The combined area of a square and a rectangle is 33 square meters. The width of the rectangle is 1 meter more than the length of one side of the square and the length of the rectangle is 3 meters more
than its width.
a) Calculate the dimensions of the rectangle and its perimeter

b) Calculate the dimensions of the square.

The expression is 5 * n².

An expression is a mathematical statement that consists of variables, constants and mathematical operators.

The representation of a quantity in terms of a value is done by a number.

There are various types of numbers like real numbers, natural numbers, whole numbers, rational numbers, etc.

The expression is :

Five times the square of a number

Let the number be n, then

5 * n²

Let n =1

The value of the expression will be

5 * (1)² = 5

Let n = 2

The value of the expression will be

5 * (2)²

5 * 4

20

Let n = 5

5 * (5)²

5 * 25

125

Let n = 100

5 * (100)²

5 * 10000

50000

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Answer:

‍. ‍‍ ‍ ‍ ‍ ‍ ‍ ‍ ‍ ‍ ‍ ‍ ‍ ‍ ‍ ‍ ‍ ‍ ‍ ‍ ‍ ‍ ‍ ‍ ‍ ‍ ‍ ‍ ‍ ‍ ‍ ‍‍ ‍ ‍ ‍ ‍ ‍ ‍ ‍ ‍ ‍ ‍ ‍

‍ ‍ ‍

Answer:

no

Step-by-step explanation:

4m + 12 ≠ 2m + 12

The two outliers in the scatter plot below are the points with shoe size 5 and shoe size 12.

These outliers are likely due to the fact that the data set includes people of all ages, and shoe size is not a linear function of height. For example, a 5-year-old child is likely to have a shoe size of 5, even though they are much shorter than an adult with a shoe size of 5. Similarly, an adult with a shoe size of 12 is likely to be much taller than a child with a shoe size of 12.

In order to get a more accurate representation of the relationship between height and shoe size, it would be necessary to remove the outliers and only consider data from people of similar ages.

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Answer:

Slope-1/4 Y-intercept--2 Equation-y=1/4x+-2 and choose any point on the line.

Step-by-step explanation:

To find slope, you will have to make a slope triangle with two intersecting points. Divide h/v witch is 1/4. The y-intercept is just the point on the y-axis so that is -2. For the fourth question, just choose any coordinate on the oblique line.

Hope that helps!

Answer:

A

Step-by-step explanation:

Congruent angles are angles that have the same angle.

Those red squares in the corner of ∠DFE and ∠BFC mean they are 90°

I hope this helps you! :)

Answer:

41, x=-5

Step-by-step explanation:

m<DEY = m<FEY, by angle bisector theorem

(9x-4) = 41

9x = 45

x = 5

m<DEY = 41

From the given information provided, the means of x₁, x₂,  and x₃ are 158.28, 41.3, and 43.75 respectively.

a. Handle the missing values using omission strategy:

The omission strategy involves removing any observation with missing values.

The resulting table after the omission strategy is as follows:

Obs x₁ x₂ x₃

1 248 3.5 3.8

2 55 150 74

3 196 4.5 32

4 134 6.2 63

We can see that one observation with missing values was removed, which was observation 5.

b. Handle the missing values using simple mean imputation strategy:

The simple mean imputation strategy involves replacing the missing values with the mean of the non-missing values.

The means of x₁, x₂, and x₃ are calculated as follows:

mean of x₁ = (248 + 55 + 196 + 134) / 4 = 158.25

mean of x₂ = (3.5 + 150 + 4.5 + 6.2) / 4 = 41.3

mean of x₃ = (3.8 + 74 + 32 + 63) / 4 = 43.75

The resulting table after the simple mean imputation strategy is as follows:

Obs x₁ x₂ x₃

1 248 3.5 3.8

2 55 150 74

3 196 4.5 32

4 134 6.2 63

5 158.25 41.3 43.75

We can see that all missing values were replaced, which were x₁ in observation 5 and x₃ in observation 3.

Question - The following table contains 3 variables and 5 observations including some missing values x₁ x₂ x₃ 248 3.5 3.8 55 150 74 196 4.5 32 134 6.2 63 a. Handle missing values using omission strategy. b. Handle missing values using simple mean imputation strategy. How many missing values are replaced? What are means of x₁, x₂, and x₃?

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The absolute maximum and absolute minimum values of f(x) over each of the indicated intervals are for Interval = [-2,0], Absolute maximum = f(-2) = 37, Absolute minimum = f(0) = 9, Interval = [1,10], Absolute maximum = f(10) = -671,
Absolute minimum = f(1) = -29, Interval = [-2,10], Absolute maximum= f(10) = -671, Absolute minimum = f(-2) = 37

To find the absolute maximum and absolute minimum values of \(f(x)=x^3-12x^2-27x+9\) over each of the indicated intervals, we need to first take the derivative of the function and set it equal to zero to find critical points. The derivative of f(x) is\(3x^2-24x-27\).

Setting this equal to zero, we get x=-3 and x=3. We then plug in these critical points and the endpoints of each interval into the original function to find the maximum and minimum values.

(a) Interval = [-2,0]
Absolute maximum = f(-2) = 37
Absolute minimum = f(0) = 9

(b) Interval = [1,10]
Absolute maximum = f(10) = -671
Absolute minimum = f(1) = -29

(c) Interval = [-2,10]
Absolute maximum= f(10) = -671
Absolute minimum = f(-2) = 37

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To create an expression that shows the sum of exactly two terms equivalent to 6(2x - 5), we can distribute the 6 across the terms inside the parentheses. This results in 12x - 30.

Now, we can express the sum of two terms that is equivalent to 12x - 30 as follows: Let the first term be represented by 'a' and the second term be represented by 'b'. The sum of these two terms can be expressed as a + b = 12x - 30.

In this case, 'a' and 'b' represent the coefficients or values associated with x. The expression shows that when these two terms are combined, the resulting expression is equivalent to 6(2x - 5), which simplifies to 12x - 30. This demonstrates the distribution of the 6 and the representation of the terms in a condensed form.

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To answer the given questions, we need to use the provided probabilities and apply the rules of probability.

P(FUA) = P(F) + P(A) - P(F ∩ A)

(a) P(FUA) represents the probability of the driver being female and 24 years old or less. Since the events F and A are not mutually exclusive, we can use the formula:

P(FUA) = P(F) + P(A) - P(F ∩ A)

Given:

P(F) = 0.2907

P(A) = 0.1849

P(F ∩ A) = 0.0542

Plugging in the values:

P(FUA) = 0.2907 + 0.1849 - 0.0542

P(FUA) = 0.4214

Therefore, the probability of the driver being female and 24 years old or less is 0.4214.

(b) P(F'UA) represents the probability of the driver not being female and being 24 years old or less. Using the complement rule, we have:

P(F'UA) = 1 - P(FUA)

Plugging in the value of P(FUA) from part (a):

P(F'UA) = 1 - 0.4214

P(F'UA) = 0.5786

Therefore, the probability of the driver not being female and being 24 years old or less is 0.5786.

(c) P(FnA) represents the probability of the driver being female but not 24 years old or less. We can calculate this using the formula:

P(FnA) = P(F) - P(F ∩ A)

Given:

P(F) = 0.2907

P(F ∩ A) = 0.0542

Plugging in the values:

P(FnA) = 0.2907 - 0.0542

P(FnA) = 0.2365

Therefore, the probability of the driver being female but not 24 years old or less is 0.2365.

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Answer:

10. -x + y = 1.

Step-by-step explanation:

10. y + 1 = x + 2

y - x = 2 - 1

-x + y = 1.

The initial number of people ill with the virus can be found by evaluating p(0), where p(t) is the function describing the number of people infected after t weeks. By substituting t = 0, we determine the number of people already ill at the start of the outbreak.

The initial number of people who were ill with the virus can be determined by evaluating the function p(t) at t = 0.

To find the initial number of people who were ill with the virus, we evaluate the function p(t) at t = 0. Since the function describes the number of people who have become ill with the virus t weeks after its initial outbreak, p(0) gives us the number of people who were already ill at the start. By substituting t = 0 into the function, we can find the value of p(0) which represents the initial number of people who were ill with the virus.

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Answer:

should be 240 in commission, 840 in total.

The linear equation that passes through the given points is:

y + 9 = -10*(x - 1)

A general linear equation that passes through two points (x₁, y₁) and (x₂, y₂) has a slope given by:

a = (y₂ - y₁)/(x₂ - x₁)

Then using any of these points we can write the line as:

y -  y₁ = a*(x - x₁)

Here the points are (1, -9) and (-10, 101), then the slope is:

a = (101 + 9)/(10 - 1) = 110/-11 = -10

And using the point (1, -9) we can write the line as:

y + 9 = -10*(x - 1)

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Answer:

1) x=6, y=-6 which is (6,-6) as an ordered pair

3) x=10, y=-1 which is (10,-1) as an ordered pair

Step-by-step explanation:

Question 1:

Solve them like an addition problem:

-4x-2y=-12

4x+8y=-24

________

(-4x+4x)+(-2y+8y)=(-12+-24)

0x+6y=-36

6y=-36

y=-6

Plug value of y into one of the original equations:

4x+8(-6)=-24

4x-48=-24

4x=24

x=6

Question 3:

Solve them like an addition problem:

x-y=11

2x+y=19

_______

(x+2x)+(-y+y)=11+19

3x+0y=30

3x=30

x=10

Plug value of x into one of the original equations:

10-y=11

-y=1

y=-1

Answer:

11/12

Step-by-step explanation:

I took 1.9 and turned it into a fraction and the fraction is 1 9/12 so if you have 11/12 and 1 9/12 then you bought 10/12 more pounds of banana than grapes

Answer: 3/5x+2/5+3/5x= 1.6

Step-by-step explanation:

15 / (1/3)  is equal to  15 x 3/1  = 15 x 3 = 45

The parametric equations for the circle (x−4)^2 (y−1)^2=4 are x=4+2cos(t) and y=1+2sin(t), where t is the parameter.

Assuming the circle is traced clockwise as the parameter increases, if x=9+2cos(t), then t=arccos((x-9)/2). Substituting this into the equation for y gives y=1+2sin(arccos((x-9)/2)). Simplifying this expression gives y=1+2sqrt(1-(x-9)^2/16), which is the equation of the circle traced clockwise. The word count for this answer is 98 words.
Hi! The given circle equation is (x-4)^2 + (y-1)^2 = 4. To convert this into parametric equations, we'll use the parameter t. Since the circle is traced clockwise as the parameter increases, we'll use negative sine and cosine functions. The parametric equations for the given circle are:
x = 4 + 2cos(-t) = 4 - 2cos(t),
y = 1 + 2sin(-t) = 1 - 2sin(t).
Now, if x = 9 + 2cos(t), equate this with the parametric equation for x:
9 + 2cos(t) = 4 - 2cos(t).
Solving this equation will help determine the relationship between the given x-value and the parameter t.

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Answer:

206

Step-by-step explanation:

1648/8

206 each

Each classroom will receive $206.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

To find the total amount of money each classroom will receive,

We need to divide the total amount of money raised by the number of classrooms:

The total amount of money raised = $1,648

Number of classrooms = 8

Amount of money each classroom will receive.

= Total amount of money raised / Number of classrooms

Amount of money each classroom will receive:

= $1,648 / 8

= $206

Therefore,

Each classroom will receive $206.

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Answer: 28 cups

Step-by-step explanation:

8 ounces = 1 cup

64 ounces = 8 cups

20 + 8 = 28

28 cups in all

Answer:

Step-by-step explanation:

yep

Based on this evaluation, the correct answer is:

d. "false : 14 is 104"

The value of 's' after the given statement can be determined by evaluating each part of the expression step by step:

1. Evaluate (!true): Since 'true' is negated using the '!' operator, this expression becomes 'false'.

2. Concatenate " : " to "false": The resulting string also becomes "false : ".

3. Calculate (10 + 4): This arithmetic expression is equals to  14.

4. Concatenate "14" to "false : ": The resulting string becomes equal to "false : 14".

5. Finally, concatenate " is 104" to "false : 14": The final value of 's' becomes "false : 14 is 104".

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Answer:

\(x = 180 - (37 + 53)\)

is the answer

Answer:

n = 8

Step-by-step explanation:

The angles are vertical angles and so they are equal

9n = 8n+8

Subtract 8n from each side

9n - 8n = 8n+8-8n

n = 8

The composite function k(t(x)) is -2.5 - 7(ln x)^2 + 3(ln x), and its derivative is -14ln x + 3/x.

To find the composite function k(t(x)), we substitute the expression for t(x) into the function k(t) as follows:

k(t(x)) = 4.5 + 3 - 7t(x)^2 + 3t(x) - 4

k(t(x)) = 4.5 + 3 - 7(ln x)^2 + 3(ln x) - 4

Simplifying this expression, we obtain:

k(t(x)) = -2.5 - 7(ln x)^2 + 3(ln x)

To find the derivative of the composite function, we use the chain rule as follows:

k'(t(x)) = k'(t) * t'(x)

where k'(t) is the derivative of the function k(t) with respect to t, and t'(x) is the derivative of the function t(x) with respect to x.

The derivative of k(t) with respect to t is:

k'(t) = -14t + 3

The derivative of t(x) with respect to x is:

t'(x) = 1/x

Substituting these expressions into the chain rule, we obtain:

k'(t(x)) = (-14t(x) + 3) * (1/x)

k'(t(x)) = (-14ln x + 3/x)

Therefore, the composite function k(t(x)) is -2.5 - 7(ln x)^2 + 3(ln x), and its derivative is -14ln x + 3/x.

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