Answer: t ≈ 20 years
Step-by-step explanation:
Since it is compounded continuously , we will use the compound interest formula:
A = P[tex]e^{rt}[/tex]
Where A is the amount when tripled
P is the initial amount
r is the rate
t is the time
since the investment is tripled , it means the A = 3P.
From the question:
A = 3P
P = $6000
r = 5.5%
t = ?
Substituting into the formula , we have
3P = P[tex]e^{rt}[/tex] , that is
3(6000) = 6000[tex]e^{0.055t}[/tex]
Dividing through by 6000 , we have
3 = [tex]e^{0.055t}[/tex]
Take the In of both sides in order to remove the exponential , that is
In 3 = 0.055t
divide through by 0.055
t = In 3 / 0.055
Therefore :
t = 19.97476888
t≈ 20 years
How do I graph 7x+2y=-10
A hotel has 150 rooms. Those with kitchen facilities rent for $100 per night in those without kitchen facilities rent for $80 per night. On a night when the hotel was completely occupied, revenues were $13,000. How many of each type of room does the hotel have?
Answer:
50 rooms with kitchen facilities and 100 rooms without kitchen facilities
Step-by-step explanation:
Let the rooms without kitchen facilities be x and those with kitchen facilities be y
Form set of equations
Since the total rooms are 15, then the first equation is
x+y=150
Therefore, x=150-y
Considering the cost of rooms and what was collected, then
80x+100y=13000
Substituting x with 150-y then
80(150-y)+100y=13000
12000-80y+100y=13000
20y=1000
[tex]y=\frac {1000}{20}=50 rooms[/tex]
Therefore, x=150-y=150-50=100 rooms
Therefore, there are 50 rooms with kitchen facilities and 100 rooms without kitchen facilities
At 1:00pm, ship A is 30 miles due south of ship B and is sailing north at a rate of 15 mi/hr. If ship B is sailing
west at a rate of 10 mi/hr, find the time at which the distance d between the ships is minimal.
Answer:
2:23 pm
Step-by-step explanation:
We can solve this considering a a right triangle
let t = travel time of both ships
therefore,
15t = distance traveled by ship A
however, it is traveling toward the point of reference, therefore we write it
(30-15t)
and
10t = distance traveled by ship B, away from the point of reference
Let d = distance between the ships at t time, (the hypotenuse of the right triangle)
[tex]d= \sqrt{(30-15t)^2+10t^2}[/tex]
and combine like terms
[tex]d= \sqrt{(900-900t+225t^2)+100t^2}[/tex]
[tex]d= \sqrt{3325t^2-900t+900}[/tex]
from this d to minimum we can find the axis of symmetry, where in
a=325 and b= -900
the t=-b/2a
[tex]t= -\frac{-900}{2\times325}[/tex]
t= 1.384 hours
now putting the value we get
[tex]d= \sqrt{3325(1.384)^2-900(1.384)+900}[/tex]
solving this we get
d= 16.64 miles
therefore,
16.64 mi apart after 1.3846 hrs, minimum distance between the ships
now, 1.384 hours = 1+60(0.348) hour
= 1 hour and 23 minutes
so, the time at which the distance d between the ships is minimal = 1:00 pm + 1 hour and 23 minutes = 2:23 pm
An engineering student answered 81 questons correctly ona 90 question test. What percent of the question did she answer correctly? questions correctly on a 90 question test. What percent of the questions she answered correctly?
Answer:
correct answer = 90%
Step-by-step explanation:
Let x be the percent of the question did she answer correctly.
Given:
An engineering student answered 81 questions correctly on a 90 question test.
Find the percent of the question did she answer correctly.
Solution:
Percentage formula is given below
% answer [tex]=\frac{correct\ answer}{total\ questions}\times 100[/tex]
% answer [tex]=\frac{81}{90}\times 100[/tex]
% answer [tex]=\frac{81\times 100}{90}[/tex]
% answer [tex]=\frac{81\times 10}{9}[/tex]
% answer [tex]=9\times 10[/tex]
% answer [tex]=90[/tex]
correct answer = 90%
Therefore, she answered 90% correctly.
Answer:
90%
Step-by-step explanation:
How do you integrate [tex]\int\limits ln({x+1}) \, dx[/tex] using integration by parts?
Thank you!
Answer:
[tex]\int \ln (x+1) \, dx=x\cdot \ln (x+1)-x+\ln (x+1)+C[/tex]
Step-by-step explanation:
Use integration by parts formula:
[tex]\int u \, dv=uv-\int v \, du[/tex]
For the integral
[tex]\int \ln(x+1) \, dx,[/tex]
[tex]u=\ln (x+1)\\ \\dv=dx,[/tex]
then
[tex]du=d(\ln (x+1))=\dfrac{1}{x+1}\ dx\\ \\v=x[/tex]
and
[tex]\int \ln(x+1) \, dx\\ \\=x\cdot \ln (x+1)-\int x\cdot \dfrac{1}{x+1} \, dx\\ \\= x\cdot \ln (x+1)-\int \dfrac{x+1-1}{x+1} \, dx\\ \\=x\cdot \ln (x+1)-\int \left(1-\dfrac{1}{x+1}\right) \, dx\\ \\=x\cdot \ln (x+1)-\int \, dx +\int \dfrac{1}{x+1} \, dx\\ \\=x\cdot \ln (x+1)-x+\ln (x+1)+C[/tex]
if you vertically stretch the quadratic parent function, f (x) = x^2 by multiplying by 7 what is the equation of the new function
Answer:
F(x)=7x^2 or G(x)=7x^2
Step-by-step explanation:
Find the exact volume of the cylinder.
A) 65π m3
B) 130π m3
C) 260π m3
D) 325π m3
Answer:
d
Step-by-step explanation:
And Another Question 35 points
Answer:
50
Step-by-step explanation:
The x-axis represents the number of broken light bulbs, as labelled on the histogram. The highest range is 41 to 50, therefore the greatest possible number of broken light bulbs is 50.
Answer:
50
Step-by-step explanation:
The last bar on the number of broken light bulbs (x) axis covers the range 41-50. Thus, 50 is the maximum number of broken light bulbs that can be and is represented in this histogram.
how do i find the perimeter of a rectangle that is 15 in. x 24 in.
You can apply the formula of perimeter of rectangle and that is 2(l+b)....
Mason bought 6 loaves of bread and 3 packages of cheese for a total of $27. The cost of a package of cheese is $1.50 more than the cost of a on loaf of bread. What is the combined cost of one loaf of bread and one package of cheese?
The combined cost of one loaf of bread and one package of cheese is $6.50.
Mason bought 6 loaves of bread and 3 packages of cheese for a total of $27. The cost of a package of cheese is $1.50 more than the cost of a loaf of bread. To find out the combined cost of one loaf of bread and one package of cheese, we need to use a system of equations.
Let the cost of one loaf of bread be x. Therefore, the cost of one package of cheese would be x + $1.50. Since Mason bought 6 loaves of bread and 3 packages of cheese, we can express the total cost as:
6x + 3(x + $1.50) = $27
Distributing the 3 into the parentheses, we get:
6x + 3x + $4.50 = $27
Combining like terms, we have:
9x + $4.50 = $27
Subtracting $4.50 from both sides, we get:
9x = $22.50
Dividing both sides by 9, we find out that one loaf of bread (x) costs:
x = $2.50
Now, adding the additional $1.50 for the cheese, we find that one package of cheese costs:
x + $1.50 = $4.00
The combined cost of one loaf of bread and one package of cheese is therefore:
$2.50 (bread) + $4.00 (cheese) = $6.50
The interest rate on the credit card is 15%. If we charge $200 to the credit card how much will pay including the interest?
Answer:
Step-by-step explanation:
Interest = 15% of 200 = 15/100 * 200 = 15 * 2 = $30
The Amount he need to pay = 200 + 30 = $230
What is the volume of a rectangular prism with length 7 in., height 3 in., and width 8 in.?
V = lwh
_in3
Answer:168
Step-by-step explanation: v=lwh
V=7x8x3
= 168
x = 15.
PQ = SQ.
Find y, explain good for brainliest
Answer:
y = 25.
Step-by-step explanation:
PQ and RQ and SQ are congruent so
x + 10 = 2x - 5
15 = x.
So PQ = 15 + 10 = 25.
But PQ = RQ = y, so
y = 25.
Tara paid $3.52 for 4 boxes of macaroni and cheese. Jarrett paid $5.40 for 6 boxes of macaroni and cheese. Which of
the following statements is true?
Tara paid more per box
Jarrett paid more per box.
Tara and Jarrett paid the same per box
Answer: Tara paid more per box
Step-by-step explanation:
What is the initial value of the function represented by this table? (5 points)
Answer:
0
4
5
9
Step-by-step explanation:
Can someone Please Help Me
Answer:
a= 63 ⁰; z= 80⁰; x= 30⁰; N= 102⁰;M = 66⁰
Step-by-step explanation:
Example 1 : the angle opposite to angle 2a is 54 degrees because it is the opposite exterior angle of 54 degrees angle so
2a+54⁰= 180⁰
2a= 180⁰-54⁰
2a= 126⁰
a= 126/2= 63⁰
EXAMPLE 2: Opposite exterior angles are equal so
z+25⁰= 105⁰-------A
z= 105⁰-25⁰
z=80⁰
It is making a straight angle so
105⁰+ 3x-15= 180⁰
3x-15=180-105
3x-15=75⁰
3(x-5)=75⁰
x-5⁰=75/3
x-5⁰=25⁰
x= 25⁰+5⁰
x=30⁰
EXAMPLE 3:
114⁰= N+12⁰ (exterior opposite angles are equal)
N= 114⁰-12⁰
N= 102⁰
114⁰+M= 180⁰ (straight angles)
M= 180⁰- 114⁰
M= 66⁰
Bill wants to post three parcels.
Parcel 1
Parcal 2
Parcel 3
Each parcel costs £1.10 to post.
How much change should he get from a £10 note?
The change Bill should receive from a £10 note after paying to post three parcels, each costing £1.10, is £6.70.
Explanation:Bill wants to post three parcels and each parcel costs £1.10 to post. The total cost for posting all three parcels would be £1.10 * 3 = £3.30. If he pays this fee with a £10 note, we can calculate the change by subtracting the total cost of posting parcels from the value of the note: £10 - £3.30 = £6.70. So, the change Bill should get back from a £10 note after posting 3 parcels each costing £1.10 is £6.70.
Learn more about Change Calculation here:https://brainly.com/question/32994491
#SPJ12
Which system of equations has no solutions
A. 3x + 4y = 5
6x + 8y = 10
B. 7x - 2y = 9
7x - 2y = 13
C. 2x - y = -11
-2x + y = 11
D. 3x + 6y = 1
x + y = 0
I need to buy a carpet-for a-room the measures 3m by 2m.how many square meters do I need?
Final answer:
To carpet a room measuring 3 meters by 2 meters, you need 6 square meters of carpet.
Explanation:
To calculate the area of a rectangular room that measures 3 meters in length and 2 meters in width, you multiply the length by the width.
Using the formula Area = length × width,
As we can see that the room is a rectangle with width 2 and length 3
So,
Length = 3 m
Width = 2 m
We find that the room's area is 6 square meters (3m × 2m = 6m²).
Therefore, to carpet a room of this size, you would need to buy 6 square meters of carpet.
The area of a rectangle is 4y + 10.
A. Represent the area of the rectangle in factored form.
B. Use the factored form to give one possible set of dimensions for this rectangle.
A) The factored form of area of rectangle is 2(2y + 5)
B) length of rectangle is 2 and width is 2y + 5 and one possible set of dimensions of rectangle is length 2 and width 7
Solution:
Given that area of rectangle is 4y + 10
A. Represent the area of the rectangle in factored form
The factored form is a parenthesized algebraic expression.
Factored form is a product of sums of products or a sum of products of sums
Given area of rectangle is 4y + 10
Taking 2 as common,
4y + 10 = 2(2y + 5)
Therefore, the factored form of given area of rectangle is 2(2y + 5)
B. Use the factored form to give one possible set of dimensions for this rectangle
The area of a rectangle is given by the formula:
area of rectangle = length x width
Therefore, area of rectangle = 2(2y + 5)
So the length of rectangle is 2 and width is 2y + 5
Or the length of rectangle is 2y + 5 and width is 2
If y = 1, then one possible set of dimensions of rectangle is:
length = 2 and width = 2(1) + 5 = 7
So one possible set of dimensions of rectangle is length 2 and width 7
Final answer:
The factored form of the area of the rectangle is 2(2y + 5).
One possible set of dimensions, based on the factored form, is a length of 2y units and a width of 5 units.
Explanation:
To represent the area of a rectangle in factored form, we look for factors of the expression 4y + 10. Both terms have a common factor of 2, so the factored form is:
2(2y + 5).
Now, to give one possible set of dimensions for the rectangle using the factored form, we can consider each factor as a dimension:
Length: 2yWidth: 5Thus, one possible set of dimensions for the rectangle could be 2y units (length) and 5 units (width).
Find the roots of this polynomial x^2 -9x+8
Final answer:
x = 1 and x = 8.
Explanation:
This can be completed through factoring the quadratic equation. To factor x^2 - 9x + 8, we look for two numbers that multiply to +8 and add to -9. These numbers are -1 and -8 since (-1) * (-8) = +8 and (-1) + (-8) = -9. Therefore, we can write the polynomial as (x - 1)(x - 8). The roots are the values of x which make each factor zero, hence we get the roots as x = 1 and x = 8.
A. 90 degrees
B. 180 degrees
C. 270 degrees
D. 360 degrees
Answer:
What was the question (I can't see the picture)
Step-by-step explanation:
Answer:
B. 180 degrees
Step-by-step explanation:
∠A, ∠B and ∠C are collective the internal angles of a triangle.
By definition, the internal angles of a triangle sum to 180degrees
hence ∠A + ∠B + ∠C = 180 degrees
(see also attached graphic for reference)
What is the algerbraic expression for the following word phrase: the product of 5 more than p and 7?
Answer:
Step-by-step explanation:
7(p+5)
Solve system of equation
2x+3y=4
2x=7y+24
Answer:
X= 5 Y= -2
Step-by-step explanation:
what is 14.79 as a rounded number
Answer:
15
Step-by-step explanation:
Answer:
15 or 14.8, depending on whether it is a ehole number on on decimal place
Step-by-step explanation:
The temperature at sunrise was -2 degrees Fahrenheit. The temperature at sunset was 18 degrees warmer than it was at sunrise. What was the temperature at sunset?
a) -20 degrees Fahrenheit
b) -16 degrees Fahrenheit
c) 20 degrees Fahrenheit
d) 16 degrees Fahrenheit
Answer:
d) 16 degrees Fahrenheit
Step-by-step explanation:
What do we know? Initial temperature: -2. Then the temperature rose by 18 degrees. We can express this mathematically:
[tex]-2+18[/tex]
If you are not particularly comfortable with negatives, you can rewrite this expression as such:
[tex]18-2[/tex]
[tex]16[/tex]
Thus the temperature at sunset was 16 degrees Fahrenheit.
Answer:
16 degrees
-2 + 18 is 16
Step-by-step explanation:
If this is wrong EXPLAIN HOW ITS WRONG
two consecutive even integers have a sum of 254. write the equation that will solve for the two integers.
Answer: 126 and 128
Step-by-step explanation: In this problem have two consecutive even integers whose sum is 254.
Consecutive even integers can be represented as followed.
X ⇒ first even integer
X + 2 ⇒ second even integer
Since the sum of these is 254, our equation reads X + X + 2 = 254.
We can simplify on the left side of the equation to get 2x + 2 = 254.
Now, we subtract 2 from both sides of the equation to get 2x = 252.
Lastly, we will divide both sides of the equation by 2 in order to isolate x. On the left side, the 2's cancel out and on the right, 252 divided by 2 is 126.
If our first integer is 126, our next consecutive even integer will be 126 + 128 which simplifies to 254.
Therefore, our two consecutive even integers are 126 and 128.
Which pair of number has the same greatest common factor as 48 and 78
Answer:
48
Step-by-step explanation:
48=2×2×2×2×3
78=13×2×3
48 has 5 factors.
At a local food store a child stole $500 from the shopkeeper's cash register to purchase goods in the store. The items the child purchased total $350 which he paid using the money he stole and received change of $150. How much money in total did the shopkeeper lose
Answer:
The shopkeeper lost $500
What is the quote that of 2^4/2^-4
Answer:
[tex]2^8[/tex]
Step-by-step explanation:
To find the quotient of:
[tex]\frac{2^4}{2^{-4}}[/tex]
Solution:
We will apply quotient rule of exponents to find the quotient of the given expression.
By Quotient rule: [tex]\frac{a^x}{a^y}=a^{(x-y)}[/tex]
Thus the quotient for the expression can be given as:
[tex]\frac{2^4}{2^{-4}}[/tex]
⇒ [tex]2^{(4-(-4))}[/tex]
⇒ [tex]2^{(4+4)}[/tex]
⇒ [tex]2^8[/tex] (Answer)
The expression [tex]\frac{2^4}{2^-4}[/tex] can be simplified to 256.
To solve the expression [tex]\frac{2^4}{2^-4}[/tex], we can use the properties of exponents :
Recall that when you divide powers with the same base, you subtract the exponents: [tex]\frac{2^a}{2^b}[/tex] [tex]=[/tex] [tex]2^(a-b)[/tex].So, for our expression : [tex]\frac{2^4}{2^-4}[/tex] = [tex]2^(4-(_4))[/tex] = [tex]2^(4+4)[/tex] = [tex]2^8[/tex].Next, calculate [tex]2^8[/tex] : [tex]2^8[/tex] = 256.Therefore, the value of the expression [tex]\frac{2^4}{2^-4}[/tex] is 256.