Answer:
36%
Step-by-step explanation:
Area of circle is
[tex]\pi {r}^{2} [/tex]
If the radius is decreased by 20%. Then the radius will be
80% of the original radius.
So our radius is 0.8.
So our area is
[tex]\pi(0.8r) {}^{2} [/tex]
[tex]\pi(0.64 {r}^{2} )[/tex]
Since pi is constant, the radius only really matters.
We went from
[tex]1 {r}^{2} [/tex]
to
[tex]0.64 {r}^{2} [/tex]
So our area will decrease by 36%
Proof: Let the radius be 10.
So the area of circle will be
[tex]\pi(10) {}^{2} = 100\pi[/tex]
Let our other radius is 8 because 8 is a 20% decrease of the orginal radius
[tex]\pi(8) {}^{2} = 64\pi[/tex]
Next, we subtract the area to find decrease in area
[tex]100\pi - 64\pi = 36\pi[/tex]
Since pi is constant, we can ignore it so our decrease in area is 36%
A 15-year bond with a 5.5% coupon and a $1,000 par value is currently priced at $940.
a. If the current market interest rate is 6.5%. Should you buy the bond? Why or why not?
b. Assuming you buy and hold this bond for 5 years. What price must you sell the bond for if you
want to earn a 7% rate of return on this investment?
A) If the current market interest rate is 6.5%, you should not buy the bond because the present value of the bond is $905.97, which is less than the current price of $940.
B) Assuming you buy and hold this bond for 5 years, the price you must sell the bond to earn a 7% rate of return on this investment is $938.50.
How is the price of bonds determined?The price of a bond can be determined by calculating the present value of the cash flows till maturity through discounting.
The present value can be computed using the present value formula or table. It can also be determined using an online finance calculator as follows:
Data and Calculations:a. If the current market interest rate is 6.5%. Should you buy the bond? Why or why not?
N (# of periods) = 15 years
I/Y (Interest per year) = 6.5%
Coupon interest rate = 5.5%
PMT (Periodic Payment) = $55
FV (Future Value) = $1,000
Results:
PV = $905.97
Sum of all periodic payments = $825 ($55 x 15)
Total Interest = $919.03
b. Assuming you buy and hold this bond for 5 years. What price must you sell the bond for if you want to earn a 7% rate of return on this investment?
N (# of periods) = 5 years
I/Y (Desired Interest per year) = 7%
Coupon interest rate = 5.5%
PMT (Periodic Payment) = $55
FV (Future Value) = $1,000
Results:
PV = $938.50
Sum of all periodic payments = $275 ($55 x 5)
Total Interest = $336.50
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Please show work and thanks
Answer:
x = 8
each side is 74
Step-by-step explanation:
set two sides equal to each other
see image
Building A and Building B are 500 meters apart. There is no road between them, so to drive from building A to Building B, it is necessary to first drive to building C and then to Building B. А 500 m b 60° B C a Find the distance from Building A to Building C. Round to the nearest whole number O 577 m O 447 m O 433 m O 250 m
The distance from building A to building C is 433m
Right angle triangle:A right angle triangle has one of its angle as 90 degrees. The sides can be found using trigonometric ratios.Therefore,
sin 60° = opposite / hypotenuse
sin 60° = b / 500
cross multiply
b = 500 sin 60°
b = 500 × 0.86602540378
b = 433.0127
b = 433 meters
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Flora received a 14% raise on her hourly wage of $16.00. Find Flora’s new hourly wage.
First 14% of 16$
[tex]\\ \rm{:}\dashrightarrow 0.14(16)=2.24[/tex]
New wage:-
16+2.24=18.24$A tank containing 500 litres of water has a leak.if one-third of the water in the tank leaked out on monday and one-seventh of the remaining water in the tank leaked out on tuesday, how much water is left in the tank?
Answer: 285.7L
Step-by-step explanation:
Tank initially had 500L of water.
On Monday a third leaked out, therefore:
Amount of water that leaked = 500L x 1/3 = 166.6667 = 166.7L
Remaining water after Monday leak = 500-166.7 = 333.3333 = 333.3L
On Tuesday a seventh of the remaining water (333.3L) leaked out, therefore:
Amount of water that leaked: (333.3333) x 1/7 = 47.6190 =47.6L
Water left after both leaks =500L - (166.6667 + 47.6190)L = 500L - 214.2857L = 285.7143L = 285.7L.
OR Water left = 333.3333L - 47.6190L = 285.7143L = 285.7L
Find the equations of the circle which is tangent to both axes and their center lies on the line 2x+3y=10
Answer:
(x - 2)² + (y - 2)² = 4
Step-by-step explanation:
The circle is tangent to both axes, so the radius = x = y
Center is on 2x + 3y = 0, so 2x + 3x = 1-
x = 2 = y
center: (2, 2)
radius = 2
equation: (x - 2)² + (y - 2)² = 2²
(x - 2)² + (y - 2)² = 4
Find the perimeter of the rectangle. Do not round.
Answer:
49 ft.
Step-by-step explanation:
Since the figure is a rectangle, the length of the top of the figure is the same as that of the bottom. Thus, we can form an equation which we can later use to find the value of x.
4x +3= 16
Minus 3 on both sides:
4x= 16 -3
4x= 13
Divide by 4 on both sides:
x= 13 ÷4
x= 3.25
Breadth of rectangle
= 2x +2
= 2(3.25) +2
= 6.5 +2
= 8.5
Perimeter of rectangle
= 2(length +breadth)
= 2(16 +8.5)
= 2(24.5)
= 49 ft.
Among fatal plane crashes that occurred during the past 65 years, 486 were due to pilot error, 52 were due to other human error, 497 were due to weather, 274 were
due to mechanical problems, and 395 were due to sabotage.
Answer:
what is the question?
Step-by-step explanation:
Which line is perpendicular to a line that has a slope of 1/2?
line HJ
line AB
line CD
line FG
Answer:
HJ
Step-by-step explanation:
For a line to be perpendicular to another line, you must find the negative reciprocal.
The negative reciprocal of 1/2 is -2.
The only line with a slope of -2 is line HJ because it goes down 2 for every 1 to the right.
Answer:
line HJ on edge
Step-by-step explanation:
You toss a fair coin 5 times. What is the probability of at least one head? Round to the nearest ten-thousandth.
Answer:
(B) 0.9688
Step-by-step explanation:
mark me brainliest!!
6. Which lines are parallel? Why?
Answer:
c║d by Converse of Corresponding Angles postulate
Step-by-step explanation:
Line 'a' is not shown as having any relationship to anything. It can be removed from the picture, and all answer choices involving line 'a' can be ignored.
Line 'b' crosses two lines (c and d), so can be considered their transversal. The marked angles are not all between c and d, nor are they all outside of c and d, so they are neither "interior" nor "exterior." Eliminating the obviously incorrect choices leaves only c║d and the choice of the Corresponding Angles postulate or its Converse.
The Corresponding Angles postulate tells you that corresponding angles are congruent where a transversal crosses parallel lines. Its Converse tells you the lines are parallel if the corresponding angles are congruent. Here, we're given angles and asked about the lines being parallel. Clearly, the applicable postulate is ...
c║d by Converse of Corresponding Angles Postulate
List all three digit numbers that have only fours and fives as it’s digit.What is the sum of all of these numbers?
Answer:
The total number of 3-digit numbers that can be formed = 2 × 2 × 2 = 8
1. 444
2. 445
3. 454
4. 455
5. 544
6. 545
7. 554
8. 555
Sum of all these numbers: 3,996
A prop assistant needs to rent a telescope to use for a scene in a movie. One company charges $57 per day plus a flat fee of $32 to rent a telescope. Another company charged $62 per day with no flat fee. For how many days would the total cost of renting a telescope be the same at both companies? Justify your answer by writing and solving an equation.
Fill in the blanks with the correct answers.
62x = 58x + 32, when x = ____. The total cost of renting a telescope would be the same at both companies for _____ day(s).
The number of days for both Companies to have the same total amount is
6.4 days
Word Problem leading to Algebraic expression
Given Data
Let the total payment be yLet the number of days be xCompany A
Charges per day = $57Flat fee = $32y = 57x+ 32 -----------------1
Company B
Charges per day = $62Flat fee = $0y = 62x + 0-----------------2
Equating 1 and 2 we have
57x+ 32 = 62x+ 0
Solving for x we have
62x-57x = 32
5x = 32
Divide both sides by 5
x = 32/5
x = 6.4 days
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Mom paid me 15.00 i now have 47’.00 how much did I start with
Answer:
You started with 32.00
Step-by-step explanation:
47 minus 15 is 32
Start time? Elapsed time 9 3/4 end time 6:00pm
Answer:
3/4 is 45 min, cause a quarter of an hour is 15 min. 6-9=-3 so you basically do Noon subtracted by another 3 hours which is 9am , then subtract those 45 min.
6pm - 6hours = 12pm
(Noon) 12 pm - 3 hours =9 am, then 45 min
9am - 45 min
8:15 am
Numbers that are greater than -2 and less than 3. Pls help
Answer:
The numbers that are greater than - 2 qnd less than 3 are:
-1,0,1&2
124 oz ______ = lb
what is the answer in the space
Answer:
7.75 is the the correct answer
A chess club with 32 members is electing a new president. Raina received 8 votes. What percentage of the club members voted for Raina?
Answer: 25%
Step-by-step explanation:
As you can see 8/32 simplified would be 1/4 which would be 1/4 and 1/4 is equal to 25%!
How long would it take to lose 30 pounds if you’re starting weight is 150
Answer:a minimum of 15 weeks to about 30 weeks.
Step-by-step explanation:
At a cost of $8 per pound, how many ounces of rice flour can be bought for $3.35?
Answer:
$41 cents
Step-by-step explanation:
$8 divided by $3.35 equals $0.41 cents
A tiger can run 1.3 miles in 2 minutes. A lion can run 2.5 miles in 3 minutes. Which runs faster, and by how much?
What is the product of 4 x 2/3
Answer:
Step-by-step explanation:
Remark
A good thing to understand is that when a whole number and a fraction are multiplied, the method is the same as multiplying 2 fractions. What that means is make the whole number into the numerator of a fraction and put a 1 where the denominator should be.
Solution
4/1 * 2/3 = 4*2 / 1 * 3 = 8/3
For what values of a are the following expressions true?
|a-5|=5-a
Answer:
this expression is true for all values of a.
Step-by-step explanation:
So if the expression is:
a - 5 = 5 - a
For this reason:
2a = 10
a = 5
a - 5 = -5 + a
0 = 0
What is the answer please i will mark at brainiest
Step-by-step explanation:
In the given figure,
Base(b)= 6cm
Height (h)= 8 cm
We know that,
[tex]area \: of \: a \: triangle \\ = \frac{1}{2} \times b \times h \\ = \frac{1}{2} \times 6 \times 8 \\ = \frac{48}{2} \\ = 24 \: cm ^{2} [/tex]
Hence, the are of the given figure is 24 cm².
!!!PLEASE HELP!!!!
How can you find the solution to a system of equations by graphing?
(Look at the image for the answers it’s multi choice)
Answer:
c. The solution to a system of equations is the point or points where they intersect
1. Draw an equilateral triangle whose each side is 4.5 cm
Answer is on the picture
Answer:
Step-by-step explanation:
, A roller is 75 cm long and has a diameter of 42 cm. It takes 800 revolutions to level a playing field 44 m long. Find the breadth of the field.
Answer:
0.18km
Step-by-step explanation:
Lateral Surface Area = 2πrh
= 2 × 22 × 21 × 75
7
= 9900m^2
Area taken by revolution = 9900 × 800
= 7920000m^2
= 7.92 km^2
breadth = 7.92km^2 ÷ 44
= 0.18km
At the beginning of the road, a tank truck was traveling full of water in water tank, but it began to leak.You can assume that the fuel consumption of the truck is directly proportional to the weight it carries, and that the water flow(in the leakage) and the speed of the truck are constant for the whole journey. After traveling for miles, the truck leaked half of the water from the water tank and consumed half of fuel tank.
If the water tank was empty the truck would have spent a sixth of the fuel tank, if it travelled the same distance and under the same conditions as above.
Disregarding the fuel tank weight, what fraction of the fuel tank would be spent if there was no leak?
[tex]\frac{1}{2}[/tex] of the water takes [tex]\frac{1}{2}[/tex] of the fuel and empty tank takes [tex]\frac{1}{6}[/tex] of the fuel, the
fraction that would will be spent if there was no leak is [tex]\underline{\dfrac{11}{18}}[/tex] of the fuel
How can the fraction of the fuel spent be found?
The given parameters are;
The volume of oil consumed = [tex]\mathbf{\dfrac{1}{2}}[/tex] of the fuel tank
Volume consumed if the water tank was empty = [tex]\dfrac{1}{6}[/tex] of the fuel tank
Let w represent the weight of the water that fills the tank.
Therefore;
[tex]The \ average \ weight \ carried \ by \ oil = \dfrac{w + \dfrac{w}{2} }{2} = \mathbf{\dfrac{3 \cdot w}{4}}[/tex]
The amount of fuel consumed by the water that leaked = [tex]\dfrac{1}{2} - \dfrac{1}{6} = \dfrac{1}{3}[/tex]
Let x represent the amount of oil used to carry only the water if there
was no leak, therefore;
[tex]\mathbf{\dfrac{\frac{3 \cdot w}{4} }{w} }= \dfrac{\frac{1}{3} }{x}[/tex]
Which gives;
[tex]\mathbf{\dfrac{3 \cdot w}{4} \times x}} = \dfrac{1}{3} \times w }[/tex]
[tex]x = \dfrac{4}{3 \times 3} = \dfrac{4}{9}[/tex]
The total amount of fuel that will be consumed without leakage is
therefore;
[tex]Total \ amount \ of \ fuel = \dfrac{4}{9} + \dfrac{1}{6} = \mathbf{ \dfrac{11}{18}}[/tex]
The amount of oil consumed if there was no leakage is therefore;
[tex]\underline{\dfrac{11}{18} \ of \ the \ fuel \ tank}[/tex]Learn more about averages here;
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While at summer camp, Mike asked a random camper from each of the 12 cabins how many siblings he or she had. The results below display the responses.
3, 2, 0, 1, 0, 2, 3, 4, 1, 2, 2, 1
If there are 48 campers altogether, use Mike’s data to infer the mean of the population. What is the mean number of siblings for the population rounded to the nearest unit?
1 sibling
2 siblings
3 siblings
4 siblings
B / 2 siblings
Step-by-step explanation:
edge 22 , hope it helped
The mean number of siblings for the population rounded to the nearest unit is 2.
What is mean?
Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data.
Gien data is:-
3, 2, 0, 1, 0, 2, 3, 4, 1, 2, 2, 1
The mean will be calculated as:-
Mean = ( 3 + 2 + 0 + 1 + 0 + 2 + 3 + 4 + 1 + 2 + 2 + 1 ) / 12
Mean = 21 / 12
Mean = 1.75
Mean = 2
Therefore the mean number of siblings for the population rounded to the nearest unit is 2.
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Find the length of the line segment whose endpoints are (-8,7) and
(6,4).
[tex]\underline{\underline{\large\bf{Given:-}}}[/tex]
[tex]\red{\leadsto}\:[/tex][tex]\textsf{} [/tex][tex]\sf Endpoints \:of \: line \: segment \:are \:(-8,7) [/tex]
[tex]\sf and \:(6,4) [/tex]
[tex]\underline{\underline{\large\bf{To Find:-}}}[/tex]
[tex]\orange{\leadsto}\:[/tex][tex]\textsf{Length of the line} [/tex][tex]\sf [/tex]
[tex]\\[/tex]
[tex]\underline{\underline{\large\bf{Solution:-}}}\\[/tex]
>>Let us consider these points on a line segment AB such that point A and B lies on opposite ends
[tex] \\A( - 8,7) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: B(6,4)\\ \bull \frac{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }{} \bull \\[/tex]
We will find distance between points by distance formula-
[tex]\red{\underline{\boxed{\sf{Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}}}}[/tex]
Here-
[tex]\sf x_2 = 6[/tex][tex]\sf x_1 = -8[/tex][tex]\sf y_2 = 4[/tex][tex]\sf y_1 = 7[/tex]Putting Values:-
[tex]\begin{gathered}\\\longrightarrow\quad \sf AB = \sqrt{(6 - (-8)) ^{2} + (4-7) ^{2} } \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\longrightarrow\quad \sf \sqrt{(6+8)^2 + (-3)^2} \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\longrightarrow\quad \sf \sqrt{14^2+ (-3)^2 } \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\longrightarrow\quad \sf \sqrt{196+ 9 } \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\longrightarrow\quad \sf \sqrt{205} \\\end{gathered} [/tex]
[tex]\longrightarrow \sf length \:of \: the \: line \:segment \:whose \: \: [/tex]
[tex]\sf endpoints \;are \: (-8,7) \:and \:(6,4) \:is \: \sqrt{205} \;units [/tex]