After graduating from college, Carlos receives two different job offers. Both pay a starting salary of $65000 per year, but one job promises a $3250 raise per year, while the other guarantees a 4% raise each year. Complete the tables below to determine what his salary will be after t years. Round your answers to the nearest dollar.
Answers
Given:
• Starting salary of each Job = $65000
,• Job 1 promises a $3250 raise per year
,• Job 2 promises a 4% raise each year.
Let's complete the given tables.
The equation to represent job 1 will be a linear equation:
y = 3250t + 65000
The equation which represents job 2 will be an exponential equation:
[tex]\begin{gathered} y=65000\mleft(1+0.04\mright)^t \\ \\ y=65000(1.04)^t \end{gathered}[/tex]Now, to complete the tables, input the different values of t into the equation and solve for y.
• For Job 1, we have the following:
• When t = 1:
y = 3250(1) + 65000 = 68250
• When t = 5:
y = 3250(5) + 65000
y = 16250 + 65000
y = 81250
• When t = 10:
y = 3250(10) + 65000
y = 32500 + 65000
y = 97500
• When t = 15:
y = 3250(15) + 65000
y =48750 + 65000
y = 113750
• When t = 20:
y = 3250(20) + 65000
y = 65000 + 65000
y = 130000
• For Job 2, we have the folllowing:
• When t = 1:
y = 65000(1.04)¹
y = 67600
• When t = 5
y = 65000(1.04)⁵
y = 65000(1.216652902)
y = 79082
• When t = 10:
y = 65000(1.04)¹⁰
y = 65000(1.480244285)
y = 96216
• When t = 15:
y = 65000(1.04)¹⁵
y = 65000(1.800943506)
y = 117061
• When t = 20
y = 65000(1.04)²⁰
y = 65000(2.191123143)
y = 142423
Therefore, we have the complete table below:
Related Questions
A rose garden is formed by joining a rectangle and a semicircle, as shown below. The rectangle is 26 ft long and 18 ft wide.
Find the area of the garden. Use the value 3.14 for pi, and do not round your answer. Be sure to include the correct unit in your answer.
Answers
The area of the rose garden formed by joining a rectangle and a semicircle is 595.17 ft².
How to find the area of a composite figure?The rose garden is formed by joining a rectangle and a semicircle. The rectangle is 26 ft long and 18 ft wide.
The area of the garden can be found as follows:
area of the garden = area of the rectangle + area of the semi circle
Therefore
area of the garden = lw + 1 / 2πr²
l = 26 ft
w = 18 ft
r = 18 / 2 = 9 ft
area of the garden = 26 × 18 + 1 / 2 × 3.14 × 9²
area of the garden = 468 + 254.34 / 2
area of the garden = 468 + 127.17
area of the garden = 595.17 ft²
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A recipe for flour requires 2 cups of flour, 1 cup of shortening, and 1 cup of milk and makes 1 dozen biscuits. how many biscuits can you make of you triple the recipe?
Answers
The given recipe for 1 dozen biscuits is
• 2 cups of flour.
,• 1 cup of shortening.
,• 1 cup of milk.
Now, we have to multiply each number by 3 in order to triple the recipe. So, the recipe for 3 dozens is
• 6 cups of flour.
,• 3 cups of shortening.
,• 3 cups of milk.
Hence, the total number of biscuits obtained from the new recipe is 36, which is equivalent to 3 dozens.findind percent proportions
Answers
Thus, the boys percantage is 45%.
ABC reflected across the x-axis and then dilated by a factor of 12
Answers
Solution:
Given the figure;
The reflection rule across the x-axis is;
[tex]P(x,y)\rightarrow P^{\prime}(x,-y)[/tex]Thus, the point A(3,1) after reflection is;
[tex]A(3,1)\rightarrow A^{\prime}(3,-1)[/tex]Then, dilated by a factor of 2 using the point (-2,1) as the center of dilation.
Thus;
[tex]\begin{gathered} A^{\prime}(3,-1) \\ (-2,1) \\ \\ A^{\prime}(5,-2) \\ \\ A^{\prime}(5,-2)\rightarrow2(5,-2)\rightarrow(10,-4) \\ \\ A^“(10,-4) \\ (-2,1) \\ \\ A^“(8,-3) \\ \\ \end{gathered}[/tex]CORRECT OPTION: (B) A"(8,-3)
Cooper wrote checks on his checking account for $20 and $35. he also deposited $63 in the account. witch number describes the change in the balance of his account
Answers
The checks he wrote are withdraw from his account, so the amounts will be substracted from its balance.
The deposit, on the contrary, will add to the balance of his account.
Then, the net change in his account will be:
[tex]\Delta=-20-35+63=8[/tex]The net change in the balance of his account is $8, increasing the original balance.
identify the table that would correctly graph the equation y=3x
Answers
To be able to determine which table would correctly graph the equation y = 3x, let's one pair of data in the table and substitute it to the equation. The data that satisfies the equation is therefore the one that would correctly graph the equation.
We get,
A.) x = 0 and y = 2
y = 3x
2 = 3(0)
2 = 0
Therefore, this table will not correctly graph the equation.
B.) x = 0 and y = 4
y = 3x
4 = 3(0)
4 = 0
Therefore, this table will not correctly graph the equation.
C.) x = 0 and y = 1
y = 3x
1 = 3(0)
1 = 0
Therefore, this table will not correctly graph the equation.
D.) x = 0 and y = 0
y = 3x
0 = 3(0)
0 = 0
Therefore, this table will correctly graph the equation.
The answer is letter D.
1. Type the number only, no variables. 5 10 8 Your answer
Answers
given expression :
[tex]\begin{gathered} \frac{5}{8}=\frac{10}{x} \\ \text{Apply cross multiplication} \\ 5x=10\times8 \\ x=\frac{80}{5} \\ x=16 \end{gathered}[/tex]Answer : 16
I have a question where I need to graph a hyperbola equation and all I am given is the equation Picture included
Answers
Given
The equation of the hyperbola is:
[tex]\frac{y^2}{9}\text{ -x}^2\text{ = 1}[/tex]We can see that this is a vertical hyperbola since y is positive.
The general equation of a vertical hyperbola is:
[tex]\begin{gathered} \frac{(y-k)^2}{a^2}\text{ -}\frac{(x\text{ -h})^2}{b^2}=\text{ 1} \\ Where\text{ }(h,k)\text{ is the center} \end{gathered}[/tex]The steps to graph a hyperbola are:
1. Determine if it is horizontal or vertical. Find the center point, a, and b.
2. Graph the center point.
3. Use the a value to find the two vertices.
4. Use the b value to draw the guiding box and asymptotes.
5. Draw the hyperbola.
Step 1: This hyperbola is vertical
center point = (0,0)
Step 2: The values of a and b
[tex]\begin{gathered} a^2=\text{ 9} \\ a\text{ = 3} \\ b^2\text{ = 1} \\ b\text{ = 1} \end{gathered}[/tex]Step 3: Draw the guiding box:
Step 4: Draw the asymptotes
The asymptotes are diagonal lines through the corners of the box
Step 5: Finally, we draw in our hyperbola. Each half starts at the vertex and continues towards the asymptotes but never actually reaches them.
Step 6:
The center point, guiding box, and asymptotes are not technically part of the answer, so a clean version of the graph would look like this:
The graph of the hyperbola is shown below:
East High School has 540 students. There are 220 girls in the school. What is the ratio of girls to boys at East High School?
Answers
11/16
1) Gathering the data
540 students
220 girls
540-220= 320
320 boys
2) Let's find out the ratio of girls to boys
Placing the number of girls in the numerator, and subsequently the number of boys as the denominator
Then simplify :
So we can state there's a ration of 11/16
There are 11 girls to 16 boys in that school
Please help:y = x + 4y = x^4Graph your system of equations and show the solution graphically to verify your solution.
Answers
Given:
[tex]\begin{gathered} y=x+4 \\ y=x^4 \end{gathered}[/tex]Graphing:
green line is y = x + 4
blue line is y = x^4
The solutions are:
(-1.28, 2.72) and (1.53, 5.53)
Answer: (-1.28, 2.72) and (1.53, 5.53)
HELP ASAP!!!
The mapping diagram represents a relation where x represents the independent variable and y represents the dependent variable.
A mapping diagram with one circle labeled x-values containing values negative 4, negative 2, 0, 1, and 3 and another circle labeled y values containing values negative 5, negative 4, negative 3, negative 2, and negative 1 and arrows from negative 4 to negative 5, negative 2 to negative 3, 0 to negative 4, 0 to negative 2, 1 to negative 3, and 3 to negative 1.
Is the relation a function? Explain.
No, because for each input there is not exactly one output
No, because for each output there is not exactly one input
Yes, because for each input there is exactly one output
Yes, because for each output there is exactly one input
Answers
Answer:
This relation is not a function. For each input, there is not exactly one output.
The relationship in the given diagram is not a function, because for each input there is not exactly one output. So Option A is correct
What are functions?Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).
Vertical line test:-
Whenever we want to check whether a given expression is a function or not we can apply a vertical line test, in this test we check for a single image of x , we are getting a single image or more.
If we get more images then it will not be a function.
For example, let us take, y² = 4ax
y = ±√4ax
For single value of x we get two values of y
Hence, it will not be a function.
Given that,
Values of x and values of y
In given diagram,
for x = 0,
there are two values of y, -4 and -2
but according to definition of y, it should give only one value
Hence, it is not a function
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20x -y= 250 solve for y
Answers
y = 20x - 250
The perimeter of rectangle A is 10 cm and its area is 6 cm2. The perimeter of rectangle B is 20 cm. What is the area of rectangle B assuming these two rectangles are similar?
Answers
The perimeter of rectangle A is 10 cm
Perimeter of A = 2x+2y=10 cm, then:
Perimeter of A = 2(x+y)=10
Perimeter of A = x+y=5
We also know that the area of A= xy= 6 cm²
Then, we can admit x=3 and y=2.
Both rectangles are similar.
[tex]\frac{x_a}{y_a_{}}=\frac{x_b}{y_b}[/tex][tex]\begin{gathered} \frac{3}{2}=\frac{x_b}{y_b} \\ x_b=\frac{3y_b}{2_{}} \end{gathered}[/tex]Perimeter of B
[tex]\begin{gathered} 2x_b+2y_b=20 \\ x_b+y_b=10 \\ \frac{3y_b}{2}+y_b=10 \\ 3y_b+2y_b=20 \\ 5y_b=20 \\ y_b=4 \end{gathered}[/tex][tex]\begin{gathered} x_b=\frac{3y_b}{2} \\ x_b=\frac{3\cdot4}{2} \\ x_b=\frac{12}{2} \\ x_b=6 \end{gathered}[/tex]Therefore
Area of B = 4 x 6 cm² = 24 cm²
true or false : the equation below is too complicated to use the isolate the radical then square both sides
Answers
The equation is [tex]\frac{\sqrt{x+3} }{\sqrt{x+1} }=3[/tex] is not true.
Given that,
The radical must first be isolated before both sides of the following equation may be squared.
The equation is [tex]\frac{\sqrt{x+3} }{\sqrt{x+1} }=3[/tex]
We have to say the equation is true or false.
The result of multiplying an integer by itself is known as the square root of the number. The radical sign represents the square root. As an illustration, √16 = 4. The radical symbol is also known as the root symbol or surds.
Take Left hand side.
[tex]\frac{\sqrt{x+3} }{\sqrt{x+1} }[/tex]
Root is
[tex]\sqrt{\frac{x+3}{x+1}}[/tex]
The right hand side is 3
The left hand side ≠ right hand side.
Therefore, The equation is [tex]\frac{\sqrt{x+3} }{\sqrt{x+1} }=3[/tex] is not true.
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I need help please give me an answer for this.
Answers
surface area of the net pyramid is 125 in²
Explanation:Surface area of a net pyamid is calculated as:
[tex]S\mathrm{}A\text{ = area of base + }\frac{1}{2}perimeter\text{ of base }\times slant\text{ height}[/tex]side of the base = 5 in
Area of the base = area of square
Area of the base = (side of the base)² = 5²
Area of base = 25 in²
Perimeter of base = perimeter of square
Perimeter of base = 4(side of the base) = 4(5)
Perimeter of base = 20 in
slant height = 10 in
Inserting the values into the formula for surface area:
[tex]\begin{gathered} S.A\text{ = }25\text{ + }\frac{1}{2}(20)(10) \\ S.A\text{ = }25\text{ + 100} \\ S\mathrm{}A\text{ = 125 in}^{2} \end{gathered}[/tex]The functions f(x), g(x), and h(x) are shown below. Select the option that represents the ordering of the functions according to their average rates of change on the interval 2−2≤x≤2 goes from least to greatest.
Answers
SOLUTION:
The formula for the average rate of change of a function is;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]For f(x);
[tex]\begin{gathered} m=\frac{30-(-10)}{2-(-2)} \\ m=10 \end{gathered}[/tex]For (x):
[tex]\begin{gathered} m=\frac{10-46}{2-(-2)}= \\ m=-9 \end{gathered}[/tex]For h(x):
[tex]\begin{gathered} m=\frac{h(2)-h(-2)}{2-(-2)} \\ m=\frac{(-2^2-5(2)+25)-(-(-2)^2-5(-2)+25)}{2-(-2)} \\ m=-5 \end{gathered}[/tex]From this calculation, ranking the average rateof change from least to greatest, swe have;
[tex]g(x),h(x),f(x)[/tex]15
Be sure to read the directions carefully and write what is asked for.
Part A: Multiply (without simplifying your answer): 5√12 2√/6 =
Part B: What perfect square can you take out of the radicand from Part A's answer?
Part C: After simplifying, what is the final answer to Part A?
Answers
The product of radical numbers is 10√72. The simplest form of the radical part is 60√2.
What is the meaning of radical?
The square root or nth root is represented by the symbol √. Expression with a square root is referred to as a radical expression. Radicand: A value or phrase included within the radical symbol. Equation with radical expressions and variables as radicands is referred to as a radical equation.
Given numbers are 5√12 and 2√6.
Now multiply the given numbers:
5√12 × 2√12
Multiply whole number with whole number and radical part with radical part:
=(5 × 2) × (√12 ×√6)
= 10 × √72
= 10√72
= 10 √(6 × 6 × 2)
Take out perfect square of the radicand:
= 10 × 6 √( 2)
= 60√2
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For questions 8 - 10, find all the solutions for x.8. 2x 4+14= 229. 8x +19 -54 +3x?10. 7x² + 12 =51- 4x?
Answers
x = 2 or x = -2
Explanation:8) 2x² + 14 = 22
collect like terms by subtracting14 from both sides of the equation:
2x² + 14 - 14 = 22 - 14
2x² + 0 = 8
2x² = 8
DIvide both sides by 2:
2x²/2 = 8/2
x² = 4
Square root both sides of the equation:
[tex]\begin{gathered} \sqrt[]{x^2}\text{ = }\pm\sqrt[]{4} \\ x\text{ =}\pm2 \\ \pm2\text{ = +2 or -2} \\ x\text{ =2 or x = -2} \end{gathered}[/tex]The figure shows two parallel lines AB and De cut by the transversals AE and BD ( in the picture ) Which statement best explains the relationship between ABC and EDC? A) ABC - EDC because m<3 = m<6 and m<1 = m<4B) ABC - EDC because m<3 = m<4 and m<1 = m<5 C) ABC = EDC because m<3 = m<4 and m<1 = m<5D) ABC = EDC because m<3 = m<6 and m<61 = m<4
Answers
ANSWER:
2nd option: ΔABC ~ ΔEDC, because m<3 = m<4 and m<1 = m<5
STEP-BY-STEP EXPLANATION:
In order to answer the question we must take into account the difference between similarity and congruence.
We can see it in the following image:
That is, similar have the same figure but not the same size, while congruent have the same size and the same figure.
We can see that in this case the triangles are similar, we know this since angles 3 and 4 are equal because they share a vertex.
So the correct answer is the 2nd option: ΔABC ~ ΔEDC, because m<3 = m<4 and m<1 = m<5
Claim: Most adults erase all of their personal information online if they could. A software firm survey of randomly selected adults showed that % of them would erase all of their personal information online if they could. Make a subjective estimate to decide whether the results are significantly low or significantly high, then state a conclusion about the original claim.
Answers
Claim: Most adults would erase all of their personal information online if they could
Sample size: 625
Yes: 50.3%
The null hypothesis, due to randomness, is p = 0.5. From the results, the claim states that p > 0.5, and the result of the survey is p = 0.503.
The result is close to the null hypothesis, so we can conclude that there is no significant evidence for the claim.
Answer:
The results are not significantly high so there is not sufficient evidence to support the claim.
If the area of a rectangle is 60 cm and the length is 5cm and the width is (x+4) find x
Answers
Answer:
8
Step-by-step explanation:
A=length*width
60=5*(x+4)
60=5x+20
40=5x subtract 20 from both sides
8=x divide by 5 on both sides
x=8
The points represented by the table lie on a line. How can you find the slope of the line from the table? What is the slope of the line? Х 2 4 6 8 y 5 1 -3 -7
Answers
The given table is
x 2 4 6 8
y 5 1 -3 -7
The formula for determining the slope of a line is expressed as
slope = (y2 - y1)/(x2 - x1)
From the table,
x1 = 2, x2 = 4
y1 = 5, y2 = 1
Slope = (1 - 5)/(4 - 2)
Slope = - 4/2
Slope = - 2
If $2000 is invested at 7% compounded continuously, what is the amount after 3 years?
Answers
Given:
Amount = $2000
rate = 7%
time = 3 year
Amount after 3 year is:
[tex]A=Pe^{rt}^{}[/tex]Where:
[tex]\begin{gathered} P\text{ = initial amount} \\ r=\text{rate} \\ t=\text{ time} \\ A=\text{ amount after t time } \end{gathered}[/tex][tex]\begin{gathered} rate=\frac{7}{100}^{} \\ =0.07 \end{gathered}[/tex][tex]\begin{gathered} A=2000e^{0.07\times3} \\ =2000e^{0.21} \\ =2000\times1.233 \\ =2467.35 \end{gathered}[/tex]After 3 year amount is 2467.35
A room is measured to be 10.0m long, 5.6m wide and 155 m high.What is the volume of the room?What is the mass in kilograms of smoke inside the room if it’s density is 1.506kg/m^3?
Answers
The rule of the volume of the solid shaped a rectangular solid is
[tex]V=L\times W\times H[/tex]L is the length
W is the width
H is the height
Since the dimensions of the room are
10 m long
5.6 m wide
155 m high
Then
L = 10
W = 5.6
H = 155
Substitute them in the rule above
[tex]\begin{gathered} V=10\times5.6\times155 \\ V=8680m^3 \end{gathered}[/tex]The volume of the room is 8680 cubic meters
The rule of the mass is
[tex]m=d\times V[/tex]m is the mass
d is the density
V is the volume
Since the density is 1.506 kg/m^3
Then d = 1.506
Since the volume is 8680 m^3
Then
[tex]\begin{gathered} m=1.506\times8680 \\ m=13072.08\operatorname{kg} \end{gathered}[/tex]The mass of the smoke inside the room is 13072.08 kg
A GPA is usually an example of a a. b. mean bimodal distribution trimodal distribution weighted average C. d. 48
Answers
I find the following data for the concept GPA:
Your GPA is calculated in two steps:
The grade awarded for each course is multiplied by the credit value for each course.
The aggregate score is divided by the total number of credits for all courses completed in the defined period of study.
So, the weighted average reflects the relative contribution made by all the courses you have undertaken based on their credit value.
From the above data, the correct option for the answer is d. weighted average.
Solve the equation using the order of operations 4(x-8)+14=-24
Answers
SOLUTION
Using the order of operations we have
[tex]\text{PEMDAS}[/tex]where
[tex]\begin{gathered} P=\text{parenthesis} \\ E=\text{Exponential } \\ M=\text{ Multiplication } \\ D=\text{Division } \\ A=\text{Addition } \\ S=\text{Subtraction } \end{gathered}[/tex]Note: Multiplication and Division operate at the same level but we consider the operation that appears first from the left hand sides of the equation given the same as Addition and subtraction.
Given the equation.
[tex]4(x-8)+14=-24[/tex]Expand the parenthesis
[tex]4x-32+14=-24[/tex]Add the like terms
[tex]4x-18=-24[/tex]Add 18 to both sides of the equation
[tex]\begin{gathered} 4x-18+18=-24+18 \\ 4x=-6 \end{gathered}[/tex]Divide both sides by 4
[tex]\begin{gathered} \frac{4x}{4}=\frac{-6}{4} \\ \\ x=\frac{-3}{2} \end{gathered}[/tex]Therefore
x= -3/2
Please just give me answer checking my answers to make sure my answers ok. I don't need the steps
Answers
Given:
The explicit formula for a geometrc sequence is given:
[tex]a_n=500\times(0.5)^{n-1}[/tex]To find the 6th term put n=6 here,
[tex]\begin{gathered} a_6=500\times(0.5)^{6-1} \\ =500\times(0.5)^5 \\ =500\times0.03125 \\ =15.625 \end{gathered}[/tex]Hence, option B is correct.
How to find the inverse of a matrix of it exists Question number 15
Answers
2x2 matrix's inverse:
[tex]\begin{gathered} A^{(-1)}=\begin{bmatrix}{a} & {b} & {} \\ {c} & {d} & {}\end{bmatrix}^{(-1)}=\frac{1}{ad-bc}\begin{bmatrix}{d} & {-b} & {} \\ {-c} & {a} & \end{bmatrix} \\ \\ \\ It\text{ exists only if: } \\ ad-bc\ne0 \end{gathered}[/tex]For the given matrix:
[tex]\begin{gathered} \begin{bmatrix}{6} & {-3} & \\ {-8} & {4} & {}\end{bmatrix} \\ \\ A^{(-1)}=\frac{1}{6\times4-(-3)\times(-8)}\begin{bmatrix}{4} & {3} & {} \\ {8} & {6} & {}\end{bmatrix} \\ \\ A^{(-1)}=\frac{1}{24-24}\begin{bmatrix}{4} & {3} & {} \\ {8} & {6} & {}\end{bmatrix} \\ \\ A^{(-1)}=\frac{1}{0}\begin{bmatrix}{4} & {3} & {} \\ {8} & {6} & {}\end{bmatrix} \\ \\ \end{gathered}[/tex]As the determinat (ad-bc) is 0 the matrix isn't a invertible matrix. The inverse of the given matrix doesn't existUse the tests for divisibility to determine which numbers divide evenly into the given number,766
Answers
Step 1: Concept
The rule for 2: 2 can divide any number that ends with even numbers 0, 2, 4, 6, 8.
The rule for 3: For a number to be divide by 3, its sum must be divided by 3.
The rule for 4: For a number to be divide by 4, the last two digits must be divided by 4
The rule for 5: For a number to be divided by 5, it must end with 0 or 5.
The rule for 6: A number is divisible by 6 if it is divisible by 2 and 3.
The rule for 8: A number is divisible by 8 if its last three digits are divisible by 8.
The rule for 9: For a number to be divisible by 9, its sum must be divisible by 9.
The rule for 10: For a number to be divided by 10, it must end with 0.
Step 2: Test for 766
766 can be divided by 2 because it ends with the even number 6.
766 cannot be divided by 3 because it sum (7+6+6 = 19) cannot be divide by 3.
766 cannot be divided by 4 because it last two digits cannot be divide by 4.
766 cannot be divided by 5 because it does not end with 0 or 5.
766 cannot be divided by 6 because it cannot be divide by 3
766 cannot be divided by 8 because the last three digits cannot be divided by 8.
766 cannot be divided by 9 because the sum of its digits cannot be divided by 9.
766 cannot be divided by 10 because the number did not end with 0.
Step 3: Final answer
2
please help. i just need to know how to complete this
Answers
1. Given:
[tex]\bar{TO}\cong\bar{AN}[/tex]Conclusion: Definition of congruence
Reason:
The line segment TO and AN are equal in length.
2. Given:
E is the midpoint of the line segment BD.
Conclusion: Definition of midpoint
Reason:
Since, E is in equidistant from the proint B and D on the line segment BD.
Therefore, using using the Definition of midpoint, E is the midpoint of the line segment BD.