You want to quit your job and return to school for an MBA degree 3 years from now, and
you plan to save $4,500 per year, beginning immediately. You will make 3 deposits in an
account that pays 5.2% interest. Under these assumptions, how much will you have 3 years from
today?
a. $14,953.30
b. $18,392.56
c. $12,560.78
d. $11,663.58
e. $16,747.70

The piecewise function for f(x) is f(x) = x - 2, x ≥ 2; -x + 2, x < 2, So the correct answer is option C.

In mathematics, a function is a rule that assigns each element of a set (called the domain) to a unique element of another set (called the range). Functions are a fundamental concept in mathematics and are used to describe relationships between variables, as well as to model and solve a wide range of mathematical problems.

A function is typically denoted using a letter such as "f", and is defined by an equation or formula that specifies how the input (or domain) values are transformed into output (or range) values. For example, the function "f(x) = 2x + 1" assigns each input value "x" to an output value equal to twice the input value plus one.

The absolute value function f(x) = |x - 2| can be written as a piecewise function by separating it into two cases:

Case 1: x - 2 ≥ 0 or x ≥ 2

In this case, the expression inside the absolute value bars becomes x - 2, so f(x) = x - 2.

Case 2: x - 2 < 0 or x < 2

In this case, the expression inside the absolute value bars becomes -(x - 2) = -x + 2, so f(x) = -x + 2.

Therefore, the piecewise function for f(x) is:

f(x) =

x - 2, x ≥ 2

-x + 2, x < 2

So the correct answer is option C.

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Answer: Hope this helps ;)

Step-by-step explanation:

Answer: 1 [tex]\frac{1}{2}[/tex]

Step-by-step explanation: Turn the mixed fraction into improper fraction, which is 9/4 and 15/4. Subtract 15/4 and 9/4 to get 3/2. Convert 3/2 into mixed number to get 1 1/2

hope it helps!!

Option B is the most expensive, with a total cost of $240 per month if the patient fills 7 prescriptions per month.

To determine which option is the most expensive, we need to calculate the total cost for each option if the patient fills 7 prescriptions per month.

For Option A, the total cost would be:

(7 x $15) + $105 = $210

For Option B, the total cost would be:

(7 x $20) + $100 = $240

For Option C, the total cost would be:

(7 x $10) + $115 = $185

For Option D, the total cost would be:

(7 x $12) + $110 = $194

Therefore, Option B is the most expensive, with a total cost of $240 per month if the patient fills 7 prescriptions per month. The other options are cheaper, with Option C being the least expensive at $185 per month.

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Answer:

perimeter=68cm

area=289cm^2

Step-by-step explanation:

the perimeter is 17+17+17+17=68cm

the area is 17×17=289cm^2

Answer:

For the Triangle it is 3 and for the quadrilateral,(trapezoid) it is 10.5

Step-by-step explanation:

for the triangle do bxh/2. and for the trapezoid divide it into a square and triangle.

Answer:

55ft2

Step-by-step explanation:

Find the area of the added rectangle

-23 - -21 = 2ft

12-7 = 5ft

A=bh = 2ft x 5ft = 10ft^2

add old area and new area

45ft^2 + 10ft^2 = 55ft^2

Answer:

55 ft2

Step-by-step explanation:

Since the x values are -21 and -23, it shows that they are 2 points away from eachother. They y values are 7 and 12 so they are 5 points away from eachother. Multiply 2 x 5 = 10 which is the area of the new garden. Since the old garden is 45 square feet, add 10 + 45 to get 55 square feet total.

Answer:

90

Step-by-step explanation:

this is the pattern: +3, *2, +3, *2, +3

so theoretically the next number would be 90.

The next number is 90.

If you observe the pattern the second number is +3 of the first number and the third number is ×2 of the second number following this pattern.

6+3=9

9×2=18

18+3=21

21×2=42

42+3=45

45×2=90

Therefore 90 is the right answer.

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The probability of each event is: P(A) = 0.34 P(B) = 0.66 P(C) = 0.89

What is Probability ?

Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.

To find the cdf F(x) of X, we can use the following formula:

F(x) = P(X ≤ x) = ∑ P(X = k) for k ≤ x

So we have:

F(0) = P(X ≤ 0) = P(X = 0) = 0.11

F(1) = P(X ≤ 1) = P(X = 0) + P(X = 1) = 0.11 + 0.23 = 0.34

F(2) = P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.11 + 0.23 + 0.25 = 0.59

F(3) = P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.11 + 0.23 + 0.25 + 0.3 = 0.89

F(4) = P(X ≤ 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.11 + 0.23 + 0.25 + 0.3 + 0.35 = 1

So the cdf F(x) of X is:

F(x) = 0 for x < 0

F(x) = 0.11 for 0 ≤ x < 1

F(x) = 0.34 for 1 ≤ x < 2

F(x) = 0.59 for 2 ≤ x < 3

F(x) = 0.89 for 3 ≤ x < 4

F(x) = 1 for x ≥ 4

b. To calculate the probability of the events A = {fewer than two lines are in use}, B = {at least two lines are in use}, C = {between one and five lines, inclusive, are in use}, we can use the cdf F(x) that we just found.

P(A) = P(X < 2) = F(1) = 0.34

P(B) = P(X ≥ 2) = 1 - P(X < 2) = 1 - F(1) = 1 - 0.34 = 0.66

P(C) = P(1 ≤ X ≤ 5) = F(5) - F(0) = 1 - 0.11 = 0.89

Therefore, the probability of each event is: P(A) = 0.34 P(B) = 0.66 P(C) = 0.89

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Answer:

In a parallelogram opposite sides are parallel to each other

Step-by-step explanation:

the opposite sides are equal that's why it is called parallelogram

Answer:

Step-by-step explanation:

1st box: it mentions "Quotient" meaning divide, if you look at the answer choices only 1 of them has division sign (the fraction one, division can e seen with ÷ or as a fraction)

2nd box: mentions "less" meaning subtract,  there are two answer choices with a subtraction sign, do note subtraction-related word problems are counter intuitive (the opposite of what you would think).  You would think its 5-x since it mentions "5"  then the "n" BUT, if you think it about it, the problem is saying there taking 5 away FROM n, so, its x-5

3rd box: it mentions "sum" meaning addition, and "twice a number" meaning 2n. So, its 2n +9

4th box: it mentions " 2 times the sum of" pay attention to the "of" part because it signifies that the "2" part of this problem is multiplied by a conjunction of two terms. So its 2(n+9)

**you could use your deductive reasoning skills to figure it out. Since the problem mentions addition and since the answer choices leave you with one addition-related answer choice, it has to be 2(n+9)**

5th box: it mentions "product" meaning multiply, also mentions "3 times a number" meaning 3n. So its, (3n)(7)

6th box:  After solving the previous 5 problems, the only answer is 5-n=x, so that's the answer for the 6th box

~lmk if u got Qs

Hours, h Total Cost

1 14

2 18

3 22

4 26

Complex algorithms frequently employ variable words to demonstrate coherence between two opposing assertions. Equations are academic expressions that are used to demonstrate the equality of different academic figures. In this case, leveling generates b + 7 rather than another algorithm that could divide 12 into two parts, evaluate the information provided by y + 7, and generate y + 7.

Here,

To find the total cost of renting the golf clubs for h hours, we can use the expression:

Total Cost = 10 + 4h

We can use this expression to complete the table as follows:

Hours, h Total Cost

1 10 + 4(1) = 14

2 10 + 4(2) = 18

3 10 + 4(3) = 22

4 10 + 4(4) = 26

Therefore, the completed table is:

Hours, h Total Cost

1 14

2 18

3 22

4 26

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Answer:

98 degrees

Step-by-step explanation:

angle 3 and angle 4 are supplementary angles, since they together add up to 180 degrees.

Since we know angle 3, we can subtract that from 180 degrees to find angle 4:

180 - 82 = 98.

Therefore, angle 4 is 98 degrees.

Most times, questionnaire, which involves list of questions or items. are  used to gather data from respondents about their attitudes, experiences, or opinions. It helps to collect quantitative and/or qualitative information.

Please provide accurate information to the best of your knowledge. Your personal information will not be disclosed.

Thank you for your participation.

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Answer:

JEWS = LIES

BLACK PPL(LIKE ME) =TRUTH

:}

Step-by-step explanation:

This question cannot be answered

Please post the diagram/chart.

Answer: there should be a diagram but where is it

Step-by-step explanation:

Answer: x times 3

Step-by-step explanation:

marks up the electric stove's wholesale price 10%. Ignoring tax, how much would he

pay for the electric stove at this store?

$0

(b)

Joe then looks at the electric stove in a department store that marks up the electric stove's wholesale price 30%.

But because of a customer loyalty program, he would receive a 20% discount off the in-store price. Ignoring tax,

how much would he pay for the electric stove at this store?

$0

(C)

Select the true statement.

Answer:

A fancy way of saying "solutions" of the equation

After answering the provided question, we can state that Therefore, the parallelograms measure of angle C is 63°.

In Euclidean geometry, a parallelogram is a simple quadrilateral with two sets of parallel sides. A parallelogram is a type of quadrilateral in which both sets of opposite sides are parallel and equal. Parallelograms are classified into four types, three of which are unique. The four different shapes are parallelograms, squares, rectangles, and rhombuses. A quadrilateral is a parallelogram when it has two sets of parallel sides. The opposing sides and angles of a parallelogram are both the same length. The interior angles on the same side of the horizontal line are also angles. 360 degrees is the total number of interior angles.

Since ABCD is a parallelogram, opposite angles are congruent. Therefore,

m∠A = m∠C

13x - 41 = 6x + 15

7x = 56

x = 8

m∠C = 6(8) + 15 = 63

Therefore, the measure of angle C is 63°.

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Answer: 4.2

Step-by-step explanation:

The snow that will be gotten daily of the line plot is redistributed equally will be 1/2.

A line plot, also known as a line graph, is a type of graph that displays information as a series of data points connected by straight lines. Line plots are often used to show how a particular variable changes over time or to compare two or more variables.

To create a line plot, you typically need to have a set of data points that represent the variable you want to graph. You then plot each data point on a graph, with the x-axis representing time or some other variable, and the y-axis representing the value of the variable you're graphing.

The snow that will be gotten daily of the line plot is redistributed equally will be:

= (1/8 + 2/8 + 3/8 + 4/8 + 5/8 + 6/8 + 7/8 + 8/8) / 9

= 36/8 / 9

= 1/2

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The total area square feet of bark dust should Jon Marc order is 839.1 square feet.

What is area?

The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.

Here we know that , area of the circle = [tex]\pi r^2[/tex] square unit.

Now radius of one flower bed = 6.5 feet. Then,

Area of the bed = [tex]3.14\times 6.5^2[/tex] = 132.6 square feet,

Now diameter of another bed = 30 feet then,

Radius = 30/2 = 15 feet. Then

Area of the bed  = [tex]3.14\times15^2[/tex] = 706.5 square feet.

Then total square feet of bark dust should Jon Marc order is

=> 132.6 + 706.5 = 839.1 square feet.

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Therefore , the solution of the given problem of unitary method comes out to be  able to afford the festival because 120 is larger than 70.

To accomplish the task, one may use this generally accepted ease, preexisting variables, as well as any significant components from the original Diocesan customizable query. If so, there might be an opportunity to interact with the item once more. Otherwise, every significant factor that affects how algorithmic evidence behaves will be gone.

Here,

The following chart allows us to determine each person's earnings:

=> Person 1: 2 hours times $8 per hour  =  $16

=>  Person 2: $4 hours x $8 per hour  =  $32 per person

=>Person  3: 3 hours x $8 per hour = $24 per person.

=> Person 4: 5 hours x $8 per hour  =  $40.

=> Person 5: One hour times $8 per hour equals $8.

Each person needs to bring at least $70 in order to join the festival. As a result, the disparity shown below can be used to describe this circumstance:

=> 16 + 32 + 24 + 40 + 8 ≥ 70

Simplifying the inequality's left side, we obtain:

=> 120 ≥ 70

We can infer that all of the friends were able to afford the festival because 120 is larger than 70.

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Answer:

perimeter =the circumference around the semicircle

22/7×34/2

=53.43cm

area = (22/7×17^2)/2

454.14cm^2

Answer :

Step-by-step explanation :

Question :

Find the perimeter and area of the semicircle.

Given : Diameter = 14 cm

Radius = 14/2 = 7 cm

Solution :

Perimeter of semicircle = πr + d

[tex]\longrightarrow \: \: \dfrac{22}{7} \times 7 + 14 \\ \\ \longrightarrow \: \: 22 + 14 \\ \\ \longrightarrow \: \: 36 \: cm \\ [/tex]

Area of semicircle = 1/2 πr²

[tex]\longrightarrow \: \: \dfrac{1}{2} \times \dfrac{22}{7} \times {(7)}^{2} \\ \\ \longrightarrow \: \: \frac{22}{14} \times 7 \times 7 \\ \\ \longrightarrow \: \: \frac{1078}{14} \\ \\ \longrightarrow \: \: 77 \: {cm}^{2} \\ \\ [/tex]

Answer:

Option B. 5 and one-third units. The value of a in triangle XYZ is 5 and two-thirds units. This is found using the Pythagorean theorem twice and solving for a.

To find the value of a, we can use the Pythagorean theorem in triangles WZY and WYX as follows:

In triangle WZY:

[tex]c^2 = 3^2 + (a + 4)^2[/tex]

In triangle WYX:

[tex]b^2 = 4^2 + a^2[/tex]

Since angle ZWX is a right angle, we can use the Pythagorean theorem in triangle ZWX as follows:

[tex]ZWX^2 = ZW^2 + WX^2[/tex]

We know that ZW = c and WX = b, so we have:

[tex]a^2 + b^2 = c^2[/tex]

Substituting[tex]c^2[/tex] in terms of a and simplifying, we get:

[tex]a^2 + b^2 = 25 + (a + 4)^2[/tex]

Expanding and simplifying, we get:

[tex]a^2 + b^2 = a^2 + 8a + 41[/tex]

Subtracting [tex]a^2[/tex] from both sides, we get:

[tex]b^2 = 8a + 41[/tex]

Substituting [tex]b^2[/tex] in terms of a in the equation [tex]a^2 + b^2 = c^2[/tex], we get:

[tex]a^2 + 8a + 41 = c^2[/tex]

Substituting[tex]c^2[/tex] in terms of a from the equation for triangle WZY, we get:

[tex]a^2 + 8a + 41 = 9 + (a + 4)^2/16[/tex]

Expanding and simplifying, we get:

[tex]16a^2 + 128a + 656 = 9a^2 + 50a + 97[/tex]

Simplifying further, we get:

[tex]7a^2 + 78a - 559 = 0[/tex]

Using the quadratic formula, we get:

[tex]a = (-78 ± sqrt(78^2 + 4(7)(559))) / 14[/tex]

a = (-78 ± sqrt(49379)) / 14

Since a represents a length in a triangle, it must be positive. Therefore, we have:

a = (sqrt(49379) - 78) / 14 ≈ 6.67

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Triangle X Y Z is shown. Angle Z W X is a right angle. An altitude is drawn from point W to point Y on side Z X to form a right angle. The length of W Y is 4, the length of Y X is a, the length of Z Y is 3, the length of Z W is c, and the length of W X is b.

What is the value of a?

A. 5 units

B. 5 and one-third units

C. 6 and two-thirds units

D. 7 units

Step-by-step explanation:

The answers to the given numerical expressions are:

(12-5)^2 + (-18) x 4 = 49 + (-72) = -23

4^3 + (15-3) ÷ 2 = 64 + 6 = 70

Answer:

Step-by-step explanation:

linear function

straight line

In given Histogram, The fraction of shows that was more than half full was 2/3 i.e. C.

What exactly is a histogram?

A histogram is a graphical depiction of numerical data distribution. It entails splitting the data range into intervals or bins and counting how many data points fall into each bin. Bins are often stated as non-overlapping, sequential intervals of a variable. The count or frequency of data points in the respective bin is represented by the height of each bar on the graph. Histograms are often used in statistics to illustrate data distribution and to find trends, outliers, and other data properties.

Now,

Given that

Total shows shown were=3+0+7+10+7+3=30

Show which has more than 150 viewers=1+7+3=20

then,

The fraction of shows that was more than half full =20/30⇒2/3.

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Answer:8.85cm

Step-by-step explanation:

we need to use sinuses theorem:

[tex]\frac{13.5}{sin90} =\frac{x}{sin41} \\sin90=1\\13.5 =\frac{x}{sin41} \\\\13.5*sin41=x\\sin41=0.65\\x=8.85[/tex]

the total area under the normal distribution curve is 0.9632.

How to find  total area under the normal distribution curve?

To find the total area under the normal distribution curve, we can use the standard normal distribution table or a calculator with a normal distribution function. We need to find the areas to the left and right of the given z-scores and add them together.

First, we can find the area to the left of z = -2.15 using the standard normal distribution table or a calculator with a normal distribution function. The area to the left of z = -2.15 is the same as the cumulative probability of a standard normal distribution with a z-score of -2.15. Using a standard normal distribution table or a calculator, we find this area to be 0.0158.

Next, we can find the area to the right of z = 1.62 using the standard normal distribution table or a calculator with a normal distribution function. The area to the right of z = 1.62 is the same as the complement of the cumulative probability of a standard normal distribution with a z-score of 1.62. Using a standard normal distribution table or a calculator, we find the complement to be 0.0526. Therefore, the area to the right of z = 1.62 is 1 - 0.0526 = 0.9474.

Finally, we can add the area to the left of z = -2.15 and the area to the right of z = 1.62 to find the total area under the normal distribution curve:

S = area to the left of z = -2.15 + area to the right of z = 1.62

S = 0.0158 + 0.9474

S = 0.9632

Therefore, the total area under the normal distribution curve is 0.9632.

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