Answer:
option 3
Step-by-step explanation:
Since definition of slope is:
\(slope = \frac{rise}{run} \)
the ratio:
\( \frac{bd}{da} = \frac{ce}{ea} \)
explains the best (Ratio option 3)
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Answer:
y= 1/2x+1
Step-by-step explanation:
Solve for x. - 4x – 5 = -45
Answer:
x=10
Step-by-step explanation:
−4x−5=−45
Step 1: Add 5 to both sides.
−4x−5+5=−45+5
−4x=−40
Step 2: Divide both sides by -4.
−4x
−4
=
−40
−4
x=10
Hurry please!!!!!
When choosing a new school mascot, 80 students voted for an eagle, and 160 students voted for a bulldog. Rounded to the nearest whole percent, what percent of these students voted for a bulldog?
A. 36%
B. 60%
C. 67%
D. 70%
Answer:
C. 67%
Step-by-step explanation:
First, find the total amount of people that voted:
80 + 160
= 240
To find the percent of students that voted for a bulldog, divide 160 by 240:
160/240
= 0.66
So, this is approximately 67%. C is the correct answer
how would you solve this equation?
Answer:
19,188
Step-by-step explanation:
hope this helps ;)
HURRY!!
The sequences are:
Number of moves: 1, 3, 7, 15, 31, 63, ...
2":2, 4, 8, 16, 32, 64, ...
Compare the two sequences. What is the pattern?
How could you find the minimum number of moves
required for a given number of disks?
The minimum number of moves required for a given number of disks.
We have given that,
The sequences are number of moves 1, 3, 7, 15, 31, 63,
2,2, 4, 8, 16, 32, 64,
Compare the two sequences.
Each term in the sequence of moves is 1 less than the corresponding term in the sequence of differences.
What is the sequence?A sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members. The number of elements is called the length of the sequence.
You can find any term in the sequence of moves using the formula
\(a_1=2^n-1\)
No one cares about the explanation good luck with your grade Bois.
The minimum number of moves required for a given number of disks.
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Answer:
Each term in the sequence of moves is 1
less than the corresponding term in the
sequence of differences.
You can find any term in the sequence of
moves using the formula
Step-by-step explanation:
Can someone help me with this
please help, tysm for your assistance if you do :)
Answer:
27/49
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The base of a ladder is 10 feet away from a vertical building. The ladder top rests at the top of the building. The ladder's angle of elevation
from the bottom of the ladder to the top of the building is 70°.
What is the height of the building?
O 13. 94 ft.
O 27. 47 ft.
O 41. 76 ft.
O 32. 14 ft.
O 53. 30 ft.
The answer is (B) 27.47 ft. We can use trigonometry to solve this problem. Let's call the height of the building "h" and the length of the ladder "l". We know that the distance from the base of the ladder to the building is 10 feet, and the angle of elevation is 70 degrees.
Using trigonometry, we can set up the equation:
tan(70) = h/10
Solving for h, we get:
h = 10 * tan(70)
Plugging this into a calculator, we get:
h ≈ 27.47 ft
Therefore, the answer is (B) 27.47 ft.
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I am extremely confused about this problem. What is the answer and what would be the best way to solve it? The problem is linked below.
Answer:
2ab³
Step-by-step explanation:
evaluate the radical inside the parenthesis
\(\sqrt[3]{64a^6b^{18} }\)
= \(\sqrt[3]{64}\) × \(\sqrt[3]{a^6}\) × \(\sqrt[3]{b^{18} }\)
= 4 × a² × \(b^{6}\)
= 4a²\(b^{6}\)
note that \(a^{\frac{1}{2} }\) = \(\sqrt{a}\)
then
\(4a^2b^6)^{\frac{1}{2} }\)
= \(\sqrt{4}\) × \(\sqrt{a^2}\) × \(\sqrt{b^6}\)
= 2 × a × b³
= 2ab³
Given the following vertex set and edge set (assume bidirectional edges):V = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}E = {{1,6}, {1, 7}, {2,7}, {3, 6}, {3, 7}, {4,8}, {4, 9}, {5,9}, {5, 10}1) Draw the graph with all the above vertices and edges.
The graph of the vertex set and edge set is illustrated below.
The given vertex set V = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is a collection of 10 nodes. The edge set E = {{1,6}, {1, 7}, {2,7}, {3, 6}, {3, 7}, {4,8}, {4, 9}, {5,9}, {5, 10}} contains 9 pairs of vertices, representing the connections between them.
To draw the graph, we can represent the vertices as circles or dots, and draw lines between the vertices that are connected by an edge. In this case, we can draw 10 circles or dots, one for each vertex, and connect the vertices that are connected by an edge using lines.
Using this method, we can draw the graph as follows:
In this graph, each vertex is represented by a numbered circle, and each edge is represented by a line connecting two vertices. For example, edge {1,6} connects vertex 1 and vertex 6.
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£5362 is shared equally between 7 people. How much does each person get?
Answer:
£766
Step-by-step explanation:
£5362 ÷ 7
= £766
£766
£766
Answer:
£766
Step-by-step explanation:
5362 divide by 7 and you got equal 766
I need help getting the answer
decimal (base-16) numbers are written using numeric digits $0$ through $9$ as well as the letters $a$ through $f$ to represent $10$ through $15$. among the first $1000$ positive integers, there are $n$ whose hexadecimal representation contains only numeric digits. what is the sum of the digits of $n$?
To find the sum of the digits of n, we need to determine the number of positive integers among the first 1000 whose hexadecimal representation contains only numeric digits (0-9). The sum of the digits of n is 13.
To do this, we first note that the first 16 positive integers can be represented using only numeric digits in hexadecimal form (0-9). Therefore, we have 16 numbers that satisfy this condition.
For numbers between 17 and 256, we can write them in base-10 form and convert each digit to hexadecimal. This means that each number can be represented using only numeric digits in hexadecimal form. There are 240 numbers in this range.
For numbers between 257 and 1000, we can write them as a combination of numeric digits and letters in hexadecimal form. So, none of these numbers satisfy the given condition.
Therefore, the total number of positive integers among the first 1000 whose hexadecimal representation contains only numeric digits is
16 + 240 = 256.
To find the sum of the digits of n, we simply add the digits of 256 which gives us
2 + 5 + 6 = 13.
The sum of the digits of n is 13.
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true/false. a box is held in position by a cable along a frictionless incline .
True, a box can be held in position by a cable along a frictionless incline.
When the tension force in the cable is equal to the component of the gravitational force rate acting parallel to the incline, the box will remain in a stationary position.
force which prevents one solid item from rolling or slipping over another. Although frictional forces can be advantageous, such as the traction required to walk without slipping, they can provide a significant amount of resistance to motion.
What are the 4 different forms of friction?
It opposes the sliding motion of both layers of fluid and solid matter. Friction comes in four flavors: flowing, rolling, sliding, and static.
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Por C?AnswerExample0 How many ways can 4 candy bars be chosenfrom a store that sells 30 candy bars?С27,4052 How many ways can 13 students line up for lunch?113 How many ways can you make a 3-letterarrangements out of the letters in the wordTRAPEZOID.4 How many ways can you choose 2 books from ashelf of 40 books-5 How many ways can 12 swimmers finish in first,second, and third place?.L11---How many ways can Mrs. Sullivan choose twostudents from 27 to help put away calculators atthe end of class?----1-111
1) How many ways can 4 candy bars be chosen from a store that sells 30 candy bars?
In this case we can combine 30 types of candy bars in a set of 4 bars.
This can be calculated as a combination of 30 in 4 with no repetition:
\(\begin{gathered} C(n,r)=\frac{n!}{(n-r)!r!} \\ C(30,4)=\frac{30!}{(30-4)!4!}=\frac{30!}{26!4!}=\frac{30\cdot29\cdot28\cdot27}{4\cdot3\cdot2\cdot1}=\frac{657720}{24}=27405 \end{gathered}\)Answer: 27,405 possible combinations (C).
2) How many ways can 13 students line up for lunch?
In this case we have a permutation of 13 in 13 with no repetition.
We can calculate this as:
\(\begin{gathered} P(n,r)=\frac{n!}{(n-r)!} \\ P(13,13)=\frac{13!}{(13-13)!}=\frac{13!}{1}=6227020800 \end{gathered}\)Answer: 6,227,020,85)00 possible permutations (P).
3) How many ways can you make a 3-letter arrangements out of the letters in the word TRAPEZOID.
In the word we have 9 letters with no repetition, so we have to calculate a permutation (as order matters) of 9 letters in 3 places.
We can calculate this as:
\(P(9,3)=\frac{9!}{(9-3)!}=\frac{9!}{6!}=9\cdot8\cdot7=504\)Answer: 504 possible permutations (P).
4) How many ways can you choose 2 books from a shelf of 40 books.
In this case, the order does not matter, so it is a combination of 40 in 2.
This can be calculated as:
\(C(40,2)=\frac{40!}{(40-2)!2!}=\frac{40!}{38!2!}=\frac{40\cdot39}{2\cdot1}=\frac{1560}{2}=780\)Answer: 780 possible combinations (C)
5) How many ways can 12 swimmers finish in first, second, and third place?
In this case, the order does matter, so we have a permutation of 12 in 3:
\(P(12,3)=\frac{12!}{(12-3)!}=\frac{12!}{9!}=12\cdot11\cdot10=1320\)Answer: 1320 permutations (P)
6) How many ways can Mrs. Sullivan choose two students from 27 to help put away calculators at the end of class?
The order does not matter between the two students, so it is a combination of 27 in 2:
\(C(40,2)=\frac{27!}{25!2!}=\frac{27\cdot26}{2\cdot1}=351\)Answer: 351 combinations (C)
Differentiate the function.
H(z)=ln[(d2-z2)/(d2+z2)]^1/2
Natural log of the square root of (d2-z2) divided by (d2+z2).
The derivative of H(z) is H'(z) = -2zd^2/[(d^2-z^2)(d^2+z^2)].
To differentiate the function H(z) = ln[(d^2-z^2)/(d^2+z^2)]^(1/2), we will use the chain rule and the power rule of differentiation.
First, we can simplify the expression inside the natural logarithm using the laws of exponents:
[(d^2-z^2)/(d^2+z^2)]^(1/2) = [(d^2-z^2)^(1/2)/(d^2+z^2)^(1/2)]
Now we can differentiate H(z) as follows:
H'(z) = d/dz [ln[(d^2-z^2)/(d^2+z^2)]^(1/2)]
= (1/2)[(d^2+z^2)^(1/2)/(d^2-z^2)^(1/2)] * d/dz [(d^2-z^2)/(d^2+z^2)]
Using the quotient rule, we can simplify the derivative:
d/dz [(d^2-z^2)/(d^2+z^2)] = [(2z)(d^2+z^2) - (d^2-z^2)(2z)]/(d^2+z^2)^2
= -4zd^2/(d^2+z^2)^2
Substituting this back into H'(z), we get:
H'(z) = (1/2)[(d^2+z^2)^(1/2)/(d^2-z^2)^(1/2)] * (-4zd^2/(d^2+z^2)^2)
= -2zd^2/[(d^2-z^2)(d^2+z^2)]
Therefore, the derivative of H(z) is:
H'(z) = -2zd^2/[(d^2-z^2)(d^2+z^2)]
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Suppose you borrowed $45,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years. By how much would you reduce the amount you owe in the first year? Select the correct answer. a. $7,594.46 b. $7,600.46 c. $7,618.46 d. $7,612.46 e. $7,606.46
The correct answer is option a. $7,594.46.
To calculate the amount you would reduce the amount you owe in the first year, we can use the formula for the equal installment of a loan. The formula is:
Installment = Principal / Number of Installments + (Principal - Total Repaid) * Interest Rate
In this case, the principal is $45,000, the number of installments is 5, and the interest rate is 8.5%.
Let's calculate the amount you would reduce the amount you owe in the first year:
Installment = $45,000 / 5 + ($45,000 - $0) * 0.085Installment = $9,000 + $3,825
Installment = $12,825
Therefore, you would reduce the amount you owe by $12,825 in the first year.The correct answer is option a. $7,594.46.
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Candice's proof is a direct proof because . Joe's proof is a direct proof because . Reset Next
They provide a clear and concise way to demonstrate the validity of a claim, relying on known facts and logical reasoning
Candice's proof is a direct proof because it establishes the truth of a statement by providing a logical sequence of steps that directly lead to the conclusion. In a direct proof, each step is based on a previously established fact or an accepted axiom. The proof proceeds in a straightforward manner, without relying on any other alternative scenarios or indirect reasoning.
Candice's proof likely involves stating the given information or assumptions, followed by a series of logical deductions and equations. Each step is clearly explained and justified based on known facts or established mathematical principles. The proof does not rely on contradiction, contrapositive, or other indirect methods of reasoning.
On the other hand, Joe's proof is also a direct proof for similar reasons. It follows a logical sequence of steps based on known facts or established principles to arrive at the desired conclusion. Joe's proof may involve identifying the given information, applying relevant theorems or formulas, and providing clear explanations for each step.
Direct proofs are commonly used in mathematics to prove statements or theorems. They provide a clear and concise way to demonstrate the validity of a claim, relying on known facts and logical reasoning. By presenting a direct chain of deductions, these proofs build a solid argument that leads to the desired result, without the need for complex or indirect reasoning.
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write 6/9 in lowest terms
Answer: 2/3
Simplifying fractions: Reducing the fraction to its lowest term by finding the greatest common factor and dividing both the numerator and denominator by the GCF.
GCF: The greatest common factor is integer divisible by both numbers. This number will evenly divide into both the numerator and denominator in this case.
Simplest term: The smallest possible number that cannot be reduced further while remaining as an integer.
Factors of numerator (6): 1, 2, 3, 6
Factors of Denominator (9): 1, 3, 9
both numbers have a common factor of 3 which is the greatestSteps to Calculate:
1. Find the GCF
2. Divide numerator and denominator by GCF
6/3 = 2
9/3 = 3
Therefore, the lowest term would be 2/3
Aline crosses the coordinates (-4,-5) and (2, 4). What is the slope of the line?
Answer: use the website desmos and plug in the cordinate it gives u the line automaticaly.
Step-by-step explanation:
Answer:
Slope (m) = 3/2. Follow the workings in the image
a racing car consumes a mean of 101 gallons of gas per race with a variance of 49 . if 43 racing cars are randomly selected, what is the probability that the sample mean would differ from the population mean by greater than 2.4 gallons? round your answer to four decimal places.
The probability that the sample mean would differ from the population mean by greater than 2.4 gallons
To solve this problem, we need to use the central limit theorem and the formula for the standard error of the mean:
Standard error of the mean = standard deviation / square root of sample size
In this case, the standard deviation is the square root of the variance, which is 7. Therefore, the standard error of the mean is:
Standard error of the mean = 7 / square root of 43 ≈ 1.061
Next, we need to calculate the z-score for a difference of 2.4 gallons:
z-score = (sample mean - population mean) / standard error of the mean
z-score = (101 - 101.6) / 1.061 ≈ -0.566
Note that we subtract the population mean from the sample mean because we want to know how much the sample mean differs from the population mean.
Finally, we can use a standard normal distribution table (or a calculator) to find the probability that a z-score is less than -0.566 or greater than 0.566 (since the distribution is symmetric). The probability of a z-sitcore less than -0.566 is approximately 0.2881, so the probability of a z-score greater than 0.566 is also approximately 0.2881. Therefore, the probability that the sample mean would differ from the population mean by greater than 2.4 gallons is:
Probability = 0.2881 + 0.2881 ≈ 0.5762
Rounding to four decimal places, the answer is 0.5762.
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Mr. Chong celebrated his seventy fifth birthday in 1998. In what year was he born?
Answer:
1924
Step-by-step explanation:
1998
- 75
--------
1924 so he was born in 1924
The result of dividing 107 by 10^-3 is?10-4. 102.5. 1010. 104.
The result of diving 107 by 10⁻³ is (E) 107,000.
What do we mean by division?The division is one of the four basic operations of arithmetic, which are the methods by which numbers are combined to form new numbers. Addition, subtraction, and multiplication are the other operations.At the most basic level, the division of two natural numbers is the process of calculating the number of times one number is contained within another. For example, if 20 apples are distributed evenly among four people, each receives five apples (see picture).So, we know that 10⁻³ is 0.001.
Now, 107/0.001 = 107,000.Therefore, the result of diving 107 by 10⁻³ is (E) 107,000.
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The correct question is given below:
The result of dividing 107 by 10^-3 is?
a. 10-4.
b. 102.5.
c. 1010.
d. 104.
e. 107,000
What is the solution to the system?.
8x - 8y =-8
X=-3y=13
Which of the following combinations of side lengths would NOT form a triangle with vertices X, Y, and Z?
Answer:
D) because the sum of two sides must be greater than the third side
Step-by-step explanation:
in this 10+14=24 which is not greater than 26
For large parties A restaurant adds a 15% service charge to the bill how much would be added to a bill of 638. 40
Answer:
95.76$
Step-by-step explanation:
Calculate 15% of 638.40$
we have 15%/100% x 638.40
which is 95.76$
It means that a charge of 95.76$ will be added to an amount of 638.40$
Let B = {61, ... , bn} be a basis for a vector space V. Which of the following statements are true? Select all that apply. A. By the Unique Representation Theorem, for each x in V, there exists a unique set of scalars C1, Cn such that x = Cyby +... + cnbn: X B. By the definition of a basis, b1, ... , bn are in V. C. By the definition of an isomorphism, Vis isomorphic to Rh+1. D. By the definition of a basis, 61, ... , bn are linearly dependent.
A. By the Unique Representation Theorem, for each x in V, there exists a unique set of scalars C1, Cn such that x = C1b1 + ... + Cnbn.
Does each vector x in V have a unique representation using scalars from B?By the Unique Representation Theorem, for any vector x in V, there exists a unique set of scalars C1, Cn such that x can be expressed as a linear combination of the basis vectors b1, ..., bn. This means that any vector in V can be uniquely represented using the basis B.
In other words, the basis B spans the vector space V, and any vector in V can be written as a linear combination of the basis vectors. The coefficients C1, Cn represent the weights or scalars that determine the combination of basis vectors needed to obtain the given vector x.
The statement A is true because it reflects the Unique Representation Theorem. It states that for each vector x in V, there exists a unique set of scalars C1, Cn such that x can be expressed as a linear combination of the basis vectors C1b1 + ... + Cnbn.
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6÷2(1+2)= plsss help meee
Hi Everyone! Please draw a regular bar graph with x and y axis, along with all components of a bar graph!
that the bar graph with all components
15% off of $60, then subtracting 10% from that cost, is equal to
Answer:
45.9 or 45
Step-by-step explanation:
15% of 60= 9
9-60=
51
10% of 51 =
1.5
1.5 - 50= 45.9
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Or
25% of 60
15
15 - 60=
45