Answer:
4.66 years
Step-by-step explanation:
Let us assume that it will take 't' years for him to repay the money that he would borrow.
We can use monthly cashflow formula:
[tex]C=Pr\frac{(1+r)^{12t}}{(1+r)^{12t}-1}[/tex]
Here, we have been given:
Monthly cashflow C=425
Loan amount P=20000
Interest rate AMR = 7.5%. Therefore, we have [tex]r=\frac{0.075}{12}[/tex]
Upon substituting these values in the formula, we get:
[tex]425=20000\cdot \frac{0.075}{12} \frac{(1+\frac{0.075}{12})^{12t}}{(1+\frac{0.075}{12})^{12t}-1}[/tex]
Upon simplifying, we get:
[tex]425=125 \frac{(1+0.00625)^{12t}}{(1+0.00625)^{12t}-1}[/tex]
[tex]425=125 \frac{(1.00625)^{12t}}{(1.00625)^{12t}-1}[/tex]
Upon solving this equation using a calculator, we get:
[tex]t=4.66[/tex]
Therefore, correct answer is 4.66 years. That is, second choice from the given options.
X+3y=5
-X+6y=3
solve the system of equation
A.X=1,Y=2
B.X=2,Y=1
C.X=1, Y=1
D.X=0, Y=2
Answer:
That all the answer hope i helped
Answer:
The answer will be B
Step-by-step explanation:
What is the equation of the line with a slope of -2 that passes through the
point (4, -3)?
y + 3 = 4(x - (-2))
y + 4 = -2(x - 3)
y + 3 = -2(x - 4)
y + 4 = 3(x - (-2))
The point-slope form of the line:
[tex]y-y_1=m(x-x_1)[/tex]
We have the slope m = -2 and the point (4, -3). Substitute:
[tex]y-(-3)=-2(x-4)\\\\\boxed{y+3=-2(x-4)}[/tex]
HELP NOW PLLLLLZZZZZ!
A hybrid car can travel 40 miles per gallon. Approximately how many gallons of fuel will the car need to travel 20 km? [1 mile = 1.6 km]
A. 0.3
B. 0.8
C. 2.5
D. 3.2
Answer: The car would need 0.3 gallons of fuel to travel 20km.
Step-by-step explanation: 40mile x 1.6km = 64km
1 gallon 1 mile 1 gallon
20km ÷ 64km = 0.3125
Answer:
In 0.3 gallon of fuel, the car will travel 20 km.
A is the correct option.
Step-by-step explanation:
We have been given that in 1 gallon of fuel the car can travel 40 miles.
Now, 1 mile = 1.6 km.
Hence, in 1 gallon the car travel 40×1.6 = 64 km
Let the car will consume x gallons of fuel to travel 20 km.
Thus, we have the equation
[tex]\frac{1}{64}=\frac{x}{20}[/tex]
ON solving for x
[tex]x=\frac{20}{64}\\\\x=0.3[/tex]
Therefore, in 0.3 gallon of fuel, the car will travel 20 km.
A is the correct option.
15. You are buying batteries, a stereo, and some CDs from the I.B. Electronics store. You can buy from this store online or in a physical store. You have a coupon for 10% off that can only be used in the physical store and a $5.00 off coupon that can only be used online. The sales tax of 5% only applies to the physical store. Shipping for the online store is a flat rate of $6.99. You are trying to decide whether to shop at the physical store or the online store. Using the pricing information below, how much would you pay at the physical store after all discounts, taxes, and shipping fees have been applied?
The total amount you would pay at the physical store after all discounts, taxes, and fees have been applied is [tex]{128.36} \)[/tex].
Let's go through the calculations again to find the final cost at the physical store after all discounts, taxes, and fees.
Physical Store Pricing:
- Batteries: 2 packs at $5.99/pack
- Stereo: 1 system at $100.00
- CDs: 3 CDs at $7.95 each
Discounts and Taxes in the Physical Store:
1. 10% Off Coupon: This coupon applies to the total purchase amount before tax.
2. Sales Tax: 5% sales tax applies to the total purchase amount after applying discounts.
Calculation Steps:
Step 1: Calculate the total cost of items before discounts and tax:
- Batteries: 2 packs × $5.99/pack = $11.98
- Stereo: $100.00
- CDs: 3 CDs × $7.95/CD = $23.85
Total before discounts: $11.98 + $100.00 + $23.85 = $135.83
Step 2: Apply the 10% off coupon:
- 10% of $135.83 = $13.583
- Total after 10% off: $135.83 - $13.583 = $122.247
Rounded to two decimal places: $122.25
Step 3: Apply the 5% sales tax:
- 5% sales tax on $122.25:
[tex]\[0.05 \times 122.25 = 6.1125\][/tex]
Rounded to two decimal places: $6.11
Step 4: Calculate the final cost at the physical store:
- Total cost after tax: $122.25 + $6.11 = $128.36
The complete question is
You are buying batteries, a stereo, and some CDs from the I.B. Electronics store. You can buy from this store online or in a physical store. You have a coupon for 10% off that can only be used in the physical store and a $5.00 off coupon that can only be used online. The sales tax of 5% only applies to the physical store. Shipping for the online store is a flat rate of $6.99. You are trying to decide whether to shop at the physical store or the online store. Using the pricing information below, how much would you pay at the physical store after all discounts, taxes, and shipping fees have been applied?
Item Quantity Physical Store Online Store
Batteries 2 packs $5.99/pack $4.99/pack
Stereo 1 system $100.00/system $90.00/system
CDs 3 CDs $7.95/CD $8.95/CD
simplify (-6a5b4c3)(5a3b2c)
[tex]\text{Use:}\\\\a^n\cdot a^m=a^{n+m}\\\\(-6a^5b^4c^3)(5a^3b^2c)\\\\=(-6\cdot5)(a^5a^3)(b^4b^2)(c^3c^1)\\\\=-30a^{5+3}b^{4+2}c^{3+1}\\\\=\boxed{-30a^8b^6c^4}[/tex]
an ordinary Fair die is a cube with the number 1 through 6 on the sides (represented by painted spots). imagine that such a die is rolled twice in succession and the face values of the two dice rolls are added together. this sum is recorded as the outcome of a single trial of random experiment.
compute the probability of each of the following events. event A: the sum is greater than 7. B: the sum is an even number
Event A Answer: [tex]\frac{5}{12}[/tex]
Step-by-step explanation:
sum greater than 7 leaves are the following combinations for 8, 9, 10, 11, and 12:
8 = 26, 35, 44, 51, 62 (5 possibilities)
9 = 36, 45, 54, 63 (4 possibilities)
10 = 46, 55, 64 (3 possibilities)
11 = 56, 65 (2 possibilities)
12 = 66 (1 possibility)
This is a total of 15 possibilities out of 36 total: [tex]\frac{15}{36}[/tex] = [tex]\frac{5}{12}[/tex]
***********************************************************************************
Event B Answer: [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
sum is an even number means both dice are odd or both dice are even. That results in the following combinations:
11 13 15
22 24 26
31 33 35
42 44 46
51 53 55
62 64 66
This is a total of 18 possibilities out of 36 total: [tex]\frac{18}{36}[/tex] = [tex]\frac{1}{2}[/tex]
Please help me out and answer!!!!!
Really struggling
Answer:
D
Step-by-step explanation:
Under a counterclockwise rotation about the origin of 90°
a point (x, y) → (- y, x)
A translation of 3 units up → + 3 in the y- direction, that is add 3 to the y- coordinate, hence
(x, y) → (- y, x) → (- y, x+ 3) → D
Which quantity is proportional to 35⁄80?
I believe this is the answer
7/16
Answer:
7/16
Step-by-step explanation:
Well the biggest number that is divisible by 35 and 80 is 5
x times x^n
Simplify it please and thank you!
Answer:
[tex]x^{n+1}[/tex]
Step-by-step explanation:
using the rule of exponents
• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]
note that x = [tex]x^{1}[/tex], hence
x × [tex]x^{n}[/tex] = [tex]x^{n+1}[/tex]
does 1/6, -3, √7, -6/5, or 4.5 comes first when the numbers are listed from least to greatest
The arrangement is as follows:
-3<-1.2<1/6<√7<4.5
What is ascending and descending order?Ascending means smallest to largest, 0 to 9, and/or A to Z and Descending means largest to smallest, 9 to 0, and/or Z to A.
Given:
1/6= 0.16667
√7= 2.645
-6/5= -1.2
So, the least number is -3 and greatest number is 4.5.
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what is the inverse of the function x + 2y + 3 = 0
The inverse of the function x + 2y + 3 = 0 is found by first expressing the function explicitly as y = -½x - 1½ and then swapping x and y to solve for the new y, yielding the inverse function y = -2x - 3.
Explanation:To find the inverse of a function, we typically swap the roles of x and y, and then solve for y. Given the function x + 2y + 3 = 0, we first write the function explicitly as y in terms of x:
y = -½x - ³2
Now let's find the inverse:
Swap x and y to get x = -½y - ³2.Solve for y. Multiply every term by 2 to get rid of the fraction: 2x = -y - 3.Rearrange the equation to solve for y: y = -2x - 3.This new function y = -2x - 3 is the inverse of the original function.
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which of the following is not an example of a rate 2 cup for every 3 cups 120 beats per minute 16 ounces for $2 8 inches per 12 hours
Make (X-12)/(x-8) equal to zero
A)-2
B)-8
C)2
D)8
Answer:
x=12 makes (X-12)/(x-8) equal to zero
x=8 makes (X-12)/(x-8) undefined
Step-by-step explanation:
(x-12)/(x-8) = 0
The first step is to multiply each side by x-8
(x-8) *(x-12)/(x-8) = 0 * (x-8)
This cancels the denominator. x≠ 8 because the denominator would equal 0 and then it becomes undefined.
x-12 = 0
Add 12 to each side
x-12+12 = 0+12
x = 12
I
the total cost of four boxes of pasta is $14 There are 16 oz of pasta in each box of the same amount what is the maximum number of boxes that can be purchased with $65
Answer:
18.5 but rounded to 19 because you cant have half of a box
Step-by-step explanation:
because each box costs 3.5 dollars because i did 1 4 divided by 4.then you want to get to 65 so i did 3.5 divided by 65 then got 18.5 which was rounded because the decimal was big This was the real decimal 18.5714286. THIS MIGHT BE WRONG
the regular price of a item is $150 the item was on sale at a discount rate of 30% what is the sales price of the item
Seclet the locations on the number line to plot the points -5 2/3 and 5 1/3
Step-by-step explanation:
5 1/3 means 5 and 1/3 more.
So first we count 5 unit on right side of 0. Then for 1/3 we will divide the length between 5 and 6 into three equal parts and select only 1 part
That location will be exact location of the point 5 1/3.
Repeat same process for -5 2/3 on left side of 0 because -5 2/3 is a negative number.
Check the attached graph for correct locations.
Answer:
nagetive-number
negative 3
Step-by-step explanation:
On order for two triangles to be similar, all corresponding pairs of angles be
Answer: similar
Step-by-step explanation:
Answer:
Answer is similar
Step-by-step explanation:
Please help me answer both questions if they are correct I’ll give brainliest
Answer:
see explanation
Step-by-step explanation:
(4)
Under a counterclockwise rotation about the origin of 90°
a point (x, y) → (- y, x), hence
C(- 3, 4) → C'(- 4, - 3)
(5)
Under a clockwise rotation about the origin of 180°
a point (x , y) → (-x, - y), hence
A(- 3, 2) → A'(3, - 2)
Regal Cinemas is selling tickets for the movie “Ghostbusters”. Tomorrow night , there are 73 tickets left to sell. If all the tickets are sold for the same price , the movie theater will make $438. Which of the following students have enough money to buy a ticket?
a. Amanda has $4.50.
b. Bernie has $7.00.
c. Chrissy has $6.50.
d. Dina has $6.00.
e. Evan has $5.00.
f. Frank has $14.00.
Who has enough money to go to the movie? ( write names below )
Answer:
Bernie, Chrissy, Dina and Frank
Step-by-step explanation:
if all 73 tickers are sold, the theatre makes $438 so each ticket is worth $438/73
this equals to $6.00 for one ticket
this means that Bernie, Chrissy, Dina and Frank have enough money to see the movie
Answer:
Bernie, Chrissy, Dina, and Frank are able to go.
Step-by-step explanation:
The question is not entirely clear. I take it that 73 tickets will bring in 438 dollars. If that is so, each ticket is selling for the solution of this proportion.
x / 1 = 438/73 Just do the division on the right
x = 6.00 dollars.
So Amanda will not be able to go.
Even will not be able to go.
Everyone else can.
I have the data in that picture , I need help answering these questions that continue with that
F: how much money will Jason have in the bank after 9 weeks
G: if Jason has $80 left, how many weeks have passed
This is for question 2 in the picture
Answer:
F $185
G 12 weeks
Step-by-step explanation:
Assuming your equation is correct
y = -35x +500
We want to let x=9
y = -35(9) +500
y = -315+500
y =185
Jason will have $185 after 9 weeks
If he has 80 dollars left we put that in for y and solve for x
80 = -35x +500
Subtract 500 from each side
80-500 = -35x +500-500
-420 = -35x
Divide each side by -35
-420/-35 = -35x/-35
12 = x
After 12 weeks he will have 80 dollars left
Of the total number of pages in a book, 62% have pictures and the rest have no pictures. There are 310 pages with pictures in the book. What is the total number of pages in the book? How many pages in the book have no pictures?
Answer:
500 total pages. 190 pages with no pictures.
Step-by-step explanation:
310 is 0.62 of the total pages. 310 divided bye 0.62 is 500.
500 minus 310 is 190 pages with no pictures.
Hope this helps!
Explain how to determine if the two expressions are equivalent using x = 6 and x = 10.
8x + 40 8(x + 5)
The expressions 8x + 40 and 8(x + 5) are equivalent because both expressions have the same value at x = 6 and x = 10
How to determine the two equivalent expressions?The expressions are given as:
8x + 40 and 8(x + 5)
When x = 6, we have:
8x + 40 = 8 * 6 + 40
8x + 40 = 88
8(x + 5) = 8(6 + 5)
8(x + 5) = 88
When x = 10, we have:
8x + 40 = 8 * 10 + 40
8x + 40 = 120
8(x + 5) = 8(10 + 5)
8(x + 5) = 120
Notice that both expressions have the same value at x = 6 and x = 10
Hence, the expressions 8x + 40 and 8(x + 5) are equivalent
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Answer:
Sample Response: If both expressions have the same value after substituting and simplifying for x = 6 and x = 10, then they are equivalent. Substitute 6 for each variable, x, in both expressions. Use the order of operations to simplify both expressions. The value of both expressions is 88. Now, substitute 10 for each variable, x, in both expressions. Use the order of operations to simplify both expressions. The value of both expressions is 120. Therefore, the expressions are equivalent.
Step-by-step explanation: trust
Subtract t2 + 5t - 6 from t2 - 8t - 7.
A)
13t - 1
B)
13t + 13
C)
−13t - 1
D)
−13t + 13
Answer:
C
Step-by-step explanation:
t² - 8t - 7 - (t² + 5t - 6)
= t² - 8t - 7 - t² - 5t + 6 ( collect like terms )
= - 13t - 1 → C
Answer: C) −13t - 1
Step-by-step explanation: usatestprep approved
2x-y=3
SHOW WORKKKKKK
Answer:
Well, y = 2x - 3.
Step 1:
Subtract 2x from both sides.
-y = -2x + 3.
Step 2:
Divide it all by negative 1.
y = 2x - 3.
IF YOU WANT TO SOLVE FOR X:
Well, x = .5y + 3/2
Which equals to:
(y + 3)/2.
Step 1:
Add y to both sides.
2x = y + 3.
Step 2:
Divide it all by 2:
x = .5y + 3/2
Which equals to:
(y + 3)/2.
They are the same.
The rule at Anna's house is that if she eats all of her vegetables and does all of her does each day, she earns 2 hours of Internet time which she can save. Anna started her week with 3 hours saved. If she eats all of her vegetables and does all of her chores each day for 4 days straight how many hours does she have after the four days she uses 6 hours of her internet time
Answer:
5 Hours
Step-by-step explanation:
Given :- 2 hours can be earned each day if she eats all of her vegetables and does all of her chores.
Saved hours at the start of the week = 3 hours
Hours earned in 4 days = 2 hours × 4
= 8 hours
Hours used in 4 days = 6 hours
Hours left after 4 days = Saved hours at the start of the week + Hours earned in 4 days - Hours used in 4 days
Hours left after 4 days = 3 + 8 - 6
= 5 hours
What is the quotient of 22,389 ÷ 13?
1,029 R12
1,706 R11
1,722 R3
1,645 R4
Answer:
1,722
Step-by-step explanation:
Answer:
1,722 remainder 3 is the correct answer. I didn't do the problem by hand, but for multiple choice answers, you can always just use a calculator to find the answer and the remainder will be given
help please having trouble SUPER EASY!
Answer:
48
because 4 * 12 is 48
Answer:
48
Step-by-step explanation:
12 x 0.25 = 48
A kite is stuck in a 36-ft tree. If the angle of elevation from the kite and the ground is 12, find the length of the kite.
Answer:
173.15 ft.
Step-by-step explanation:
Please find the attachment.
Let L be the length of kite.
We have been given that a kite is stuck in 36-ft tree. The angle of elevation from the kite and the ground is 12.
We can see from our attachment that kite and tree form a right triangle. height of tree is opposite of angle of elevation and length of kite is hypotenuse.
Since we know that Sine relates the opposite and hypotenuse of a right triangle, so we will use sine to find the length of kite.
[tex]sin(12)=\frac{36}{L}[/tex]
[tex]L=\frac{36}{sin(12)}[/tex]
[tex]L=\frac{36}{0.207911690818}[/tex]
[tex]L=173.1504364105882792\approx 173.15[/tex]
Therefore, the length of kite is 173.15 ft.
a) 2/3 divided by 1/4 b) 7/5 multiply by 8 c) 2/5-1/3 d)3/10+2 7/12
[tex]a)\\\dfrac{2}{3}\div\dfrac{1}{4}=\dfrac{2}{3}\cdot\dfrac{4}{1}=\dfrac{8}{3}=2\dfrac{2}{3}\\\\b)\\\dfrac{7}{5}\cdot8=\dfrac{56}{5}=11\dfrac{1}{5}\\\\c)\\\dfrac{2}{5}-\dfrac{1}{3}\\\text{common denominator is (5)(3) = 15}\\\\\dfrac{2\cdot3}{5\cdot3}-\dfrac{1\cdot5}{3\cdot5}=\dfrac{6}{15}-\dfrac{5}{15}=\dfrac{1}{15}\\\\d)\\\dfrac{3}{10}+2\dfrac{7}{12}\\\text{common denominator is 60}\\\\\dfrac{3\cdot6}{10\cdot6}+2\dfrac{7\cdot5}{12\cdot5}=\dfrac{18}{60}+2\dfrac{35}{60}=2\dfrac{53}{60}[/tex]
Amanda is riding her bicycle. She takes 5 hours to ride 62.5 kilometers. What is her speed?
Answer:
12.5 per kilometers
Step-by-step explanation:
to find speed is going to be distance divided by time so 62.5/5
so her speed is going to be 12.5
Amanda's average speed while riding her bicycle is found by dividing the total distance of 62.5 kilometers by the total time of 5 hours, resulting in an average speed of 12.5 kilometers per hour.
To calculate her speed, we use the formula for speed, which is speed = distance ÷ time. Applying the given values, we have speed = 62.5 kilometers ÷ 5 hours.
Therefore, Amanda's average speed is 12.5 kilometers per hour. This calculation involves dividing the total distance traveled by the total time taken, resulting in the average speed over the journey.