step-by-step explanation:

A function is the inverse of another function if it "undoes" the original function. In other words, if you apply the original function to an input and then apply the inverse function to the result, you get the original input.

To find the inverse of a function, you can swap the input and output values of the original function, and then solve for the new input variable. For example, if the original function is f(x) = y, the inverse function would be f^-1(y) = x.

Given the function f(x) = -2, 3, 8, 13, it is not possible to find a simple algebraic inverse function for the given values of x = -1, 0, 1, 2. The inverse of a function is only well-defined if the function is one-to-one, meaning that for every output value, there is only one input value that maps to it. In this case, the function does not appear to be one-to-one, so it does not have an inverse function.

The other endpoint of the line segment is (13.8, 6).

The midpoint of a line segment is the point that lies exactly halfway between the two endpoints.

In this case, we have one endpoint, (6.9), and the midpoint (0,-6). Here is how we find the other endpoint:

To find the other endpoint, we need to subtract the midpoint from the given endpoint and then multiply by 2. The midpoint formula is given by:

M = (x1 + x2) / 2 and (y1 + y2) / 2

Where M is the midpoint, (x1, y1) and (x2, y2) are the coordinates of the two endpoints.

So, in our case, the other endpoint will be given by:

(x2, y2) = 2 * (6.9, 0) - (0, -6)

Expanding the expression, we get:

x2 = 2 * 6.9 - 0 = 13.8

y2 = 2 * 0 - (-6) = 6

Therefore, the other endpoint of the line segment is (13.8, 6).

Complete question:

Find the other end point of the line segment with the given endpoint and midpoint endpoint: (6.9), midpoint (0,-6)

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The size of angle BAC in the given circle is 50°

A circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape.

Since, no figure is given, we will draw a circle according the given information, [attached in the solution]

So, we get a circle with center O, having chords, BC, which is extended to F, DC and AB,

We have, Angle CBD = 28° and angle FCD = 78°

Therefore,

∠ DCB = 180° - ∠ DCF [Linear pair]

∠ DCB = 180° - 78°

∠ DCB = 102°

In Δ DCB,

∠ DCB + ∠ BCD + ∠ BDC = 180°

∠ BDC = 180° - (102°+28°)

∠ BDC = 50°

Since, the angles made by the same chord are equal in measure,

Therefore,

∠ BDC = ∠ BAC

Therefore,

∠ BAC = 50°

Hence, the size of angle BAC in the given circle is 50°

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Answer:

Cosine (cos)

Step-by-step explanation:

Sine, Cosine, and Tangent have their own properties.

Cosine is adjacent over hypotenuse. We have the angle of 59, the line adjacent is 17 and the hypotenuse is x. You could also do it for the right angle.

Answer:

x * 2.54 = centimeters

Step-by-step explanation:

The equation to convert inches to centimeters is as follows:

x inches * 2.54 cm/inch = y centimeters

Where x is the number of inches and y is the equivalent length in centimeters.

To elaborate, the conversion factor between inches and centimeters is 2.54 cm/inch, meaning that for every inch there are 2.54 centimeters. To convert from inches to centimeters, we simply multiply the number of inches by the conversion factor. This gives us the equivalent length in centimeters.

The statistics interpreted from the given data is:

a. Median = 26.5

b. Q1 = 22.5

c. Q3 = 60

d. IQR = 37.5

e. Range = 95

The given data sample of this year’s grants(given in thousands of dollars) in ascending order is :

5 22 23 25 26 27 50 70 90 100

The median of a data set is the middle value when the data is arranged in ascending or descending order. When number of values is even, there are two values in the middle, so we take the average of the two. So the median is

= (26 + 27)/ 2

= 26.5

The first quarter or the lower quartile (Q1), is the value under which 25%, that is first quarter of the data points are found when they are arranged in increasing order. Here Q1 is  0.25*10,  that is 2.5th value, but its not possible. So we should interpolate

Q1 = 22.5

Similarly third quartile, Q3 is the value under which 75% of the data points are found when they are arranged in increasing order. So

Q3 = (70 + 50)/2

= 60

And inter quartile range (IQR)

= Q3 - Q1

= 60 - 22.5

= 37.5

Range is

= 100 - 5

= 95

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The break-even point refers to the amount of revenue necessary to cover the total fixed and variable expenses incurred by a company.

In business accounting, the break-even point refers to the amount of revenue necessary to cover the total fixed and variable expenses incurred by a company within a specified time period.

To calculate the break-even point in units use the formula:

Break-Even point (units) = Fixed Costs ÷ (Sales price per unit – Variable costs per unit) or in sales dollars using the formula: Break-Even point (sales dollars) = Fixed Costs ÷ Contribution Margin.

Insurance Requirements the part of a commercial contract in which the types and minimum amounts of insurance the parties agree to provide in connection with their performance of the contract are specified.

A break even point is used in multiple areas of business and finance. In accounting terms, it refers to the production level at which total production revenue equals total production costs. In investing, the break even point is the point at which the original cost equals the market price.

Therefore, the break-even point refers to the amount of revenue necessary to cover the total fixed and variable expenses incurred by a company.

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On solving the provided question we can say that The inequality we have here is  -5(x-3) ≥ 3[4-(x+4)] => 15/17 ≥ x

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.

The inequality we have here is

-5(x-3) ≥ 3[4-(x+4)]

-5x + 15 ≥ 12x

15 ≥ 17x

15/17 ≥ x

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There are seven kids tickets and 4 adult tickets.

We know that we have to solve the simultaneous equation here;

Let cost of one kids ticket be x and the cost of one adult ticket be y

3x + 9y = 75 ---- (1)

8x + 6y = 67 ----- (2)

We then have that multiplying (1) by 8 and (2) by 3

24x + 72 y = 600 ---- (3)

24x + 18 y = 201 --- (4)

Subtract (4) from (3)

54 y = 399

y = 7

Then;

3x + 9(7) = 75

x = 4

We are going to end up having that there are seven kids tickets and 4 adult tickets.

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Answer: 101.6

Since we are trying to find the sides of both the triangles, we will need to use the Sin, Cos, & Tan trigonometry functions. There are 3 equations:

[tex]Sin (Angle) = \frac{Opposite}{Hypotenuse} \\Cos (Angle) = \frac{Adjacent}{Hypotenuse} \\Tan (Angle) = \frac{Opposite}{Adjacent}[/tex]

For this triangle shown in the picture, we can infer that the 88 is OPPOSITE to the 60° and 30° angles. So we already have the opposite, and since we are trying to find the adjacent, we will use the formula that consists both opposite and adjacent, which is the following:

[tex]Tan(Angle) = \frac{Opposite}{Adjacent}[/tex]

Since [tex]x[/tex] is only a part of the long triangle, we will subtract the small triangle's side from the big one, which will give us [tex]x\\[/tex].

We can input our values to solve each triangle's side lengths.

(You have to use the calculator for these)

Small one:

[tex]Tan(60) = \frac{88}{Adjacent}\\Adjacent = \frac{88}{Tan(60)}\\Adjacent = \frac{88\sqrt{3} }{3} = 50.807 (3 d.p)[/tex]

Big one:

[tex]Tan(30) = \frac{88}{Adjacent} \\Adjacent = \frac{88}{Tan(30)} \\Adjacent = 88\sqrt{3} = 152.420 (3d.p)[/tex]

Now, to calculate [tex]x[/tex] , we will subtracat the small one from the big one like this: (it is better to input the values with the surds and not the real numbers for accurate marks and calculations)

[tex]88\sqrt{3} - \frac{88\sqrt{3} }{3} = 101.6 (1 d.p)[/tex]

That is the answer. If you did not understand it completely, please reach me back and I will help you :)

Answer:

3

28

Step-by-step explanation:

The expression (f/g) (4) is equal to f(4) / g(4).

f(4) = 4^2 + 2*4 - 3 = 16 + 8 - 3 = 21

g(4) = 4^2 - 9 = 16 - 9 = 7

So, (f/g) (4) = 21 / 7 = 3.

The expression (f + g) (4) is equal to f(4) + g(4).

f(4) = 4^2 + 2*4 - 3 = 16 + 8 - 3 = 21

g(4) = 4^2 - 9 = 16 - 9 = 7

So, (f + g) (4) = 21 + 7 = 28.

The equation expressing the statement is A = k/r, where k is the constant of proportionality. Given that r = 3 and A = 7, the constant of proportionality can be found by rearranging the equation to k = A × r and substituting the given values to calculate: k = 7 × 3 = 21.

The statement "A varies inversely as r" can be expressed mathematically as an equation: A = k/r, where k is the constant of proportionality. This equation states that A is proportional to 1/r, meaning that as r increases, A decreases, and as r decreases, A increases. To find k, we can rearrange the equation to k = A × r and substitute the given values. In this case, if r = 3 and A = 7, then k = 7 × 3 = 21. Therefore, the constant of proportionality is 21. This equation can be used to determine the values of A, given a value of r, or the values of r, given a value of A. For example, if r = 4, then A = k/4 = 21/4 = 5.25. Conversely, if A = 10, then r = k/A = 21/10 = 2.1. This equation can be used to determine the values of A and r for any given situation.

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The answer options that are quadratic functions include the following:

B. y = (5x - 3x^2)/4 + 1.

C. y = 2x^2 - 3x + 7.

In Mathematics, a quadratic function can be defined as a mathematical expression which defines and represent the relationship that exists between two (2) or more variable on a graph, with a maximum exponent of two.

Generally speaking, the standard form of a quadratic function is given by this mathematical expression;

ax² + bx + c = 0

Where:

In this context, we can reasonably infer and logically deduce that the expressions that are quadratic functions include both y = (5x - 3x²)/4 + 1 and y = 2x² - 3x + 7 because they have a maximum exponent of two.

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