Compound interest formula is [tex]A = P(1+r)^t[/tex]
Where P is the principal amount
r is the rate of interest
t is number of years
Brian invests $10,000 in an account earning 4% interest, compounded annually for 10 years
P = 10,000 , r= 4% = 0.04 , t =10
Plug in all the values
[tex]A = 10000(1+0.04)^{10}[/tex] = 14,802.44
Chris invests $10,000 in an account earning 7% interest, compounded annually for 5 years.
P = 10,000 , r= 7% = 0.07 , t =5
Plug in all the values
[tex]A = 10000(1+0.07)^5[/tex] = 14,025.52
Brian balance after the interest period = $ 14,802.44
Chris balance after the interest period = $ 14,025.52
Balance in Brian's account is more than Chris account
Maria is ordering copy paper for her office. The office is low on white paper and on blue paper. She will pay $3.50 per realm of white paper and $3.75 per realm of blue paper. If the purchase order is for $36.00 and she ordered 10 realms of paper, how many realms of white paper will she receive
. Convert 5π/3 to degrees
If there is a ratio of 3 to 2, than how many are there in the first number if there is a total of 80?
Answer:
48
Step-by-step explanation:
The total number of "ratio units" is 3+2 = 5, so each stands for 80/5 = 16 items. Then 3 ratio units stand for 3×16 = 48 items.
3 : 2 = 48 : 32
The first number is 48.
Jenna uses 18 inches if ribbon for each box she wraps how many yds of ribbon does she need to wrap 4 boxes
Your brother and sister took turns driving on a 580 mile trip that took 10 hours to complete. your brother drove at a constant speed of 55 miles per hour and your sister drove at a constant speed of 60 miles per hour. how long did each person drive.
Using a system of equations, it is found that the brother drove for 4 hours and the sister drove for 6 hours on their 580-mile, 10-hour trip.
To solve this problem, let's assign variables to the unknown quantities. Let x be the number of hours your brother drove and y be the number of hours your sister drove. We know they drove for a combined total of 10 hours and covered 580 miles together. This gives us two equations:
Equation 1 (Total Time): x + y = 10Equation 2 (Total Distance): 55x + 60y = 580Since there are two equations with two unknowns, we can solve for x and y by using substitution or elimination method. Let's use the substitution method:
Solve Equation 1 for y: y = 10 - xSubstitute y into Equation 2: 55x + 60(10 - x) = 580Simplify and solve for x: 55x + 600 - 60x = 580, which gives us -5x = -20, so x = 4.Now substitute x back into Equation 1 to find y: y = 10 - 4, so y = 6.Therefore, your brother drove for 4 hours, and your sister drove for 6 hours.
On a recent trip, sarah's car traveled 20 mph faster on the first 110 miles than it did on the remaining 80 miles. the total time for the trip was 4 hr. find the speed of sarah's car on the first part of the trip.
The angle of elevation from a boat to the top of a lighthouse is 22°. The lighthouse is 32 meters tall.
What is the distance from the boat to the base of the lighthouse?
Enter your answer as a decimal. Round only your final answer to the nearest tenth.
98 POINTS PLEASE HELP
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Determine the standard form of the equation for the circle
With center (h,k)=(-5,1/2) and radius r=1
A) (x-5)^2 + (y + 1/2)^2 = 1
B) (x-5) + (y - 1/2) = 1
C) (x+5)^2 + (y - 1/2)^2 = 1
D) (x+5)^5 + (y- 1/2)^2 = 105/2
Hello!
I believe the answer is C) (x+5)^2 + (y - 1/2)^2 = 1.
I hope it helps!
please please please someone help me no one on this site will help me. i so confused. please help.
PLEASE SOMEONE HELP ME!!!!! ILL GIVE BRAINLIEST
1. A model rocket is launched from a roof into a large field. The path of the rocket can be modeled by the equation y = –0.04x2 + 8.3x + 4.3, where x is the horizontal distance, in meters, from the starting point on the roof and y is the height, in meters, of the rocket above the ground. How far horizontally from its starting point will the rocket land?
A. 208.02 m
B. 416.30 m
C. 0.52 m
D. 208.19 m
2. A catapult launches a boulder with an upward velocity of 184 ft/s. The height of the boulder (h) in feet after t seconds is given by the function h= -16t^2 + 184t + 20. How long does it take the boulder to reach its maximum height? What is the boulder's maximum height.
A. Reaches a maximum height of 11.6 feet after 5.75 seconded.
B. Reaches a maximum height of 549 feet after 11.5 seconds.
C. Reaches a maximum height of 549 feet after 5.75 seconds.
D. Reaches a maximum height of 23.2 feet after 11.6 seconds.
3. A ball is thrown into the air with an upward velocity of 32 ft/s. Its height (h) in feet after t seconds is given by the function h= -16t^2 + 32t + 6. How long does it take the ball to reach its maximum height? What is the ball’s maximum height? Round to the nearest hundredth, if necessary.
A. Reaches a maximum height of 22 feet after 1.00 second.
B. Reaches a maximum height of 22 feet after 2.00 seconds.
C. Reaches a maximum height of 44 feet after 2.17 seconds.
D. Reaches a maximum height of 11 feet after 2.17 seconds.
From here you should be able to calculate the answer. One of them is -0.52 which is not the one you use. Minus heights do not matter in these problems yet. The other root is your answer.
Problem Two
Problem two is the usual way to express what happens to a projectile in the air. It again is going to be solved by the quadratic equation.
There are two ways to do this problem. If you know physics, you can solve it using the projectile formulas. If you don't , then you can use the trick in the previous problem. You can calculate how long it takes to hit the ground (h will then be zero).
This problem is rather nasty for someone who has not taken physics. There is another trick. You have to divide the time you get from the previous step by 2. When you solve the quadratic for h = 0, you get 11.6 seconds. But that is the time it takes to hit the ground. Half time is when the boulder will be at it's highest point. t = 11.6 / 2 = 5.8 (which your answers record as 5.75).
h = 0
a= -16
b = 184
c = 20
[tex]\text{x = }\dfrac{ -b \pm \sqrt{b^{2} - 4ac } }{2a} [/tex]
[tex]\text{x = }\dfrac{ -184 \pm \sqrt{184^{2} - 4*(-16)*(20) } }{2*(-16)} [/tex]
The answer from this equation is t = 11.6
The time you want is t = 5.75. You can calculate the maximum height by putting 5.75 in for t.
Problem 3
Problem 3 is done exactly the same way as problem two. You just have different numbers. When h = 0 the time taken to reach zero = 2.17 seconds. Therefore the time you want to put into the original equation for the maximum height is 1/2 of 2.17 seconds. From there you can find the maximum height.
Note: there is a lot of math in here. I have gotten you past the physics. I have also alluded to the answers. I think you should be able to carry out the rest.
The volumes of two spheres are in a ratio of 1:8. what is the ratio of their radii?
what is the value of this expression 3*[(7+8)*2+6] A.64 B.87 C.96 D.108
Six years ago annabelle was twice as old as jason was. now, annabelle is four years older than jason. how old is jason now?
The present age of Jason is given as 10 years.
How to solve a linear equation?A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.
The given problem can be solved as follows,
Suppose the age of Jason 6 years ago was x.
Then, the age of Annabelle 6 years ago was 2x.
Their present ages are x + 6 and 2x + 6 years respectively.
As per the question, the following equation can be formed as follows,
2x + 6 = x + 6 + 4
=> 2x - x = 10 - 6
=> x = 4
Thus the present age of Jason is 4 + 6 = 10 years.
Hence, the age of Jason now is 10 years.
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prestonshelton
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Hello!
You can use the Pythagorean Theorem
c is the hypotenuse which is the side across the right angle
a and b are the other sides
Put in the values you know
Square the numbers
Subtract 25 from both sides
Take the square root of both sides
a = 10.9
The answer is D) 10.9 centimeters
Hope this helps!
A mirror frame in the shape of an oval is shown below. The ends of the frame form semicircles:
An oval is formed by a rectangle with semicircles at each end. The length of the rectangle is 62 inches. The width of the rectangle is 27 inches.
Which of the following is the perimeter of the inner edge of the frame?
(π = 3.14)
146.78 inches
208.78 inches
293.56 inches
347.56 inches
Answer: P=208.78 in
i took the test on flvs its right
Mr bartley is taking the theater club on a field trip he wrote the the folowing function for the school treasure 52(25+2)
Answer:
The answer is 1,404
Step-by-step explanation:
To do this operation, you should be aware of the order of operations. PEMDAS is a good way to remember the order of operations:
1. Parenthesis
2. Exponents
3. Multiplication
4. Division
5. Addition
6. Substraction
Therefore, the first thing we have to do is the parenthesis.
(25+2) = 27
And now, we can do the multiplication
52*27 = 1,404.
ms blankenship had 80 dollars to purchase school supplies for her class.she bought 32 glue sticks and 32 boxes of crayons.each glue stick cost 1.40 and each box of crayons vost 0.59 .how much money did ms blankenship have left after these purchases
Simplify the expression 1 + 2a - 3(4+5a) + 6(7-8a)
Answer:
31 - 61a
Step-by-step explanation:
We distribute, being especially careful with the negative signs:
1 + 2a - 3(4 + 5a) + 6(7 - 8a)
1 + 2a - 3 * 4 - 3 * 5a + 6 * 7 - 6 * 8a
1 + 2a - 12 - 15a + 42 - 48a
31 - 61a
The required simplified expression of the given expression is 31 - 61a.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
As mentioned in the quesiton, to simplify the expression 1 + 2a - 3(4+5a) + 6(7-8a),
⇒ 1 + 2a - 3(4+5a) + 6(7-8a),
⇒ 1 + 2a - 12 - 15a + 42 - 48a
Adding alike terms,
⇒ 31 - 61a
Thus, the required simplified expression of the given expression is 31 - 61a.
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what is 4.6 repeating as a fraction???
please help!! :'(
x=4.66¯6
Then 10x=46.66¯6
So 10x−x=46.66¯6
4.66¯6.−−−−−−−− subtract
9x=42
Divide both sides by 9
x=429=423
Using the rate of $8 for every 2 pounds of rice, how much would a 1/2 pound of rice cost
Hi, I don't feel very confident about my work in this calculus problem and I would appreciate it if anyone else could note any corrections or ways to improve my answers. My problem is split into parts A, B, C, and D and my work is in green. Thank you!
1.
A. 3.75
B. 1.5
C. 3
D. 4.5
2.
A. 30
B. 16
C. 8
D. 15
1)
b: 3.75 since it is half of the segment that measures 7.5, this is proven because the line in the middle is a bisector of the top and bottom line indication that both half measure the same; 3.75
2) 15 not sure why
What formula would I use to find A?
The angle of elevation from point A to the top of a cliff is 38 degrees. If point A is 80 feet from the base of the cliff, how high is the cliff?
A.
60.50 ft.
B.
62.50 ft.
C.
63.50 ft.
D.
61.50 ft.
What is the surface area of this square pyramid?
Round your answer to the nearest tenth.
The answer is 192.8 yd²
pls help with this pre-calc question on vectors!!
A game involves rolling a fair six-sided die. If the number facing upward on the die is a whole number multiple of three, the player wins an amount equal to the number on the die times $20. If the number is not a multiple of three, the player gets nothing. What is the expected value of a player's winnings on each roll?
Answer:
$30
Step-by-step explanation:
To find the expected value, first we find the outcomes for the sample space.
Rolling a 6-sided die, we have
1, 2, 3, 4, 5, 6
There are 2 values that are whole number multiples of 3: 3 and 6.
There is a 1/6 chance of rolling a 3 and a 1/6 chance of rolling a 6.
There is a 1/6 chance of rolling a 1, 1/6 chance of rolling a 2, 1/6 chance of rolling a 4, and 1/6 chance of rolling a 5.
Next we multiply the value won or lost by each probability.
If the player rolls a 3, they win 3(20) = 60. Multiplying it by its probability, we have
1/6(60) = 60/6 = 10
If the player rolls a 6, they win 6(20) = 120. Multiplying it by its probability, we have
1/6(120) = 120/6 = 20.
If the player rolls a 1, 2, 4 or 5, they win nothing. 0 times all of these will be 0.
Lastly, we add together these products:
10+20+0+0+0+0 = 30
Richard can read 1/4 of a book in 3/5 of an hour. At this rate, how much can Richard read in one hour
A gazebo is located in the center of a large circular lawn with a diameter of 300 feet. straight paths extend from the gazebo to a sidewalk around the lawn. if two of the paths form a 45 angle, how far would you have to travel around the sidewalk to get from one path to the other? Round your answer to the nearest foot
Answer: 118
Step-by-step explanation:
1.To solve this problem you must apply the formula for calculate the arc length, which is:
arc length=2πr(central angle/360)
r=300 feet/2
r=150 feet
central angle=45°
2. When you substitute the values, you obtain
arclength=118
What is the length of AB?
Anyone know the answer?