In the figure above, ABCD, BEFG, and DHIJ are squares with AB= 2(DH) and DH = 2(BE). If a point is chosen at random inside square ABCD, what is the probability it will be in the shaded region?
(A) 1/2
(B) 5/8
(C) 11/16
(D) 3/4​

Expressions using words: 2/5 as the sum of 4 and 8.

Expression with using numbers: 2/5 x(8+4)

Value = 12 2/5.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

First, the Expressions using words

2/5 of the product of 8 and 4.

4 times as mush as 2/5 of 8.

2/5 as the sum of 4 and 8.

Now, Expression with using numbers

2/5 + (8+4)

2/5 x (8 x 4)

4 x (2/5 x 8)

2/5 x(8+4)

Values are: 2 2/5, 4 2/5, 32 2/5, 12 2/5.

Now, the Answers is

Expressions using words: 2/5 as the sum of 4 and 8.

Expression with using numbers: 2/5 x(8+4)

Value = 12 2/5.

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Quadrile 1: 70 Quartile 3: 90 Median: 83.5 Lowest: 58 The average of the five summaries is maximum: 102.

The mean of even a dataset, often described as the mean and median, is the sum including all values divided by the overall number of values (as opposed to the geometric mean). This represents the most often used indicator of central tendency and is constantly referred to as the "mean." This is obtained by dividing the number of values contained within the dataset by the sum of all the values. Calculations can be conducted using either raw data or data that has been integrated into frequency tables. A number's average is called to as its average. Simple statistics can be used to determine: After adding up all the digits, divide by the number of digits total. the sum divided by the number.

given

The first quartile, median, third quartile, and maximum are the five summaries that make up the distribution of the ordered observation.

Five-number formula overview

Minimum: The first piece of the set

(n+1)/4 is the first quartile.

Average: (n+1)/2

Quartile three: 3(n+1)/4

Maximum: The set's final component

The five-digit grade summary (90, 85, 97, 76, 89, 58, 82, 102, 70, 67)

58 minimum

70 in the top quartile

Average: 83.5

90th percentile:

The most: 102

Quadrile 1: 70 Quartile 3: 90 Median: 83.5 Lowest: 58 The average of the five summaries is maximum: 102.

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The probability of getting a number greater than or equal to 2 is 0.8333( 3 decimal place)

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

Probability = sample space/ total possible outcome

The total outcome on a standard six-sided die is 6

The sample space of getting a number greater or equal to 2 is 2,3,4,5,6 = 5

Therefore the probability of getting a number greater or equal to 2 is = 5/6

= 0.833 ( 3 decimal place)

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The angle between the 3D vectors a = (3, -1, 2) and b = (1, -1, -2) is 2.23 radians. The angle between a = (0, -1, -3) and b = (2, 3, -1) is 2.43 radians.

The angle between two vectors a and b in three-dimensional space can be found using the dot product formula:

cos(θ) = (a * b) / (||a|| * ||b||)

Where ||a|| and ||b|| represent the magnitude (length) of vectors a and b, respectively, and "*" represents the dot product of the two vectors. The dot product is given by:

a * b = a1 * b1 + a2 * b2 + a3 * b3

Where a1, a2, and a3 are the components of vector a, and b1, b2, and b3 are the components of vector b. The angle θ is then calculated using the inverse cosine function:

θ = arccos(cos(θ))

Finally, the angle θ is expressed in radians.

For the first problem, we have:

a = (3, -1, 2)

b = (1, -1, -2)

So, we have:

a * b = 3 * 1 + (-1) * (-1) + 2 * (-2) = 3 - 1 - 4 = -2

||a|| = [tex]\sqrt{(3^2 + (-1)^2 + 2^2)} = \sqrt{(14)}[/tex]

||b|| = [tex]\sqrt{(1^2 + (-1)^2 + (-2)^2) }= \sqrt{(6)}[/tex]

cos(θ) = [tex](-2) / (\sqrt{(14)} * \sqrt{(6)} ) = -\sqrt{(2)} / \sqrt{(21)[/tex]

θ = arccos[tex](-\sqrt{(2)} / \sqrt{(21)})[/tex] = 2.23 radians (rounded to two decimal places)

For the second problem, we have:

a = (0, -1, -3)

b = (2, 3, -1)

So, we have:

a * b = 0 * 2 + (-1) * 3 + (-3) * (-1) = -3

||a|| = [tex]\sqrt{(0^2 + (-1)^2 + (-3)^2)} = \sqrt{(10)}[/tex]

||b|| = [tex]\sqrt{(2^2 + 3^2 + (-1)^2)} = \sqrt{(14)}[/tex]

cos(θ) = [tex]-3 / (\sqrt{(10)} * \sqrt{(14)}) = -3 / \sqrt{(140)}[/tex]

θ = arccos[tex](-3 / \sqrt{(140)})[/tex] = 2.43 radians (rounded to two decimal places)

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An equation of a line using slope-intercept format goes through the point (4, 2) and is parallel to y = 1/2x - 3 is y = x/2.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

From the information provided above, we have the following slope and data points on the line:

In Geometry, two (2) lines are parallel under the following conditions:

m₁ = m₂ ⇒ 1/2 = 1/2

At data point (4, 2), a linear equation of this line can be calculated in point-slope form as follows:

y - 2 = 1/2(x - 4)

y - 2 = x/2 - 2

y = x/2 - 2 + 2

y = x/2

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Angles in a triangle add to 180 degrees

make a little equation for that

58 + 42 + x = 180

simplify

100 + x = 180

x = 180 - 100

x = 80

Hope this helps,

- Jeron :- )

The coordinates of the point H of the parallelogram is H ( 2 , 0 )

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

Let the parallelogram be represented as EFGH

Now , the coordinates of the parallelogram is given by

Substituting the values in the equation , we get

The coordinate of E = E ( 1 , 3 )

The coordinate of F = F ( 3 , 5 )

The coordinate of G = G ( 4 , 2 )

The coordinate of H = H ( x , y )

Now , the difference in the x coordinates of F and G = ( 4 - 3 ) = 1

The difference in the y coordinates of F and G = ( 2 - 5 ) = -3

So , the coordinates of the point H = x coordinate of E + 1 and y coordinate of E - 3

On simplifying the equation , we get

The coordinate of H = H ( 2 , 0 )

Hence , the coordinates of the parallelogram is H ( 2 , 0 )

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Answer:

1:3

Step-by-step explanation:

the greatest common factor is 3 so to simplify divide both sides by 3.

Answer: $51,000

Step-by-step explanation:

At first, I multiplied 8,500 times 3 then the outcome I got was 25,500 so now I'm going to try multiplying 8,500 times 6 which equals 51,000 but I'm sorry if I got the answer wrong

The value of the two numbers in b is 15 and 18

To get the values we would have to set up an equation system

Such that we would have:

the smaller number is given as c

Then the bigger number is given as c + 3

The equation would be

c + c + 3 = 33

then

2c = 33 - 3

2c = 30

From here we would have to divide both sides of the equation by 2

2c / 2 = 30 / 2

c = 15

33 - 15 = 18

Hence the numbers are given as 15 and 18

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Answer:

Below

Step-by-step explanation:

y= mx + b     is the slope intercept form of a line  

                           m = slope     and       b = y-axis intercept

Plug in the given values

y = -4/5 x -3

Answer:

3 trombones

Step-by-step explanation:

9 divided by three is 3.

I'm fifty years old the sentence is a discrete variable and not continuous variable as age is counted in concrete numbers and it does not involve complex numbers.

Discrete data is a sort of numerical information that consists of full, concrete numbers with predetermined, set values that can be counted. Complex numbers and fluctuating data values taken over a predetermined period of time are examples of continuous data.

Numerical information that is continuous refers to the unspecified number of measurements that could be made between two realistic sites.

Despite the fact that these numbers are frequently gathered via accurate measurements, they are not necessarily neat and orderly as those in discrete data. Measuring a specific issue repeatedly enables us to establish a defined range, within which we can predictably gather more data.

I'm fifty years old the sentence is a discrete variable as age is counted in concrete numbers and it does not involve complex numbers.

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The parent function of the function f(x) = 3√(-8x - 4) will be h(x) = √x.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function is given below.

f(x) = 3√(-8x - 4)

Simplify the function, then we have

f(x) = 3√(-8x - 4)

f(x) = 6√- (2x + 1)

Divide the equation by 6, then we have

g(x) = √(-2x - 1)

Replace -(2x + 1) with x, then we have

h(x) = √x

The parent function of the function f(x) = 3√(-8x - 4) will be h(x) = √x.

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Answer:

Rewrite the equation by factoring –8 from the radicand and taking the cube root to get –2 in front of the radical symbol.

The graph is reflected over the x-axis.

The graph is also reflected over the y-axis.

The graph is vertically stretched by a factor of 2.

The graph is translated ½ unit to the left.

Step-by-step explanation: All possible answers for edge

Answer:

The missing number is 300,000.

Step-by-step explanation:

To find the missing number, we can set up an equation based on the information given. If 80% of a number is equal to 240,000, we can write:

0.80x = 240,000

To find x, we can divide both sides of the equation by 0.80:

x = 240,000 / 0.80 = 300,000

So, the missing number is 300,000.

The following information can be extracted from the system of triangles ABC and DEF:

Case A: 3 / 5 = y / z

Case D: m ∠ C = m ∠ F

Case E: Δ ABC ~ Δ DEF

In this problem we find a representation of a system with two similar triangles, that is, two triangles with two congruent internal angles and proportional sides. Then, the following relationships are derived below:

m ∠ A = m ∠ D

m ∠ B = m ∠ E

m ∠ C = m ∠ F

AB / DE = BC / EF = AC / DF

6 / 10 = y / z = x / w

3 / 5 = y / z = x / w

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If the interval size is decreased from $200 to $100, then option a. The height of the bars will decrease.

The height of the bars will decrease if the interval sizes in a histogram are reduced while the scale remains constant. When the intervals are compressed,

For a particular set of data, there will be more histogram bars, but fewer data points will make up each interval. Reducing the interval size will also reduce the height of the histogram's bars because the height of the bars represents the number of items in each interval.

Hence, if the interval size is decreased from $200 to $100, then option a. The height of the bars will decrease.

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The population is 900 gasoline stations. The sample is 800. The parameter is price of gasoline. The statistics is for 900 stations and not all stations.

The ratio of the sum of the values in a particular set to all the values in the set is the mean value, which is the definition of the average. The average formula has numerous practical uses. If we were asked to determine the average male height in India or the average age of the men and women in a group, we would add up all the data and divide it by the total number of data points.

The population is 900 gasoline stations.

The sample is 800.

The parameter is price of gasoline.

The statistics is for 900 stations and not all stations.

The sample selected is a good sample as it covers most of the gas stations.

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Answer:

a.) (1,4), (-2,3), (0,4)

b.) (4,1), (3,-2), (4,0)

Step-by-step explanation:

a. When we want to find the reflection over the Y axis, that means the X coordinate signs reflect. For A, it says (-1,4). To reflect it, we reflect the X coordinate, so now it's (1,4) instead. You'll do that to the other two.

b. When rotating, you would switch the numbers of the coordinates and switch the sign of X. For the first one (-1,4), we'll switch it to (1,4). Not we'll switch the numbers around to make it (4,1). You'll do that for the other two

Answer:

C.

Step-by-step explanation:

Its more likely to happen

Answer:

0.15% of 12000 is equal to 18.

Step-by-step explanation:

To calculate 0.15% of 12000, we first convert 0.15% to a decimal. To do this, we divide 0.15 by 100:

0.15 ÷ 100 = 0.0015

Next, we multiply this decimal by 12000:

0.0015 × 12000 = 18

So, 0.15% of 12000 is equal to 18.

The amount of the down payment for the house, given the market value and the amount your bank requires is $ 36, 000

The bank that you work for requires that for mortgage loans, the applicants ( in this case Mr. and Mrs. Brady) , should be able to pay 1 / 5 of the market value of the property as down payment.

The down payment is therefore :

= Market value of house x Requirement of bank

= 180, 000 x 1 / 5

= 180, 000 / 5

= $ 36, 000

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The rest of the question is:

Your bank requires 1/5 of the market value as a down payment.

What is the amount (in $) of the down payment?

1080 quarts can be made in 36 hours.

The rate per day is 30 quarts.

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

150 quarts of icecream = 5 hours

This can be written as,

5 hours = 150 quarts

Divide both sides by 5.

1 hour = 30 quarts

Multiplying 36 on both sides.

36 hours = 36 x 30 quarts

36 hours = 1080 quarts

Thus,

1080 quarts can be made in 36 hours.

30 quarts per day.

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Answer: The Zeros Are(in order) -3,-2,-1,1, 1.5 ALL have a multiplicity of 1.

Step-by-step explanation: Since the 0's cross the graph and don't "bounce" on the x-axis, they're all for a multiplicity of 1.

Answer:

15.1

Step-by-step explanation:

15.0782 is between 15.0 and 15.1.  It is closer to 15.1

1. store A sells at cheaper rate.

2. Runner B tun at faster rate.

3. Submarine 2 will reach at depth of -1056 feet at faster rate.

4.  Kira collected 18.33 points in one hour.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

1. Store A: y= 0.40 x

so, the unit rate is 0.40.

Store B:

the cots of 3 pound carrot= 20.16

and, the cost of 48 ounce carrot = 20.16

and, cost per ounce= 20.16 /48= 0.42

so, the unit rate is 0.42.

Thus, store A sells at cheaper rate.

2. The unit rate rate of runner A

= 54/4.5

= 12

and, the unit rate of runner B

= 275/20
= 13.75

Thus, Runner B tun at faster rate.

3. Submarine 1 descends at rate of 22 feet.

and Submarine 2 descends at rate of = 480/20 = 24 feet.

Thus, Submarine 2 will reach at depth of -1056 feet at faster rate.

4. Jess collected 18 points in one hour.

and, Kira collected 18.33 points in one hour.

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Answer:

Four thousand two hundred and

Step-by-step explanation: