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.
What is the value of b2 - 4ac for the following equation? 2x2 - 2x - 1 = 0 -4 12 0
Answer:
I think you mean the equation is
[tex]2 {x}^{2} - 2x - 1 = 0[/tex]
And you must find
[tex]delta = {b}^{2} - 4ac = 4 + 8 = 12[/tex]
The length of the base of an isosceles triangle is x. The length of a leg is 3x-4. The perimeter of the triangle is 97. Find x.
Answer I do not know i am not there yet i am sorry
Step-by-step explanation:
:(
what is the answer to 0.7(1.5 + y) = 3.5y - 1.47
Answer:
0.9
Step-by-step explanation:
0.7*(1.5 + y) = 3.5y - 1.47
or, (0.7*1.5) + 0.7y = 3.5y - 1.47
or, 1.05 + 1.47 = 3.5y - 0.7y
or, 2.52 = 2.8y
or, y = 2.52/2.8
or, y = 0.9
Hope this will help. Please mark me brainliest.
12. In the diagram below…
What is the length of CB?
1) 3.2
2) 4.8
3) 16.2
4) 19.2
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]
What are the vertices of triangle PQR?
Answer: D. P, Q and R.
Step-by-step explanation:
The vertices of the triangle PQR - it is P, Q and R.
Math
Help
Will
Give
Brainlist
:))
Answer:
2/3 mi
Step-by-step explanation:
Multiply the length of one side of a square by 4 to find the perimeter.
(1/6)(4) = 4/6
Simplify. The common factor is 2.
4/6 = 2/3
A train leaves at 14:56 and arrives at 16:43. It travelled at an average speed of 135 km/h. How far did it travel? Give your answer in km to 1DP.
Answer:
240.8
Step-by-step explanation:
→ Calculate time taken
16:43 - 14:56 = 1 hour and 47 minutes
→ Write the speed formula and make distance the subject
Speed = Distance ÷ Time ⇔ Distance = Speed × Time
→ Convert 1 hour and 47 minutes into decimal format
1.78333333 or [tex]1\frac{47}{60}[/tex]
→ Substitute values into formula
135 × [tex]1\frac{47}{60}[/tex] = 240.75
Solve the givin proportions
Answer:
x=(6×6)/9=4
just cross multiply and get your answer
Answer:
x=4
Step-by-step explanation:
Step 1
Represent the ratios as fractions
6/9=x/6
Step 2
Cross-multiply the numerators and denominators
9x=6×6
9x=36
9x/9=36/9
Therefore x=4
Which is the graph of linear inequality 2y > x-2?
Answer:
top line third option with shaded above.
Step-by-step explanation:
it's the third option because it's a
dotted line because it's not included (since it doesn't say greater than or equal to). Also, greater than is shaded above the line.
The third graph is the correct representation of the given inequality.
What are linear inequalities?Linear inequalities are defined as a mathematical expression that compares two expressions using the inequality symbol.
The given inequality is 2y > x-2.
i.e y > (x-2)/2
Since the inequality sign does not contain an equals sign, the line is drawn as a dashed line.
The upper region satisfies the inequality.
Hence, the upper shaded portion with the dashed line is the correct graph for the given inequality.
To learn more about linear inequality, use the link given below:
https://brainly.com/question/11897796
#SPJ2
Solve the following system of equations using all three methods. Must show your work. 4x + y = 2 3x - 3y = 9
Part A: Solve by graphing.
Part B: Solve by substitution.
Part C: Solve by elimination.
Describe the process and steps you used to solve each method.
Answer:
Step-by-step explanation:
you do part a
Equation 1: 4x+y=2
Equation 2: 3x-3y=9
b
Divide equation 2 by 3
x-y=3
add y to both sides
x=3+y
Sbustitute this into equation 1
4(3+y)=2
12+4y+y=2
5y= -10
y= -2
Plug this into equation 1
4x-2=2
x=1
Part c.
Equation 1: 4x+y=2
Equation 2: 3x-3y=9
divide equation 2 by 3
x-y=3
add the two equations
(x-y)+(4x+y)=2+3
5x=5
x=1
Plug this into equation 1
4(1)+y=2
4+y=2
y= -2
For part a just create a table and graph it
need help with this asap!
Answer:
Step-by-step explanation:
1 ) 2 + 7t [ there are no like terms , so no further simplifying ]
2) 6r + ( - 16 r )
= 6 r - 16 r [ both are like terms ]
= - 10 r
3) (3x + 2 ) + ( 2x - 4 )
= 3x + 2 + 2x - 4
= 3x + 2x - 4 + 2 [ arranging like terms together ]
= 5x - 2
4) (8 n² - 3 n + 6 ) + ( n - 2 )
= 8n² - 3n + 6 + n - 2
= 8n² - 3n + n + 6 - 2 [ bringing like terms together ]
= 8n² - 2n + 4
Answer:
1.) 2 + 7 t
2.) - 10 r
3.) 5 x - 2
4.) 8 n² - 2 n + 4
Step-by-step explanation:
1.) 2 + 7 t
No like terms, so no further simplifying.
2.) 6 r + ( - 16 r )
6 r - 16 r. ... ( combine like terms)
- 10 r
3.) ( 3 x + 2 ) + ( 2 x - 4 )
= 3 x + 2 + 2 x - 4
combine like terms
= 3 x + 2 x - 4 + 2
= 5 x - 2
4.) ( 8 n ² - 3 n + 6 ) + ( n - 2 )
= 8 n² - 3 n + 6 + n - 2
combine like terms
= 8n² - 3 n + n + 6 - 2
= 8 n² - 2 n + 4.
The probability that a student takes calculus or is on scholarship is 0.85. The probability that a student is on scholarship is 0.61 and the probability that a student is taking calculus is 0.31. If a student is randomly chosen, find the probability that the student is taking calculus and is on scholarship.
Answer:
0.07
Step-by-step explanation:
According to the Question,
Let C denote the event that a student takes calculus & S denote the event that a student is on scholarship.
Given, The probability that a student takes calculus or is on scholarship is 0.85 [P(C ∪ S)=0.85] . The probability that a student is on scholarship is 0.61 [P(S)=0.61] . and the probability that a student is taking calculus is 0.31 [P(C)=0.31] .We have,
⇒P(C ∪ S)=0.85 , P(C)=0.31 , P(S)=0.61
We Know, P(C∩S) = P(C) + P(S) − P(C∪S)
Then, Put the Above Values in the Equation, we get
So, P(C∩S) = 0.31 + 0.61 - 0.85 ⇒ 0.07
Thus, The probability that the student is taking calculus and is on scholarship is 0.07What is 1/3 divided into 7 equal parts
Please help I made another one but I said I why on accident
Answer:
1/21
Step-by-step explanation:
1/3 / 7 = 1/3 / 7/1 = 1/3 * 1/7 = 1/21
Answer:
21
Step-by-step explanation:
1/3 x 7/1 you flip the 7 and you will have 1/3x1/7 and then u 7x3 and u will get 21
Evaluate e^4 to one decimal place
Answer:
The answer is going to be the general form for e^x = 1 + x/(1!) + + x^2/(2!) + x^3/(3!) +.....,. till infinity so : e^4 = 1 + 4/1 + 16/ 2 + 64/6 + 256/24 + 1024/ 120 + 4096/720 + 16384/5040 +...till the fraction is<0.1 = 54.6
X 3 + 3 x 2 − x + 2 x 2 + 6 x − 2. Which expression is equivalent to this product after it has been fully simplified? x3 + 5x2 + 5x – 2 x3 + 2x2 + 8x – 2 x3 + 11x2 – 2 x3 + 10x2 – 2
Answer:
[tex](x^3 + 3x^2 - x + 2)(x^2 + 6x -2) = x^5 + 9x^4+ 15x^3 + 2x^2 + 10x -4[/tex]
Step-by-step explanation:
Given
[tex](x^3 + 3x^2 - x + 2)(x^2 + 6x -2)[/tex]
Required
The equivalent expression
We have:
[tex](x^3 + 3x^2 - x + 2)(x^2 + 6x -2)[/tex]
Open bracket
[tex](x^3 + 3x^2 - x + 2)(x^2 + 6x -2) = x^5 + 6x^4 - 2x^3 + 3x^4 + 18x^3 - 6x^2 -x^3 + 6x^2 - 2x + 2x^2 + 12x -4[/tex]
Collect like terms
[tex](x^3 + 3x^2 - x + 2)(x^2 + 6x -2) = x^5 + 6x^4 + 3x^4- 2x^3 -x^3 + 18x^3 - 6x^2 + 6x^2 + 2x^2- 2x + 12x -4[/tex]
Evaluate like terms
[tex](x^3 + 3x^2 - x + 2)(x^2 + 6x -2) = x^5 + 9x^4+ 15x^3 + 2x^2 + 10x -4[/tex]
Divide. Express your answer in simplest form.
10/11 ÷ 2/3
Answer:
[tex]1\frac{4}{11}[/tex]
Step-by-step explanation:
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: \frac{15}{11} }}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
➺[tex] \frac{10}{11} \div \frac{2}{3} [/tex]
➺[tex] \: \frac{10}{11} \times \frac{3}{2} [/tex]
➺[tex] \: \frac{10 \times 3}{11 \times 2} [/tex]
➺[tex] \: \frac{30}{22} [/tex]
➺[tex] \: \frac{15}{11} [/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]
Sum of cubes:
(a + b)(a2 – ab + b2) = a3 + b3
Difference of cubes:
(a – b)(a2 + ab + b2) = a3 – b3
Which products result in a sum or difference of cubes? Check all that apply.
(x – 4)(x2 + 4x – 16)
(x – 1)(x2 – x + 1)
(x – 1)(x2 + x + 1)
(x + 1)( + x – 1)
(x + 4)(x2 – 4x + 16)
(x + 4)(x2 + 4x + 16)
Answer:
C and E
Step-by-step explanation:
Answer:
3 and 5
Step-by-step explanation:
The solution of this problem is in this picture.
Is the following shape a square? How do you know? A. Yes, the opposite sides are parallel, and all sides are the same length. B. No, because opposite sides are not parallel. C. There is not enough information to determine. D. No, because the sides are not congruent.
Answer:
A
Step-by-step explanation:
Answer:
NO
Step-by-step explanation:
No, because the sides are not congruent.
The total cost of Anfä's trip to the dentist was $628.35. She paid a flat fee of $89.95 which included the checkup:
cleaning and then had 4 cavities filled, each of which cost the same amount. Which shows the correct equation and
value of x, the cost of each cavity filling?
Answer:
The cost of each cavity filling was $ 134.60.
Step-by-step explanation:
Given that the total cost of Anfa's trip to the dentist was $ 628.35, and she paid a flat fee of $ 89.95 which included the checkup: cleaning and then had 4 cavities filled, each of which cost the same amount, to determine which shows the correct equation and value of x, the cost of each cavity filling, the following calculation must be performed:
(628.35 - 89.95) / 4 = X
538.4 / 4 = X
134.6 = X
Therefore, the cost of each cavity filling was $ 134.60.
Whats the last info I need?
Answer:
Step-by-step explanation:
Properties of the similarity of two triangles,
1). Corresponding angles of two triangles should be equal.
2). Corresponding sides of two triangles should be proportional.
By applying second property in the given triangles RTY and CVB,
[tex]\frac{CV}{RT}=\frac{TY}{VB}=\frac{CB}{RY}[/tex]
[tex]\frac{15}{10}= \frac{9}{6}= \frac{CB}{RY}[/tex]
[tex]1.5= 1.5= \frac{CB}{RY}[/tex]
Ratio of sides CB and RY should be 1.5 for the similarity of two triangles.
Therefore, additional information required for the similarity of two triangles is "the measure of third sides of both the triangles should be known"
Aaron has a combination of nickels, dimes, and quarters in his pocket. Aaron's collection of coins is represented in the matrix below.
1
1
1
14
2 0 -1 0
.05 10 252.15
Which of the following is NOT a correct verbal interpretation of one of the equations in the system?
O Aaron has twice as many quarters as nickels.
O Aaron has no nickels.
O Aaron has a total of 14 coins.
The total value of the coins is $2.15.
6
7
8
8
9
10
Answer:
Aaron has no nickels
Step-by-step explanation:
eg
What is the same as 3(4 + 5 + 6)?
Answer:
45Step-by-step explanation:
3(4 + 5 + 6)
= 3(15)
= 3 × 15
= 45 (Ans)
if £2000 is placed into a bank account that pays 3% interest compound into how much will be in the account after 2 years?
Answer: The answer is £2121.8.
You can check this formula....
What is the mean? If the answer is a decimal, round it to the nearest tenth.
-4 1 4 -1
4 -1 -2 -6 3-5
-8
Answer: if its decimal and it wants you to round to next place to the tenths place
Step-by-step explanation: if it means to look at the hundredth's place to find your answer if its bigger than five your second number will add up if its lower than five it stays the same
Does someone know what the answer is? Help, please!
Answer:
if I'm not wrong it should be A
Write two solutions for the following equation 2x+3y=24.
Answer: (12, 0) and (0, 8)
Step-by-step explanation:
This equation is in standard form. We can sub in a number for x to solve for y and vice versa.
Let's sub in 0 for x.
[tex]2x+3y=24\\2(0)+3y=24\\3y=24\\\frac{3y}{3} =\frac{24}{3} \\y=8[/tex]
When x is 0 y is 8 giving us the coordinate (0, 8).
Now lets sub in 0 for y
[tex]2x+3(0)=24\\2x=24\\\frac{2x}{2} =\frac{24}{2} \\x=12[/tex]
When y is 0 x is 12 giving us the coordinate (12, 0)
Step-by-step explanation:
Begin by solving for y
3y = -2x + 24 divide by 3
y =-(2/3)x + 24
Choose x so that it is divisible by 3
Let x = 6 which 3 can divide into evenly
y = -(2/3)*6 + 24 3 into 6 is 2 so you are left with
y = - 2 * 2 + 24
y = - 4 +24
y = 20
By a similar mthed, let x = 15
y = -2/3 x + 24
y = -2/3 * 15 +24
y = -2 * 5 + 24
y = -10 + 24
y = 14
So your two solutions are
(6,20)
(15,14)
If JK = 4, KL = 3x, and JL = 7x, what is JL? Simplify your answer and write it as a proper fraction, mixed number, or integer.
Answer:
JL = 7
Step-by-step explanation:
If JK = 4, KL = 3x, and JL = 7x, what is JL?
From the diagram given in tbe question,
JK + KL = JL
4 + 3x = 7x
Collect like terms
4 = 7x - 3x
4 = 4x
4x = 4
x = 4/4
x = 1
Since JL from the diagram = 7x
Hence:
7 × 1 = 7
JL = 7
What quadratic equation could be solved to find any solutions to the system of equations?
y = -51 +6
y = 12 + 71 - 11
Replace the values of a, b, and in the equation to formulate the correct equation.
Answer:
Step-by-step explanation:
x²+7x-11=-5x+6
x²+7x+5x-11-6=0
x²+12x-17=0
[tex]x=\frac{-12\pm \sqrt{12^2-4*1*(-17)} }{2*1} \\=\frac{-12 \pm \sqrt{144+68} }{2} \\=\frac{-12 \pm \sqrt{212}}{2} \\=\frac{-12+2\sqrt{53}}{2}\\=-6 \pm \sqrt{53}[/tex]
Help Please with these
Problem 17
Focus on one of the triangles. It has legs of 8 and 15. Use the pythagorean theorem to find the hypotenuse is 17.
Basically you're solving for c in a^2+b^2 = c^2. Use a = 8 and b = 15.
The diameter is 17 and the circumference is
C = pi*d = pi*17 = 17pi
Answer: 17pi==============================================
Problem 18
This figure has four faces, so this is a tetrahedron. The "tetra" is greek that translates to "four".
Another possible name for this figure is triangular pyramid because we have a pyramid with a triangular base.
Answer: Triangular pyramid or tetrahedron