Martin deposits $200 in a savings account that earns 5% annual interest. Four years later, Cary deposits $200 in an account earning the same interest. Let M represent the balance in Martin’s account and let C represent the amount of money in Cary’s account.
Complete question :
Martin deposits $200 in a savings account that earns 5% annual interest. four years later, cary deposits $200 in an account earning the same interest. let m represent the balance in martins account and let c represent the amount of money in carys account. choose the pair of expressions that describe the accounts y years after martin opened his account. martin: 200(1.05)y cary: 200(1.05)y+4 martin: 200(1.05)y+4 cary: 200(1.05)y4 martin: 200(0.05)y cary: 200(0.05)y4 martin: 200(1.05)y cary: 200(1.05)y4 choose the equation that relates the balances in the accounts y years after martin opened his account. c = m(1.05)4y m = c(1.05)4y c = 1.22m m = 1.22c
Answer:
m = m = 200(1.05)^y+4
c = m = 200(1.05)^y
m = 1.22c
Step-by-step explanation:
The future value can be represented as :
Future value, F = P(1 + r)^n
r = interest rate = 5% = 0.05 , n = number of years ;
For Martin :
m = 200(1 + 0.05)^n
For cyan :
c = 200(1 + 0.05)^n
y years after Martin
Cyan opened 4 years after Martin :
Representing in terms of y
Cyan = y ; Martin = y +4
m = m = 200(1.05)^y+4
c = m = 200(1.05)^y
From. Indices :
(1.05)^y+4 = 1.05^y * 1.05^4
Hence,
m = 200 * 1.05^y * 1.05^4
c = 200 * 1.05)^y
Hence,
m = c * 1.05^4
m = c * 1.2155
m = c * 1.22
m = 1.22c
Answer:
the first question is d and so is the second one
Find the volume of the prism or pyramid below
Answer:
6.3 Cubic cm
Step-by-step explanation:
[tex]V=A*h=(1.8*1.2+.5*1.1*1.8)*2=6.3cm^{3}[/tex]
Bill can hit a bucket of 323 golf balls in 17 hours.
How many golf balls can Bill hit in 23 hours?
Motorbikes have two wheels and cars have four wheels. There are a number of
motorbikes and cars in a parking lot. There are 14 motorbikes. Altogether, there are
324 wheels. How many cars are in the parking lot?
A.74 cars
B.148 cars
C.296 cars
D.310 cars
Answer:
74 Cars
Step-by-step explanation:
If each motorbike has 2 wheels then we need to find how many wheels the motorbikes already take up.
We do this by doing 14*2 and we get 28 wheels.
Afterwards, we subtract this from the total of 324 to see how many wheels are left over. 324-28=296
Now we know the remaining amount of wheels and with this we can get our final answer!
Since there are 296 remaining wheels and each car takes up 4 we can divide 296 by 4 to see how many cars would be able to get their full set of tires.
296/4 = 74 and that;s how you get 74 cars!
*I think LOL*
wegnerkolmp2741o can you please answer this I will mark brainliest
An isosceles triangle has two 5.5 cm sides and two 32.4° angles. Explain how to determine the perimeter of the triangle. Include a diagram in your solution. You do NOT need to solve.
Answer:
see below
Step-by-step explanation:
The drawing in blue is what we are told in the problem.
We are given two sides and two angles. It is an isosceles triangle with two equal sides and two equal angles. Draw a perpendicular bisector ( it makes a 90 degree angle. Now we have two identical right triangles. We can use trig functions to find x
cos theta = adj/ hyp
cos 32.4 = x / 5.5
Solving for x
5.5 cos 32.4 =x
Now we have 2x for the third side of the triangle
2( 5.5 cos 32.4) is the third side
P = 5.5 + 5.5 + 2( 5.5 cos 32.4)
Answer:
See the Below
Step-by-step explanation:
Draw a circle with a radius of 5.5 and center at A.Take any point B on the circle and join AB.Draw a line thru B making an angle 32.4 with AB which intersects the circle at D. Extend AD on both sides.Draw two circles with a radius of 5.5cm and centers B and D which intersect the line BD at E and F.Measure length EF, which is the perimeter of triangle ABD.=20.3 cm.Method 2. Assume that base of the triangle =x cm.x/2= 5.5 cos 32.4 and x=11*cos 32.4 =11*0.844=9.287Perimeter = 20.287What is the awnsers helppppp
Answer: 0.77
Step-by-step explanation:
Answer:
0.23
Step-by-step explanation:
the chart adds up to 1 as a whole so 23% chose football and there is a 23% chance the next person will also choose football.
How do I solve this math problem? The answer is: x = a^2/a-3
Answer:
I love algebra anyways
the ans is in the picture with the steps
(hope it helps can i plz have brainlist :D hehe)
Step-by-step explanation:
How to solve problem?
Answer:
m<ADE = 57 degrees
Step-by-step explanation:
Angles of a quadrilateral add up to 360. We are already given 69 and 45, which can both be subtracted from 360, leaving us with 246. Since the two remaining angles are congruent, 246 can be divided by 2 to find the remaining measure(s). We are left with 123. However, m<ADE is supplementary to this. So we subtract 123 from 180. The final answer is 57 degrees.
if Tom had 78 apples and he gave to the shop for 80% and he put it on sale for another 10% what many apples would Tom get in the end?
Answer:
he has to many apples
Step-by-step explanation:
Never gonna give you up
Never gonna let you down
Never gonna run around and desert you
Never gonna make you cry
Never gonna say goodbye
Never gonna tell a lie and hurt you
Please
Solve for the value of k.
Answer:
k = 13
Step-by-step explanation:
The sum of the angles is 180 since they form a straight line
4k-7 + 90 + 3k+6 = 180
Combine like terms
7k+89=180
Subtract 89 from each side
7k+89-89 = 180-89
7k =91
Divide each side by 7
7k/7 = 91/7
k = 13
Which is a factor of 10?
OA. 40
B. 10
C. 30
D. 20
Answer: B. 10
Explanation: Any number is a factor of itself.
We can rule out choices A, C and D because those values are larger than 10. They are multiples of 10, but not factors of 10.
please help me find the area
Answer:
17,290 yd2
Step-by-step explanation:
I rlly don't know how u were taught to solve it but what I did was multiply all the sides
What is the initial value of the function represented by this table?
Answer:
2
Step-by-step explanation:
3+2=5 and 5+2 =7 and on x side just add 1
PLEASE HELP!!!!
WILL MARK BRAINLIEST!!!
Solve for X.
Multiple choice!
Thank you!
Answer:
6x - 21 = 105 (vertically Opposite angles)
6x = 105 + 21
6x= 126
x=126/6
x= 21°
That should be the fifth option
OR
Another Way of solving
(6x - 21) + 75 = 180 ( angles on a straight line)
6x -21 + 75 =180
6x + 54 = 180
6x =180 - 54
6x = 126
x=126/6
x=21°
[tex] \large \sf \star \: \green{Answer} \: \star[/tex]
x = 21 °
Step-by-step explanation:
Here,
Angle 75 ° and ( 6 x - 21 ) are on straight line so it's supplementary angles and we know that sum of all angles of supplementary angles is 180 °.So, 6 x - 21 ° + 75 ° = 180 °6 x - 21 ° + 75 ° = 180 °
6 x + 54° = 180 ° ...( Combine like terms)
subtract 54 ° from each sides
54° - 54° + 6 x = 180 ° - 54 °
6 x = 126°
x = 126 ° / 6 ...( Divide by 6 )
x = 21 °
simplify the expression (c^7)^9(c^0)^5
Answer:
c^63 Your welcome !!
Step-by-step explanation:
in order for the parallelogram to be a rhombus x=?
Answer:
x = 12
Step-by-step explanation:
In a rhombus, the diagonal is also the bisector of the angle, so the two vlaue must be congruent
2x + 35 = 8x- 37
6x = 72
x = 12
Question 16 of 20
If a study estimated that 22% of students ride their bikes to school, and the
error range is +2%, what percentage of students might actually ride their bikes
to school?
O A. 22% -24%
O B. 2% - 22%
O C. 20% - 22%
ОО
D. 20% - 24%
SUBMIT
PREVIOUS
Answer:
D) 20%-24%
Step-by-step explanation:
The margin of error is ±2%, which means that the true proportion it can be 2% above the average proportion or 2% below the average proportion. Therefore, the percentage of students that might actually ride their bikes to school is 20%-24%.
Answer: A. 22%-24%
Step-by-step explanation: There's a +2% error range, so you just add 2% to the existing percentage to get your range of 22% (the original percentage) through 24% (the percentage you get after adding 2%)
5(a^6+2a^5)-6a(5a^4-7a^3)
Answer:
a4(5a2−20a+42)
Step-by-step explanation:
Factor 5(a6+2a5)−6a(5a4−7a3)
5a6−20a5+42a4
=a4(5a2−20a+42)
Make me brainliest!
What is the value of z in the equation 3z+9=z?
Short Response
Shantelle wants to rent a mid-size car for one day. Value Rent-a-Car charges $20 a day plus $0.20 per
mile, and Best Rent-a-Car charges $30 a day plus $0.10 per mile for rental of the same mid-size car.
Part A) Write an equation in slope intercept form, y=mx+b, for each car:
Value Rent-a-Car: y=0.20x+20
Best Rent-a-Car: y=0.10x+30
Part B: Determine the mileage where the rental charges are the same.
9514 1404 393
Answer:
100 miles
Step-by-step explanation:
A. The answers shown are correct
__
B. Equate the values of y and solve for x.
0.20x +20 = 0.10x +30
0.10x = 10 . . . . . . . subtract (20+0.10x)
x = 100 . . . . . . . . divide by 0.10
The rental charges are the same for 100 miles.
Crawling Crayfish!
Big Claw, the crayfish, challenged Flicker to a 60 em race. Since Big Claw is much
larger, he offered to give Flicker a 10 cm head start Flicker agreed and the race
began. After 5 seconds, Big Claw had crawled 6 cm and Flicker had crawled 4 cm.
If they continue at this rate, who do you predict will win the race? justify your
prediction
How many seconds have elapsed when Big Claw and Flicker are tied?
Answer: Crayfish, 25 s
Step-by-step explanation:
Given
The length of race is 60 cm
Flicker gets a 10 cm head-start
Cray fish covers 6 cm in 5 s i.e. its speed is
[tex]\Rightarrow \dfrac{6}{5}=1.2\ cm/s[/tex]
Flicker covers 4 cm in 5 s, its speed is
[tex]\Rightarrow \dfrac{4}{5}=0.8\ cm/s[/tex]
Time taken by Cray fish to cover the race is
[tex]\Rightarrow t_1=\dfrac{60}{1.2}\\\\\Rightarrow t_1=50\ s[/tex]
Time taken by flicker to cover race with 10 cm head start
[tex]\Rightarrow t_2=\dfrac{60-10}{0.8}\\\\\Rightarrow t_2=62.5\ s[/tex]
Time taken by crayfish is less. Hence, crayfish wins the race
When they both covers the same distance, they tied momentarily i.e.
[tex]\Rightarrow 1.2t=10+0.8t\\\Rightarrow 0.4t=10\\\\\Rightarrow t=\dfrac{10}{0.4}\\\\\Rightarrow t=25\ s[/tex]
After 25 s, they tied the race.
The size of a large milkshake is 1.4 times the size of a medium milkshake. Write 1.4 as a percent. F u
Answer:
1.4%
Step-by-step explanation:
1.4 = [tex]\frac{14}{1000}[/tex]
=[tex]\frac{14/10}{1000/10}[/tex]
=[tex]\frac{1.4}{100}[/tex]
=1.4%
In 2010 there were 3200 tigers in the wild. In 2016 there were 3890 tigers in the wild. What is the percentage increase?
Step-by-step explanation:
3890 - 3200
=690
(690÷3200) x 100%
=21.56%
Answer:
21.56/ 21.6/ 22 (depending on the decimal places you want)
Step-by-step explanation:
Current figure- original figure / Original figure * 100
3890-3200 = 690
690/3200 = 0.215625
0.215625 * 100 = 21.56 / 21.6 / 22
* means multiply
For one roadway section, the average number of cars passing a point is 2200 pcphpl (i.e. passenger cars per hour per lane). The cars travel at an average speed of 42 mph. What is the average distance (in feet) between common points (e.g. the front bumper) on successive cars in one lane
Answer:
The average distance between common points on successive cars in one lane is of 100.8 feet.
Step-by-step explanation:
This question is solved by proportions, using a rule of three.
The cars travel at an average speed of 42 mph
Each mile has 5280 feet, so in 1 hour, the distance is of 42 miles = 221760 feet.
2200 pcphpl (i.e. passenger cars per hour per lane).
2200 cars in 221760 feet. Thus:
[tex]d = \frac{221760}{2200} = 100.8[/tex]
The average distance between common points on successive cars in one lane is of 100.8 feet.
Represent 1/3 of 1/4
Answer:
1/12
Step-by-step explanation:
Answer:
1/12
Step-by-step explanation:
the word 'of' in math means to multiply so 1/3 of 1/4 means to multiply them together
1/3 x 1/4 = 1/12
A force of 4 pounds is required to hold a spring stretched 0.4 feet beyond its natural length. How much work (in foot-pounds) is done in stretching the spring from its natural length to 0.6 feet beyond its natural length
Answer:
the work done in stretching the spring from its natural length is -1.8 ft.lb
Step-by-step explanation:
Given the data in the question;
From Hook's law, the magnitude of force applied on a spring is expressed as follows;
|F| = k|x|
where F is the force applied the spring, k is the spring constant, x is the length extension
Now, given that; F = 4 pounds = 4 lb and x = 0.4 ft
we substitute
4 = k × 0.4
k = 4 / 0.4
k = 10 lb/ft
Also, Hook's law can be expressed as follows;
F = -kx ---------- let this be equation 1
Now, work done by a force applied between two points is expressed as follows;
dW = Fdx ----------- let this be equation 2
substitute equation 1 into equation 2
dW = (-kx )dx
we integrate both side
∫(dW) = ∫((-kx )dx)
W = -k∫xdx
W = -k[tex]\frac{x^2}{2}[/tex]
w = -[tex]\frac{1}{2}[/tex]kx²
we substitute 10 lb/ft for k and 0.6 ft for x
w = -[tex]\frac{1}{2}[/tex] × 10 lb/ft × (0.6 ft)²
w = -[tex]\frac{1}{2}[/tex] × 10 lb/ft × 0.36 ft²
w = -1.8 ft.lb
Therefore, the work done in stretching the spring from its natural length is -1.8 ft.lb
Select the two correct solutions of the inequality x + 8 > 14
2
4
6
8
10
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\text{x + 8 } \mathsf{>}\large\text{ 14}[/tex]
[tex]\large\textsf{SUBTRACT 8 to BOTH SIDES}[/tex]
[tex]\large\text{x + 8 - 8 }\mathsf{>}\large\text{ 14 - 8}[/tex]
[tex]\large\textsf{CANCEL out: \text{8 - 8} because that gives you \text{0}}[/tex]
[tex]\large\textsf{KEEP: \text{14 - 8} because that helps what you are comparing to the \text{x}}[/tex]
[tex]\large\text{x }\mathsf{> }\large\text{ 14 - 8}[/tex]
[tex]\large\text{14 - 8 = \boxed{\bf 6}}\large\checkmark[/tex]
[tex]\large\text{x }\mathsf{>}\large\text{ 6}[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: \bf x}\mathsf{\bf >}\large\text{ \bf 6 }}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
To find the constant vector C, we use the given initial condition v(0) = k, we also know that at t = 0, the general equation for v() i:s Comparing both equations for V(0) and solving for C, we have C = k. Substituting it back into the general equation, we have
V(t) = 4ti + 5tj + c = ______.
Answer:
4ti + 5tj + k
Step-by-step explanation:
Initial condition V(0) = k
at t = 0
general equation for v(t )
V(0) = 0i + 0j + c = k
when we compare V(0) and solve for c , c = k
back to general equation
V(t) = 4ti + 5tj + c = 4ti + 5tj + k
Express tan J as a fraction in simplest terms.
J
34
K
L
16
Answer:
tanJ = 8/15
Step-by-step explanation:
find JK the adjacent side uisng th pythagorean theorem
a² + 16² = 34²
a² = 34² - 16²
a² = 900
a = 30
--------------------
tan = opp/adj
tanJ = 16/30
Reduce
tanJ = 8/15
If f(x) = 4x - 3 and g(x) = x + 4, find (f-g)(x).
A. 3x-7
B. 5x-1
C. 5x - 7
D. 7 - 3x
9514 1404 393
Answer:
A. 3x -7
Step-by-step explanation:
Substitute for f and g, then collect terms.
(f -g)(x) = f(x) -g(x) = (4x -3) -(x +4)
(f -g)(x) = 4x -3 -x -4 = (4-1)x +(-3-4)
(f -g)(x) = 3x -7
