Given:
Principal value = $2300
Rate of interest = 14% compounded continuously.
To find:
The time taken by Brad's investment to triple.
Solution:
The formula for amount after the compound interest (Continuously) is:
[tex]A=Pe^{rt}[/tex]
Where, P is the principal, r is the rate of interest in decimal and t is the time period.
Triple of Brad's investment is
[tex]3\times \$ 2300=\$ 6900[/tex]
Substituting [tex]A=6900,P=2300\ r=0.14[/tex], we get
[tex]6900=2300e^{0.14t}[/tex]
[tex]\dfrac{6900}{2300}=e^{0.14t}[/tex]
[tex]3=e^{0.14t}[/tex]
Taking natural log on both sides, we get
[tex]\ln 3=\ln e^{0.14t}[/tex]
[tex]1.0986=0.14t[/tex] [tex][\because \ln e^x=x][/tex]
[tex]\dfrac{1.0986}{0.14}=t[/tex]
[tex]7.84714=t[/tex]
After approximating the value, we get
[tex]t\approx 7.85[/tex]
Therefore, Brad's investment will take 7.85 years to triple.
(Factorize it)
Here it is:
Answer:
D: (x^2 + 3x + 9) (x^2 - 3x + 9)
-
G: (x^2 + 3x + 5) (x^2 - 3x + 5)
Answer:
[tex]d) \: \: ( {x}^{2} + 3x + 9)( {x}^{2} - 3x + 9)[/tex]
[tex]g) \: \: ( {x}^{2} + 2x + 5)( {x}^{2} - 2x + 5)[/tex]
Step-by-step explanation:
Hope it is helpful....
4.
3.7 cm
4.5 cm
2.2 cm
V=
Answer:
[tex]V=36.63cm^3[/tex]
Step-by-step explanation:
Volume formula for rectangular prism is [tex]V=lwh[/tex]
Volume = length * width * height
[tex]V=4.5*2.2*3.7[/tex]
[tex]V=36.63[/tex]
Hope this helps
Look below at the picturess!!! pls help me i will give you 100 points !
Answer:
1/4
Step-by-step explanation:
because there 25% change
Answer:
for the blue its 1/4 or 2/8 and not likely.
For the yellow one it is 7/8 and likely.
There are a total of 40 red, yellow or blue balls in a box. Each ball is marked with a number out of 1, 2, 3 and 4 on the side. The figure in the shaded area below each shows the number of balls in that category. For example, the number of red balls marked with the number "1" is 12. What is the minimum number of balls to be taken out of the box to ensure that you have at least one ball of each color and each marked number?
Answer:
9
Step-by-step explanation:
Question:
Minimum number of balls to ensure there is at least one ball of each colour marked with each number.
The quantity of distinct numbers are:
red: 4
Yellow 3
Blue 2
So the minimum number of balls to satisfy the given requirements is
4+3+2= 9
Jacob drove 450 miles at an average rate of 65 miles per hour. Rounded to the nearest tenth of an hour, how long did the trip take
Time = distance / speed
Time = 450 miles / 65 miles per hour
Time = 6.9 hours
A 3050 foot long road travels directly up a 550 foot tall hill. Select the equation that can be used to solve for the angle of elevation (0) from the bottom of the hill.
Answer:
d is the answer ✌sin ०=3000/3050
Kip has a collection of 68 marbles. Each glass marble has a mass of 18.5 grams. Each steel marble has a mass of 66 grams. What is the total mass of 48 glass marbles and 20 steel marbles in kilograms? PLS HELP!
Answer:
2.208 kg
Step-by-step explanation:
Total mass of glass marble
= 18.5×48
= 888 g
Total mass of steel marble
= 66×20
= 1320 g
Total mass of 68 marble including steel 20 and glass 48
= 888 + 1320
= 2208 g
In kilograms 2208
= 2.208 kg
Please mark as brainliest answer
1. Brad spent $1,200 on a credit card this
month. The credit card charges 24.77%
interest compounded continuously. If
Brad does not have to pay any monthly
minimums and makes no payments, how
long will it take until Brad owes the
credit card company $2,400?
Answer:
about 3 years
Step-by-step explanation:
Using the compound interest formula;
A = P(1+r)^t
Given
Amount A == $2400
Principal P = $1200
rate = 24.77% = 0.2477
Substitute the given values
2400 = 1200(1+0.2477)^t
2400/1200 = (1+0.2477)^t
2 = (1+0.2477)^t
ln 2 = tln1.2477
t = ln2/ln1.2477
t = 3.13
Hence it will take about 3 years until Brad owes the credit card company $2,400
What are the solutions to the equation (2x+1)^2-(x+13)=3x^2-2x+2
Please help me with these three questions...
I will be really thankful for help
Answer:
1. Terminating
2. 60
3. I don't know
Step-by-step explanation:
Which of the following will result in a rational answer?
multiplying π by a fraction
adding the square root of a non perfect square to a whole number
adding the square root of a perfect square to π
multiplying a fraction by a repeating decimal.
Answer:
multiplying a fraction by a repeating decimal
Step-by-step explanation:
any fraction is rational
any repeating decimal is rational
therefore, product of the two would be rational
don't mind the purple dot
Answer:
option A
Step-by-step explanation:
22 : 15 + 10hours = 8 : 15
8 : 15 + 35 minutes = 8 : 50
Therefore the difference = 10 hours 35 minutes
The second term in a sequence is 13. The term to term rule is "add 6"
Write an expression, in terms of n, for the nth term of the sequence.
Answer:
[tex]a_{n}[/tex] = 6n + 1
Step-by-step explanation:
This is an arithmetic sequence with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 13 - 6 = 7 and d = 6 , then
[tex]a_{n}[/tex] = 7 + 6(n - 1) = 7 + 6n - 6 = 6n + 1
Answer:
the first few terms would be
7, 13, 19, 25, 31
nth term = 7 + 6(n+1)
nth term = 7+ 6n + 6
nth term = 6n + 13
During a canoeing trip, it takes Raymond 4 hours to paddle 12 miles upstream. It takes him 3 hours to make the return trip paddling downstream. Find the speed of the canoe in still water
Answer:
During a canoeing trip, it takes Raymond 4 hours to paddle 12 miles upstream. It takes him 3 hours to make the return trip paddling downstream. Find the speed of the canoe in still water
Step-by-step explanation:
sorry i dont know
pls no time help me fast no links ill report u and no brainlist
Answer:
Step-by-step explanation:
Line segment Point Point Distance Proof
AB A(-3 , 4) B(2,4) 5 2 - (-3) = 2 +3 = 5
BC B(2,4) C(5,4) 3 5 - 2 = 3
CD C(5,4) D(5,-1) 5 4 -(-1) = 4 +1 = 5
DE D(5 , -1) E(5,-3) 2 -1 -(-3) = -1 +3 = 2
EF E(5, -3) F(-5,-3) 10 5 - (-5) = 5+5 = 10
The television show September Road has been successful for many years. That show recently had a share of 20, meaning that among the TV sets in use, 20% were tuned to September Road. Assume that an advertiser wants to verify that 20% share value by conducting its own survey, and a pilot survey begins with 11 households have TV sets in use at the time of a September Road broadcast. Find the probability that none of the households are tuned to September Road. P(none)
Answer:
[tex]P(none) = 0.0859[/tex]
Step-by-step explanation:
Given
[tex]p =20\%[/tex] --- proportion of household that tuned to September
[tex]n =11[/tex] --- selected households
Required
[tex]P(none)[/tex]
Using the complement rule, the proportion that did not tune (q) is:
[tex]q= 1 - p[/tex]
[tex]q= 1 - 20\%[/tex]
[tex]q= 1 - 0.20[/tex]
[tex]q= 0.80[/tex]
So, the probability that none of the 11 tuned in is:
[tex]P(none) = q^{11}[/tex]
[tex]P(none) = 0.80^{11}[/tex]
[tex]P(none) = 0.0859[/tex]
52 %of U.S. Adults have very little confidence in newspapers. You randomly select 10 U.S. Adults. Find the probability that the number of U.S. Adults who have very little confidence in newspapers is (a) exactly five, (b) at least six, and (c) less than four.
Answer:
a. P(x = 5) = 0.24
b. P(x ≥ 6) = 0.43
c. P(x < 4)= 0.14
Step-by-step explanation:
According to the Question,
Given, 52 %of U.S. Adults have very little confidence in newspapers & We have to randomly select 10 U.S. Adults.⇒We use Binomial Probability Formula
[tex]P(X = x ) = \frac{n!}{x!((n-x)! } * p^{x} * (1-p)^{n-x}[/tex]
Where, p=0.52 & n=10
a. The probability that the number of U.S. adults who have very little confidence in newspapers is exactly five . So, (x=5)
Thus, [tex]P(X = 5 ) = \frac{10!}{5!((10-5)! } * 0.52^{5} * (1-0.52)^{10-5}[/tex]
On Solving Above Equation we get,
P(5)=0.2441 ≈ 0.24
b. The probability that the number of U.S. adults who have very little confidence in newspapers is at least 6 . So, (x≥6)
Then,
P(x≥6) = P(6)+P(7)+P(8)+P(9)+P(10)
P(x≥6) = [tex]\frac{10!}{6!((10-6)! } * 0.52^{6} * (1-0.52)^{10-6}[/tex] + [tex]\frac{10!}{7!((10-7)! } * 0.52^{7} * (1-0.52)^{10-7}[/tex] +[tex]\frac{10!}{8!((10-8)! } * 0.52^{8} * (1-0.52)^{10-8}[/tex] + [tex]\frac{10!}{9!((10-9)! } * 0.52^{9} * (1-0.52)^{10-9}[/tex]+[tex]\frac{10!}{10!((10-10)! } * 0.52^{10} * (1-0.52)^{10-10}[/tex]
On solving above equation we get,
P(x≥6) = 0.4270 ≈ 0.43
c. The probability that the number of U.S. adults who have very little confidence in newspapers is less than 4 . So, (x<4)
Then,
P(x < 4)=P(3) + P(2)+P(1)+P(0)
P(x<4) = [tex]\frac{10!}{3!((10-3)! } * 0.52^{3} * (1-0.52)^{10-3}[/tex] + [tex]\frac{10!}{2!((10-2)! } * 0.52^{2} * (1-0.52)^{10-2}[/tex]+ [tex]\frac{10!}{1!((10-1)! } * 0.52^{1} * (1-0.52)^{10-1}[/tex] + [tex]\frac{10!}{0!((10-0)! } * 0.52^{0} * (1-0.52)^{10-0}[/tex]
On solving we get,
P(x < 4)= 0.1410 ≈ 0.14
A roll of nickels is worth $2.00. Write and
solve an equation to determine the number
of nickels in a roll.
Answer: 20 nickels to make $2.00
Step-by-step explanation:
Answer:
5x = 200
x=40
Step-by-step explanation:
state wether the product of √3 and √9 is rational or irrational. explain your answer
√9 is rational and √3 irrational number
Simplify by factorising first
Answer:
x+8
Step-by-step explanation:
Simplify the numerator
list the factors of 16
16: 1, 2, 4, 8, 16
look for two factors that add up to the b value
in this case it is 18
by looking at the factors 2 and 8 add up 10
so you can rewrite the numerator as [tex]x^{2}+2x+8x+16[/tex]
Split the trinomial into two separate binomials each having one of the factors that add up to 10
So it should be [tex]x^{2} +2x and 8x+16[/tex]
Factor both binomials
you can factor an x from the first one
Then it is x(x+2)
Factor an 8 from the second one
8(x+2)
So it should be [tex]x(x+2) 8(x+2)[/tex]
This can rewritten as (x+8)(x+2)
So now you have [tex]\frac{(x+2)(x+8)}{x+2)}[/tex]
simplify it by canceling out the two (x+2)'s
this is because (x+2)/(x+2) is 1
Finally you get x+8
Does anyone know the answer to this ?!? ( links and answers that have nothing to do with the question will be reported.)
Answer:
the triangle was 2x scale (*2)
it was reflected across y=0
and translated x +2
Step-by-step explanation:
1. Convert the quinary number 42 into binary number.
Answer:
42 in binary number is 101010.
If p and q vary inversely and p is 22 when q is 5, determine q when p is equal to 2.
Answer:
q = 55
Step-by-step explanation:
[tex]p\ \alpha\ \frac{1}q} \\\\p = k \times \frac{1}{q}\\\\22 = k \times \frac{1}{5}\\\\22 \times 5 = k\\\\k = 110\\\\[/tex]
Find q when p = 2
[tex]p = k \times \frac{1}{q}\\\\2 = 110 \times \frac{1}{q}\\\\2 \times q = 110\\\\q = \frac{110}{2}\\\\q = 55[/tex]
given log base3 4 = log base 1/27 k , find the value of k .
Answer:
k =0.156
Step-by-step explanation:
According to the Question,
We Have To apply Just some Basic Properties of log here.
[tex]log_{3}4 = log_{1/27}k\\\frac{log_{}4 }{log_{}3 } = \frac{log_{}k }{log_{}1/27 }\\\\\frac{log_{}4 }{log_{}3 } = \frac{log_{}k }{log_{}1-log_{27} }\\\\frac{log_{}4 }{log_{}3 } = \frac{log_{}k }{0-3*0.4771} }\\\[/tex]
0.620/0.4771 = ㏒k / -1.4313
㏒k = -1.86
k = anti㏒(-1.86)
k =0.156
Find the missing side. Round to the nearest tenth.
A.7.4
B.4.4
C.6.4
D.5.4
Answer:
option D
Step-by-step explanation:
take 39 degree as reference angle
using cos rule
cos 39 = adjacent / hypotenuse
0.77 = x / 7
x = 7*0.77
x = 5.39
x = 5.4
Answer:
D. 5.4
Step-by-step explanation:
Using trigonometric ratio
cos 39 = x/7
cross multiple
x = cos39(7)
x=5.4
What are the next 3 terms in the following geometric sequence:
512, 256, 128, ___, ___, ___
A. 92, 66, 28
B. 1024, 2048, 4096
C. 64, 32, 16
D. 32, 8, 2
Answer:
C. 64, 32, 16
Step-by-step explanation:
This geometric sequence is made by dividing the numbers by 2:
512 ÷ 2 = 256
256 ÷ 2 = 128
Hence, the next term will be
128 ÷ 2 = 64
64 ÷ 2 = 32
32 ÷ 2 = 16
Therefore, the correct answer is C.
The next 3 terms in the given geometric sequence are 64, 32, and 16, respectively. The correct option is C.
What is geometrical series?A geometric series is the collection of an unlimited number of terms with a fixed ratio between them.
The given series is a geometric sequence, therefore, the common ratio between any two terms will be the same. Therefore, we can write, the ratio as,
Common ratio, r = a₂ / a₁ = 256 / 512 = 1/2
Now, the nth term of the given sequence can be defined as,
aₙ = a₁ × r⁽ⁿ⁻¹⁾
= 512 × (1/2)⁽ⁿ⁻¹⁾
Therefore, the next term of the given geometric progression will be,
a₄ = 512 × (1/2)³ = 64
a₅ = 512 × (1/2)⁴ = 32
a⁶ = 512 × (1/2)⁵ = 16
Hence, the next 3 terms in the given geometric sequence are 64, 32, and 16, respectively.
Learn more about Geometrical Series here:
https://brainly.com/question/4617980
#SPJ2
I was doing my khan and i got stuck
6=2(y+2)
Answer:
[tex]y=1[/tex]
Step-by-step explanation:
Given:
[tex]6=2(y+2)[/tex]
Distribute the parenthesis
[tex]6=2y+4[/tex]
Subtract both sides by 4
[tex]2=2y[/tex]
Divide both sides by 2 to get [tex]y[/tex] alone
[tex]1=y[/tex]
Hope this is helpful
Solve the system by substitution.
— бу = x
x + y = -30
Step-by-step explanation:
-6y + y=-30
-5y = -30
y=6
x=-6 ×6= -36
solve the system of equations y=2x-3 and y=x^2-3
I have attached some answers in the photos below hope you find them useful
Answer:
0 and 1
Step-by-step explanation:
Given :
[tex]y= 2x-3\\y=2x^{2} -3[/tex]
Now equate the both equation :
[tex]2x-3=2x^{2} -3[/tex]
2x=2[tex]x^{2}[/tex]
x-[tex]x^{2}[/tex]=0
x(1-x)=0
x=0
1-x=0
x=1
Therefore, x=0,1
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