The volume of the fish tank is approximately 3,693,142,608 cubic inches
How to solveTo find the volume of the rectangular prism-shaped fish tank, we need to multiply its width, length, and height.
Given the dimensions are 2014 inches wide, 1012 inches long, and 1812 inches tall, the calculation is as follows:
Volume = Width × Length × Height
Volume = 2014 in × 1012 in × 1812 in
Upon calculating the product, we get:
Volume ≈ 3,693,142,608 cubic inches
The volume of the fish tank is approximately 3,693,142,608 cubic inches
N.B: None of the answer choices has the correct answer.
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How do you solve for average daily balance?
Therefore , the solution of the given problem of unitary method comes out to be (Sum of Daily Balances) / Average Daily Balance (Number of Days in Period).
Definition of a unitary method.The well-known minimalist approach, current variables, and any crucial elements from the initial Diocesan tailored query can all be used to accomplish the work. In response, you can be granted another chance to utilise the item. If not, important impacts on our understanding of algorithms will vanish.
Here,
You must be aware of an account's daily balance over a specific time period in order to determine the average daily amount. how to get an average daily balance:
The time frame for which you wish to compute the average daily balance should be chosen. This could, for instance, be a month, a quarter, or a year.
Find the account balance at the end of each day during the specified period.
Sum up each day's balance for the duration.
By the number of days in the time frame, divide the sum. You are then given the daily average balance.
The formula for determining the typical daily balance is as follows:
=> (Sum of Daily Balances) / Average Daily Balance (Number of Days in Period)
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The average price of a two-bedroom apartment in the uptown area of a prominent American city during the real estate boom from 1994 to 2004 can be approximated by p(t) = 0.17e⁰.¹⁰ᵗ million dollars (0 ≤ t ≤ 10) where t is time in years (t = 0 represents 1994). What was the average price of a two-bedroom apartment in this uptown area in 2002, and how fast was it increasing? (Round your answers to two significant digits.) p(8) = $ million p' (8) = $ million per yr
In 2002, the average price of a two-bedroom apartment in the uptown area was approximately $0.316 million, and it was increasing at a rate of about $0.0328 million per year.
To find the average price of a two-bedroom apartment in 2002 (t=8), you need to evaluate the given function p(t) = 0.17e^(0.10t) at t=8:
p(8) = 0.17e^(0.10 * 8)
p(8) = 0.17e^0.8 ≈ 0.316 million dollars
To find the rate at which the price was increasing in 2002, you need to find the derivative of the function p(t) with respect to t, and then evaluate it at t=8:
p'(t) = d/dt (0.17e^(0.10t))
p'(t) = 0.17 * 0.10 * e^(0.10t)
Now, evaluate p'(t) at t=8:
p'(8) = 0.17 * 0.10 * e^(0.10 * 8)
p'(8) ≈ 0.0328 million dollars per year
So, in 2002, the average price of a two-bedroom apartment in the uptown area was approximately $0.316 million, and it was increasing at a rate of about $0.0328 million per year.
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Find the absolute maximum and absolute minimum values off on each interval. (If an answer does not exist, enter DNE.) f(x) = -2x2²+ 8x + 400 (a) (-5, 11 ) Absolute maximum Absolute minimum: (b) (-5, 11 ) IN Absolute maximum: Absolute minimum: (C) (-5, 11) Absolute maximum: Absolute minimum:
The absolute maximum value of the function on the interval (-5, 11) is 670, which occurs at x = -5, and the absolute minimum value is approximately 400.847, which occurs at x ≈ 1.154.
To find the absolute maximum and minimum values of the function f(x) = -2x^3 + 8x + 400 on the interval (-5, 11), we need to consider the critical points and the endpoints of the interval.
First, we find the derivative of the function:
f'(x) = -6x^2 + 8
Setting f'(x) = 0 to find the critical points, we get:
-6x^2 + 8 = 0
x^2 = 4/3
x = ±√(4/3)
Since only √(4/3) is within the interval (-5, 11), this is the only critical point we need to consider.
Next, we evaluate the function at the endpoints of the interval:
f(-5) = -2(-5)^3 + 8(-5) + 400 = 670
f(11) = -2(11)^3 + 8(11) + 400 = -1666
Finally, we evaluate the function at the critical point:
f(√(4/3)) = -2(√(4/3))^3 + 8(√(4/3)) + 400 ≈ 400.847
Therefore, the absolute maximum value of the function on the interval (-5, 11) is 670, which occurs at x = -5, and the absolute minimum value is approximately 400.847, which occurs at x ≈ 1.154.
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A bag of fertilizer at Home Depot is labeled: 4-lb bag Scotts 20-27-5 Starter Fertilizer 5,000 Sq. Ft. $12. 98 each. You just resodded your lawn and the salesman at Home Depot says this is the fertilizer your new lawn needs. Your lawn is 7400 sq. Ft. And you plan on fertilizing it twice this year. How many bags should you buy for the year?
The total number of bags farmers need to buy to fertilize the lawn twice a year is 3.
The label on the fertilizer bag is 4lb bag can fertilize 5000 Sq. Ft.
4lb = 5000
1lb = 5000/4
1lb = 1250
1lb bag can fertilize 1250 Sq. Ft.
To fertilize 7400 sq. Ft. lawn twice a year
Total = 7400 + 7400
Total = 14800
No. of 1lb bag can need to fertilize 14800 sq. Ft. lawn = 14800/1250
No. of 1lb bag can need to fertilize 14800 sq. Ft. lawn = 11.84
As each bag is 4lb
No. of bags needed = 11.84/4
No. of bags needed = 2.96 ≈ 3
Total no. of bag needed is 3
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A certain product is marked down to $82. 81 after a 15. 5% decrease. Determine the original price. (4 points)
$69. 90
$92. 50
$98. 00
$128. 35
The original price of the product was approximately $98.00.
How to determine the original price of a product after a given markdown?To determine the original price before the 15.5% decrease, we can use the following equation:
Original price - (15.5% of original price) = $82.81
Let's solve for the original price:
Original price - (0.155 * Original price) = $82.81
Simplifying the equation:
0.845 * Original price = $82.81
Dividing both sides by 0.845:
Original price = $82.81 / 0.845
Calculating the original price:
Original price ≈ $98.00
Therefore, the original price of the product was approximately $98.00.
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Using the probability distribution represented by the graph
below, find the probability that the random variable, X, falls
in the shaded region.
Using probability, we can find probability of the random variable, x falling in the shaded region as to be 5/8.
Define probability?Probability is the ratio of favourable outcomes to all other potential outcomes of an event. The symbol x can be used to express the quantity of successful outcomes for an experiment with 'n' outcomes. The following formula can be used to determine an event's probability.
Positive Outcomes/Total Results = x/n = Probability(Event)
Let's look at a simple example to better understand probability. Imagine that we need to predict whether it will rain or not. The right response to this question is "Yes" or "No." Whether it rains or not is uncertain. Probability is used to predict the outcomes when tossing coins, rolling dice, or drawing cards from a deck of cards.
Here in the question,
Total region = 8.
Shaded region = 5
So, probability of falling in the shaded region = 5/8
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What is the scale factor for the similar figures below?
The value of the scale factor for the similar figures is 1/3
What is the scale factor for the similar figures?From the question, we have the following parameters that can be used in our computation:
The similar figures
The corresponsing sides of the similar figures are
Original = 12
New = 4
Using the above as a guide, we have the following:
Scale factor = New /Original
substitute the known values in the above equation, so, we have the following representation
Scale factor = 4/12
Evaluate
Scale factor = 1/3
Hence, the scale factor for the similar figures is 1/3
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Karoline needs to jog 30.5
miles over the next 7
days to train for a race.
She plans to jog 4.25
miles each day.
Answer: 7x=30.5
Step-by-step explanation: If you were to answer this equation with the given information it would not be correct. 7(4.25)=29.75. You need to go through BEDMAS to answer this.
You what you need to do is divide 30.5 by 7 to get the amount she needs to jog for a week, if you do that you get 4.37 miles each day to get to 30.5 in a week.
Find the lateral area of the rectangular prism with height h, if the base of the prism is:
Square with the side 2 cm and h=125mm
The lateral area of the rectangular prism with base square with the side 2 cm and height 125 mm is 10,000 mm².
How to find the lateral area of rectangular prism?To calculate the lateral area of a rectangular prism, we need to add up the areas of all its lateral faces.
In this case, the base of the prism is a square with side length 2 cm. Since there are four lateral faces on a rectangular prism, and each lateral face of the rectangular prism is a rectangle, we know that the length and width of each lateral face is equal to the height of the prism, which is 125 mm.
First, let's convert the side length of the base to millimeters to match the unit of the height:
2 cm = 20 mm
Now, we can calculate the lateral area of the rectangular prism as follows:
Lateral area = 4 x (length x height)
= 4 x (20 mm x 125 mm)
= 10,000 mm²
Therefore, the lateral area of the rectangular prism with base square with the side 2 cm and height 125 mm is 10,000 mm².
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(-2+3)x[4-(-8)] find x
Answer:
x = (-2 + 3) * (4-(-8))
Step-by-step explanation:
Ali uses 21/2 scoops of drink mix to make 10 cups of drinks how much drink mix which you need to use to make one cup of the drink
The drink mix that is needed to make one cup of drink is 21/20
How to calculate the amount of drink mix needed to make a cup of drink?Ali uses 21/2 scoops of drink mix to make 10 cups off drinks
The amount of drink mix needed to make one cup can be calculated as follows
21/2= 10
x= 1
cross multiply both sides
10x= 21/2
Divide by the coefficient of x which is 10
x= 21/2 ÷ 10
x= 21/2 × 1/10
x= 21/20
Hence the drink mix needed to make one cup is 21/20
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As President of Spirit Club, Rachel organized a "Day of Decades" fundraiser where students could pay a fixed amount to dress up as their favorite decade. Of the 19 students who participated, 15 of them dressed up as the '40s.
If Rachel randomly chose 16 of the participants to take pictures of for the yearbook, what is the probability that exactly 13 of the chosen students dressed up as the '40s?
Write your answer as a decimal rounded to four decimal places.
The probability of choosing exactly 13 students who dressed up as the 40s out of the 16 selected students is approx. 0.4334.
What is the probability of choosing exactly 13 students who dressed up as the 40s?We can model this situation as a hypergeometric distribution, where we have a population of 19 students, 15 of whom dressed up as the 40s.
We want to choose a sample of 16 students and find the probability that exactly 13 of them dressed up as the '40s.
The probability of choosing exactly 13 students who dressed up as the 40s can be calculated:
(number of ways to choose 13 students who dressed up as the 40s) * (number of ways to choose 3 students who dressed up as other decades) / (total number of ways to choose 16 students)
The number of ways to choose 13 students who dressed up as the '40s is the number of combinations of 15 choose 13:
(15 choose 13) = 105
The number of ways to choose 3 students who dressed up as other decades is the number of combinations of 4 choose 3, which is:
(4 choose 3) = 4
The total number of ways to choose 16 students from 19 is the number of combinations of 19 choose 16, which is:
(19 choose 16) = 969
105 * 4 / 969 = 0.4334
Therefore, the probability of choosing exactly 13 students who dressed up as the 40s = 0.4334 (rounded to four decimal places)
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6. A certificate of deposit (CD) pays 2. 25% annual interest compounded biweekly. If you
deposit $500 into this CD, what will the balance be after 6 years?
The balance of the CD after 6 years will be $678.35.
To calculate the balance of the CD after 6 years, we need to use the formula:
[tex]A = P(1 + r/n)^{(nt)[/tex]
Where:
A = the balance after 6 years
P = the initial deposit of $500
r = the annual interest rate of 2.25%
n = the number of times the interest is compounded per year (biweekly = 26 times per year)
t = the number of years (6)
Plugging in the values, we get:
A = [tex]500(1 + 0.0225/26)^{(26*6)[/tex]
A = 500(1.001727)¹⁵⁶
A = 500(1.3567)
A = $678.35
Therefore, the balance of the CD after 6 years will be $678.35.
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Complete the table to find the derivative of the function Original Function Rewrite 3 y = 2 (2x)-2 12 Differentiate Simplify 1 24x X
The derivative of the function y = 2(2^x)-2 is 12 * 2^x ln(2) or 12ln(2)x(2^x-1).
To find the derivative of the function y = 2(2^x)-2, we will use the power rule and the chain rule of differentiation.
Apply the power rule to the function y = 2(2^x)-2. The power rule states that if f(x) = x^n, then f'(x) = nx^(n-1).
y' = [2(2^x)-2]'
= 2[(2^x)-2]'
= 2ln(2^x)'
Apply the chain rule to (2^x)'. The chain rule states that if f(x) = g(h(x)), then f'(x) = g'(h(x))h'(x). In this case, g(x) = 2^x, so g'(x) = ln(2)*2^x.
y' = 2ln(2^x)'
= 2ln(2^x)
= 2ln(2)x(2^x-1)
Therefore, the derivative of the function y = 2(2^x)-2 is 12 * 2^x ln(2) or 12ln(2)x(2^x-1).
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Which points lie on the graph of the inverse of f(x)=5x−2?
Select all that apply.
Points lie on the graph of the inverse of f(x)=5x−2.
Hence, the correct option is C,E,F.
To find the points on the graph of the inverse of f(x), we need to switch the x and y coordinates of each point on the graph of f(x). Then, we can simplify the equation to isolate y and get the inverse function.
f(x) = 5x - 2
y = 5x - 2 (replace f(x) with y)
x = 5y - 2 (switch x and y)
x + 2 = 5y (add 2 to both sides)
y = (x + 2)/5 (divide both sides by 5)
So, the inverse function of f(x) is
[tex]f^{-1}[/tex](x) = (x + 2)/5
Now, we can substitute each point from the given options into the inverse function to see if it lies on the graph of the inverse of f(x).
1. (0, -2)
[tex]f^{-1}[/tex](0) = (0 + 2)/5 = 2/5
No, this point does not lie on the graph of the inverse of f(x).
2. (1, 3)
[tex]f^{-1}[/tex](1) = (1 + 2)/5 = 3/5
No, this point does not lie on the graph of the inverse of f(x).
3. (-2, 0)
[tex]f^{-1}[/tex](-2) = (-2 + 2)/5 = 0
Yes, this point lies on the graph of the inverse of f(x).
4. (2/5, 1)
[tex]f^{-1}[/tex](2/5) = (2/5 + 2)/5 = 6/25
No, this point does not lie on the graph of the inverse of f(x).
5. (0, 2/5)
[tex]f^{-1}[/tex](0) = (0 + 2)/5 = 2/5
Yes, this point lies on the graph of the inverse of f(x).
6. (3, 1)
[tex]f^{-1}[/tex](3) = (3 + 2)/5 = 1
Yes, this point lies on the graph of the inverse of f(x).
Therefore, the points that lie on the graph of the inverse of f(x) are (-2, 0), (0, 2/5) and (3, 1),
Hence, the correct option is C,E,F.
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The scale factor for a set of values is 4. If the original measurement is 9, what is the new measurement based on the given scale factor?
The new measurement based on the given scale factor of 4 is 36. The scale factor is the ratio of the new size of an object to its original size. In this case, the scale factor is 4, which means the new size is 4 times larger than the original size.
If the original measurement is 9, then the new measurement can be calculated by multiplying the original measurement by the scale factor.
New measurement = Original measurement x Scale factor
New measurement = 9 x 4
New measurement = 36
Therefore, the new measurement based on the given scale factor of 4 is 36.
To explain it further, imagine you have a drawing that is 9 inches wide. If you were to increase the scale factor to 4, the new drawing would be 4 times larger, which means it would be 36 inches wide. This concept is commonly used in architecture, engineering, and other fields where scaling drawings or models is necessary to represent them accurately. Understanding scale factors is important in order to make accurate and proportional changes to objects and designs.
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Ben's Barbershop has a rectangular logo for their measuresb 7 1/5 feet long with an area that is exactly the maximum area allowed by thr building owner.
Create an equation that could be used to determine M, the unknown side length of the logo
An equation that could be used to determine M, the unknown side length of the logo is X = (36/5) x M
Let's assume that the unknown side length of the logo is 'M'. The logo is a rectangle, and the area of a rectangle is given by multiplying its length and width. Since we know the length of the logo is 7(1)/(5) feet, we can write the equation:
A = L x W
where A is the area of the logo, L is the length of the logo, and W is the width of the logo.
Substituting the given values, we get:
A = (7(1)/(5)) x M
or
A = (36/5) x M
Now, we know that the area of the logo is exactly the maximum area allowed by the building owner. Let's assume this maximum area is 'X'. So, we can write another equation:
A = X
Combining both equations, we get:
X = (36/5) x M
This is the required equation that could be used to determine the unknown side length 'M' of the logo if we know the maximum area allowed by the building owner 'X'.
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Suppose a particle moves along a continuous function such that its position is given by f(t)=1/7 t^3-4t-12 where f is the position at time t, then determines the value of r such that f(r)=0.
When we look at [tex]f(t)=1/7 t^3-4t-12[/tex], this is a cubic equation, and solving it analytically is not straightforward.
How to solveTo find the value of r such that f(r) = 0, we need to solve the equation:
[tex]1/7 r^3 - 4r - 12 = 0[/tex]
This is a cubic equation, and solving it analytically is not straightforward.
Yet, it is possible to obtain the value of r that meets the equation using numerical schemes such as Newton-Raphson or bisection. Additionally, one can take advantage of calculation tools and graphical software to calculate an estimation of r.
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For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 40 N acts on a certain object, the acceleration
of the object is 10 m/s². If the force is changed to 36 N, what will be the acceleration of the object?
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
1 The Shake Shop sells their drinks in cone-shaped cups that are 7 inches tall The small size has a diameter of 3 inches, and the large size has a diameter of 5 inches. Use 3. 14 for a 7 in a What is the volume of the small shake to the nearest tenth?
The volume of small cone-shaped cups is 11.8 in³.
To find the volume of the small shake in a cone-shaped cup that is 7 inches tall and has a diameter of 3 inches, we can use the formula for the volume of a cone:
V = 1/3 πr²h
where V = volume
r = radius
h = height of the cone
Given, diameter of come is 3 inches
We know r = d/2
r = 3/2
= 1.5
Substituting the value in the formula
V = 1/3 × 3.14 × 7 × (1.5)²
= 11.78
Rounding to nearest tenth
V = 11.8
Hence, the volume of small cone-shaped cups is 11.8 in³.
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Bricks are going to be packed into a crate which has a space inside of 2.8m3. The volume of each brick is 16000cm3. Given that an exact number of bricks that can be packed into the crate. how many bricks can it hold
The crate can hold 175 bricks.
What is the maximum number of bricks that can be packed into a crate with an internal volume of 2.8 m³, given that the volume of each brick is 16000 cm³?
First, we need to convert the volume of the crate from cubic meters to cubic centimeters because the volume of each brick is given in cubic centimeters.
1 m = 100 cm
Volume of crate = 2.8 m3 = 2.8 x (100 cm)3 = 2,800,000 cm3
Now we can find the number of bricks that can be packed into the crate by dividing the volume of the crate by the volume of each brick:
Number of bricks = Volume of crate / Volume of each brick
= 2,800,000 cm3 / 16,000 cm3
= 175 bricks
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Plot the points A(-2,1), B(-6, -9), C(-1, -11) on the coordinate axes below. State the
coordinates of point D such that A, B, C, and D would form a rectangle. (Plotting
point D is optional.)
The value of the coordinates of point D is, (3, - 1)
We have to given that;
All the coordinates of rectangles are,
A(-2,1), B(-6, -9), C(-1, -11)
Now, Let the fourth coordinate of rectangle is,
D (x, y)
Hence, Midpoint of AC and BD are same.
So., Midpoint of AC is,
⇒ AC = (- 2 + (- 1))/ 2, (1 + (- 11))/2
= (- 3/2 , - 5)
And, Midpoint of BD,
⇒ BD = (- 6 + x)/2, (- 9 + y)/2
By comparing;
⇒ (- 6 + x)/2 = - 3/2
⇒ - 6 + x = - 3
⇒ x = - 3 + 6
⇒ x = 3
⇒ (- 9 + y)/2 = - 5
⇒ - 9 + y = - 10
⇒ y = -10 + 9
⇒ y = - 1
Thus, The value of the coordinates of point D is, (3, - 1)
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37% of 42 is equal to 74% of what number?
Answer: 50
Step-by-step explanation:
37 is 74 percent of what number
We already have our first value 37 and the second value 74. Let's assume the unknown value is Y which answer we will find out.
As we have all the required values we need, Now we can put them in a simple mathematical formula as below:
STEP 1 37 = 74% × Y
STEP 2 37 = 74/100× Y
Multiplying both sides by 100 and dividing both sides of the equation by 74 we will arrive at:
STEP 3 Y = 37 × 10074
STEP 4 Y = 37 × 100 ÷ 74
STEP 5 Y = 50
Finally, we have found the value of Y which is 50 and that is our answer.
Twenty people each choose a number from a choice of, 1,2,3,4 or 5. the mode is larger than the median. the median is larger than the mean
fill in a set of possible frequency
To satisfy the conditions that the mode is larger than the median, and the median is larger than the mean, one possible set of frequencies is 1 person chooses 1, 3 people choose 2, 4 people choose 3, 1 person chooses 4 and 11 people choose 5 This results in a mode of 5, a median of 4, and a mean of approximately 3.75.
Since we are given that the mode is larger than the median, that means that at least 11 people must choose the same number. Let's assume that 11 people choose the number 5.
Now, since the median is larger than the mean, we want to make sure that the remaining 9 people choose numbers that are smaller than 5. If they all choose 1, 2, or 3, then the median will be 3, which is larger than the mean. Therefore, we need to make sure that at least one person chooses 4.
So one possible set of frequencies could be
1 person chooses 1
3 people choose 2
4 people choose 3
1 person chooses 4
11 people choose 5
This set of frequencies gives us a mode of 5 (since 11 people choose 5), a median of 4 (since the middle value is 4), and a mean of
(11 + 32 + 43 + 14 + 11*5) / 20 = 3.7
Since the median is larger than the mean, this set of frequencies satisfies all the given conditions.
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The following dot plots show the amount of time it takes each person, in a random sample, to complete two similar problems. what is the mean time for each problem? make a comparative inference based on the mean values.
the mean time for problem 1 is ___ minutes.
If the mean time for problem 1 is 10 minutes, and the mean time for problem 2 is 15 minutes, The dot plots show the amount of time it takes each person in a random sample to complete two similar problems.
To find the mean time for each problem, we need to add up all the times and divide by the total number of people in the sample. Let's assume that the first dot plot represents problem 1 and the second dot plot represents problem 2.
After calculating the mean times for each problem, we can make a comparative inference based on the mean values. For instance, if the mean time for problem 1 is 10 minutes, and the mean time for problem 2 is 15 minutes, we can infer that problem 2 takes longer to complete on average than problem 1.
Comparative inference refers to the process of comparing two or more sets of data to draw conclusions about their similarities or differences. In this case, we are comparing the mean times for two similar problems to see which one takes longer on average.
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The Average Rate Of Change In The Interval (0, 2) Of The Function F F(X) = X^2 – 3x Is
To find the average rate of change of a function in a given interval, we need to calculate the difference in the function values at the endpoints of the interval and divide it by the length of the interval.
In this case, the interval is (0,2) and the function is f(x) = x^2 - 3x.
At the left endpoint, x=0, we have f(0) = 0^2 - 3(0) = 0.
At the right endpoint, x=2, we have f(2) = 2^2 - 3(2) = -2.
Therefore, the difference in the function values is f(2) - f(0) = -2 - 0 = -2.
The length of the interval is 2 - 0 = 2.
So the average rate of change of f(x) over the interval (0,2) is:
(-2)/2 = -1
Therefore, the average rate of change of f(x) over the interval (0,2) is -1.
Hi! To find the average rate of change in the interval (0, 2) for the function f(x) = x^2 - 3x, you can use the following formula:
Average Rate of Change = (f(b) - f(a)) / (b - a)
In this case, a = 0 and b = 2. First, calculate the function values at these points:
f(0) = (0)^2 - 3(0) = 0
f(2) = (2)^2 - 3(2) = 4 - 6 = -2
Now, apply the formula:
Average Rate of Change = (f(2) - f(0)) / (2 - 0) = (-2 - 0) / (2) = -2 / 2 = -1
So, the average rate of change in the interval (0, 2) for the function f(x) = x^2 - 3x is -1.
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Express u = (7, -10) as a linear combination u = rv + sw, where v = (2, 1) and w = (1,4).
(Use symbolic notation and fractions where needed.)
To express u = (7, -10) as a linear combination u = rv + sw, where v = (2, 1) and w = (1,4), we need to find the values of r and s such that:
u = rv + sw
Substituting the given values, we get:
(7, -10) = r(2, 1) + s(1,4)
Using the symbolic notation, we can write this as a system of equations:
7 = 2r + s
-10 = r + 4s
We can solve this system of equations by using the elimination method:
Multiply the second equation by 2:
7 = 2r + s
-20 = 2r + 8s
Subtracting the first equation from the second, we get:
-27 = 7s
Dividing both sides by 7, we get:
s = -27/7
Substituting this value of s into the first equation, we get:
7 = 2r - 27/7
Multiplying both sides by 7, we get:
49 = 14r - 27
Adding 27 to both sides, we get:
76 = 14r
Dividing both sides by 14, we get:
r = 38/7
Therefore, u = (7, -10) can be expressed as the linear combination:
u = (38/7)(2,1) + (-27/7)(1,4)
Using fractions where needed, the answer is:
u = (76/7, 38/7) + (-27/7, -108/7)
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Given the following side lengths of a triangle 2,10,11 what type of triangle is formed
The type of triangle formed from the side lengths of a triangle 2, 10, 11 is a scalene triangle.
Based on the given side lengths of a triangle (2, 10, 11), we can determine the type of triangle formed by examining their relationships. First, let's check if these side lengths can form a valid triangle using the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides must be greater than the length of the remaining side. In this case, 2 + 10 > 11, 2 + 11 > 10, and 10 + 11 > 2, so a triangle can be formed.
Now let's identify the type of triangle. There are three main categories to consider: equilateral, isosceles, and scalene. An equilateral triangle has all three sides equal in length, which doesn't apply here. An isosceles triangle has two sides with equal lengths, but in this case, all three sides have distinct lengths. Therefore, the triangle is a scalene triangle, meaning it has no sides of equal length.
In summary, the triangle formed by side lengths 2, 10, and 11 is a scalene triangle because all three sides have different lengths and satisfy the Triangle Inequality Theorem.
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27. the value of a certain car can be modeled by the function
y = 18000(0.76)', where t is time in years. will the value of the function ever be 0?
The function given is y = 18000(0.76)^t, where y represents the value of the car and t represents the time in years.
This is an exponential decay function, meaning that the value of the car decreases over time. To determine if the value of the function will ever be 0, we would need to find if there exists a time t when y = 0. Let's analyze the function:
0 = 18000(0.76)^t
In an exponential decay function, the base (0.76 in this case) is between 0 and 1, so as time (t) increases, (0.76)^t will approach 0, but it will never actually reach 0. Thus, the value of the car will keep decreasing over time but will never be exactly 0.
In summary, the value of the function, which represents the car's value, will never be 0, but it will get infinitely close to 0 as time progresses. This is a characteristic of exponential decay functions, where the value never reaches 0 but approaches it as time goes on.
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Help please! This is for a grade... (35 points)