John drew a scale drawing of his bedroom. The drawing measures 15 in. wide by 18 in. long. He used a scale of 3 in. = 2 ft. What is the area of John’s actual bedroom?

Therefore, the retirement account must contain $2,758,686.58 when you retire in order to withdraw $4000 at the end of each quarter for 30 years.

To find the amount that the retirement account must contain when you retire, we can use the formula for the future value of an annuity due:

FV = PMT * [(1 + r/n)^(n*t) - 1] / (r/n) * (1 + r/n)

Where FV is the future value, PMT is the payment amount, r is the interest rate, n is the number of compounding periods per year, and t is the number of years.

In this case, PMT = $4000, r = 0.07, n = 4 (since the account is compounded quarterly), and t = 30.

Plugging these values into the formula, we get:

FV = 4000 * [(1 + 0.07/4)^(4*30) - 1] / (0.07/4) * (1 + 0.07/4)

FV = 4000 * [(1.0175)^120 - 1] / (0.0175) * (1.0175)

FV = 4000 * 11.9478 / 0.0175 * 1.0175

FV = $2,758,686.58

Therefore, the retirement account must contain $2,758,686.58 when you retire in order to withdraw $4000 at the end of each quarter for 30 years.

Round your final answer to the nearest cent, the retirement account must contain $2,758,686.58.

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We can plot the two points (-2, 3) and (0, 4) and draw a straight line passing through both points. The resulting line has a slope of 1/2 and y-intercept of 4.

Graphs are used to help people understand and interpret information in a way that is easy to see and analyze. There are many different types of graphs, each with its own characteristics and applications.

Some common types of graphs include:

Line graph: A line graph displays data as a series of points connected by lines, typically used to show trends or changes over time.

Bar graph: A bar graph displays data as bars of different heights, typically used to compare values or quantities.

Pie chart: A pie chart displays data as a circle divided into slices, typically used to show proportions or percentages.

To find the y-coordinate for each x-coordinate, we can substitute each value of x into the equation y = (1/2)x + 4 and simplify:

When x = -2:

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

y = -1 + 4

y = 3

So, the point (-2, 3) is on the line.

When x = 0:

y = (1/2)(0) + 4

y = 0 + 4

y = 4

So, the point (0, 4) is on the line.

We can complete the table as follows:

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

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

0 y = (1/2)(0) + 4 4

To graph the line, we can plot the two points (-2, 3) and (0, 4) and draw a straight line passing through both points. The resulting line has a slope of 1/2 and y-intercept of 4.

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Iliana needs to play for 16 hours to get a total of 200 XP.

What is  slope-intercept form ?

The slope-intercept form is a way to write the equation of a line in two variables, usually x and y. It is called "slope-intercept" form because it gives the slope of the line and the y-intercept of the line.

The slope-intercept form is given by:

y = mx + b

where m is the slope of the line and b is the y-intercept, which is the point where the line crosses the y-axis.

We can use the points on the graph to find the equation of the line that relates playing time (x) to total XP (y). To do this, we can use the slope-intercept form of a line:

y = mx + b

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

To find the slope, we can use any two points on the line. Let's use points A and B:

m = (y2 - y1) / (x2 - x1) = (50 - 25) / (4 - 2) = 25/2

Now we can write the equation of the line in slope-intercept form:

y = (25/2)x + b

To find the value of b, we can substitute one of the points on the line into the equation. Let's use point A:

25 = (25/2)(2) + b

b = 0

So the equation of the line is:

y = (25/2)x

Now we can use this equation to find how many hours Iliana needs to play to get 200 total XP. We can set y = 200 and solve for x:

200 = (25/2)x

x = (2/25) * 200

x = 16

Therefore, Iliana needs to play for 16 hours to get a total of 200 XP.

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The answer is x(2-5x).

In factorization, you just need to identify the common factors and accordingly solve as per your requirement!

To factor the expression 2x-5x^(2) completely, we need to find the greatest common factor (GCF) of the two terms and factor it out. The GCF of 2x and 5x^(2) is x. So we can factor it out of the expression:

2x-5x^(2) = x(2-5x)

Now, the expression is factored in completely. The final answer is:

x(2-5x)

Therefore, factoring the expression 2x-5x^(2) gives the answer x(2-5x).

I hope this helps! Let me know if you have any further questions.

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The data point 1.8 falls outside the range of 1.798, so it can be considered an outlier.

An outlier is a data point that is significantly different from other data points in a data set. Outliers can occur due to errors in data collection or measurement, or they can be legitimate data points that are simply far outside the range of the other data. In statistical analysis, it is important to identify outliers and decide whether to remove them from the data set or keep them and analyse them separately.

There are several methods for identifying outliers, including graphical methods and statistical methods such as the use of z-scores or the interquartile range.

To identify outliers in this data, we can start by calculating some basic statistical measures such as the mean and standard deviation.

The mean of the given data is:

(1.11 + 1.13 + 1.40 + 1.32 + 1.14 + 1.28 + 1.13 + 1.8 + 1.10 + 1.20) / 10 = 1.304

The standard deviation of this data is:

sqrt(((1.11 - 1.304)²  + (1.13 - 1.304)² + (1.40 - 1.304)² + (1.32 - 1.304)² + (1.14 - 1.304)² + (1.28 - 1.304)² + (1.13 - 1.304)² + (1.8 - 1.304)² + (1.10 - 1.304)² + (1.20 - 1.304)^2) / 9) = 0.247

One common rule of thumb for identifying outliers is to consider any data point that falls more than 2 or 3 standard deviations from the mean to be an outlier. Using this rule, we can identify any values that fall outside the range:

1.304 - 2 * 0.247 = 0.81

1.304 + 2 * 0.247 = 1.798

1.304 - 3 * 0.247 = 0.563

1.304 + 3 * 0.247 = 2.045

Based on this rule, we can see that the data point 1.8 falls outside the range of 1.798, so it can be considered an outlier.

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The location of B' after the rotation on the coordinate plane of 90 degrees clockwise about the origin is

90 degree clockwise rotation refers to the rotation of a figure on a coordinate plane about a fixed point in the clockwise direction. Every point (x, y) will rotate to in order to rotate the figure 90 degrees clockwise around a point (y, -x).

This then means that the B will go from B ( 7, 3 ) to B' ( 3, - 7 ) after a clockwise rotation about the origin.

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The length of the top of the workbench is 13m and the width is 7m.

To find the length and the width, we can use the formula for the area of a rectangle, which is A = L x W, where A is the area, L is the length, and W is the width. We can plug in the given values and solve for the unknowns.

Let's start by assigning variables to the length and the width. Let's call the width x and the length x + 6 (since the length is 6m greater than the width).

Now we can plug these values into the formula:

A = L x W

91 = (x + 6) x x

91 = x2 + 6x

Now we can rearrange the equation to solve for x:

x2 + 6x - 91 = 0

We can use the quadratic formula to solve for x:

x = (-6 ± √(62 - 4(1)(-91))) / (2(1))

x = (-6 ± √(36 + 364)) / 2

x = (-6 ± √400) / 2

x = (-6 ± 20) / 2

The two possible solutions are:

x = (-6 + 20) / 2 = 7

x = (-6 - 20) / 2 = -13

Since the width cannot be negative, the only valid solution is x = 7. This means that the width is 7m and the length is x + 6 = 7 + 6 = 13m.

So the length of the top of the workbench is 13m and the width is 7m.

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Answer: the last option

Step-by-step explanation:

Standard derivation reflects the degree if dispersion  of a data set

so the answer is 1,1,1,1,2,2,2,2

There would be 40,320 ways can 8 people be arranged on 8 chairs in a row. There are 5,040 ways can 8 people be seated around a circular table. There are  128 committees can be selected from the people if ps has to be the chair of the committee

(a) The number of ways that 8 people can be arranged on 8 chairs in a row is 8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40,320. This is because there are 8 choices for the first chair, 7 choices for the second chair, and so on until there is only one choice for the last chair.

(b) The number of ways that 8 people can be seated around a circular table is (8-1)! = 7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5,040. This is because we can fix one person in one seat and then there are 7 choices for the next seat, 6 choices for the next seat, and so on until there is only one choice for the last seat.

(c) The number of committees that can be selected from the 8 people if Ps has to be the chair of the committee is 2^(8-1) = 2⁷ = 128. This is because there are 7 people left to choose from and each person can either be on the committee or not on the committee, which gives us 2 choices for each person.

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In the triangle ABC, the value of AC is obtained as 5 units.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

A triangle ABC is given.

The measure of AB is given as 10 units.

The measure of KB is given as 2 units.

The measure of KM is given as 1 unit.

According to the indirect measurement -

AB / AC = KB / KM

Substitute the values in the equation -

10 / AC = 2 / 1

2 AC = 10

AC = 5  

Therefore, the value of AC is obtained as 5 units.

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The long division process is explained below.

Division is one of the operation in mathematics where number is divided  into equal parts as that of a definite number.

While doing long division method, you have to follow certain steps.

Consider an example 259 ÷ 9.

259 is the dividend, 9 is the divisor.

First consider the first digit of the dividend, which is 2. But 2 is not greater than or equal to 9.

So take the next digit also and so consider the first two digits.

The first two digits of the dividend is 25.

25 is not a multiple of 9.

The number which is a multiple of 9 nearer to but less than 25 is 18.

18 = 2 × 9.

Write 2 in the quotient and subtract 25 - 18 = 7

Now 7 is less than 9. So bring down the next (third) digit of the dividend, which is 9.

So the number we get is 79.

Again 79 is not a multiple of 9. The nearest lesser multiple of 9 is 72.

72 = 9 × 8

So write 8 in the quotient.

Remainder is 79 - 72 = 7

So we get the quotient as 28 and the remainder is 7.

Hence the simplification of the long division is explained.

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hi

im pretty sure that this is the answer

hope this helps

good luck;)

The possible arrangement is 3960.

Permutation is a mathematical calculation of the number of ways a particular set can be arranged, where the order of the arrangement matters.

Given that, Bart wants to plant 8 trees in a row along his fence.

Possible arrangement of 4 birches = 5 x 4 x 3 x 2 x 1 = 120

If 3 birches are next to each other, therefore, 6 possible arrangement are possible = A₄⁴ x A₅² = 480

Similarly,

If 2 birches are next to each other, therefore, 6 possible arrangement are possible = A₄⁴ x A₅² = 480

If 4 birches are not next to each other, therefore, possible arrangement are possible = A₄⁴ x A₅⁴ = 2880

Therefore, total arrangements = 120+480+480+2880 = 3960

Hence, the possible arrangement is 3960.

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Answer:

I think the question is incomplete

To find the new coordinates of the points after Louis multiplied each x-coordinate and y-coordinate of triangle ABC by -2, we can use the following formulas:

New x-coordinate = -2 * old x-coordinate

New y-coordinate = -2 * old y-coordinate

Let's apply these formulas to each point in triangle ABC:

Point A: (-3, 4)

New x-coordinate of A = -2 * (-3) = 6

New y-coordinate of A = -2 * 4 = -8

New coordinates of A: (6, -8)

Point B: (1, 1)

New x-coordinate of B = -2 * 1 = -2

New y-coordinate of B = -2 * 1 = -2

New coordinates of B: (-2, -2)

Point C: (5, -2)

New x-coordinate of C = -2 * 5 = -10

New y-coordinate of C = -2 * (-2) = 4

New coordinates of C: (-10, 4)

Therefore, the new coordinates of the points after Louis multiplied each x-coordinate and y-coordinate of triangle ABC by -2 are:

A: (6, -8)

B: (-2, -2)

C: (-10, 4)

The possible rational roots are:

±1/1, ±3/1, ±5/1, ±15/1, ±1/1, ±1/2, ±3/2, ±5/2, ±15/2

A function is a mathematical rule that assigns a unique output value for each input value. It is a set of ordered pairs where the first element is the input and the second element is the output.

To list all the possible rational roots of x⁴ - 2x³ -6x² + 22x - 15 = 0, we need to find all the factors of the constant term -15 (in this case, they are 1, -1, 3, -3, 5, -5, 15, and -15) and all the factors of the leading coefficient 1 (in this case, they are 1 and -1). Then, we form all possible fractions of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient. Therefore, the possible rational roots are:

±1/1, ±3/1, ±5/1, ±15/1, ±1/1, ±1/2, ±3/2, ±5/2, ±15/2

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The correct match of each root word with its meaning are :

(i) Anthropology⇔(d) man

(ii) Psychology⇔(c) mind    

(iii) Economy⇔(e) law  

(iv) Democracy⇔(b) people

(v) Judicious⇔(a) judge

The term (i) Anthropology is related to (d) man because,

The term "Anthropology" is called the study of human-societies and cultures and their development.

The term (ii) Psychology is related to (c) mind ,

The term "Psychology" is defined as the scientific-study of behavior and mental processes of mind;

The term (iii) Economy is related to (e) law,

The Economy can be termed as the social science that deals with the production, distribution, and consumption of goods and services and their management.

The economy and practices of commerce are governed by certain laws or principles. So,  the best option to match economy is law.

The term (iv) Democracy is related to (b) people ,

Democracy is defined as system of government by the whole population or all the eligible members of a state, typically through elected representatives.

The term (v) Judicious is related to (a) judge,

The word "judge" is a derived from the word "judicious", which means, showing and using sound judgement.

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The given question is incomplete, the complete question is

Match the below root of each word to its meaning.

(i) Anthropology       (a) judge

(ii) Psychology          (b) people

(iii) Economy             (c) mind

(iv) Democracy         (d) man

(v) Judicious              (e) law

According to the information we can infer that the statement that establishes a correct interpretation of the model is the model associates a score of 80 with 2 hours of studying.

To select the correct statement we must replace the value of (t) in the equation and check the relationship between the results of the students in the test and the hours spent studying.

According to the above, if we replace t by two we can infer that the result would be y = 80 as shown below:

So the correct answer would be statement C.

On the other hand, to identify the percentage to which the number of seventh grade students who have a laptop is equivalent, we must add the total number of students in this grade and then find the percentage with a rule of three:

So the correct answer would be 42% because this value is the closest and we could approximate it.

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Answer: d = [tex]\sqrt{109}[/tex]

Step-by-step explanation:

Use the distance formula. [tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y{1})^2[/tex]

[tex]d=\sqrt{(3-(-7))^2+(1-4)^2[/tex]

d = [tex]\sqrt{(10)^2+(-3)^2}[/tex]

d = [tex]\sqrt{100+9}[/tex]

d = [tex]\sqrt{109}[/tex]

Given- Two points as (-7,4) and (3,1)

To find- The exact distance between them

Explanation - we know the distance formula is

[tex]d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]

here

[tex]x_1=-7, x_2=3\\y_1=4, y_2=1[/tex]

Substituting these values we get

[tex]d=\sqrt{(-7-3)^2+(1-4)^2} \\d=\sqrt{10^2+3^2} \\d=\sqrt{100+9} \\d=\sqrt{109} \\d=10.44[/tex]

Hence the distance between them is 10.44

Final answer- the distance between the points is 10.44

Answer:

See below.

Step-by-step explanation:

We are asked to solve this expression.

We should first identify that (-5) will be a positive 5 due to 2 negatives cancelling each other out.

We should have;

[tex]-2 \frac{1}{3}+5[/tex]

To make adding a bit more simpler for this type of problem, we should turn both values into Improper Fractions.

Improper Fractions are 2 or more fractions that have a greater numerator than a denominator. You can see why they're called improper.

Good Examples:

[tex]\frac{4}{3} \ and \ \frac{3}{2} \\4 > 3\\ 3 > 2[/tex]

Bad Examples:

[tex]\frac{3}{4} \ and \ \frac{4}{4} \\3 < 4\\4 = 4[/tex]

Let's turn these values into Improper Fractions.

[tex]\frac{1}{3} - \frac{3}{3} - \frac{3}{3} = -\frac{7}{3}[/tex]

[tex]5=\frac{5}{1}[/tex]

Make the Denominators Equal:

[tex]\frac{5}{1} \times \frac{3}{3} = \frac{15}{3} \ (5)[/tex]

Now, we can simply add.

[tex]-\frac{7}{3} + \frac{15}{3} = \frac{8}{3}[/tex]

Reverse, turn [tex]\frac{8}{3}[/tex] into a mixed fraction.

[tex]\frac{8}{3} - \frac{3}{3} \ (1) - \frac{3}{3} \ (2) = 2\frac{2}{3}[/tex]

Our final answer is [tex]2\frac{2}{3} .[/tex]

Answer: All questions and answers from the Mathematics Part I (solutions) Book of Class 9 Math Chapter 4 are provided here for you for free.

Step-by-step explanation:

The vector s₁ in the set can be expressed as a linear combination of the vectors s₂ and s₃:

s₁ = (-4/3)s₂ + (1/3)s₃

The set S = {(5,4),(−1,1),(2,0)} is linearly dependent if there exists a nontrivial linear combination of the vectors in the set whose sum is the zero vector. In other words, if there exists scalars a, b, and c such that:

a(5,4) + b(−1,1) + c(2,0) = (0,0)

Expanding the above equation gives us:

(5a - b + 2c, 4a + b) = (0,0)

This implies that:

5a - b + 2c = 0

4a + b = 0

Solving the above system of equations gives us:

a = 1/3, b = -4/3, c = 1/3

Therefore, the nontrivial linear combination of the vectors in the set whose sum is the zero vector is:

(1/3)(5,4) + (-4/3)(−1,1) + (1/3)(2,0) = (0,0)

To express the vector s₁ in the set as a linear combination of the vectors s₂ and s₃, we can use the above solution and write:

s₁ = (-4/3)s₂ + (1/3)s₃

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Answer:

Step-by-step explanation:

Dang, they made this a little harder. Now we need to actually calculate a slope. Good thing is, it's relatively easy. Slope is basically the rate of change, or the rise of the function over the run, which is shown as:

Δy/Δx

We can use two points to find the slope. I will use (2,795) and (4,1525)

(y1 - y2) / (x2 - x1)

(1525 - 795) / (4 - 2)

730 / 2

365

This is our slope, 365x.

Now we need the y-intercept, which is where the line hits the y-axis. It seems to be at 100, so the new equation is:

y = 365x + 100

If we want to know how many followers Lauren will have in 2018, we just use 7 for x years after 2011, since 2018 is 7 after 2011.

y = 365(7) + 100

y = 2555 + 100

y = 2655

Lauren has 2655 followers in 2018.

Station 6-

The x-intercept tells us when the depth below the sea level is 0 feet.

The y-intercept tells us the starting depth when the time is 0.

The meaning of the slope being -10x is that the depth below the sea level decreases 10 feet per minute. Hope this helps, and sorry for seeing this late!

Answer:

$2.50

Step-by-step explanation:

The rate of change of with respect to for this function is 1.75.

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

P = (-2, -7.5)

Q = (4, 3)

Using the two given points, we can find the slope of the line passing through them using the slope formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) = (-2, -7.5) and (x2, y2) = (4, 3)

slope = (3 - (-7.5)) / (4 - (-2))

= 10.5 / 6

= 1.75

Hence, the rate of change (i.e., the slope) of the line passing through points P and Q is 1.75.

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Answer 13

Step-by-step explanation:Place all numbers in order from youngest to oldest. and the one in the middle is the median

Answer:13

Step-by-step explanation:

The answers are given in the solution below.

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.

Given that, are circles, we need to find the value of x in each of them,

Using the property of circle,

1) ∠ TSU = 1/2(arc LV + arc TU)

98° = 1/2(70° + 25x+1)

196 = 71+25x

25x = 125

x = 5

2) ∠ BAC = 1/2(arc DR + arc CB)

10x-5 = 1/2(4x+18 + 132)

20x-10 = 4x+18+132

16x = 160

x = 10

3) arc FR = 360° - 245°

arc FR = 115°

∠ FSR = 1/2(245-115)

8x+1 = 65

8x = 64

x = 8

4) ∠ EDF = 1/2(arc CF - arc DF)

5x+1 = 1/2(13x+19-4x-5)

5x+1 = 1/2(9x+14)

10x+2 = 9x+14

x = 12

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To solve this problem, we first need to find a common denominator for the fractions in the parentheses.

The common denominator for 12 and 8 is 24, so we can rewrite the fractions as (14/24) and (9/24). Then, we can add these fractions together to get (14/24) + (9/24) = (23/24). Next, we can subtract this fraction from (3/8) by finding a common denominator for 8 and 24, which is 24. We can rewrite (3/8) as (9/24) and then subtract (23/24) from it to get (9/24) - (23/24) = (-14/24). Finally, we can simplify this fraction to get (-7/12).

So, the final answer is:
(3/8) - ((7/12) + (3/8)) = (3/8) - ((14/24) + (9/24)) = (9/24) - (23/24) = (-14/24) = (-7/12)

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