[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$6000\\ r=rate\to 3.5\%\to \frac{3.5}{100}\dotfill &0.035\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases} \\\\\\ A=6000\left(1+\frac{0.035}{1}\right)^{1\cdot 4}\implies A=6000(1.035)^4\implies A\approx 6885[/tex]
The revenue function for a bicycle shop is given by R(x)=x⋅p(x) dollars where x is the number of units sold and p(x)=800−0.5x is the unit price. Find the maximum revenue.
Answer:
The maximum revenue is $320,000
Step-by-step explanation:
To find the maximum of a function f, the procedure is as follows:
Find the first derivative of f.Equate the derivative to 0. Solve the resulting equation to get the critical points.Try all the critical points in the original function and select the one that maximizes it.The revenue function for a bicycle shop is
R(x)=xp(x), where p(x)=800-0.5x. Substituting:
[tex]R(x)=x(800-0.5x)=800x-0.5x^2[/tex]
Find the first derivative of R:
R'(x)=800-x
Equate to 0:
800-x=0
Solve:
x=800
There is only one critical point. Substitute it into the revenue function:
[tex]R(800)=800(800)-0.5(800)^2=320,000[/tex]
The maximum revenue is $320,000
What is the volume of a sphere with a radius of 2.5 units?
Answer: A sphere (from Greek σφαῖρα—sphaira, "globe, ball") is a geometrical object that is a three-dimensional analog to a two-dimensional circle. A sphere is the set of points that are all at the same distance r from a given point in three-dimensional space. That given point is the center of the sphere, and r is the sphere's radius. The earliest known mentions of spheres appear in the work of the ancient Greek mathematicians.
Step-by-step explanation: The formula used to calculate the sphere radius is: r = ∛((3/4) · V / π) Symbols. r = Sphere radius; V = Sphere volume; π = Pi = 3.14159… The volume of Sphere. Enter the volume contained within a sphere. The radius of Sphere. This is the radius of a sphere that corresponds to the specified volume.
[tex] \sf \large \: If \: y = Sin x \: * Cos \: 2x \: Find \frac{dy}{dx} [/tex]
Thanku!
Answer:
cos (x) cos (2x) - 2sin(x) sin(2x)Solution:
(See the solution in the photo)
Answer:
[tex]\sf -5\cos \left(x\right)+6\cos ^3\left(x\right)[/tex]
explanation:
[tex]\sf y = sin(x) * cos(2x)[/tex]
[tex]\rightarrow \sf \frac{d}{dx}\left(sin\left(x\right)\ * \:\:cos\left(2x\right)\right)[/tex]
[tex]\sf \bold {Apply\:the\:Product\:Rule}:\quad \left(f\cdot g\right)'=f\:'\cdot g+f\cdot g'[/tex]
[tex]\rightarrow \sf \frac{d}{dx}\left(\sin \left(x\right)\right)\cos \left(2x\right)+\frac{d}{dx}\left(\cos \left(2x\right)\right)\sin \left(x\right)[/tex]
[tex]\sf \bold{ Apply \ differentiation \ rule \ \ \ : } \ \ \ sin(x) = cos(x) \ \ and \ \ cos(x) = -sin(x)[/tex]
[tex]\rightarrow \sf \cos \left(x\right)\cos \left(2x\right)+\left(-\sin \left(2x\right)\ * \:2\right)\sin \left(x\right)[/tex]
[tex]\rightarrow \sf \cos \left(x\right)\cos \left(2x\right)\left-2\sin \left(2x\right)\sin \left(x\right)[/tex]
[tex]\sf \bold {use \ the \ formulae \ : \ cos(2x) = 2cos^2(x) - 1} \ {and} \ \ \sf \bold{sin(x) = 2 sin x cos x}[/tex]
[tex]\rightarrow \sf cos(x) (2cos^2 (x) -1) -2(2sin(x)cos(x)sin(x))[/tex]
[tex]\rightarrow \sf 2cos^3 (x) - cos(x) - 4sin^2(x) cos(x)[/tex]
[tex]\rightarrow \sf -5\cos \left(x\right)+6\cos ^3\left(x\right)[/tex]
Which shows one way to determine the factors of 12x3 – 2x2 18x – 3 by grouping?.
The equation which shows the one way to determine the factors of provided equation by grouping is,
[tex]2x^2(6x-1)+3(6x-1)[/tex]
What is a factor of polynomial?Polynomial equations is the expression in which the highest power of the unknown variable is n (n is real number).
Factor of a polynomial is the terms in linear form, which are when multiplied together, give the original polynomial equation as result.
The provided polynomial equation is,
[tex]12x^3 - 2x^2 +18x - 3[/tex]
To factorize the above polynomial equation, make the groups, by taking out the greatest common factor.
[tex]12x^3 - 2x^2 +18x - 3\\2x^2(6x-1)+3(6x-1)\\(6x-1)(2x^2+3)[/tex]
Hence, the equation which shows the one way to determine the factors of provided equation by grouping is,
[tex]2x^2(6x-1)+3(6x-1)[/tex]
Learn more about factor of polynomial here;
https://brainly.com/question/24380382
when 8 is added to 1/3 of a number, the result is 23 find the number
Answer:
The number would be 5!
Step-by-step explanation:
23-8=15
15/3=5
Have a wonderful day!! :)
Answer:
8+x/3=23
Step-by-step explanation:
x/3=15
x=15x3=45
Convert 2.19 liters to milliliters.
Enter your answer in the box.
Hey there!
1 litres = 1000 milliliters
To find the value we multiply litres × 1000
=> 2.19 × 1000
=> 2190
Therefore, 2.19 to milliliters is 2190 millilitres
32000 divided by 14 needs to be an whole number.
Answer:2,286:L
Step-by-step explanation: you just round .
The 32000 divided by decimal 14 does not yield a whole number.
To determine if 32000 divided by 14 results in a whole number, to check if 14 is a factor of 32000. If it is, then the division will yield a whole number.
Let's divide 32000 by 14:
32000 ÷ 14 = 2285.7142857142857...
The division does not result in a whole number. The result has decimal places, indicating that 14 is not a factor of 32000.
To know more about decimal here
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#SPJ6
The number of siblings each student at a softball game has is recorded. The graph below shows the probability distribution of having any number of siblings, X, for a randomly selected student. Which number of siblings is least likely?.
The number 4 siblings are least likely to be selected
What is the number of a sibling to be selected?Probability is the likelihood of an event occurring or not. Probability value ranges from impossibility(0) to certainty(1).
The lower the value, the less likely the event is bound to occur.
From the probability distribution table, the probability of having 4 siblings at the game is 0.
This is the lowest out of all the given values in the probability distribution table. Therefore, it is the least likely event.
Thus the number 4 siblings are least likely to be selected
To know more about probability follow
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(;-;) I NEED HELP W THIS PLSSS HELP WILL MARK BRAINLIEST
Answer:
With respect to angle A, a is opposite, b is adjacent, c is the hypotenuse
With respect to angle B, b is opposite, a adjacent, and c is the hypotenuse.
Step-by-step explaination:
To find the opposite side of an angle of a right triangle - look at the side that is directly across from that angle. For example, angle A shows that the side directly across from it is side a.
To find the adjacent side of an angle of a right triangle - look at the side that is right next to it and connected to the 90 degree angle. For example, angle B shows that the side that is next to it and connected to the 90 degree angle is side b.
The hypotenuse will always be the longest side opposite the 90 degree angle.
Solve the inequality and SHOW ALL WORK Plz Help Now Due In 15 minutes
−(1+5x)−6(−1+5x)≤−65
[tex] - 1 - 5x + 6 - 30x \leqslant - 65[/tex]
[tex] - 35x + 5 \leqslant - 65[/tex]
Factoring -5
[tex] - 5(7x - 1) \leqslant - 65[/tex]
Divided sides by -5
##############################
Point :
If the sides of an inequality are multiplied by or divided by a negative number, the direction of the inequality changes and returns.
##############################
[tex] \frac{ - 5}{ - 5}(7x - 1) \geqslant \frac{ - 65}{ - 5} \\ [/tex]
[tex]7x - 1 \geqslant 13[/tex]
Plus sides 1
[tex]7x - 1 + 1 \geqslant 13 + 1[/tex]
[tex]7x \geqslant 14[/tex]
Divided sides by 7
[tex] \frac{7}{7}x \geqslant \frac{14}{7} \\ [/tex]
[tex]x \geqslant 2[/tex]
Done ♥️♥️♥️♥️♥️
Let c(t) be the number of customers in Starbucks t hours after 6:00am. Explain the meaning of the statement
Anita needs to build a house for a school project. The base of the house is a rectangle where the length of a rectangle is 8 more than the width. Its area is 240 ft sq
L = lengh
W = width
french reasoning ( hello from France ) !
The base of the house is a rectangle where the length of a rectangle is 8 more than the width.
=> L = W + 8
and
Its area is 240 ft sq
W x L = 240
L = W + 8
W x L = 240
=> W x (W+8) = 240
W² + 8W - 240 = 0
Δ = 8² - 4*1*(-240) = 32²
W' = (-8 + 32) / 2 = 12 ft
W'' = (-8 - 32) / 2 = impossible
at the end
W the width = 12 ft
and then the lengh = 12 + 8 = 20
area = 12 x 20 = 240 ft²
Four people each deliver food to people’s homes. Curtis charges a flat flee of $2.50 for each delivery plus $0.20 per mile for each mile he drives. For one delivery, Curtis drives 6 miles. How much does Curtis charge to deliver the food?
Please show your work
Answer:
$3.70
Step-by-step explanation:
0.2 x 6 = 1.2
1.2 + 2.5 = 3.7
A large container holds 7 gallons of water. It begins leaking at a
constant rate. After 8 minutes, the container has 5 gallons of
water left.
At what rate is the water leaking and After how many minutes will the container be empty?
Answer:
The container will take 25 minutes to go from full to empty.
Step-by-step explanation:
In 15 minutes, the container has lost 3 gallons of water (
5
−
2
=
3
).
Since the leak is at a constant rate, we can determine that every five minutes the container loses one gallon.
So for the container to lose the full 5 gallons will take 25 minutes (
5
×
5
=
25
A guy wire supports a cell-phone tower. The guy wire makes a 55° angle with the ground and touches the ground 34 ft from the base of the tower. What is the length of the guy wire, rounded to the nearest foot? 20 ft 28 ft 49 ft 59 ft A right triangle. The base is labeled 34 feet. The angle made between the base and the hypotenuse is labeled 55 degrees. The angle made between the base and the perpendicular is marked as a right angle.
The length of the guy wire (rounded to the nearest foot) is 20 ft. Then the correct option is A.
What is a right-angle triangle?It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.
A guy wire supports a cell phone tower.
The guy wire makes a 55° angle with the ground and touches the ground 34 ft from the base of the tower.
Base = 34 ft.
The length of the wire will be given as
[tex]\rm Wire \ length = 34 * cos\ 55^o\\\\Wire \ length = 19.5 \approx 20 \ ft[/tex]
The length of the wire is 20 ft. Then the correct option is A.
More about the right-angle triangle link is given below.
https://brainly.com/question/3770177
Answer:
is 59ft
Step-by-step explanation:
just took the test
Which equation is set up appropriately to solve for the variable y?*
1 point
W
(4y – 4)º
Z
52°
Y
Зу°
Х
MZWXY + m_YWX = m_XYW
MLZYW + m_YWX = m2WXY
ОА
B
Please don’t send me a link
Answer:
finde the equation exponent statment for the foollwing
im bad at angles pls help lol
n<DEH =
Exact form:
x = 29/2
Decimal form:
x = 14.5
Mixed number form:
x = 14 1/2
Total:
(12x+6) = 180
QUESTION 2n<HEG =
Exact form:
x = 179/7
Decimal form:
x = 25.57142857
Mixed number form:
x = 25 4/7
Total:
(7x+1) = 180
QUESTION 3n<GEF =
Exact form:
x = 91/3
Decimal form:
x = 30.3
Mixed number form:
x = 30 1/3
Total:
(6x-2) = 180
Hope it helps!!!Brainliest pls!!!Please help me ASAP!!!!!
Answer:
Since
x=−5 is a vertical line, there is no y-intercept and the slope is undefined.
Slope: Undefined
y-intercept: No y-intercept
Step-by-step explanation:
Simplify -|-5 + 2|.
7
3
-7
-3
Answer:
-3
Step-by-step explanation:
-|-5+2|
= -|-3|
= - 3
Hope it helps
Answer:
-3
Step-by-step explanation:
-|-5+2|
-|-3| absolute value of -3 is 3
-3
The graph shows information about the costs of taxi journeys in France.
For each journey, there is a fixed charge plus a charge for the distance travelled.
a) How much is the fixed charge?
Jean makes two journeys by taxi.
One journey is 6km more than the other journey.
b) Work out the difference between the costs of these two journeys.
The fixed charge is about 5 pound. For extra 6 km, extra cost is about 9 pound
What is a linear equation?A linear equation is in the form:
y = mx + b
Where m is the rate of change and b is the initial value of y.
From the graph:
The fixed charge is about 5 pound.
Using the point (0, 5) and (20, 35)
Charge per mile = (35 - 5) / (20 - 0) = 1.5 pound per mile
For extra 6 km, extra cost = 1.5 * 6 km = 9 pound
Find out more on linear equation at: https://brainly.com/question/2972832
13 The circumference of the circle and the perimeter of the rectangle are equal.
The circle has a diameter of 20 cm.
The rectangle has a length of 18 cm.
Not drawn accurately
x
20 cm
18 cm
Work out the width of the rectangle, marked x on the diagram.
cm.
Round your answer to 1 decimal place.
Help!!!
Answer:
Step-by-step explanation:
Note:
Circumference of a circle = [tex]\pi d[/tex]
Where d = diameter
We are given the diameter is 20cm, d = 20
Circumference of circle = [tex]\pi d[/tex] = 20 [tex]\pi[/tex]
Also, perimeter of a rectangle = 2 times length + 2 times width
We are told the length = 18 , width = x
Perimeter of rectangle = 2 times 18 + 2 times x
Perimeter of rectangle = 36 + 2x
The question also tells us that the circumference of the circle is EQUAL to the perimeter of the rectangle:
So this means:
Since Circumference of circle = 20[tex]\pi[/tex] ,
Perimeter of rectangle = 36 + 2x .
We can write:
Circumference of circle = perimeter of rectangle
20[tex]\pi[/tex] = 36 + 2x
Subtract 36 from both sides
20[tex]\pi[/tex] - 36 = 2x
Divide both sides by 2 to solve for "x".
x = [tex]\frac{20\pi - 36 }{2} = ?[/tex]
Plug it into your calculator and then just round it to 1 decimal place.
Please Help Its A Math Problem!! A baseball player hits a baseball 4 feet above the ground with an initial velocity of 80 feet per second.
Write an equation for this situation?
Question options:
h(t)=−16t2+80t+4
h(t)=−16t2+4t+80
h(t)=−16t2+84t
h(t)=−16t2+84
Answer: h(t)=[tex]16x^{2} \\\\[/tex]+80t+4
Step-by-step explanation:
80 if feet per second so it's 80*seconds where seconds equals t
this gets you 80*t or 80t.
You need to add 4 because that's the initial height to start with so 16x^2+80t+4
Answer:
The answer is A
Step-by-step explanation:
Find the measure of angle c in the triangle below. Then find the length of segment BC
Answer:
Step-by-step explanation:
[tex]\sqrt{54y^{11}z^{5} }[/tex]
What, do you want that thing to be answered? There is a app that does your math for you in a few seconds i hope ya know. I dont think anyone here could figure that out either.
Solve for x + 5 = 30
Answer:
25
Step-by-step explanation:
can some one help me please
Answer:
Step-by-step explanation:
i think it is reflection in the line y=-1
The bumper car ride at the state fair has 2 red cars, 3 green cars, and 3 blue cars. Janet is first in line for the ride and is assigned a car at random. Sarah is next in line and is randomly assigned a car. What is the probability that both Janet and Sarah will drive a red bumper car? Express your answer as a percent. If necessary, round your answer to the nearest tenth.
96.4%
25%
6.3%
3.6%
The probability (in percentage form) is 3.6%, so the correct option is the last one.
How to find the probability?First, Janet is assigned to a car. We want to find the probability that it is a red car. All the cars have the same probability of being assigned, then the probability of getting a red car is equal to the quotient between the number of red cars and the total number of cars:
p = 2/(8) = 1/4
Now there is 1 red car left and 7 cars in total left.
Sarah is next on line, the probability that she gets a red car will be:
q = 1/7
The joint probability (the probability of both of these events happening) is given by the product of the two individual probabilities, so we get:
P = (1/4)*(1/7) = 0.036
If we multiply this by 100%, we get:
P = 100%*0.036 = 3.6%
So the correct option is the last one.
If you want to learn more about probability, you can read:
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What is the answer for 1-n/5=12?
Answer:
n= -5
Step-by-step explanation:
1-n/5 = 12
cross 1 to the other side.
new equation :
-n/5 = 11
Multiple 5 on both sides
divide the negative sign on n on both sides
n = -55
a2 - b2 - 2a + 1 plss give me answer fast
Answer:
( a − 1 + b )( a − 1 − b )
.
Answer:
(a−1+b)(a-1−b)
Step-by-step explanation:
pls answer pls pls pls
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