Able Cable offers the fastest mean downloading speed among the three providers with a speed of 4.0 Mbps.
How to determine the fastest internet provider?We can calculate the mean (average) download speed for each provider and compare them to determine which company offers the fastest mean downloading speed.
Based on the given data, the mean download speed for each provider is:
City Net: (3.6 + 3.7 + 3.7 + 3.6 + 3.9) / 5 = 3.7 megabits per second (Mbps)
Able Cable: (3.9 + 3.9 + 4.1 + 4.0 + 4.1) / 5 = 4.0 Mbps
Tel-N-Net: (3.9 + 3.7 + 4.0 + 3.6 + 3.8) / 5 = 3.8 Mbps
Therefore, Able Cable offers the fastest mean downloading speed among the three providers with a speed of 4.0 Mbps.
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Sammy Speedster drives a truck for the Quick 'N Fast Delivery
Service. Every day he drives a route from Houston to San Antonio, a
distance of 200 miles. In his logbook, he keeps a record of the
amount of time it takes to drive the route.
what's a reasonable domain and range?
In this scenario, the domain would be the set of all possible values for the amount of time it takes Sammy Speedster to drive from Houston to San Antonio. Since he is driving on a daily basis, the domain could be considered a continuous range from zero to some maximum value, perhaps 10 hours.
It's possible that Sammy could complete the trip in less than 3 hours if he were driving at a very high speed, but this would not be a common occurrence. Therefore, a reasonable domain could be considered to be between 3 and 10 hours.
The range, on the other hand, would be the set of all possible distances that Sammy could drive in the allotted time. Since we know that the distance is a constant 200 miles, the range would simply be 200 miles. It's possible that Sammy could drive more than 200 miles in a day if he were assigned additional routes, but this would not be relevant to this scenario.
In summary, a reasonable domain for Sammy's logbook would be between 3 and 10 hours, and the range would be a constant 200 miles.
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PLEASE HELP ME!!!!!!!!!!!!
The relationship between the squares formed by the sides of a right triangle is defined by Pythagorean Theorem, which states that the square on the hypotenuse side is the sum of the squares on the other two sides.
How can the Pythagorean Theorem describe the relationship between the sides of a right triangle?According to Pythagorean Theorem, the square formed by the side length of the hypotenuse side of right triangle is equivalent to the sum of the squares formed by the lengths of the other two sides
Let a, b, and c represent the lengths of the sides of the right triangle, where;
a = The length of the hypotenuse side
b = The length of a leg of the right triangle
c = The length of the other leg of the right triangle
The area of each squares are therefore;
Area of the square formed by the hypotenuse side = a²
Area of the square formed by the legs = b² and c²
Therefore; a² = b² + c²
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What is the actual perimeter of the kitchen? (ft^2)
Explain
The actual perimeter of the kitchen is 8 inch
How to find the perimeterTo find the perimeter, we have to get the length of all of the sides of the kitchen
The kitchen is a rectangle
perimeter of rectangle = 2(l + b)
= 2 (2 1/4 + 1 3/4)
2(9/4 + 7/4)
2 * 4
= 8
The perimeter of the kitchen is 4 inch
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I will give brainlyest
based on the possessions you currently own and the possessions you plan on
purchasing before moving into an apartment, create a list of the contents and their value
(amount they are worth) that you would use in determining the cost of your renters insurance.
remember, if an item is not listed, then you will not be able to receive money in case it is lost or
stolen.
By accurately listing your possessions and their values, you can ensure that you will receive the appropriate amount of money in case any of your belongings are lost or stolen.
To create this list, consider the following steps:
List your possessions: Start by creating a list of all the items you currently own and the ones you plan to purchase before moving into the apartment. Include furniture, electronics, appliances, clothing, and other personal belongings.
Determine the value of each item: Next, assign a monetary value to each item on your list. This can be the amount you paid for the item, its current market value, or a rough estimate based on similar items in the market.
Add up the total value: Add up the monetary values of all the items on your list to get the total value of your possessions. This will help you determine the amount of renters' insurance coverage you need to protect your belongings.
Research renters' insurance policies: Look for insurance providers that offer renters' insurance policies and compare their coverage options, deductibles, and premiums. Choose a policy that best suits your needs and budget.
Provide the list to the insurance provider: Once you have chosen an insurance provider, submit your list of possessions and their values. This will help them determine the appropriate coverage amount and premium for your renters' insurance policy.
Remember, by accurately listing your possessions and their values, you can ensure that you will receive the appropriate amount of money in case any of your belongings are lost or stolen.
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The carpet for the office you completed cost $576. If you're using the same carpet in the new client's bedroom, how much will it cost? Round up to the nearest whole dollar. (Hint: You may want to find the area of each room and the cost of the carpet per square foot. )
The cost of a similar carpet in the client's bedroom is $225 when the area of the bedroom is 120 square feet.
Given Data:
Cost of Carpet = $576
length of office room = 16
Width of office room = 19.2
length of Bedroom = 12
Width of Bedroom = 10
We need to determine the area of the office and the bedroom. we can determine it by using the Area of a rectangle formula which is given as,
Area of a rectangle = length × width
Area of Office = length of office room × width of office room
= 16 × 19.2
= 307.2 square feet
Area of Bedroom = length of Bedroom × width of Bedroom
= 12 × 10
= 120 square feet
Therefore, the area of the office is 307.2 square feet, and the area of the Bedroom is 120 square feet.
From the above data, the area of the office is 307.2 square feet and the carpet will cost $576 for the office. we need to find the cost of the carpet for the 120 square feet bedroom, let's assume the cost as x, and cross multiply we get,
x = 120 × 576 / 307.2
x = 69120 / 307.2
x = $225
Therefore, the cost of the bedroom carpet is $225.
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Verify that the function
f(x) = -4x^2 + 12x - 4 In x attains
an absolute maximum and absolute minimum
on [1/2, 2].
Find the absolute maximum and minimum
values.
The function f(x) = -4x² + 12x - 4 attains an absolute maximum of 3 at x = 1/2 and an absolute minimum of -8 at x = 2 on the interval [1/2, 2].
To help you verify and find the absolute maximum and minimum values of the function f(x) = -4x² + 12x - 4 on the interval [1/2, 2].
Step 1: Find the critical points by taking the derivative of f(x) and setting it to 0.
f'(x) = -8x + 12
Step 2: Solve f'(x) = 0 to find critical points.
-8x + 12 = 0
x = 3/2
Step 3: Evaluate the function f(x) at the critical point and the interval's endpoints.
f(1/2) = -4(1/2)^2 + 12(1/2) - 4(1/2) = 3
f(3/2) = -4(3/2)^2 + 12(3/2) - 4(3/2) = 1
f(2) = -4(2)^2 + 12(2) - 4(2) = -8
Step 4: Compare the function values and determine the absolute maximum and minimum values.
The absolute maximum value is 3 at x = 1/2.
The absolute minimum value is -8 at x = 2.
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show, not solve for x
Answer:
Step-by-step explanation:
Jose reads his book at an average rate of
2. 5
2. 5 pages every four minutes. If Jose continues to read at exactly the same rate what method could be used to determine how long it would take him to read
20
20 pages?
To determine how long it would take Jose to read 20 pages at his average rate, you can use a proportion.
Let x be the time in minutes it would take Jose to read 20 pages.
Then, you can set up the following proportion:
2.5 pages / 4 minutes = 20 pages / x minutes
To solve for x, you can cross-multiply:
2.5 pages * x minutes = 4 minutes * 20 pages
2.5x = 80
Finally, divide both sides by 2.5 to isolate x:
x = 32
Therefore, it would take Jose 32 minutes to read 20 pages at his average rate.
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Please help, I don't understand this geometry problem!!
Nisha is looking out the window of her apartment building at a sculpture in a park across the street. The top of Nisha's window is 60 feet from the ground. The angle of depression from the top of Nisha's window to the bottom of the sculpture is 25°. What is the distance along the ground between the building and the sculpture? Round your answer to the nearest hundredth.
25.36 feet
27.98 feet
100.22 feet
128.67 feet
The distance along the ground between the building and the sculpture is approximately 27.98 feet. Rounded to the nearest hundredth, the answer is 27.98 feet.
How to calculate the distance along the ground between the building and the sculptureFrom the problem statement, we know that angle BAC is 25 degrees and AC is 60 feet. We want to find AB, which is the horizontal distance between A and B.
We can use trigonometry to find AB. Let's use the tangent function:
tan(25) = AB / AC
Solving for AB, we get:
AB = AC * tan(25)
Substituting the values we know, we get:
AB = 60 * tan(25)
Using a calculator, we get:
AB ≈ 27.98 feet
Therefore, the distance along the ground between the building and the sculpture is approximately 27.98 feet. Rounded to the nearest hundredth, the answer is 27.98 feet.
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Question content area top
Part 1
Sandra
biked
700
meters
on Friday. On Saturday,
she
biked
4
kilometers. On Sunday,
she
biked
2
kilometers,
600
meters. How many
kilometers
did
Sandra
bike over the three days
For each of the following lengths, estimate the perimeter of an isosceles right triangle whose short sides have that length
A. Length of shirt sides is 0. 75
The perimeter of an isosceles right triangle whose short sides have that length 0.75 units is 2.56 units.
Given that, an isosceles right triangle whose short sides have that length 0.75 units.
Let the longest side be x.
Here, x²=0.75²+0.75²
x²=1.125
x=√1.125
x=1.06 units
Now, the perimeter = 0.75+0.75+1.06
= 2.56 units
Therefore, the perimeter of an isosceles right triangle whose short sides have that length 0.75 units is 2.56 units.
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help mif with dis math probles pwees
For this above box plot prompt, the answer are given below.
What is the explanation for the response?Part A
From the box plots, we can see that the Red Team has the least variability and spread of times, followed by the Blue Team and then the Green Team.
The Red Team's box is the smallest, indicating that their times are more tightly clustered together.
Blue Team:
Q1: 75
Q2: 82
Q3: 87
IQR: 12
Upper fence: Q3 + 1.5IQR = 87 + 1.512 = 105
There are no outliers
Green Team:
Q1: 70
Q2: 75
Q3: 80
IQR: 10
Upper fence: Q3 + 1.5IQR = 80 + 1.510 = 95
There is one outlier at 90
Red Team:
Q1: 80
Q2: 83
Q3: 87
IQR: 7
Upper fence: Q3 + 1.5IQR = 87 + 1.57 = 98.5
There are no outliers
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A triangle has base b and height h. The base is doubled. Complete the description of how the height
must change so that the area remains the same. Complete the explanation of the reasoning.
The area of the original triangle is - 0,6 2. The area of the new triangle is
$(201)2 =
-0,1 2. Therefore, the height must be
This must equal the original area,
(select)
When the base of a triangle is doubled, the height must be halved to maintain the same area. This is because the area of a triangle is proportional to the product of its base and height. Area of the new triangle is b₁h₂.
Given that a triangle has base b and height h, and the base is doubled. We need to find how the height must change so that the area remains the same.
The area of the original triangle is (1/2) b₁h₁.
Let's assume that the original base is b₁ and the original height is h₁.
Now, the base is doubled, so the new base is 2b₁.
Using the formula for the area of a triangle, we can find the area of the new triangle as
Area of the new triangle = (1/2) × base × height
= (1/2) × 2b₁ × h₂
= b₁h₂
where h₂ is the new height of the triangle.
Since we want the area of the new triangle to be equal to the area of the original triangle, we can equate the two expressions for the area
b₁h₁ = b₁h₂
Simplifying, we get
h₂ = h₁/2
Therefore, the height must be halved when the base is doubled to keep the area of the triangle constant.
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--The given question is incomplete, the complete question is given
" A triangle has base b and height h. The base is doubled. Complete the description of how the height
must change so that the area remains the same. Complete the explanation of the reasoning.
The area of the original triangle is (1/2) b₁h₁. The area of the new triangle is 1/2 (2b₁)h₂ =_____ This must equal the original area (1/2) b₁h₁. Therefore, the height must be_____"--
(a) Determine the critical value(s) for a right-tailed test of a population mean at the
α=0. 10
level of significance with
20
degrees of freedom.
(b) Determine the critical value(s) for a left-tailed test of a population mean at the
α=0. 10
level of significance based on a sample size of
n=15.
(c) Determine the critical value(s) for a two-tailed test of a population mean at the
α=0. 01
level of significance based on a sample size of
n=11
The critical value for a right-tailed test of a population mean at α=0.10 level of significance with 20 degrees of freedom is 1.325.
The critical value for a left-tailed test of a population mean at the α=0.10 level of significance based on a sample size of n=15 is -1.345.
The critical value(s) for a two-tailed test of a population mean at the α=0.01 level of significance based on a sample size of n=11 is -2.718 and 2.718.
To find the critical values, we need to use a t-distribution table or a statistical software that provides the critical t-values for a specific level of significance and degrees of freedom.
For part (a), since it's a right-tailed test, the critical value will be positive, and we need to look for the t-value that corresponds to an area of 0.10 to the right of the mean in the t-distribution table. With 20 degrees of freedom, the critical value is 1.325.
For part (b), since it's a left-tailed test, the critical value will be negative, and we need to look for the t-value that corresponds to an area of 0.10 to the left of the mean in the t-distribution table. With 15 degrees of freedom, the critical value is -1.345.
For part (c), since it's a two-tailed test, we need to split the significance level equally between the two tails. We need to find the t-values that correspond to an area of 0.005 to the left of the mean and 0.005 to the right of the mean in the t-distribution table. With 11 degrees of freedom, the critical values are -2.718 and 2.718.
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I Need help with this (if you can’t see zoom in)
Answer: 45 (depends on what the rightmost angle is)
Step-by-step explanation:
All angles of a triangle add up to 180 degrees.
Two angle measures are provided, 100 and 35 (?)
Add up the two to get 135, and subtract from 180
180 - 135 = 45 degrees.
I might be seeing the rightmost angle measure wrong but I think it's 35, if it's not you can still apply the same strategy, just add the two given angles and subtract that from 180 to find x.
In a certain junior high school made the following expenses in raising a poultry farm: 3 large coops at ghc650 each, 1500 day old chicks at ghc75 for 100 chicks, 1000 bags of feed at ghc1.75 a bag, transport for conveying the 1000 bags of feed at 50gp per bag, druhs and vaccines at ghc120 , other expenses amounted to ghc13.60. a.) calculate the total expenditure
The total expenditure for raising the poultry farm is GHC 5458.60.
To calculate the total expenditure for raising the poultry farm, you need to sum up all the expenses:
1. Cost of 3 large coops at GHC650 each:
Total cost of coops = 3 coops * GHC650/coop
= GHC1950
2. Cost of 1500 day-old chicks at GHC75 for 100 chicks:
Total cost of chicks = (1500 chicks / 100 chicks) * GHC75
= GHC1125
3. Cost of 1000 bags of feed at GHC1.75 per bag:
Total cost of feed = 1000 bags * GHC1.75/bag
= GHC1750
4. Transport cost for conveying the 1000 bags of feed at 50gp (GHC 0.50) per bag:
Total transport cost = 1000 bags * GHC0.50/bag
= GHC500
5. Cost of drugs and vaccines at GHC120:
6. Other expenses amounted to GHC13.60.
Now, add up all these expenses to find the total expenditure:
= Cost of coops + Cost of chicks + Cost of feed + Transport cost + Cost of drugs and vaccines + Other expenses
= GHC1950 + GHC1125 + GHC1750 + GHC500 + GHC120 + GHC13.60
= GHC5458.60
So, the total expenditure is GHC5458.60.
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Find the area of the region bounded by the curve y=sin(x) and
the x-axis between x=0 and x=4pi."
The area of the region bounded by the curve y=sin(x) and the x-axis between x=0 and x=4pi is 0.
To find the area of the region bounded by the curve y=sin(x) and the x-axis between x=0 and x=4pi, we can use the following steps:
1. Determine the function: In this case, the function is y=sin(x).
2. Identify the interval: The interval is from x=0 to x=4pi.
3. Integrate the function over the given interval: We'll integrate y=sin(x) with respect to x from 0 to 4pi.
∫(sin(x) dx) from 0 to 4pi.
4. Find the antiderivative: The antiderivative of sin(x) is -cos(x).
-∫(cos(x) dx) from 0 to 4pi.
5. Apply the fundamental theorem of calculus: We'll evaluate the antiderivative at the upper limit (4pi) and subtract the antiderivative evaluated at the lower limit (0).
[-cos(4pi)] - [-cos(0)]
6. Calculate the values: cos(4pi) = 1 and cos(0) = 1.
[-1] - [-1]
7. Determine the area: The area is the difference between the values calculated in step 6.
[-1 - (-1)] = 0
The area of the region bounded by the curve y=sin(x) and the x-axis between x=0 and x=4pi is 0.
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Los 2/3 mas la edad de Juan es igual a los 3/5 menos la edad de Julia. ¿Que fraccion representa la edad de juan respecto a la edad de Julia?
The fraction representing Juan's age relative to Julia's age is -1/10. This means that Juan's age is one-tenth less than Julia's age.
Let's start by translating the given statement into an equation:
[tex]2/3J = 3/5 - 2/3Jl[/tex]
where J is Juan's age and Jl is Julia's age.
Now we can simplify this equation by first multiplying both sides by 15 (the least common multiple of 3 and 5) to get rid of the denominators:
[tex]10J = 9 - 10Jl[/tex]
Next, we can isolate J on one side of the equation by adding 10Jl to both sides:
[tex]10J + 10Jl = 9[/tex]
Finally, we can factor out a 10 from the left-hand side:
[tex]10(J + Jl) = 9[/tex]
Dividing both sides by 10, we get:
[tex]J + Jl = 9/10[/tex]
Now we can express Juan's age as a fraction of Julia's age by dividing both sides of this equation by Jl:
[tex]Jl/Jl + J/Jl = 9/10Jl[/tex]
Simplifying this, we get:
1 + J/Jl = 9/10
Subtracting 1 from both sides, we get:
[tex]J/Jl = 9/10 - 1[/tex]
[tex]J/Jl = -1/10[/tex]
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find the missing side length
Answer:
6.5
Step-by-step explanation:
Use pythagorean theorem:
[tex]a^{2} +b^{2} =c^{2}[/tex]
a=6
b=2.5
c=hypotenuse
[tex]6^{2} +2.5^{2} =c^{2}[/tex]
simplify
[tex]36 +6.25=c^{2}\\42.25=c^{2}[/tex]
take square root of both sides
[tex]c=6.5[/tex]
The missing side length is 6.5 units.
Hope this helps!
Lin's smart phone was fully charged when she started school at 8:00 a. M. At 9:20 a. M. , it was 90%
charged, and at noon, it was 72% charged.
1. When do you think her battery will die?
2. Is battery life a function of time? If yes, is it a linear function? Explain your reasoning.
1. It's impossible to determine exactly when Lin's battery will die without more information on her phone's battery capacity and usage patterns. However, we can estimate that it will likely die sometime after noon if the rate of battery drain remains constant.
2. Yes, battery life is a function of time. The longer a battery is in use, the more its charge will deplete. However, it is not necessarily a linear function as the rate of battery drain can vary depending on factors such as usage patterns, app activity, and temperature. In this specific case, it appears that the rate of battery drain may be slowing down as the percentage decrease from 90% to noon is less than the decrease from fully charged to 90%.
In calculus and related areas, a linear function is a function whose graph is a straight line, that is, a polynomial function of degree zero or one. For distinguishing such a linear function from the other concept, the term affine function is often used. A linear function from the real numbers to the real numbers is a function whose graph (in Cartesian coordinates) is a non-vertical line in the plane. The characteristic property of linear functions is that when the input variable is changed, the change in the output is proportional to the change in the input.
Linear functions are related to linear equations.
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A backyard fencing company charges difference prices for different amounts of fences.
The company charges $30 per foot for fences up to 300 feet and $25 per foot for fences over 300 feet.
a) Write a piecewise defined function for the cost of fencing a backyard.
The piecewise defined function for fencing the backyard would be 30(300) + 25(x - 300), if x > 300, or 30x, if 0 < x ≤ 300, as seen below.
What is a piecewise function?A piecewise defined function is a function that is defined by different formulas on different intervals or "pieces" of its domain. This means that the formula used to calculate the output (the function value) of the function depends on the value of the input (the independent variable).
For this particular question, let C be the cost of fencing a backyard and let x be the length of the fence in feet. Then, we can write the piecewise defined function as:
C(x) = 30x, if 0 < x ≤ 300 OR
C(x) = 30(300) + 25(x - 300), if x > 300
In other words, if the length of the fence is less than or equal to 300 feet, the cost is simply 30 times the length of the fence. If the length of the fence is greater than 300 feet, the cost is the cost of the first 300 feet (30 times 300), plus 25 times the additional length of the fence beyond 300 feet.
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Position vector = 3 ti + tj + 1/4t^2k
Time = 2
Find the velocity vector, speed, and acceleration vector of the object.
the velocity vector of the object is v(2) = 3i + j + k, the speed is sqrt(11), and the acceleration vector is a(t) = (1/2)k.
We're given the position vector and time and asked to find the velocity vector, speed, and acceleration vector of the object. Let's solve this step-by-step.
1. Differentiate the position vector with respect to time (t) to find the velocity vector:
Position vector: r(t) = 3ti + tj + (1/4)t^2k
Velocity vector: v(t) = dr(t)/dt = d(3ti)/dt + d(tj)/dt + d((1/4)t^2k)/dt
v(t) = 3di/dt + dj/dt + (1/2)tk
v(t) = 3i + j + (1/2)tk
2. Plug in the given time (t = 2) into the velocity vector to find the velocity at that time:
v(2) = 3i + j + (1/2)(2)k
v(2) = 3i + j + k
3. Find the speed by calculating the magnitude of the velocity vector:
Speed = |v(2)| = sqrt((3^2) + (1^2) + (1^2))
Speed = sqrt(9 + 1 + 1)
Speed = sqrt(11)
4. Differentiate the velocity vector with respect to time (t) to find the acceleration vector:
Acceleration vector: a(t) = dv(t)/dt = d(3i)/dt + d(j)/dt + d((1/2)tk)/dt
a(t) = 0i + 0j + (1/2)k
So, the velocity vector of the object is v(2) = 3i + j + k, the speed is sqrt(11), and the acceleration vector is a(t) = (1/2)k.
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Color the circles, so it would be certain you get an orange one.
Answer:
1 orange
Step-by-step explanation:
you just color 1 circle.
Please help!!!!!!
Carillo Industries collected $108,000 from customers in 2020. Of the amount collected, $25,000 was for services performed in 2019. In addition, Carillo performed services worth $36,000 in 2020, which will not be collected until 2021. Carillo Industries also paid $72,000 for expenses in 2020. Of the amount paid, $30,000 was for expenses incurred on account in 2019. In addition, Carillo incurred $42,000 of expenses in 2020, which will not be paid until 2021.
Whatâs the cash basis income and the accrual basis net income?
The cash basis income for Carillo Industries is $41,000 and the accrual basis net income is $35,000.
How are the income bases?
The cash basis income for Carillo Industries, based on the cash received and paid during the year, is $41,000. The accrual basis net income, based on revenue and expenses earned/incurred during the year, regardless of whether cash was exchanged, is $35,000.
In 2020, Carillo Industries collected $108,000 from customers, of which $25,000 was for services performed in 2019 and $36,000 will not be collected until 2021.
The company paid $72,000 for expenses in 2020, of which $30,000 was for expenses incurred in 2019, and $42,000 of expenses in 2020 will not be paid until 2021. By calculating the cash and accrual basis, Carillo Industries can understand its financial performance from different perspectives.
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Homeowners in different parts of the country heat their homes with liquid propane gas. The gas is stored in tanks similar to the one shown. In terms of Pi , what is the volume of the gas tank, to the nearest hundredth cubic foot?
The volume of the gas tank is given as follows:
V = 15.19π ft³.
How to obtain the volume of the cylinder?The volume of a cylinder of radius r and height h is given by the equation presented as follows:
V = πr²h.
The dimensions for this problem are given as follows:
r = 1.5 ft -> as it is half the diameter of 3 ft.h = 6.75 ft.Hence the volume of the tank is given as follows:
V = π x 1.5² x 6.75
V = 15.19π ft³.
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solve the equation
(2\3)to the power of X=16\81
I need to find the expense and percent of the budget monthly total and annual expenses please help
The job in Lubbock is better as he would have more savings
The job in Lubbock has a lower income but also lower expenses and more savings
What is a Financial Goal?A financial goal is a specific and measurable objective that an individual or organization sets for themselves to achieve with their finances. It could be anything from saving for a down payment on a house, paying off debt, building an emergency fund, or planning for retirement.
The annual expenses in Austin is $36,000
The annual expenses in Lubbock is $30,000
The job in Lubbock is better and more viable and economical
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A= l . w
x is 3 and y is 7
(xy+1) (xy-1)
Answer:
462
Step-by-step explanation:
1. Start by substituting the value of x and and
2. You then multiply the substituted value in each brace and add 1 and subtract 1 from each bracket respectively
3. After getting your final answer in each bracket multiply them
4. You then get your final answer as 462
The critical number of the function f(x) = 5x2 + 7x – 10 is The function f(x) = -2x3 + 39x2 – 240x + 2 has two critical numbers A < B with A = and B =
The critical numbers of f(x) = -2x^3 + 39x^2 - 240x + 2 are A = 5 and B = 8.
To find the critical numbers of a function, we need to find the values of x where the derivative of the function is zero or undefined.
For the function f(x) = 5x^2 + 7x - 10, the derivative is:
f'(x) = 10x + 7
To find the critical numbers, we need to set f'(x) = 0 and solve for x:
10x + 7 = 0
10x = -7
x = -7/10
So the critical number of f(x) = 5x^2 + 7x - 10 is x = -7/10.
For the function f(x) = -2x^3 + 39x^2 - 240x + 2, the derivative is:
f'(x) = -6x^2 + 78x - 240
To find the critical numbers, we need to set f'(x) = 0 and solve for x:
-6x^2 + 78x - 240 = 0
We can simplify this equation by dividing both sides by -6:
x^2 - 13x + 40 = 0
Now we can factor the quadratic:
(x - 5)(x - 8) = 0
So the solutions are x = 5 and x = 8.
To determine which critical point is A and which is B, we need to check the sign of the second derivative of f(x) at each critical point.
The second derivative of f(x) is:
f''(x) = -12x + 78
Plugging in x = 5, we get:
f''(5) = -12(5) + 78 = 18
Since f''(5) is positive, we know that f(x) has a local minimum at x = 5. Therefore, x = 5 is the critical point A.
Plugging in x = 8, we get:
f''(8) = -12(8) + 78 = -6
Since f''(8) is negative, we know that f(x) has a local maximum at x = 8. Therefore, x = 8 is the critical point B.
Therefore, the critical numbers of f(x) = -2x^3 + 39x^2 - 240x + 2 are A = 5 and B = 8.
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(3x^3 y^2)^3 (2x^4 y^2)^2
Simplify fully
NEED HELP ASAPPPP!!!!!