The amount that Leo has earned as interest, given the amount that Leo deposited, and the compounding period, is $2, 945.12
How to find the interest earned?First, find the weekly rate on the account:
= Annual rate / Number of weeks in a year
= 2.5 % / 52
= 0.048 %
The number of periods is:
= Number of years x Weeks per year
= 13 x 52
= 676 weeks
The amount that Leo would have earned after 13 years is:
= Deposit x ( 1 + rate) ^ number of periods
= 7, 671.12 x ( 1 + 0.048%) ⁶⁷⁶
= $10, 616.24
The interest earned is:
= Amount earned - Amount deposited
= 10, 616.24 - 7, 671.12
= $2, 945.12
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Identify the variable expression for “Two times the difference of x and the square of 7”
Answer:
Step-by-step explanation:
The square of 7 is:
[tex](7)^2=49[/tex]
The difference x and square of 7 is:
[tex]x-49[/tex]
Two times the difference of x and square of 7 is:
[tex]2(x-49)[/tex]
Rewrite cos(x+4pi/3) in terms of sin(x) and cos(x)
Answer:
x8659-3358468854---6666x
Answer:
[tex]\frac{\sqrt{3} }{2}[/tex] sinx - [tex]\frac{1}{2}[/tex] cosx
Step-by-step explanation:
using the sum identity for cosine
cos(a + b) = cosacosb - sinasinb
then
cos(x + [tex]\frac{4\pi }{3}[/tex] )
= cosxcos([tex]\frac{4\pi }{3}[/tex]) - sinxsin([tex]\frac{4\pi }{3}[/tex] )
[ [tex]\frac{4\pi }{3}[/tex] is an angle in the third quadrant where sin and cosine < 0 ]
[ the related acute angle to [tex]\frac{4\pi }{3}[/tex] = [tex]\frac{4\pi }{3}[/tex] - π = [tex]\frac{\pi }{3}[/tex] ]
= cosx × - cos([tex]\frac{\pi }{3}[/tex] ) - sinx × - sin([tex]\frac{\pi }{3}[/tex] )
= cosx × - [tex]\frac{1}{2}[/tex] - sinx × - [tex]\frac{\sqrt{3} }{2}[/tex]
= - [tex]\frac{1}{2}[/tex] cosx + [tex]\frac{\sqrt{3} }{2}[/tex] sinx
= [tex]\frac{\sqrt{3} }{2}[/tex] sinx - [tex]\frac{1}{2}[/tex] cosx
Solve for x and y
12x+3y=162
[tex]f(x) = -x × -x - 2[/tex]
what expression is equivalent to cd√22
ONE OF THESE ANSWERS
a. √22c^d^
b. √22cd
c. √22c4d4
d. √22cd^
The expression equivalent to cd[tex]\sqrt{22}[/tex] is b)[tex]\sqrt{22}[/tex]cd.
What is expression?
Mathematical statements are called expressions if they have at least two terms that are related by an operator and contain either numbers, variables, or both. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it. a collection of symbols, numbers, and operators (like and) that represent the value of something. Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression.
Here the given expression is ,
=> cd[tex]\sqrt{22}[/tex] which is ,
=> c×d×[tex]\sqrt{22}[/tex]
=>[tex]\sqrt{22}[/tex]cd.
Therefore the expression equivalent to cd[tex]\sqrt{22}[/tex] is b)[tex]\sqrt{22}[/tex]cd.
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Thomas has $1,300 to paint the figure below. If it costs $5 for every square unit of paint, will Thomas have enough money to paint the entire surface area (outside only) of the figure?
Using the dimensions of the figure, Thomas will have enough money to paint the surface area.
What are the dimensions of a figure?The dimensions of a two-dimensional figure are its lengths and widths.
The product of the length and width results in the surface area, which is stated in square units.
How is the conclusion reached?Since Thomas has $1,300, and the squared surface of the figure is equal to 260 square units, when $5 is multiplied into 260, the product is $1,300.
This amount is equal to the money available to Thomas for the painting.
If the dimensions produced a surface area of more or less than 260 square units, we can calculate Thomas' ability to complete the painting based on the information.
The length of the figure is given as 20 units.
The width of the figure is given as 13 units.
The surface area of the figure = 260 square units
The cost of paint per square unit = $5
The total cost for painting the figure = $1,300 ($5 x 260)
The amount available to Thomas for the painting = $1,300
Difference between the total cost and the available amount = $0.
Thus, we can assert that, given the dimensions of the figure, Thomas can complete the painting with the available funds.
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Question Completion:Length of the figure = 20 units
Width of the figure = 13 units
Write the standard form of the complex number
sqrt 108[cos(−30°) + i sin(−30°)]
Answer:
[tex]9-3\sqrt{3} i.[/tex]
Step-by-step explanation:
[tex]1. \ cos(-30)=\frac{ \sqrt{3}}{2}; \ sin(-30)=-0.5;[/tex]
[tex]2. \sqrt{108} (cos(-30)+isin(-30))=\frac{\sqrt{108} \sqrt{3}}{2}-i*\sqrt{108}*0.5=9-3\sqrt{3} i.[/tex]
You toss a coin 950 times and record the results. You then look through your results and find that at one point you got 11 heads in a row. What is the probability of getting 11 heads in 11 tosses?
Should you be surprised to find this "streak" in your set of 950 tosses? Explain.
1/2048 is the probability of getting 11 heads in 11 tosses.
What is probability ?It is predicated on the likelihood of something occurring. The rationale behind probability is the foundation of theoretical probability. If a coin is tossed, the theoretical probability of getting a head is 1/2.Probability = ( Favourable outcome) / (Total number of outcomes) P = n (E) / n (S) Where P is the probability, E is the event and S is the sample space.Probability of getting heads in one toss = 1/2
Probability of getting heads in 11 tosses = [tex](1/2)^{11[/tex]= 1/2048 (a one in 2048 chance of occurrence)
It should, therefore, NOT be surprising in a sample space of 950 (which is more than double 2048), that 11 heads can be obtained in a row.
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1/2048 is the probability of getting 11 heads in 11 tosses.
What is probability ?It is predicated on the likelihood of something occurring. The rationale behind probability is the foundation of theoretical probability. If a coin is tossed, the theoretical probability of getting a head is 1/2.Probability = ( Favourable outcome) / (Total number of outcomes)P = n (E) / n (S) Where P is the probability, E is the event and S is the sample space.Probability of getting heads in one toss = 1/2Probability of getting heads in 11 tosses = = 1/2048 (a one in 2048 chance of occurrence)It should, therefore, NOT be surprising in a sample space of 950 (which is more than double 2048), that 11 heads can be obtained in a row.To learn more about Probability refer,
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Question 3
0.5 pt=
Jim wants to buy a computer. The total cost is $947. If he can save $60 a month, how
long will it take for him to save up for the computer? Round UP to the next whole
number of months!!
Maximum of 16 months, will take Jim to save $947.
What is cost?Cost is the sum of money needed to produce, market, and sell goods and services or to purchase assets. A cost is added to costs when anything is sold or consumed. The charge to expense in the case of an asset may be postponed for quite some time. The conversion of assets from the balance sheet to expenses in the income statement is based on the cost concept.Total Cost of Computer = $947
Amount that Jim can save monthly = $60
Let time taken by Jim to save amount which is equal to cost of computer = x months
So, the equation for the above statement can be written as: 60x = 947
Dividing both sides by, 60
[tex]\frac{60x}{60} =\frac{947}{60}[/tex]
[tex]x=\frac{947}{60} =15.78[/tex]
⇒Number of months=16
Maximum of 16 months, will take Jim to save $ 957.
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The height of a building is proportional to the number of floors. The figure shows the height of a building with 7 floors. Complete parts a and b.
well, the height of the building is 119 feet, as we can see right there on the picture. Now, there are 7 floors from the ground up, so the ratio is simply
[tex]\cfrac{\stackrel{overall~height}{119}}{\underset{floors}{7}}\implies \cfrac{17}{1}\implies \stackrel{unit~rate}{17}\hspace{5em}\cfrac{17~feet}{1~floor}\qquad \begin{array}{llll} \textit{each floor is}\\ \textit{17 feet high} \end{array}[/tex]
The average (A) of two numbers, m and n, is given by the formula A = m+t/2 . Find
the average of the two numbers 36 and 72.
The solution is
Answer:
[tex]54[/tex]
Step-by-step explanation:
Formula for average A of two numbers m and n is:
[tex]A=\frac{m+n}{2}[/tex]
Substitute the value m=36 and n=72
[tex]A=\frac{36+72}{2}[/tex]
This is equivalent to:
[tex]A=\frac{108}{2}[/tex]
The average is:
[tex]A=54[/tex]
Find the distance between the point (5,12) and the line y = 5x + 12 (rounded to the nearest hundredth).
A. 1.36 units
B. 2.19 units
C. 4.81 units
D. 4.90 units
The distance between the point (5,12) and the line y = 5x + 12 is 4.90 units
How to find the distance between a point and a line?
If a point P with the coordinates (x₁, y₁), and we need to know its distance from the line represented by ax + by + c = 0
Then the distance of a point from the line is given by the formula:
d = (ax₁ + by₁ + c) / √(a² + b²)
Given: the point (5,12) and the line y = 5x + 12. The line can be written as
5x-y+12 = 0. Thus:
x₁ = 5, y₁ = 12, a = 5, b = -1, c = 12. Substitute these into the formula:
d = (ax₁ + by₁ + c) / √(a² + b²)
d = (5×5 + (-1×12) + 12) / √(5² + (-1)²)
d = 25/√26 = 4.90 units
Therefore, the distance between the point and the line is 4.90 units. Option D is the answer
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Given the line below. a. Determine the slope of the line. Show all work on how you found the slope or determined the slope from the graph. b. In two or more complete sentences, explain why it is possible or it is not possible to write the equation of the given line in the traditional version of the point-slope form of a line.
The slope of the vertical line in the given graph is undefined.
The equation of the line is x = 2.
How to Write the Slope of a Vertical Line?The slope of a vertical line is usually undefined because the horizontal change (change in x) is equal to 0. Thus, we cannot divide a number by 0. Therefore, the slope of a vertical line is undefined.
The line given is a vertical line that intersects the x-axis at 2. Its slope is undefined. Since its slope is undefined, it is impossible to write the equation of the vertical line in the traditional version of the point-slope form. Hence, it is written as x = b, where b is the point where the x-axis is intersected by the line.
Slope of the line is undefined. The equation is x = 2.
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John bought 75kg of chocolate. He packed the chocolate equally in 7 bags. How much chocolate did he pack in each bag?
Answer: 10.7142857kg in each bag
Step-by-step explanation: If you divide 75 by 7 you would get 10.7142857. There fore there is about 10.7142857kg of chocolate in each bag.
2. Estimate the subtotal for a $14.00 shirt, a $27.00 pair of pants, and a $62.00 jacket.
Answer:
$100
Step-by-step explanation:
Round each price to the nearest 10 and add.
$10 + $30 + $60 = $100
Answer: $100
Out of the 25 families that Tod deliver magazines to on Friday, 10 families were home and the test were away. How is the fraction of magazines that were delivered to families who were home written as a decimal?
The fraction of magazines that were delivered to families who were at home is 0.4 if total number of families are 25 out of which 10 were at home and rest are away.
Total number of families = 25
Families at home = 10
So the ratio of the required families
= Families at home/total number of families
= 10/25
= 2/5
To convert the fraction into decimal form, we have to divide and we get
= 0.4
Hence, the number of families in decimal to which magazines got delivered are 0.4
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Sarah is 11 4/5 years old. Greg is 1 1/6
years younger than Sarah and Jane is 1 1/3 years younger than Greg. How old is Jane?
first off, let's convert all those mixed fractions to improper fractions and then subtract.
[tex]\stackrel{mixed}{11\frac{4}{5}}\implies \cfrac{11\cdot 5+4}{5}\implies \stackrel{improper}{\cfrac{59}{5}} ~\hfill \stackrel{mixed}{1\frac{1}{6}}\implies \cfrac{1\cdot 6+1}{6}\implies \stackrel{improper}{\cfrac{7}{6}} \\\\\\ \stackrel{mixed}{1\frac{1}{3}}\implies \cfrac{1\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{4}{3}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{Sarah}{\cfrac{59}{5}}\hspace{5em}\stackrel{Greg}{Sarah - \cfrac{7}{6}} \hspace{5em}\stackrel{Jane}{Greg - \cfrac{4}{3}} \\\\\\ \stackrel{\textit{\LARGE Jane} }{\cfrac{59}{5}~ - ~\cfrac{7}{6}~ - ~\cfrac{4}{3}}\implies \cfrac{(6)59~~ - ~~(5)7~~ - ~~(10)4}{\underset{\textit{using this LCD}}{30}}\implies \cfrac{279}{30}\implies \cfrac{93}{10}\implies {\Large \begin{array}{llll} 9\frac{3}{10} \end{array}}[/tex]
Simplify 4 – 8 × 2.
Question 18 options:
A)
–8
B)
–10
C)
–4
D)
–12
Answer:
D
Step-by-step explanation:
4 - 8 × 2 ← perform multiplication before doing subtraction
= 4 - 16
= - 12
Help me please!!!!!!
The digit in the ones place is 7, The digit in the tenths place is 6, and The digit in the tens place is 4.
What do you mean by place value?
In mathematics, each digit in an integer has a place value. Place value refers to the value that a digit in a number represents dependent on where it sits within the number.
For instance, 700 or 7 hundreds is the place value of the number 7. But 7,432 has a place value of 7,000, or 7,000. The place value of the digits changes despite the fact that they are the same in both numbers due to their position.
The chart is attached in the answer by which we can conclude that The digit in the ones place is 7, The digit in the tenths place is 6, and The digit in the tens place is 4.
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Height (in.)
12
10
8642
Candle Height
0123456
Time (h)
12" candle:
8" candle:
12" candle
Step 1: Identify two points and 41
Step 2: Find the slope and simplify
Step 3: Label the answer with units
8" candle
Step 1: Identify two points and
Step 2: Find the slope and simplify
&
Step 3: Label the answer with units
By using the formula for slope of a line, it can be calculated that
For 12'' candle
Two points are (1, 10) and (4, 2)
Slope = [tex]-\frac{8}{3}[/tex]
For 8'' candle
Two points are (3, 4) and (6, 0)
Slope = [tex]-\frac{4}{3}[/tex]
What is slope of a line?
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta\\[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
Here,
For 12'' candle
Two points are (1, 10) and (4, 2)
Slope =
[tex]\frac{2-10}{4-1}\\-\frac{8}{3}[/tex]
For 8'' candle
Two points are (3, 4) and (6, 0)
Slope =
[tex]\frac{0-4}{6 - 3}\\-\frac{4}{3}[/tex]
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A Chevrolet Sonic Hatchback costs $14,800.00. With a 12 % down payment, you can have an amortized loan for 6 years at a rate of 4.5%. What will the monthly payment be? car cost in total, money paid in interest
Based on the loan amount and the number of years, the monthly payment, total cost of the car, and amount of interest to be paid are as follows:
Payment each month: $206.74Total cost of the car was $14, 885.$1, 861.52 must be paid in interest.How do I calculate the required interest?Find the loan amount first:
= Car expense x ( 1 - down payment percent)
= 14, 800 x ( 1 - 12%)
= $13024
the monthly rate and the total number of periods, then:
Daily rate calculation:
= Annual Rate / Twelve-Month Period
= 4.5% / 12
= 0.375%
Counting periods:
= Years multiplied by Months per year
6 years times 12
72 months
These enable the following formula to determine the monthly payment:
= Loan Amount / 72-period Annuity Present Value Interest Factor of 0.375%
13024 / 62.995976235992
= $206.74
Total amount repaid on the auto loan:
= Amount Due Each Month x The Number of Months
= 206. 74 x 72
= $14, 885. 52
Accordingly, the total amount of interest paid was:
= Amount borrowed - Amount paid toward the car's cost
= 14, 885.52 - 13, 024
= $1, 861.52
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Please help will mark Brainly
Answer:
D
Step-by-step explanation:
y-7 = -1/2 (x-(-2)
y-7 = -1/2 (x+2)
y -7 = -1/2 x - 1
y = -1/2 x -1 +7
y = -1/2 x + 6
When solving: 1,175 ÷ 5, using partial quotients, how would you decide which power of 10, when multiplied by 5, should be subtracted first?
I need a step by step example please
Using partial quotient, the place value while subtracting is determined by the dividend.
The place value should never be more than the dividend not up to a tens place value less than the dividend's place valueHow to perform division using partial quotientsdivisor dividend quotient multiplication subtraction new dividend
5 1175 200 200 * 5 = 1000 1175 - 1000 = 175
5 175 30 30 * 5 = 150 175 - 150 = 25
5 25 5 5 * 5 = 25 25 - 25 = 0
The quotient is then added as
= 200 + 30 + 5
= 235
Assuming the quotient was written 2. While subtracting, the dividend for the first value (1175) is in thousands. placing the the 2 in thousands makes it more than the dividend hence the 2 should be in hundreds
1175 - 2000 incorrect
1175 - 200 correct
for the second stage
175 - 150 correct (since 150 < 175)
last stage
25 - 25
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Tanvi and her friend Beth are making cookies for their school's cookie swap. Tanvi mixes 1
cup of chocolate chips and 3 cups of plain sugar cookie dough in a small bowl. Beth mixes 2
cups of chocolate chips and 6 cups of plain sugar cookie dough in a larger bowl. Once the
cookies are baked, the girls are ready for a chocolaty snack. Whose batch of cookies was
more chocolaty?
Correct statement for whose batch of cookies was more chocolaty is option (c) Neither, The batches were equally chocolaty
Consider Tanvi's cookies
Number of cups of chocolate chips = 1 cups
Number of cups of plain sugar = 3 cups
Total number of cups = 1 + 3 = 4 cups
Then the fraction of chocolate = 1 / 4
= 0.25
Consider Beth's cookies
Number of cups of chocolate chips = 2 cups
Number of cups of plain sugar = 6 cups
Total number of cups = 2 + 6 = 8 cups
Then the fraction of chocolate = 2 / 8
= 1 / 4
= 0.25
Hence, correct statement for whose batch of cookies was more chocolaty is option (c) Neither, The batches were equally chocolaty
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Question
Rewrite the equation to represent the resistance of resistor 2, R₂, in terms of RT and R₁
R₂=(RT-R₁)/(RT R₁)
R₂=(R₁+R₂)(RT R₁)
R₂=(RT R₁)(R₁-1)
R₂=(RT R₁)(R₁-RT)
The equation for resistor 2, R₂ is (d) R₂ = R₁Rt/(R₁ - Rt)
How to rewrite the equation for resistor 2, R₂?From the question, we have the following parameters that can be used in our computation:
Rt = R₁R₂/(R₁ + R₂)
The question implies that we make R₂ the subject of the formula
So, we have
Rt = R₁R₂/(R₁ + R₂)
Cross multiply the equations
(R₁ + R₂)Rt = R₁R₂
Open the brackets
So, the equation becomes
R₁Rt + R₂Rt = R₁R₂
Collect the like terms
R₁R₂ - R₂Rt = R₁Rt
Factor out R₂
R₂(R₁ - Rt) = R₁Rt
Make R₂ the subject
R₂ = R₁Rt/(R₁ - Rt)
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Answer:
2, R₂ is (d) R₂ = R₁Rt/(R₁ - Rt)
Step-by-step explanation:
What function is being described Justify each part of your function, explaining how you determined it.
My function has a vertical asymptote at x = -5 and x = 3 , a point discontinuity at x = 2. It has end behavior of f(x) goes to 0 as x goes to negative infinity and f(x) goes to 0 as x goes to positive infinity. The domain is (-inf, -5)U(-5, 2)U(2, 3) U (3,inf).
The end behavior of the function is as x tends to infinity, f(x) tends to zero. It is power function.
What is the end behavior of a polynomial function?The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.
The degree and the leading coefficient of a polynomial function given is determine the end behavior of the graph.
Given that function has a vertical asymptote at x = -5 and x = 3 , a point discontinuity at x = 2.
The end behavior of f(x) goes to 0 as x goes to negative infinity and f(x) goes to 0 as x goes to positive infinity.
The domain is (-inf, -5)U(-5, 2)U(2, 3) U (3,inf).
Hence, we can conclude that the end behavior of the function is as x tends to infinity, f(x) tends to zero.
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what's 0/0, with full steps
Answer:
undefined
Step-by-step explanation:
division by zero is undefined
Division Property of zero
For any nonzero real number a
The quotient of "a" and 0 is undefined. That is a/0 is undefined
If you can do your homework at a rate of 9.3 minutes for every problem, how
many problems could be done after 8.13 hours? Round to a whole number.
Answer:
52 problems
Explanation:
8.13 hours
8.13 hours × 60 minutes = x minutes
487.8 minutes
487.8 minutes ÷ 9.3 minutes = 52.4516129 problems
If the cost, C(x), for manufacturing x units of a certain product is given by
C(x)=x²-18x+67
find the number of units manufactured at a cost of $8450.
The number of units manufactured at a cost of $8450 is x = 101.
What is a function?A function is a relation where every input is connected to only one possible output from a set of available inputs.
The given function is C(x) = x² - 18x + 67.
To find the number of units manufactured at a cost of $8450, substitute C(x) = 8450 into the given equation and solve for x:
8450 = x² - 18x + 67
x² - 18x + 67 - 8450 = 0
x² - 18x - 8383 = 0
x² - 101x + 83x - 8383 = 0
x(x - 101) + 83(x - 101) =0
(x + 83)(x - 101) = 0
(x + 83) = 0 or (x -101) = 0
x = -83 or x = 101
Since the number of manufactured units cannot be negative, it follows
x = 101.
Hence, the number of units manufactured at a cost of $8450 is x = 101.
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What amount will Chris and Allison report for taxable interest on their Form 1040? The couple's partially completed Form 1040, page 1, is shown below. You may use the form to assist you in answering this question.
Answer:
Step-by-step explanation:
