What are the period and amplitude of the function?
A - period: π ; amplitude: 4
B - period: π ; amplitude: 2
C - period: 2π ; amplitude: 4
D - period: 2π ; amplitude: 2
Answers
Final answer:
The amplitude of a wave is its maximum displacement from equilibrium and can be directly read from the equation as A, while the period is the time for one complete cycle, inversely related to frequency as T = 1/f. Given a frequency of 2.0 MHz, the period is 5.0 x 10⁻⁷ seconds, with the amplitude being 30 V/m.
Explanation:
The period and amplitude of a sinusoidal function can be determined from its formula or graph. For example, in the given context, if we are presented with a wave with an amplitude of 30 V/m and a frequency of 2.0 MHz, we can calculate the period. We know that the period (T) of a wave is the inverse of the frequency (f), so T = 1/f. Given the frequency of 2.0 MHz, or 2.0 x 106 Hz, the period T is 5.0 x 10-7 seconds (since 1 Hz = 1/s). The amplitude is the maximum displacement from the equilibrium position, in this case, 30 V/m. The amplitude is typically denoted by A in the wave equation y(x, t) = A sin(kx - wt + p), and the period can be derived from the angular frequency with T = 2π/ω.
For a physical representation, observing a wave plotted on a graph such as in Figure 24.8(b) or a given wave function, the amplitude is seen as the distance from the equilibrium position (center line) to the peak, and the period is the time it takes for one complete cycle of the wave. Understanding these concepts is crucial for analyzing waves whether in physics or mathematics.
Related Questions
A shopper paid $7.75 for 2.5 pounds of broccoli. What is the unit price (cost per pound) of broccoli
Answers
Answer:
$3.1
Step-by-step explanation:
7.75/2.5 = 3.1
Answer:3.1
Step-by-step explanation:
7.75/2.5=3.1
find angle ABC 8x+16+6x-60=180
Answers
Move negative 44 to the other side as a positive so equation becomes
14x=224
Divide both sides by 14
224/14 which is 16
So x is equal to sixteen
What is the approximate length of the diameter, d? *
A) 125ft
B) 80ft
C) 250ft
D) 40ft
Answers
Answer:
C) 250 feet
Step-by-step explanation:
Let the diameter of the circle be d feet.
[tex] \therefore \: C = \pi d \\ \therefore \: 250\pi = \pi d \\ d = \frac{250\pi}{\pi} \\ d = 250 \: ft[/tex]
An asymptote for a function f(x) is a straight line which is approached but never reached by f(x).
Select the appropriate response:
True
or
False
Answers
Answer:
True
Step-by-step explanation:
That is the definition of a asymptote. It is approached but will never get to the line.
Answer: True!
Step-by-step explanation:
An asymptote for a function f(x) is a straight line which is approached but never reached by f(x)
What the area of a circle with the diameter of 10 kilometers
Answers
Given:
Given that the diameter of the circle is 10 kilometers.
We need to determine the area of the circle.
Radius of the circle:
The radius of the circle can be determined using the formula,
[tex]r=\frac{d}{2}[/tex]
Substituting d = 10, we get;
[tex]r=\frac{10}{2}[/tex]
[tex]r=5[/tex]
Thus, the radius of the circle is 5 kilometers.
Area of the circle:
The area of the circle can be determined using the formula,
[tex]A=\pi r^2[/tex]
Substituting r = 5, we get;
[tex]A=(3.14)(5)^2[/tex]
[tex]A=(3.14)(25)[/tex]
[tex]A=78.5[/tex]
Thus, the area of the circle is 78.5 square kilometers.
Determine the radius, which is 5 kilometers, before calculating the area of a circle with a diameter of 10 kilometers. Next, find the area, or roughly 78.54 km², using the formula Area = π × (radius)².
How to Calculate a Circle's Area
You can use the following formula to get the area of a circle with a given diameter:
π × (radius)² equals area.
You must first determine the circle's radius. Half of the diameter is the radius. With a ten-kilometer diameter:Radius is equal to diameter / 2 (10 km / 2 = 5 km).Next, compute the area using the following formula:Area is equal to π × (radius)², π × (5 km)², and π × 25 km², or 78.54 km².Consequently, 78.54 km² is the approximate size of the circle with a diameter of 10 km.
Celia buys 1 fish and 2 portions of chips.
The total cost is £5.60
Celia and Dave share the £5.60 cost in the ratio 4 : 3
Work out how much Celia pays and how much Dave pays.
Answers
Answer:
Cecilia=£3.20
Dave=£2.40
Step-by-step explanation:
-The sum of the ratios is:
[tex]\sum{Ratios}=4+3\\\\=7[/tex]
#To find out how much each pay, your multiply the individuals ratio divide by the sum of the ratios times the cost;
[tex]Cecilia=\frac{4}[7}\times 5.60\\\\=\£3.20\\\\Dave=Total- Cecilia's\\\\=5.60-3.20\\\\=\£2.40[/tex]
Hence,Cecilia pays £3.20 and Dave pays £2.40
through: (4, -2), parallel to y = - 3/4x - 4
Answers
Answer:
y = -3/4x +1
Step-by-step explanation:
Parallel lines have the same slope, so the slope of the line you want is -3/4. The point-slope form of the equation of a line is useful when you have this information:
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
y -(-2) = -3/4(x -4)
If you want slope-intercept form, you can rearrange this ...
y +2 = -3/4x +3
y = -3/4x +1 . . . . . . subtract 2 from both sides
Brian invests $10,000 in an account earning 4% interest, compounded annually for 10 years. Five years after Brian's initial investment, Chris invests $10,000 in an account earning 7% interest, compounded annually for 5 years. Given that no additional deposits are made, compare the balances of the two accounts after the interest period ends for each account. (round to the nearest dollar) A) Chris has $766 more in his account than Brian. B) Brian has $766 more in his account than Chris. C) Chris has $1,593 more in his account than Brian. D) Brian has $1,593 more in his account than Chris.
Answers
Answer:
Brian has $776 more account in his account than Chris.
Step-by-step explanation:
Compound interest Formula:
[tex]A=P(1+r)^t[/tex]
[tex]I[/tex]= A-P
A= Amount after t years
P= Initial amount
r= Rate of interest
t= Time in year
Given that,
Brian invests $10,000 in an account earning 4% interest, compounded annually for 10 years.
Here P = $10,000 , r= 4%=0.04, t=10 years
The amount in his account after 10 years is
[tex]A=10000(1+0.04)^{10}[/tex]
=$14802.44
≈$14802
Five years after Brian's investment,Chris invests $10,000 in an account earning 7% interest, compounded annually for 5 years.
Here P = $10,000 , r= 7%=0.07, t=5 years
The amount in his account after 5 years is
[tex]A=10000(1+0.07)^{5}[/tex]
=$14025.51
≈$14026
From the it is cleared that Brian has $(14802-14026)=$776 more account in his account than Chris.
Answer:
B) Brian has $766 more in his account than Chris
Step-by-step explanation:
Compound interest formula is [tex]A = P(1+r)^{2}[/tex]
P - principal amount
r - rate of interest
t - number of years
Brian invests $10,000 in an account earning 4% interest, compounded annually for 10 years
P = 10,000
r= 4% = 0.04
t = 10
Plug in all the factors
[tex]Brian = 10000(1+0.04)^{10}= $14,802[/tex]
Chris invests $10,000 in an account earning 7% interest, compounded annually for 5 years.
P = 10,000
r= 7% = 0.07
t =5
Plug in all the factors
[tex]Chris = 10000(1+.07)^{5 } = $14,026[/tex]
$14,802 - 14,026 = $776
i need the steps for 27
Answers
This list gives facts about a library.
Study the list carefully. Then, use the drop-down menu to complete the statement
below about the list.
Width in Feet: 96
Length in Feet: 128
Bookshelves: 39
Computers: 17
Total: 280
make sense to add the items on the list because these quantities
be expressed using the same unit
The number 280
have meaning for the library
Answers
The total of 280 makes no sense because it tries to combine unrelated measurements and counts, such as library dimensions with the count of items like bookshelves and computers. Dimensions and counts are separate numerical categories and should be considered independently.
Explanation:The library dimensions, bookshelves, and computers are individual elements that depict various characteristics of the library. The sum provided i.e., 280, cannot portray any sensible information about the library because it mistakenly incorporates unrelated physical dimensions (length and width in feet) with the count of items (bookshelves and computers). This is like adding apples and oranges which, conceptually, makes no sense.
The dimensions of the library, the number of bookshelves, and the number of computers are distinct items that aren't inter-convertible or comparable as they belong to different quantitative categories. They should be considered independently to provide meaningful information about the library.
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Bobby wants to determine the most popular snack for the student at his school which question would be the best question to get statistical data?
Answers
Answer:
by taking a survey
Step-by-step explanation:
PLZ WHOEVER ANSWERS THIS ASAP GETS 20 POINTS
Answers
Answer:
Step-by-step explanation:
A random sample of 240 adults over the age of 40 found that 144 would use an online dating service. Another random sample of 234 adults age 40 and under showed that 131 would use an online dating service. Assuming all conditions are met, which of the following is the standard error for a 90 percent confidence interval to estimate the difference between the population proportions of adults within each age group who would use an online dating service?A) 1.44240 B) 1.65144240 C) 1.96144240 D) 2.75474 E) 1.65275474
Answers
The options at the end of the question are not typed properly, the correct options are given below.
A. √[144/240(1−144/240)/240] + [131/234(1−131/234)/234]
B. 1.65√[144/240(1−144/240)/240] + [131/234(1−131/234)/234]
C. 1.96√[144/240(1−144/240)/240] + [131/234(1−131/234)/234]
D. √[275/474(1−275/474)/474] + [275/474(1−275/474)/474]
E. 1.65√[275/474(1−275/474)/474] + [275/474(1−275/474)/474]
Given Information:
Confidence interval = 90%
Sample size of adults over the age of 40 = n₁ = 240
Sample size of adults under the age of 40 = n₂ = 234
Number of adults over the age of 40 who would use an online dating service = 144
Number of adults under the age of 40 who would use an online dating service = 131
Required Information:
standard error = ?
Answer:
standard error = 0.075
Step-by-step explanation:
The population proportion of adults over the age of 40 who would use an online dating service is,
p₁ = 144/240
p₁ = 0.6
The population proportion of adults under the age of 40 who would use an online dating service is,
p₂ = 131/234
p₂ = 0.56
The Standard Error is given by
SE = z*√(p₁(1 - p₁)/n₁ + p₂(1 - p₂)/n₂)
Where z is the corresponding z-score value for the 90% confidence level that is 1.65
SE = 1.65*√(0.6(1 - 0.6)/240 + 0.56(1 - 0.56)/234)
This is the equation corresponding to the correct option B given in the question.
SE = 1.65*0.0453
SE = 0.075
Therefore, 0.075 is the standard error for 90% confidence interval to estimate the difference between the population proportions of adults within each age group who would use an online dating service.
0.075 is the standard error for 90% confidence interval to estimate the difference between the population proportions of adults within each age group who would use an online dating service.
Given that,
Confidence interval = 90%
Sample size of adults over the age of 40 = n₁ = 240
Sample size of adults under the age of 40 = n₂ = 234
Number of adults over the age of 40 who would use an online dating service = 144
Number of adults under the age of 40 who would use an online dating service = 131
We have to determine,
The standard error for a 90 percent confidence interval to estimate the difference between the population proportions of adults within each age group who would use an online dating service.
According to the question,
The population proportion of adults over the age of 40 who would use an online dating service is;
[tex]P_1 = \dfrac{140}{244} = 0.6[/tex]
The population proportion of adults under the age of 40 who would use an online dating service is,
[tex]P_2 = \dfrac{131}{234} = 0.56[/tex]
Therefore, The Standard Error is given by,
[tex]Standard\ error = z \times \sqrt{\dfrac{p_1(1-p_1)}{n_1} + \dfrac{p_2 (1-p_2)}{n_2} } \\\\[/tex]
Putting all the values in the given formula,
[tex]= 1.65 \times \sqrt{\dfrac{0.16(1-0.16)}{240} + \dfrac{0.56(1-0.56)}{234} } \\\\\\= 1.65 \times \sqrt{\dfrac{0.16(0.84)}{240} + \dfrac{0.56 (0.44)}{234} } \\\\\\= 1.65 \times \sqrt{0.00056+0.0010}\\\\= 1.65 \times 0.0453\\\\= 0.075[/tex]
Hence, 0.075 is the standard error for 90% confidence interval to estimate the difference between the population proportions of adults within each age group who would use an online dating service.
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Is the data point, P, an outlier, an influential point, both, or neither?
The regression equation for a set of paired data is = –23.8 + 2x. The values of x run from 100 to 400. A new data point, P(194, 364.2), is added to the set.
a. Influential point
b. Outlier
c. Both
d. Neither
Answers
Answer:
Option a) Influential point is correct.∴ the point P(194,364.2) is an influential point.Step-by-step explanation:
Given that the regression equation for a set of paired data is = -23.8 + 2x. The values of x run from 100 to 400.
A new data point, P(194, 364.2), is added to the set.
From the given we can write it as y = -23.8+2x
Put x=194 in the above equation we get,
[tex]y(194) = -23.8+2\times 194[/tex]
[tex]=-23.8+ 388[/tex]
= 364.2
∴ y(194)=364.2Hence, point P(194,364.2) is on regression line and it is not outlier.
∴ the point P(194,364.2) is an influential point.Hence option a) Influential point is correct.Solve logx = 6.4 by changing it to exponential form.
a. X= 6.4
b. X= 6.4^10
c. X=-64
d. x= 10^6.4
answer is D
Answers
Answer:
d. x= 10^6.4
Step-by-step explanation:
[tex] log_{10}(x) = 6.4 \\ x = {10}^{6.4} \\ [/tex]
GET THIS RIGHT AND YOU'LL GET (100) POINTS
Answers
Answer:
10 13 3 12 2
Step-by-step explanation:
there is no true pattern, the numbers written out in letters are listed alphabetically in order
What happens if 0 is one of the coordinates?
Answers
Answer:
Its is just 0
Step-by-step explanation:
Answer:
Then it would be on a line
Step-by-step explanation:
6.
Find the x intercepts of the following function:
y = 2x + 3
_______
x +4
Select the appropriate response:
A) −3/9
B) −3/3
C) −3/4
D) −3/2
Answers
Answer:
D) -3/2
Step-by-step explanation:
x intercept is when y = 0
(2x + 3)/(x + 4) = 0
2x + 3 = 0
x = -3/2
3. Mrs. Prater has 42 flower seeds to plant in flower pots for her front yard. She puts 3
seeds in each pot. Each pot costs $5. What is the total cost of the flower pots?
A. $14
B. $15
C. $70
D. $630
Answers
Answer:$70
Step-by-step explanation: if there are 3 seeds in each pot, you start by dividing 42 by 3. This equals 14. This shows how many pots you will need to use up all of the seeds. So to find how much it will cost, you multiply the amount of pots by the cost of each pot. So 14 times 5, which equals 70.
United Express, a national package delivery service, charges a base price for overnight delivery of packages weighing 1 pound or less and a surcharge for each additional pound (or fraction thereof). A customer is billed $29.00 for shipping a 7-pound package and $64.00 for a 27-pound package. Find the base price and the surcharge for each additional pound.
Answers
Answer:
The base charge = $18.5 and surcharge for each pound is = $1.75
Step-by-step explanation:
Solution:
- Denote:
Base charge = $x ...... For for Weight ≤ 1 lbs
Additional charge = $y / unit pounds
- We are given that the customer is billed $29.00 for shipping a 7-pound package. We can express this statement in terms of "x" and "y".
- The 1-pound out of 7 pounds will be charged with $x and remaining 6 additional pounds of weight will be charged "$y" for each unit of weight.
$x + ( 7 - 1 )*$y = $29.00 .... Eq1
- Similarly for a receipt of $64.00 for a 27-pound package. The 1-pound out of 27 pounds will be charged with $x and remaining 26 additional pounds of weight will be charged "$y" for each unit of weight.
$x + ( 27 - 1 )*$y = $64.00 .... Eq2
- Now solve the two equations simultaneously by subtracting Eq1 from Eq2:
(26 - 6 )*$y = $(64 - 29)
20*$y = $35
y = 1.75
$x = 29 - 6*1.75
x = 18.5
- The base charge = $18.5 and surcharge for each pound is = $1.75
There
to this
equation representing the number of seconds
elapsed between the dolphin exiting and
reentering the water.
Answers
Answer:
This is nonlinear.
Step-by-step explanation:
Answer:
There are two real solutions to this equation, representing the number of seconds elapsed between the dolphin exiting and reentering the water.
Step-by-step explanation:
Need help with this work. ASAP! Thank you
Answers
Answer:
(6/5,0)
(0, 6/8)
Step-by-step explanation:
[tex]5x=6-8y[/tex]
when y = 0 x-intercept
when x = 0 y-intercept
Answer:
x-intercepts- (1.2,0)
y-intercepts- (0,0.75)
Step-by-step explanation:
Please help will mark Brainliest
Answers
Answer:
It i s 6
Step-by-step explanation:
Very six
The Greasy Spoon Restaurant offers 6 appetizers and 14
main courses. In how many ways can a person order a
two-course meal?
84
112
20
196
Answers
Answer:
84 - if they can only have an appetiser and a main course
Step-by-step explanation:
We have 6 * 14 distinct combinations.
If we could also have 2 appetisers or 2 main courses, that brings us up to 316 combinations ([tex]6*14 + 6^2 + 14^2[/tex]) - this is not an options so we do not need to consider this.
When Hailey commutes to work, the amount of time it takes her to arrive is normally distributed with a mean of 21 minutes and a standard deviation of 3.5 minutes. Out of the 211 days that Hailey commutes to work per year, how many times would her commute be between 19 and 26 minutes, to the nearest whole number?
Answers
Answer: 135 days
Step-by-step explanation:
Since the amount of time it takes her to arrive is normally distributed, then according to the central limit theorem,
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = standard deviation
From the information given,
µ = 21 minutes
σ = 3.5 minutes
the probability that her commute would be between 19 and 26 minutes is expressed as
P(19 ≤ x ≤ 26)
For (19 ≤ x),
z = (19 - 21)/3.5 = - 0.57
Looking at the normal distribution table, the probability corresponding to the z score is 0.28
For (x ≤ 26),
z = (26 - 21)/3.5 = 1.43
Looking at the normal distribution table, the probability corresponding to the z score is 0.92
Therefore,
P(19 ≤ x ≤ 26) = 0.92 - 28 = 0.64
The number of times that her commute would be between 19 and 26 minutes is
0.64 × 211 = 135 days
Answer:
135
Step-by-step explanation:
aniel Bowen borrowed $10,000 for 3 years
at 13% rate of interest. Find the simple
interest.
Answers
Answer:
fylinh rhthkrjehtegjhgjebjbebkbkbkertgbgrbkrt
Find the area of this parallelogram
Answers
Answer:
84cm^2
Step-by-step explanation:
Area of a parallelogram is Base times Height
Area = BxH
plug in
B = 14
H = 6
A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 45 pounds each, and the small boxes weigh 25 pounds each. There are 120 boxes in all. If the truck is carrying a total of 4300 pounds in boxes, how many of each type of box is it carrying?
Answers
Answer:
50(115-y) + 25y = 4125 [from eq2]
5750 - 50y + 25y = 4125 [distribute]
5750 - 25y = 4125
-25y = -1625
y = 65 [divide both sides by (-25)]
There are 65 small boxes.
Put that value into either equation (now, which is easier?) to solve for x:
x = 115 - y
x = 115 - 65
x = 50
There are 50 large boxes.
- Mring0506
The required number of boxes that the truck contain is 55 small boxes and 65 large boxes.
Given that, the large boxes weigh 45 pounds each, and the small boxes weigh 25 pounds each. There are 120 boxes in all, the truck is carrying a total of 4300 pounds.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Let the number of large boxes will be l and the number of small boxed be s,
According to the question,
l + s = 120
l = 120 - s - - - - - (2)
Again,
45l + 25s = 4300
put l in the above equation,
45[120 - s] + 25s = 4300
5400 - 45s + 25s = 4300
20s = 1100
s = 1100/20
s = 55
Now,
l = 120 - 55
l = 65
Thus, the required number of boxes that the truck contain is 55 small boxes and 65 large boxes.
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A canned food manufacturer has its manufacturing plants in three locations across a state. Their product has to be transported to 3 central distribution centers, which in turn disperse the goods to 72 stores across the state. Which of the following is most likely to be the objective function in this scenario?a. A time-series plot
b. A network graph
c. A scatter chart
d. A contour plot
Answers
The objective function in this scenario is minimizing the cost of shipping goods from the plant to the store.
What is Linear Problem?The goal of the Linear Programming Problems (LPP) is to determine the best value for a given linear function. The ideal value may be either the highest or lowest value. The specified linear function is regarded as an objective function in this situation.
The most likely goal function, if we were to create a linear programme for this situation, would be to reduce the cost of shipping from the plants to the stores. This is important since it can become an expensive bottleneck.
Despite the fact that there are three factories and three stores, the costs will not be minimized if the same amount of goods are produced in each plant and carried to a specific store. In fact, the likelihood that each facility generates a distinct volume of items further exacerbates the issue.
Finding the optimal distribution of shipping commodities from each facility to each retailer is important as a result.
Hence, the objective function is minimizing the cost of shipping goods from the plant to the store.
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The options are missing in the question, which are as follow:
a. minimizing the quantity of goods distributed across the stores
b. minimizing the cost of shipping goods from the plant to the store
c. decreasing the cost of their raw material sourcing
d. increasing the number of goods manufactured at the plant
Following the birth of a child, a parent wants to make an initial investment Upper P 0 that will grow to $70 comma 000 for the child's education at age 17. Interest is compounded continuously at 6%. What should the initial investment be? Such an amount is called the present value of $70 comma 000 due 17 years from now.
Answers
The present value, or initial investment, needed to grow to $70,000 for the child's education at age 17 with continuous compounding at 6% is approximately $25,260.21.
To calculate the initial investment, or present value, needed to grow to $70,000 for the child's education at age 17 with continuous compounding at an interest rate of 6%, we can use the formula for continuous compound interest. The formula is:
PV = FV / e^(rt)
Where PV is the present value, FV is the future value, e is Euler's number (approximately 2.71828), r is the interest rate, and t is the time period.
In this case, we have:
FV = $70,000
r = 6% or 0.06
t = 17 years
Using the formula, we can calculate the present value:
PV = 70000 / e^(0.06 * 17)
By plugging in the values into the formula and solving, we find:
PV ≈ 70000 / e^(1.02)
PV ≈ 70000 / 2.7696
PV ≈ 25260.21
Therefore, the initial investment, or present value, required to grow to $70,000 for the child's education at age 17 with continuous compounding at 6% is approximately $25,260.21.