By using the formula of compound interest we can say that at the end of second year Mrs. Smith will have $65,771.58.
What is Compound Interest?The interest earned from the initial deposit plus the cumulative interest is known as compound interest.
A = P(1 + r/n)^(nt), where P is the principle balance, r is the interest rate, n is the number of times interest is compounded per time period, and t is the total number of time periods, is the formula for compound interest.
Given that,
For first year,
P (principal) = $60,000.00
R = 4.3%
n = 1
t = 1
First, convert R as a percent to r as a decimal
r = R/100
r = 4.3/100
r = 0.043 rate per year,
Then solve the equation for A
A = P(1 + r/n)^nt
A = 60,000.00(1 + 0.043/1)^(1×1)
A = 60,000.00(1 + 0.043)^(1)
A = $62,580.00
A = P + I where,
P (principal) = $60,000.00
I (interest) = $2,580.00
So, by the end of second year Mrs. Smith will have $62,580.00.
Now, the amount calculated from first year will become the principle for second year.
For second year,
P (principal) = $62,580.00
R = 5.1%
n=1
t=1
First, convert R as a percent to r as a decimal
r = R/100
r = 5.1/100
r = 0.051 rate per year,
Then solve the equation for A
A = P(1 + r/n)^nt
A = 62,580.00(1 + 0.051/1)^(1×1)
A = 62,580.00(1 + 0.051)^(1)
A = $65,771.58
A = P + I where,
P (principal) = $62,580.00
I (interest) = $3,191.58
So, by the end of second year Mrs. Smith will have $65,771.58.
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Use the Distributive Property to rewrite each expression.
4(x + 2y - 3)
Answer:4x + 8 y -12
Step-by-step explanation:
the price of a tv is £950 plus VAT at 20% .what is the total cost of the TV?
1140 is the final price.
Step-by-step explanation: 20% of 950 is 190, so add that to 950 and you get 1140
Hans needs to rent a moving truck. Suppose Company A charges a rate of $40 per day and Company B charges a $60 fee plus $20 per day. for what number of days is the cost the same. Please also explain how you got the answer
Answer: x=3
Step-by-step explanation:
1. Hans needs to rent a moving truck. Suppose Company A charges $40.00 per day and Company B charges a $60.00 fee plus $20.00 per day, for what number of days is the cost the same?
Let x = # of days, since Company A charges $40/day then cost after x days = 40x
Let x = # of days, since Company B charges $20/day plus $60 fee, then cost after x days = 20x + 60
a. For what # of days is the cost the same?
When the cost is the same => 40x = 20x + 60
40x - 20x = 60
20x = 60
x = 60/20
x = 3
The cost is the same after 3 days.
Checking:
$40(3) = $20(3) + $60
$120 = $60 + $60
$120 = $120
y = -4.2x + 7.9 in standard form
The equation of the line y = -4.2x + 7.9 expressed in standard form is 42x + 10y = 79.
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is written as axe + by = c, where a and b are the coefficients of the variables x and y, respectively, and c is a constant. On the other hand, we can write the equation in point-slope form, (y - y1) = m, if we know the slope m and a point on the line (x, y).
Given the equation of a line, multiply both sides by 10 to turn the decimals into integers.
y = -4.2x + 7.9
10y = 10(-4.2x + 7.9)
10y = -42x + 79
Rewriting it in standard form ax + by = c,
10y = -42x + 79
42x + 10y = 79
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a rectangle has perimeter 24 m. express the area a of the rectangle as a function of the length, l, of one of its sides.
The Expression for the Area a of the rectangle as a function of length L is given by A(L) = 12L - L^2 .
Let,
length, L, and the width, W, are components that help determine the area, A, and the perimeter, P of the rectangle. These are given by the following equations
A=LW
P=2L+2W
Given,
Perimeter of the Rectangle = 24m.
We are asked to express the perimeter of the rectangle as a function of the length, L, of one of its sides.
We will first set up the equation of the Perimeter of the rectangle. We can let the width of the rectangle be W.
P = 2L+2W
24 = 2L+2W
12 = L+W
W = 12-L
Since we want to express the Area as a function of L, we have to find the value of W in terms of L. This is so we can eliminate the width in the equation for the Area. The Area as a function of L is as follows.
A(L, W) = LW
A(L) = L(12-L)
A(L) = 12L-L^2
Therefore, the Area as a function of L is given by A(L) = 12L-L^2.
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PLSS HELP :((
will mark brianlist if its the correct answer ty
place these number from least to greatest
-3
6
3.1
-2.5
1/4 -3/4
5) 2(n + 5) = 20
what is the answer need immediately
Solve the linear system
4x +9y = -72
4x +9y = 54
This needs to be answered in x and y
Answer:
no solution
Step-by-step explanation:
4x + 9y = - 72 → (1)
4x + 9y = 54 → (2)
multiply (1) by - 1
- 4x - 9y = 72 → (3)
add (2) and (3) term by term
0 + 0 = 126 , that is
0 = 126 ← not possible
This indicates the system has no solution
(-7,10) perpendicular to 2x - 3y= -3 using slope-intercept form
y = -3/2x - 20.5 is the line crossing through (-7,10) perpendicular to 2x - 3y= -3
In an equation, parallel lines have the opposite reciprocal slope. In other words, if a line's slope is a positive fraction, its reciprocal slope is negative.
Here given that 2x - 3y= -3
can also be written as
y = 2/3x + 1
Here 2/3 is the slope and 1 is the y-intercept
To find a parallel line to the following equation, use the opposite reciprocal slope and point, then solve using the point-slope formula.
y - y₁ = m(x - x₁)
We have, m = -3/2, x₁ = -7 and y₁ = 10
y - 10 = -3/2(x - (-7))
y - 10 = -3/2(x + 7)
y - 10 = -3/2x - 21/2
y = -3/2x - 21/2 + 10
y = -3/2x - 20.5
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MP Reason Abstractly If y varies directly with x-
direct variation. Then find each value.
9. If y = 14 when x = 8, find y when x = 12.
how can i solve literal equations?
Literal equations are equations containing two or more variables. Our goal is to solve for just one variable with respect to others. If it is known to us that how to solve regular equations, then literal equations are very easy to solve.
Literal equation is also termed as simultaneous equation ,
where more than 1 variable is present and can be solved by inputting value entirely into 1 variable form
For example,
x+ y=6
x-y=2
now putting x=y+2 from the second equation,
y+2+y=6
2y+2=6
y+1=3
y=2
x=y+2=2+2=4
To solve a literal equation means to express one variable with respect to the other variables in the equation.
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Equations that have two or more variables are considered literal equations. Our aim is to solve for a single variable in relation to other variables. Literal equations are fairly simple to solve if we know how to solve regular equations.
Simultaneous equation is another name for a literal equation.
where a problem with more than one variable can be handled by entering all of the values into a single variable form.
For Example :
x + y = 6
x - y = 2
Now putting x = y + 2 from the equation
y + 2 +y = 6
2y + 2 = 6
2y = 6-2
2y = 4
y = 2
Hence,
x = y + 2 = 2 + 2 = 4
To express one variable in relation to the other variables in an equation is to solve it literally.
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(-125) power -1/3
Evaluate this with step by step
based on the boxplot, the top 25 percent of the cars have a typical gas mileage of at least how many miles per gallon? 15
The number if miles per gallon is 35 miles.
How to solve the box plot.
From the information, it was stated that the box plot shows a gas mileage for twenty cars.
Therefore, based on the boxplot, the top 25 percent of the cars have a typical gas mileage of at least 35 miles per gallon.
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20796
A leather recliner with a regular price of $795.00 is on sale for 15% off. What is the sale price of the recliner?
Answer:
$675.75
Step-by-step explanation:
To find the sale price of the recliner, we can multiply 15% by the regular price.
15% = 0.15
(0.15)(795.00) = $119.25
This gives us the amount that the sale takes off from the regular price. We can subtract that from the regular price to find the sale price.
795.00 - 119.25 = $675.75
A bonus shortcut way to get our answer would be to subtract 15% from 100%.
100% = 1.00
1.00 - 0.15 = 0.85
This tells us that the sale price is 85% of the regular price. Using this information, we can multiply 85% by the regular price to also get our sale price.
85% = 0.85
(0.85)(795.00) = $675.75
water main construction a water main is to be constructed with a 20% grade in the north direction and a 10% grade in the east direction. determine the angle θ required in the water main for the turn from north to east.
The value of the angle θ required in the water main for the turn from north to east is 87.40°.
According to the statement
We have to find that the value of the angle.
So, For this purpose, we know that the
An angle is created when two straight lines or rays meet at a standard endpoint.
From the given information:
a main is to be constructed with a 20% grade within the north direction and a tenth grade within the east direction.
Then
Let n = North
and e = east
Then
using vectors,
n = j + 0.20 k
e = i + 0.25 k
And the
n · e = 1x0 + 0x1 + 0.20×0.25 = 0.05
Now take magnitude then
|n|·|e| = i(1² + 0.20²)·i(1²+0.25²) = 1.105
Now,
E° = arccos((n · e)/|n|·|e|)
E° = arccos(0.05/1.105)
E° = arccos (0.0452)
E° = 87.40°
So, The value of the angle θ required in the water main for the turn from north to east is 87.40°.
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There were approximately 3.3 * 10 8 people in the united states of america in 2010 the average person ate 1.5 * 10 2 lb of sugar that year approximately how many pounds of sugar were eaten in the us in 2010
Amount of sugar eaten in the US in 2010 = 4.95 x 10¹⁰ lb
Approximate number of people in the United States of America in 2010 = 3.3 x 10⁸
Amount of sugar ate by an average person in US = 1.5 x 10² lb
We have to find an approximate amount of sugar eaten in US in 2010.
It will be the product of the number of people in US and the sugar ate by a person in US.
So, Amount of sugar eaten in the US in 2010 approximately = 3.3 x 10⁸ x1.5 x 10²
= 4.95 x 10¹⁰ lb
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the domain of consists of numbers x for which not equals equals not equals 0 that are in the domains of both f and g. both f and g. either f or g.
The statement is true that the domain of f(x)/g(x) consists of numbers "x" that are in the domains of both f(x) and g(x) for which g(x) is not equal to 0.
A function's area is the set of its available inputs, or the set of enter values for which the characteristic is described. The area is the collection of objects that the system will take delivery of as inputs within the characteristic machine paradigm.For the function f(x)/g(x) to be defined, g(x) must now not be equal to 0.hence, the domain of the characteristic f(x)/g(x) consists of all of the numbers "x" which can be inside the domain names of each the functions f(x) and g(x) for which g(x) is not 0.To learn more about functions, visit :
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Ava read a total of 40 books over 5 months. If Ava has read 72 books so far, how many months has she been with her book club? Assume the relationship is directly proportional.
========================================================
Explanation:
She read 40 books over 5 months. This means her unit rate is 8 books per month (since 40/5 = 8)
x = number of months
(unit rate)*(number of months) = total books read
8x = 72
x = 72/8
x = 9
-------------
Another way to solve
(40 books)/(5 months) = (72 books)/(x months)
40/5 = 72/x
40x = 5*72 ... cross multiplying
40x = 360
x = 360/40
x = 9
What is the frozen food example of the free market and exit concept?
Answer: Food is Food
Step-by-step explanation:
The probability that a bus is on time is 0.75. Sarah takes the bus to school two days a week. Calculate the probability the bus is late on each of those days
The probability the bus is late on each of those days will be 0.0625.
How to calculate the probability?It should be noted that the probability that a bus is on time is 0.75. The probability that it's late will be:
= 1 - 0.75
= 0.25
Therefore, the probability the bus is late on each of those days will be:
= 0.25 × 0.25
= 0.0625
Therefore, the probability is 0.25.
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-14<4x+6<18
Please break it down for me
Basically, this is a domain. Well, a condition.
It's saying that any value that you subsitute in x , which is then multiplied by 4 and added 6, must ALWAYS be greater than -14, but lesser than 18.
What is the equation of the given line?
y = 5
x = 3
x = 1
y = 3
Answer:
y=x+2
Step-by-step explanation:
use the formula y=mx+c
first u find m which is the gradient 3-1/5-3 = 2/2=1
sub in any point to find the c
5=1(3)+c
c=2
y=1x+2
Describe and correct the error in solving the equation below.
Answer:
86
Step-by-step explanation:
What is the value of the digit 7 in the population of Memphis? What is the value of the digit 1 in the population of Denver? How many times as great as the value of the digit 1 in the population of Cleveland in this value?
PLSS HELP IT WILL MAKE ME FAIL
The number of times that the value of the digit 1 in the population of Cleveland in this value is 10.
How to illustrate the information?Based on the information, it should be noted 7 is in ten thousand place for Memphis. This means that it represents 70000.
It should be noted the 1 in Denver is in the same place. It represents 10000. On Cleveland, this is 1000.
Therefore, the number of times will be:
= 10000 / 1000
= 10
Therefore, the correct option is 10.
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Cleveland population 431,369 Denver population 610,345
Memphis population 676,640 What is the value of the digit 7 in the population of Memphis? What is the value of the digit 1 in the population of Denve?How many times as great the value of the digit 1 in the population of Cleveland is this value?
convert 1264 base 8 to base 10
1264₈ = 1•8³ + 2•8² + 6•8¹ + 4•8⁰
1264₈ = (2³)³ + 2•(2³)² + 3•2•2³ + 2²
1264₈ = 2⁹ + 2⁷ + 3•2⁴ + 2²
1264₈ = 512 + 128 + 3•16 + 4
1264₈ = 692
After converting the base, 1264 base 8 is equal to 692 base 10.
To convert a number from base 8 (octal) to base 10 (decimal), we need to evaluate the value of each digit in the base 8 number and then calculate the equivalent decimal value.
Given the number 1264 in base 8, we can break it down into its digits:
1 * 8³ + 2 * 8² + 6 * 8 + 4 * 1
Simplifying this expression:
1 * 512 + 2 * 64 + 6 * 8 + 4 * 1
Evaluating the multiplication:
512 + 128 + 48 + 4
Adding the products together:
692
In summary, to convert a number from base 8 to base 10, we evaluate the value of each digit by multiplying it with the corresponding power of 8, and then sum up the results. This gives us the equivalent decimal value of the number.
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Which expression is equivalent to (9^-2x3^5)-2?
Answer:
1
Step-by-step explanation:
3^-4 x 3^5
3 - 2
=1
Given L is between N and M, NL = 6x - 5, LM = 2x + 3, and NM = 4x + 9. Determine if L is the midpoint of segment MN. Justify your answer using sound mathematical reasoning.
Answer: L isn't the midpoint of segment MN.
Step-by-step explanation:
NL+LM=NM
6x-5+2x+3=4x+9
8x-2=4x+9
8x-2+2=4x+9+2
8x=4x+11
8x-4x=4x+11-4x
4x=11
Divide both parts of the equation by 2:
2x=5.5
NL=6x-5
NL=(2x)(3)-5
NL=(5,5)(3)-5
NL=16.5-5
NL=11.5
LM=2x+3
LM=5.5+3
LM=8.5
NL≠LM
Hence, L isn't the midpoint of segment MN.
In summary, based on the given lengths and mathematical reasoning, we have determined that point L is the midpoint of segment MN because the lengths of NL and LM are equal when x = 2.
We must compare the lengths of the two segments NL and LM and see if they are identical in order to establish whether point L is the midpoint of segment MN.
NL = 6x - 5
LM = 2x + 3
The lengths of NL and LM ought to be equal if L is the middle of segment MN. To put it another way, NL and LM ought to be equal.
Constructing the equation
6x - 5 = 2x + 3
Now, solve for x:
6x - 2x = 3 + 5
4x = 8
x = 2
As soon as we know the value of x, we can put it back into the NL and LM formulas to get their lengths at x = 2:
NL = 6x - 5 = 6 * 2 - 5 = 12 - 5 = 7
LM = 2x + 3 = 2 * 2 + 3 = 4 + 3 = 7
The lengths of NL and LM are both 7 units.
Point L is in fact the middle of segment MN because both segments NL and LM have similar lengths.
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to determine whether or not number of complaints influences accidents occurring in an area, charles has designed a survey. what is the explanatory variable?
In the survey study, the explanatory variable is: number of complaints .
What is an Explanatory Variable?An explanatory variable can be described as a type of independent variable that is manipulated by the researcher which explains the or predict the differences that occurs in a response variable.
For example, number of complaints is the independent variable that the dependent variable, "accidents that occurs in an area" depends on. That is, it explains or predicts the accidents that occurs in an area.
Therefore, we can conclude that, in the survey study, the explanatory variable is: number of complaints .
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PLEASE ANSWER QUICK
Evaluate the expression when n = 3:
−|−4n|
Answer:
12
Step-by-step explanation:
-4 X 3 =-12
=-(-12)
=12