Keith Hernandez has asked Jerry and Kramer to help him move into a new apartment on Sunday morning. He has asked them both in case one of them does not show up. From past experience, Keith knows that there is a 41% chance that Jerry will not show up and a 31% chance that Kramer will not show up. Even though Jerry and Kramer know each other, their decisions can be assumed to be independent.
a. What is the probability that both Jerry and Kramer will show up? (Round your answer to 2 decimal places.)
Probability
b. What is the probability that at least one of them will show up? (Round your answer to 2 decimal places.)
Probability
c. What is the probability that neither Jerry nor Kramer will show up? (Round your answer to 2 decimal places.)
Probability

The equation of the circle with radius 9 and center ( -1,-8 ) is( x + 1 )² + ( y + 8  )² = 81.

The standard form equation of a circle with center (h, k) and radius r is:

( x - h )² + ( y - k )² = r²

Given that the circle has a center of (-1, -8) and the radius is 9.

Hence; from the standard form of the equation of the circle:

Center ( h , k ) = ( -1, -8 )

h = -1

k = -8

And radius r = 9

Plug these values into the above formula and simplify.

( x - h )² + ( y - k )² = r²

( x - ( -1 ) )² + ( y - ( -8 ) )² = 9²

Simplify

( x + 1 )² + ( y + 8  )² = 81

Therefore, the equation of the circle is ( x + 1 )² + ( y + 8  )² = 81.

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Answer:

The probability that a randomly selected small cube is rolled and the face on the top is black is P=0.2.

Step-by-step explanation:

We have a cube, with the faces painted black, that each side is divided in 5, so we end up with 125 cubes.

We have to calculate the probability that a randomly selected cube is rolled and the face on the top is black.

This probability is equal to the proportion of black area in the total area of the cube.

We can define the side of the original cube as A=5a, being a the side of the small cubes.

The area that is painted black is equal to the sum of 6 squares of side A. In terms of a, that is:

\(S_b=6\cdot A^2=6\cdot(5a)^2=6\cdot25a^2=150a^2\)

The total area of the 125 small cubes is:

\(S=125(6a^2)=750a^2\)

Then, the ratio of black surface to the total surface is:

\(s_b/s=(150a^2)/(750a^2)=0.2\)

Then, we can conclude that the probability that a randomly selected small cube is rolled and the face on the top is black is P=0.2.

Answer and Step-by-step explanation:

This graph is a One to One Function.

For a function to be one-to-one, each x value must have its own y-value, which is the case for this graph.

The y value of a point where a vertical line intersects a graph represents an output for that input x value. If you draw a vertical line on the graph, and it intersects more than once, then the graph does not define as a function because that x value has more than one output (y).

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I hope this helps!

Dolma will receive Rs.153,486.69 at the beginning of BS 2080 as detailed below

What is effective after-tax rate of return?

The effective after-tax rate of return in this case is determined as the 9% deposit return rate multiplied by 1 minus the tax rate as stated below:

effective after-tax rate of return= gross rate of return*(1-tax rate)

The gross rate of return is the return on the deposit before considering the tax rate.

gross rate of return=9%

tax rate=5%

effective after-tax rate of return=9%*(1-5%)

effective after-tax rate of return=8.55%

The future value of the deposit after three years(beginning of 2077-2080=3years), is determined using the future value formula of a single cash flow below:

FV=PV*(1+r)^N

FV=future value after 3 years=unknown

PV=Rs.120,000

r=8.55%

N=3

FV=120000*(1+8.55%)^3

FV=120000*(1,0855)^3

FV=120,000*1.279055776375

FV=Rs.153,486.69

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Answer:

f(x) on x = 4

h(x) on x = -2

Step-by-step explanation:

for h(x) the axis of symmetry is x = -2 based on the graph

for f(x) = -2(x-4)² + 2 we must find for x intercept so take f(x) = 0

0 = -2(x-4)² + 2

-2 = -2(x-4)²

-2/-2 = (x-4)²

1 = (x-4)²

x-4 = √1

x-4 = 1 and x-4 = -1

so

x - 4 = 1

x = 5

x - 4 = -1

x = 3

so x intercept occured in x = 3 and x = 5

so the symmetry axis is in the middle x =4

(actually there's an easiest way, you can find the x axis from the form of y = a(x+b)² + c. The x-axis must be -b)

The axis of symmetry for each function is f(x) on x = 4, and h(x) on x = -2, after applying the transformation.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The graph of the function is shown in the picture.

From the graph:

For f(x) = -2(x-4)² + 2 we must find for x-intercept so take f(x) = 0

For h(x) the axis of symmetry is x = -2 based on the graph

0 = -2(x-4)² + 2

After solving:

x = 5

x - 4 = -1

x = 3

Thus, the axis of symmetry for each function is f(x) on x = 4, and h(x) on x = -2, after applying the transformation.

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To find the number that makes the ratio equivalent to 1:6 and 9: x, we can proceed as follows:

We can check this result as follows:

Then, the value that makes the ratio equivalent to 1:6 is 54 (9:54.) The number is 54.

\(750\) grams is \(25%\)\(%\) percentage of \(3\) kilograms.

A percentage is a number or ratio that represents a fraction of \(100\).

\(\text{Percentage}=\dfrac{\text{actual value}}{\text{total value}}\times 100\)

\(3\) kilograms = \(3000\) grams

So, the required percent = \(\frac{750}{3000}\) × \(100\) = 25

Thus, \(750\) grams is \(25%\)\(%\) percent of \(3\) kilograms.

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The customer will pay $6.30 for the 60 local calls that all lasted 3 minutes.

To find out how much the customer will pay, we need to calculate the total cost for all the local calls.
Step 1: Calculate the total number of minutes for all the calls
Since the customer made 60 local calls and each call lasted 3 minutes, we can multiply 60 by 3 to get the total number of minutes.
60 calls * 3 minutes/call = 180 minutes
Step 2: Calculate the total cost for all the minutes
The customer pays $0.035 per minute for local calls. To find the total cost, we can multiply the total number of minutes by the cost per minute.
180 minutes * $0.035/minute = $6.30

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D-(x-4)(4x+1) is your answer

Answer:

4x²-15x-4

doing middle term factorization

4x²-16x+x-4

4x(x-4)+1(x-4)

(x-4)(4x+1)

The probability that a randomly selected riverside high school student is in twelfth grade is 0.4

The complete question is in the attached image

From the image, we have:

The probability is then calculated as:

P = 200/500

Divide

P = 0.4

Hence, the probability that a randomly selected riverside high school student is in twelfth grade is 0.4

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Answer:

the answer is C

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

How do we get from 4 to 20? Multiply 4 * 5 = 20.

How do we get from 20 to 100? Multiply 20 * 100.

Thus the answer is C where you multiply 5 by the previous function output.

I saw this pattern from experience, however you could also solve another way:

Simply plug in to the given functions in each answer choice.

For example, A:

f(1) = 4

f(n) = 16 * f(n - 1), for n >= 2

Now test values of n and check if they match the table.

f(1) = 4. This matches the table

f(2) = 16 * f(2 - 1) = 16 * f(1) = 16 * 4 = 64. This does not match the table.

You continue this process with the rest of the answer choices until you find a function, f(n), that gives the correct output of the table.

Plan B: Choose 14 of the 28 plants at random. Apply Brand X fertilizer to those 14 plants and Brand Y fertilizer to the remaining 14 plants.

A sample is only a small portion of the population.

Let's imagine you were interested in determining the average income for all Americans in your population.

Instead of knocking on every door in America because of time and money constraints, you decide to ask 1,000 random people. Your sample consists of these a thousand persons.

Given, A gardener wants to determine which of two brands of fertilizer is best for the plants.

And the gardener decides to conduct an experiment using 28 individual plants.

Plan A will be a biased sampling and the experiment would not yield

desired results.

Therefore, The gardener should choose 14 of the 28 plants at random. Apply Brand X fertilizer to those 14 plants and Brand Y fertilizer to the remaining 14 plants.

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The explanatory variable is the clients while the response variable is change in duration.

A causal relationship is said to exist between variables whereby the occurrence of an event is as a result of another event.

In a causal relationship between variables, a value may represent explanatory variable while another value may represent a response variable.

An explanatory variable is the variable where observation of changes are being made such as the clients while the response variable are the outcome of the observation such as the duration of the run by each client.

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The inside length of the longer NBA caskets in inches is, 85.6745

A statistical measure of the degree of variation or dispersion in a set of values is the standard deviation. It offers a way to measure how far apart the individual values in a data set are from the set's mean (average). The square root of the variance is used to calculate the standard deviation, which is denoted by the symbol (sigma).

We are given the distribution here as:

From standard normal tables, we have here:

P(Z < 2.0537) = 0.98

Therefore, P(Z > 2.0537) = 1 - 0.98 = 0.02

Therefore 2.0537 is the z score that would be used here. ( As we are given here that for tallest 2% of the male basketball players, the special caskets for the NBA would be too tall )

Therefore the longest length here is computed as:

= Mean + 2.0537xSD

= 79 + 2.0537x3.25

= 85.6745 inches is the required length here.

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The disadvantages of the mode are: For many sets of data there is no mode.

The mode is a measure of central tendency that represents the most frequently occurring value in a dataset.

However, one of the disadvantages of the mode is that for many sets of data, there may not be a distinct mode. In such cases, the data may have a uniform distribution where all values occur with equal frequency, or it may have multiple modes with similar frequencies.

The mode is not affected by extremely large or small values. It only considers the frequency of values and not their magnitude. Therefore, extreme values do not influence the mode.

The statement that the mode can only be computed for interval-level data or higher is incorrect. The mode can be computed for any type of data, including nominal, ordinal, interval, and ratio data. It is applicable to categorical as well as numerical data.

The main disadvantage of the mode is that for many datasets, there may not be a distinct mode.

The correct option is: For many sets of data there is no mode.

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Step-by-step explanation:

The executive's total compensation package consists of four main components basic salary, short-term incentives, long-term incentives and perquisites. A basic salary this is regarded as a “fixed” element of pay and it does not normally vary in relation to company performance.

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Answer:

Step-by-step explanation:

The equation is poorly written and I cannot unfortunately solve it.

Answer:

x ≥ 4

x ≥ 1

Step-by-step explanation:

x+4≥8

x≥ 8-4

x ≥ 4

closed brackets means x exists [ and closed c's mean it does not exist (

X: [4,infinty], does not exist (-infinity,4]

5x-2≥3

5x≥3+2

5x/5 ≥ 5/5

x ≥ 1

X: [1,infinty], does not exist (-infinity,1]

The length of line BC as shown in the diagram below is 5√3.

Length is the distance between two points.

To calculate the length of Line BC, we use the formula below.

Formula:

Where:

From the diagram,

Given:

Substitute these values into equation 1

Hence, BC is 5√3.

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Answer:

10

Step-by-step explanation:

The equation of the line that passes through (4, 3) and (-4, -1) is y = -x/2 + 5. So, correct option is A.

To find the equation of the line that passes through two given points, we use the slope-intercept form of a linear equation, which is:

y = mx + b

where m is the slope of the line and b is the y-intercept.

First, we need to find the slope of the line using the two given points. The formula for finding slope between two points is:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

Substituting the given points into the formula, we get:

m = (-1 - 3) / (-4 - 4) = -4/8 = -1/2

Now we know the slope, we can use one of the given points (4, 3) and substitute the slope into the slope-intercept form of the equation and solve for b.

y = mx + b

3 = (-1/2)(4) + b

3 = -2 + b

b = 5

Therefore, the equation of the line that passes through (4, 3) and (-4, -1) is:

y = -x/2 + 5

So, correct option is A.

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Complete question is:

What is the equation of the line that passes through (4, 3) and (-4, -1)?

Choices:

y = -x/2 + 5

y=2x+7

y=x/2 +1

y= -x/2 +7

The value of x and y in the cyclic quadrilateral are 18 and 148.

We have,

Cyclic quadrilaterals are polygons with four vertices that all lie on a common circle.

- Opposite angles: The opposite angles of a cyclic quadrilateral are supplementary, meaning they add up to 180 degrees.

- Consecutive angles: The consecutive angles of a cyclic quadrilateral are supplementary as well.

- Opposite sides: The opposite sides of a cyclic quadrilateral are in a ratio.

So,

5x - 26 + 116 = 180

101 + y - 69 = 180

Now,

Solving for x and y.

5x - 26 + 116 = 180

5x = 180 - 116 + 26
5x = 90

x = 18

And,

101 + y - 69 = 180

y = 180 - 101 + 69

y = 148

Thus,

The value of x and y are 18 and 148.

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Answer:

x = 20

Step-by-step explanation:

We know that the vertically opposite angles are equal.

Accordingly,

41 = 2x + 1

Subtract 1 from both sides.

41 - 1 = 2x

40 = 2x

Divide both sides by 2.

x = 20

The equations that could be used to solve for the number of male runners (m) in the race are (m+75)/m = 3 / 2 and 150 + 2m = 3m. The correct options are A and B.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Given that at a running race, the ratio of female runners to male runners is 3 to 2. There are 75 more female runners than male runners.

The ratio is written as,

f/ m = 3 / 2

There are 75 more female runners than male runners.

f = m + 75

The equation can be written as,

f / m = 3 / 2

( m + 75 ) / m = 3 / 2

Or

150 + 2m = 3m

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Vector v can be written as the sum of two vector components, \(v_x = -5i\)  and \(v_y = 6j\)

To write vector v as the sum of two vector components, we need to decompose it into two vectors along different directions.

v = -5i + 6j

w = 3i + 4j

We can decompose vector v into two components, one along the x-axis and the other along the y-axis.

Let's denote the component along the x-axis as \(v_x\) and the component along the y-axis as \(v_y.\)

The x-component, \(v_x,\) represents the projection of vector v onto the x-axis and can be found using the dot product of v and the unit vector i:

\(v_x = v . i = (-5i + 6j) . i = -5i . i + 6j . i = -5\)

Similarly, the y-component, \(v_y,\) represents the projection of vector v onto the y-axis and can be found using the dot product of v and the unit vector j:

\(v_y = v . j = (-5i + 6j) . j = -5i . j + 6j . j = 6\)

Now, we can write vector v as the sum of its components:

\(v = v_x + v_y = -5i + 6j\)

So, vector v can be written as the sum of two vector components: -5i along the x-axis and 6j along the y-axis.

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The equation represents the image of the line y = 3x +1 is y' = 3(x - 3) +1.

Each point in a figure is moved the same distance in the same direction using a type of transformation known as translation.

For example, this transformation moves the parallelogram to the right 5 units and up 3 units. It is written ( x , y ) → ( x + 5 , y + 3 ) .

Given:

The transformation that translates function y = f(x) by h units right and k units up is

y' = f(x -h) +k

We have y= 3x+ 1

So, After translating 3 units to x axis the function will become

y' = 3(x - 3) +1

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