Answer:
I'm going to assume that this is compound interest, as simple interest in this case would not make sense.
Let A be the final amount ( in this case, after 4 years). A = 20,000(1+0.042/12)^12*4. In this formula, I am assuming that the interest compounds 12 times a year, or every month. I am also assuming that he pays it off once he hits the 4-year mark.
If the assumptions are correct, he would be paying $23651.79 at the 4-year mark.
Step-by-step explanation:
Final answer:
Marco will owe approximately $23,521.93 on his unsubsidized student loan after graduation, calculated using the future value formula for a loan with compounded interest.
Explanation:
To calculate the amount Marco will owe after he graduates, we need to apply the formula for the future value of a loan when interest is compounded annually and no payments are made until after a certain period. Since Marco's unsubsidized student loan does not require payments while he is in school, the interest will be capitalized and added to the principal amount of the loan.
The formula for future value FV of a present value PV after n periods at an interest rate r is:
FV = PV * (1 + r)ⁿ
Where:
PV is the initial loan amount ($20,000)
r is the annual interest rate (4.2% or 0.042 as a decimal)
n is the number of periods (years in this case) before he starts repaying the loan (4 years)
Using the formula, we get:
FV = $20,000 * (1 + 0.042)⁴
FV = $20,000 * (1.042)⁴
F = $20,000 * 1.1760965435
FV = $23,521.93
Thus, Marco will owe approximately $23,521.93 once he graduates, before he starts making any payments on the loan.
A restaurant claims to have served 352,000,000 hamburgers. What is this number in scientific notation?
Answer:
3.52 × 10⁸
Step-by-step explanation:
Scientific notation is written in: Number that is in the ones place × 10^power.
Here, the number is 3.52, since 3 has the largest placement.
The power on the 10 should be the number of 0's on 352,000,000/3.52. That is 100,000,000. That number has 8 0's, so the power is to the 8th.
Putting that together, this number in scientific notation in 3.52 × 10⁸.
Bob sold small and large beach umbrellas. Small ones cost $10 each and large ones cost $25 each. One afternoon Bob sold 10 umbrellas and made $190. How many of each size umbrella did he sell?
Answer:
4 Small, 6 Large
Step-by-step explanation:
We can start by finding values that would help add our two prices together.
We know that each large umbrella is $25, so if we keep adding until we can add up the umbrellas to 10, then we'll get our answer.
1 Large: $25
2 Larges: $50
3 Larges: $75
4 Larges: $100
5 Larges: $125
6 Larges: $150
Now don't forget, we need 10 umbrellas in total, and we know that we need 4 more umbrellas to get to 10, and we need 40 more dollars to get to 190.
40/10 = 4
6 Larges, 1 Small = $160
6 Larges, 2 Small = $170
6 Larges, 3 Small = $180
6 Larges, 4 Small = $190
the dot plot shows the mass, in grams, of several substances in an experiment. How many substances has their mass recorded during the experiment?
Answer:
the answer would be 13
Step-by-step explanation:
The dot plot showed that 13 substances had their mass recorded during the experiment
What is a graph?A graph is used to provide a pictorial representation or diagram so as to represents data in an orderly way. Examples of graphs are histogram, box plot, pie chart, dot plot.
A Dot Plot is used to provide a graphical display of data using dots.
From the dot plot:
Number of substances = 4 + 1 + 2 + 2 + 4 = 13
The dot plot showed that 13 substances had their mass recorded during the experiment
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Hi, can someone help me? I'm trying to get this all done before tomorrow. Thanks ;)
Answer:
B. 6.5 ≤ x
Step-by-step explanation:
Nathan's pay for the week, including x extra hours, will be ...
250.25 +9.50x
We want that to be at least 312, so the inequality is ...
250.25 +9.50x ≥ 312
9.50x ≥ 61.75 . . . . . . . . subtract 250.25
x ≥ 6.5 . . . . . . . . . . . . . . divide by 9.5
The graph showing a solid dot at x=6.5 and an arrow extending to the right will be the correct graph of this solution.
A smartphone for $150.00 cash, or $25.00 down and $12.00 per month for 11 months
Answer:
150 CASH
Step-by-step explanation:
if you do 25 down and 12 dollar for 11 month you pay 7 more dollars
Final answer:
The cost of financing the smartphone with a down payment and monthly payments would be $157.00, compared to a one-time cash payment of $150.00.
Explanation:
The question posed involves comparing the cost of purchasing a smartphone either with a one-time cash payment or financing it with a down payment followed by monthly payments. To calculate the total cost of the financing option, you add the down payment to the product of the monthly payment amount and the number of months for repayment. In this case, we use the following calculation: $25.00 down payment + ($12.00 per month × 11 months) = $25.00 + $132.00 = $157.00. The total cost when financing the smartphone would be $157.00, which is $7.00 more than the upfront cash payment of $150.00.
What is the missing number that makes the number sentence true
20+ ( ?) x 14 )-12 =50
Answer:
Missing number is 3.
Step-by-step explanation:
20+(?)x14)-12=50
8+14?=50
14?=50-8
14?=42
?=3
Answer:
The missing number is 3
Step-by-step explanation:
Let the missing number be y
20 + (y × 14) - 12 = 50
Opening the brackets;
20 + 14y - 12 = 50
14y = 50 + 12 - 20
14y = 42
y = [tex]\frac{42}{14}[/tex] = 3
Order the following measures from least to greatest: 0.5 m, 30 in, 1.25 ft, 17cm
Answer:
30 in, 0.5 m, 1.25 ft, 17 cm
30in, 0.5m, 1.25, 17cm
1/2x+3/2(x+1)-1/4=5
Answer:
x= 15/8
Step-by-step explanation:
we need to solve the equation to find the value of x by adding like terms and then finding the value of x.
[tex](\frac{1}{2})x+(\frac{3}{2})(x+1)-(\frac{1}{4})=5\\(\frac{1}{2})x + (\frac{3}{2})x + (\frac{3}{2}) - (\frac{1}{4}) = 5\\Adding\,\,like\,\,terms\,\\(\frac{(1+3)x}{2}) + (\frac{6-1}{4})=5\\(\frac{4x}{2}) + (\frac{5}{4})=5\\2x= 5- \frac{5}{4}\\2x = \frac{20-5}{4}\\2x= \frac{15}{4}\\x= \frac{15}{4*2}\\x= \frac{15}{8}[/tex]
The value of X is ratio of fifteen to eight. That is, x = 15/8
ALGEBRIAC EQUATIONAlgebraic equation comprises of unknown variables with equality sign.
To evaluate 1/2x+3/2(x+1)-1/4 = 5, Find the LCM in the left hand side.
[tex]\frac{x}{2}[/tex] + [tex]\frac{3(x+1)}{2}[/tex] - [tex]\frac{1}{4}[/tex] = 5
At the Left hand side, the L.C.M is 4
[tex]\frac{2x+6(x+1)-1 }{4} = 5[/tex]
Cross multiply
2x + 6x + 6 - 1 = 20
8x + 5 = 20
Collect the like terms
8x = 20 - 5
8x = 15
Make x the subject of the formula
x = 15/8
Therefore, x = 15/8 in the given algebraic equation.
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Samantha threw an apple out of a window from the tenth floor of her apartment building. The equation y = -16t2 + 120 can be used to represent the fruit's height above the ground, where t represents time, after she thew the apple. How long did it take the apple to hit the ground? Round your answer to the nearest hundredth.
Answer:
2.74
Step-by-step explanation:
The height of the apple when it hits the ground is zero
Equate to zero and solve for t
- 16t² + 120 = 0 ( subtract 120 from both sides )
- 16t² = - 120 ( divide both sides by - 16 )
t² = 7.5 ( take the square root of both sides )
t = [tex]\sqrt{7.5}[/tex] ≈ 2.74
A price increases from $82 to $89.38. What is the percent change?
Answer:
9%
Step-by-step explanation:
89.38/82 = 1.09
.09% increase
or 9%
The answer is 9% I think
Find the values for a and b that would make the equality true. 4(ax^2 -5x+3)=8x^2 +bx+12
Answer:
a 2 and b -20
Step-by-step explanation:
Answer:
a = 2 and b = -20
Step-by-step explanation:
4(ax^2 -5x+3)=8x^2 +bx+12 should be multiplied out. Next, we equate the coefficients of the several powers of x:
4ax² - 20x + 12 = 8x² + bx + 12
Then 4a = 8, so a = 2
and -20 = b
The chart shows the marginal revenue of producing apple pies.
According to the chart, the marginal revenue
decreases by ten dollars as production increases.
increases by ten dollars as production increases.
falls to zero dollars as production increases.
remains the same as production increases.
Answer:
(d) remains the same as production increases
Step-by-step explanation:
All of the numbers in the Marginal Revenue column are the same. That means we can conclude marginal revenue ...
remains the same as production increases.
Answer:
(d) remains the same as production increases
Step-by-step explanation:
One number is 5 times another number. The product of the two numbers is 245. Find the two numbers.
Let's assume the unknown number is x and as another one is 5 times the number then second number is 5x
》x × 5x = 245
》5x square =245
》x square =245÷5
》x square =49
》x=7
So 5x = 5×7=35
imagine you pour some hot soup into a bowl, and you place your hands on the outside of the bowl and the outside is warm, how did the heat from the soup through the bowl to your hands?
Answer:
conduction
Step-by-step explanation:
the process by which heat or electricity is directly transmitted through a substance when there is a difference of temperature or of electrical potential between adjoining regions, without movement of the material.
Three 3/10 converted into a decimal
Answer:
3.3
Step-by-step explanation:
3 3/10 = 3 + 3/10 = 3 + 0.3 = 3.3
Angles T and U are a linear pair. Angle U measure (9x+6) and Angle T measures(6x+9). What is the value of x, in degrees?
Answer:
11 degrees.
Step-by-step explanation:
"Angles T and U are a linear pair. Angle U measure (9x+6) and Angle T measures(6x+9). What is the value of x, in degrees?"
We know that a linear pair MUST add up to 180 degrees, therefore (9x+6)+(6x+9)= 180
Now for some algebra-
(9x+6)+(6x+9)= 180
6 and nine can both be divided by 3, so we will do that for simplicity:
((9x+6)+(6x+9)= 180)/3=
(3x+2)+(2x+3)=60
We will now separate the parenthesis, as they serve no purpose anymore.
(3x+2)+(2x+3)=60
3x+2+2x+3=60
Combine terms
5x+5=60
Take away the 5 to isolate the variables
5x+5=60
-5
5x=55
Divide by 5
5x=55
/5
x=11
The value of x is 11 degrees.
What is M
A.
42°
B.
50°
C.
58°
D.
100°
Answer:
C. 58°
Step-by-step explanation:
m∠ACB=(180-138)°
m∠B + m∠A +∠mACB =180
80+ m∠A + (180 -138) =180
80 + m∠A - 138 = 0
m∠A = 58
Answer:
C
Step-by-step explanation:
The external angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ACD is an exterior angle of the triangle and
∠A and ∠B are the 2 opposite interior angles, hence
∠A + ∠B = 138, that is
∠A + 80 = 138 ( subtract 80 from both sides )
∠A = 58° → C
Find the difference between (15,-17) and (-20,-5)
Answer:
37 units
Step-by-step explanation:
The horizontal distance between these two points is 35 and the vertical is 12.
Treat these distances as the lengths of the legs of a right triangle whose hypotenuse we want to determine:
d^2 = 35^2 + 12^2 = 1369, so d = the distance between these two points = d = sqrt(1369) = 37 units
The difference between the points (15,-17) and (-20,-5) is calculated by subtracting the coordinates, resulting in a difference of (35, -12).
To find the difference between the two points (15,-17) and (-20,-5), we need to subtract the coordinates of the second point from the coordinates of the first point.
For the x-coordinates: 15 - (-20) = 15 + 20 = 35
For the y-coordinates: -17 - (-5) = -17 + 5 = -12
Therefore, the difference between the two points is (35, -12).
Drag each tile to the correct box. Arrange these bank balances from highest debt to lowest debt. Liz -$22 Kevin -$42 Paul -$10 Henry -$32 Jenny -$28 Sean -$20 Kelly -$3
Answer:
Kevin-$42, Henry-$32,Jenny -$28, Liz -$22, Sean -$20, Paul -$10, Kelly -$3
Answer:
kevin, henry, jenny, liz, sean, paul, kelly
Step-by-step explanation:
i did the pretest and got it right!
find the length of the missing side. if necessary, round to the nearest tenth.
A. 44
B. 22
C. 15.6
D. 484
the answer to this question would be c- 15.6
The measures of three angles of a triangle are given by 4x-1,2x+1 and 6x. What is the measure of the largest angle
Answer:
The largest angle is 6x,and 6x=90
So, the measure of the largest angle is 90
Step-by-step explanation:
First, you create an equation by adding the three angles together and equal to 180,because a triangle has 180 degrees.
The result will be 15.If x=15 ,you need to plug it in.
the largest angle is 6x,So, 6.15=90
90 degrees
The problem states the measures of three angles of a triangle as 4x-1, 2x+1, and 6x. According to the basic theorem that the sum of the angles in a triangle is 180 degrees, if we add these angles together, and equate them to 180, we get the equation 4x - 1 + 2x + 1 + 6x = 180. Adding like terms simplifies this to 12x = 180, and dividing each side by 12 gives us x = 15. Therefore, the largest angle is 6x, which would be 6 * 15 = 90 degrees.
Scott went snowboarding down a mountain. The trail was 2 miles long and took him 5 minutes to complete. If Tom snowboards three times as fast, how long would it take him to get down the mountain?
Answer:
1 minute and 40 seconds or 1 2/3 minute
Step-by-step explanation:
If it took Scott 2 miles for 5 minutes, than it took him 2.5 minutes to do 1 mile. For 3 times as fast, we need to divide by 3. 2.5/3= 5/2*1/3=5/6. It is 2 miles, so 5/6*2=10/6=5/3=1 2/3 minute. 2/3 minute=40 seconds. So, the answer is 1 minute and 40 seconds or 1 2/3 minute.
Answer:
1 minute and 40 seconds or 1 2/3 minute(s)
Step-by-step explanation:
A store had 800 T-shirts in stock for a weekend sale.T-shirts are sold in packs of 4 each.During the sale,20 packs of T-shirts were sold on Saturday, and 70 more packs were sold on Sunday.
During the weekend sale, a total of 360 T-shirts were sold from the initial stock of 800 T-shirts in packs of 4. This resulted in 440 T-shirts leftover in stock after the sale.
Explanation:In the context of the store scenario, we have an initial stock of 800 T-shirts, which are sold in packs of 4 each. On Saturday, 20 packs are sold, resulting in a reduction of 20 packs times 4 shirts per pack, which equals 80 shirts. On Sunday, 70 more packs are sold, which corresponds to 70 packs times 4 shirts per pack, totaling 280 shirts sold on Sunday. Adding up the shirts sold on both days, we get 80 + 280, which equals 360 shirts sold in total during the weekend. To find the remaining stock, we subtract the total shirts sold from the initial stock: 800 shirts - 360 shirts = 440 shirts remaining after the sale.
The total cost of 5 boxes of pasta is $13. There are 12 ounces of pasta in each box. Each box of pasta cost the same amount. What is the cost in dollars of the maximum number of boxes needed to total 48 ounces of pasta?
Answer: $10.40
Explanation:
First, find the cost of 1 box of pasta. 13/5 = 2.6, so $2.60 a box.
Next, find how many boxes there are. 48/12 = 4, so 4 boxes of pasta.
Finally, multiply 4*2.6 to get the final cost.
Which is the approximate measure of this angle?
Answer:
120 degrees aka answer D
Step-by-step explanation:
Answer:
D. 120°.
Step-by-step explanation:
Since the angle is obtuse (greater than 90), it cannot be 30°, since 30° is an acute angle.
The angle cannot be 90° since the angle is obtuse, and red curved line is not a square.
The line would be straight if the angle was 180°, so the most reasonable answer would be D. 120°.
The graph of f(x) is shown below has the same shape as the graph of g(x)= x^4 but is shifted 3 units to the left. What is the equation
A. Any horizontal transformations or reflections you make to y = x^4 must be contained within the parentheses.
Shawn bought 8 boxes of erasers. Each of the erasers is either pink or blue. Each box has x pink erasers and y blue erasers in it. The expression shown below represents the total number of erasers Shawn bought.
8(x + y)
Which expression also represents the total number of erasers Shawn bought?
Question 7 options:
a 8x + 8y
b 8x + y
c 8xy
d 8 + x + y
Answer:
A
Step-by-step explanation:
You need to distribute the 8 to everything in the equation. You need to keep the sign in the middle. So in the end you would get 8x+8y.
Final answer:
Option a), 8x + 8y, accurately represents the total number of erasers Shawn bought since it's obtained by distributing the number of boxes, 8, to both x and y inside the parentheses.
Explanation:
The expression 8(x + y) represents the total number of erasers Shawn bought, where x is the number of pink erasers in each box and y is the number of blue erasers in each box. Since Shawn bought 8 boxes, and each box contains x pink erasers and y blue erasers, we need to multiply the sum of pink and blue erasers in one box by the number of boxes to get the total. Hence, the correct expression that also represents the total number of erasers Shawn bought is option a), 8x + 8y which is obtained by distributing the 8 to both x and y inside the parentheses.
Order numbers to least to greatest 0.8,8%,18%,1/8,8/18
Answer 8%, 1/8, 18%, 8/18, 0.8
Step-by-step explanation:
0.8 = 80%
1/8 = 12.5%
8/18 = 44.4%
8% < 12.5% < 18% < 44.4% < 80%
a large rectangular swimming pool is 1,000 feet long 100 feet wide and 10 feet deep how much water does the pool hold?
ANSWER
The swimming pool can hold 1,000,000 cubic feet of water.
EXPLANATION
The capacity of water the pool holds is the volume of water in the swimming pool.
The swimming pool is rectangular, therefore its volume can be calculated using the formula,
[tex]V = l \times w \times h[/tex]
where l=1000ft is the length, w=100ft is the width and h=10ft is the height of the pool.
We substitute all these values into the formula to get:
[tex]V = 1000 \times 100 \times 10 = 1000000 {ft}^{3} [/tex]
The swimming pool can hold 1,000,000 cubic feet of water.
The amount of water the pool can hold is 1,000,000 ft³.
What is the amount of water the pool can hold?In order to determine the amount of water the pool can hold, we have to determine the volume of the rectangular swimming pool. Since the swimming pool has the shape of a cuboid, the formula for the volume of a cuboid would be used.
Volume = length x width x height
1000 x 100 x 10 = 1,000,000 ft³
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Line AB is parallel to Line CD. Line AC and Line BD are perpendicular to Line AB and Line CD. What is the relationship between AC and BD?
Line AC and Line BD are perpendicular to each other.
Explanation:In this scenario, we have Line AB parallel to Line CD, and both Line AC and Line BD are perpendicular to Line AB and Line CD. Since two perpendicular lines intersect at a 90-degree angle, we can say that Line AC and Line BD are also perpendicular to each other. This means that Line AC forms a 90-degree angle with Line BD.