The theta notation for the function f (n) = (n3/2), g(n) = (n5/2) is Θ(n5/2).
What is theta notation? Theta notation is used to describe the asymptotic performance of an algorithm. It specifies a tight bound on the growth rate of the algorithm, i.e., an upper bound and a lower bound.
It is represented using the Greek letter theta (Θ).In the case of the given functions,
f (n) = (n3/2), g(n) = (n5/2),
we can determine their theta notation as follows:
We have f (n) = (n3/2).
Let's find g (n) / f (n):g (n) / f (n) = (n5/2) / (n3/2) = n
Therefore, g (n) is greater than or equal to f (n) multiplied by a constant c1, which is 1, for all n greater than or equal to 1.
This implies that the lower bound of the function is n3/2, which means that the lower bound of the function is n3/2.
Hence, the theta notation of f (n) is Θ(n3/2).
Similarly, for g (n) = (n5/2), let's find f (n) / g (n):f (n) / g (n) = (n3/2) / (n5/2) = 1 / n
Therefore, f (n) is less than or equal to g (n) multiplied by a constant c2, which is 1, for all n greater than or equal to 1.
This implies that the upper bound of the function is n5/2, which means that the upper bound of the function is n5/2.
Hence, the theta notation of g (n) is Θ(n5/2). Therefore, the theta notation for the function f (n) = (n3/2), g(n) = (n5/2) is Θ(n5/2).
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Wrote the equation an the answer for brainliest!
Answer: 66.50+5g= 83.50
g=3.4
Step-by-step explanation:
About 75% of MCC students believe they can achieve the American dream and about 65% of Ferris State Universtiy students believe they can achieve the American dream. Construct a 99% confidence interval for the difference in the proportions of Montcalm Community College students and Ferris State University students who believe they can achieve the American dream. There were 100 MCC students surveyed and 100 FSU students surveyed. a. With 99% confidence the difference in the proportions of MCC and FSU students who believe they can achieve the American dream is (round to 3 decimal places) and (round to 3 decimal places). b. If many groups of 100 randomly selected MCC students and 100 randomly selected FSU students were surveyed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population proportion of the difference in the proportions of MCC students and FSU students who believe they can achieve the American dream about percent will not contain the true population difference in proportions.
a. With 99% confidence, the difference in proportions is between -0.023 and 0.223. b. 99% of the confidence intervals will contain the true population proportion, and about 1% will not contain the true population difference in proportions.
a. To construct a confidence interval for the difference in proportions, we can use the following formula:
CI = (p1 - p2) ± zα/2 * √((p1*(1-p1)/n1) + (p2*(1-p2)/n2))
where:
p1, p2 = proportion of MCC, FSU students who believe they can achieve the American dream
n1, n2 = sample size of MCC, FSU students
zα/2 = critical value from the standard normal distribution for a 99% confidence level, which is 2.576
So,
CI = (0.75 - 0.65) ± 2.576 * √((0.75*(1-0.75)/100) + (0.65*(1-0.65)/100))
CI = 0.10 ± 0.123
CI = (−0.023, 0.223)
Therefore, with 99% confidence, the difference in proportions of MCC and FSU students who believe they can achieve the American dream is between -0.023 and 0.223.
b. Approximately 99% of these confidence intervals will contain the true population proportion of the difference in proportions of MCC students, and FSU students who believe they can achieve the American dream.
And about 1% will not contain the true population difference in proportions. This is because we constructed a 99% confidence interval.
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1. Of the 1081 members of the town, 21 attended the Fall Harvest Festival. What is the population of this study? What is the sample?
Answer:
Population is 1081
Sample is 21
Step-by-step explanation: Snap Add?
how many odd numbers are there with middle digit 5 and no digit repeated between 20,000 and 69,999?
There are 252 odd numbers with the middle digit as 5 and no repeated digits between 20,000 and 69,999.
To determine the number of odd numbers with the middle digit as 5 and no repeated digits between 20,000 and 69,999, we need to consider the possible combinations for the remaining digits.
Since the middle digit is fixed as 5, we have three remaining digits to consider: the thousands digit, hundreds digit, and units digit.
Thousands Digit:
The thousands digit cannot be 0, 5 (as it is the middle digit), or 6 (to stay within the given range). So, we have 7 possible options: 2, 3, 4, 7, 8, and 9.
Hundreds Digit:
The hundreds digit can be any digit from 0 to 9, excluding the already used digits in the thousands and middle positions. So, we have 9 possible options.
Units Digit:
The units digit must be an odd number, excluding 5 (as it is the middle digit) and any digit already used in the thousands and hundreds positions. So, we have 4 possible options: 1, 3, 7, and 9.
By multiplying the number of options for each digit, we obtain the total number of odd numbers meeting the given conditions:
7 (thousands) * 9 (hundreds) * 4 (units) = 252
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When a boy stands on the bank of a river and looks across to the other bank, the angle of depression is 12°. If he climbs to the top of a 10 ft tree and looks across to other bank, the angle of depression is 15°. What is the distance from the first position of the boy to the other bank of the river? How wide is the river? Give your answers to the nearest foot.
Please look at the scanned picture.
To finish an order on time, a company has to produce 40 items each day. But the company manages to complete 20 more items each day than it needs to, and finishes the order 3 days ahead of time. In how many days was the company supposed to finish the order?.
The company was supposed to finish the order in 9 days.
What is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Here, we have
The company must have produced 60 items daily if it produced 20 more than the daily average of 40 items.
The company had 120 products to make, which should have taken three days (120 items, 40 items/day), but it finished in just two days (120 items, 60 items/day). They completed this order one day earlier than expected.
However, the issue is that they completed 3 days ahead of schedule. Thus, our estimate is 360 items or three times 120 items.
According to this, they should have completed their order in 9 days (360 things, at a rate of 40 items per day), but they did so in 6, at a rate of 60 items per day. Since 6 is three fewer than 9, our assumption of 360 items was accurate.
We've demonstrated that the business should have completed the order in 9 days.
Let the desired number of days be x.
Then, the company finished its order in x - 3 days.
Since the number of items produced is the number of days times items per day, and it doesn't change:
number of items = 40 items/day * x days
= 60 items/day * (x - 3) days
40x = 60(x - 3) = 60x - 180
180 = 20x
x = 9
Hence, the company was supposed to finish the order in 9 days.
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QUESTION 1 Solve. -10x + 5 = 7x + 5
Answer:
x=0
Step-by-step explanation:
At the start of the day, a roofer rested a 3 m ladder against a vertical wall so that the foot of the ladder was 80 cm away from the base of the wall. During the day, the ladder slipped down the wall, causing the foot of the ladder to move 50 cm further away from the base of the wall. How far down the wall, in centimetres, did the ladder slip? Give your answer to the nearest 1 cm.
The ladder slipped approximately 289 cm down the wall.
To determine how far down the wall the ladder slipped, we can consider the ladder as the hypotenuse of a right triangle formed with the wall.
Initially, the ladder forms a right triangle with the wall and the ground, where the base (foot of the ladder) is 80 cm away from the wall. Let's denote the distance the ladder slipped down the wall as d cm.
Using the Pythagorean theorem, we have:
(80 cm)^2 + d^2 = (300 cm)^2
Simplifying the equation, we get:
6400 cm^2 + d^2 = 90000 cm^2
Rearranging the equation and solving for d, we have:
d^2 = 90000 cm^2 - 6400 cm^2
d^2 = 83600 cm^2
Taking the square root of both sides, we find:
d ≈ √83600 cm
d ≈ 289 cm
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Work out the size of angle PRQ.show working out
Answer:
I got full 3 marks for this but you might have to reword depending on how your mathswatch was set
Step-by-step explanation:
12-2=10
10×180=1800
1800/12=150
=150˚
150/2=75
=75
what is the measure of <x
Answer:
Y=76⁰
X=104⁰
Z=104⁰
Step-by-step explanation:
Y is equal to 76 bcz directly opposite angles are equal
x=180-76 which is 104⁰ bcz angles on a straight line add up to 180⁰
Multiply. (9x−2)(3x−8) Enter your answer, in standard form, in the box.
Answer:
27 x 2 −78 x + 16
Step-by-step explanation:
Answer:
27x^2-78x+16
Step-by-step explanation:
took the test
6: What is the volume of a cylinder
with a diameter of 10 feet and a
height of 8 feet? Use 3.14 for 1.
cubic feet
Answer: 628 cubic feet
Step-by-step explanation: First, find the area of the circle. Using the formula "TTr^2", you can find the area of the circle. Since the diameter is given, and not the radius, divide 10 by 2, and it gives you 5. Now, use the formula. 5 x 5 = 25, and then multiply it by 3.14 which gives you 78.5. Now that we have found the area of the circle, multiply the area by 8 to find the volume of the cylinder. 78.5 x 8 is 628 cubic feet, and that is the volume of the cylinder.
D 3b. Triangle A has an area of 30cm² and a height of 5. What is the base?
The base of triangle will be 12 cm.
WHAT IS TRIANGLE ? HOW TO FIND ITS AREA ?A triangle is a three-sided polygon.
The area of a rectangle is commonly known to be b*h, where b is the base and h is the height. Using the formula for a rectangle, we can get the area of a triangle.
A rectangle is split into two congruent triangles by a diagonal. The area of each triangle is equal to half the size of the rectangle.
As a result, the triangle's area A may be calculated using the equation A=1/2*b*h, where b denotes the triangle's base and h its height.
CALCULATIONAREA OF TRIANGLE = 1/2*b*h
base = area of triangle * 2 / h
= 30 * 2 / 5
= 12 cm.
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зх
It’s a square root
Answer:
what?
Step-by-step explanation:
the original price of a jacket was $74.00 .A store manager marked the price down by
25 1/2% . By how much was the price reduced?
PLEASE HELP ME ASAP!!!!!!!!!
TY! :)
Answer:
No solution.
Step-by-step explanation:
Tried a lot but the answer is constantly 0. I guess it's A.
Answer:
C. infinite
Step-by-step explanation:
A raisin cookie recipe call for flour and raisins in the ratio 3/5 : 1/4. if Natilie used 3 cups of flour, how many cups of raisins did she use? write you answer as a mixed number.
The ratio of flour and raisin in cookie recipe is,
\(\begin{gathered} \frac{f}{r}=\frac{\frac{3}{5}}{\frac{1}{4}} \\ =\frac{3}{5}\cdot\frac{4}{1} \\ =\frac{12}{5} \end{gathered}\)Determine the cups of raisins required for 3 cups of floor.
\(\begin{gathered} \frac{3}{r}=\frac{12}{5} \\ r=\frac{3\cdot5}{12} \\ =\frac{5}{4} \\ =1\frac{1}{4} \end{gathered}\)Thus, cups of raisins required is 1 1/4.
If r = 7 units and x = 5 units, then what is the volume of the cylinder
The cylinder's volume is 245 cubic units as a result.
Define the cylinder's volume?It is possible to determine how much material a cylinder can carry by using its volume, which is known as its capacity in geometry. Cubic measurements for a cylinder's volume include cm³, m³, in³, etc.
The formula V = r²h is used to determine the volume of a cylinder, where r is the radius of its circular base and h is the height between the bases' perpendicular centers.
As a result, if r = 7 units and x = 5 units, we can use the formulas below to get the cylinder's volume:
V = πr²h
V = π(7)²(5)
= 245 cubic units per volt
Consequently, the size of the cylinder 245 cubic units as a result.
Complete question given below:
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If r = 7 units and x = 5 units, then what is the volume of the cylinder(height=x)?
The volume of the cylinder is 245π cubic units.
What is cylinder?The cylinder is a three-dimensional shape having a circular base. A cylinder can be seen as a set of circular disks that are stacked on one another.
The formula for the volume of a cylinder is:
V = πr²h
where r is the radius of the base, h is the height, and π is the mathematical constant pi (approximately equal to 3.14).
Substituting r = 7 units and h = 5 units into the formula, we get:
V = π(7)²(5)
V = π(49)(5)
V = 245π
Therefore, the volume of the cylinder is 245π cubic units. Note that the volume is an exact value in terms of π, and cannot be simplified further without a numerical approximation of π.
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Of the 12 pieces of fruit in the kitchen, seven-twelfths are peaches. How many peaches are in the kitchen?
Answer:
7
Step-by-step explanation:
7/12 of 12
7/12 × 12
7/1 × 1
= 7
Alice needs to rent a car while on vacation. The rental company charges $17.95, plus 15 cents for each mile driven. If Alice only has $40 to spend on the car rental, what is the maximum number of miles she can drive?
Answer:
Alice can drive 147 miles
Step-by-step explanation:
At first you subtract $17.95 from $40.
Then you are left with $22.05
Finally, you divide $22.05 by $0.15
And you get 147, so she can drive 147 miles without going over her limit.
The data set {+3, -1, -2, +1} shows The moves a player made forward or backward in a board game graph the moves the player made explain the meaning of the role in the situation.
We have the data set:
\(\mleft\lbrace+3,-1,-2,+1\mright\rbrace\)This shows the moves a player made forward or backward in a board game. Then, graphically, this is:
In this situation, 0 means that the player stayed at his position.
I really need help with this
I think its Igneous Rock but I'm not so sure...
THANKS
Answer:
That is igneous
Step-by-step explanation:
Sandra is 1.8 m tall. She stood 0.9 m from the base of the mirror and could see the top of
the cliff in the mirror. The base of the mirror is 5.4 m from the base of the cliff. What is
the height of the cliff?
The cliff rises 10.8 metres in height.
To determine the height of the cliff, we can use similar triangles and apply the concept of proportions.
Let's denote the height of the cliff as "h."
According to the given information, Sandra is 1.8 m tall and stands 0.9 m from the base of the mirror. The distance between the base of the mirror and the base of the cliff is 5.4 m.
We can form a proportion based on the similar triangles formed by Sandra, the mirror, and the cliff:
(Height of Sandra) / (Distance from Sandra to Mirror) = (Height of Cliff) / (Distance from Mirror to Cliff)
Plugging in the values we know:
1.8 m / 0.9 m = h / 5.4 m
Simplifying the equation:
2 = h / 5.4
To solve for h, we can multiply both sides of the equation by 5.4:
2 * 5.4 = h
10.8 = h
Therefore, the height of the cliff is 10.8 meters.
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Please someone end my suffering
Surface Area
Answer:
107 in ²
Step-by-step explanation:
Surface area of the triangular prism = bh + L(s1 + s2 + s3)
Where,
b = 2 in.
h = 8 in.
s1 = 8.2 in.
s2 = 2 in.
s3 = 8 in.
L = 5 in.
Substitute
Surface area = 2 × 8 + 5(8.2 + 2 + 8)
Surface area = 16 + 5(18.2)
Surfaces area = 16 + 91
Surface area = 107 in ²
solve the functions for b I am having many difficulties
From the figure we see that the function in b, only asigns values for the points in -3, -1, 1, 3 and 4 of the x axis.
Then it's domain is
\(\text{Dom}=\lbrace-3,-1,1,3,4\rbrace\)To find the range of the figure in b, we have to see what values does it take in the y axis, we notice that this values are -4, 0, 1, 4 and 5. Hence
\(\text{Range=}\lbrace-4,0,1,4,5\rbrace\)In the case of c. we notice that the lines go on (that's is why it's represented by arrows). We note that if the lines go on, eventually they will take all the values on the x axis. Then
\(\text{Dom=(-}\infty,\infty)\)For the range we notice that it will take all the positive values on the y axis. then
\(\text{Range}=\lbrack0,\infty)\)In the case of the function a, we notice that the function assigns values to every point from -4 to 4 on the x axis. Then we can conclude that the domain is
\(\text{Domain=}\lbrack-4,4\rbrack\)We also notice that the values that y takes are from 0 to 4, therefore
\(\text{Range}=\lbrack0,-4\rbrack\)Please help me I'm stuck. I will give 30 points for this one. Given triangle ABC tilde triangle PQR and your scale factor Complete the hotspots for these similar triangles and show work
The value for the hotspots of the similar triangles ∆ABC and ∆PWR are:
(1). angle B = 68°
(2). PQ = 5cm
(3). BC = 19.5cm
(4). area of ∆PQR = 30cm²
What are similar trianglesSimilar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.
(1). angle B = 180 - (22 + 90) {sum of interior angles of a triangle}
angle B = 68°
Given that the triangle ∆ABC is similar to the triangle ∆PQR.
(2). PQ/7.5cm = 12cm/18cm
PQ = (12cm × 7.5cm)/18cm {cross multiplication}
PQ = 5cm
(3). 13cm/BC = 12cm/18cm
BC = (13cm × 18cm)/12cm {cross multiplication}
BC = 19.5cm
(4). area of ∆PQR = 1/2 × 12cm × 5cm
area of ∆PQR = 6cm × 5cm
area of ∆PQR = 30cm²
Therefore, the value for the hotspots of the similar triangles ∆ABC and ∆PWR are:
(1). angle B = 68°
(2). PQ = 5cm
(3). BC = 19.5cm
(4). area of ∆PQR = 30cm²
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Pls answer this I will give 10 points and brainlest for 4 to 6 answers
Answer:
wheres the question
Step-by-step explanation:
Please help I will mark brainiest and give 20 points! ASAP
Answer:
1 - Square pyramid
2 - Cube
3 - Right triangular pyramid
4 - Rectangular pyramid
5 - Triangled pyramid
Step-by-step explanation:
Hope this helps
Maybe brainliest?
Answer:
Step-by-step explanation:
cube 2
rectangle prism 3
right triangle prism 4
square pyramid 1
triangular pyramid 5
Rewrite 48 + 60 using the distributive property
Answer:
12* ( 4+5)
Step-by-step explanation:
48 = 12 * 4
60 = 12 * 5
48 + 60 = 12*4 + 12*5
= 12*( 4 + 5)
= 12* 9
= 108
In the soup can below, the height is approximately 538 inches and the diameter is 3 inches.
What is the area of the label if the combined lips of the can are 38 inches and there is about 12 inch of overlap for the glue.
If the can's combined lips measure 38 inches and the adhesive overlaps by around 12 inches, the label's surface area will be 50 square inches.
What is the area?The space filled by a flat form or the surface of an item is known as the area.
The number of unit squares that cover the surface of a closed-form is the figure's area. Square centimeters and other similar units are used to measure area.
Given data;
Height of can,\(\rm H=5 \frac{3}{8} \ inch\)
Height of label,
\(\rm h=5\frac{3}{8} -\frac{3}{8} \\\\ h= 5 \ inch\)
Diameter,\(\rm d= 3 \ inch\)
The area of the label is;
A = ( overlap area + circumfereence ) h
\(\rm A = [\frac{1}{2} + 2 \pi \times \frac{3}{2} ] \\\\ A =[ \frac{1+6\pi}{2} ] \times 5 \\\\ A = 49.6 \ inch^2\)
Hence, the label's surface area will be 50 square inches.
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