A 1.03% rate of return is built into the annuity.
First optionTo receive a single payment today of $4,500,000Second optionTo receive an annual payment of $250,000.Term is equal to 20 years.Let the rate of return be x%.A series of payments paid at regular intervals is known as an annuity. Regular savings account deposits, mortgage payments, insurance premiums, and pension payments are all examples of annuities. The periodicity of payment dates allows for the classification of annuities.At this rate, the present value of the annuity is $4,500,000.The present value of the first option equals the present value of the second option. $4,500,000 = $250,000[1/x + 1/x² + … + 1/x^20]Upon solving, we get approximately x is 1.03%.To learn more about annuity, visit :
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6t^2/5+11t^1/5+3=000
You didn't provide a lot of info regarding the given question, however if you are looking to solve for t:
_______________________________________________
Isolate the variable by dividing each side by factors that do not contain the variable.
Solution's Exact Form:
[tex]t=-\frac{1}{243},-\frac{243}{32}[/tex]
_______________________________________________
Hope this helps! If not, please provide further info if you can regarding this question and I'll see what else I can do to help. If this did help however, lmk! Thanks and good luck!
can some please explain to me how my teacher get to the part that i highlight. (2^-5)^-3x i'm so lost someone please explain
Answer:
see explanation
Step-by-step explanation:
using the rules of exponents
[tex]\frac{1}{a^{m} }[/tex] = [tex]a^{-m}[/tex]
then
[tex]\frac{1}{32}[/tex] = [tex]\frac{1}{2^5}[/tex] = [tex]2^{-5}[/tex]
and
[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex] , so
[tex](2^{-5}) ^{-3x}[/tex]
a population has mean of 0.1 and standard deviation of 2.1.what is the probability that the mean of a random sample of size 900 will be negative
Answer on Question #54875
–
Math
–
Statistics
and Probability
A normal population has a mean of 0.1 and standard deviation 2.1. Find the probability that the
mean of a sample of size 900 will be negative.
Solution
In accordance with the given problem, we have the following data:
μ
=
0
.
1
,
σ
=
2
.
1
and
n
=
900
. It is known that
푥
~
M
(
μ
,
σ
2
)
and
z
~
N
(
0
,
1
)
Please help me
The elevation of Kristianstad, Sweden, a city founded by King Christian IV of Denmark, is meters . Which of these describes the elevation of Kristianstad?
The best description for the elevation of Kristianstad is below sea level.
How to find what describes the elevation of Kristianstad?The elevation of Kristianstad, Sweden, a city founded by King Christian IV of Denmark, is -2 meters .
The best option that describes the elevation of Kristianstad is as follows:
Therefore,
At sea level the elevation will be at 0 meters.
Above sea level the elevation will be above 0 meters. That will make the elevation to be positive
Below sea level the elevation will be below 0 meters. That will make the elevation to be negative.
Therefore, the best description for the elevation of Kristianstad is below sea level.
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Liberty middle school has 600 students in honors class three out of eight students walk to school how many students are at the school can be expected to walk to school
Answer:
225 students
Step-by-step explanation:
600 students, and [tex]\frac{3}{8}[/tex] of students walk to school
[tex]600 * \frac{3}{8} = 225[/tex]
225 students can be expected to walk to school
Given: 2 ( x + 3)-8=10
Prove: x = 6
Answer:
x=6
Step-by-step explanation:
2(x+3)-8=10
use 2 to multiply the one in the bracket
(2x+6)-8=10
group like terms
2x-2=10
send all constant terms to one side of the equation
2x=10+2
2x=12
divide both side by the coefficient of x
2x/2=12/2
x=6
Officials begin to release water from a full man-made lake at a rate that would empty the lake in 14
14
weeks, but a river that can fill the lake in 25
25
weeks is replenishing the lake at the same time. How many weeks does it take to empty the lake? Express your answer as a fraction reduced to lowest terms, if needed
Answer:
[tex]\frac{350}{11} weeks[/tex]
Step-by-step explanation:
Let V be the volume of water in the lake and w be the number of weeks to empty the lake
Since it takes 14 weeks to empty the lake by water release, the empty rate = V/14
But at the same time the river is replenishing the lake at a rate of V/25 since it will take 25 weeks to fill the empty lake
Net empty rate = Empty rate - replenishment rate = [tex]\frac{V}{14} - \frac{V}{25} = \frac{V}{w}[/tex]Divide the equation by V to eliminate V giving[tex]\frac{1}{14} - \frac{1}{25} = \frac{1}{w}[/tex]
Multiply by 350 (14 x 25) to eliminate the denominators[tex]25 - 14 = \frac{350}{w}[/tex] ==> [tex]11 = \frac{350}{w}[/tex]
Multiply both sides by w to cancel the denominator w11w = 350
Divide both sides by 11 to getw = [tex]\frac{350}{11 }[/tex] weeks
A superhero recently asked his nemesis how many cats she has. She answered with a riddle: "Five-sixths of my cats plus six"
How many cats does the nemesis have?
There are 6 faces on a standard die. How many faces are on 5 dice?
Answer: 30
Step-by-step explanation: just do 6*5, 6 faces for five die is thirty faces
There are 30 faces on 5 dice in total.
Given that a standard die has 6 faces on it, we need to determine the number of the faces on 5 dice.
A standard die has 6 faces. If you have 5 dice, each with 6 faces, you can calculate the total number of faces by multiplying the number of dice by the number of faces on each die:
Total number of faces = Number of dice × Number of faces on each die
Total number of faces = 5 dice × 6 faces/die
Total number of faces = 30 faces
So, there are 30 faces on 5 dice.
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What is the measurement of this angle ?
The measurement of the given angle is a 90 degree.
According to the statement
We have to find that the measurement of this angle.
So, For this purpose, we know that the
An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.
From the given information:
In the given figure, the measurement of the angle we have to find.
A 90-degree angle is a right angle and it is exactly half of a straight angle. It always corresponds to a quarter turn.
And from the figure it is clearly visible that the line of the angle exactly matches with the 90 degree.
Then the angle is 90 degree.
So, The measurement of the given angle is a 90 degree.
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A washer and a dryer cost $813
combined. The washer costs $87
less than the dryer. What is the cost of the dryer?
The cost of the dryer will be $450
In the given sum the combined cost of the washer and dryer is $813
let the cost of the dyer be x
the cost of the washer will be (87 - x) as it is mentioned in the question washer costs $87 less than the dryer
According to the problem :
∴ x + (x-87) = 813
=> x+x-87 = 813
=> 2x - 87 = 813
=> 2x = 813 +87
=> 2x = 900
=> x = 900/2
=> x = 450
So the cost of the dryer is $450
The cost of the washer is = x - 87 = 450 - 87 = $363
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maths geometry questions
pleas help
Step-by-step explanation:
remember, a parallelogram is a quadrilateral with 2 pairs of parallel and equal sides, and 2 pairs of correspondingly equal angles. and its diagonals are intersecting each other in their midpoint.
with that in mind
(i)
because ABCD is a parallelogram, AD = BC, and AB = CD.
and angle A = angle C (and angle B = angle D).
therefore, as AE = FC, this also means that ED = BF.
via SAS (side angle side) it is clear that the triangles ABE and CDF are congruent.
therefore, EB = DF.
as ED is part of AD, and BF is part of BC, it is also clear that ED || BF.
together with ED = BF this means that EB || DF.
so, we have with BEDF 2 pairs of parallel and equal sides. and that is a parallelogram.
(j)
BCDE and ABCG are parallelograms.
so, BC = DE = AG, CD = BE, AB = CG.
due to the midpoint intersection rule of the diagonals of parallelograms, we also know
GE = CG = AB, DG = BG.
and as CG || AB, then also GE || AB.
together with AB = GE that means that AE = BG and AE || BG.
so, we have with ABGE again 2 pairs of parallel and equal sides. and that is a parallelogram.
22.83/0.06 = __________
Answer: 380.5
Step-by-step explanation: you can type it into desmos graphing calculator
A student receives the following grades, with an A worth 4 points, a B worth 3 points, a C worth 2 points, and a D worth 1 point. What is the student's weighted mean grade point score? B in 2 two-credit classes D in 1 two-credit class A in 1 three-credit class C in 1 three-credit class
The student's GPA is of 2.33.
What is GPA?Grade Point Average (GPA) is the measure used to summaries your academic achievement at Griffith.
Given:
A worth 4 points,
B worth 3 points,
C worth 2 points,
D worth 1 point
The GPA is
= 3(3) + 1(3) + 2(4) + 2(2)/9+3+4+2
=9+3+8+4/18
=2.33
Hence, The student's GPA is of 2.33.
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Solve the system of equations.
x + y = 8
y=x²- 4
The solution for the given system of equations is (3,5) and (-4,12).
Given two systems of equations i.e. x+y=8 and y=[tex]x^{2}[/tex]-4 and asked to solve them.
⇒x+y=8; let's assume this equation as A
⇒ y=[tex]x^{2}[/tex]-4; let's assume this equation as B
From equation A
⇒y=8-x
From equation B
⇒y=[tex]x^{2}[/tex]-4
Equating both the values of y
⇒8-x=[tex]x^{2}[/tex]-4
⇒[tex]x^{2}[/tex]-8-4+x=0
⇒[tex]x^{2}[/tex]-12+x=0
{solving quadratic equation}
⇒[tex]x^{2}[/tex]-12+4x-3x=0 { factorizing the quadratic equation}
⇒[tex]x^{2}[/tex]+4x-3x-12=0
⇒x(x+4)-3(x+4)=0
⇒(x-3)(x+4)=0
Therefore, the value's of x=3,-4
⇒if x=3
From equation A
⇒y=8-3=5
For x=3 ; y=5
⇒if x=-4
From equation A
⇒y=8-(-4)=12
For x=-4 ; y=12
Therefore,The solution for the given system of equations is (3,5) and (-4,12).
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There are five questions listed below. Each question includes the quantity 43. Match the 43 in each question on
the left to which part of the problem it represents on the right -- the base, percent, or amount. Some answer
options on the right will be used more than once.
What number is 15% of 43?
43% of 300 is what number?
12% of what number is 43?
43 is what percent of 106?
What percent of 43 is 6?
percent
base
amount
Click and hold an item in one column, then drag it to the matching item in the other column. Be sure your
What number is 15% of 43?
43 here is the base43% of 300 is what number?
Here 43 is the percent12% of what number is 43?
43 is used here as amount43 is what percent of 106?
43 is used here as amountWhat percent of 43 is 6?
43 here is the baseWhat is base?The base as used in the question refers to the main number that is a=to say the number on which other calculation are focused on.
What is percent?Percent is a term used in mathematics to refer to a fraction with a denominator of one hundred. Numbers in percent is accompanied with the percent symbol which is %. Any number having that symbol means that the number is a fraction with a denominator of one hundred.
What is amount?The term amount as used refers to the result gotten when some mathematical operation is being done on the base.
The calculations to the questions asked are below:
What number is 15% of 43?
= 15/100 x 43
= 6.45
43% of 300 is what number?
= 43/100 x 300
= 129
12% of what number is 43?
= 12/100 x 43
= 5.16
43 is what percent of 106
= 43/106 * 100
= 40.56%
What percent of 43 is 6
= 6/43 x 100
= 13.95%
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Consider Line 2, which has the equation: y = = - 1/3x + 14, Give the equation of the line parallel to Line 2 which passes through: (-7,4).
The equation of teh second line is y = -1/3x + 5/3
How to determine the equation?The first equation is given as
y = -1/3x + 14
The slope of the above equation is
m = -1/3
Parallel lines have equal slope
So, the slope of the other line is
m = -1/3
The equation is then calculated as
y = m(x - x1) + y1
So, we have
y = -1/3(x + 7) + 4
Expand
y = -1/3x - 7/3 + 4
Evaluate
y = -1/3x + 5/3
Hence, the equation of teh second line is y = -1/3x + 5/3
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Prove that for all integers a, b, n, if n = a + b, then a ≤ n/2 or b ≤ n/2 using proof by contradiction.
From the example that if a = 3 and b = 3 so the value of n = 6. It means that a ≤ n/2 and b ≤ n/2.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given that all integers a, b, and n, if n = a + b, then a ≤ n/2 or b ≤ n/2. Let the value of a = 3 and b = 3 now the value of n will be:-
n = a + b
n = 3 + 3 = 6
a = 3, n = 6 then a ≤ n/2.
b = 3, n = 6 then b ≤ n/2.
Therefore, the example that if a = 3 and b = 3 so the value of n = 6. It means that a ≤ n/2 and b ≤ n/2.
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which is greater -2.75 or -2.25
Answer: -2.25
Step-by-step explanation:-2.25 because it is closer to 0
Bennett is setting up a light display for a wedding with two 10-foot strands of lights. The lights will be attached to the top of a pole and to two stakes on the ground forming two right triangles. If the distance from the base of the pole to each stake is the same as the height of the pole, how tall, in feet, should the pole be? Round your answer to the nearest tenth.
The height of the pole is 7.1 feet.
Given that a light display for a wedding with two 10-foot strands of lights and top of a pole and to two stakes on the ground forming two right triangles.
The Pythagorean theorem, also known as the Pythagoras theorem, explains the relationship between the three sides of a right triangle.
The two sides of triangle are equal that is x and and the third side is 10.
Now, we will apply the pythagoras theorem, we get
B²+P²=H²
Here B=P+x and H=10
x²+x²=(10)²
2x²=100
Now, we will divide both sides with 2, we get
2x²/2=100/2
x²=50
Now, we will take square root on both sides, we get
√x²=√50
x=√50
x=7.07106781
The Round to the nearest tenth is x=7.1 feet.
Hence, the height of the pole when wedding with two 10-foot strands of lights and the lights will be attached to the top of a pole and to two stakes on the ground forming two right triangles is 7.1 feet.
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how many different digits appear when 1/110 is written as a recurring decimal
The number of different digits that appear when [tex]\frac{1}{110}[/tex] is written as a recurring decimal is two digits i.e 9,0.
Given the fraction [tex]\frac{1}{110}[/tex]
Recurring decimal:
A repeating decimal, also known as a recurring decimal, is a decimal representation of a number whose digits are periodic (repeating at regular intervals) and whose infinitely repeated portion is not zero. It is possible to demonstrate that a number is rational if and only if its decimal representation repeats or terminates.
⇒[tex]\frac{1}{110}[/tex]=0.0090909090.....
Therefore,The number of different digits that appear when [tex]\frac{1}{110}[/tex] is written as a recurring decimal is two digits i.e 9,0.
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Urgent Please!
• What expression would represent the area of a square with side length 10?
—-
•Part C: What expression would represent the area of a square with side length 20?
—-
•Part D: What expression would represent the increase in area caused by changing the side length from 10 to 20?
Answer: B. 100
C. 400
D. 300
Step-by-step explanation:
A=area of square. s=side length of square.
B. A=s^2
A=10^2
A=100
C. A=20^2
A=400
D. I=Increase in Area
I=20^2 -10^2
I=400-100
I=300
Write an expression to represent: 9 more than the quotient of 2 and x
Expression for given numerical is: 9+ (2/x)
Given that we have an word equation that is 9 more than the quotient of 2 and x
A quotient is a quantity produced by the division of two numbers.
Quotient of 2 and x is [tex]\frac{2}{x}[/tex].
Nine(9) more than 2/x is = 9+ (2/x)
So we have an expression that is:
9+ (2/x)
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Last year, Salma invested her money in two purchases. She purchased a certificate of deposit for $3000 that paid 5% interest per year and purchased $7000 in corporate bonds paying 4% interest per year. Answer the questions below. Do not do any rounding.
Answer:
a. $2850
b. $6720
Step-by-step explanation:
a.
3000(1-0.05) = $2850
b.
7000(1-0.04) = $6720
You are getting on a plane to visit family 1200 miles away. The plane you are boarding will travel on
average 500 miles per hour. How long will the trip take you?
Answer:
2.4 hours or 2 hours and 24 minutes
Step-by-step explanation:
Distance = rate times time
d = rt
1200 = 500t Divide both sides by 500
2.4 = t
It will take 2.4 hours. We can convert the .4 into minutes by using a unit multiplier 60 minutes = 1 hour.
[tex]\frac{.4hours}{1}[/tex] x [tex]\frac{60minutes}{1hour}[/tex] The words hours cancel out and we are left with
.4 x 60 = 24 minutes.
HELP THIS IS DUE TOMORROW!
Algebra 2 question!
Picture attached below
Answer:
[tex]\dfrac{4+\sqrt{3}}{4}-\dfrac{(3+4\sqrt{3})}{12}i[/tex]
Step-by-step explanation:
Given expression:
[tex]\dfrac{4+\sqrt{3}}{3+\sqrt{-3}}[/tex]
[tex]\textsf{Apply radical rule}:\quad \sqrt{-a}=\sqrt{a}\sqrt{-1}[/tex]
[tex]\implies \dfrac{4+\sqrt{3}}{3+\sqrt{3}\sqrt{-1}}[/tex]
[tex]\textsf{Apply imaginary number rule}:\quad \sqrt{-1}=i[/tex]
[tex]\implies \dfrac{4+\sqrt{3}}{3+\sqrt{3}i}[/tex]
Multiply by the conjugate of the denominator:
[tex]\implies \dfrac{4+\sqrt{3}}{3+\sqrt{3}i} \cdot \dfrac{3-\sqrt{3}i}{3-\sqrt{3}i}[/tex]
[tex]\implies \dfrac{(4+\sqrt{3})(3-\sqrt{3}i)}{(3+\sqrt{3}i)(3-\sqrt{3}i)}[/tex]
[tex]\implies \dfrac{12-4\sqrt{3}i+3\sqrt{3}-\sqrt{3}i\sqrt{3}}{9-3\sqrt{3}i+3\sqrt{3}i-\sqrt{3}i\sqrt{3}i}[/tex]
[tex]\implies \dfrac{12+3\sqrt{3}-4\sqrt{3}i-3i}{9-3i^2}[/tex]
[tex]\implies \dfrac{12+3\sqrt{3}-(3+4\sqrt{3})i}{9-3i^2}[/tex]
[tex]\textsf{Apply imaginary number rule}:\quad i^2=-1[/tex]
[tex]\implies \dfrac{12+3\sqrt{3}-(3+4\sqrt{3})i}{9-3(-1)}[/tex]
[tex]\implies \dfrac{12+3\sqrt{3}-(3+4\sqrt{3})i}{12}[/tex]
Separate the fractions:
[tex]\implies \dfrac{12+3\sqrt{3}}{12}-\dfrac{(3+4\sqrt{3})i}{12}[/tex]
Simplify:
[tex]\implies \dfrac{4+\sqrt{3}}{4}-\dfrac{(3+4\sqrt{3})}{12}i[/tex]
You work in a nursery with
20 children aged 3 - 5 years.
Your current room size is
415m² and does not meet
floor space requirements.
The room needs to increase
in size by 11%.
How big should the room
be?
Answer:
The room should be 460.65 [tex]m^{2}[/tex].
Step-by-step explanation:
First, you have to convert the percentage to a fraction.
11% = 0.11
Then add one to that number.
0.11 + 1 = 1.11
Multiply the number with the original room size.
415 * 1.11 = 460.65 ([tex]m^{2}[/tex])
If AB=8x+2 and BC=4x+18 find AC
We get that value of AC after adding AB and BC as 12 x + 20.
We are given that:
AB = 8 x + 2 and BC = 4 x + 18
We need to find AC.
For this, we will add AB and BC.
Adding AB and BC, we get that:
AB + BC = AC
Substituting the values of AB and BC in the equation which are given to us:
AC = 8 x + 2 + 4 x + 18
Combining the like terms, we get that:
AC = 12 x + 20.
Therefore, we get that value of AC after adding AB and BC as 12 x + 20.
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67 and 113 multiples of 3,6 and 7
The number 67 and 113 are not the multiples of 3,6 and 7.
What is defined as the multiples?Multiples are the results of multiplying one whole number from another whole number.
A multiple is a products produced by multiplying one number by another. For instance, if we say 4 5 = 20, 20 is a multiple of 4 as well as 5.Every number multiplies itself.A number's multiples are infinite.A number's multiple is equal or greater to the number on its own (except for 0).Now, for the given question;
As, 67 and 113 are not completely divisible by 3. They are not multiple of 3.
67 and 113 are not entirely divisible by 6. So, they are also not the multiple of 6.
Now, 67 and 113 are also not entirely divisible by 7. Thus, they are also not the multiple of 7.
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Question 15 (1 point)
Given the following definitions:
U = {1, 2, 3, 4, 5, 6, 7}
A = {1, 2, 4, 5]
B = {1, 3, 5, 7}
How many elements are in AUB?
Answer:
6
Step-by-step explanation:
The union is defined as the set of all elements in at least one of the sets.
[tex]A \cup B=\{1,2,3,4,5,7\}[/tex]
So, there are 6 elements.
