The statement is false.
O(nlogn), commonly known as loglinear complexity, denotes that n times will be required to perform logn operations.
The term "1 half n (n space plus log space n )space" is equivalent to O(n log n) which is a class of functions that grow asymptotically no faster than n log n.
On the other hand, the term "omicron (n squared)" is equivalent to o(n^2), which is a class of functions that grow asymptotically slower than n^2.
As a result, it is untrue to say that there is a single half-n (n space plus log n)space element in the omicron (n squared) space.
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Write an equivalent expression without parentheses. Then simplify the result.
7m- (2+4m)
Which expression is equivalent to 7m - (2 + 4m)?
OA. 7m-2-4m
OB. 7m.-2+ 4m
OC. 7m+2-4m
OD. 7m + 2 + 4m
The equivalent expression to 7m - (2 + 4m) is 7m - 2 - 4m. The first option from the given options is
Equivalent expressions.Algebraic expressions that produce the same final expression are said to be equivalent expressions. If the values of two algebraic expressions can be obtained by replacing the variables, then the expressions are equivalent. Using the equal symbol (=), equivalent phrases are represented or illustrated to one another.
From the information given;
= 7m - (2 + 4m)
= 7m - 2 - 4m
Therefore, we can conclude that the equivalent expression to 7m - (2 + 4m) is 7m - 2 - 4m.
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2) g(x) = 4x + 5
f(x)=-3x²-3x
Find g(x) + f(x)
Answer:
[tex]\huge\boxed{\sf -3x\² + x + 5}[/tex]
Step-by-step explanation:
Given functions:g(x) = 4x + 5
f(x) = -3x² - 3x
Add both functionsg(x) + f(x):= 4x + 5 + (-3x² - 3x)
= 4x + 5 - 3x² - 3x
Combine like terms= 4x - 3x + 5 - 3x²
= x + 5 - 3x²
= -3x² + x + 5[tex]\rule[225]{225}{2}[/tex]
Greta has two pet lizards, Draco and Lizzy. For every 11 crickets Greta feeds Draco, she always feeds Lizzy 8 crickets. Last week, Greta fed Draco 77 crickets.
The number of crickets Great fed last week to Lizzy is 56.
What are proportions?Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.
Given that, For every 11 crickets Greta feeds Draco, she always feeds Lizzy 8 crickets.
Last week, Greta fed Draco 77 crickets.
Let the number of crickets Great fed last week be x.
Now, 11:8::77:x
11x=77×8
x=7×8
x=56
Therefore, the number of crickets Great fed last week to Lizzy is 56.
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"Your question is incomplete, probably the complete question/missing part is:"
Greta has two pet lizards, Draco and Lizzy. For every 11 crickets Greta feeds Draco, she always feeds Lizzy 8 crickets. Last week, Greta fed Draco 77 crickets. How many crickets did Greta feed Lizzy?
At a construction site, sand is poured from a truck into a conical pile. The pile has a diameter of 12
feet and is 10 feet tall. Which of the following best describes the volume of the sand?
The volume of the sand which is equal to the volume of the cone will be 376.8 cubic feet.
What is the volume of the cone?Let h be the height of the cone and A be the base area of the cone.
Then the volume of the cone will be given as,
Volume = (1/3) × A × h
At a construction site, sand is poured from a truck into a conical pile. The pile has a diameter of 12 feet and is 10 feet tall.
The base area of the cone is given as,
A = π × (d/2)²
A = 3.14 × (12 / 2)²
A = 3.14 × 36
A = 113.04 square feet
Then the volume of the cone is given as,
V = 1/3 × 113.04 × 10
V = 376.8 cubic feet
The volume of the sand which is equal to the volume of the cone will be 376.8 cubic feet.
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Solve for x.
X
A
=
2
C
1
B
1
E
X
D
Step-by-step explanation:
ABC and ADE are similar triangles.
that means they have the same angles, and there is one scaling factor for all sides from one triangle to the other.
so, we see that AB = 2, AD = 2+1 = 3
the scaling factor f from AB to AD is then
AB × f = AD
2 × f = 3
f = 3/2
the same scaling factor now applies between BC and DE (= x).
BC × f = x
1 × 3/2 = x
x = 3/2 = 1.5
if the sum of two consecutive even numbers is 42 find the number
Answer:
20 and 22
Step-by-step explanation:
if the sum of two consecutive even numbers is 42 find the number
42 - 2 = 40 remove the difference (2)
40 : 2 = 20 find the smallest number
20 + 2 = 22 find the largest number
------------------------------------
(20 + 22 = 42)
the average number of dropout for a school dsitrict has been 305 per year with a standard eveiation of 50. what is the probility that the number of dropouts next year will be: g
The probability that the number of dropouts next year will be exactly 305 is virtually zero, the probability of less than 305 is 68%, greater than 305 is 32%, and within one standard deviation of 305 is 95%.
Probability of dropouts next year being exactly 305: 0
Probability of dropouts next year being less than 305: 0.68
Probability of dropouts next year being greater than 305: 0.32
Probability of dropouts next year being within one standard deviation of 305: 0.95
The probability that the number of dropouts next year will be exactly 305 is virtually zero. This is because the standard deviation of 50 suggests that the number of dropouts is likely to be different from 305.
The probability that the number of dropouts next year will be less than 305 can be calculated using the normal distribution. The probability that the number of dropouts will be less than 305 is approximately 0.68, or 68%.The probability that the number of dropouts next year will be greater than 305 can be calculated using the normal distribution. The probability that the number of dropouts will be greater than 305 is approximately 0.32, or 32%.The probability that the number of dropouts next year will be within one standard deviation of 305 (i.e. between 255 and 355) can be calculated using the normal distribution. The probability that the number of dropouts will be within one standard deviation of 305 is approximately 0.95, or 95%.
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How many envelopes can be made from a sheet of paper measuring 324 cm by 172 cm, if
each envelope requires a piece of paper of size 18 cm by 12 cm?
Answer: 258 envelopes
Step-by-step explanation:
assume you have applied to two different universities (let's refer to them as universities a and b) for your graduate work. in the past, 10% of students (with similar credentials as yours) who applied to university a were accepted, while university b accepted 50% of the applicants. assume events are independent of each other. a. what is the probability that you will be accepted to both universities?
If 10% of students who applied to university a were accepted, while university b accepted 50% of the applicants. The probability of being accepted to both universities is 0.05, or 5%.
The probability of being accepted at University A is 10%, which means the probability of not being accepted at University A is 90% (or 0.9). The probability of being accepted at University B is 50%, which means the probability of not being accepted at University B is 50% (or 0.5).
Since the events of being accepted at each university are independent of each other, we can use the multiplication rule of probability to find the probability of being accepted at both universities.
P(A and B) = P(A) x P(B)
where P(A and B) represents the probability of being accepted at both universities, P(A) represents the probability of being accepted at University A, and P(B) represents the probability of being accepted at University B.
Plugging in the values we have:
P(A and B) = 0.1 x 0.5 = 0.05
Therefore, the probability of being accepted to both universities is 0.05, or 5%. This means that there is a very low chance of being accepted at both universities, given the acceptance rates provided.
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m ∠ a = ____ degrees
Answer:
m<a = 44°
Step-by-step explanation:
Left triangle:
95 + 39 + x = 180
x = 46
Right triangle:
46 + 90 + a = 180
a = 44
Solve this system of linear equations:
4x - 2y = 8
y=-2
Step 1: Plot the x-intercept of the first equation.
Equations by Graphing
d
-6-4-2
6
4
2
-2
4
-6
Y
2
4 6
x+
x
y
A solution to this system of linear equations is (1, -2).
How to graph the solution to this system of equations?In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;
4x - 2y = 8 ......equation 1.
y = -2 ......equation 2.
Next, we would use an online graphing calculator to plot the given function as shown in the graph attached below.
Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant IV and it is given by the ordered pair (1, -2).
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HI PLEASE HELP NEED ANSWERS ASAP :(!!
2. Two observers are 600 ft apart on opposite sides of a flagpole. The angles of elevation from the
observers to the top of the pole are 19 and 21°. Find the height of the flagpole. Round to the nearest
foot.
After finding the sides of the triangle using sine law, we found that the height of the flagpole is found to be 110.89 ft.
What is meant by sine law?
The law of sines specifies how many sides there are in a triangle and how their individual sine angles are equal. The sine law, sine rule, and sine formula are additional names for the sine law.
The side or unknown angle of an oblique triangle is found using the law of sine. Any triangle that is not a right triangle is referred to as an oblique triangle. At least two angles and their corresponding side measurements should be used at once for the sine law to function.
Given,
The distance between two observers = 600 ft
The angle of elevation of the first observer = 19°
The angle of elevation of the second observer = 21°
We are asked to find the height of the flagpole.
The figure is given below.
There are 2 right triangles, ΔABD and ΔCBD.
We will start with ΔABC.
∠B = 180 - (∠A+∠C) = 180 - (21+19) = 140
Now using sine law, we can find lengths a and b.
According to sine law,
b/sin21 = a/sin 19 = 600/sin 140
From this,
b/sin 21 = 600/sin 140
b/0.36 = 933.43
b = 336.03ft
Also,
a/sin 19 = 600/sin 140
a/0.33 = 933.43
a = 308.03ft
Now using ΔABD,
sin 21 =h/a
0.36 = h/308.03
h = 110.89 ft
Therefore after finding the sides of the triangle using sine law, we found that the height of the flagpole is found to be 110.89 ft.
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There are purple, white and blue counters in a bag in the ratio 16:18:3
There are 78 more purple counters than blue counters.
How many white counters are there?
Answer:
Step-by-step explanation:
Step-by-step explanation:
Let's call the number of purple counters "x". This means that the number of blue counters is x - 78, and the number of white counters is 18x.
According to the ratio, the sum of the number of purple and blue counters is 16x + (x - 78) = 17x - 78.
And the sum of all counters is 16x + 18x + 3x = 37x.
Knowing that the sum of all counters is the same, we can set the two sums equal to each other:
37x = 17x - 78 + 37x
So, we have:
74x = 17x - 78 + 37x
57x = -78
x = -78/57
Since x can't be negative, we have to reject this solution.
However, the number of white counters can be found by multiplying 18 by the number of purple counters:
18 * x = 18 * (x/57) = (18/57) * x = (18/57) * 78 = 72
Therefore, there are 72 white counters in the bag.
suppose that a senate committee is composed of 15 senators of whom 4 are left-handed. what proportion of the committee are left-handed? either give the exact fraction or decimal, or round to three decimal places.
The proportion of the committee that is left-handed is 4/15, which is equivalent to 0.267 when rounded to three decimal places.
A proportion is a way of expressing the relationship between two quantities. It is often written as a fraction, where the numerator represents the quantity of interest, and the denominator represents the total quantity.
In this case, we are interested in the proportion of left-handed senators, so the numerator will be the number of left-handed senators, which is 4. The denominator will be the total number of senators in the committee, which is 15. Therefore, the proportion of left-handed senators can be written as:
4/15
This fraction can also be expressed as a decimal by dividing the numerator (4) by the denominator (15) using a calculator or long division. When rounded to three decimal places, the decimal equivalent of the fraction is:
0.267
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monique is 2 years older than vanessa. the sum of their ages is 32.let v represent vanessas age.which of the following equations can be used to find vanessas age?
a.v+2=32
b.2v -2=32
c.v+(v-2)=32
d.v+(v+2)=32
The correct option is a. The equation used to find Vanessa's age is v + 2 = 32.
What is an equation?A mathematical statement known as an equation utilises the equals sign to demonstrate the equality of two expressions. It may be used to address a variety of issues and can contain both numbers and variables. Algebraic operations including addition, subtraction, multiplication, division, and exponentiation are frequently used in equations.
In the given question, Vanessa's age may be calculated using the equation a. v+2=32. This equation shows that Vanessa's age plus 2 equals 32, implying that Vanessa's age is 30. We may solve this equation by removing 2 from both sides, yielding v=30. This equation is valid for determining Vanessa's age because it specifies that Vanessa's age plus Monique's age equals 32.
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Some girl needs to earn R500 in interest so she will have enough to buy a used bicycle. She puts R2000 into an account that earns 5% per year simple interest. How long will she need to leave her money in the account to have enough money for the bicycle?
The money needs to be in the account for 5 years on simple interest at the rate 5% to earn R500.
What is simple interest?The interest on a loan or principal amount can be easily calculated using simple interest. Simple interest is a notion that is employed across a wide range of industries, including banking, finance, automobiles, and more. When you pay back a loan, the monthly interest is deducted first, and any remaining funds are applied to the principle.
Let us suppose the time period as x.
The simple interest is given as:
SI = PRT/100
Where,
SI = Simple Interest = 500
P = Principal = 2000
R = Rate = 5%
T = x
Substituting the values:
500 = (2000)(5)(x) / 100
500 = 100x
x = 5 years
Hence, the money needs to be in the account for 5 years on simple interest at the rate 5% to earn R500.
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1/4 of the sum of 18 and 6. What does that mean? It it like converting 18 plus 6 to a fraction?
Answer:
See below
Step-by-step explanation:
Sum of 18 and 6 = 24
1/4 of the sum of 18 and 6 is asking you what is the result of dividing 24 by 4
In a way you can think of it as a fractional question but the answer is a whole number
[tex]\dfrac{1}{4} \cdot (18 + 6) = \dfrac{1}{4} \cdot 24 = \dfrac{24}{4} = 6\\[/tex]
A middle school club is planning a homecoming dance to raise money for the school. Decorations for the dance cost $80, and the club is charging $10 per student that attends.
Which graph describes the relationship between the amount of money raised and the number of students who attend the dance?
The total amount y collected from x students is y = 10x.
The graph is given below.
What is an expression?An expression contains terms with addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The club is charging $10 per student that attends.
This means,
Number of students = x
The total amount y collected from x students.
y = 10x
The graph is given below.
Thus,
y = 10x is the total amount y collected from x students is
The graph is given below.
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What does the Pythagorean Theorem and its converse state if each triangle is a right triangle?
The Pythagorean Theorem is a fundamental theorem in Euclidean geometry that relates to the sides of a right triangle.
The Pythagoras Theorem states that : in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of squares of lengths of other two sides.
Mathematically, the Pythagoras Theorem is written as:
⇒ c² = a² + b² ;
where c is = length of the hypotenuse, and a and b are the lengths of the other two sides of the right triangle.
The Converse of Pythagoras Theorem states that : If in a triangle, the square of the length of the longest side is equal to the sum of squares of lengths of other two sides, then triangle is a right triangle.
Both the Pythagorean Theorem and its converse apply only to right triangles, which are triangles that have a right angle .
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The lengths of the three sides of a triangle (in inches) are consecutive integers. If the
perimeter is 27 inches, find the value of the shortest of the three side lengths.
The value of the shortest of the three side lengths is 3 inches.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
The lengths of the three sides of a triangle (in inches) are consecutive integers.
The three sides are x, x+1 and x+2 which are consecutive.
We know that perimeter of a triangle is the sum of the three sides of a triangle.
Add the three Consecutive sides to find the perimeter.
Perimeter of triangle=x+x+1+x+2
The perimeter of triangle is 27 inhces.
27=3x+3
Substitute 3 from both sides
24=3x
Divide by 3 on both sides
8=x
Hence, the value of the shortest of the three side lengths is 3 inches.
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Find the perimeter of the rectangle in the given diagram.
Recall: To find the perimeter of a rectangle, add all of its sides.
15
Perimeter =
9
A
The perimeter of the rectangle in the given diagram is: D. 42 units.
How to determine the perimeter of this rectangle?In order to determine the perimeter of this rectangle, we would have to find the length of the third side of the right-angled triangle by using Pythagorean's theorem. Mathematically, Pythagorean's theorem is given by this mathematical expression:
a² + b² = c²
Where:
a, b, and c represents the side lengths of a right-angled triangle.
9² + b² = 15²
81 + b² = 225
b² = 225 - 81
b = √144
b = 12 units.
Mathematically, the perimeter of a rectangle can be calculated by using this mathematical expression;
P = 2(L + W)
Where:
P represents the perimeter of a rectangle.L represents the length of a rectangle.W represents the width of a rectangle.P = 2(9 + 12)
P = 42 units.
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Lamonte is going to invest in an account paying an interest rate of 4% compounded
continuously. How much would Lamonte need to invest, to the nearest cent, for the
value of the account to reach $12,300 in 8 years?
The amount that needs to be invested at the interest rate of 4% compounded continuously is P = $8932.461.
What is compound interest?Compound interest, also known as interest on principal and interest, is the practise of adding interest to the principal amount of a loan or deposit. It occurs when interest is reinvested, or added to the loaned capital rather than paid out, or when the borrower is required to pay it, so that interest is generated the next period on the principal amount plus any accumulated interest. In finance and economics, compound interest is common.
Given that the interest is compounded continuously.
For the given situation the formula of compound interest is:
[tex]A = Pe^{rt}[/tex]
where, A is the amount = $12300
P is the principal amount
r is the rate = 4% = 0.04
t is the time = 8 years
Substituting the values we have:
[tex]12300 = Pe^{(0.04)(8)}\\\\P = \frac{12300}{e^{(0.04)(8)}} \\\\P =8932.461[/tex]
Hence, the amount that needs to be invested at the interest rate of 4% compounded continuously is P = $8932.461.
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The top of building A is 418 feet high. This is about 3 times as high as the top of building B.
About how high is the top of building B?
Select the numbers that correctly complete the sentence.
The top of building B is between
Choose...
feet high.
Answer:139.33 or 139 ft high
Step-by-step explanation: since building A is three times as high as building B, we can use the equation 418/3=B, which results in 139.33, and if rounding it needed you could round it to 139
For the following right triangle, find the side length A15 B20
Answer:
Step-by-step explanation:
you first take A15 and square it. Then you take B20 and square it also. Then you add them together and that is your answer. the hypotenuse of a triangle.
Answer: Side length C will be 25
Step-by-step explanation:
C^2 = A^2+B^2
15^2+20^2=C^2
225+400=625
Take square root of 625 to get side C
Josh’s backpack can hold at most 35 pounds. His science textbook weighs 8 pounds, his math textbook weighs 4 pounds, and his binder weighs 2 pounds. He has three more textbooks, how much can each one weigh?
Answer:
7
Step-by-step explanation:
35-8-4-2=21
21/3=7
Answer:
7 pounds
Step-by-step explanation:
8+4+2=14
35-14=21
21/3=7
Anthony makes 6 1/8 gallons of lemonade for a family picnic. His family drinks 2 1/4 gallons of the lemonade. Which of these containers is the SMALLEST Anthony can use to store the remaining lemonade?
Answer:
3 and 7/8 gallons remaining
Step-by-step explanation:
You did not give the container options, but hopefully this will help
what is the interest rate on an investment of $470 at for seven years with an ending balance of 683.85
Answer:
Step-by-step explanation:
To find the interest rate on an investment of $470 for seven years with an ending balance of $683.85, you can use the formula for simple interest:
I = P * r * t
Where I is the interest earned, P is the principal amount ($470), r is the interest rate, and t is the number of years (7).
Rearranging the formula to solve for r:
r = I / (P * t)
Substituting the given values:
r = (683.85 - 470) / (470 * 7)
r = 213.85 / 3290
r = 0.0649 or 6.49%
So, the interest rate on the investment of $470 for seven years with an ending balance of $683.85 is 6.49%.
what is the mode of the number of girl in the three classes?
There is no mode of the number of girl in the three classes.
What is Mode of the Data?The value that appears the most frequently in a data collection when it is unique is known as the mode, and like the median and mean, it can be used to measure central tendency. However, occasionally there is either no mode or more than one mode.
Given:
The data for boys: 15, 12, 12
The data for Girls: 14, 12, 16
As, mode is the most repeating data.
We can see that the data repeats in boys but not for the Girls.
So, number of boys have the mode but the number of girls do not have the mode.
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What was the first vaccine created for? A. Measles B. Polio C. Small pox D. Mumps
In 1798, the first vaccination (for small pox) was discovered. The most notable achievement of these efforts has been the elimination of smallpox sickness from the world.
Hence, option (c) is correct choice.
In 1721, Lady Mary Wortley Montagu introduced smallpox vaccination to Europe by requesting that her two children be immunised against the disease, as she had seen done in Turkey. Dr. Edward Jenner developed the world's first effective vaccination. He discovered that those who had cowpox were resistant to smallpox.
Edward Jenner, a rural doctor from Berkeley (Gloucestershire), England, conducted the world's first vaccine in 1796. Jenner injected an eight-year-old kid, James Phipps, with pus from a cowpox lesion on a milkmaid's hand.
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