The correct answer is option A which is the ordered pair of point P’ will be (8.75, 5.25).
What is scale factor?The scale factor is defined as the proportion of the new image's size to that of the previous image. decision-making.
here, we have,
If pentagon OPQRS is dilated by a scale factor of 7/4 from the origin, to create O’P’Q’R’S’, what is the ordered pair of point P’
Multiply the coordinates of point P by the scale factor 7/4 to get the coordinates of P'.
Given : P(-5,3)
P' (x,y) = P (-5 x 7/4 , 3 x 7/4)
= P(-8.75, 5.25)
Therefore the correct answer is option A which is the ordered pair of point P’ will be (-8.75, 5.25).
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The middle school band is going to take a field trip either to a water park or to an amusement park. The band director surveyed all of the middle school band members to determine the preferred field trip. The results are displayed in the table below.
Field Trip Survey
Students Amusement Park Water Park Total
Seventh-Grade 14 26 40
Eighth-Grade 16 64 80
Total 30 90 120
Which statement is true about the results of the survey?
Responses
A 33% of the students prefer the amusement park.33% of the students prefer the amusement park.
B 25% of the eighth-grade students prefer the amusement park.25% of the eighth-grade students prefer the amusement park.
C 67% of the students prefer the water park.67% of the students prefer the water park.
D 65% of the seventh-grade students prefer the water park.
The statement which is true is D. 65% of the seventh-grade students prefer the water park.
What is Percentage?Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.
A : Total number of students = 120
Number of students who prefer amusement park = 14 + 16 = 30
Percentage of students who prefer amusement park = 30 / 120 = 0.25 = 25%
B : Total number of eighth grade students = 80
Number of eighth grade students who prefer amusement park = 16
Percentage = 16 / 80 = 0.2 = 20%
C : Total number of students = 120
Number of students who prefer water park = 26 + 64 = 90
Percentage = 90 / 120 = 0.75 = 75%
D : Total number of seventh grade students = 40
Number of seventh grade students who prefer water park = 26
Percentage = 26 / 40 = 0.65 = 65%
Hence the option D is the correct percentage.
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Colin the Conservationist has been investigating the IUCN Red Data list of species.
Between 66 and 67 thousand species have been assessed and placed on the list.
Your task is to work out the number of species in each of 7 categories.
There are 78 species which are "extinct in the wild".
11 times that many have gone "extinct" since 1500AD.
Respectively 6 and 9 times as many species as have gone
"extinct" are on the "critically endangered" and "endangered" lists.
24,570 species are listed as threatened, which means they are
"vulnerable", "endangered" or "critically endangered".
The number of "near threatened"
species is 468 more than a third of
the number which are "vulnerable".
The good news is that there are
7,098 more species on the "least
concern" list than in all the other
categories combined
Based on the IUCN Red Data list of species, by solving the data we get the number of species in each category as
Extinct in the Wild = 78 Extinct = 858Critically Endangered = 5,148Endangered = 7,722Threatened = 24,570Vulnerable = 12,700Near Threatened = 4,838Least Concern = 7,098Total = 67,000
The answer which has been provided above gives the number of species that are present in each of the 7 categories of the IUCN Red Data List.
The IUCN Red Data List is a list of species that are globally threatened.
The categories that are present in the IUCN Red Data List are
Extinct in the Wild, Extinct, Critically Endangered, Endangered, Threatened, Vulnerable, Near Threatened, and Least Concern.
The number of species in each category is calculated based on the given information:
There are 78 species that are extinct in the wild.
Hence,
Extinct in the Wild: 7811 times that many have gone extinct since 1500 AD.
Hence,
Extinct: 78 × 11 = 858 species.6 and 9 times as many species have gone extinct are on the critically endangered and endangered lists respectively.
Hence,
Critically Endangered: 858 × 6 = 5,148 species.Endangered: 858 × 9 = 7,722 species.24,570 species are listed as threatened In the IUCN Red Data list.
Hence,
Threatened: 24,570.According to the list, the number of near-threatened species is 468 more than a third of the number which is vulnerable.
Hence,
Vulnerable = 12,700 Near Threatened: (12,700 ÷ 3) + 468 = 4,838 species.According to the data, there are 7,098 more species on the least
Least Concern = 7,098The total number of species on the IUCN Red Data List is calculated by adding up the number of species in each category:
Total: 78 + 858 + 5,148 + 7,722 + 24,570 + 4,838 + 7,098 = 67,000 species.Learn more about IUCN:
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The first five terms of a pattern are given below.
37, 42, 47, 52, 57
Which expression can be used to determine the nth term of the pattern?
The expression aₙ = 37 + (n - 1)5 can be used to determine the nth term of the arithmetic sequence pattern?
What is an Arithmetic sequenceAn arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
The nth term of an arithmetic sequence is derived using; aₙ = a + (n - 1)d where a is the first term and d the common difference
Given the first term as 37, we have that;
a₁ = a + (1 - 1) d = 37
a₁ = a = 37
for the second term 42, substituting 37 for a;
a₂ = 37 +(2 - 1)d = 42
37 + d = 42
d = 42 - 37 {subtract 37 from both sides}
d = 5
Therefore, the arithmetic sequence increase by a common difference 5 and the expression aₙ = 37 + (n - 1)5 can be used to determine the nth term of the arithmetic sequence pattern?
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do the three lines 3x1−12x2=4, 6x1 39x2=−76, and −3x1−51x2=80 have a common point of intersection? explain.
Yes, the three lines have a common point of intersection. This point is located where all three equations equal the same value, which in this case is (4,-4).
Yes, the three lines 3x1−12x2=4, 6x1 39x2=−76, and −3x1−51x2=80 have a common point of intersection. This point is located where all three equations equal the same value. To find this point, one must solve the three equations simultaneously. First, one can subtract the first equation from the third equation, which will result in a new equation equal to −3x1 + 48x2 = 76. From there, one can subtract the second equation from the new equation, resulting in a new equation equal to −45x2 = 132. From this equation, one can solve for x2 and the result is x2 = -4. Then, one can substitute the value of x2 into any of the original equations to solve for x1 and the result is x1 = 4. Therefore, the common point of intersection for these three equations is (4, -4).
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What is the value of v?
Answer:
39°
Step-by-step explanation:
Information we need to know
The triangle is a SAS triangleTwo of the angles are equalAngles in a triangle add up to 180°As we know, one of the angles in this triangle is 39° this means that the angle opposite it would also be 39°! This is because as the triangle is SAS v and the given 39 has to be equal
Have a lovely day :)
Answer:
39°
Step-by-step explanation:
Triangle HJI is an isosceles triangle.
In isosceles triangles the base angles are congruent which means their measures are equal.
So the measure of m∠HIJ = 39°
Scarlett usually rides her bike about 1 and 1/5 hours every day. The distance between the library and school is 7/8 mile. Yesterday the bike had a problem and Scarlett only rode her bike 2/3 of the way from school to the library and walked the rest of the way. How far did she ride her bike
Scarlett typically rides her bike for around 1 and a half hours per day, thus she covered a distance of 7/12.
what is distance ?The overall uninspired velocity of an object will be its distance. Distance is the amount of space an object has traveled, regardless of where it began or ended. Distance would be the measurement of said size or extent of the separation between two places. It is important to keep in mind that the distance between two spots and the traveled between them aren't the same thing. Distance traveled is the sum of a line's length joining various places. Distance refers to the actual travel path of a body. Path length is another term for it. For instance, if an object is traveling from board to point P, the path's length will be similar to OP = 360 m.
given
We are aware of: t = 1 1/5 d = 7/8
Write down and replace 7/8 = v * (1* 1/5)
Remove the connecting element: 7/4 * 1/3
As a single fraction, write:
7 / 4*3
Determine the quotient or product: 7/12
Response: 7/12
Scarlett typically rides her bike for around 1 and a half hours per day, thus she covered a distance of 7/12.
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PLEASE HELP ASAP
An element with a mass of 660 grams decays by 5.1% per minute. To the nearest tenth of a minute, how long will it be until there are 280 grams of the element remaining?
The time in minutes until there are 280 grams of the element remaining is given as follows:
16 minutes.
How to model the situation?A decaying exponential function is modeled as follows:
y = a(1 - r)^t.
In which the parameters are given as follows:
a is the initial amount.r is the decay rate, as a decimal.The parameter values for this problem are given as follows:
a = 660, r = 0.051.
Hence the function is modeled as follows:
y = 660(0.949)^t.
The time until there are 280 grams remaining is given as follows:
280 = 660(0.949)^t.
(0.949)^t = 280/660
tlog(0.949) = log(280/660)
t = log(280/660)/log(0.949)
t = 16 minutes.
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you decide to roll 2 6 sided dice once. what is the probability that the sum of the spots on the dice will add up to a 5
The probability of rolling a 5 with two 6-sided dice is 1/9 or approximately 0.11.
This can be found by calculating the number of combinations that add up to 5. There are 2 combinations that add up to 5: (1, 4) and (2, 3). Out of 36 possible combinations of rolling 2 dice (6 x 6), there are only 2 combinations that give us a sum of 5, so the probability is 2/36 or 1/18 or approximately 0.11.
Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event is impossible, and 1 means the event is certain to happen. A probability of 0.5 means that the event has an equal chance of happening or not happening.
The probability of an event is calculated by dividing the number of favorable outcomes by the number of possible outcomes. For example, if you flip a fair coin, the probability of getting heads is 1/2 because there are two possible outcomes (heads or tails) and only one of them is favorable (heads).
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The probability of rolling a 5 with two 6-sided dice is 1/9 or approximately 0.11.
This can be found by calculating the number of combinations that add up to 5. There are 2 combinations that add up to 5: (1, 4) and (2, 3). Out of 36 possible combinations of rolling 2 dice (6 x 6), there are only 2 combinations that give us a sum of 5, so the probability is 2/36 or 1/18 or approximately 0.11.
Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event is impossible, and 1 means the event is certain to happen. A probability of 0.5 means that the event has an equal chance of happening or not happening.
The probability of an event is calculated by dividing the number of favorable outcomes by the number of possible outcomes. For example, if you flip a fair coin, the probability of getting heads is 1/2 because there are two possible outcomes (heads or tails) and only one of them is favorable (heads).
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Pablo took out an 80/20 mortgage to buy a house that cost $140,000. The first (80%) mortgage has an interest rate of 4. 75%, and the second (20%) mortgage has an interest rate of 7. 525%. Both the first mortgage and the second mortgage are 30-year fixed-rate mortgages. What is the total monthly mortgage payment for the house?
To find the total monthly mortgage payment, we need to calculate the monthly payments for both the first (80%) and second (20%) mortgages and then add them together.
First, we'll find the monthly payment for the first mortgage:
Loan amount: $140,000 x 80% = $112,000
Interest rate: 4.75% / 12 months = 0.0395%
Loan term: 30 years x 12 months/year = 360 months
Monthly payment: $112,000 * (0.0395% / (1 - (1 + 0.0395%)^-360)) = $527.64
Next, we'll find the monthly payment for the second mortgage:
Loan amount: $140,000 x 20% = $28,000
Interest rate: 7.525% / 12 months = 0.0627%
Loan term: 30 years x 12 months/year = 360 months
Monthly payment: $28,000 * (0.0627% / (1 - (1 + 0.0627%)^-360)) = $184.07
Finally, we'll add the monthly payments for both mortgages to get the total monthly payment:
Total monthly payment: $527.64 + $184.07 = $711.71
So, the total monthly mortgage payment for Pablo's house is $711.71.
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what’s the square root of 50, 147,96 and -8 square root 16
a box of 12 donuts will be distributed to 12 kids. each kid will get exactly one donut. there are 4 chocolate donuts, 4 jelly donuts, and 4 glazed donuts. how many ways are there to distribute the donuts? it matters which kid gets which flavor of donut.
The No Of ways are there to distribute the donuts = 34650
What is Probability?
Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.
Number of ways to distribute 12 donuts in 12 kids so that each kid got one donut = 12!
Though, there are 4 chocolate, 4 jelly and 4 glazed donuts.
Hence,
Total number of ways to distribution the donuts
= 12/4*4*4
= 34650
Total number of ways = 34650
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The No Of ways there to distribute the donuts = 34650
What is Probability?
Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.
Number of ways to distribute 12 donuts in 12 kids so that each kid got one donut = 12!
Though, there are 4 chocolate, 4 jelly and 4 glazed donuts.
Hence,
Total number of ways to distribute the donuts
= 12/4*4*4
= 34650
Total number of ways = 34650
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Suppose A Deck Of 52 Cards Is Shuffled And The Top Two Cards Are Dealt.A) How Many Ordered
5. Suppose a deck of 52 cards is shuffled and the top two cards are dealt.
a) How many ordered pairs of cards could possibly result as outcomes?
Assuming each of these pairs has the same chance, calculate:
b) the chance that the first card is an ace;
c) the chance that the second card is an ace (explain your answer by a symmetry argument as well as by counting);
d) the chance that both cards are aces;
e) the chance of at least one ace among the two cards.
6. Repeat Exercise 5, supposing instead that after the first card is dealt, it is replaced, and shuffled into the deck before the second card is dealt.
Suppose a deck of 52 cards is shuffled and the top two cards are dealt..
[tex]\left \P {{52} \atop {2}} \right.[/tex] =52!50! = 52 ×51 = 2652.
Now assuming each of the pairs has the same chance, calculate the probabilities for the following events
the chance that the first card is an ace;
There are 4aces in a deck, so the probability is
P (A)=
[tex]\frac{4}{52}\\ =\frac{1}{13}[/tex]
the chance that the second card is an ace
Again, there are 4aces in a deck, so the probability is
P(B)=
[tex]\\ \\ \frac{4}{52}\\ =\frac{1}{13}[/tex]
the chance that both cards are aces
There are 4aces in the deck. We already have the number ofpossible ordered pairs from P(A), each of which is equally likely. How many different ordered pairs give both aces? The answer is the number of permutations of two cards among four.
= [tex]\left \ P{4} \atop {2}} \right. \\\frac{4!}{2!}[/tex]
= 4*3
= 12
The probability that both cards are aces is therefore
[tex]\frac{\left \P {{4} \atop {2}} \right. }{\left \P{{52} \atop {2}} \right. }[/tex]
=12 /2652
=1/221
the chance of at least one ace among the two cards.
How many different permutations of the first two cards give at least one ace? The number that give two aces is P42, from above. The number that give an ace as the first card but not the second card is 4×48, since there are4aces, and after choosing one ace, there are 48 that possible non-aces for the second card. Likewise there are 48 ×4ways to choose an ace as the second card, but not the first. Thus the total number of ways that the two cards can have at least one ace is
P42+ 4 ×48 + 4 ×48 = 396.
The probability of of selecting at least one ace among the first two cards
= 396/3652
P (D)= 33 /221
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POINTS UP FOR GRABS!!!
9 i think
i’m pretty sure it’s 9 i just done it
Salary Payable at the beginning of the month totals $24,000. During the month, salaries of $128,000 were accrued as expense. If ending Salary Payable is $14,000, what amount of cash did the company pay for salaries during the month?
Answer:
118000
Step-by-step explanation:
cash out flow = beg balance - end balance
= 24 -14 =10K
128K - 10K =118K
actual pay out is 118K
answer quick
A state map shows 4 towns that are evenly spaced 3 inches apart from one another. The actual distance between each town is 57 miles. Which of the following correctly identifies the scale used in this map?
A.
1 inch equals 14.25 miles
B.
1 inch equals 76 miles
C.
1 inch equals 19 miles
D.
1 inch equals 17.6 miles
The statement that identifies the scale used in this map would be = 1 inch equals 19 miles. That is option C.
What is a map?A map is a diagram that can be used to represent the location and distance of various areas of a country or state.
In the map, there are 4 towns which are separated by 3 inches apart.
The actual distance apart = 57 miles
Therefore the actual scale that was used is calculated as follows;
3 inches = 57 miles
1 inch = X miles
make X mile the subject of formula;
X miles = 57/3 = 19 miles.
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Write 5.2288888… repeating as a fraction
Answer: 529/8
Step-by-step explanation:
6.4 divided by 49.92
Answer:
12.82
Step-by-step explanation:
6.4/49.92
multiply both the numerator and denominator with 100 since the denominator is to hundredth place
6.4×100/49.92×100
640/49.92=
compute in the calculator to get answer as;
12.82
Answer:
This is an approximate answer so I not sure if it is accurate.
0.1282051282
Hoped it helped and was the right answer
Express the ratio below in its simplest form.
4.5
:
3
1/2
Answer:
9 : 7
Step-by-step explanation:
given the ratio
4.5 : 3 [tex]\frac{1}{2}[/tex] , that is in decimal form
4.5 : 3.5 ( multiply both parts by 10 to clear the decimal )
= 45 : 35 ( divide both parts by 5 )
= 9 : 7 ← in simplest form
Answer:
9:7
Step-by-step explanation:
Convert all the numbers to either decimal or fraction. The operation becomes simple.
Simplifying after converting to decimal
Convert 3 1/2 to decimal 3 1/2 = 3 + 1/2
1/2 = 0.5
3 + 1/2 = 3 + 0.5 = 3.4
Ratio 4.5:3.5 = 4.5/3.5
Divide by 5 to give
[tex]\dfrac{4.5 /5 }{3.5/5} = 0.9/0.7\\\\[/tex]
Multiply both numerator and denominator by 10
0.9 x 10 = 9
0.7 x 10 = 7
So the ratio becomes 9/7 = 9:7
Simplifying after converting to fraction
4.5 = 4 + 0.5
0.5 = 1/2
5.5 = 4 + 1/2 = 4 1/2
Convert to mixed fraction:
4 1/2 = (4 x 2 + 1)/2 = 9/2
Convert 3 1/2 to fraction
3 1/2 = (3 x 2 + 1)/2 = 7/2
So 4.5 : 3 1/2 = 9/2 : 7/2
Multiplying by 2 we get the same answer: 9:7
Choose whichever approach you feel comfortable with
How you would convert the repeating, nonterminating decimal to a fraction? Explain the process as you solve the problem. 0.1515…
The process of converting repeating, non-terminating decimal to a fraction has been explained below. On conversion of 0.1515…, we get the fraction as 5/33.
What is a non-terminating decimal?
Non-terminating decimals are those decimal numbers that never reach an end since there is no endpoint in their decimal digits.
We are given a repeating, non-terminating decimal as 0.1515…
So, let x = 0.1515151515 ...(1)
Here, .15 is repeating
So, we will move one set of the repeating digits in front of the decimal.
By this, we get
100x = 15.1515151515 ...(2)
Now, on subtracting (1) from (2), we get
⇒100x - x = 15.1515151515 - 0.1515151515
⇒99x = 15
⇒x = 15/99
⇒x = 5/33
Hence, this way we can convert repeating, non-terminating decimal to a fraction.
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72+10t = 34+14t what is the anser
Answer:
9.5
Step-by-step explanation:
72 + 10t = 34 + 14t
72 - 34 = 14t - 10t
38/4 = 4t/4
9.5 = t
2078/08/20, A machine was valued Rs.20,000 whereas its original value was Rs. 17,500.
it is an accountancy question..please answer fast
The depreciation if production during the first year is 6,000 and total estimated production during the working life of the machine is 60,000 units is 15000.
How to calculate the depreciationCost of machine = Rs. 1,70,000; Scrap value = Rs. 20,000;
Depreciation in production during the first year = 6,000 units;
Production units during the life of the machine = 60,000 units
Depreciation rate per unit = (Rs. 1,70,000 - Rs. 20,000)/ 60,000 units
= Rs. 2.5
Depreciation of first year = 6,000 * Rs. 2.5 = Rs. 15,000
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Complete question
If the original cost of a machine is Rs. 170,000, estimated scrap value Rs. 20,000, what is the depreciation if production during the first year is 6,000 and total estimated production during the working life of the machine is 60,000 units.
Mr. Lin received a box of books in the shape of a rectangular prism. The volume of the box is 486 . What is the width of the box?Use the formula , where l is the length of the prism, h is the height, V is the volume, and w is the width.
The width of the box of books which Mr. Lin recieved which is in the shape of Rectangular Prism is (486/l*h) units.
What is a rectangular Prism ?A three-dimensional solid form having six sides, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.
According to the face form or the angle the faces make with the base, there are two different varieties of rectangular prisms.
A right rectangular prism has faces that are perpendicular to each of its bases. All of the side faces in this are rectangles.An oblique rectangular prism is one in which the faces are not parallel to the bases. In this prism, the faces are really parallelograms.Below are several characteristics of a rectangular prism that make it simple to recognize one.
There are 6 faces, 8 vertices, and 12 edges on a rectangular prism.The faces of a right rectangular prism are rectangles, but the faces of an oblique rectangular prism are parallelograms.It has three dimensions: height, breadth, and length.A rectangular prism has congruent opposite faces.The length of the rectangular Prism is l.
Width is w , height is h
Therefore,
Volume (V) = lbh
We know Volume is 486
so we casn find the width of the rectangular prism as 486/lh
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HELP PLSSS!!!
Prove the diviibility of the following number: 45^45 x 15^15 by 75^30
The proof of divisibility is correct in this question.
DivisibilityThe capacity of one integer (the divisor) to divide another integer (the dividend) equally and without leaving a residual is known as divisibility in mathematics. Alternatively said, if a dividend is divisible by a divisor, the division will produce a whole number or an integer. The formula for this connection is "dividend divisor = integer." Using divisibility criteria, which are based on the characteristics of numbers and their prime factorizations, is a typical method of checking for divisibility. In subjects such as number theory, cryptography, and others, the ability to divide a number by another number can have significant ramifications.
According to the question
It is necessary to demonstrate that the phrase 45*45*15*15 may be divided by 75*30. We must first comprehend the characteristics of the numbers' prime factorization in order to do this.
The number 75 may be represented as 31 * 52, and when it is raised to the 30th power, it becomes 75^30 = 31 * 52^30 = 3^30 * 5^60. Similar to how 45 may be expressed as 3^2 * 5^1, 3^90 * 5^45 is equal to 45^45 = (3^2 * 5^1)^45. Additionally, 15 may be written as 3 * 5 1, which means that 15 = 3 * 5 * 15.
75 = 3^1 * 5^2,
∴ 75^30 = (3^1 * 5^2)^30 = 3^30 * 5^60.
It follows that 75^30, or 3^30 * 5^60, divides 45^45 * 15^15, or 3^90 * 5^45 * 3^15 * 5^15, as 3^30 divides 3^90 and 5^60 divides 5^45.
45 = 3^2 * 5^1,
∴ 45^45 = (3^2 * 5^1)^45 = 3^90 * 5^45.
15 = 3^1 * 5^1,
∴ 15^15 = (3^1 * 5^1)^15 = 3^15 * 5^15.
In other words, the equation 45*45*15*15 may be evenly divided by 75*30 without any residual, proving that it is divisible by 75*30. The division may be used to confirm this, but it can also be demonstrated by the fact that all of the dividend's prime factors—45*45*15*15—are included in the divisor's prime factorization, 75*30, in the multiples necessary to divide it evenly.
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The proof of divisibility is correct in this question.
Divisibility
The capacity of one integer (the divisor) to divide another integer (the dividend) equally and without leaving a residual is known as divisibility in mathematics. Alternatively said, if a dividend is divisible by a divisor, the division will produce a whole number or an integer. The formula for this connection is "dividend divisor = integer." Using divisibility criteria, which are based on the characteristics of numbers and their prime factorizations, is a typical method of checking for divisibility. In subjects such as number theory, cryptography, and others, the ability to divide a number by another number can have significant ramifications.
According to the question,
It is necessary to demonstrate that the phrase 45*45*15*15 may be divided by 75*30. We must first comprehend the characteristics of the numbers' prime factorization in order to do this.
The number 75 may be represented as 31 * 52, and when it is raised to the 30th power, it becomes [tex]75^{30}=(31*52^{30})=(3^{30}*5^{60})[/tex]. Similar to how 45 may be expressed as [tex](3^2*5^1)[/tex]. [tex](3^{90}*5^{45})[/tex] is equal to [tex]45^{45}=(3^2*5^1)^{45}[/tex]. Additionally, 15 may be written as 3 * 5 1, which means that 15 = 3 * 5 * 15.
[tex]75=3^1*5^2[/tex],
∴ [tex]75^{30}=(3^1*5^2)^{30}=3^{30}*5^{60}[/tex].
It follows that [tex]75^{30}[/tex], or [tex](3^{30}*5^{60})[/tex], divides [tex](45^{45}*15^{15})[/tex] or [tex](3^{90}*5^{45}*3^{15}*5^{15})[/tex], as [tex]3^{30}[/tex] divides [tex]3^{90}[/tex] and [tex]5^{60}[/tex] divides [tex]5^{45}[/tex].
[tex]45=3^2*5^1[/tex]
∴ [tex]45^{45}=(3^*5^1)^{45}=3^{90}*5^{45}[/tex]
[tex]15=3^1*5^1[/tex]
∴ [tex]15^{15}=(3^1*5^1)^{15}=3^{15}*5^{15}[/tex]
In other words, the equation 45*45*15*15 may be evenly divided by 75*30 without any residual, proving that it is divisible by 75*30. The division may be used to confirm this, but it can also be demonstrated by the fact that all of the dividend's prime factors—45*45*15*15—are included in the divisor's prime factorization, 75*30, in the multiples necessary to divide it evenly.
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Find parametric equations for the line that is tangent to the given curve at the given parameter value. r(t) = (2t^2) i + (3t + 4) j + (2t^3) k, t = t_0 = 3 What is the standard parameterization for the tangent line? x= y= z =
The standard parameterization for the tangent line is x = 12t + 18 , y = 3t + 13 , z = 54t + 54
Equation of this type is known as a parametric equation; it uses an independent variable known as a parameter (commonly represented by t) and dependent variables that are defined as continuous functions of the parameter and independent of other variables.
Given that,
Given that, t = t0 = 3, I + (3t + 4) j + (2t 3) k
In order to get the tangent line to the curve at t=3, (x, y, z) = 18, 13, and 54,
r'(t) = 4t, 3, > and r'(t=3) = 12, 3, 54>. (18, 13, 54)
finally,
x = 12t + 18
y = 3t + 13
z = 54t + 54
The tangent line's usual parameterization is as follows:
x=12t+18, y=3t+13, and z=54t+54
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let n ≥ 9. how many trees are there on vertex set [n] in which at least one vertex has degree n − 3?
n−4 out of the n−3 neighbors of [tex]v_0[/tex] are leaves, except for [tex]v_k[/tex], which has degree 3 and is adjacent to [tex]v_0[/tex], [tex]v_n_-_1[/tex]. and [tex]v_n[/tex] . [tex]v_n[/tex] and [tex]v_n_-_1[/tex] are both leaves.
Now, According to the question:
It is easy to show that a tree with n ≥ 9 can have at most one vertex of degree n - 3. It is [tex]v_0[/tex].
Now, there are n - 1 - (n - 3) = 2 vertices that are not adjacent to [tex]v_0[/tex], it is also
[tex]v_n_-_1[/tex] and [tex]v_n[/tex]
Then a desired tree can be of 3 possible forms:
1. n - 4 out of n - 3 neighbors of [tex]v_0[/tex] are leaves, except for [tex]v_k[/tex], which has degree 2 and is adjacent to both [tex]v_0[/tex] and [tex]v_n_-_1[/tex]. [tex]v_n_-_1[/tex] has degree 2 and is adjacent to [tex]v_k[/tex] and [tex]v_n.v_n[/tex] is a leaf.
2. n − 5 out of the n − 3 neighbors of [tex]v_0[/tex] are leaves, except for [tex]v_j[/tex] and [tex]v_k[/tex]. [tex]v_j[/tex]has degree 2 and is adjacent to [tex]v_0[/tex] and [tex]v_n_-_1[/tex]. [tex]v_k[/tex] also has degree 2 and is adjacent to[tex]v_0[/tex] and [tex]v_n[/tex]. [tex]v_n[/tex] and [tex]v_n_-_1[/tex] are both leaves.
3. n−4 out of the n−3 neighbors of [tex]v_0[/tex] are leaves, except for [tex]v_k[/tex], which has degree 3 and is adjacent to [tex]v_0[/tex], [tex]v_n_-_1[/tex]. and [tex]v_n[/tex] . [tex]v_n[/tex] and [tex]v_n_-_1[/tex] are both leaves.
It is then easy to computer the number of trees in each form and sum them up.
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The rule C=6. 3r give the approximate circumference C of a circle a a function of it radiu r. Identify the independent and dependent variable in thi relationhip. Explain your reaon
The independent variable in this relationship is the radius (r) and the dependent variable is the circumference (C). This is because the circumference is dependent on the radius of the circle, meaning that if the radius changes, the circumference will change accordingly.
Identify the independent and dependent variableStep-by-step explanation given below
Step 1: The rule states that the relationship between the circumference (C) and the radius (r) is C = 6.3r.
Step 2: This means that the circumference of a circle is a function of its radius.
Step 3: The independent variable in this relationship is the radius (r) because it is what is used to determine the circumference.
Step 4: The dependent variable in this relationship is the circumference (C) because it is what is being determined by the radius.
This is because the circumference is dependent on the radius of the circle, meaning that if the radius changes, the circumference will change accordingly.
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HELP ASAP PLS!!!!…..,,,
The first value of the given exponential expression would be 3.
What is an exponential function?
An exponential function is a mathematical function of the form f(x) = aˣ, where "a" is a positive constant and x is a real number. The function represents an exponential growth or decay, depending on the value of "a". If "a" is greater than 1, the function increases rapidly as x increases. If "a" is between 0 and 1, the function decreases as x increases.
In the exponential expression y = 3 * q⁵, the first value is 3.
Hence, the first value of the given exponential expression would be 3.
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consider a point at a location 2.79 cm away from a 4.89-nc charge.
The electric field at this point is given by E = k * q/r^2 = (8.99e9 N * m^2/C^2) * (4.89e-9 C) / (2.79e-2 m)^2 = 7.76e6 N/C where q is the charge (4.89e-9 C), and r is the distance from the charge (2.79e-2 m).
1. First calculate the electric field, E, using the equation E = k * q/r^2, where k is Coulomb's constant (8.99e9 N * m^2/C^2), q is the charge (4.89e-9 C), and r is the distance from the charge (2.79e-2 m).
2. Plugging in the values, we get E = (8.99e9 N * m^2/C^2) * (4.89e-9 C) / (2.79e-2 m)^2 = 7.76e6 N/C.
The electric field at this point is given by E = k * q/r^2 = (8.99e9 N * m^2/C^2) * (4.89e-9 C) / (2.79e-2 m)^2 = 7.76e6 N/C.
The complete question is :
Consider a point at a location 2.79 cm away from a 4.89-nc charge. What is the electric field at this point?
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You design a tree house using a coordinate plane in which the coordinates are measured in meters (m ).
The vertices of the rectangular floor are (0, 5), (4, 3), (4,13), and (8, 11).
Part A: What is the perimeter of the tree house floor?
__ m
Part B: What is the area of the tree house floor?
__ m²
Part A: The perimeter of the tree house floor is 32 m.
Part B: The area of the tree house floor is 40 m².
Tree House Area and PerimeterPart A: The perimeter of the rectangular floor can be found by adding up the lengths of all four sides.
The first side has a length of 4 m and extends along the x-axis from (0, 5) to (4, 5).The second side has a length of 10 m and extends along the y-axis from (4, 5) to (4, 15).The third side has a length of 8 m and extends along the x-axis from (4, 15) to (0, 13).The fourth side has a length of 10 m and extends along the y-axis from (0, 13) to (0, 5).So the perimeter is 4 + 10 + 8 + 10 = 32 m.Part B: The area of the rectangular floor can be found by multiplying the length by the width.
The length is 4 m and the width is 10 m, so the area is 4 * 10 = 40 m².This is about a tree house design using a coordinate plane in which the coordinates are measured in meters (m). The task is to calculate the perimeter and the area of the rectangular floor of the tree house, given the vertices of the floor. The perimeter is found by adding up the lengths of all four sides of the rectangular floor, and the area is found by multiplying the length by the width.
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how many 2-letter code words can be formed from the first 3 letters of the alphabet if no letter can be used more than once?
The number of 2 letter codes that can be formed is 6 with no letter repeated using Permutation.
What is Permutation and Combination ?A permutation of a set is, broadly speaking, a rearranging of its elements if the set is already sorted, or arranging its members into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."
A permutation is a combination and an ordered arrangement of possible outcomes. For instance, there are 5 chairs, and 3 people should occupy them. There are five different methods to seat the first person, four ways to sit the person after them, and three ways to seat the third. As a result, we multiply the alternatives at our disposal to get the total number of configurations for seating 3 people in 5 seats. 5 4 3 are the methods we carry it out. It can be done in 60 different ways. You may write 5 4 3 as (5!) / (2!) (or) (5!) / (5 - 3), as you can see. .
Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order.
The first 3 letters of alphabet are a, b and c
The number of 2 letter codes that can be formed is 3*2 = 6 with no letter repeated.
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