Answers
The graph in this problem is the graph of y = 2sin(x), not y = x, as it has a amplitude of 2.
How to define a sine function?The standard definition of the sine function is given as follows:
y = Asin(B(x - C)) + D.
For which the parameters are given as follows:
A: amplitude.B: the period is 2π/B.C: phase shift.D: vertical shift.The function in this problem has an amplitude of 2, with no phase shift, no vertical shift and period of 2π, hence it is defined as follows:
y = 2sin(x)
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Related Questions
A cylinder has a height of 5 feet. Its volume is 1,570 cubic feet. What is the radius of the cylinder? Use ≈ 3.14 and round your answer to the nearest hundredth.
Answers
The radius of the cylinder is equal to 10 feet.
How to calculate the volume of a cylinder?In Mathematics and Geometry, the volume of a cylinder can be calculated by using the following formula:
Volume of a cylinder, V = πr²h
Where:
V represents the volume of a cylinder.h represents the height of a cylinder.r represents the radius of a cylinder.By substituting the given parameters into the formula for the volume of a cylinder, we have the following;
V = πr²h
1,570 = 3.14 × r² × 5
1,570 = 15.7r²
r² = 1,570/15.7
r² = 100
Radius, r = √100
Radius, r = 10 feet.
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please assist with these questions thanks
Answers
1a. The percentage total return is -19.56%
1b. The dividend yield is 2.42%.
1c. The capital gains yield is -21.98%.
2a. The arithmetic average annual return on large-company stocks in nominal terms is 14.5%.
2b. The arithmetic average annual return on large-company stocks in real terms is 9.67%.
3a. The real return on long-term government bonds is 3.195%
3b. The real return on long-term corporate bonds is 3.291%
How to calculate the percentage total return?In Financial accounting, the percentage total return (P) can be calculated by using this formula;
P = [(Ending price - Initial price) + Dividend] ÷ Initial price
P = [(71 - 91) + 2.20] ÷ 91
P = -0.1956 or -19.56%
1b. For the dividend yield, we have:
Dividend yield = Dividend ÷ Initial price
Dividend yield = 2.20 ÷ 91
Dividend yield = 0.0242 or 2.42%
1c. For capital gains yield, we have:
Capital gains yield = (Ending price - Initial price) ÷ Initial price
Capital gains yield = (71 - 91) ÷ 91
Capital gains yield = -0.2198 or -21.98%.
Part 2.
a. The arithmetic average of annual return on large-company stocks in nominal terms is equal to 14.5%.
b. For arithmetic average annual return in real terms, we have:
(1 + 0.145) = (1 + r)(1 + 0.044)
r = (1.145/1.044) - 1
r = 9.67%
Part 3.
a. For real return on the long-term government bonds, we would apply Fisher equation:
(1 + i) = (1 + r)(1 + h)
Where:
i is the nominal interest rate.r is the real interest rate.h is the inflation rate.(1 + 0.066) = (1 + r)(1 + 0.033)
1 + r = 1.066/1.033
r = 3.195%
b. For real return on long-term corporate bonds:
(1 + 0.067) = (1 + r)(1 + 0.033)
1 + r = 1.067/1.033
r = 3.291%
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Enter the number that belongs in the green box
Answers
The angle measure that belongs in the green box is given as follows:
70.67º.
What is the law of sines?We consider a triangle with side lengths and angles related as follows, as is the case for this problem:
Side length of a is opposite to angle A.Side length of b is opposite to angle B.Side length of c is opposite to angle C.Then the lengths and the sines of the angles are related as follows:
sin(A)/a = sin(B)/b = sin(C)/c.
The relation for this problem is given as follows:
sin(x)/12 = sin(76º)/12.34
Applying cross multiplication, the missing angle measure is given as follows:
sin(x) = 12 x sine of 76 degrees/12.34
sin(x) = 0.9436.
x = arcsin(0.9436)
x = 70.67º.
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what is the square root of 1/121
Answers
Answer:
11
Step-by-step explanation:
example 11×11 = 121
therefore squreroots = 11
which of following is equal to 9\( \sqrt{64} \)\( \sqrt{100} \)\( \sqrt{121} \)\( \sqrt{81} \)
Answers
We have 4 expressions of square roots and we want to know which one is equal to 9.
We can find this by writing:
\(\sqrt[]{x}=9\)where x is the number within the square root.
Then, we can solve as:
\(\begin{gathered} \sqrt[]{x}=9 \\ (\sqrt[]{x})^2=9^2 \\ x=81 \end{gathered}\)Answer: the square root of 81 is equal to 9.
What is the difference between Earth's highest mountain and its deepest ocean canyon? What is the difference between Mars' highest mountain and its deepest canyon? Which difference is greater? How much greater is it?
Answers
earth's difference= 65,233 ft
mars difference= 101,000 ft
greater one is= mars
difference of= 35,767 ft
Gabriel receives a 25% raise at his job. If his new pay is $360.00 per week, what was he getting paid before his raise?
Answers
Answer:
360 *.25. then once you get that, subtract the new pay by the .25. 270 is the amount.
Step-by-step explanation:
360 x .25 = 90. then, you doo 360-90=270.
Anyone good with calculus? Please help.
Answers
First take a time derivative of a function describing motion,
\(\frac{d}{dt}h(t)=\frac{d}{dt}-4.9t^2+19.6t-14.6=-9.8t+19.6\).
Finding the maxima of the function is obtained by determining where the critical points are. You can find the critical points by equating the derivative with 0 and solving for t,
\(\frac{d}{dt}h(t)=0\)
\(-9.8t+19.6=0\implies t=\frac{19.6}{9.8}=\boxed{2}\).
So at 2 seconds the ball peaks in height.
To find out the height feed 2 to the function h.
\(h(2)=-4.9\cdot2^2+19.6\cdot2-14.6=\boxed{5}\).
So at 2 seconds the ball reaches maximum height of 5 meters.
Hope this helps :)
Using the information in the Box-and-Whisker plot below, what is the 2nd Quartile?
A. 5
B. 12.5
C. 20
D. 27.5
Answers
The answer would be (C) 20.
Answer:
The 2nd quartile, also known as the median, is the middle value of a dataset, or the value that separates the lower half of the data from the upper half. In a box-and-whisker plot, the 2nd quartile is represented by the line in the middle of the box.
In the given box-and-whisker plot, the 2nd quartile is 12.5, which is the middle value of the data set. This can be determined by looking at the scale on the x-axis and finding the value that is in the middle of the box.
Option B, 12.5, is the correct answer.
Step-by-step explanation:
Matt cut a circle into 8 equal sections. He drew an angle that measures the same as the total measure of 5
of the sections in the circle. What is the measure of the angle Matt drew?
The total measure of the angle Matt drew is degrees
Answers
Answer:
135
Step-by-step explanation:
Find the unit rate (constant of proportionality) of the distance traveled.
Number of hours
0.25 1.5 2.5 3
Distance traveled (km) 3 18 30 36
Answers
Answer:
12.
Step-by-step explanation:
if to re-write the given condition, then
\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)
it is clear, the required constant is 12 (12 per hour).
Erika's toy is valued at €450. Its value increased by 10% then decreases by 10% the year after. What is the value of Erika's toy after these two changes?
Answers
Answer:
€445.50-------------------------
Initial value of the toy is €450.
After 10% increase the value is:
€450 + 10% = €450*1.1 = €495After further 10% decrease the value becomes:
€495 - 10% = €495*0.9 = €445.50The final value of the toy is €445.50.
find the product in lowest terms 24/18x2/17x34/3
Answers
Answer:
Step-by-step explanation:
To find the product of the given fractions in lowest terms, we can multiply the numerators and denominators together, and then simplify the resulting fraction:
(24/18) * (2/17) * (34/3)
First, we can simplify the fractions by reducing any common factors in the numerators and denominators:
24/18 = (212)/(29) = 12/9 = 4/3
2/17 = 2/17
34/3 = (2*17)/3 = 34/3
Now we can multiply the simplified fractions:
(4/3) * (2/17) * (34/3) = (4234)/(3173) = 272/153
The product of the given fractions in lowest terms is 272/153.
Find the area of the circle. Use 3.14 for the value of pi. I need to find the radius before finding the area
Answers
Solution
Given the circle as shown below,
diameter = 10.2
\(\begin{gathered} \text{radius }=\text{ diameter/2} \\ r=\frac{d}{2}=\frac{10.2}{2}=5.1in \end{gathered}\)Area of a circle = πr²
where π = 3.14
\(\begin{gathered} A=\pi r^2 \\ A=3.14(5.1)^2 \\ A=3.14(26.01) \\ A=81.67in^2 \end{gathered}\)Therefore the area of the circle = 81.67in²
iris is playing a game at the school carnival. There is a box of marbles, and each box has a white, a green, a red, and a orange marble. there is also a spinner separated into 4 equal sections. How many outcomes are in the sample space for pulling a marble out of the box and spinning the spinner?
Answers
There are 16 outcomes in the sample space for pulling a marble out of the box and spinning the spinner.
What is probability?
Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
To find the total number of outcomes in the sample space for pulling a marble out of the box and spinning the spinner, we need to multiply the number of outcomes for each event.
The number of outcomes for pulling a marble out of the box is 4, since there are 4 marbles in the box.
The number of outcomes for spinning the spinner is 4, since there are 4 equal sections on the spinner.
To find the total number of outcomes, we multiply the number of outcomes for each event:
Total number of outcomes = Number of outcomes for pulling a marble out of the box x Number of outcomes for spinning the spinner
Total number of outcomes = 4 x 4
Total number of outcomes = 16
Therefore, there are 16 outcomes in the sample space for pulling a marble out of the box and spinning the spinner.
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If the dimensions of the gym were 24 ft. by 45 ft., how much distance did he save on one lap?
Answers
Answer:
18
Step-by-step explanation:
One trip around the gym would be 138 ft.
If we cut the diagonal, we use the Pythagorean theorem to find the distance of the hypotenuse, which is 51 ft.
One trip with the shortcut is 119 ft. (24 + 45 + 51 = 119).
Subtract 119 ft. from 138 feet and you have 18 ft. shorter route than walking the entire perimeter.
Tom bought a comic book for $5 at a discount of 20%. How much did the comic book
cost originally?
Answers
Answer:
0.4cents
Step-by-step explanation:
60 families from each school in the district were given a survey asking them their primary method of transportation. 65% of the families surveyed said they would need bus transportation. 15% of families surveyed said they would walk to school. 18% of families surveyed said they would use their own transportation (parent drop off). 2% of those surveyed did not respond. What is the sample and what is the population in this scenario?
Answers
a) The sample in this scenario is 60 families from each school in the district.
b) The population is the total number of families in the school district.
What is the sample?The sample refers to the representative subset of the population surveyed or studied to learn more about the whole population.
The sample of families surveyed = 60 families from each school in the district
The population = the number of families in the school district
The percentage of families surveyed who need bus transportation = 65%
The percentage of families surveyed who would walk to school = 15%
The percentage of families surveyed who would use own transportation = 18%
The percentage of non-respondents = 2%
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Scientists are studying a bacteria sample. The
function f(x) = 245(1.12) gives the number of
bacteria in the sample at the end of x days.
Which statement is the best interpretation of one of
the values in this function?
The initial number of bacteria is 12.
The initial number of bacteria decreases at a rate of 88% each
day.
The number of bacteria increases at a rate of 12% each day.
The number of bacteria at the end of one day is 245.
Answers
The best interpretation of one of the values of the function is that the rate increases by 12% each day.
Step-by-step explanation:
Given:
F(x)=245(1.12)^x
To Find:
statement is the best interpretation of one of the values of the function
Solution:
Depending upon the values given the statement can be developed
As the function is itself the exponential growth structure ,
In this the statement ,Growth can be significantly depends on all factor
Such as time period initial value and rate.
But here the formula is simplified as ,
Here A= initial value r=rate and t =time period
Here A=245 and 1+r=1.12
i.e r=0.12 i.e 12%
Hence the rate give the best interpretation and more information about the function and scenario.
The graph shows the distance traveled by an Olympic-level sprinter over time during a race.
Find the slope of the line, and complete the sentences below.
100 meter race graph of a diagonal line on a coordinate plane going up and to the right with Time in seconds on the x axis and Distance in meters on the y axis. The line begins at the origin and passes through the point 2 comma 20.
Answers
9514 1404 393
Answer:
slope: 10 m/srepresents speed in meters per secondStep-by-step explanation:
The slope is the change in the quantity on the vertical scale, divided by the corresponding change in the quantity on the horizontal scale.
Here, the line goes from 0 to 100 meters on the vertical scale, corresponding to a change from 0 to 10 seconds on the horizontal scale. So, the slope is ...
m = (100 m)/(10 s) = 10 m/s . . . . slope of the line
The ratio of distance to time is given the name "speed", so ...
the slope represents the sprinter's speed in meters per second.
The sum of two numbers is 56, and their difference is 10. What are the numbers?
ОА.
33 and 23
OB.
30 and 26
OC.
20 and 36
OD
20 and 30
Answers
\(\huge\mathtt\purple{Answer :- }\)
Given :- Sum of the two numbers = 56Difference between the two numbers = 10To Find :- Two numbers Solution :-Let the two numbers be 'm' and 'n'
Now we can get,
1) m + n = 56
2) m - n = 10
1) First we will solve the first equation,m + n = 56
n = 56 - m
2) Now, solve the second equation,m - n = 10
By substituting n = 56 - m we get,
m - (56 - m) = 10
56 - m - m = 10
56 - 2m = 10
-2m = 10 - 56
-2m = -46
m = - 46/-2
m = 23Now, we will find 'n' by the equation 1 ,
n = 56 - m
n = 56 - 23
n = 33Hence, The two numbers are (A) 23 and 33 Let's verify :-33 + 23 = 56
33 - 23 = 10
Hence, verified
6th grade math i mark as brainliest
Answers
Answer:
16
Step-by-step explanation:
Find the probability that a randomly chosen point in the figure lies in the shaded region. Round your
answer to the nearest hundredth
Please help !
Answers
Answer:
0.31
Step-by-step explanation:
the area of shaded region =
(2×½×8×10) = 80
the total area of fig. =
½×(34+18)×10 = 260
the probability = 80/260 = 0.31
A cylinder has a base diameter of 16 feet and a height of 4 feet.
Answers
Answer:
Step-by-step explanation:
radius = 16/2 = 8
Then you can apply the formula to calculate the base area, lateral surface or surface or even perimeter
268 cubic feet
Step-by-step explanation:
=PI 8^2 (3/4)
A straight line is given as 2 x+4 -2 y-5=-3 z-6 (a) Determine the vector equation of the straight line. (b) Find the intersection point between the straight line with the plane yz
Answers
Answer:
a) r(t) = (10, 5, -5) + (5, 5, 0)*t
b) (0, -5, -5)
Step-by-step explanation:
a) 2x + 4 -2y -5 = -3z -6
2x - 2y +3z +5 =0
(10, 5, -5)
(15, 10, -5)
(5, 5, 0)
r = (10, 5, -5) + (5, 5, 0)*t
b) The yz plane is given by the equation x = 0.
x = 0 in the vector equation of a straight line if and only if t = -2, than r ( - 2) = (0, -5, -5) is the desired intersection point.
The average groundhog weighs about 8 pounds and eats 1/3 of their weigh each day in apples, beans, clover, bark, and flowers. If a den has five groundhogs living in it, how many pounds of vegetation will the group eat in the month of February if it isn't a leap year?
Answers
Answer: Vegetable consumption per month is 17.33 pounds and fruits consumption per month is 10.47 pounds.
Step-by-step explanation:
How many two-digit, positive integers can be formed from the digits 1, 3, 5, and 9, if no digit is repeated?
24
16
12
Answers
Answer:
12
Step-by-step explanation:
Using Permutation Formula :
⁴P₂4! / 2!4 x 3 x 2! / 2!4 x 312Jocelyn bought 45 whistles at a store. Each whistle cost $0.59 . What was the total cost of the whistles Jocelyn bought
Answers
Multiply the number of whistles (45) by the cost of each whystle ($0.59)
45 x 0.59 = $26.55
Total cost = $26.55
The equation T^2=A^3 shows the relationship between a planets orbital period, T, and the planets mean distance from the sun, A in astronomical units, AU. If planet y is twice the mean distance from the sun as planet x. by what fsctor is the orbital period increased?
Answers
Answer:
2 * A^(3/2).
Step-by-step explanation:
Given that planet y is twice the mean distance from the sun as planet x, we can denote the mean distance of planet x as "A" and the mean distance of planet y as "2A".
The equation T^2 = A^3 represents the relationship between the orbital period (T) and the mean distance from the sun (A) for a planet.
Let's compare the orbital periods of planet x and planet y using the equation:
For planet x:
T_x^2 = A^3
For planet y:
T_y^2 = (2A)^3 = 8A^3
To find the factor by which the orbital period is increased from planet x to planet y, we can take the square root of both sides of the equation for planet y:
T_y = √(8A^3)
Simplifying the square root:
T_y = √(2^3 * A^3)
= √(2^3) * √(A^3)
= 2 * A^(3/2)
Now, we can express the ratio of the orbital periods as:
T_y / T_x = (2 * A^(3/2)) / T_x
As we can see, the orbital period of planet y is increased by a factor of 2 * A^(3/2) compared to the orbital period of planet x.
Therefore, the factor by which the orbital period is increased from planet x to planet y depends on the value of A (the mean distance from the sun of planet x), specifically, it is 2 * A^(3/2).
Solve the following system of equations.
-4x-5y=6
9x+7y=12
Answers
The values of x is 6 and y is (-6).
What is Solution of Equation?An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.
Given:
-4x-5y=6............(1)
9x+7y=12..................(2)
Solving Equation (1) and (2) we get
-36 x - 45y = 54
36x + 28y = 48
____________
-17y= 102
y= -6.
and, -4x -5y= 6
-4x - 5(-6) = 6
-4x + 30 = 6
-4x = 6-30
-4x = -24
x= 6
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