Answer: " 80 " ; that is, the number: "eighty."
____
Step-by-step explanation:
Note the order of operations:
PE MD AS ;
Please Excuse My Dear Aunt Sally.
____
in which:
Parentheses are the first priority; if they occur.
then:
Exponents are the second priority if they occur.
followed by:
Multiplication and
Division; if any of these occur; and the priority is from the left-hand side to the right-hand side—if they occur. So; multiplication does not necessarily take priority over division. Rather, "Multiplication and Division" are treated equally, as the "next priority", from "left to right"—as they occur/if they occur;
followed by:
Addition and
Subtraction; of any of these occur; and the priority is from the 'left-hand side to the right-hand side—if they occur. So; addition does not necessarily take priority over subtraction. Rather, "Addition and Subtraction" are treated equally, as the "next priority", from "left to right"—as they occur/if they occur.
____
So: For our given problem; we can solve:
" 8(6 + 4) " ; which is the same as:
" 8 * (6 + 4) ";
We have a "multiplication" and a "parentheses" ;
So: The "parentheses" take first priority:
____
"(6 + 4) = 10 " ;
now: " 8 * (6 + 4) " ;
= 8 * 10 = 80 ; which is our answer:
____
Alternate method:
Note the distributive property of multiplication:
→ a(b + c) = ab + ac ;
So: 8 (6 + 4) = (8*6) + (8*4) ;
= 48 + 32;
= 80 ; which is our correct answer!
____
Hope this answer was helpful to you!
Please reply if you have any questions! Wishing you well!
____
Suppose an individual makes an initial investment of $2,800 in an account that earns 6%, compounded monthly, and makes additional contributions of $100 at the end of each month for a period of 12 years. After these 12 years, this individual wants to make withdrawals at the end of each month for the next 5 years (so that the account balance will be reduced to $0). (Round your answers to the nearest cent.)
(a) How much is in the account after the last deposit is made?
$
(b) How much was deposited?
$
(c) What is the amount of each withdrawal?
$
(d) What is the total amount withdrawn?
$
a) The total amount in the account after the last deposit is $26755.96.
b) A total of $16900 was deposited.
c) Amount of each withdrawal is $517.
d) The total amount withdrawn is $31020.
What is future value?The worth of a present asset at some point in the future based on an estimated rate of growth is known as future value (FV). For investors and financial planners, the future value is crucial because they use it to predict how much an investment made now will be worth in the future.
FV of a single deposit of $ 2800 can be computed as
FV₁ = PV(1+r)ⁿ
PV = $ 2800
r = 6% = 0.06/12
r = 0.005
n= number of periods
= 12 yr × 12 months = 144
FV₁ = 2800 (1 + 0.005)¹⁴⁴
= 2800 (1.005)¹⁴⁴
= 2800(2.0507)
= 5741.96
The FV of monthly deposits can be computed using the formula for the FV of the annuity:
FV₂ = C x [(1+r) n -1/r]
Periodic cash deposit, C = $100
So,
FV = 100 × [((1.055)¹⁴⁴ - 1)/0.005]
= 100 × [(2.0507 - 1)/0.005]
= 100 × [1.0507/0.005]
= 100 × 210.14
= $21014
The total future value of the account is given by
= $5741.96 + $21014
= $26755.96
b) Total deposit = Initial investment amount + amount of monthly deposits
= 2800 + (100 × 144)
= 2800 +14400
= 16900
c) Formula for PV of an annuity can be used to compute monthly withdrawals as:
PV = A x [1-(1+r)⁻ⁿ/r]
So, A = PV/[1-(1+r)⁻ⁿ/r]
PV = $26755.96
n= number of periods = 5 × 12 = 60
r = 0.005 per month
A = 26755.96/ [1- (1+0.005)⁻⁶⁰/0.005]
A = 26755.96/ [1- (1.005)⁻⁶⁰/0.005]
A = 26755.96/ [1- (0.7413)/0.005]
= 26755.96/ [0.2587/0.005]
= 26755.96/(51.74)
= 517.12
So, the amount of each withdrawal for five years is $517.
d) Total amount withdrawn is
= number of withdrawals × amount of each withdrawal
= 60 × 517
=31020
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SOME ONE PLS HELP RNNNNNNN ! WILL GIVE BRAINLEST
Answer:
below
Step-by-step explanation:
point -1,-4
y - -4 = 3 ( x - -1)
y + 4 = 3 ( x+1) <====== I think this is a far as they want you to take it
y = 3x -1 slope - intercept form
2.64 to nearest whole number
Answer:
3
Step-by-step explanation:
2.64 rounded to the nearest whole number would be 3. This is because if a number is 5 or greater than 5, it rounds up, but if a number is under 5, it would round down. Since we are looking at the number to the right of the 2 in 2.64, and because we are looking for the nearest whole number, it would round up to 3. 6 is greater than 5, so we automatically know that we round up.
Work out 132% of 96 m
Give your answer as a decimal in metres (m).
Answer:
126.72m
Step-by-step explanation: 1.32 x 96 = 126.72, I struggled with that stuff too no shame
You deposit $500 in an account earning 4% interest compounded annually. How much will you have
in the account in 15 years?
The total amount will have in the account in 15 years is $900.47
What is compound interest?
Compound Interest is the interest calculated on the cumulative amount, rather than being calculated on the principal amount only.
Amount,[tex]A=P[1+(\frac{R}{100})^{T}][/tex], where P is the principal, R is the rate of interest per unit time period and n is the time period.
Compound Interest, CI = Amount – Principal
Using the formula,
[tex]A=P[1+(\frac{R}{100})^{T}][/tex]
Where,
A=Total Amount(To be calculated)
P=Principal of money deposited=$500
R=Annual interest rate=4%
T=Time in years=15 years
⇒[tex]A=500(1+\frac{4}{100}[/tex][tex])^{15}[/tex]
⇒A=500(1+0.04[tex])^{15}[/tex]
⇒A=500(1.04[tex])^{15}[/tex]
⇒A=500*1.80094351
⇒A=$900.47
Hence,the total amount will have in account in 15 years is $900.47
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What type of connection can you make between markups and tips or taxes? What type of connection can you make between markdowns and discounts? Explain your answer.
Markup adds an increase in the original price of an item, and tips or taxes add money to a bill. Hence, the connection between markups and tips or taxes.
Discounts are given in order to lower the price of an item from its original price, and markdown is the price that is reduced from an item's original price.
What is the difference between Markup and Markdown?
Markup price is the increase in an item (by a certain percentage) over the original price.
Markdown prices are reductions in an item's selling price from its initial selling price expressed as a rate (markdown percentage).
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In a baseball league of six teams, how many games are needed to complete the schedule if each team plays seven games with each other team?
If the six teams of a baseball league , and each team plays seven games with each other , then the number of games to be played is 105 .
in the question ,
it is given that
the number of teams in the baseball league = 6
number of matches that each team plays with each other = 7 .
Number of ways two teams can be selected out of 6 teams = C(6,2)
and they need to play 7 games with each other ,
so the number of games required to complete the schedule is
= 7 × C(6,2)
= 7 × 15
= 105
Therefore , the number of matches that is needed to complete the schedule is 105 .
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29. Find x and the dimensions of the rectangle below.
A = 126 ft²
x+2
x-3
The x value is 12, length is 14 feet and breath is 9 feet when the area of rectangle is 126 square feet.
Given that,
The rectangle has a surface area of 126 square feet.
The length is x+2 and the breath is x-3.
We have to find the x value, length and breath.
We know that,
The area of the rectangle is length × breath.
126=(x+2)(x-3)
126= x²-3x+2x-6
126= x²-x-6
x²-x-6-126=0
x²-x-132=0
x²-12x+11x-132=0
x(x-12)+11(x-12)=0
(x-12)(x+11)=0
x-12=0 or x+11=0
x=12 or x=-11
We take the x as positive so its 12.
Length is x+2=12+2=14
Breath is x-3=12-3=9
Therefore, The x value is 12, length is 14 feet and breath is 9 feet when the area of rectangle is 126 square feet.
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What is a graph theory in math?
Answer:
Graph theory is used in dealing with problems that have a reasonably natural graph/network structure.
Explanation:
For example,
road networks - nodes = towns
road junctions, arcs = roads
Communication networks - telephone systems
'Computer systems'
Foreign exchange/multinational tax planning (network of fiscal flows).
Hope it helped! :)
Graph theory is applied to problems that have a fairly natural graph/network structure.
What is graph theory?Graph theory is the study of graphs in mathematics, which are mathematical structures used to model pairwise relationships between objects. In this context, a graph is made up of vertices (also known as nodes or points) connected by edges (also called links or lines).
Graph Theory is the study of relationships. Graph theory, given a set of nodes and connections that can abstract anything from city layouts to computer data, provides a useful tool for quantifying and simplifying the many moving parts of dynamic systems.
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7 (4-x)=84
74-x)7=84/7
4-x-12
4-x-4=-12-4
-x=-16
-x/=1=-16/-1
=16
Answer Is=16 How do I Check my answer??
Answer:
x = - 8
Step-by-step explanation:
7(4 - x) = 84 ( divide both sides by 7 )
4 - x = 12 ( subtract 4 from both sides )
- x = 8 ( multiply both sides by - 1 )
x = - 8
As a check
substitute x = - 8 into the left side of the equation and if equal to the right side then it is the solution.
7(4 - (- 8) )
= 7(4 + 8)
= 7(12)
= 84 = right side
Then x = - 8 is the solution to the equation
Which is the graph of y=LxJ-2?
Answer:
the third one is the answer.
Step-by-step explanation:
take 0 at the x value, the greatest integer function of 0 is 0 its self. so when you take 0, Y=[x]-2 become -2. so the y-axis Crosses in (0,-2).
Can someone help me I don’t understand this question it’s geometry
The triangle with all sides is are given below
What is a triangle?
Triangles are three-sided closed polygon formed by the intersection of three lines. It is encountered a lot in everyday life. It is one of the basic shapes of geometry. It has three sides, three angles, and three vertices.
Given, angle A =30, b=6
we know cos 30 = √3/2
√3/2 = b/c
√3/2=6/c
c =6/√3/2= 6.9
Similarly for a=13, b =13
using pythagoras theorem,
c^2=a^2+b^2
=18.38
Hence, we can write the rest part
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hey i need help asap with this homework problem.
The amount in Mrs. Piazza's account after 4 years is 8960 dollars.
What is simple interest?Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time. In simple interest, the principal amount is always the same, unlike compound interest where we add the interest of previous years principal to calculate the interest of the next year.
Principal(P) = 8000
time(T) = 4 years
rate(R) = 3%
simple interest = PRT/100
Simple interest = 8000 x 3 x 4 / 100
simple interest is 960 dollars
Amount after 4 years = principal + interest
= 8000 + 960
= 8960 dollars
In conclusion, the Amount after 4 years is 8960 dollars
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Write the equation of the parabola that has the same shape as f(x)=-3x² but with vertex (5,9) in the form f(x)=a(x-h)²+k
f(x)=
$8 is what percent of $8?
Answer:
100%?
Step-by-step explanation:
If Elon and Jeff work together, they can finish the work in 3 hours. If Jeff works together with Bruce, they
can make this work done in 6 hours. Elon and Bruce can finish this work in 4 hours. How much time would
it take to finish the work if all three worked together? pls helpp
Answer:
2 2/3 hours
Step-by-step explanation:
You want to know the time it would take Elon, Jeff, and Bruce working together, if Elon and Jeff can complete the work in 3 hours, Jeff and Bruce take 6 hours, and Elon and Bruce take 4 hours.
Total of ratesJob completion time problems like this one are more easily understood in terms of rate of completion. If we let e, j, and b represent the rates of job completion in jobs per hour for each of Elon, Jeff, and Bruce, respectively, then the given relations can be written ...
e +j = 1/3
j +b = 1/6
e +b = 1/4
Adding these equations together gives ...
(e +j) +(j +b) +(e +b) = (1/3) +(1/6) +(1/4)
2(e +j +b) = 3/4 . . . . . . . simplify
e + j + b = 3/8 . . . . . . . . divide by 2
The total rate of job completion when Elon, Jeff, and Bruce work together is 3/8 job per hour. The hours it takes them to do one job is the reciprocal of this:
1/(3/8 job/hour) = 8/3 hour/job
It would take Elon, Jeff, and Bruce 2 2/3 hours to complete the work if they worked together.
__
Additional comment
For this problem, we don't need to know the individual completion times. If we were to figure them we'd find them to be (working alone) ...
Elon: 4.8 hoursJeff: 8 hoursBruce: 24 hours3. Two of the vertices of an equilateral triangle are (0, -a)
and (0, a). The third vertex is on the x-axis to the right of
the origin. Name the coordinates of the third vertex.
The third coordinate of the equilateral triangle is [tex](\sqrt3a,0)[/tex]. Ir can be obtained by distance formula.
What is distance formula?
It gives the distance between two coordinates.
Distance formula is given by the following expression:
[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Consider the third cordinate is (x,0) and x is positive because it is on tight side on the x axis.
Now, since the triangle is equilateral hence, the distance of (x,0) from (0, -a) and (0, a) should be equal to distance between (0, -a) and (0, a).
Now, caculate the distance between (0,-a) and (0, a).[tex]\sqrt{(0-0)^2+(-a-a)^2}=2a[/tex]
Now, distance between (x,0) and (0, a) should be 2a.
[tex]\sqrt{(x-0)^2+(0-a)^2}=2a\\\sqrt{x^2+a^2}=2a[/tex]
Now, square on both the sides.
[tex]x^2+a^2=4a^2\\x^2=3a^2\\x=\sqrt3a[/tex]and [tex]-\sqrt3a[/tex]
But the negative value of x is not possible because the coordinate lies on the right side.
Hence, the third coordinate of equilateral triangle is [tex](\sqrt3a,0)[/tex].
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Solve this system of equations by graphing. First graph the equations, and then type the
solution.
y = 5/2x - 1
y = 2x - 3
Click to select points on the graph.
The solution of the system equation is (-4,-11).
What is system equation?
One or more equations involving a number of variables make up a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations.
Here the given system equation is,
=> y = 5/2x-1------->1
=> t=2x-3---------->2
Put 1 into 2 then
=> 5/2x-1=2x-3
=>1/2 x=-2
=> x=-4
Put x=-4 into 2 then,
=> y=-8-3=-11.
Hence the solution of the system equation is (-4,-11).
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I need help with this
The value of b is 405 in the given polynomial (a+3)⁵=a⁵+15a⁴+90a³3²+270a²+ba+243
What is Polynomial?Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.
Given,
(a+3)⁵=a⁵+15a⁴+90a³3²+270a²+ba+243,
We need to find the value of b
The binomial formula for (a+b)⁵=a⁵+5a⁴b+10a³b²+10a²b³+5ab⁴+b⁵
Now let us find (a+3)⁵
We just need to replace b with 3 in above formula.
(a+3)⁵=a⁵+5a⁴3+10a³3²+10a²3³+5a3⁴+3⁵
=a⁵+15a⁴+90a³3²+270a²+405a+243
Hence the value of b is 405 in the given polynomial a⁵+5a⁴b+10a³b²+10a²b³+5ab⁴+b⁵
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The population of a city has increased by 24% since it was last measured. If the current population is 65,100, what was the previous population?
Answer: 49476
Step-by-step explanation:
What is the approximate percent decrease from 1865 to 1240?
Answer: It should be 33.5%
DUE TOMORROW :)) PLEASE HELPPP :))
Answer:
x = 10
Step-by-step explanation:
The angles are supplemental
100 -2x + 10x = 180 Combine like terms
100 + 8x = 180 Subtract 100 from both sides of the equation
8x = 80 Divide both sides by 8
x = 10
What theorem is used to find the side of a triangle in a right triangle?
A. midsegment theorem
B. base angle theorem
C. triangle proportionality theorem
D. Pythagorean theorem
Suppose you want to have $500,000 for retirement in 35 years. Your account earns 4% interest. How much would you need to deposit in the account each month?
The answer, the money needs to be deposited each month is $557.47.
What is simple interest?
A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,
The future money plan to have 500000
Retirement in 35 years.
The interest 4%.
number of time periods = 35 years * 12 months per year = 420
interest will be .4166666667% per month
The formula = [tex]p(\frac{(1+r/n)^{r/n} -1 }{\frac{r}{n} } )[/tex]
⇒500000*(.014/12) = d(3.98-1)
⇒d = 1666.7/2.98 = 557.47
Hence the money needs to be deposited each month is $557.47
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Which has greatest rate help please
The last function having the greatest rate of change.
What is rate of change?
The pace at which one quantity changes in relation to another quantity is known as the rate of change function. Simply said, the rate of change is calculated by dividing the amount of change in one item by the equal amount of change in another.
Consider the first function,
From this function we get two points (2, 1) and (-2, -1).
To find rate using this points.
Rate = [tex]\frac{y_2-y_1}{x_2-x_1} = \frac{-1-1}{-2-2} = \frac{-2}{-4}=\frac{2}{4} =\frac{1}{2}[/tex]
Consider the second function,
The second function is a vertical line of x = -3.
Since the rate of vertical line is undefined.
Consider the third function,
The third function is a horizontal line y = 4.
Since two points having the same y - value.
Hence, the rate is zero.
Consider, the last function,
From last function we get two points (1, 5) and (-3, -3).
So,
Rate = [tex]\frac{-3-5}{-3-1} = \frac{-8}{-4} = \frac{8}{4} = 2[/tex]
Hence, the last function having the greatest rate.
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trying to find the logarithm
The expression of logarithm will be -In4 x k .
Given,
In the question:
The expression of the logarithms is:
In[tex](\frac{1}{4^k} )[/tex]
To solve the above expression:
Now, According to the question:
In([tex]\frac{1}{4^k}[/tex])
Apply laws of logarithm to simplify the expression
-In[tex]4^k[/tex]
Express the logarithm of a power of an expression as the power times the logarithm of the expression
-k x In4
Multiply the monomials :
-In 4 x k
Hence, The expression of logarithm will be -In4 x k .
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Can you please help me
What is the solution to -1-7?
H
+
-10-9-8-7-6-5-4-3-2-1 0 1 2 3 4 5 6 7 8 9 10
0-8
O-6
06
08
Answer:
Please be more specific
Step-by-step explanation:
1.) Solve the following equation for w: 3w-4(w-3) = 6
Answer: w=6
Step-by-step explanation: 1. Simplify. Distribute the -4 to the w and the -3. -4*w is -4w and -4*-3 is +12, so your left with 3w-4w+12=6.
2. simplify again. 3w-4w is -w.
3. -w+12=6. Subtract w to both sides, so its -w=-6. The negatives cancel out, so w just equals 6.
Plsssssssss helpppppppppppp
Answer: It is C
Step-by-step explanation:
The slop for Kitten A is 1/4 or 4
Kitten B has a slop of 2/6 or 3 so the answer is,
C Kitten B/rate of change 4A box contains 17 calculators, 5 of which are defective.
If five calculators are randomly selected from the box, in how many ways can all the selected calculators be defective?
There are _____ different ways for all 5 selected calculators to be defective.
If five calculators are randomly selected from the box, in how many ways can all the selected calculators be non-defective?
There are _____ different ways to for all 5 selected calculators to be non-defective.
There is only 1 way for all 5 selected calculators to be defective.
There are 792 different ways for all 5 selected calculators to be non-defective.
Given, that a box contains 17 calculators, 5 of which are defective.
So, there are 12 non-defective calculators.
Now, five calculators are selected randomly from the box.
We are asked the number of ways in which all the selected calculators are defective.
So, the number of ways in which all selected 5 calculators be defective is,
C(5 , 5) i.e. we only select 5 defective calculators.
C(5 , 5) = 1.
So, there is only 1 way for all 5 selected calculators to be defective.
Now, we are asked the number of ways in which all the selected calculators are non-defective.
So, the number of ways in which all selected 5 calculators be non-defective is,
C(12 , 5) i.e. we select 5 calculators from the 12 non-defective calculators.
C(12 , 5) = (12×11×10×9×8)/(5×4×3×2×1)
C(12 , 5) = 792
So, there are 792 different ways for all 5 selected calculators to be non-defective.
Hence, there is only 1 way for all 5 selected calculators to be defective.
There are 792 different ways for all 5 selected calculators to be non-defective.
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