Omar needs to invest $9,788, to the nearest dollar, for the value of the account to reach $32,400 in 20 years
What is compound interest rate?Compound interest is computed as interest on the principle of an account plus any accrued interest.
Compound interest can be calculated using the following formula:
x = P (1+r/n[tex])^{nt}[/tex]
,where x = compound interest
P = principal (the initial deposit or loan amount)
r = annual interest rate
n = the number of compounding periods per unit of time
t = the number of time units the money is invested or borrowed for
Given:
Omar is going to invest in an account paying an interest rate of 6% compounded monthly.
A = $32,400 in 20 years
First, convert R as a percent to r as a decimal
r = R/100
r = 6/100
r = 0.06 per year,
Then, solve the equation for P
P = A / (1 + r/n[tex])^{nt}[/tex]
P = 32,400.00 / (1 + 0.06/12[tex])^{(12)(20)}[/tex]
P = 32,400.00 / (1 + 0.005[tex])^{240}[/tex]
P = $9,787.91
P = $9788 to the nearest dollar.
Therefore, the investing amount is $9,788.
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Given that the two triangles are similar, solve for x if AU = 20x + 108, UB = 273, BC = 703, UV = 444, AV = 372 and AC = 589.
The value of x in the similar triangles is 18
How to solve similar triangles?Similar triangles have the same shapes but may have different sizes.
Corresponding side of similar triangles are a ratio of each other.
Therefore,
UV / BC = AU / AB
Hence,
UV = 444 units
BC = 703
AU = 20x + 108
AB = 20x + 108 + 273 = 20x + 381
Therefore,
444 / 703 = 20x + 108 / 20x + 381
cross multiply
444( 20x + 381) = 703(20x + 108)
8880x + 169164 = 14060x + 75924
8880x - 14060x = 75924 - 169164
-5180x = -93240
x = -93240 / -5180
x = 18
Therefore, the value of x in the similar triangles is 18
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Simplify the following
Answer:
29/12
Step-by-step explanation:
hello :
2/3 +5/6 +11/12 = (2×4)/(3×4) + (5×2)/(6×2) + 11/12
2/3 +5/6 +11/12 = 8/12 +10/12 +11/12 = (8+10+11)/12
2/3 +5/6 +11/12 = 29/12
Answer:
[tex]2\frac{5}{12}[/tex]
Step-by-step explanation:
To add fractions, we have to make sure that they have the same denominators. To do that, we have to find their lowest common multiple (LCM).
The LCM of 3, 6, and 12 is 12.
Then we have to multiply the numerator and denominator of each fraction by a number so that the denominator becomes the LCM (12).
[tex]\frac{2}{3} + \frac{5}{6} + \frac{11}{12}[/tex]
⇒ [tex]\frac{2 \times 4}{3 \times 4} + \frac{5 \times 2}{6 \times 2} + \frac{11 \times 1}{12 \times 1}[/tex]
⇒ [tex]\frac{8}{12} + \frac{10}{12} + \frac{11}{12 }[/tex]
⇒ [tex]\frac{8+10+11}{12}[/tex]
⇒ [tex]\frac{29}{12}[/tex]
⇒ [tex]\bf 2\frac{5}{12}[/tex]
find the interest accrued on a $7500 loan with a 2.5% interest rate over 4 years
The interest obtained after 4 years from a loan of $7500 is = $750
Calculation of generated interestThe principal amount of the loan = $7500
The rate at which the interest is paid is = 2.5%
The time that it will take to pay the interest = 4 years
Using the formula for Simple interest;
SI= P×T×R/100
SI = 7500×4 × 2.5/100
SI= 75000/100
SI=$750
Therefore, the interest accrued on a $7500 loan with a 2.5% interest rate over 4 years is = $750
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Find the y-intercept of the line.
y=0.2x-6.9
y-intercept:
Answer:
0.2
Step-by-step explanation:
y = mx + b The slope is the number before the x.
Use the slope-intercept form to estimate the slope and y-intercept.
Slope: 0.2
y-intercept: (0,−6.9)
What is slope-intercept form?The slope intercept form in math exists as one of the forms utilized to estimate the equation of a straight line, given the slope of the line and intercept it forms with the y-axis.
The slope-intercept form exists y = mx + b, where m exists the slope and b exists the y-intercept.
y = mx + b
Use the slope-intercept form to estimate the slope and y-intercept.
Slope: 0.2
y-intercept: (0,−6.9)
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What is the value of the expression 7 + (16 − 7) ÷ 3 + 8?
12
15
17
18
The solution to the expression is 18
The CEO of a local tech company wants to estimate the proportion of employees that are pleased with the cleanliness of the breakrooms. She considers two methods of obtaining a sample of 600 employees from the 4,700 employees at the company.
Part A: To make the process easier, the CEO considers surveying the first 600 employees who enter a company annual conference center. Identify the type of sampling method proposed and discuss why this sampling method might be biased. (5 points)
Part B: The second method the CEO is contemplating involves using a random number generator app to choose a simple random sample of 600 employees from a list of 4,700 employee names. How could she implement this method? (5 points)
The type of sampling method proposed is a convenience sampling because it's a non-probability sampling method.
What is convenience sampling?Convenience sampling can be defined as a type of non-probability sampling method which involves surveying and selecting representatives that are easily accessible.
The CEO could implement the second sampling method as follows:
Assign a serial number to each employees of the total 4,700 employee names.Use a random number generator software to obtain 600 random numbers.The 600 random numbers in Step 2 above forms the desired sample of 600 employees out of 4,700 employees at the company.Read more on convenience sampling here: https://brainly.com/question/1445924
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PLS HEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEELP
Answer:
let the first and second table box as 12345 and abcde
1,a
2,c
3,e
4,b
5,d
Step-by-step explanation:
you can use
y=mx+b form m is slope , b is y intercept
m with variable x and b without any variable I.e it is real value
How much, including taxes of 12%, would you pay for an item with a retail price of $194.95?
Answer:
$217.88
Step-by-step explanation:
12% of 194.95 plus the original cost of 194.94 equals the total
1.12*194.54 = $217.8848
Rounded: $217.88
look at the pictures
The function is increasing on the interval (3, ∞)
Interval of a functionGiven the rational function shown below
g(x) = -2√x-3
For the function to be a positive function, the value in the square root must be positive such that;
x - 3 = 0
Add 3 to both sides
x = 0 + 3
x = 3
Hence the interval where the function is increasing is (3, ∞)
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Lewis High School is going to select a committee. The committee will have a faculty member, a male student, a female student, and a parent.
Here are the positions and the people interested in each.
Position People interested
Faculty members Dr. Wright, Mr. Torres, Mrs. Lee, Ms. Reed
Male students Jose, Ali, Tony
Female students Donna, Keiko, Rita
Parent Dr. Wilson, Dr. Patterson, Ms. Rivera, Mrs. Ross, Ms. Bell
The number of possible committees from the given list is; 120 committees
How to Solve Probability Combinations?From the given list, we can say that;
Number of faculty members = 4
Number of male students = 2
Number of female students = 3
Number of parents = 5
Thus, the number of ways to fill the 4 member committee is calculated from probability combination as;
Number of committees = 4 * 2 * 3 * 5 = 120 possible committees
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what two numbers add to the number 30
Answer:
15+15
Step-by-step explanation:
Two 15's added together can equal 30
Levada borrows $30,900 from her bank to open a florist shop. She agrees to repay the money in 18 months with simple annual interest of 5.5%
Levada borrows $30,900 from her bank to open a florist shop at rate of 0.98% per month.
How to calculate simple interest amount?If the initial amount (also called as principal amount) is P, and the interest rate is R% annually, and it is left for T years for that simple interest, then the interest amount earned is given by:
[tex]I = \dfrac{P \times R \times T}{100}[/tex]
It is given that Levada borrows $30,900 from her bank to open a florist shop. She agrees to repay the money in 18 months with simple annual interest of 5.5%.
P = $30,900
T = 18 months
Interest = 5.5%
Interest rate = P×R×T
5.5 = 30,900 × R × 18
R = 0.000988
Or, R = 0.98% per month.
The complete question is
"a) How much must she pay the bank in 18 months?"
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Which of these is smaller? 1/3 or 35%
1/3 = 1/3 × 100%
= 33%
☆ 33 % < 35 %
Therefore
* 1/3 is the smaller one.
☆...hope this helps...☆
_♡_mashi_♡_
The comparison of 1/3 and 35% in decimals shows that 1/3 is smaller than 35%.
Given that:
The fraction is 1/3 and the number in percentage is 35%.
The conversion of a fraction to a percentage can be obtained by dividing the numerator by the denominator and multiply by 100.
The decimal form of the fraction 1/3 is 33.33...%
1/3 ≈ 0.3333...
0.3333... * 100 ≈ 33.33...%
The value 35% is already in percentage.
Since, both the values are in percentage form, it can be easily compared.
On comparing, the resultant would be
33.33...% < 35%
Since 35% is greater than 33.33...%
It can be concluded that 35% is larger than 1/3.
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will give brainliest please help
Answer:
A. 7x + 3x = 10x, B. 6s - 3s + 4s = 7s, C. 4T - 6T = -2T, D. 4xy + 3xy + x = 7xy + x, E. (6x) ^2 = 36x^2, F. 6x/2x = 3.
Step-by-step explanation:
A. explanation: Add 7x and 3x. B. explanation: Simplify the expression. C. explanation: Subtract 6T from 4T. D. explanation: Add 4xy and 3xy. E. explanation: Simplify the explanation. F. explanation: Simplify the expression.
Answer: give her brainliest
Step-by-step explanation:
hey mackenzie :)
You own 17 CDs. You want to randomly arrange 5 of them in a CD rack. What is the probability that the rack ends up in alphabetical order?
The probability that all five end up in alphabetical order is; 1/120.
What is the probability that the rack ends up in alphabetical order?To evaluate the given probability; first, the number of possible arrangements is;
17P5 = 742,560 possible arrangements.
However, the chance of an alphabetical order arrangement in each case is; 1 out of 5! possible arrangements.
Hence, we have that the number of possible alphabetical arrangement is; (1/120) × 742,560 = 6188.
Hence, the required probability is; 6188/742,560 = 1/120
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guillermo has sold 95,47,114, and 72 appliances in the last fourth months,respectively.how many appliances will he need to sell this month to maintain an average of 80 sales per month?
The number of appliances that Guillermo needs to sell this month to main an average of 80 sales per month is 72 units.
What is an average?An average refers to a central value obtained after adding together several amounts and then dividing this total by the number of variables added.
An average is a central value in a dataset.
Data and Calculations:Average sales per month = 80 units
Number of months involved = 5 months
Total for five months based on the average = 400 units
Total units sold in four months = 328 (95 + 47 + 114 + 72)
Sales units required to meet the average target = 72 (400 - 328)
Thus, the number of appliances that Guillermo needs to sell this month to main an average of 80 sales per month is 72 units.
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The measure of the second angle of a triangle is three times the measure of the first. The measure of the third angle in the triangle is 12 degrees less than twice the measure of the first angle. Find the measures of each angle in the triangle.
Answer:
First angle:
x =32
Second angle:
3x
3(32) = 96
Third angle:
2x - 12
2(32) -12 =52
Step-by-step explanation:
x + 3x + 2x - 12 = 180 The sum of the interior angles of a triangle is 180
6x -12 = 180 Combine the x terms
6x = 192 add 12 to both sides
x = 32
Check: 52 + 96 + 32 = 180
Find the measure of Angle E if Arc AB = 80 degrees and Arc CD = 38. Round to the nearest tenth.
The measure of angle E in the secant intersection is 21 degrees.
How to find the angle of intersected secant?When two secants intersect outside a circle, the circle divides the secants into segments that are proportional with each other
Therefore,
m∠E = 1 / 2 (∠AB - ∠CD)
m∠E = 1 / 2 (80 - 38)
m∠E = 1 / 2 (42)
m∠E = 42 / 2
m∠E = 21 degrees.
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A race track is miles long. If the car race is 200 laps then how many miles will the drivers travel during the race?
The drivers will travel 200x miles during the race.
What is Unit of Measurement?A definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
Given that A race track is miles long
The car race is 200 laps then we have to find the number of miles the driver travel.
If the race track is x miles long, then one lap around the track is x miles.
If the race is 200 laps, the total distance covered by the drivers is:
200 laps × x miles/lap = 200x miles.
Therefore, the drivers will travel 200x miles during the race.
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Simplify √-50.
O 5√2
O 5i-√2
O-5√2
-5i√2
Answer: [tex]5i\sqrt{2}[/tex]
Step-by-step explanation:
[tex]\sqrt{-50}\\\\=\sqrt{-1} \sqrt{50}\\\\=5i\sqrt{2}[/tex]
Which of the following systems of linear inequalities is represented by the
solution graphed below?
A. y>2 and ysx
B. y 22 and y
C. x>2 and y2x
D. x22 and y> x
Answer: B
Step-by-step explanation:
The line y=2 is solid and shaded above, so it represents [tex]y \geq 2[/tex].
This allows us to eliminate all the options except for B.
I need help with this geometry question asap!
Answer:
(a) Theorem 9
Step-by-step explanation:
Any of the given theorems can be used to prove lines are parallel. We need to find the one that is applicable to the given geometry.
AnalysisThe marked angles are between the parallel lines (interior) and on opposite sides of the transversal (alternate).
Theorem 9 applies to congruent alternate interior angles.
Solve for x. Find all solutions from 0 to 2 π . Show all work as you solve each problem - you may need more space to show your work for each. Remember there may be more than 1 solution for x.
Questions are attached below
Answer:
x=189
Step-by-step explanation:
please mark me as brainiest
I need help on this question please help me
The expression that shows the best use of the associative and commutative properties is [tex][\frac{3}{4}+(-\frac{2}{4})]+[9 +2+(-5)][/tex]. The correct option is C. [tex][\frac{3}{4}+(-\frac{2}{4})]+[9 +2+(-5)][/tex]
Associative and Commutative propertiesFrom the question, we are to determine the expression that shows the best use of the associative and commutative properties
The given expression is
[tex]\frac{3}{4}-5+9 -\frac{2}{4}+2[/tex]
To easier simplify the expression, we can group the fractions together and group the whole numbers together
That is,
[tex][\frac{3}{4}+(-\frac{2}{4})]+[9 +2+(-5)][/tex]
Hence, the expression that shows the best use of the associative and commutative properties is [tex][\frac{3}{4}+(-\frac{2}{4})]+[9 +2+(-5)][/tex]. The correct option is C. [tex][\frac{3}{4}+(-\frac{2}{4})]+[9 +2+(-5)][/tex]
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CAN sb HELP MI >_>
what it 0.00000000000000035467 in the scientific notation
Answer:
3.5467 × 10^-16
Mark all the relative minimum points in the graph.
See attached!
The relative minimum point in the graph is (-6, 2)
How to determine the relative minimum?To do this, we simply locate a point that at a lower level, when compared to its neighboring points
Using the above highlight, there is only one relative minimum point in the graph
And the point is located at (-6,2)
Hence, the relative minimum point in the graph is (-6, 2)
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Compute the monthly payments for each add-on interest loan. The amount of the loan is $1150. The annual interest rate is 6%. The term of the loan is 4 years
The monthly payments for each add-on interest loan is computed to be $29.71.
Given Information and Formula Used
Principal Amount of the loan, P = $1150
Rate of Interest of the loan, R = 6%
Term of loan in years, T = 4
The formula for simple interest is given as follows,
I = (P × R × T)/100
The formula for amount of add-on interest loan is given by, A = P + I
Calculating the Interest of the Loan
Interest of the loan, I = (P × R × T)/100
Now, substituting the given values of P, R, and T in the above formula, we get,
I = $ (1150 × 6 × 4)/100
I = $ 27600/100
I = $276
Calculating the Total Monthly Payment for the Loan
Amount of loan, A = P+I
A = $1150 + $276
A = $1426
Monthly payment of the loan with interest = A/(4×12)
= $ 1426/48
= $29.71
Thus, the monthly payments for each add-on interest loan comes out to be $29.71.
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Type the correct answer in each box. If necessary, round your answer(s) to the nearest hu The vertices of AABC are A(-2, 2), B(6, 2), and C(0, 8). The perimeter of AABC is
Answer:
22.81
Step-by-step explanation:
The distance formula can be used to find the distances between pairs of vertices. The perimeter is the sum of those distances.
Side lengthsThe distance formula is ...
d = √((x2 -x1)^2 +(y2 -y1)^2)
Using this formula the triangle side lengths are ...
AB = √((6 -(-2))^2 +(2 -2)^2) = √(8^2) = 8
BC = √((0 -6)^2 +(8 -2)^2) = √(6^2 +6^2) = 6√2
CA = √((-2 -0)^2 +(2 -8)^2) = √(4 +36) = √40
The perimeter of the triangle is the sum of these lengths:
P = 8 +6√2 +2√10 ≈ 22.8098
The perimeter is about 22.81 units.
50 POINTS!!!!!!!! PLEASE ANSWER THIS QUICKLY WITH AN EXPLANATION!!!!!!!!! ANSWER ALL OF THEM
Answer:
(b) 27°
(c) 34°
( ) 27°
Step-by-step explanation:
Angle relations involving lines, parallel lines, and triangles come into play here.
angles of a linear pair total 180°angles of a triangle total 180°vertical angles are congruentcorresponding angles at a transversal crossing parallel lines are congruent(b)The interior angles at W and Y will be the supplement of the exterior angles at those points. The sum of interior angles is 180°.
(180° -6x) +90° +(180° -4x) = 180°
270° = 10x . . . . . . . . . add 10x and simplify
27° = x
(c)The vertical angles at S are congruent. This tells us ...
3x +∠PSQ = 4x
∠PSQ = x
The sum of angles in triangle PSQ is 180°, so we have ...
x +x +(180° -68°) = 180°
2x = 68° . . . . . . . . add 60°-180°
x = 34° . . . . . . . . . divide by 2
( )Angles BAD and EDF are corresponding angles, hence congruent. The sum of angles in triangle BAD is 180°.
2x +2x +72° = 180°
4x = 108° . . . . . . subtract 72°
x = 27° . . . . . . . . divide by 4
would anyone be able to help me with this?
This graph has its maximum at 4. There is no minimum while the inflection is at 2, 10/3.
How to solve for the maximum of the graphWe have ( x-2²) (x-4)
x-2²) = 0, or x - 4
x - 2 = 0, x = 2
Hence we can see that the graph has its minimum at x = 4
b. The graph here does not have a local maximum
c. Next we have to find the point of inflectionTo do this you have to differentiate the equation
Use the product rule of differentiation in order to solve for the solution.
(x-2)²[ (x-4) 2 (x-2)]
This would then give us
x -2, 3x -10
In both equations we have to make x the subject of the equation
X = 2, x = 10/3
Hence the point of inflection is 2 and 10/3
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