Answer:
A. 4.29
Step-by-step explanation:
The average of a set of numbers is the sum of the numbers divided by the total numbers present.
Sum of numbers: Instead of having to write out 2.5 twenty-two times and 5.7 twenty-eight times, we can remember that adding 2.5 twenty-two times is the same as multiplying 2.5 and 22 while adding 5.7 twenty-eight times is the same as multiplying 5.7 and 28. Thus, our numerator for the average is (2.5 * 22) + (5.7 * 28)
Total number of people: We know that there are 50 people in all since 22 + 28 = 50. Thus, our denominator for the average is 50
Average: We divide our numerator by our denominator and simplify to find our average:
Average = ((2.5 * 22 + (5.7 * 28)) / 50
Average = (55 + 159.6) / 50
Average = 214.6 / 50
Average = 4.292
Average = 4.29
Thus, the average and our answer is A. 4.29
1. Use the following information to answer questions 1a and 1b
Suppose we drop a ball from a height of 10 feet. After each bounce, it returns to a height that is k% of the height from which it last fell. After the 5th bounce, it returns to a height of 9.04 feet. We will ignore things like friction and air resistance so that the terms form a geometric sequence.
a) Determine k.
1. 97.51%
2. 98.00%
3. 98.83%
4. 99.15%
b) How many bounces does it take until the ball bounces back to a height less than 3 inches (1/4 of a foot)?
1. 163
2. 183
3. 203
4. 223
a) Value of K is Option 3. 98.83%
b) It takes Option 2. 183 bounces for the ball to bounce back to a height of less than 3 inches (1/4 of a foot).
a) To determine k, we can use the formula for the nth term of a geometric sequence:
[tex]a_n[/tex] = [tex]a_1[/tex] * [tex]r^{(n-1)}[/tex]
where a_1 is the initial term, r is the common ratio, and n is the term number.
We know that [tex]a_1[/tex] = 10 feet and [tex]a_5[/tex] = 9.04 feet, so we can set up the equation:
[tex]a_5[/tex] = [tex]a_1[/tex] * [tex]r^{(5-1)}[/tex]
9.04 = 10 * [tex]k^4[/tex]
Solving for k, we get:
k = [tex](9.04/10)^{(1/4)}[/tex] = 0.9883 or 98.83%
Therefore, the answer is (Option 3) 98.83%.
b) We can use the formula for the nth term of a geometric sequence again to find the height of the ball after the nth bounce:
[tex]a_n[/tex] = 10 * [tex]k^{(n-1)}[/tex]
We want to find the smallest n such that a_n < 1/4 foot, or 0.25 feet. Substituting k = 0.9883, we get:
10 * [tex]0.9883^{(n-1)}[/tex] < 0.25
Solving for n, we get:
n > log(0.25/10) / log(0.9883) + 1
n > 183.3
Since n must be a whole number, the smallest n that satisfies this inequality is n = 184. Therefore, it takes 183 bounces for the ball to bounce back to a height of less than 3 inches (Option 2).
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A sphere and a cylinder have the same radius and height. The volume of the cylinder is 50 ft.
hl
What is the volume of the sphere?
The volume of a sphere can be calculated using the formula V = (4/3)πr³, where V is the volume and r is the radius.
Given that the sphere and the cylinder have the same radius and height, we can assume that the radius of both shapes is the same.
Let's denote the radius as 'r'. The volume of the cylinder is given as 50 ft³.
The volume of the cylinder is calculated using the formula V = πr²h, where h is the height.
Since the height of the cylinder is not given, we cannot determine the exact value of 'r' or calculate the volume of the sphere.
However, if we assume that the height of the cylinder is equal to its diameter (which is twice the radius), we can proceed with the calculation.
If the height of the cylinder is equal to 2r, the volume of the cylinder becomes:
50 = πr²(2r)
50 = 2πr³
Dividing both sides of the equation by 2π gives:
25 = πr³
Now, we can substitute this value of πr³ into the volume formula of the sphere:
V = (4/3)πr³
V = (4/3)(25)
V = 100/3
Therefore, if the height of the cylinder is equal to its diameter, the volume of the sphere would be 100/3 ft³. However, please note that this assumption might not necessarily be valid without further information about the relationship between the height and radius of the cylinder.
Answer: The Volume of the sphere is 100/3 cubic feet.
Step-by-step explanation:
It is clearly seen in the given figures, the height is two times the radius. Therefore, h is equal 2r.
We know that,
The volume of the sphere is π x r^2 x h. (r is radius and h is height)
So putting the values of height, h in the above formula, we get:
πxr^2x2r
= 2 * π * r^3.
= 2 * π * r^3 = 50
= π * r^3 = 25
We get, r^3 = 7.957747155
Therefore, r = 1.996472712
Now that we have the measure of the radius, we can find the volume of the sphere!
(4 / 3) * π * r^3
(4/3) * π * (1.996472712)^3
= (4/3) * π * 7.957747155
= (4/3) * π * (25 / π)
= (4/3) * 25
= 100/3 cubic feet.
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Convert 2553 base 7 to base 10
Step by step explanation
Answer:
2553(base 7) = 969(base 10)
Step-by-step explanation:
3 in units place means 3.
5 in the 7's place means 5 × 7 = 35
5 in the 7²'s place means 5 × 7² = 5 × 49 = 245
2 in the 7³'s place means 2 × 7³ = 2 × 343 = 686
3 + 35 + 245 + 686 = 969
Find absolute and relative change as a percentage.
The U.S. per person consumption of beef decreased from 67.8 pounds in 2000 to 57.7 pounds in 2020.
The relative change is approximately -14.9%, indicating a decrease of approximately 14.9% in per person consumption of beef from 2000 to 2020.
How to determine the absolute and relative change as a percentage.To find the absolute and relative change as a percentage in the U.S. per person consumption of beef from 2000 to 2020, we can follow these steps:
Calculating the absolute change:
Absolute change = Final value - Initial value
= 57.7 pounds - 67.8 pounds
= -10.1 pounds
Step 2: Calculate the relative change:
Relative change = (Absolute change / Initial value) * 100
= (-10.1 pounds / 67.8 pounds) * 100
≈ -14.9%
The absolute change is -10.1 pounds, indicating a decrease in per person consumption of beef.
The relative change is approximately -14.9%, indicating a decrease of approximately 14.9% in per person consumption of beef from 2000 to 2020.
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A new pair of trainers are bought for £100. They then decrease in value by 20% each year. How much will they be worth in 2 years' time?
Answer:
[tex]\boxed{\boxed{\sf{\:\:\:\green{£64}\:\:\:}}}[/tex][tex]\\[/tex]
Step-by-step explanation:
In the first year, the trainers will be worth 80% of their original value, which is:
[tex]\rm\implies{£100 \times 0.8 = £80}[/tex]
[tex]\\[/tex]
In the second year, they will be worth 80% of their value after the first year:
[tex]\rm\implies{£80 \times 0.8 = \boxed{\boxed{\sf{\:\:\:\green{£64}\:\:\:}}}}[/tex]
[tex]\\[/tex]
[tex]\\[/tex]
[tex]\therefore[/tex] The trainers will be worth £64 in 2 years' time.
What is the best prediction for the number of times that it will land on orange?
Answer:
20 times
Step-by-step explanation:
There are 5 color options that are all the same size.
So orange = 1/5.
(1/5) * 100 = 20 times
miriam is studying a type of plant that grows at a constant rate. Every month, she visits two of these plants and measures their heights. she made this table. Miriam want an equation she can use to find Plant A’s height in centimeters (a) given Plant AB’s height in centimeters (b).
The equation that represents the situation is a = b- 4.
Since the plant grows at a constant rate, we can assume that the height of the plant is increasing linearly with time.
Let's use the data from Week 1 and Week 2 to find the rate of growth for each plant:
For Plant A: Growth rate = (24 cm - 22 cm) / (2 weeks - 1 week) = 2 cm/week
For Plant B: Growth rate = (28 cm - 26 cm) / (2 weeks - 1 week) = 2 cm/week
Since the growth rate is constant, we can use the equation of a line to model the height of each plant over time:
For Plant A: a = 2t + b, where t is the time in weeks and b is the initial height of the plant.
For Plant B: b = 2t + c, where c is the initial height of Plant B.
We can find the values of b and c by substituting the data from Week 1 into these equations:
For Plant A: 22 = 2(1) + b, so b = 20.
For Plant B: 26 = 2(1) + c, so c = 24.
Now we can substitute these values into the equations for Plant A and Plant B:
Plant A: a = 2t + 20
Plant B: b = 2t + 24
To find an equation that gives Plant A's height in terms of Plant B's height, we can solve the equation for t in terms of b:
b = 2t + 24
2t = b - 24
t = (b - 24) / 2
Then we can substitute this expression for t into the equation for Plant A:
a = 2t + 20
a = 2[(b - 24) / 2] + 20
a = b - 24 + 20
a = b - 4
So the equation we were looking for is:
a = b - 4
Therefore, to find Plant A's height in centimeters given Plant B's height in centimeters, we simply subtract 4 from Plant B's height.
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Post Test: Connecting Algebra Classes
A circle is defined by the equation given below.
2² +²2-2y
= 0
What are the coordinates for the center of the circle and the length of the radius?
12.app.edmentum.com/assessments-delivery/ua/la/launch/49003916/45317916/aHR0cHM6Ly9mMiShcHAUZWRtZW5odWouY29tL2xlYXJuZXItdw
Next O Post Test: Connecting Algebra and Geometry through Coordinates
OA. (-1,-1), 4 units
B.
(,1), 2 units
OC. (-, -1), 2 units
OD. (,1), 4 units
The coordinates for the center of the circle are (1/2, 1), and the length of the radius is 2 units. Option C is a correct choice.
To find the coordinates of the center of the circle and the length of the radius, we need to rewrite the equation of the circle in standard form, which is (x - h)² + (y - k)² = r². Here, (h, k) represents the coordinates of the center of the circle, and r represents the radius.
Given equation: x² + y² - x - 2y - 1 = 0
To convert it into standard form, we complete the square for the x and y terms separately.
Rearranging the equation:
x² - x + y² - 2y = 1
Completing the square for x:
(x² - x + 1/4) + (y² - 2y) = 1 + 1/4
Completing the square for y:
(x² - x + 1/4) + (y² - 2y + 1) = 1 + 1/4 + 1
Simplifying:
(x - 1/2)² + (y - 1)² = 9/4
Comparing it with the standard form, we can see that:
Center coordinates: (1/2, 1)
Radius: √(9/4) = 3/2 = 1.5 units
Therefore, the correct answer is C. The coordinates for the center of the circle are (1/2, 1), and the length of the radius is 2 units.
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Question -
A circle is defined by the equation given below. x² + y² - x - 2y - 1 = 0 What are the coordinates for the center of the circle and the length of the radius?
A. (-1,-1), 2 units −1),
B. (- 1/2 ,1), 4 units
C. (1/2 , 1), 2 units
D. (-1/2 ,-1), 4 units
If anyone can help with any of these probability questions, I'll give more points and brainiest!! Idaho Jones regains consciousness and next to her are 4 blodegradable packing peanuts. 5 seconds later each peanut has split in half, and each half grows into a full-size peanut. This repeats in the next 5 seconds. She sees a door with a keypad. A sign next to it has a timer indicating 10 seconds have passed and says the code is the number of peanuts when the timer reaches 100. (After 10 secords there were 16 peanuts.) Idaho realizes she must escape before then or the peanuts could suffocate her. Show how she figures out the code to open the door, and write what the code is
A mans
Idaho gets out and closes the door behind her. She is in a room with one exit, and the lock requires a key. There's a table with a briefcase that is also locked. It has a three-digit combination. The first part of the combination is on a wheel with all 10 digits. The second wheel has only 5 digits, and the third has 3 digits. How many combinations are possible?
150
combinations
The briefcase holds a key and out Idaho goes. She is met by an enchanted skeleton that directs her to a wall where a shelf has room for 5 books. The 5 ancient books are on the floor. She puts them on the shelf, but nothing happens. She realizes they must be put in the correct order. How many attempts will Idaho need to make if she doesn't get it right until her last attempt
Answer: let me explain!
Step-by-step explanation: So this might seem really confusing at first, but it’s actually suuuuuuper easy :P
So, if you think about it, every five seconds the amount of peanuts…well I don’t know how to explain it but let me show you this with numbers.
(4x2)x2x2x2 and so on. The number multiplies by two every five seconds from there. So figure out how many groups of five second there are in 100 seconds by dividing!
It’s 20!
So since 5 happens 20 times, and every time 5 happens, 2 happens, 2 also happens 20 times! (If that makes any sense)
So that answer would be 8x*twenty twos*
Which is…*drumroll please*
8,388,608
I even double checked!
And for the briefcase skeleton thing
She needs to try it 25 times because there are 5 books and each book can be switched with the other 4 times if the first one doesn’t work, therefore you need to multiply and the equation would be 5^2, or in other words, 25.
Don’t forget ur units!
Hope this helps :P
An ice cream cone has a heig
ht of 6 inches and a diameter of 2.5 inches. If it’s only filled to the top of the cone, about how much ice cream can the cone hold?
Amount of ice cream can the cone hold is, 9.8 inches³
We have to given that;
An ice cream cone has a height of 6 inches and a diameter of 2.5 inches.
Hence, We get;
Radius of cone = 2.5 / 2 = 1.25 inches
Since, We know that;
Volume of cone is,
V = πr²h/3
v = 3.14 × 1.25² × 6 / 3
V = 9.8 inches³
Hence, Amount of ice cream can the cone hold is, 9.8 inches³
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Select the graph for the solution of the open sentence. Click until the correct graph appears. |x| + 3 > 3
The correct graph of the inequality ( |x| + 3 > 3) is attached accordingly.
Here is how the above was solvedRecall that the absolute value (or modulus) of a real number x is its non-negative value regardless of its sign. For example, 5 has an absolute value of 5, and 5 has an absolute value of 5.
A number's absolute value can be conceived of as its distance from zero along the real number line.
So, given |x| + 3 > 3
Add minus three to both sides
|x| + 3 + (-3) > 3 + (-3)
|x| > 0
Thus, the absolute value of x is
x > 0 or x < -0
put in the form of inequality, we have
x > 0 or x < 0
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DO THE MATH: Billie offers a product for $40 with free shipping. But the shipping is in reality $15 per unit of the product sold. What is the actual selling price of the product, not including shipping costs?
$55
$35
$25
$15
Is this correct? Or what do you think the answer is please
The partial fraction of the given rational expression is [tex]\frac{25}{(x+1(x+2)} =\frac{25A}{3(x-1)} -\frac{25B}{3(x+2)}[/tex]
Solving partial fractionsGiven the following equation below:
[tex]\frac{25}{(x+1(x+2)}[/tex]
We are expression as the sum of partial fractions
Let the numerator of both partial expressions be A and B to have:
[tex]\frac{25}{(x+1(x+2)} =\frac{A}{x-1} +\frac{B}{x+2}[/tex]
Simplifying the expression, we will have;
[tex]\frac{25}{(x+1(x+2)} =\frac{A(x+2)+B(x-1)}{x-1(x+2)}[/tex]
Cancelling the denominator:
25 = A(x+2) + B(x-1)
If x - 1 = 0, then x = 1. Substitute to have:
25 = A(1+2)
3A = 25
A = 25/3
If x + 2 = 0, x = -2
25 = B(-3)
B = -25/3
Substitute into the function to have:
[tex]\frac{25}{(x+1(x+2)} =\frac{25A}{3(x-1)} -\frac{25B}{3(x+2)}[/tex]
This gives the partial fraction of the given rational expression.
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The levels in the game currently go up to 60. Using your model, extend the maxHP for each level up to level 70.
How do I figure out this?
To calculate the maxHP values for levels 62-70 by plugging in the appropriate level values into the formula.
One way to extend the maxHP for levels beyond 60 is to use the same formula that was used to calculate the maxXP for levels 1-60, but with the appropriate values plugged in.
The formula for the maxHP for a given level can be approximated as:
maxHP = baseHP x (1 + level/5)²
where baseHP is the starting HP for level 1 (in this case, it's 330).
To extend the maxHP for levels 61-70, you can simply plug in the appropriate level values into the formula and calculate the corresponding maxHP values.
For example, to find the maxHP for level 61, you would plug in level = 61:
maxHP = 330 x (1 + 61/5)²
maxHP ≈ 2619.9
Similarly, you can calculate the maxHP values for levels 62-70 by plugging in the appropriate level values into the formula.
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A noodles factory gives 10% commission to a wholesaler for selling its produtcs. After giving the commission to the wholesaler, the company recieves Rs 315000 in baishakh. Find the total sales of noodles by the wholesaler in baisakh.
Answer: 350000
Step-by-step explanation: Let the total sale of noodles by the wholesaler be x.
Given: Commission for the wholesaler is 10%
After receiving a 10% commission the company got rupees 315000.
x-10% of x =315000
x - 10\100 = 315000
x-x\10 = 315000
10x - 10\10 =315000
9x = 3150000
x= 3150000\9
x= 350000
PLEASE HELP
At a recent baseball game of 5,000 in attendance, 150 people were asked what they prefer on a hot dog. The results are shown.
Ketchup Mustard Chili
63 27 60
Based on the data in this sample, how many of the people in attendance would prefer chili on a hot dog?
900
2,000
2,100
4,000
Answer:
I would go with 900 but I’m not for sure
Step-by-step explanation:
If you have a system of two equations with two unknowns, and the graphs of
the two equations do not intersect, the system must have
A. at least 1 solution
B. exactly 1 solution.
C. no solution
D. more than 1 solution
If you have a system of two equations with two unknowns, and the graphs of the two equations do not intersect, the system must have no solution.
option C.
What is the solution of the two equations?When we have a system of two linear equations in two variables, it can be represented graphically as two lines in a plane. The solution to the system corresponds to the point of intersection of these lines.
If the two lines do not intersect, then they are parallel. In this case, there is no point that satisfies both equations, which means that there is no solution to the system of equations.
In other words, if the two graphs do not intersect, it means that there are no values of the two unknowns that can simultaneously satisfy both equations.
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It takes a hose 4 minutes to fill a rectangular aquarium 8 inches long, 9 inches wide, and 10 inches tall. How long will it take the same hose to fill an aquarium measuring 27 inches by 29 inches by 35 inches?
Answer: 9" x 10" x 11" = 990 cubic inches.
990 cubic inches / 5 minutes = 198 cubic inches per minute
22" x 23" x 33" = 16698 cubic inches
16698/198 = 84 and 1/3 minutes
1 hour 24 minutes and 20 seconds
is this correct? please helpp.
The distance between the points are matched as;
1. 10. 6
2. 7. 6
3. 7. 1
How to determine the valuesUsing the Pythagorean theorem, we have that the square of the hypotenuse side is equal to the sum of the squares of the other two sides, we have that;
1. Opposite = 8
Adjacent = 7
Substitute the values
x² =8² + 7²
Find the square
x² = 64 + 49
x = √113
x = 10. 6
2. x²= 3² + 7²
Find the square value
x² = 9 + 49
x² = 58
Find the square root
x = 7. 6
3. x² = 5² + 5²
find the value
x² = 50
x = √50
x = 7. 1
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A triangle has sides with lengths of 8 miles, 11 miles, and 17 miles. Is it a right triangle?
Answer:
Step-by-step explanation:
No
for it to be a right angle triangle the longest side would have to be the square root of 8 squared plus 11 squared which is 13.6
answer
no Pythagorean theorem doesnt work
steps
8²+11² should equal 17²
BUT
121+64=185
17²=289
Sm answer this asap 100 points.
At a recent football game of 8,450 in attendance, 150 people were asked what they prefer on a hot dog. The results are shown.
Ketchup Relish Chili
54 36 60
Based on the data in this sample, how many of the people in attendance would prefer ketchup on a hot dog?
4,225
3,380
3,127
3,042
An estimated 3,042 people in attendance would prefer relish on a hot dog.
Given that;
For a recent football game of 8,450 in attendance,
And, 150 people were asked for they prefer on a hot dog.
Now, For number of people in attendance would prefer relish on a hot dog, we can use the proportion of people in the sample who preferred relish:
By proportion we get;
x = (54/150) x 8450
x = 54 * 56 1/3
x = 3042
Therefore, An estimated 3,042 people in attendance would prefer relish on a hot dog.
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A triangle has a base of 14 feet and a height of 6 feet. By how much does the base need to increase for the area to increase
by 1.2 square feet?
The height of the triangle must increase by 4.29 feet so that the area would increase by 1.2 square feet.
How to find the area of a triangle?To calculate the area of a triangle, you can use the formula presented as follows:
[tex]\sf Area = \huge \text(\dfrac{1}{2}\huge \text) \times base \times height[/tex]
In which the parameters are given as follows:
"base" is the length of the side of the triangle that is perpendicular to the height."height" is the length of the perpendicular line segment from the base to the opposite vertex.Considering the triangle that has a base of 14 feet and a height of 6 feet, the area of the triangle is given as follows:
[tex]\sf A = 0.5 \times 14 \times 6[/tex]
[tex]\sf A = 42 \ square \ feet.[/tex]
An increase of 1.2 square feet would lead to an area of 43.2 square feet, hence the height would be of:
[tex]\sf 4.2h = 43.2[/tex]
[tex]\sf h = \dfrac{43.2}{4.2}[/tex]
[tex]\sf h = 10.29 \ feet[/tex].
Then the increase in the height would be of:
[tex]\sf 10.29 - 6 = 4.29 \ feet[/tex].
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please help! I need a explanation on why it’s B and please use simple terms I could understand
The correct statement regarding the proportional relationships is given as follows:
D. The first bucket will be completely filled 11 minutes before the second bucket.
What is a proportional relationship?A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.
The equation that defines the proportional relationship is given as follows:
y = kx.
In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.
For the first bucket, the equation is given as follows:
y = 0.4x.
Meaning that 0.4 gallons are inserted each minute, hence the time to insert 2 gallons is given as follows:
2/0.4 = 5 minutes.
For the second bucket, the constant is taken from the graph as follows:
k = 0.5/4
k = 0.125.
Hence the time is given as follows:
2/0.125 = 16 minutes.
Hence the difference is of:
16 - 5 = 11 minutes.
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how can i do that? thanks.
The limit as n approaches infinity of ((n+1)⁶-(n-1)⁶)/((n+1)⁵+(n-1)⁵) is 6.
To evaluate the limit as n approaches infinity of the expression ((n+1)⁶-(n-1)⁶)/((n+1)⁵+(n-1)⁵), we can simplify it using algebraic manipulations.
Let's expand the numerator and denominator using the binomial:
Numerator:
((n+1)⁶-(n-1)⁶) = [n⁶ + 6n⁵ + 15n⁴ + 20n³ + 15n² + 6n + 1] - [n⁶ - 6n⁵ + 15n⁴ - 20n³ + 15n² - 6n + 1]
= 12n⁵ + 40n³ + 12n
Denominator:
((n+1)⁵+(n-1)⁵) = [n⁵ + 5n⁴ + 10n³ + 10n² + 5n + 1] + [n⁵ - 5n⁴ + 10n³ - 10n² + 5n - 1]
= 2n⁵ + 20n³ + 2n
Now, let's simplify the expression by canceling out common terms:
((n+1)⁶-(n-1)⁶)/((n+1)⁵+(n-1)⁵) = (12n⁵ + 40n³ + 12n) / (2n⁵ + 20n³ + 2n)
As n approaches infinity, we can see that the highest power of n in the numerator and denominator is n⁵.
We can divide all terms by n⁵ to determine the limit:
lim(n→∞) [(12n⁵ + 40n³ + 12n) / (2n⁵ + 20n³ + 2n)]
= lim(n→∞) [(12 + 40/n² + 12/n⁴) / (2 + 20/n² + 2/n⁴)]
= 12/2
= 6
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Can someone help me with this please !
Answer:
Step-by-step explanation:
1. The figure is a rectangular prism.
Formula: V = lwh
Given: 13 ft x 7ft x 9 ft
Substitute the values to the formula and solve.
V = lwh
V = 13ft(7ft)(9ft)
V = 819 ft³
2. The given figure is a triangular prism. Notice that the base forms a right triangle.
Formula: V = 1/2bhl
Given:
b = 9m
h = 12m
l = 16 m
Substitute the given values to the formula and solve.
V = 1/2(9m)(12m)(16m)
V = 864 m³
3. This is a cylinder
Formula: V = πr²h
Given:
r = 11 yd
h = 26 yd
Solve:
V = π (11yd)²(26yd)
V = 9883.45 yd³
4. The figure is a rectangular prism.
Formula: V = lwh
Given dimensions: 9m x 9m x 13.5m
Solve:
V = 9m(9m)(13.5m)
V = 1093.5 m³
5. The figure is a triangular prism
Formula: V = 1/2bhl
Given:
b = 15yd
h = 13 yd
l = 24 yd
Solve:
V = 1/2 (15yd)(13yd)(24yd)
V = 2340 yd³
We want to solve the following equation.
x³ + 3x² - x = |x-1|
Two of the solutions are a~-0.7 and 0.5.
Find the other solution.
Hint: Use a graphing calculator.
Round your answer to the nearest tenth.
x~
The other solution to the equation x³ + 3x² - x = |x-1| is approximately x~ = -2.6.
1. Start by plotting the graphs of both sides of the equation on a graphing calculator.
2. The left side of the equation, x³ + 3x² - x, can be plotted as a curve.
3. The right side of the equation, |x-1|, can be plotted as a V-shaped graph with the vertex at (1, 0).
4. Find the intersection points of the two graphs.
5. By observing the graph, it can be seen that the two given solutions, a~ = -0.7 and b~ = 0.5, are present.
6. Identify the other solution, which is the third intersection point.
7. Determine the approximate x-coordinate of the third intersection point by reading the value from the graph.
8. Round the obtained x-coordinate to the nearest tenth.
9. The other solution is approximately x~ = -2.6.
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HELP ME I NEED TO PASS THIS TEST!!!!! Pleaseeee
Just 2 questions & you get points!!!!
1. The best equation for circle A is (x + 4)² + (y + 2)² = 9. Option D
2. The equation of the circle with coordinates (1, 1) (1, 11) is (x - 1)² + (y - 6)² = 25. Option A
How do we find the equation of each circle?1. For the equation of circle A, we can pick out the coordinates we see.
Circle A has its midpoint at (-4, -2) and its edges at (-4, 1) and (-4, -5).
The equation of a circle in a plane is (x - h)² + (y - k)² = r²
the circle has a radius of 3 units (from -2 to 1 or from -2 to -5)
(x - (-4))² + (y - (-2))² = 3²
when we simplify, it becomes (x + 4)² + (y + 2)² = 9
2. The equation of a circle with diameter AB. A (1, 1), B(1, 11) is
h = (x₁ + x₂)/2 ⇒(1 + 1)/2 = 1
k = (y₁ + y₂)/2⇒ (1 + 11)/2 = 6
the center of the circle is at (1, 6).
A and B which are (1, 1) and (1, 11), it's clear that the diameter is 10 units (11 - 1). Thus, the radius is 5 units.
(x - h)² + (y - k)² = r²
Substituting the obtained values we get
(x - 1)² + (y - 6)² = 5²
which becomes
(x - 1)² + (y - 6)² = 25
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Can someone please answer and provide an explanation for these problems?
Answer:
32) (x+12)(2)+(y)(2)=25
Step-by-step explanation:
(x-a)(2)+(y-b)(2)=r(2)
(x-(-12)(2)+(y-0)(2)=5(2)
(x+12)+(y)=25
Answer(s):
(32) - [tex](x +12)^2 + y ^2 = 25[/tex]
(33) - [tex](x +2)^2 + (y+6 )^2 = 36[/tex]
(34) - [tex](x -8)^2 + (y+1 )^2 = 100[/tex]
(35) - [tex](x -13)^2 + (y+12 )^2 = 1[/tex]
Step-by-step explanation:
To solve these types of problems, it is only a matter of memorizing the equation of a circle and plugging in values appropriately.
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{The Equation of a Circle:}}\\\\(x - h)^2 + (y - k)^2 = r^2\\\text{Where} \ r \ \text{is the radius of the circle and} \ (h,k) \ \text{is the center of the circle.}\end{array}\right}[/tex]
For the following problems, find the equation of a circle with the given information.
(32) - [tex]\text{Center at} \ (-12,0) \ \text{and a radius,} \ r=5[/tex]
(33) - [tex]\text{Center at} \ (-2,-6) \ \text{and a radius,} \ r=6[/tex]
(34) - [tex]\text{Center at} \ (8,-1) \ \text{and a radius,} \ r=10[/tex]
(35) - [tex]\text{Center at} \ (13,-12) \ \text{and a radius,} \ r=1[/tex]
Question #32:
[tex](x - h)^2 + (y - k)^2 = r^2\\\\\Longrightarrow (x - (-12))^2 + (y - 0)^2 = (5)^2\\\\\Longrightarrow \boxed{ (x +12)^2 + y ^2 = 25}[/tex]
Question #33:
[tex](x - h)^2 + (y - k)^2 = r^2\\\\\Longrightarrow (x - (-2))^2 + (y - (-6))^2 = (6)^2\\\\\Longrightarrow \boxed{ (x +2)^2 + (y+6 )^2 = 36}[/tex]
Question #34:
[tex](x - h)^2 + (y - k)^2 = r^2\\\\\Longrightarrow (x - 8)^2 + (y - (-1))^2 = (10)^2\\\\\Longrightarrow \boxed{ (x -8)^2 + (y+1 )^2 = 100}[/tex]
Question #35:
[tex](x - h)^2 + (y - k)^2 = r^2\\\\\Longrightarrow (x - 13)^2 + (y - (-12))^2 = (1)^2\\\\\Longrightarrow \boxed{ (x -13)^2 + (y+12 )^2 = 1}[/tex]
Thus, all problems have been solved.
Which of the following equations represents a linear function?
x = 3
y = 3x2
y equals negative one third times x plus 1
3x − 4 = 7
The Linear function is y equals negative one third times x plus 1
A linear function is a function that has a constant rate of change, meaning that as one variable (usually x) increases or decreases by a certain amount, the other variable (usually y) also changes by a constant amount.
Out of the four given equations, the only one that represents a linear function is the third one:
y equals negative one third times x plus 1
This is because the equation has a constant rate of change of -1/3 for any change in x. For example, if we increase x by 3, y will decrease by 1 (because 3*(-1/3) = -1). Similarly, if we decrease x by 3, y will increase by 1. This constant rate of change is what makes the equation represent a straight line when graphed.
The other three equations do not represent linear functions.
The first equation, x = 3, is not a function at all because there are multiple possible y values for the given x value of 3.
The second equation, y = 3x2, is a quadratic function because it contains an x2 term, which means that the rate of change of y with respect to x is not constant.
The fourth equation, 3x - 4 = 7, is a linear equation but not a function because for any given x, there is only one corresponding value of y. However, when the equation is solved for y, it becomes y = 3x - 3, which represents a linear function with a constant rate of change of 3.
The linear function is y equals negative one third times x plus 1
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A bag contains marbles of four different colors: 4 blue marbles 12 red marbles 8 green marbles 2 yellow marbles what is the probability of not picking a red marble out of the bag
Answer:
The total number of marbles in the bag is 4 + 12 + 8 + 2 = 26.
The probability of not picking a red marble out of the bag is equal to the number of marbles that are not red divided by the total number of marbles in the bag.
The number of marbles that are not red is 4 (blue) + 8 (green) + 2 (yellow) = 14.
Therefore, the probability of not picking a red marble out of the bag is 14/26 or 7/13.
So the probability of not picking a red marble is 7/13.