Answer:
The answer to your problem is, F = 15N
Step-by-step explanation:
You have: F = ka
Where F is the force acting on the object, A is the object's acceleration and is the constant of proportionality.
Which will be our letters that we will NEED to use for today.
You can calculate the constant of proportionality by substituting F = 18 and a = 6 into the equation and solving for k: Then we can now figure out the “ formula of expression “
18 = k6
k = [tex]\frac{18}{6}[/tex]
K = 3
We would need to calculate the force when the acceleration of the object becomes 5 m/s², as following: F = 3 x 5 ( Basic math )
= F = 15
Thus the answer to your problem is, F = 15N
3. Take f(x, y) = › Y. Show that this function is differentiable at (0, 0) (you can only use the definition of differentiability). Is this function differentiable
at all points in R^2?
This function is not differentiable at all points in [tex]R^2[/tex]. To see this, consider the points on the x-axis, where y = 0. At these points, the function is not differentiable because it has a sharp corner.
To show that the function f(x, y) = |y| is differentiable at (0, 0), we need to show that there exists a linear transformation L such that:
[tex]lim (h,k) - > (0,0) [f(0+h,0+k) - f(0,0) - L(h,k)] / \sqrt{(h^2 + k^2)} = 0[/tex]
where f(0,0) = 0 since |0| = 0.
We have:
f(0+h,0+k) - f(0,0) = |k|
Now we need to find L(h,k), which is a linear transformation of (h,k) that approximates f(0+h,0+k) - f(0,0) near (0,0). We can take:
L(h,k) = 0
Since L is a constant function, it is a linear transformation. Also, we have:
f(0+h,0+k) - f(0,0) - L(h,k) = |k|
So we have:
[tex]lim (h,k) - > (0,0) [f(0+h,0+k) - f(0,0) - L(h,k)] / \sqrt{(h^2 + k^2) } = lim (h,k) - > (0,0) |k| / \sqrt{(h^2 + k^2)}[/tex]
Using the squeeze theorem, we can show that this limit is equal to 0, since[tex]|k| < = \sqrt{(h^2 + k^2)}[/tex] for all (h,k) and[tex]lim (h,k) - > (0,0)\sqrt{ (h^2 + k^2) } = 0.[/tex]
Therefore, f(x, y) = |y| is differentiable at (0,0).
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8. Brock placed a 20 foot ladder against the side of the house. The base of the ladder was 6 foot from the base of the house. How high does the ladder reach on the side of the house? Draw a picture and solve. (Round to tenth)
Step-by-step explanation:
1st i think u divide 20 and 6 and then round tht to the tenth place because we already know our answer is going to be a decimal bc 6 cant go into 20.
This data is an example of (?)
The given data is an example of a nonlinear function. Therefore, the answer is A.
The given data consists of two sets of numbers, X and Y, where each value of X has a corresponding value of Y. We can observe that the points do not lie on a straight line. Instead, the plotted points form a curved shape, which indicates that the relationship between X and Y is not a linear function.
A linear function is a function where the relationship between the input variable (X) and output variable (Y) is a straight line. In this case, we can observe that as the value of X increases, the value of Y increases at an increasing rate, which means the relationship between X and Y is not linear.
In particular, the relationship between X and Y is a quadratic function since the values of Y are the squares of the corresponding values of X.
Therefore, the answer is A.
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An amusement park has 2 drink stands and 18 other attractions. What is the probability that a randomly selected attraction at this amusement park will be a drink stand? Write your answer as a fraction or whole number.
Considering the definition of probability, the probability that a randomly selected attraction at this amusement park would be a drink stand is 1/10.
Definition of probabilityProbability establishes a relationship between the number of favorable events and the total number of possible events.
The probability of any event A is defined as the ratio between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases:
P(A)= number of favorable cases÷ number of possible cases
Probability that a selected attraction is a drink standIn this case, you know:
Total number of drink stands= 2 (number of favorable cases)Total number of other attractions= 18Total number of attraccions = Total number of drink stands + Total number of other attractions= 20 (number of possible cases)Replacing in the definition of probability:
P(A)= 2÷ 20
Solving:
P(A)= 1/10
Finally, the probability in this case is 1/10.
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More help please????
The value of sin(θ) = √15/4
The value of csc(θ) = [tex]\sqrt[4]{\frac{15}{15} }[/tex]
The value of sec(θ) = 4
The value tan(θ) = ±√15
The value of cot(θ) = ±√15/15
How to find the value using the trigonometric ratioWe can use the identity sec²(theta) - 1 = tan²(theta) to find the value of tan(theta).
Given sec(θ) = 4, we have:
sec²(θ) = 4² = 16
Then, using the identity:
tan²(θ) = sec²(θ) - 1 = 16 - 1 = 15
Taking the square root of both sides, we get:
tan(θ) = ±√(15)
Since sec(θ) is positive, we know that cos(theta), which is the reciprocal of sec(θ), is also positive. This tells us that θ is in the first or fourth quadrant, where sin(θ) is also positive.
Therefore:
sin(θ) = √(1 - cos²θ))
= √(1 - (1/16))
= √15/16)
= √(15))/4
Using the reciprocal identities, we can find the values of csc(θ) and cot(θ):
csc(θ) = 1/sin(θ)
= 4√(15)
[tex]\sqrt[4]{\frac{15}{15} }[/tex]
cot(θ)
= 1/tan(θ)
= ±√(15)/15
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At the beginning of the summer, the water level in an underground well was -3 feet. During the hot summer months, the water level fell 4 feet. The expression -3 -4 gives the water level in feet at the end of the summer.
What was the water level at the end of the summer?
Answer:
-7 feet
Step-by-step explanation:
-3-4 = -7, so it is -7 feet
1) A politician is about to give a campaign speech and is holding a 'stack of ten cue cards, of which the first 3 are the most important. Just before the speech, she drops all of the cards and picks them up in a random order. What is the probability that cards #1, #2, and #3 are still in order on the top of the stack? A) 0. 139% B) 3. 333% C) 0. 794% D) 0. 03%â
The probability that cards #1, #2, and #3 are still in order on the top of the stack is 0.03%. Therefore, the correct option is D.
To find the probability, we need to calculate the number of ways in which the first 3 cards can remain in order on the top of the stack, and divide it by the total number of ways the cards can be arranged.
The number of ways in which the first 3 cards can remain in order is 3! (3 factorial), because there are 3 cards and they can be arranged in 3! = 6 ways.
The total number of ways the cards can be arranged is 10!, because there are 10 cards and they can be arranged in 10! = 3,628,800 ways.
So, the probability is:
3! / 10! = 6 / 3,628,800 = 0.000166 = 0.0166%
We can convert it to a percentage by multiplying by 100:
0.0166 x 100 = 1.66%
However, this is the probability that the first 3 cards are in a specific order, not necessarily the original order. Since the question asks for the probability that the original order is maintained, we need to divide the probability by 3!, which gives:
0.0166 / 3! = 0.000277 = 0.0277%
This is closest to answer choice D) 0.03%.
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A third candle, in the shape of a right circular cone, has a volume of 16 cubic inches and a radius of 1. 5 inches. What is the height, in inches, of the candle? Round your answer to the nearest tenth of an inch.
The height of the right circular cone ,candle is approximately 6.8 inches.
To find the height of the third candle, which is a right circular cone with a volume of 16 cubic inches and a radius of 1.5 inches, we will use the formula for the volume of a cone: V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.
1. Substitute the given values into the formula: 16 = (1/3)π(1.5)^2h
2. Simplify the equation: 16 = (1.5^2 * π * h) / 3
3. Solve for h:
a. Multiply both sides by 3: 48 = 1.5^2 * π * h
b. Divide by π: 48/π = 1.5^2 * h
c. Divide by 1.5^2: (48/π) / 1.5^2 = h
4. Calculate the height, and round to the nearest tenth: h ≈ 6.8 inches
The height of the candle is approximately 6.8 inches.
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HELP!!! A lake currently has a depth of 30 meters. As sediment builds up in the lake, its depth decreases by 2% per year.
This situation represents [exponential growth or exponential decay]
The rate of growth or decay, r, is equal to [. 98 or. 02 or 1. 02]
So the depth of the lake each year is [1. 02 or. 98 or. 02]
times the depth in the previous year.
It will take between [11 and 12 or 9 and 10 or 3 and 4 or 5 and 6]
years for the depth of the lake to reach 26. 7 meters
This situation represents exponential decay because the depth of the lake decreases over time.
Exponential decay is a mathematical term used to describe the process of decreasing over time at a constant rate where the amount decreases by a constant percentage at regular intervals. It is a type of exponential function where the base is less than 1.
In other words, the quantity is decreasing by a fixed percentage at regular intervals.
The rate of decay, r, is equal to 0.98 because the depth decreases by 2% per year.
So the depth of the lake each year is 0.98 times the depth in the previous year. It will take between 5 and 6 years for the depth of the lake to reach 26.7 meters.
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PLEASEEEEEEEEEEEEEEEEEEE
Answer:
< 3 = 3x + 105°
Step-by-step explanation:
There is remot angle theory which is the exterior angle is congrent to the other non adjecent angle in triangle.
so <1 + <EDF = <3
(3x + 15 ) ° + 90° = <3
3x°+ 105° = <3
< 3 = 3x + 105° .... so the measur of angle 3 interms of x is 3x + 105°
Let x and y be the numbers represented on the number line.
1. Ifp is the product of x and y, what point can represent p on the number line?
2. Use the information from (1) to find the point representing qon the number line if q is the
quotient of x and y. Explain your reasoning.
To find the point representing the product p of x and y on the number line, locate x and y on the number line and find their product. To find the point representing the quotient q of x and y on the number line, locate x and the reciprocal of y (1/y) on the number line, and find their product.
If p is the product of x and y, the point on the number line that represents p can be found by locating x and y on the number line and then finding their product. For example, if x is at 2 and y is at -3, then their product p is (-6) and is located at the point on the number line that corresponds to -6 which corresponds to point P.
To find the point representing q on the number line if q is the quotient of x and y, we can use the fact that the quotient is the same as the product of x and the reciprocal of y.
In other words, q = x / y = x * (1/y). Therefore, if we locate x and 1/y on the number line, their product gives us the point representing q. For example, if x is at 4 and y is at -2, then 1/y is -1/2 and is located at -2 on the number line. The product of 4 and -1/2 is -2, which corresponds to the point on the number line that represents q.
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The Volume, V, in liters, of air in the lungs is approximated by the the model, V = -0.0374+3 +0.1525+2 +0.1729t, during a five second respiratory cycle. In here, t is measured in second
The model approximates the volume, V, in liters, of air in the lungs during a five-second respiratory cycle using the equation V = -0.0374t + 3 + 0.1525t^2 + 0.1729t.
The given equation represents a mathematical model for estimating the volume of air in the lungs during a respiratory cycle. It is a quadratic equation with three terms: -0.0374t, 0.1525t^2, and 0.1729t.
The term -0.0374t represents the linear decrease in volume over time, indicating that the volume decreases by 0.0374 liters for every second of the respiratory cycle.
The term 0.1525t^2 represents the quadratic relationship between volume and time squared, indicating that the rate of change of volume with respect to time is influenced by the square of time.
The term 0.1729t represents the linear increase in volume over time, indicating that the volume increases by 0.1729 liters for every second of the respiratory cycle.
Overall, this model provides an approximation of the volume of air in the lungs during a five-second respiratory cycle, taking into account both linear and quadratic relationships with time.
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Using the change-base formula, which of the following is equivalent to the logarithmic expression below?
log7 18
The logarithmic expression log7 18 is equivalent to log 18 / log 7 using the change-base formula.
The change-base formula states that the logarithm of a number to a certain base can be converted to the logarithm of the same number to a different base by dividing the logarithm of the number to the first base by the logarithm of the number to the second base.
In this case, we want to convert log7 18 to a logarithm with base 10. Therefore, using the change-base formula, we can write:
log7 18 = log 18 / log 7
Using a calculator, we can evaluate the right-hand side of the equation to get:
log7 18 = 1.2553 / 0.8451
log7 18 = 1.4845 (rounded to four decimal places)
Therefore, the logarithmic expression log7 18 is equivalent to log 18 / log 7, which is approximately equal to 1.4845.
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Find the sum of the first 36 terms of the following series, to the nearest integer.
7,12,17....
To the nearest integer, the sum of the first 36 terms of the given series is 3,402.
Given series is 7, 12, 17,,,. we have to find the sum of the first 36 terms of the series.
We can observe that the series is an arithmetic sequence.
Here, [tex]a_{1}=7[/tex]
d = 12 - 7 = 5
and n = 36
We know that the formula for the nth term of A.P. is
[tex]a_{n}=a_{1}+(n-1)d[/tex]
[tex]a_{36}=7+(36-1)5[/tex]
= 7 + 35*5
= 7 + 175
[tex]a_{36}=182[/tex]
We know the sum of n terms in A.P. is
[tex]S_{n}=\frac{n}{2}(a_{n}+a_{1})[/tex]
[tex]S_{36}=\frac{36}{2}(7+182)[/tex]
= 18(189)
= 3,402
Hence, the sum of the first 36 terms of the given series is 3,402.
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$3,900 at 1% compounded
annually for 6 years
_____________________________
A = P (1 + 1%) n = 3,900 (1 + 1%) ⁶= $4,139.92_____________________________
There are 160 customers at Harris Teeter. 48 of them are children.What percent of the customers at Harris Teeter are adults?
PLEASE I NEED EXPLANATION
The percent of the customers at Harris Teeter that are adults is 70%
Calculating the percentage of the customers that are adultsFrom the question, we have the following parameters that can be used in our computation:
Customers = 160
Children = 48
using the above as a guide, we have the following:
Adults = Customers - Children
substitute the known values in the above equation, so, we have the following representation
Adults = 160 - 48
So, we have
Adults = 112
Next, we have
Percentage = 112/160 * 100%
Evaluate
Percentage = 70%
Hence, the percentage is 70%
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Need help please answer
Borrar la selección
Pregunta 2: En una restaurante para 94 personas hay 19 mesas en las se pueden
sentar 4,5 o 6 personas. Si sabemos que en el total de mesas con 4 ó 5 sillas se
pueden acomodar 64 personas, ¿Cuántas mesas tienen 4 sillas?
There are 9 tables with 4 chairs in the restaurant.
Let's establish the variables:
Let x be the number of tables with 4 chairs
Let y be the number of tables with 5 chairs
Let z be the number of tables with 6 chairs
We know that there are a total of 19 tables, therefore:
x + y + z = 19 (equation 1)
We also know that the total number of people that can be accommodated in tables with 4 or 5 chairs is 64, therefore:
4x + 5y = 64 (equation 2)
We want to find the value of x, so we need to eliminate y from the equations above. We can do this by multiplying equation 2 by 4, and then subtracting it from equation 1:
x + y + z - 16x - 20y = 19 - 256
Simplifying:
-15x - 19y = -237
Dividing both sides by -19:
x = 9
Therefore, there are 9 tables with 4 chairs.
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Translated Question: Clear the selection Question 2: In a restaurant for 94 people there are 19 tables that can seat 4.5 or 6 people. If we know that the total number of tables with 4 or 5 chairs can accommodate 64 people, how many tables have 4 chairs?
How many years would it take for the price of pizza’s ($8.00) to triple with a growth rate of 1.05? Explain how you found your answer.
It would take 1.53 years for the price of pizza to triple with a growth rate of 1.05.
Calculating the number of yearsTo find the number of years it takes for the price of pizza to triple with a growth rate of 1.05, we need to use the formula for exponential growth:
A = P(1 + r)^t
Where:
A = final amount (triple the original price, or 3*$8 = $24)
P = initial amount ($8)
r = growth rate (1.05)
t = time in years
Substituting the values into the formula, we get:
$24 = $8(1 + 1.05)^t
Simplifying:
3 = (1 + 1.05)^t
Taking the logarithm of both sides with base 10:
log(3) = t*log(1 + 1.05)
t = log(3) / log(1 + 1.05)
Using a calculator, we get:
t ≈ 1.53
Therefore, it would take approximately 1.53 years for the price of pizza to triple with a growth rate of 1.05.
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As a reward for Musa's diligence and agreement, his father decided to distribute a sum of money amounting to 5,800 dinars to him and his brothers, the one with the highest average taking the largest amount, while that the one with the third rank gets an amount that is half of what the one with the first rank takes. Translate this situation as an equation with an unknown X, where X is the amount that the first rank takes. Solve the resulting equation , Solve an exact value . Gives exclusively between two consecutive natural numbers Each of the three sums
The amount that the first rank takes is 1934 dinars, and the amounts that the second and third ranks take are 967 dinars and 483.5 dinars (rounded to 484 dinars), respectively.
Let's assume that there are three brothers, including Musa. Let X be the amount of money that the brother with the highest average takes, and let Y be the amount of money that the brother with the third rank takes.
According to the given conditions, we can write the following equations:
X + Y + (5800 - X - Y) = 5800 (The total amount of money distributed should be equal to 5800 dinars)X > Y (The brother with the highest average should take the largest amount)X is an integer valueLet's simplify equation 1:
X + Y = 2900
Also, we know that:
X = (2Y + X)/2
(The amount that the third rank takes is half of what the first rank takes)
Simplifying this equation:
2X = 2Y + X
X = 2Y
Substituting this value of X in equation X + Y = 2900:
3Y = 2900
Y = 2900/3
Y ≈ 966.67
As the amount given must be a whole number between two consecutive natural numbers, we can round Y to the nearest natural number:
Y = 967
Then, X = 2Y = 2*967 = 1934
Therefore, the amount that the first rank takes is 1934 dinars, and the amounts that the second and third ranks take are 967 dinars and 483.5 dinars (rounded to 484 dinars), respectively.
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Solich sandwich shop had the following long-term asset balances as of december 31, 2021: accumulated cost depreciation book value land $ 77,000 − $ 77,000 building 442,000 $ (83,980 ) 358,020 equipment 245,000 (46,400 ) 198,600 patent 160,000 (64,000 ) 96,000 solich purchased all the assets at the beginning of 2019 (3 years ago). the building is depreciated over a 20-year service life using the double-declining-balance method and estimating no residual value. the equipment is depreciated over a 10-year useful life using the straight-line method with an estimated residual value of $13,000. the patent is estimated to have a five-year service life with no residual value and is amortized using the straight-line method. depreciation and amortization have been recorded for 2019 and 2020. problem 7-7a part 1 required: 1. for the year ended december 31, 2021, record depreciation expense for buildings and equipment. land is not depreciated. (if no entry is required for a transaction/event, select "no journal entry required" in the first account field.)
No journal entry is required for the land since it is not depreciated.
To record depreciation expense for buildings and equipment for the year ended December 31, 2021, we need to calculate the depreciation amounts for each asset based on their respective methods.
For the building, we will use the double-declining-balance method. The annual depreciation expense is calculated as (2 / 20) x $442,000 = $44,200. Since depreciation has already been recorded for 2019 and 2020, the accumulated depreciation balance for the building as of December 31, 2020 is $83,980. Therefore, the 2021 depreciation expense for the building is $44,200 - $83,980 = $(-39,780). We record this as follows:
Building Depreciation Expense: $39,780
Accumulated Depreciation - Building: $39,780
For the equipment, we will use the straight-line method. The annual depreciation expense is calculated as ($245,000 - $13,000) / 10 = $23,200. Since depreciation has already been recorded for 2019 and 2020, the accumulated depreciation balance for the equipment as of December 31, 2020 is $46,400. Therefore, the 2021 depreciation expense for the equipment is $23,200, and we record it as follows:
Equipment Depreciation Expense: $23,200
Accumulated Depreciation - Equipment: $23,200
No journal entry is required for the land since it is not depreciated.
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Geometry question I need help with:
We denote triangle ABC, angle A measures 90°, angle B measures 30° and angle C measures 60°.
We apply the cosine of 30 degrees, becuase m(∡A) = 90° and find the hypotenuse of triangle ABC:
cos = (adjacent side) / (hypotenuse)
⇔ cos B = AB/BC ⇔
⇔ cos 30° = 8√3/v ⇔
⇔ √3/2 = 8√3/v ⇔
⇔ √3 • v = 2 • 8√3 ⇔
⇔ v√3 = 16√3 ⇔
⇔ v = 16√3 ÷ √3 ⇔
⇔ v = 16 millimeters
Hope that helps! Good luck! :)
Patty and Carol leave their homes in different cities and drive toward each other on the same highway.
• They start driving at the same time.
• The distance between the cities where they live is 300 miles.
• Patty drives an average of 70 miles per hour.
. Carol drives an average of 50 miles per hour.
Enter an equation that can be used to find the number of hours, t, it takes until Patty and Carol are at the same
location.
The equation to find the number of hours, t, until Patty and Carol are at the same location is: 70t + 50t = 300.
1. Patty and Carol start driving at the same time, towards each other on the same highway.
2. The distance between their cities is 300 miles.
3. Patty drives at an average speed of 70 mph, so in t hours she covers 70t miles.
4. Carol drives at an average speed of 50 mph, so in t hours she covers 50t miles.
5. As they drive towards each other, the sum of the distances they cover should equal the total distance between their cities.
6. Therefore, combining the distances covered by Patty and Carol, we get: 70t (Patty's distance) + 50t (Carol's distance) = 300 (total distance).
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A backyard swimming pool has a diameter of 16 feet and a height of 4 feet. A hose is used to fill the pool with a flow rate of 30 gallons per minute. A. How long will it take to fill the pool? B. If h represents the depth of the water, find dh/dt
Hose will take about 63.7 minutes to fill the pool and the the depth of the water is increasing at a rate of about 0.0079 feet per minute.
First, let's find the volume of the pool. The pool is in the shape of a cylinder with a height of 4 feet and a diameter of 16 feet, so its radius is half of the diameter, or 8 feet. The volume of a cylinder is given by
V = πr^2h
Plugging in the values, we get
V = π(8 ft)^2(4 ft)
V = 256π cubic feet
Next, let's convert the flow rate to cubic feet per minute. One gallon is equal to 0.1337 cubic feet, so the flow rate is
30 gallons/min x 0.1337 ft^3/gallon = 4.011 ft^3/min
Finally, we can use the formula
time = volume/flow rate
Plugging in the values, we get
time = 256π ft^3 / 4.011 ft^3/min
time ≈ 63.7 minutes
So it will take about 63.7 minutes to fill the pool.
Let's use the formula for the volume of a cylinder again to relate the volume of the water in the pool to its depth
V = πr^2h
We can solve this formula for h
h = V/πr^2
Taking the derivative of both sides with respect to time, we get
dh/dt = d/dt (V/πr^2)
The radius of the pool does not change, so we can treat it as a constant and take it out of the derivative
dh/dt = (1/πr^2) dV/dt
We know the flow rate is constant at 4.011 cubic feet per minute, so the rate of change of the volume of water in the pool is
dV/dt = 4.011
Plugging in the values, we get
dh/dt = (1/π(8 ft)^2) (4.011 ft^3/min)
dh/dt ≈ 0.0079 ft/min
So the depth of the water is increasing at a rate of about 0.0079 feet per minute.
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Use the Evaluation Theorem to compute the following definite integrals: (a) e^3 - e (b) 0 (c) 295/6
To use the Evaluation Theorem to compute the definite integrals, follow these steps:
Step 1: Identify the function and the interval
In this case, we have three separate integrals to evaluate:
(a) ∫(e^3 - e) dx
(b) ∫0 dx
(c) ∫295/6 dx
Step 2: Find the antiderivative of the function
(a) The antiderivative of (e^3 - e) is (e^3x/3 - ex) + C.
(b) The antiderivative of 0 is simply C, where C is the constant of integration.
(c) The antiderivative of 295/6 is (295/6)x + C.
Step 3: Evaluate the antiderivative at the given interval
(a) Since no specific interval is given, we cannot evaluate the integral using the Evaluation Theorem.
(b) Since no specific interval is given, we cannot evaluate the integral using the Evaluation Theorem.
(c) Since no specific interval is given, we cannot evaluate the integral using the Evaluation Theorem.
What are definite Intregal's: Definite integral is the area under a curve between two fixed limits.we can say that the definite integral that represents the area of the surface generated by revolving the curve on the indicated interval about the x-axis. Unfortunately, without specific intervals, we cannot use the Evaluation Theorem to compute the definite integrals. Please provide the intervals for each integral, and we can help you compute them.
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Mr. Ali has 15. 8 litres of juice. He fills equal numbers of 400 ml and 1 litre juice bottles to sell. If Mr. Ali has 3200 ml of juice left,how many equal numbers of juice bottles did he fill?
Mr. Ali filled 6 of the 400 ml juice bottles and 8 of the 1 liter juice bottles.
First, convert 15.8 liters to milliliters:
15.8 L = 15,800 mL
Let x be the number of 400 ml juice bottles filled, and let y be the number of 1 liter juice bottles filled.
The total amount of juice filled can be represented as:
400 ml/bottle * x + 1000 ml/bottle * y = 15,800 ml
Simplifying, we get:
4x + 10y = 158
We also know that there are 3200 ml of juice left:
400 ml/bottle * (x - 3200/400) + 1000 ml/bottle * y = 0
Simplifying, we get:
x + 2.5y = 28
We now have two equations with two variables. Solving for x and y, we get:
x = 6
y = 8
Therefore, Mr. Ali filled 6 of the 400 ml juice bottles and 8 of the 1 liter juice bottles.
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Which triangles are similar?
OA. Triangles B and C
OB. Triangles A, B, and C
C. Triangles A and C
OD. Triangles A and B
Answer:
C. Triangles A and C.
Step-by-step explanation:
In triangles A and C, the ratios of corresponding sides are equal, and the corresponding angles are congruent.
A student drilled a hole into a six-sided die and filled it with a lead weight, then proceeded to roll the die 200 times here are the observed frequencies 27 31 42 40 28 and 32 use a 0. 05 significance level to test the claim that the outcomes are not equally likely find the test statistic x^2 and critical value for the goodness-of-fit needed to test the claim
To test the claim that the outcomes of rolling the modified die are not equally likely, we can use a chi-square goodness-of-fit test. We will use a significance level of 0.05.
The null hypothesis is that the outcomes are equally likely. The alternative hypothesis is that the outcomes are not equally likely.
First, we need to calculate the expected frequencies assuming that the outcomes are equally likely.
Since the die has six sides, each outcome has a probability of 1/6. Therefore, the expected frequency for each outcome is 200/6 = 33.33.
To calculate the test statistic [tex]x^2[/tex], we can use the formula:
[tex]x^2 = Σ (observed frequency - expected frequency)^2 / expected frequency[/tex]
where Σ is the sum over all outcomes.
Using the observed and expected frequencies given in the problem, we get:
[tex]x^2 = (27 - 33.33)^2 / 33.33 + (31 - 33.33)^2 / 33.33 + (42 - 33.33)^2 / 33.33 + (40 - 33.33)^2 / 33.33 + (28 - 33.33)^2 / 33.33 + (32 - 33.33)^2 / 33.33[/tex]
[tex]x^2 = 3.02[/tex]
The degrees of freedom for this test is 6 - 1 = 5 (since there are 6 sides on the die).
Using a chi-square distribution table (or calculator), we can find the critical value for a significance level of 0.05 and 5 degrees of freedom to be 11.070.
Since the test statistic x^2 = 3.02 is less than the critical value of 11.070, we fail to reject the null hypothesis.
Therefore, we do not have enough evidence to conclude that the outcomes of rolling the modified die are not equally likely.
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Find the area of the composite figure.Round Your Answer To The Nearest Hundreth if needed
Answer:
[tex]A = 68.75 \text{ square inches}[/tex]
Step-by-step explanation:
First, we need to identify the trapezoid's dimensions:
base 1 = 16
base 2 = 11.5
height = 5
Then, we can plug these values into the trapezoid area formula:
[tex]A = \dfrac{b_1+b_2}{2} \cdot h[/tex]
[tex]A = \dfrac{16 + 11.5}{2} \cdot 5[/tex]
[tex]A = \dfrac{27.5}{2} \cdot 5[/tex]
[tex]A = \dfrac{137.5}{2}[/tex]
[tex]\boxed{A = 68.75 \text{ square inches}}[/tex]
Ortion of
a student is randomly chosen from the group.
what is the probability that the student likes cola b and does not like cola a?
o 0.1
0.2
0.3
o 0.4
Out of the 100 students, 20 like only cola b. Therefore, the probability that a randomly chosen student likes only cola b and does not like cola a is 0.2 or 20%, which is the answer. The answer is option B.
The probability that the student likes cola b and does not like cola a can be calculated as follows
Let's start by finding the number of students who like only cola b. We know that 50 students like cola b in total, but 30 of those students also like cola a. Therefore, the number of students who like only cola b is
50 - 30 = 20
So, out of 100 students, 20 like only cola b. Therefore, the probability that a randomly chosen student likes only cola b is
P(likes only cola b) = 20/100 = 0.2
Therefore, the probability that the student likes cola b and does not like cola a is 0.2.
The answer is option B: 0.2.
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--The given question is incomplete, the complete question is given
" In a class of 100 students, 60 students likes cola a, 50 students likes cola b and 30 students likes both.
From class a student is randomly chosen from the group.
what is the probability that the student likes cola b and does not like cola a?
0.1
0.2
0.3
0.4 "--
