Vijay inherited some money from his grandfather and put it in a bank account that earns 6% interest compounded annually. After 3 years, Vijay had $4,000.00 in the bank account. How much interest did he earn? Round your answer to the nearest cent.
We have in this question a case of Annual Compound Interest. The formula for this case is as follows:
[tex]A=P(1+r)^n_{}_{}[/tex]Where:
A = accrued amount.
P = Principal (starting amount).
r = interest rate.
n = number of years.
We have from the question:
r = 6%
n = 3 years.
P = $4,000.00
A = it is the unknown amount.
We can determine A to then find the interest he earned. Thus, we can proceed as follows:
[tex]A=4000(1+0.06)^3\Rightarrow A=4000(1.06)^3\Rightarrow A=4764.064[/tex]This previous amount is the accrued amount (the starting amount plus the interest after 3 years annually compounded).
Therefore, the amount Vijay earned in interests (after 3 years) is:
[tex]4764.064-4000=764.064[/tex]And, rounding this amount to the nearest cent, we have that, finally, the earned interest (after 3 years) is $764.06.
Estimate the quotient using compatible numbers.61.32 divided by 11.7 =
Answer:
5
Explanation:
Given the quotient:
[tex]61.32\div11.7[/tex]First, we estimate each of the numbers:
[tex]\begin{gathered} 61.32\approx60\text{ (to the nearest tens)} \\ 11.7\approx12\text{ (to the nearest whole number)} \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} 61.32\div11.7\approx60\div12 \\ =5 \end{gathered}[/tex]8. Irene's score on Test 1 was 120. Her score on test 2 was 108. What is the percent decrease from Test 1 to Test 2? A. 10% B. 11% C. 12% D. 13%
Test 1 : 120
Test 2 : 108
120 x = 108
x= 108/120
x= 0.9
0.9 x 100 = 90%
100%-90% = 10%
A.10%
The revenue function R in terms of the number of units sold, x, is given as R = 290x-0.52x^2where R is the total revenue in dollars. Find the number of units sold x that produces a maximum revenue?Your answer is x=What is the maximum revenue?$
Solution
Step 1:
The function reaches a maximum where the derivative is equal to 0.
Find the first derivative of the function.
Step 2:
Write the function
[tex]R(x)\text{ = 290x - 0.52x}^2[/tex]Step 3
Find the first derivative
[tex]\begin{gathered} R(x)=\text{ 290x -0.52x}^2 \\ R^{\prime}(x)\text{ = 290 - 1.04x} \end{gathered}[/tex]Step 4:
The function reaches a maximum where the derivative is equal to 0.
[tex]\begin{gathered} 290\text{ - 1.04x = 0} \\ 1.04x\text{ = 290} \\ \text{x = }\frac{290}{1.04} \\ \text{x = 278.8 }\approx\text{ 279} \end{gathered}[/tex]So the number of units which produce the maximum revenue = 279
Step 5:
Substituting this value in the original equation gives the revenue:
[tex]\begin{gathered} R\text{ = 290x - 0.52x}^2 \\ R\text{ = 290}\times279\text{ - 0.52 }\times\text{ 279}^2 \\ R\text{ = 80910 - 42034.14} \\ R\text{ = \$38875.86} \end{gathered}[/tex]Maximum revenue = $38875.86
how are the processes for converting 5/8 to decimal and to a percentage similar and how are the processes different
To convert 5 to a decimal, divide it by 8.
To convert a decimal to a percent, multiply it by 100.
What is decimal and percentage conversion?
To convert a percentage to a decimal, divide by 100. So 25% is 25/100, or 0.25. To convert a decimal to a percentage, multiply by 100 (just move the decimal point 2 places to the right) and give the % symbol.
Consider, the given fraction, 5/8
Divide 5 by 8 to change a decimal.
So, 5/8 = 0.625
Now to convert decimal 0.625 into a percent.
Multiply 0.625 by 100 to get 62.5%.
So, the conversion of fraction into decimal is 0.625 and the decimal into percent is 62.5%.
To know more about decimal and percentage conversion, click on the link
https://brainly.com/question/155580
#SPJ1
You want to know the number of minutes that you can use on your $45.00 phone card. The card company chargesyou $0.50 for the first minute and $0.05 for cach additional minute. Solve the formula $45.00 = $0.50 + $0.05mfor m. Justify each step with an algebraic property of equality.
To solve m:
1. Subtract 0.50 in both sides of the equation (subtraction property of equality):
[tex]\begin{gathered} 45.00-0.50=0.50-0.50+0.05m \\ 44.5=0.05m \end{gathered}[/tex]2. Divide both sides of the equation into 0.05 (Division property of equality):
[tex]\begin{gathered} \frac{44.5}{0.05}=\frac{0.05}{0.05}m \\ \\ 890=m \end{gathered}[/tex]3. Rewrite the equation (Symmetric property):
[tex]m=890[/tex]Then, you can use 890 minutes on your $45.00 phone card.Determine which if any of given ordered pairs satisfy the system of linear equations
Solution:
The equations are given below as
[tex]\begin{gathered} x+3y-z=-11-----(1) \\ 2x-y+2z=11------(2) \\ 3x+2y+3z=6------(3) \end{gathered}[/tex]Step 1:
Make x the subject of the formula from equation (1)
[tex]\begin{gathered} x+3y-z=-11 \\ x=-11-3y+z-----(4) \end{gathered}[/tex]Step 2:
Substitute equation (4) in equations (2) and (3)
[tex]\begin{gathered} 2x-y+2z=11 \\ 2(-11-3y+z)-y+2z=11 \\ -22-6y+2z-y+2z=11 \\ -7y+4z=11+22 \\ -7y+4z=33-----(5) \\ \\ 3x+2y+3z=6 \\ 3(-11-3y+z)+2y+3z=6 \\ -33-9y+3z+2y+3z=6 \\ -7y+6z=6+33 \\ -7y+6z=39------(6) \end{gathered}[/tex]Step 3:
Substract equation 5 from 6
[tex]\begin{gathered} -7y-(-7y)+4z-6z=33-39 \\ -2z=-6 \\ z=3 \end{gathered}[/tex]Step 4:
Substitute the value of z=3 in equation (4)
[tex]\begin{gathered} -7y+4z=33 \\ -7y+4(3)=33 \\ -7y+12=33 \\ -7y=33-12 \\ -7y=21 \\ y=-3 \end{gathered}[/tex]Step 4:
Substitute y=-3, z= 3 in equation (4)
[tex]\begin{gathered} \begin{equation*} x=-11-3y+z \end{equation*} \\ x=-11-3(-3)+3 \\ x=-11+9+3 \\ x=1 \end{gathered}[/tex]Hence,
The final answer is
[tex]\Rightarrow(1,-3,3)[/tex]ONLY THE ORDERED PAIR ( 1, -3, 3) satisfies the system of linear equations
OPTION B is the right answer
Al gets paid semimonthly. His gross pay for each pay period is $750.He has 18% withheld for taxes and 48 withheld for personal deductions.What is the amount of his annual net pay?a. $7,200b. $14,040c. $15,300d. $15,600
so given $750 as gross pay
18% withheld for taxes
48 withheld for personal term this also means 4%
18% = 0.18
4% = 0.04
so to get the annual net,
750 x (1 - 0.18 - 0.04) x 24
= 14040
=$14, 040
this makes option B the corect answer
You are given the following problem" "A car burns 0.85 gallons of gas per hour when idling. Express this rate in quarts per minute." Which of the given conversion factors will be useful to solve this problem?
Given,
A car burns 0.85 gallons of gas per hour.
We know,
0.85 gallon = 3.4 quartz.
1 hour=60 min.
Thus,
0.85 gallon per hour=3.4/60 quart per min=0.057 quart per min.
Thus the conversion factor is 0.057 quart per min.
Angles K and M are vertical angles. K’s measurement is 72 degrees. What is the measure of M ?
If two angles are vertical and congruent, the angle is the same:
[tex]\begin{gathered} K=M \\ M=72 \end{gathered}[/tex]The measure of M is 72°
You need a 50% alcohol solution. On hand, you have a 300 mL of a 40% alcohol mixture. You also
have 80% alcohol mixture. How much of the 80% mixture will you need to add to obtain the desired
solution?
You will need
—————————mL of the 80% solution
You will need 100 mL of the 80% solution and solve the question by using percentage concept.
What is the percentage?
A percentage is a number or ratio that can be expressed as a fraction of 100.
Assume that x mL of 80% solution is needed.
The amount of alcohol in 300 mL of a 40% alcohol mixture is
300 mL × 40% = 300 × (40/100) = 120 ml.
The amount of alcohol in 300 mL of a 40% alcohol mixture is
300 mL - 120 mL = 180 mL.
The amount of alcohol in x mL of a 80% alcohol mixture is
x mL × 80% = x × (80/100) = (8x)/10 ml.
The amount of alcohol in x mL of a 80% alcohol mixture is
x - (8x)/10 ml = (2x)/10 mL.
Total amount of alcohol is 120 + (8x)/10 mL
Total amount of water is 180 + (2x)/10 mL
The meaning of 50% alcohol solution is the amount of alcohol and water is equal.
120 + (8x)/10 = 180 + (2x)/10
(8x)/(10)- (2x)/10 = 180 -120
(6x)/(10) = 60
x = 100
To learn more about percentage, you can visit below link:
https://brainly.com/question/897301
#SPJ1
13. You can afford a $1,800 per month mortgage payment. You've found a 30-year loan at 5.5% interest.(a) How big of a loan can you afford? $(b) How much total money will you pay the bank? $(c) How much of that money is interest? $
Step-by-step explanation:
Given
Principal = $1,800
interest rate = 5.5%
Using the below formula to calculate the mortgage
[tex]\begin{gathered} m\text{ = }\frac{p\cdot\text{ r (}1+r)^n}{(1+r)^n\text{ - 1}} \\ \text{Where P = principal, r = interest rate} \\ m\text{ = \$1800} \\ r\text{ = 5.5\% } \\ r\text{ = }\frac{5.5}{100}\text{ = 0.055} \\ \text{ since it is per month, hence the interest rate is given as} \\ r\text{ = }\frac{0.055}{12}\text{ = 0.00458} \\ n\text{ = 12 }\cdot\text{ 30} \\ n\text{ = 360} \\ 1800\text{ = }\frac{P\cdot0.00458(1+0.00458)^{360}}{(1+0.00458)^{360}\text{ - 1}} \\ 1800\text{ = }\frac{P\cdot0.00458(1.00458)^{360}}{(1.00458)^{360}\text{ - 1}} \\ 1800\text{ = }\frac{P\cdot0.00458\cdot\text{ 5.1812}}{5.1812\text{ - 1}} \\ 1800\text{ = }\frac{P\cdot\text{ 0.0237}}{4.1812} \\ \text{Cross multiply} \\ 1800\cdot\text{ 4.1812 = P }\cdot\text{ 0.0237} \\ 7526.16\text{ = P }\cdot\text{ 0.0237} \\ p\text{ = }\frac{7526.16}{0.0237} \\ P=\text{ \$317, 559. 50} \end{gathered}[/tex]Hence, the loan he can afford is $317, 559. 50
Part B
The total money he will pay to the bank is calculated as follows
Total amount = 1800 * 360
Total amount = $648, 000
How many pairwise comparisons are needed to learn the outcome of an election involving n=15 candidates ?
Remember that
The formula for the number of independent pairwise comparisons is k(k-1)/2, where k is the number of conditions
In this problem
k=15
substitute
15(15-1)/2=105
therefore
The answer is 105Suppose one-seventh of the employees of a certain company work in the Southeastern region. If the company employs 247 workers in that region, what is the total number of employees working for the company?How many total employees?
Given:
One-seventh of the employees of certain companies work in the Southeastern region. If the company employs 247 workers in that region,
Required:
Find the total number of employees.
Explanation:
Let the number of employees be x.
According to the question
[tex]\begin{gathered} \frac{1}{7}x=247 \\ x=247\times7 \\ x=1729 \end{gathered}[/tex]Final Answer:
The total number of employees working is 1729.
The order in which you perform operations matters in a numerical expression. O A. True B. False
Answer:
A. True
Explanation:
Consider the numerical expression below:
[tex]9+2\times3[/tex]If we solve from the left to the right, we have:
[tex]9+2\times3=11\times3=33\text{ (Wrong Solution)}[/tex]This result is incorrect.
However, by the order of operations, multiplication comes before addition, so we rightly have:
[tex]9+2\times3=9+6=15[/tex]We see that if we do not follow the order of operations, our results will not be accurate.
Therefore, the order in which you perform operations matters in a numerical expression.
The answer is True.
43. For the first art project, 15 students will equally share a 50-pound packageof clay. Later, each student will be given an additional 2 pounds of clay forthe second project.Which equation could be used to find p, the total number of pounds ofclay used per student?Bp = (50 - 15) - 2p = 15 + (50 = 2)p = (50 = 15) - 2p = 2 + (50 - 15)
The equation that could be used to find the total number of pounds of clay used per student is:
p = 2 + 50/15
Explanation:The equation that could be used to find the total number of pounds of clay used per student is:
p = 2 + 50/15
This shows the addition of the extra 2 pounds of clay for the second project with the 50 pounds of clay shared by all 15 students
Long division ( polynomial by binomial) ( x^3 - 216) / ( x-6)
Given:
[tex]\frac{x^3-216}{x-6}[/tex]We will use the long division to find the answer
The long division will be as shown in the following picture:
So, the answer will be:
[tex]x^2+6x+36[/tex]Is there enough information given to prove that the following pairs of triangles are congruent? If so, state the postulate or theorem that supports youranswer. If not, state NONE.Word Bank:HL AA CPCTC AAS SSS None SAS
Answer: There is not enough information to conclude they are congruent, NONE.
Explanation
Postulates or theorems
• Hypotenuse Leg (HL) postulate:, when two right triangles have a congruent hypotenuse and a corresponding congruent leg, these are congruent.
,• Angle-Angle (AA) postulate:, two triangles are similar if two corresponding angles are congruent.
,• Corresponding Parts of Congruent Triangles are Congruent (CPCTC): ,when two triangles are congruent, their corresponding sides and angles are also congruent.
,• Angle Angle Side (AAS) Theorem: ,two angles and the non-included side of two triangles are congruent, and if the angles and the side are corresponding parts in each triangle, then the triangles are congruent.
,• Side Side Side (SSS) Postulate: i,f three sides of two triangles are congruent between each other, then the two triangles are congruent.
,• Side Angle Side (SAS) Postulate: ,two angles and the included side of two triangles are congruent, and if the angles and the side are corresponding parts in each triangle, then the triangles are congruent.
We do not know if the sides are congruent as we are not given any information about it, we just know that the three angles are congruent.
Based on the latter, we can conclude that all postulates or theorems involve the congruence of the sides with the exception of AA postulate. However, the AA postulate states that if it is true, the triangles are similar (same shape) but not necessarily congruent (same size).
Therefore, we have not enough information to conclude the triangles are congruent, we would need the to know the congruency of at least one side of both triangles.
4х - Зу = 4 2х + 4 y = 3*solving system by elimination*
Answer
x = (25/22)
y = (2/11)
Explanation
4х - Зу = 4
2х + 4y = 3
We are asked to solve the system of equations by elimination
To do that, we will multiply the first equation by 1 and the second equation by 2
(4х - Зу = 4) × 1
(2х + 4y = 3) × 2
4x - 3y = 4
4x + 8y = 6
Subtract equation 1 from equation 2
4x + 8y = 6
- (4x - 3y = 4)
4x - 4x + 8y + 3y = 6 - 4
0 + 11y = 2
11y = 2
Divide both sides by 11
(11y/11) = (2/11)
y = (2/11)
Using one of the equations, we can solve for x
2x + 4y = 3
2x + 4(2/11) = 3
2x + (8/11) = 3
2x = 3 - (8/11)
2x = (33/11) - (8/11)
2x = (25/11)
x = (25/22)
Hope this Helps!!!
Use a table of values with at least 5 values to graph the following function:
A function take an input and produce a unique output.
[tex]y=2^x[/tex]y is the output
x is the input
[tex]\begin{gathered} x=1y=2^x=2^1\text{ = 2} \\ x=2y=2^{2\text{ = 4}} \\ x=3y=2^3\text{ = 8} \\ x=4y=2^4\text{ = 16} \\ x=5y=x^5\text{ = 32} \end{gathered}[/tex]The function C(x) = 300x + 180 gives the cost for a college to offer x sections of an introductory class in CPR (cardiopulmonary resuscitation). The function R(x) = 390x gives the amount of revenue the college brings in when offering x sections of CPR. Find the point where the cost equals the revenue by graphing each function on the same coordinate system. (x, y) =
Cost = Revenue
Then
300x + 180 = 390x
x= (390-300)/180= 180/90 = 2
Now graph both functions
1. Select the equations that are true.In the figure shown, lines f and g are parallel.1. Circle all equations that are true.456A. mZ3+ m25 = 180 because they are a linear pair.B. m3 = m25 because they are alternate interior angles.C. m 3 = m_2 because they are vertical angles.D. m 2+ m24 = 180 because they are a linear pair.E. m24 = mZ5 because they are alternate interior anglesF. mZ1 = m28 because m25 = m28 are vertical anglesand mZ1 = m25 are corresponding anglesG. m27 = m_3 because they are corresponding angles.
As shown at the graph:
What is Three subtracted from a number that equals 63
Explanation
To compute the answer, let us make the unknown number y
Thus
We can represent the given statement as
[tex]y-3=63[/tex]The next step will be to solve for y
[tex]\begin{gathered} add\text{ 3 to both sides} \\ \\ y-3+3=63+3 \\ y=66 \end{gathered}[/tex]Therefore, the number is 66
Charlie is flying a kite one afternoon and steps on the end of the string to have hishands free to take a picture. The string is 135 feet long and forms a 68-degree anglewith the ground. How high is his kite at this time? Round to the nearest foot, andenter the number only.AV
The string of the kite, ground and hieght of the kite makes the right angle triangle.
The hypotenuse side of triangle is 135 feet long.
Determine the height of the kite by usng the trigonometry.
[tex]\begin{gathered} \sin 68=\frac{h}{135} \\ h=0.9272\cdot135 \\ =125.172 \\ \approx125 \end{gathered}[/tex]So answer is 125 feet.
Drag the expressions in order from least to greatest value.
Then, from least to greatest value, the order is:
[tex]1\frac{1}{2}-\frac{5}{8}[/tex][tex]1\frac{1}{8}+\frac{1}{4}[/tex][tex]1\frac{7}{8}-\frac{1}{4}[/tex]The figure shown was created by placing the vertices of a square on the circle. Thesquare has side lengths of 7cm and the circle has a diameter of 10 cm.Which measurement is closest to the area of the shaded region of the figure insquare centimeters?
To answer this question, we need to find the area of the square, and then the area of the circle. Then, we need to subtract from the area of the circle, the area of the square.
The area of the square is given by the formula:
[tex]A_{\text{square}}=s^2[/tex]The side of the square is 7cm. Then, the area is:
[tex]A_{\text{square}}=(7\operatorname{cm})^2\Rightarrow A_{square}=49\operatorname{cm}^2[/tex]Now, the area of the circle is given by the formula:
[tex]A_{\text{circle}}=\pi\cdot r^2[/tex]The diameter of the circle is equal to 10cm. The radius of the circle is half of the measure of the diameter. Then, the radius is equal to 10/2 ---> r = 5cm. Then, we have:
[tex]A_{\text{circle}}=\pi\cdot(5\operatorname{cm})^2\Rightarrow A_{circle}=\pi\cdot25\operatorname{cm}\approx78.54\operatorname{cm}^2[/tex]Now, to find the shaded area, we need to subtract from this area, the area of the square:
[tex]A_{\text{shaded}}=A_{\text{circle}}-A_{\text{square}}=78.54\operatorname{cm}-49\operatorname{cm}=29.54\operatorname{cm}^2[/tex]Therefore, the shaded area is closest to 29.5 square centimeters (third option) (if we round our result to the nearest tenth.)
For the equation, find three ordered pairs solutions by completing the table. Then use any of the ordered pairs to graph the equation X-y=3
for y=0
[tex]\begin{gathered} x-0=3 \\ x=3\to y=0 \end{gathered}[/tex]To graph this function we solve for and give x values:
[tex]y=x-3[/tex][tex]\begin{gathered} x=0\to y=-3 \\ \\ x=1\to y=-2 \\ \\ x=2\to y=-1 \\ \\ x=3\to y=0 \end{gathered}[/tex]Each week, Tasha saves 60% of the money she earns babysitting and spends the rest. This week she earned $20.00. How much more money did she save than spend this week?
Answer:
$4.00 more saved than spent
Step-by-step explanation:
Given that Tasha saves 60% of her earnings and that she earned $20.00 this week, we need to find the amount she saved and subtract this amount and the amount she earned.
Letting A represent the amount Tasha saves and e represent her earnings, we can find how much she saved using
A(e) = 0.60e
A(20) = 0.60 * 20 = 12
Since she only earned $20.00, we can find the amount she spent by subtracting 12 from 20:
20 - 12 = 8
Finally, we can find how much more she saved than spent this week by subtracting 8 from 12:
12 - 8 = $4.00
Tyee has 10 1/4 yards of ribbon to make bows. Each bow is made from a piece of ribbon that is 3/5 yard long. What is the maximum number of complete bows Tyee can make?
Given:
Tyee has 10 1/4 yards of ribbon to make bows.
The length of each bow = 3/5 yards
We will find the maximum number of bows by divided the total length by the length of one bow.
so, the number of bows will be as follows:
[tex]10\frac{1}{4}\div\frac{3}{5}=\frac{41}{4}\div\frac{3}{5}=\frac{41}{4}\times\frac{5}{3}=\frac{205}{12}=17\frac{1}{12}[/tex]The number of bows will be an integer number
so, the answer will be:
The maximum number of complete bows = 17
what is this 3+12c-4c
what is this 3+12c-4c
step 1
combine like terms
3+(12c-4c)
answer is
3+8c