Unions, intersections, and complements involving 2 sets

The area of the composite figure is 41 ft square.

The figure is a composite figure. A composite figure is a figure that has two or more shapes.

Therefore, the area of the composite figure is the sum of the individual area of the shapes.

Therefore,

area of the figure = area of rectangle 1 + area of rectangle 2

area of rectangle 1 = lw

where

Therefore,

area of rectangle 1 = 2 × 4 = 8 ft²

area of rectangle 2 = 11 × 3 = 33 ft²

Hence,

area of the figure =  = 8 + 33

area of the figure = 41 ft²

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Using the formula of simple interest, the time it will take to accumulate to $3200 at a rate of 4.5% is 71.35 years

Simple interest is a method of calculating the interest charge on a loan or deposit. It is based on the principle of earning interest only on the initial amount (principal) that was borrowed or deposited.

The formula for simple interest is:

I = P * r * t

where:

I is the interest amount

P is the principal amount

r is the interest rate (expressed as a decimal)

t is the time period (in years)

Substituting the values into the formula;

A = P(1 + rt)

3200 = 760(1 + 0.045(t))

3200 = 760 + 34.2t

34.2t = 3200 - 760

34.2t = 2440

t = 2440 / 34.2

t = 72.35 years

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Answer:

YES, x = 8

Step-by-step explanation:

plug in 8 for x and see if both sides are equal

3/4 times 8 = 24/4 or 6

Answer:

Step-by-step explanation:

If we solve it as....

[tex]\mathrm{\cfrac{3}{4}x=6}[/tex]

[tex]\mathrm{4\times\cfrac{3}{4}x=6\times\:4}[/tex]

[tex]\mathrm{3x=24}[/tex]

[tex]\mathrm{\cfrac{3x}{3}=\cfrac{24}{3}}[/tex]

[tex]\mathrm{x=8}[/tex]

Yes, 8 would be the solution!

___________________

Hope this helps!

After 40 years, the account has a total balance of $49.450.80.

Any loans or borrowings come with interest. the portion of the loan's value that lenders use to calculate interest. By lending money (via a bond or certificate of deposit, for instance), or by depositing funds into an interest-bearing bank account, consumers can earn interest.

Let's assume that he starts with $0 in the account and makes a monthly contribution of $100 for 40 years, which is equal to 40 x 12 = 480 months.

The total contributions would be $100 x 480 = $48,000.

The interest earned on the account balance can be calculated as follows:

Interest = Account balance * Interest rate

At the end of each year, the interest is added to the account balance. So, after 40 years, the balance would be:

Year 1: $48,000 * 1.5% = $720

Balance = $48,000 + $720 = $48,720

Year 2: $48,720 * 1.5% = $730.80

Balance = $48,720 + $730.80 = $49,450.80

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The equation of the line which is parallel to the line x = -4 will be x = -3.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given that the equation of the line is x = -4. The y-intercept is zero for the line.

The equation of the line parallel to the equation will be,

x = -3

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Answer:

Given that s = 1.5, the expressions that have a value of 13.5 are:

(1) 5s + 8 = 5 × 1.5 + 8 = 13.5

(2) 2s^2 + 9 = 2 × 1.5^2 + 9 = 13.5

Note: The value of any other expression will depend on the specific formula and the value of other variables used in the expression.

Answer:

285.76 kilograms       1.1 cubic yard

Step-by-step explanation:

Answer:

1.11121 cubic yards.

Step-by-step explanation:

First, let's convert the weight of 1 bag of garden soil from pounds to kilograms:

1 lb = 0.45359237 kg

42 lbs = 42 * 0.45359237 kg = 19.05 kg

So, the weight of 1 bag of garden soil is 19.05 kilograms.

Next, let's find the weight of 15 bags of garden soil:

15 bags * 19.05 kg/bag = 285.75 kg

So, 15 bags of garden soil weigh 285.75 kilograms.

Next, let's find the volume of 15 bags of garden soil in cubic yards:

1 cubic foot = 0.037037 cubic yards

2 cubic feet * 15 bags = 30 cubic feet

30 cubic feet = 30 * 0.037037 cubic yards = 1.11121 cubic yards

So, 15 bags of garden soil have a volume of 1.11121 cubic yards.

The measure of each angle in the regular polygon is 154.3 degrees

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

Number of sides, n = 14

The measure of each angle is calculated as

Angle = ( n − 2 ) × 180/n

substitute the known values in the above equation, so, we have the following representation

Angle = (14 − 2) × 180/14

Evaluate

Angle = 154.3

Hence, the angle is 154.3

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Option D is correct, SA = 2π(1.3)2 + 2.6π(4.4) square feet is used calculate the surface area of the cylinder.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Given that cylinder with diameter labeled 2.6 feet and height labeled 4.4 feet

The surface area of cylinder is given by the formula =2πrh+2πr²

The radius is Diameter/2

2.6/2=1.3

The radius is 1.3

Surface area =2π(1.3)(4.4)+2π(1.3)²

So =2.6π(4.4)+2π(1.3)²

Hence, Option D is correct, SA = 2π(1.3)² + 2.6π(4.4) square feet is used calculate the surface area of the cylinder.

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Answer:

Step-by-step explanation:

Answer:

a. To find the weight corresponding to the highest 20 percent of coffees, we need to find the z-score that corresponds to the 0.8 cumulative probability.

Using a standard normal table or a calculator that can compute z-scores, we can find that the z-score corresponding to a cumulative probability of 0.8 is 0.8416.

Next, we use the z-score formula to find the weight:

Weight = Mean + (z-score * Standard Deviation)

Weight = 400 + (0.8416 * 20) = 448.32 g

So, the weight corresponding to the highest 20 percent of coffees is approximately 448.32 g.

b. To find the weight corresponding to the middle 60 percent of coffees, we need to find the z-scores that correspond to the cumulative probabilities of 0.2 and 0.8.

Using a standard normal table or a calculator that can compute z-scores, we can find that the z-score corresponding to a cumulative probability of 0.2 is -0.8416, and the z-score corresponding to a cumulative probability of 0.8 is 0.8416.

Next, we use the z-score formula to find the weights:

Weight Lower Bound = Mean + (z-score * Standard Deviation)

Weight Lower Bound = 400 + (-0.8416 * 20) = 351.68 g

Weight Upper Bound = Mean + (z-score * Standard Deviation)

Weight Upper Bound = 400 + (0.8416 * 20) = 448.32 g

So, the weight corresponding to the middle 60 percent of coffees ranges from approximately 351.68 g to approximately 448.32 g.

c. To find the weight corresponding to the highest 80 percent of coffees, we use the same process as in (a) to find the z-score that corresponds to the cumulative probability of 0.8, which is 0.8416.

Next, we use the z-score formula to find the weight:

Weight = Mean + (z-score * Standard Deviation)

Weight = 400 + (0.8416 * 20) = 448.32 g

So, the weight corresponding to the highest 80 percent of coffees is approximately 448.32 g.

d. To find the weight corresponding to the lowest 15 percent of coffees, we need to find the z-score that corresponds to the cumulative probability of 0.15.

Using a standard normal table or a calculator that can compute z-scores, we can find that the z-score corresponding to a cumulative probability of 0.15 is -0.9332.

Next, we use the z-score formula to find the weight:

Weight = Mean + (z-score * Standard Deviation)

Weight = 400 + (-0.9332 * 20) = 346.64 g

So, the weight corresponding to the lowest 15 percent of coffees is approximately 346.64 g.

Step-by-step explanation:

Two numbers that are in both sequences are the numbers 17 and 32.

A sequence can be described as a set of numbers each with a defined interval between one another. For example, in the sequence 2, 4, 6, 8, 10, the interval is 2.

To find two common numbers, let's expand the sequences as it is shown below:

First sequence: In this sequence, the interval is 5.

2 7 12 17 22 27 32

Second sequence: In this sequence, the interval is 3.

-4 -1 2 5 8 11 14 17 20 23 26 29 32

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7/8 of sixteen times a half of 30 is 210.

What is a PEMDAS rule?

PEMDAS is an acronym that stands for the order of operations in mathematics: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

To calculate this, we can follow the order of operations, which is also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction):

Start with the expression inside the parentheses: half of 30 is 15.

Multiply 16 by 15: 16 times 15 is 240.

Find 7/8 of 240:

7/8 of 240 = (7/8) x 240

                  = 210

Hence, 7/8 of sixteen times a half of 30 is 210.

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Answer:

The total possible outcomes that exist are:

                            2400

Step-by-step explanation:

We are given four dices:

first is a standard 6-faced die.

The second die has 4 faces.

Third dice has 10 faces.

Fourth dice has 10 faces.

Now when all the dice are thrown together then the total number of possible outcomes are:

( Since there are 4 numbers possible for the first die, 6 for second and 10 each for third and fourth)

                   The answer is:

                          2400

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Answer:

You figure out the slope

Step-by-step explanation:

Rise/Run is a formula that calculates the slope.  This determines the direction of the line and how steep it is.

Answer:

its a math term yw my boy

Step-by-step explanation:

a) The required margin of error and lower and upper limits are:-

E =0.124

Lower limit =3.026

Upper limit =  3.274

b) sample size is n = 27.

An estimated range for an unknown parameter is known as a confidence interval. The 95% confidence level is the most popular, however other levels, such as 90% or 99%, are occasionally used when computing confidence intervals.

The margin of error will be calculated as:-

a) Margin of error (E) :

[tex]E = Z_c\times \dfrac{\sigma}{\sqrt{n}}[/tex]

E =0.124

Margin of error = E =0.124

The lower and upper limits are calculated as:-

Lower limit = x-E

L= 3.15 - 0.124

L= 3.026

Lower limit =3.026

Upper limit = x + E

U= 3.15 + 0.124

U= 3.274

Upper limit =  3.274

b) The following equation may be used to calculate the right number of samples, n when is already known:

Margin of error = 0.13

Sample size (n):

[tex]n = (\dfrac{Z_c\sigma}{E})^2[/tex]

[tex]n = (\dfrac{1.28\times 0.36}{0.09})^2[/tex]

n = 26.21

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Answer:

you see

Step-by-step explanation:

a).The function1 changes at greater rate of 45.

b). At x = 1; the function1 = 45 and function2 = 50.

c).The functions are equal to 90 at x = 2.

A function in the equation form "y = mx + c" represents a straight line in a two-dimensional coordinate system. "y" and "x" are variables representing the coordinates of points on the line, "m" is the slope of the line, and "c" is the y-intercept, which is the point at which the line crosses the y-axis.

The slope "m" represents the rate at which the line rises or falls as x increases. The y-intercept "c" determines the location of the line along the y-axis. This equation is known as the slope-intercept form of a linear equation.

For the function1, when y = 0 and x = 0, we can solve for c and m as follows:

0 = 0m + c

c = 0

when y = 90 and x = 2;

90 = 2m + 0

m = 45

Hence, the function1 with y = 45x changes at a greater rate of 45.

At x = 1:

for function1;

y = 45(1) + 0 = 45

for function2;

y = 40(1) + 10 = 50.

At the point when x = 2:

for function1;

y = 45(2) + 0 = 90

for function2;

y = 40(2) + 10 = 90.

Therefore, the function1 changes at greater rate of 45. At x = 1; the function1 = 45 and function2 = 50. The functions are equal to 90at x = 2.

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The values of the piecewise functions at the indicated limits using the equations obtained from the graph are;

[tex]\lim \limits_{x \to2^+}\frac{f(x) - 4}{f(x+ 3)} = \underline{-\frac{2}{3} }[/tex]

[tex]\lim \limits_{x\to 3^-}[/tex] f(f(x) + 4) = 7

[tex]\lim\limits_{h\to 0} \frac{f(2+ h)-f(2)}{h}[/tex] DNE

A piecewise function is a function that has rules or definition based on the interval of reference of the function.

The graphed function, f(x), comprising of several piecewise functions, indicates that as x → 2⁺, we get;

The points on the line of the graph are;

(1, 1), and (3, 3)

The slope of the graph as x tends to 2⁺ is therefore;

Slope = (3 - 1)/(3 - 1) = 1

The equation of the line is therefore;

y - 1 = x - 1

y = f(x) =  x

Therefore;

f(x) - 4 = x - 4

f(x + 3) = x + 3

[tex]\lim \limits_{x\to 2^+} \frac{f(x) -4}{f(x + 3)} = \frac{x - 4}{x + 3} | x = 2[/tex]

The piecewise function for the interval, x → 3⁻ is; f(x) = x, therefore;

f(f(x) + 4) = f(x + 4) = x + 4

[tex]\lim \limits_{x\to 3^-}f(f(x) + 4)[/tex] = x + 4, where; x = 3, therefore;

[tex]\lim \limits_{h\to 0} = \frac{f(2 + h)-f(2)}{h}[/tex], can be found as follows;

The equation of the function at x = 2 is; y = f(x) = x

f(2 + h) = 2 + h

f(2) = 2

Therefore;

[tex]\frac{f(2 + h)-f(2)}{h}[/tex] = (2 + h - 2)/h = h/h

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The domain of the function for this situation is given as follows:

B. All whole numbers greater than or equal to 0 and less than or equal to 7.

The domain of a function is the set that contains all the values assumed by the input of the function.

Hence, on a graph, the domain is given by the values assumes on the horizontal axis of the graph.

The values that compose the domain of the graph are given as follows:

0, 1, 2, 3, 4, 5, 6 and 7.

Which is best described by option B.

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Answer:

EF, GH

Step-by-step explanation:

both go on forever from one point

Answer:

A and B

Step-by-step explanation:

Because they go infinitly in one direction and end in another.

Grayson would need to invest approximately $10,994 to the nearest dollar for the value of the account to reach $15,000 in 5 years.

What is continuously compounded interest?

Continuous compounded interest indicates that an account balance is constantly earning interest and reinvesting that money so that it, too, earns interest.

The formula for continuous compounding is given by:

[tex]A = Pe^{rt}[/tex]

where A is the amount in the account after t years, P is the principal amount (the amount invested), r is the annual interest rate, and e is the base of the natural logarithm.

We want to find P when A = $15,000, r = 0.04, and t = 5 years.

Substituting these values into the formula, we get:

[tex]15000 =Pe^{0.04*5}[/tex]

Simplifying the right-hand side, we get:

[tex]15000 =Pe^{0.2}[/tex]

Dividing both sides by e^(0.2), we get:

[tex]P= \frac{15000}{e^{0.2}}[/tex]

Using a calculator, we get:

P ≈ $10,994

Therefore, Grayson would need to invest approximately $10,994 to the nearest dollar for the value of the account to reach $15,000 in 5 years.

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-1/10 should be subtracted from 1/2 to get 4/10.

A fraction is of the form → (x/y).

For example, we can write fractions as → 2/3.

Fractions and ratios represent the same aspect. We can write -

2 : 3 = 2/3

4 : 7 = 4/7

Given is to solve the expression -

(1/2) - ? = 4/10

We can write the expression as -

(1/2) - (x) = (4/10)

(x) = 4/10 - 1/2

(x) = 4/10 - 5/10

(x) = -1/10

Therefore, -1/10 should be subtracted from 1/2 to get 4/10.

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{Question in English -

What fraction subtracted from 1/2 equals 4/10?}

If "a" is a root of a polynomial, then (x-a) is a factor of the polynomial.

If the multiplicity of a root a is "p", then (x-a)^p is a factor of the polynomial.

Based on the roots and multiplicity, we have:

    P(x) = k · (x-2)^2 · (x-0) · (x - (-2))

    P(x) = k · (x-2)^2 · (x-0) · (x+2)

We need that "k" up front to account for any vertical stretch or compression to hit the exact point (5,189).

To find "k", we plug in that point and solve for "k":

     189 = k · (5-2)^2 · (5-0) · (5+2)

     189 = k · (3)^2 · (5) · (7)

     189 = k · 315

     0.6 = k

So the final answer is: P(x) = 0.6 · (x-2)^2 · (x-0) · (x+2)

The short-run total cost is TC is wL + rK and short-run average cost curve is TC/Q. The SMC is 4.01 and the SMC curve intersects the SAC curve at its lowest or minimum points because the average cost is a weighted average of the marginal cost and the fixed cost.

A. To calculate the firm’s short-run total cost curve, we need to calculate the total cost at each level of output. The short-run total cost can be represented as follows:

TC = wL + rK,

where w is the wage rate, L is the labor used, r is the interest rate, and K is the capital used. In this case, w = $4 and r = $1.

To calculate the short-run average cost curve, we need to divide the total cost by the level of output:

SAC = TC / Q

Where Q is the level of output.

B. The short-run marginal cost function can be calculated as the change in total cost for a small change in the level of output:

SMC = dTC / dQ

At a level of output of 25, the labor used is L = 25 / 2 = 12.5. The total cost can be calculated as follows:

TC = 4 * 12.5 + 1 * 100 = 50 + 100 = 150

So, the short-run average cost is SAC = 150 / 25 = $6 and the short-run marginal cost is SMC = dTC / dQ. To calculate the derivative, we need to use the production function given:

Q = 2 * sqrt(KL)

Taking the derivative with respect to L, we get:

dQ / dL = (1 / (2 * sqrt(KL))) * 2K = K / (sqrt(KL))

Substituting the values, we get:

SMC = 4 + (1 / (sqrt(100 * 12.5)))

At a level of output of 200, the labor used is L = 200 / 2 = 100. The total cost can be calculated as follows:

TC = 4 * 100 + 1 * 100 = 400

So, the short-run average cost is SAC = 400 / 200 = $2 and the short-run marginal cost is SMC = dTC / dQ. To calculate the derivative, we need to use the production function given:

Q = 2 * sqrt(KL)

Taking the derivative with respect to L, we get:

dQ / dL = (1 / (2 * sqrt(KL))) * 2K = K / (sqrt(KL))

Substituting the values, we get:

SMC = 4 + (1 / (sqrt(100 * 100)))

SMC = 4.01

C. To draw the graph for the SAC and SMC, we need to calculate the SAC and SMC for different levels of output. We can then plot the SAC and SMC against the level of output to obtain the graphs.

D. The SMC curve intersects the SAC curve at its lowest or minimum points because the average cost is a weighted average of the marginal cost and the fixed cost. When the level of output is low, the marginal cost is high and the fixed cost is a large portion of the total cost. As the level of output increases, the marginal cost decreases and the fixed cost becomes a smaller portion of the total cost. As a result, the average cost decreases and reaches a minimum at the point where the marginal cost intersects the average cost.

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If a value of "y" is greater than 10, then it is a solution to the inequality 10 < y. If it is less than or equal to 10, then it is not a solution.

What is inequality?

In mathematics, an inequality is a statement that describes a relationship between two values, expressing that one value is greater than, less than, or equal to the other value. Inequalities are denoted by symbols such as "<" (less than), ">" (greater than), "≤" (less than or equal to), "≥" (greater than or equal to), or "≠" (not equal to).

The inequality 10 < y means that "y" is greater than 10. To determine whether a given value of "y" is a solution to this inequality, we simply need to check whether that value is indeed greater than 10.

For example:

If y = 11, then 10 < y is true, because 11 is greater than 10.

If y = 10, then 10 < y is false, because 10 is not greater than 10 (they are equal).

If y = 9, then 10 < y is false, because 9 is not greater than 10.

Hence, if a value of "y" is greater than 10, then it is a solution to the inequality 10 < y. If it is less than or equal to 10, then it is not a solution.

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Convert the problem to standard form and write the initial tableau with slack variables:

Maximize

[tex]Z = 7*3 + 6*4 + 18*5 + 14*6 - 3*1 - 3*2 - 4*5 - 4*6[/tex]

Subject to:

[tex]x1 + x2 + s1 = 4000\\x3 - (1/3)*1 + (1/3)*5 = 0\\x4 - (1/3)*2 + (1/2)*6 = 0\\x3*1 + 3*2 + 3*3 + 3*4 + 3*5 + 2*6 + s2 = 6000[/tex]

All variables are non-negative.

Tableau

 x1  x2  x3  x4  x5  x6  s1  s2   b

Z -3 -3 7 6 18 14 0 0 0

s1 1 1 0 0 0 0 1 0 4000

s2 3 3 3 3 3 2 0 1 6000

x5 0 0 1 0 1/3 0 0 0 0

x6 0 0 0 1 0 1/2 0 0 0

The basic variables are s1, s2, x5, and x6.

Step 1: Choose  entering variable. The most positive coefficient in objective row is 18, corresponding to x5. x5 enters the basis.

Step 2: Choose the leaving variable. The minimum ratio of right-hand side to coefficient of x5 is 12000/(1/3) = 36000,

corresponding to s1. s1 leaves the basis.

Step 3: Perform, pivot operation to make x5 the basic variable for s1. Divide, pivot row by 1/3 and subtract appropriate multiples of the pivot row from other rows to make other entries in column 5 zero.

 x1    x2    x3    x4     x5     x6   s1    s2       b

Z -3 -3 7 6 18 14 0 0 0

x5 0 0 1 0 1/3 0 0 0 0

s2 3 3 3 3 2 2/3 2/3 0 1/3 24000

x3 1 0 1/3 0 1/3 0 -1/3 0 0

x4 0 1 0 1/3 0 1/2 -1/6 0 0

The basic variables are x5, x3, x4, and s2.

Step 4: Choose the entering variable. The most positive coefficient in the objective row is 7, corresponding to x3. x3 enters the basis.

Step 5: Determine the leaving variable. The right-hand side's minimum ratio to the coefficient of x3 is 0, indicating that x3 can be increased without bound. This implies that the optimal solution is unbounded and that there is no finite optimal value for the problem.

As a result, the simplex algorithm demonstrates that the given linear programming problem lacks a feasible solution. This means that it is not possible to meet all of the constraints at the same time.

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The IQR is the best measure of variability, and it equals 45.

Data variation can be caused by a variety of sources. Variability is also known as data spread. The standard deviation is a measure of variability since it measures the spread of data.

The range is the best measure of variability for the data shown, and its value is 45.

The range is defined as the difference between the largest and smallest values in a set of data.

In this case, the largest score is 88 and the smallest score is 20, so the range is 88 - 20 = 68.

The IQR (interquartile range) is another measure of variability, but it is not the best measure for this data set because the data set has only a few values and does not form a normal distribution. The IQR is a more appropriate measure for larger data sets that form a normal distribution.

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