Answer:
i think it is $106,800.00
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 6.5%/100 = 0.065 per year.
Solving our equation:
A = 60000(1 + (0.065 × 12)) = 106800
A = $106,800.00
The total amount accrued, principal plus interest, from simple interest on a principal of $60,000.00 at a rate of 6.5% per year for 12 years is $106,800.00.
The simple interest rate for this loan is 78%.
What is simple interest?It is the interest calculated on the principal at a given rate for a time period.
We have,
If Steven borrows $60,000 at an interest rate of 6.5%, the total amount of interest he will pay over 12 years can be calculated as:
I = Prt
where I is the interest, P is the principal amount borrowed ($60,000), r is the interest rate as a decimal (0.065), and t is the time period in years (12). Substituting the given values, we get:
I = 60000 x 0.065 x 12
I = $46,800
The simple interest rate is the ratio of the total interest paid to the principal borrowed, expressed as a percentage:
simple interest rate = (total interest/principal borrowed) x 100
Substituting the given values, we get:
simple interest rate = (46800 / 60000) * 100
simple interest rate = 78%
Therefore,
The simple interest rate for this loan is 78%.
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Describe the steps you would use to factor the
trinomial 4x2 - 4x - 3.
-
Answer:
5-4x
Step-by-step explanation:
8 - 4x - 3
5 - 4x
. The selling price of 15 articles is Rs 1,500 at a gain of 8%. Find C.P of each article
Rs. 92.59 is each article's CP
Step-by-step Explanation:-
As per conditions given,
[tex]1500 \div 15 \div (1 + 8[/tex]%)
[tex] = > 100 \div 1.08[/tex]
[tex] = > approx. \: 92.59[/tex]
Hence, the CP of each article is Rs. 92.59
how many spaces are there total? 5) Jerry had 153 songs on his MP3 player. If he deleted 63 songs, what is the ratio of songs he kept to songs he deleted?
PLEASE HELP ME!! I ALREADY DID THE FIRST ONE BUT IM SO CONFUSED ABOUT THE OTHERS!!!
Answer:
i) 134
ii) Number of bottles sold on Tuesday: [tex]\dfrac{x}{45}[/tex]
iii) Number of bottles sold on Wednesday: [tex]\dfrac{(x-75)}{48}[/tex]
iv) [tex]x=3915[/tex]
Therefore, 87 bottles were sold on Tuesday and 80 bottles were sold on Wednesday
Step-by-step explanation:
i) You need to ensure that the values are both in the same format (either both in dollars, or both in cents).
45 cents = 45/100 dollars = 0.45 dollars
60.30 ÷ 0.45 = 134
ii) both values are in cents, so no need to convert one of them.
Let n be the number of bottles sold.
So 45n = x
Therefore, n = x/45
ii)
Let n be the number of bottles sold.
So 48n = (x - 75)
Therefore, n = [tex]\dfrac{(x-75)}{48}[/tex]
iv)
Number of bottles sold on Tuesday: [tex]\dfrac{x}{45}[/tex]
Number of bottles sold on Wednesday: [tex]\dfrac{(x-75)}{48}[/tex]
If the number of bottles sold on Tuesday was 7 more than those sold on Wednesday:
[tex]\implies \dfrac{x}{45}-7=\dfrac{(x-75)}{48}[/tex]
multiply both sides by 48:
[tex]\implies \dfrac{48x}{45}-336=x-75[/tex]
multiply both sides by 45:
[tex]\implies 48x-15120=45x-3375[/tex]
[tex]\implies 3x=11745[/tex]
[tex]\implies x=3915[/tex]
Therefore, 87 bottles were sold on Tuesday and 80 bottles were sold on Wednesday
Ethan's monthly salary is $1850. In a particular month, he spent 20.5% of his salary on room rental, $690 on food and $940 on other expenses. Express the amount that he overspent as a percentage of his monthly salary, giving your answer correct to 2 decimal places.
Answer:
He overspent 8.61% as a percentage of his monthly salary.
Step-by-step explanation:
Answer:
8.61% (2 dp)
Step-by-step explanation:
Salary = 1850
Food = 690
Other = 940
Rent = 20.5% = 20.5/100 = 0.205
Therefore, 20.5% of the salary = 0.205 x 1850 = 379.25
Total spent = 690 + 940 + 379.25 = 2009.25
Percent change = [ (difference between initial and final value) ÷ initial value] x 100
=[(2009.25 - 1850) ÷ 1850] x 100 = 8.61% (2 dp)
Just an answer and a simple explanation. Please and Thank you!
Answer:
x = 15°
Step-by-step explanation:
If you use Vertical Angles, you can move the two algebraic expressions next to each other and totaling 90° (because m and n are perpendicular)
x + 21 + 3x + 9 = 90°
combine like terms.
4x + 30 = 90
subtract 30 from both sides.
4x = 60
divide by 4.
x = 60/4
x = 15
2. Find the area of the shaded region. Express your answer in terms of
3 in
6 in
9 in
12 in
18 in
Answer:
Step-by-step explanation:
Find the area of the rectangle. A = length * width
Find the area of each circle. A = π*radius*radius
Subtract the area of each circle from the area of the rectangle.
A = length * width
A = (3+6+9+12) * 18
A = 30 * 18
A = 540 square inches
Bottom circle
A = π * radius * radius. (radius is 1/2 of the diameter)
A = 3.14 * 6 * 6
A = 133.04 square inches
Middle circle
A = π * radius * radius
A = 3.14 * 4.5 * 4.5
A = 63.59 square inches
Top circle
A = π * radius * radius
A = 3.14 * 3 * 3
A = 28.26 square inches
Subtract the circles from the rectangle.
540 - 133.04 - 63.59 - 28.26 = 315.11 square inches is the area of the shaded part.
Use the diagram below of similar triangles to find the value of y.
Answer:
y = 10.5
Step-by-step explanation:
Δ MOP and Δ MNQ are similar then the ratios of corresponding sides are in proportion, that is
[tex]\frac{OP}{NQ}[/tex] = [tex]\frac{MO}{MN}[/tex] ( substitute values )
[tex]\frac{y}{7}[/tex] = [tex]\frac{8+4}{8}[/tex] = [tex]\frac{12}{8}[/tex] ( cross- multiply )
8y = 84 ( divide both sides by 8 )
y = 10.5
hey can someone please give me a step by step explian the answer
Answer:
x = 9/2
Step-by-step explanation:
The outside triangle is also a right triangle, with hypotenuse 8 and side 6.
The missing side can be calculated with pythagoras as:
[tex]\sqrt{8^2-6^2} = \sqrt{28}[/tex]
Now for the vertical line, lets call it y, which is a side for two "back to back" triangles, you can do pythagoras twice:
left triangle: [tex]y^2 + (8-x)^2 = 28[/tex]
right triangle: [tex]y^2 + x^2 = 6^2[/tex]
Eliminating y², you can solve:
[tex]28 - (8-x)^2 = 36 - x^2[/tex]
[tex]28 -x^2 + 16x - 64 = 36 - x^2[/tex]
[tex]16x = 36 + 64 - 28[/tex]
[tex]x = \frac92[/tex]
Use given triangle to fill in the blank.
Answer:
The choice first
[tex] \tan(x) = \frac{12}{5} [/tex]
Write the equation in standard form. Identity the center and radius.
x² + y2 + 8x-4y-7=0
Answer:
equation;
[tex](x + 4) {}^{2} + (y - 2) {}^{2} = 27[/tex]
Center (-4,2)
Radius is
[tex]3 \sqrt{3} [/tex]
Step-by-step explanation:
Since the x^2 and y^2 have the same coeffiecent this will be a circle in a form of
[tex](x - h) {}^{2} + (y - k) {}^{2} = {r}^{2} [/tex]
Where (h,k) is center
r is the radius
So first we group like Terms together
[tex] {x}^{2} + 8x + {y}^{2} - 4y - 7 = 0[/tex]
Add 7 to both sides
[tex] {x}^{2} + 8x + {y}^{2} - 4y = 7[/tex]
[tex]( {x}^{2} + 8x) +( {y}^{2} - 4y) = 7[/tex]
Since the orginal form of the equation of the circle has a perfect square we need to complete the square for each problem
[tex] (\frac{8}{2} ) {}^{2} = 16[/tex]
and
[tex]( - \frac{4}{2} ) {}^{2} = 4[/tex]
so we have
[tex] {x}^{2} + 8x + 16 + {y}^{2} - 4y + 4y = 7 + 16 + 4[/tex]
[tex] {x}^{2} + 8x + 16 + {y}^{2} - 4y + 4y = 27[/tex]
[tex](x + 4) {}^{2} + (y - 2) {}^{2} = 27[/tex]
To find our center, h is -4 and k is 2
so the center is (-4,2)
The radius is
[tex] \sqrt{27} = 3 \sqrt{3} [/tex]
So the radius is 3 times sqr root of 3.
The table shows the membership cost for two CD clubs. How many CDs would you need to buy in a year in order for the total cost of both memberships to be the same?
CD Club Membership
Club #1: Annual Fee = 50$ and Cost Per CD = 7.50$
Club #2: Annual Fee = 35$ and Cost Per CD = 8.00$
Answer:
Club 1: 16 would be 120
Club 2: 15 would be 120
Lisa pours 1/4 a 1 liter bottle of coke for each of her 4 family members. What is the decimal of coke they each receive?
Answer:
.25
Step-by-step explanation:
Answer:
if there are 4 people and she pours 1/4 of a 1-liter coke bottle equally, it means that she gave each member 25% or 0.25 of a liter or bottle of coke
In 2020, summer camp registration was $15
more than it was in 2021. In 2020, registration
was $285. By what percentage did the summer
camp registration decrease in 2021?
Answer:
I think your answer is 5.25% or it could be 5.3 or 5
5.26 percent of the summer camp registration decreased in 2021
What is the percentage?The ratio of two numbers that has no dimensions is what is known as a percentage. It may be used to determine how much one number exceeds another when comparing two figures, or it is used to compare the two statistics to a uniform grid.
In 2020, there was a $285 membership fee for summer camp.
It is stated that the membership cost for summer camp increased by $15 in 2020 compared to 2021. We can calculate the summer camp registration cost for 2021 using the data given.
In 2021, there was a $285-$15 membership fee for summer camps.
there was a $270 membership fee for summer camps.
The gradual decrease in the summer enrichment registration price must be determined = (Drop/Initial Value)*100 represents the proportion decrease.
= (15/285)*100 represents the percentage decline.
The membership price for summer camps has decreased by 5.26 percent.
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is it true or false is this a function (pls help)
Answer: True
Use the vertical line test to determine whether or not a graph represents a function. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. If the vertical line touches the graph at more than one point, then the graph is not a function.
Answer:
True
Step-by-step explanation:
Using the vertical line test since it only passes through the graph once it is a function
Miles is buying a chair that regularly costs $250. Today the chair is on sale for 30% off. The sales tax of 6% is taken on the sales price. What will be the total cost, including tax, if Miles buys the chair today. (I ALREADY KNOW THE ANSWER. BUT I NEED THE WORK FOR THE ANSWER TO SHOW MY TEACHER) (the answer is $185.50)
Step-by-step Explanation:
First find out what is the price after 30% off.
250 · 0.3 = 75
250 - 75 = 175
Then find the tax and add it on. Remember to calculate the tax AFTER the discount.
175 · 0.06 = 10.50
175 + 10.50 = 185.50
Fourteen equals fifteen decreased
by an unknown number.
Answer:
14 = 15 - x
Step-by-step explanation:
14 = 15 - x
14 = 15 -1
14 = 14
Hope this helps!
Krista’s mom has told her she need to make the pen 21 the size that she had planned (5 feet long by 4 21 feet wide). What will the area be? What are two possible lengths and widths she could use?.
The area of Krista’s mom new pan is 11 1/4 ft² and two possible dimensions are (5 , 4 1/2) and (4 1/2 , 2 1/2)
What is the area of a rectangle?Area of a rectangle is the product of the length of the rectangle and the width of the rectangle. It can be given as,
[tex]A=a\times b[/tex]
Here, (a)is the length of the rectangle and (b) is the width of the rectangle
The dimensions of pan which, Krista’s mom, had planned is 5 feet long by 4 1/2 feet wide. Therefore, the length of the pen is 5 feet and the width of the pan is 4 1/2 feet.
Thus, the area of this rectangular pan is,
[tex]A=5\times4\dfrac{1}{2}\\A=5\times\dfrac{9}{2}\\A=22\dfrac{1}{2}\rm ft^2[/tex]
The area of the pan is 22 1/2 ft².
Now, Krista’s mom has told her she needs to make the pen 1/2 the size. Thus the area of new pan is,
[tex]A=\dfrac{22\dfrac{1}{2}}{2}\\A=\dfrac{\dfrac{45}{2}}{2}\\A=\dfrac{45}{4}}\\A=11\dfrac{1}{4}}\\[/tex]
For this area, possible dimensions are 4 1/2 and 2 1/2.
Hence, the area of Krista’s mom new pan is 11 1/4 ft² and two possible dimensions are (5 , 4 1/2) and (4 1/2 , 2 1/2)
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FIRST PART OF MY LAST QUESTION ONLY FOR ONE PERSON TO uSE
Answer:
C
Step-by-step explanation:
You just need to convert some of the mixed numbers so that they have a denominator (of the fraction part) as 8:
10 4/8 = 10 1/2
10 6/8 = 10 3/4
11 2/8 = 11 1/4
Isaac planted 64 fewer trees than Leon. Leon planted t trees. Write an expression that
shows how many trees Isaac planted.
What are the values of a 1 and r of the geometric series? 1 3 9 27 81.
For the given geometric series the value of the common ratio(r) is 3, while the value of a₁ is 1.
What is geometric series?A series of numbers whose any two consecutive numbers are always in a common ratio of that series.
Given to us
Series, 1 3 9 27 81
To find the value of the common ratio(r), we will simply find the ratio of any two consecutive numbers, therefore,
[tex]r = ratio = \dfrac{3}{1} = 3[/tex]
As we can see the common ratio of the given series is 3, therefore, every next number will be thrice the number before.
We need to find the value of a₁ for the given series, and as we know that a₁ is the first number of the series with which the series is starting, therefore,
a₁ = 1
Hence, for the given geometric series the value of the common ratio(r) is 3, while the value of a₁ is 1.
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Which of the following modifications to the list of assets and liabilities below would result in a positive net worth? Home owned $105,000. Mortgage owed $100,000. Car valued at $26,000. Car loan of $22,000. Investment fund of $4,500. Savings of $1,500. Credit card balance of $15,000. A. Lowering mortgage by $1,000. B. Increasing investment fund by $500. C. Adding $100 to savings. D. All of the above. Please select the best answer from the choices provided A B C D.
Answer:
I think its D
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
Triangle ABC is equilateral, what is the value of X, What is the measure of angle B
Answer:
x = [tex]\sqrt{48}[/tex]
Angle B = 60 degrees
Step-by-step explanation:
Since the triangle is equilateral, we know that all sides will be 8 units long. Side CB is split in half so each half (CD and DB) are 4 units long. Side CA is 8 units long and is the hypotenuse for triangle ACD. To find the unknown side (AD aka x):
4^2 + x^2 = 8^2. use the pythagorean theorem
16 + x^2 = 64. subtract 16 from both sides
x^2 = 48. take the square root of both sides
x = [tex]\sqrt{48}[/tex]
For angle B, we know that all the angles in triangle ABC will be the same since it is an equilateral triangle.
180/3 = 60. total sum of all angles in a triangle will be 180 so divide that by total angles (3)
Angle B = 60 degrees
The value of x is 6.92 units.
The measure of angle B is 60 degree.
What is Pythagoras theorem?The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.
According to the Pythagoras theorem, the square of the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of the squares of the other two sides.
Given:
Since the triangle is equilateral all sides will be 8 units long.
and, CD or DB = 1/2 (CB)
= 4 units long.
Now, In ΔACD using Pythagoras theorem
4² + x² = 8²
16 + x² = 64
x² = 48
x = 6.92 unit.
and, We know all three angles of Equilateral triangle are Equal in measure.
So, 180/3 = 60.
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Please I’m confused…
Answer:
I believe it should be
4 : 1 : 200
Step-by-step explanation:
2) What percent of 87 is 55 ?
Answer:
If you don't add decimals a 63.
Step-by-step explanation:
because 55 out of 87 correct on a test would be a 63%
According to the graph, what is the value of the constant in the equation below?
well, let's take a look at the graph hmmmm as "x" is moving further towards the right, the line is going down, or namely "y" is lessening and lessening, which is another way to say that "y" is inversely proportional to "x".
well, we know a few points on the line hmmm let's use say hmm (10 , 8) to get the constant of proportionality. Any point will do btw, we're just using this one.
[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\stackrel{\textit{"H" varies inversely with "w"}}{H=\cfrac{k}{w}}\qquad \textit{we know that} \begin{cases} H=8\\ w=10 \end{cases} \\\\\\ 8=\cfrac{k}{10}\implies \boxed{80=k}[/tex]
3 ratios equivalent to 5 : 2
Answer:
25/10 ,30/12,10/4
Step-by-step explanation:
1) 5/2*5/5
2)5/2*6/6
3)5/2*2/2
5) −r − 10r 6) −2x + 11 +6x 7) 11r − 12r 8) −v + 12v 9) −8x −11x 10) 4p + 2p
pls help me simplify this
Look at the shaded shapes drawn on a square grid.
A
B
Steven says:
The area of rectangle A is double the area of square B.
Is he correct?
Explain your answer:
Answer:
No. Steven is not correct.
Step-by-step explanation:
The area of shape A is 15 (either multiply 5 x 3 or just count squares). The area of shape B is 9.
15 is not double 9.
What number is plotted on the number line?
Answer:
The number 0.7 is plotted on the number line.
Answer:
0.7.Step-by-step explanation:
Count up 0 to 1.
Stop at the point.
If you stop at the point, you should know what the point is.
The point is graphed at 0.7.