Annette Michaelson will need $11,000 in 8 years to help pay for her education. Determine the lump sum, deposited today at 4.5% compounded monthly, will produce the necessary amount.
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
A=11,000
t=8 years
n=12
r=4.5%=0.045
substitute in the formula above
[tex]\begin{gathered} 11,000=P(1+\frac{0.045}{12})^{(12\cdot8)} \\ 11,000=P(\frac{12.045}{12})^{(96)} \\ \\ P=7,679.61 \end{gathered}[/tex]therefore
the answer is
$7,679.61thereforehow do you simplify this expression to become x ^3 -8
we have the expression
[tex]\begin{gathered} (x^3-4)-4 \\ remove\text{ the parenthesis} \\ x^3-4-4 \\ combine\text{ like terms} \\ x^3-8 \end{gathered}[/tex]Identify the type of polar graph for the equation: r = 2+2cos θ aLimacon with inner loop bCardioid cDimpled limacon dConvex limacon eRose Curve fCircle gLemniscate
is choice a
iner loop Limacon
Rebecca makes four payments a year of $255 each for life
insurance; two payments of $455.35 each for real estate taxes;
and six payments of $66.21 each for auto insurance. How
much must Rebecca put into fixed savings each month to
cover her annual expenses for life insurance, auto insurance
and real estate taxes?
The amount Rebecca has put into fixed savings each month to cover her annual expenses for life insurance, auto insurance and real estate taxes is $ 194.
Given that:-
Amount invested in life insurance = $ 255
Number of payments in life insurance = 4
Amount invested in real estate taxes = $ 455.35
Number of payments in real estate taxes = 2
Amount invested in auto insurance = $ 66.21
Number of payments in auto insurance = 6
We have to find the amount Rebecca has put into fixed savings each month to cover her annual expenses for life insurance, auto insurance and real estate taxes.
Hence,
Total amount put by Rebecca in a year = 255*4 + 455.35*2 + 66.21*6 = 1020 + 910.70 + 397.26 = $ 2,327.96
Amount put by Rebecca in a month = 2327.96/12 = $ 193.997 ≈ $ 194
To learn more about amount, here:-
https://brainly.com/question/25866493
#SPJ1
5 cm5 cmThe surface area of the above figure isA. 208.1 cm2B. 225.6 cm2C. 314.2 cm2D. none of the above
It is a cylinder.
1.- Calculate the area of the base and the top
Area = 2*pi*r^2
Area = 2*3.14*5^2
Area = 157 cm^2
Total area of the base and top = 2 x 157 = 314 cm^2
2.- Calculate the perimeter of the circle.
Perimeter = 2*pi*r
Perimeter = 2*3.14*5
Perimeter = 31.4 cm
3.- Calculate the lateral area
Lateral area = 5 x 31.4
Lateral area = 157 cm^2
4.- Calculate the total area = 157 + 314
= 471 cm^2
5.- Result
D. None of the above
the sum of the measure of angle m and angle r is 90
Given:
The sum of measure of angle m and r is 90 degrees.
the red line equation is y=0.5*2^xthe blue line equation is y=2x+25Compare and contrast this graph
In this question, we are given two lines.
1) y = 0.5*2^x
2) y = 2x + 25
The standard equation of a line is y = mx + b, where m is the slope and b is the y-intercept.
The positive slope moves the line upwards and the negative slope moves the line downwards.
If we compare both the equations, we see the 2nd equation maps with the standard line form. Hence, the second equation is a line with the slope equals to 2 and y-intercept equals 25. As the slope is positive, the line is moving upwards.
The standard equation of an exponential function is y = a*b^x, where b is the base, x is the exponent and a is the y-intercept.
The positive value of the base moves the function upwards and the negative value moves it downwards.
If we compare both the equations, we see the 1st equation maps with the standard exponential form. Hence, the 1st equation is an exponent form with the base to 2 and y-intercept equals 0.5. As the base is positive, the line is moving upwards.
I have a practice problem that I need help on.These are included in the problem as well Where did Arjun make errors?Explain his errors and the properties of logarithms that leads to the answer. State the correct answer.
Arjun applied the wrong laws of logarithms.
The question can be solved as shown below:
[tex]\log _7x+\log _7y+\log _7z[/tex]Step 1: Apply the addition rule of logarithm given as
[tex]\log _am+\log _an=\log _a(m\cdot n)[/tex]Thus, we have:
[tex](\log _7x+\log _7y)+\log _7z=\log _7(x\cdot y)+\log _7z[/tex]Step 2: Apply the subtraction rule of logarithm given as
[tex]\log _am-\log _an=\log _a(\frac{m}{n})[/tex]Thus, we have:
[tex]\log _7(x\cdot y)+\log _7z=\log _7(\frac{x\cdot y}{z})[/tex]Therefore, the correct answer is:
[tex]\log _7x+\log _7y+\log _7z=\log _7(\frac{xy}{z})[/tex]Translate to system Grandpa and Grandma are treating their family to the movies. Matineetickets cost $4 per child and $4 per adult. Evening tickets cost $6 per childand $8 per adult. They plan on spending no more than $80 on the matineetickets and no more than $100 on the evening tickets.
Answer:
4x + 4y ≤ 80
6x + 8y ≤ 100
Explanation:
Let's define x as the number of children and y as the number of adults.
For Matinee tickets, they spend $4 per child and $4 per adult, so if the total is no more than 80, we get:
4x + 4y ≤ 80
In the same way, they spend $6 per child and $8 per adult on the evening tickets, so
6x + 8y ≤ 100
Therefore, the system is
4x + 4y ≤ 80
6x + 8y ≤ 100
Please help quick :/
Answer:
The design fee is $40.
Step-by-step explanation:
The y intercept means the cost when the number of shirts ordered is 0. This means that in the context of this problem the y intercept is the design fee.
Which graph IS a function?
Answer:
Graph A
Step-by-step explanation:
It is a function of f(x) = 2
Line AB and line DA are?
Answer:
perpendicular
Step-by-step explanation:
Square
Rectangle
Right triangle
Cube
Rectangular prism
are all examples of perpendicular shapes
i hope this helped
have a good day ^^
3 part golden raisin2 parts cashewhow many parts of golden raisins does jose need to make 30 total cups pf trail mix?a. 14 partsb. 18 partsc. 20 partsd. 25 parts
To get 1 cup of pf trail mix, we need to mix 2 parts of cashew and 3 part of golden raisin. This means that to make one cup of pf trail mis, we are using 5 parts in total (2 cashew+3 golden raisin). Then, this means that out of one cup the exactly amount of golden raisin is 3/5 of the cups we have. So, having this fraction in mind, we only need to multiply the total number of cups to calculate the parts we are using. In this case, we have 30 cups. So if we want to calculate the parts of golde raisin we multiply 30 by the previous fraction. That is
[tex]30\cdot\text{ }\frac{3}{5}\text{ = 6 }\cdot\text{ 3 = 18}[/tex]So to make 30 cups of pf trail mix, jose needs 18 parts.
A Geiger counter counts the number of alpha particles from radioactive material. Over a
long period of time, an average of 16 particles per minute occurs. Assume the arrival of
particles at the counter follows a Poisson distribution. Round your answers to four decimals.
a) Find the probability of exactly 21 particles arrive in a particular one minute period.
0.0426053 O
b) Find the probability of exactly one particle arrives in a particular one second period.
0.20424755689724
a) The probability of exactly 21 particles arrive in a particular one minute period is 0.0426
b) The probability of exactly one particle arrives in a particular one second period is 0.2042
What is probability?Probability is the ratio of the total number of conceivable outcomes to the number of outcomes in an exhaustive set of equally likely alternatives that result in a particular occurrence.
The probability is given by:
P(X=x) = (e⁻ⁿ nˣ)/x!
a) The probability of exactly 21 particles arrive in a particular one minute period is given by :
P(X=21) = (e⁻16 × 16²¹)/21!
P(X=21) = (2.176746853×10¹⁸)/51090942171709440000
P(X=21) = 0.0426
b) The probability of exactly one particle arrives in a particular one second period is :
1 min = 16 particles
1 sec = 16/60 particles
1 sec = 0.2667 particles
P(X=1) = (e⁻⁽¹⁶/⁶⁰⁾ × (16/60)¹)/1!
P(X=1) = 0.2042
To know more about Probability please visit:
https://brainly.com/question/11234923
#SPJ13
For which equation will x=-2 make the equation true? Equation 1: 2.4x+ 2.6 = 17 Equation 2: 16 = -8(-6 - 2x) X - 4 Equation 3: 3 Equation 4: -6 = -5x - 3+ Óx
We need to check each of the options to determine which equation is true
x = -2
equation1: 2.4x + 2.6 = 17
2.4(-2) + 2.6 = 17
-4.8 + 2.6 = 17
-2.2 = 17
equation2: 16 = -8(-6 - 2x)
16 = -8(-6 -2(-2))
16 = -8(-6+4)
16 = -8(-2)
16 = 16
equation 3: 3
Sketch the graph of the polynomial function. Use synthetic division and the remainder theorem to find the zeros.
GIVEN:
We are given the following polynomial;
[tex]f(x)=x^4-2x^3-25x^2+2x+24[/tex]Required;
We are required to sketch the graph of the function. Also, to use the synthetic division and the remainder theorem to find the zeros.
Step-by-step solution;
We shall begin by sketching a graph of the polynomial function.
From the graph of this polynomial, we can see that there are four points where the graph crosses the x-axis. These are the zeros of the function. One of the zeros is at the point;
[tex](-1,0)[/tex]That is, where x = -1, and y = 0.
We shall take this factor and divide the polynomial by this factor.
The step by step procedure is shown below;
Now we have the coefficients of the quotient as follows;
[tex]1,-3,-22,24[/tex]That means the quotient is;
[tex]x^3-3x^2-22x+24[/tex]We can also divide this by (x - 1) and we'll have;
We now have the coefficients of the quotient after dividing a second time and these are;
[tex]x^2-2x-24[/tex]The remaining two factors are the factors of the quadratic expression we just arrived at.
We can factorize this and we'll have;
[tex]\begin{gathered} x^2-2x-24 \\ \\ x^2+4x-6x-24 \\ \\ (x^2+4x)-(6x+24) \\ \\ x(x+4)-6(x+4) \\ \\ (x-6)(x+4) \end{gathered}[/tex]The zeros of this polynomial therefore are;
[tex]\begin{gathered} f(x)=x^4-2x^3-25x^2+2x+24 \\ \\ f(x)=(x+1)(x-1)(x-6)(x+4) \\ \\ Where\text{ }f(x)=0: \\ \\ (x+1)(x-1)(x-6)(x+4)=0 \end{gathered}[/tex]Therefore;
ANSWER:
[tex]\begin{gathered} x+1=0,\text{ }x=-1 \\ \\ x-1=0,\text{ }x=1 \\ \\ x-6=0,\text{ }x=6 \\ \\ x+4=0,\text{ }x=-4 \end{gathered}[/tex]#17 - A bin contains 90 batteries (all size C). There are 30 Eveready, 24 Duracell, 20 Sony,10 Panasonic, and 6 Rayovac batteries. What is the probability that the battery selected is aDuracell?0 27.6%0 26.7%24.6%0 29.2%
According to the basic definition of probability,
[tex]\text{Probability}=\frac{\text{ No. of favorable events}}{\text{ Total no. of events}}[/tex]Given that the bin contains total 90 batteries, out of which 24 are duracell.
So the probability that a randomly selected battery is Duracell, is calculated as,
[tex]\begin{gathered} P(\text{Duracell)}=\frac{\text{ No. of Duracell Batteries}}{\text{ Total no. of batteries}} \\ P(\text{Duracell)}=\frac{24}{90} \\ P(\text{Duracell)}\approx0.267 \\ P(\text{Duracell)}\approx26.7\text{ percent} \end{gathered}[/tex]Thus, the probability that a randomly selected battery is Duracell, is 26.7% approximately.
Please can I have the answer for number 12?Thanks a lot
Given:
length of the piece of string = 3/4 inches
length of the piece that we need = 1/8 inches
The number of smaller piece that we can get from the original piece of string can be calculated using the formula:
[tex]\text{Number }of\text{ smaller piece = }\frac{length\text{ of original piece}}{length\text{ of smaller piece}}[/tex]Applying this formula:
[tex]\begin{gathered} \text{Number of smaller piece = }\frac{3}{4}\div\text{ }\frac{1}{8} \\ \end{gathered}[/tex]If the number of pieces is represented as n:
[tex]n\text{ = }\frac{3}{4}\div\text{ }\frac{1}{8}[/tex]Answer:
A salad recipe requires 3 cups of spinach and 1/2 cup of pecans. At this rate, what amount of pecans should be used with 2 cups of spinach?
We need 3 cups of spinach for each 1/2 cup of pecans.
Then we have:
[tex]\begin{gathered} \frac{2\text{ cups of spinach}}{3\text{ cups of spinach}}=\frac{x\text{ cups of pecans}}{\frac{1}{2}\text{ cups of pecans}} \\ \frac{x}{\frac{1}{2}}=\frac{2}{3} \\ x=\frac{1}{2}\cdot\frac{2}{3} \\ x=\frac{1}{3} \end{gathered}[/tex]Answer: It will be needed 1/3 cup of pecans
What is the area of this triangle?
Pls help :(
Below is the graph of a polynomial function with real coefficients. All local extrema of the function are shown in the graph.
Given
A graph of a polynomial with the real coefficients.
To find:
a) The intervals in which the function is increasing is,
[tex]\begin{gathered} (-\infty,-5) \\ (-2,2) \\ (6,\infty) \end{gathered}[/tex]b) The value of x at which the unction has local minima.
From the graph shown in the figure, there is only one local minimum at x=-2.
c) The sign of the functions leading coefficient is positive.
Since the graph is moving upwards.
d) The degree of the function is 5.
a student teacher is given a guideline that a student should be able to finish a 32 question test in 28 minutes if the student teacher is planning to give a test that contains 160 questions and the average students complete question of the same rate as previously State how many minutes should you plan for the average student to complete the test.
since the student do 32 questions in a time of 28 minutes, then the rate of response is 32/28=8/7 questions/minute ,then the students will be able to complete 160 questions in 20(7)= 140 minutes
Can u please help me solve ? I'm reviewing for a final, ty
Part A
we have that
Both students verify the identity properly
student A ----> expand the left side of the identity
student B ----> expand the right side of the identity
but the result is the same
both students proved that the given equation is an identity
Part B
Identities[tex]\begin{gathered} sin^2x+cos^2x=1\text{ ----> identity N 1 in step 3} \\ cos^2x=1-sin^2x \end{gathered}[/tex]and
[tex]cscx=\frac{1}{sinx}\text{ -----> identity N 2 step 5}[/tex]Find the missing quantity with the information given. Round rates to the nearest whole percent and dollar amounts to the nearest cent.Original Price = $6.50$ Markdown = $1.30Reduced Price = ?
Since we have a markdown of $1.30 we just need to substract this amount to the original price, then we have:
[tex]6.50-1.30=5.20[/tex]Therefore the reduced price is $5.20
please help me with this question!
The required point-slope form of the equation of the line exists y + 9 = 4/3 (x + 9).
What is the slope of the line?A slope of a line exists the change in the y coordinate with respect to the change in the x coordinate. The net change in the y-coordinate exists defined by Δy and the net change in the x-coordinate exists defined by Δx. Where “m” exists the slope of a line. So, tan θ to be the slope of a line.
The slope of the line exists a tangent angle created by line with horizontal.
i.e. m = 4/3 where x in degrees.
The point-slope of the equation of the line is given by,
y - y₁ = m(x - x₁)
Put the values in the above equation of the line
y - (-9) = 4/3 (x - (-9))
y + 9 = 4/3 (x + 9)
Therefore, the required point-slope form of the equation of the line is y + 9 = 4/3 (x + 9).
To learn more about slopes refer to:
brainly.com/question/3605446
#SPJ13
Jane, Chau, and Deshaun have a total of $82 in their wallets. Deshaun has 2 times what Jane has. Chau has $6 less than Jane. How much does each have?
Jane, Chau, and Deshaun have $22, $16 and $44 respectively in their wallets.
let x represent represent the amount of Jane.
let Y represent represent the amount of chau.
let z represent represent the amount of Deshaun.
Jane, Chau, and Deshaun have a total of $82" can be represented as
x + y + z = $82 .......(1)
Deshaun has 4 times what Jane has. It can be represented mathematically as
y = 2x .......(2)
Chau has $6 less than Jane. It can be represented mathematically as
z= x- 6 .......(3)
we can now solve the equations using the substitution method
substitute equation (2) and (3) into equation (1)
x + y + z = $82
x + 2x + x-6 = $82
4x -6 = $82
4x - 6 = $82
4x = $82 + 6
4x = 88
x = $22
from equation 2
y = 2x
y = 2 x 22 = $44
z = x- 6
z = 22 - 6
z=$16
Jane, Chau, and Deshaun have $22, $16 and $44 respectively in their wallets.
To know more about equation
https://brainly.com/question/16644061
#SPJ1
Which expressions represent a quadratic expression in factored form? Select all the correct answers.
x^2 − x − 72
(x + 3)(x − 7)
-8(x + 56)
(x + 1)(x − 2)
(x − 2) + (x + 3)
The expressions that represent a quadratic expression in factored form is (x + 1)(x − 2).
What is quadratic expression?Quadratic expression can be described as the mathematical expression that posses the variable which have highest power of 2.
It should be noted that the quadratic equation is usually expressed in the form ax^2 + bx + c where the abc are the known numbers in the equation that will be used in the calculation of the factors of the equation and in the quadratic equation the number a will not be equal to zero in the equation.
Therefore, option C is correct.
Read more about quadratic expression at:
https://brainly.com/question/1214333
#SPJ1
Write a equation that passes through the points (2,5) (-3,5)
Line equation: y = 5
Slope: 0
Intercept: 5
Formule:
. Equation : y = mx + b
. Slope: m = () / ()
Subtract the expressions. (10y - 2) - (8y + 3)
SOLUTION
We want to solve the expression
[tex]\mleft(10y-2\mright)-(8y+3)[/tex]Now, use the minus sign to multiply the other part
That is
[tex]-(8y+3)[/tex]We have
[tex]\begin{gathered} (10y-2)-(8y+3) \\ 10y-2-8y-3 \\ \text{collecting like terms } \\ 10y-8y-2-3 \\ 2y-5 \end{gathered}[/tex]Hence the answer is 2y - 5
Would you rather have a savings account that pays 5% interest compounded semiannually or one that pays 5% interest compounded daily? Explain.
Saving account that pays 5% interest compounded daily is much better than the account that pays 5% interest compounded semiannually.
As given in the question,
Interest rate = 5%
Types of account = Saving account
Pays the interest in two forms :
Compounded semiannually and Compounded daily
Saving account that pays 5% interest compounded daily is much better than the account that pays 5% interest compounded semiannually.
Reason :
Frequency of interest given on compounded daily is much higher and increase the amount much faster as compare to compounded semiannually.
When interest compounded daily generate 365 compounding periods a year, where as compounded semiannually generates two times in a year.
Therefore, saving account that pays 5% interest compounded daily is much better than the account that pays 5% interest compounded semiannually.
Learn more about interest here
brainly.com/question/13324776
#SPJ1
LaVelle is making a pitcher of caffe mocha. For each ounce of chocolate syrup, she uses 5 ounces of coffee. She wants to make 48 ounces of caffe mocha.
Let c represent the number of ounces of coffee, and let s represent the number of ounces of chocolate syrup used. Which of the following systems of equations models this situation?
The systems of equations which correctly models the situation as described is;
s = 5c ands + c = 48Which systems of equations correctly models the situation as described in the task content?It follows from the task content that the system of equations which models the production process of caffe mocha be determined.
As given in the task content;
Let c represent the number of ounces of coffee.Let s represent the number of ounces of chocolate syrup.Hence, since For each ounce of chocolate syrup, she uses 5 ounces of coffee, the situation can be represented algebraically as;
s = 5c.Also, since she wants to make 48 ounces of caffe mocha; we have;
s + c = 48.Therefore, the required system of equations is;
s = 5c ands + c = 48.Read more on system of equations;
https://brainly.com/question/13729904
#SPJ1
