Bashir would need to invest $18,900, to the nearest hundred dollars, for the value of the account to reach $29,000 in 19 years.
Describe Investment?Investment refers to the allocation of money or capital to an asset or a project with the expectation of generating a profit or earning an income. Investment can take many forms, including the purchase of stocks, bonds, real estate, or other financial products, as well as the financing of a business or a startup.
Investing involves risk, as the potential return on investment is not guaranteed. Investors must carefully evaluate the potential risks and returns of each investment opportunity before deciding where to allocate their capital.
Investment can be divided into two main categories: short-term and long-term. Short-term investments, such as savings accounts and money market funds, offer relatively low returns but also have lower risk. Long-term investments, such as stocks and real estate, have higher potential returns but also higher risk.
To find the amount that Bashir needs to invest to reach $29,000 in 19 years, we can use the formula for the future value of an investment:
Future Value = Principal * (1 + (Interest Rate ÷ Number of Compounding Periods))^(Number of Compounding Periods x Time in Years)
In this case, the interest rate is 5.7% compounded quarterly, so:
Interest Rate ÷ Number of Compounding Periods = 5.7 ÷ 4 = 1.425%
And the time in years is 19, so the number of compounding periods is 4 * 19 = 76.
Now, we can plug in the values into the formula:
Future Value = Principal * (1 + (1.425 ÷ 100))^(76)
Future Value = Principal * (1.01425)^76
Future Value = 29,000
Solving for Principal, we get:
Principal = 29,000 ÷ (1.01425)^76
Rounding to the nearest hundred dollars, we get:
Principal = $18,900
So, Bashir would need to invest $18,900, to the nearest hundred dollars, for the value of the account to reach $29,000 in 19 years.
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Need help (Just started circles) please explain how to solve every thing.
prove 2^a , 2^b , 2^c forms a geometric sequence when a , b , c forms an arithmetic sequence.
Answer: Given that a, b, and c form an arithmetic sequence, so they are equally spaced, meaning the difference between each of them is constant. Let's denote the common difference between a, b, and c as d.
So, we have:
a = b - d
c = b + d
Using these two equations, we can prove that 2^a, 2^b, and 2^c form a geometric sequence.
We have:
2^a = 2^b / 2^d
2^c = 2^b * 2^d
Since the product of two powers of the same base is equivalent to the power of the base with the sum of the exponents, we have:
2^a * 2^c = 2^b * 2^b * 2^d * 2^d = 2^(b+b+d+d) = 2^(2b+2d)
So, we have:
2^a * 2^c = 2^(2b+2d) = 2^(2b) * 2^(2d) = 2^b * 2^b * 2^d * 2^d = 2^b * 2^c
This means that 2^a, 2^b, and 2^c form a geometric sequence, with the common ratio of 2^d.
Step-by-step explanation:
pls I need solutions to this. find the sum of the 1st and three term of the gp, whose 3rd term is 27 and whose 6th term is 8
The sum of the 1st and three-term of the GP is 87.75.
What is geometric progression?
A geometric progression often referred to as a geometric sequence, is a series of non-zero values where each term following the first is obtained by multiplying the preceding value by a constant, non-zero number known as the common ratio.
Here, we have
Given: 3rd term is 27 and whose 6th term is 8
Let the GP terms are a, ar, ar², ar³, ar⁴ and ar⁵,
Given ar² = 27 and ar⁵ = 8
Take the ratio of the sixth term to the third term:
ar⁵ / ar² = 8/27 => r³ = (2/3)³
r = 2/3
We know that
ar² = a(2/3)² = 27
=> a(4/9) = 27
=> a = 27*9/4 = 243/4
So, the terms are 243/4, 243/4*(2/3), 243/4*(4/9), 243/4*(8/27), 243/4*(16/81), 243/4*(32/243)
= 243/4 + 27
= 60.75 + 27
= 87.75
Hence, the sum of the 1st and three-term of the GP is 87.75.
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the cash price of a bike is 220. hire-purchase is 300 .if the deposit is 10% followed by 10 equal monthly installments find the amount you pay each month
Answer:
$27/month
Step-by-step explanation:
300-220=80
100%= 300
1%= 300÷100
= 3
10%= 3×10
= 30
300-30=270
270÷10= $27
Write the ratio for cos a! Please
The ratio of the CosA will be 12 / 37 for the right-angle triangle.
What is trigonometry?The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry. The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.
Given that there is a right angle triangle having the Hypotenuse = 37, Base = 12, and Height = 35.
The value of CosA will be calculated as:-
CosA = Base / Hypotenuse
CosA = 12 / 37
Therefore, the ratio of the CosA will be 12 / 37 for the right-angle triangle.
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Frets are small metal bars positioned across the neck of a guitar so that the guitar can produce the notes of a specific scale. To find the distance a fret should be placed from the bridge, multiply the length of the string by 2−12, where n is the number of notes higher than the string’s root note. Where should a fret be placed to produce a G note on the E string (3 notes higher)
1)List what is given in this word problem?
2)state the equation for desmos 5
3)what is the X value? x = ?
4)what is the Y valuie? y = ?
Since the length of the string is not specified, we cannot find the Y value (fret position) exactly.
Given in this word problem:
Length of the string: Not specified
Number of notes higher than the root note: 3 (G note is 3 notes higher than the E string's root note)
Scale: Not specified
The equation for the fret position can be represented as follows:
fret position = length of string * 2^(-12 * n)
where n is the number of notes higher than the root note.
To find the X value, we need to know the length of the string, which is not specified in the problem.
To find the Y value, we need to calculate the fret position using the equation:
fret position = length of string * 2^(-12 * n)
fret position = length of string * 2^(-12 * 3)
fret position = length of string * 2^-36
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When graphed in the xy-plane, what is the y-coordinate of the vertex of the parabola with equation y=-3(x-4)(x+6)
Answer: A
Step-by-step explanation:
Convert the equation into quadratic form (y=ax^2+bx+c)
y=-3(x-4)(x+6) = y=-3x^2-6x+72
Calculate -b/2a
which is 6/-6=-1
then put the value -1 into the equation for x.
-3+6+72=75
The answer is therefore A.
√52x^4 solve ……………….
Answer:
2[tex]\sqrt{13x^{2} }[/tex]
Step-by-step explanation:
To simplify the expression √52x^4, we can break it down as follows:
√(52x^4) = √(4 * 13 * x^4)
Since the square root of a product is equal to the product of the square roots, we can simplify further:
√(4 * 13 * x^4) = √4 * √13 * √(x^4)
The square root of 4 is 2, and the square root of x^4 is x^2:
2 * √13 * x^2
Therefore, the simplified expression is 2√13x^2.
Answer:
[tex]\large\text{$2\sqrt{13}\;x^2$}[/tex]
Step-by-step explanation:
Given expression:
[tex]\sqrt{52x^4}[/tex]
Prime factorization is the process of representing a positive integer as a product of its prime factors.
The prime factorization of 52 is 2² · 13. Therefore, rewrite 52 as 2² · 13:
[tex]\sqrt{2^2 \cdot 13 \cdot x^4}[/tex]
[tex]\textsf{Apply the radical rule:} \quad \sqrt{abc}=\sqrt{\vphantom{b}a}\sqrt{b}\sqrt{c}[/tex]
[tex]\sqrt{2^2} \sqrt{13} \sqrt{x^4}[/tex]
[tex]\textsf{Apply the radical rule:} \quad \sqrt{a^2}=a, \quad a \geq 0[/tex]
[tex]2\sqrt{13} \sqrt{x^4}[/tex]
[tex]\textsf{Apply the radical rule:} \quad \sqrt[n]{a^m}=a^{\frac{m}{n}},\quad \textsf{assuming} \;a\geq 0[/tex]
[tex]2\sqrt{13} \;x^{\frac{4}{2}}[/tex]
[tex]2\sqrt{13} \;x^2[/tex]
Therefore, the simplified expression is:
[tex]\large\boxed{2\sqrt{13}\;x^2}[/tex]
The area of a rhombus is 360 sq cm if one of its diagonal is 40 cm , find the other diagonal
Based on the information of area of rhombus and length of diagonal, the other diagonal of rhombus is 10.5 cm in length.
The diagonal and area of rhombus are related to each other by the formula -
Area = diagonal1 × diagonal2/2
Keep the values in formula to find the diagonal.
360 = 40 × diagonal 2/2
Rewriting the formula -
Diagonal 2 = (360 × 2)/40
Performing multiplication on Right Hand Side of the equation
Diagonal 2 = 420/40
Performing division on Right Hand Side of the equation
Diagonal 2 = 10.5 cm
The other diagonal is 10.5 cm.
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Find the value of y.
Find the value of x.
Answer:
y=4,x= -1
Step-by-step explanation:
2y-3 =y+1
2y-y=1+3
y=4
∆CBD
2x+7=2y-3
2x+7=5
2x= 5-7
2x= -2
x= -1
Joey is training for a 5k race. She runs the same distance two days in a row. On the first day, she runs 5 laps around the track, and then runs additional 1. 5 miles. The next day she runs 3 laps, and an additional 4 miles. Analyze the text to answer the following questions
Answer:
Step-by-step explanation:
What is Joey's total distance run on the first day?
Joey runs 5 laps around the track, which we can assume is 1 mile per lap. So, she runs 5 miles. Additionally, she runs 1.5 miles, so her total distance run on the first day is 5 + 1.5 = 6.5 miles.
What is Joey's total distance run on the second day?
Joey runs 3 laps around the track, which we can assume is 1 mile per lap. So, she runs 3 miles. Additionally, she runs 4 miles, so her total distance run on the second day is 3 + 4 = 7 miles.
Given rectangle C D E F below, DG = 15 If CG = 3x+6, solve for x
The numerical value of x in the expression 3x + 6 is 3.
What is the numerical value of x?The diagonals of a rectangle bisects each other and are equal.
Given that;
DG = 15CG = 3x + 6Value of x = ?Since the diagonals of a rectangle bisects each other and are equal.
DG = CG
Plug in the given values and simplify.
15 = 3x + 6
Solve for x
Subtract 6 from both sides
15 - 6 = 3x + 6 - 6
9 = 3x
Divide both sides by 3
9/3 = 3x/3
9/3 = x
3 = x
x = 3
Therefore, the value of x is 3.
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A laundry detergent box measures 12 inches by 8 inches by 2.5 inches. What is the volume of the detergent box?
Answer:
240in^3
Step-by-step explanation:
V = whl
= (12in)(8in)(2.5in)
= 240 in ^3
HELP QUICK (5 star and brainliest if correct) If masha buys three roses she will have 7 dollars left. To buy nine roses, Masha will need to borrow 11 dollars from her father. How many dollars does Masha have?
Let's start by setting up a system of equations to represent the given information:
3r = m - 7
9r = m + 11
where r is the cost of one rose, and m is the total amount of money that Masha has.
We can solve this system of equations using the elimination method:
Multiplying the first equation by 3, we get:
9r = 3m - 21
Subtracting the second equation from this, we get:
0 = -4m - 32
Simplifying, we get:
m = -8
Therefore, Masha has $-8, which means she owes money. This indicates that there may be an error in the problem statement or data provided.
Answer:
Masha has 16 dollars.
Step-by-step explanation:
3x + 7 = Masha's total money
9x = Masha's total money + 11 (after borrowing)
We can use the first equation to find the value of 3x, which is Masha's total money if she buys three roses:
3x + 7 = Masha's total money
3x + 7 = Masha's total money
3x = Masha's total money - 7
We can substitute the second equation to solve for Masha's total money:
9x = Masha's total money + 11
9x = (3x + 7) + 11
9x = 3x + 18
6x = 18
x = 3
Now we know that one rose costs 3 dollars. We can use the first equation to find Masha's total money if she buys three roses:
3x + 7 = Masha's total money
3(3) + 7 = Masha's total money
9 + 7 = Masha's total money
Masha's total money = 16
a door of length 2m and breadth 1m is fitted in a wall. The length of the wall is 4.5m and the breadth is 3.6m. Find the cost of white washing the wall, if the rate of white washing the wall is rupees20 per metre square
Answer:
16.2m^2
16.2*20=324
324 rupees
Step-by-step explanation:
HELP ASAP WILL GIVE BRAIN DUE IN 20 MIN
Answer:
E
Step-by-step explanation:
Given that f(x)= ax/bx-4, x≠4/b, x≠0. If f(1)=-2 and f(2)=2, find a+b.
The sum of a and b is obtained as follows:
a + b = 5.
How to obtain the values of a and b?The function for this problem is defined as follows:
f(x) = ax/[bx - 4]
f(1) = -2 means that when x = 1, y = -2, hence:
-2 = a/(b - 4)
a = -2b + 8
f(2) = 2 means that when x = 2, y = 2, hence:
2 = 2a/(2b - 4)
2a = 4b - 8
a = 2b - 4.
Equaling the two equations, the value of b is obtained as follows:
-2b + 8 = 2b - 4
4b = 12
b = 3.
Hence the value of a is ob:
a = 2b - 4
a = 2(3) - 4
a = 2.
Hence the sum is of:
a + b = 2 + 3
a + b = 5.
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I need help , come on ! Please
(a) The equation to find x is 4x + 22 = 90.
(b) The degree of each angle:
m∠1 = 51°m∠2 = 39°The sum of angle 1 and 2 is equal to right angle.
What is the value of right angle?The value of a right angle is equal to 90°.
In the figure, we have a right angle and one line in it. It makes two angles 1 and 2 with
m∠1 = (3x)°m∠2 = (x + 22)°(a) Find an equation to find x!
(b) Find the degree measure of each angle!
The sum of angle 1 and 2 is equal to 90°. So,
m∠1 + m∠2 = 90
3x + x + 22 = 90
4x + 22 = 90
This is the equation to find x. Then, we find x.
4x + 22 = 90
4x = 90 - 22
4x = 68
x = 68/4
x = 17°
The degree measure of each angle will be
m∠1 = 3x
m∠1 = 3(17)
m∠1 = 51°
m∠2 = x + 22
m∠2 = 17 + 22
m∠2 = 39°
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Find the number that is exactly halfway between 1/10 and 4/5
Answer:
Step-by-step explanation:
1/10 = 0.1
4/5 = 0.8
What's halfway between 1 and 8?
Let's show it on a number line:
¬ ¬
_0____1____2_____3______4_____5____6_____7_____8__________
It's 4 and 5, therefore it's 4.5
0.45 comes halfway through 1/10 and 4/5
Expressed as a fraction: 45/100 = 9/20
Hope that helps! Please make me brainliest!
Answer: 0.45
Step-by-step explanation:
Which statements are true the ordered pair (1, 2) and the system of equations?
y=-2x+4
7z-2y=3
Select each correct answer.
O The ordered pair (1, 2) is not a solution to the system of linear equations.
When (1, 2) is substituted into the second equation, the equation is true.
Q. When (1, 2) is substituted into the first equation, the equation is false.
□ When (1, 2) is substituted into the second equation, the equation is false
When (1, 2) is substituted into the first equation, the equation is true.
The ordered pair (1, 2) is a solution to the system of inear equations.
Answer:
The statements that are true about the ordered pair (1, 2) and the system of equations are:
When (1, 2) is substituted into the first equation, the equation is true.
The ordered pair (1, 2) is a solution to the system of linear equations.
So, the correct options are:
When (1, 2) is substituted into the first equation, the equation is true.
The ordered pair (1, 2) is a solution to the system of linear equations.
Step-by-step explanation:
The width of a rectangle is 4.25y-7.5 feet and its length is 7.5y+8 feet. Find the perimeter of the rectangle.
Answer:
23.50y+1
Step-by-step explanation:
2(4.25y-7.5+7.5y+8)
2(4.25y+7.5y-7.5+8)
2(11.75y+0.5)
2(11.75y) + 2(0.5)
23.50y + 1
Express the radical using the imaginary unit, i
Express your answer in simplified form.
Answer:
Step-by-step explanation:
root of -48 is equal to 4iroot3, so plus/neg 4iroot3
the process of converting individual raw scores in a distribution to a set of scores for which we know the percentiles is:
The process of converting individual raw scores in a distribution to a set of scores for which we know the percentiles is known as "normalizing the data" or "standardizing the data."
The steps for standardizing the data are as follows:
Order the raw scores in the distribution from smallest to largest.
Assign each score a percentile rank. This is the percentage of scores in the distribution that are equal to or lower than the score. For example, if a score has a percentile rank of 75, it means that 75% of the scores in the distribution are equal to or lower than that score.
Convert the raw scores to standardized scores (also known as z-scores). This is done by subtracting the mean of the distribution from each score and then dividing by the standard deviation of the distribution. The resulting standardized score represents the number of standard deviations above or below the mean that the raw score falls.
The process of standardizing the data helps to put the raw scores into a common context, which makes it easier to compare scores from different distributions and to draw meaningful conclusions about the data. Additionally, standardized scores can be used to determine the probability of a score falling within a particular range.
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FLOWER GARDEN Erin is planning her summer garden. The table shows the number of bulbs she has according to type and color of flower. If Erin randomly selects one of the bulbs, what is the probability that she selects a bulb for a yellow flower or a dahlia? Round your answer to the nearest tenth of a percent.
Probability that Erin selects a bulb for a yellow flower or a dahlia is 52.8%.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.
Probability(Event) = Favorable Outcomes/Total Outcomes = x/n
Given, by the table
Total number of flowers = 5+4+3+3+1+2+2+5+6+0+1+4 = 36
Number of yellow flowers = 4 + 1 + 5 + 1 = 11
Number of Dahlia flowers = 5 + 4 + 3 = 12
Number of yellow Dahlia = 4
Probability of selecting bulb for a yellow flower P(y)= 11/36
Probability of selecting bulb for dahlia P(d) = 12/36
Probability of selecting bulb for yellow Dahlia P(y and d) = 4/36
Probability of selecting bulb for yellow flower or dahlia
= P(y) + P(d) - P(y and d)
= 11/36 + 12/36 - 4/36
= (11 + 12 - 4)/36
= 19/36
= 0.528
= 52.8%
Hence, 52.8% is probability that she selects a bulb for a yellow flower or a dahlia.
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Lauren spent 1^3/8 hour cleaning the house, 7/8 hour doing the laundry, and 1^5/8 preparing food. How many hours did Lauren spend doing all the work?
Need step by step please.
Lauren spent a total of 10 hours on the duties if he spent 1 3/8 hour cleaning, 7/8 hour doing laundry, and 1 5/8 cooking dinner.
What is fraction?A fraction is a portion of a whole or, more broadly, any number of equal pieces. In ordinary English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters.
Here,
To find the total time Lauren spent on the tasks, we need to add the time she spent cleaning the house, doing the laundry, and preparing food.
Cleaning the house: 1 3/8 hours
Doing the laundry: 7/8 hours
Preparing food: 1 5/8 hours
Adding these three quantities, we get:
1 3/8 + 7/8 + 1 5/8 = 1 3/8 + 7/8 + (2 3/8)
Next, we simplify each fraction by finding a common denominator of 8:
(18/8) + (7/8) + (28/8) = 1 + 7 + 2 = 10
So, Lauren spent a total of 10 hours on the tasks if he spent 1 3/8 hour cleaning the house, 7/8 hour doing the laundry, and 1 5/8 preparing food.
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(2+5root7)/(2-5root7) = a+b root7
class 9
with complete explanation pls
The value of a and b are -179/171 and -20/171 respectively.
What is rationalization of surd?Rationalising surds is where we convert the denominator of a fraction from an irrational number to a rational number. In more complex cases, it is useful to multiply the denominator by its conjugate to cancel out the surds in the denominator.
(2+5√7)/(2-5√7)
by rationalization
(2+5√7)/(2-5√7) × (2+5√7)/(2+5√7)
=( 4+10√7 + 10√7 + 175)/4+10√7 - 10√7- 175
= (20√7+179)/-171
= -20/171 √7 -179/171
therefore the value of a = -179/171 and b = -20/171
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bryan takes out a loan of £800. This debt increases by 28% every year. How much money will bryan owe after 14 years?
Answer: £3136
Step-by-step explanation:
First you want to find 28% of 800 to find out how much it increases by every year.
So 800*0.28= 224
And then you want to multiply 224 to 14 years to see how much he has to pay in 14 years
224*14=3136
Your answer: £3136
I need help solving this problem
The width of the rectangular will be x+4.
What is a rectangle?
Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees. Quadrilaterals are typically four-sided closed shapes, and there are numerous varieties of them. Square, rectangle, rhombus, kite, and trapezoid are the most typical shapes. Four closed sides make up a quadrilateral. Quadrilaterals are the following figures: a four-sided figure. The form features a single set of parallel sides and no right angles.
Area of the rectangle is A = a*b
Given Length is = x+7
And the area is x² +11x+28
So the width is = x² +11x+28 / x+7
x² +7x+4x+28/x+7
=(x+7)(x+4)/x+7
=x+4
Hence the width of the rectangular will be x+4.
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can someone please help me(15 points will give brainliest!!!)
Answer:
m = -2
b = -3
Step-by-step explanation:
Point slope formula of a line = [tex]y-y_{1} = M(x-x_{1} )[/tex]
Where x1 and y1 are the coordinates of the point and M is the slope.
Given slope = -2
Point = (-7,11)
So x1 = -7 and y1 = 11
Substituting the values in the point-slope formula, we get:
[tex]y-11 = -2(x - (-7))[/tex]
[tex]= > y = -2x -14 + 11[/tex]
Or
[tex]y = -2x -3[/tex]
Thus, m = -2 and b = -3
an expression is given. -2y+3/2x+7/4 which are equivalent to the given expression select each answer
Option D and E are equivalent to the given expression.
How to find equivalent expressionFirst we find the x and y values of the equation -2y+3/2x+7/4.
For example x= 0, substitute:
-2y+3/2x+7/4=0
-2y=-7/4
y=7/8
For example y=0, substitute:
-2y+3/2x+7/4=0
3/2x=-7/4
x=-7/6
Then we look for choices A, B, C, D and E, which one produces x=-7/6 and y=7/8 if for example x=0 and y=0.
And those that have the same value are equations D and E.
What is equivalent equation?Equivalent equations are systems of equations that have the same solutions. Identifying and solving equivalent equations is a valuable skill, not only in algebra class, but also in everyday life.
The simplest example of an equivalent equation doesn't have any variables.
For example, these three equations are equivalent to each other:
3 + 2 = 5
4 + 1 = 5 5 + 0 = 5
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