The justification for the proof based on the information will be:
lm = np (Given)
lp = mn (Given)
(1) lmn = lm * n
Justification: Associative property of multiplication
(2) lmn = np * n
Justification: Substitute lm = np
(3) lmn = n * np
Justification: Commutative property of multiplication
(4) lmn = npl
Justification: Substitute lp = mn
Therefore, lmn = npl.
How to explain the informationThe associative property of multiplication is one of the fundamental properties of arithmetic. It states that the grouping of factors does not affect the result of multiplication.
In other words, when you multiply three or more numbers, you can change the grouping of the factors without changing the product.
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A. Given the following statements Let x e N, where N = {1,2,3,4,5). = a) VX EN,x + 4 < 2. b) 3x E N. x + 2 > 5. 1. Find the truth value of a) and b). 2. What is the negation of a) and b). B. Prove the following assertions (Using either direct or indirect proof) 1. If x is even and y is odd, then x + 2y is even. 2. If x and y are odd, then (x + 3) + y is odd. +2 n(n+1)
We have proved the first assertion that "If x is even and y is odd, then x + 2y is even" using direct proof. However, the second assertion "If x and y are odd, then (x + 3) + y is odd" is not true.
A.
The truth value of statement a) VX EN, x + 4 < 2 is false because there is no natural number x in the set N = {1, 2, 3, 4, 5} that satisfies the inequality x + 4 < 2.
The truth value of statement b) 3x EN, x + 2 > 5 is true because for all natural numbers x in the set N = {1, 2, 3, 4, 5}, the inequality 3x + 2 > 5 holds.
The negations of the given statements are:
Negation of a): ~ (VX EN, x + 4 < 2) which is EX EN, ~(x + 4 < 2), i.e., there exists an x in N such that x + 4 is not less than 2.
Negation of b): ~ (3x EN, x + 2 > 5) which is EX EN, ~(x + 2 > 5), i.e., there exists an x in N such that x + 2 is not greater than 5.
B.
To prove the assertion "If x is even and y is odd, then x + 2y is even" using direct proof, we assume that x is even and y is odd. We can express x as 2a (where a is an integer) and y as 2b + 1 (where b is an integer). Substituting these values into x + 2y, we get 2a + 2(2b + 1) = 2(a + 2b + 1), which is clearly an even number. Hence, x + 2y is even.
To prove the assertion "If x and y are odd, then (x + 3) + y is odd" using direct proof, we assume that x and y are odd. We can express x as 2a + 1 and y as 2b + 1. Substituting these values into (x + 3) + y, we get (2a + 1 + 3) + (2b + 1) = 2(a + b + 2), which is clearly an even number. This contradicts the assertion, and therefore, it is not true.
In summary, we have proved the first assertion that "If x is even and y is odd, then x + 2y is even" using direct proof. However, the second assertion "If x and y are odd, then (x + 3) + y is odd" is not true.
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Which number line shows - graphed?
Answer:
The second one down is the answer
Step-by-step explanation:
YO PLEASE HELPPPPPPPPPPPPPPP
Answer:
the second, and fourth one's are triangles, and the 1st and 2nd are not
Step-by-step explanation:
We know that the angles in a triangle add up to 180 degrees. So we need to find which angles add up to 180 degrees. We have:
56+34+42=132
That means the first one can't be a measures of a triangle.
75+55+50=180
Second one is a triangle.
35+32+23=90
Third isn't a triangle
124+64+16=180
So all in all, the second, and fourth one's are triangles, and the 1st and 2nd are not
Mother put 22 apples in each basket. How many baskets did she use for 390 apples?
Answer:
To find the no. of baskets used to put 390 apples we have to divide 390/22 which is 17.7272727273,
so to put 390 apples we need approximately 18 baskets.
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HELPPP I need the answers for number 4, 5, and 6.
35 points!!!!
ANSWERING ONE WOULD BE FINE
Answer:
4. H
5. A
6. H
Step-by-step explanation:
For 4
Supplementary angles have a sum of 180
so 3x + 96 = 180
now we just use basic algebra to solve for x
step 1 subtract 96 from each side
180 - 96 = 84
now we have 84=3x
step 2 divide each side by 3
3x/3=x
84/3=28
we're left with x = 28
so the answer to #4 is H
For 5
Remember the sum of the angles in a triangle is 180
So we can calculate the missing angle by subtract the given angles (90 and 66 in this case) from 180 NOTE: ( the 90 came from the little square at the bottom right of the triangle. This square indicates that the angle is a right angle and a right angle has a measure of 90 degrees)
so x = 180 - 90 - 66
180 - 90 = 90
90 - 66 = 24
so we can conclude that x = 24 and the answer is A
For 6
Angle 2 and angle 4 are vertical angles
If you didn't know vertical angles are congruent
SO if one angle equal 120 degrees the other angle also equal 120 degree therefore the answer to number 6 is H
(1 point) Match the confidence level with the confidence interval for μ. 1.1.645 2. x ±2.575 3. x ±1.96 A. 95% B. 99% C. 90% (
The correct matching of the confidence level with the confidence interval for μ is as follows:
x ± 1.96 --> A. 95%
x ± 2.575 --> B. 99%
x ± 1.645 --> C. 90%
A confidence level of 95% corresponds to a critical value of 1.96. This means that if we construct a confidence interval by taking the sample mean (x) and adding or subtracting 1.96 times the standard error, we can be 95% confident that the true population mean (μ) falls within this interval.
A confidence level of 99% corresponds to a critical value of 2.575. Similarly, constructing a confidence interval using the sample mean and adding or subtracting 2.575 times the standard error will give us a wider interval within which we can be 99% confident that the true population mean falls.
A confidence level of 90% corresponds to a critical value of 1.645. Constructing a confidence interval using the sample mean and adding or subtracting 1.645 times the standard error will give us a narrower interval within which we can be 90% confident that the true population mean lies.
These critical values are based on the standard normal distribution and are chosen to achieve the desired level of confidence.
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The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $4 and each adult ticket sells for $8. The auditorium can hold a maximum of 110 people. The drama club must make at least $570 from ticket sales to cover the show's costs. Also, they must sell at least 20 student tickets and a maximum of 70 adult tickets. If xx represents the number of student tickets sold and yy represents the number of adult tickets sold, write and solve a system of inequalities graphically and determine one possible solution.
Answer:
hgfxjdt
Step-by-step explanation:
Which function matches the table?
Answer:
B. f(x) =3
Step-by-step explanation:
sbwveivdebeudh
A woman bought a bag of rice 5700 naira and in 3 weeks later, she could only buy 2/4 of the bags for 5700 naira. Find the percentage?
Answer: 100% increase
Step-by-step explanation:
You need the find the cost per bag in those weeks.
Three weeks ago, she could buy a bag for N5,700.
Three weeks after that, she could only buy half a bag for the same amount. A bag therefore costs:
= 5,700 ÷ 2/4
= N11,400
The percentage increase is:
= (11,400 - 5,700) / 5,700
= 100%
Alicia bought a new game that was 15% off. The discount took 4.65. What was the original price of the shirt?
Answer:
If 31 is a option I would pick it.
Step-by-step explanation:
The problem we are solving is:
15% of ____ is 4.65.
This means that 0.15 x ? = 4.65
So ? = 4.65 / 0.15
Therefore ? = 31.
So the original number is 31.
Will Mark Brainliest To First Correct Answer.
Properties of Kites on IXL. I Only need to get one more correct and dont want to get reset...
Step-by-step explanation:
[tex]ei = \sqrt{ {45}^{2} - {27}^{2} } = \\ = \sqrt{2025 - 729} = \\ = \sqrt{1296} = \\ = 36[/tex]
What is the distance between two points located at (−6, 2) and (−6, 8) on a coordinate plane?
A 4 units
B 6 units
C 10 units
D 12 units
Answer:
6 units
Step-by-step explanation:
Answer:
6 units (B)
Step-by-step explanation:
8 - 2 = 6
Your parents gave you $0.35 on Sunday and then gave you twice as much money on Monday as they did on Sunday. On Tuesday, they gave you twice as much money as they gave you monday. The pattern continued for a week. How much money did your parents give you on Saturday??
Answer:
$22.40 im pretty sure its right
Step-by-step explanation:
sorry if im late and mark me brainliest if im right
someone help pleas ewill give brain
Answer:
[tex]x=5[/tex]
Step-by-step explanation:
Equation - [tex]10=2x[/tex]
Solve - divide both sides by 2 - [tex]5 = x[/tex]
If the quadrilateral below is a trapezoid, find: x=
Answer:
x=4
Step-by-step explanation:
Consecutive sides in a trapezoid are supplementry, which means they add up to 180. So, your equation is 14x-15+139=180
14x+124=180 (first make the numbers as clean as you can on both sides)
14x=56 (move all of the numbers to one side, so subtract 124 from both sides)
x=4 (simplify to get your answer, so divide by 14)
(hope this helps :P)
What are the coordinates of the vertex of the parabola described by the equation below? y = -5(x + 2)^2 + 7
A. (2, -7) O B. (-7,-2) O C. (7,2) O D. (-2,7)
After inspecting the expression and comparing it with the standard equation of the parabola, the location of the vertex is (x, y) = (- 2, 7). (Correct choice: D) #SPJ5
How to determine the location of the vertex of the parabola by algebraic meansThe vertex is the bound point that characterizes parabolas and which can be a maximum or a minimum but never both. As we know the standard equation of the parabola, we can determine the location of the vertex, whose coordinates are (x, y) = (h, k), by just interpretating the equation, whose form is:
y - k = a · (x - h)² (1)
After inspecting the expression and comparing it with the standard equation of the parabola, the location of the vertex is (x, y) = (- 2, 7). (Correct choice: D) #SPJ5
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If the sin 90º = 1, then which statement is true?
Answer:
cos 0° = 1, because the cosine and sine are complements
Step-by-step explanation:
Here is the formula: sin 0 = cos (90°- 0) or cos 0 = sin (90°- 0)
So it would be: cos 0° = sin (90° - 0°) = sin 90° = 1
i need help with this...
the answer is 60 :) good luckStep-by-step explanation:
use upper and lower sums to approximate the area of the region using the given number of subintervals (of equal width). (round your answers to three decimal places.) y = 1/x
The given function is y = 1/x. We need to use upper and lower sums to approximate the area of the region using the given number of subintervals (of equal width).
Given Function: y = 1/x Number of Subintervals: 6Width of Subinterval: (b-a)/n = (5-1)/6 = 4/6 = 2/3For Lower Sum, we take the minimum value of each subinterval and sum them up.
Lower Sum: ∑ i=1^n f(x_i*)Δx=∑ i=1^n f(a+iΔx)ΔxNow,
we calculate the Lower Sum: ∑ i=1^6 f(x_i*)Δx=∑ i=1^6 f(1+i(2/3))2/3=∑ i=1^6 2/(3(i+1))=0.903
For Upper Sum, we take the maximum value of each subinterval and sum them up.
Upper Sum: ∑ i=1^n f(x_i**)Δx=∑ i=1^n f(a+(i-1)Δx)ΔxNow,
we calculate the Upper Sum: ∑ i=1^6 f(x_i**)Δx=∑ i=1^6 f(1+i(2/3))2/3=∑ i=1^6 2/(3i)=1.361
Hence, the Lower Sum of the given function is 0.903 and the Upper Sum is 1.361.
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find the radius of the congruent circles. Thanks and hope you have a good rest of your day!!
Answer:
the radius is 10 since 10 plus ten is 20
Each day Mrs. Yoder assigns 15 addition and 12 multiplication problems as homework. What is the total number of addition and multiplication problems assigned after 5 days?
Answer:
135
Step-by-step explanation:
What is the length of cloth needed to make 24 shirts if each shirt is made from .75 yards of material?
18 yds.
B
23.25 yds.
с
32 yds.
D
51 yds
Answer:
18
Step-by-step explanation:
24*0.74 = 18
what is the length of the hypotenuse of the triangle when x = 3?
Answer:
2√73 I believe
Step-by-step explanation:
Input x with 3
2(3) = 6
5(3) + 1 = 16
16 squared is 256
6 squared is 36
A square plus B squared is C squared
square root of 292
I added the question and the example for reference. Please help! whoever is correct i will give brainliest!
Answer:
It would be 828 inches cubed
Step-by-step explanation:
Because the boxes on top and bottom are both 6x8x6 and the middle portion is 6x7x6
6x8x6=288
6x7x6=252
288+288+252=828
Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 24 days and a standard deviation of 8 days. Part (a) Part (b) + Part (c) Part (d) 66% of all trials of this type are completed within how many days? In other words, find the 66th percentile. (Round your answer to two decimal places.)
Let X be the duration of a particular type of criminal trial. We know that the mean of X is μ = 24 days and the standard deviation of X is σ = 8 days.
We are asked to find the 66th percentile of X, which is the value x such that P(X ≤ x) = 0.66. Using the standard normal distribution, we have Z = (X - μ) / σ ~ N(0, 1).Thus, we can write: P(X ≤ x) = P(Z ≤ (x - μ) / σ) = 0.66We need to find the value of x that satisfies this equation. Using a standard normal distribution table or calculator, we can find that the corresponding z-score is approximately 0.43.
Thus, we have:0.43 = (x - μ) / σ0.43 * 8 = x - 24x ≈ 27.44Therefore, the 66th percentile of the duration of a particular type of criminal trial is 27.44 days (rounded to two decimal places).Part (a): The 66% of all trials of this type are completed within 27.44 days (rounded to two decimal places).
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Can someone help please
Answer:
M=13
Step-by-step explanation:
Take the average of the two numbers:
(0+26)/2=13
In the small town of Middleton, there are only two restaurants that serve pizza- a small family owned Italian restaurant and a new franchise pizza restaurant. In a recent review of the franchise, a food critic reported that the pizza was delicious as promised. The only negative review that the franchise received from the critic was in reference to the inaccurate delivery time quoted during the online order process. In response to the article, the franchise owner used a program to analyze the online pizza orders that took place during the week before the review. He chose to track the orders at 6pm each day. He recorded his results in the frequency table below.
Use the frequency table to create a box and whisker plot of the On Time data values. In your final answer, include all calculations necessary to create the box and whisker plot.
Use the frequency table to create a box and whisker plot of the Late data values. In your final answer, include all calculations necessary to create the box and whisker plot.
Answer: 1.
Yes , the data franchise owner is collecting, will be helpful in order to counter the criticism from the critic. As he has a record for every delivery they are making on daily basis.
2.
The scenario is that for every fifth customer , the owner cross the four lines he makes. Thus a pack of five and easy to remember. As the data on regular week days is less, As can do the same for the third customer. Crossing the 2 lines for 3rd customer.
3.
With this provision of crossing the third customer, the owner can have a better check on the late delivery. As it will bring in his notice earlier as compared to fifth crossing.
4.
With the data as provided in the table, we can come to the conclusion that on weekends , i.e. both on time delivery and late deliveries are high in numbers. It must be because of high demand on that days. So owner must make some provision like hiring some more delivery boys for weekend in order to reduce the late deliveries.
Step-by-step explanation:
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A single number cube is rolled twice and the two numbers are added.
PART A:
How can you determine the total number of possible outcomes
Answer:
well if you where talking about the dice the awnser is 6 and if you are tlking about the shirts then you can do 3 times 3 i thik is the right awnser
Step-by-step explanation:
1. a dice is a cube a cube has 6 sides a single number dice is a dice that only has numbers that are by themselves so the awnser can only be on the dice 6 to 9 so now we know that it is 6 now 6 times 2 is 12 because it got rolled twice
2.
A birthday cake is being made using a cylindrical baking pan. The radius of the pan is 4 inches, and the height is 5 inches.
Which formula represents the correct way to calculate the volume of the cake?
O V = (4)(5)
O V = r(4)(5)
O V = $(5) (4)
O V = $(4)?(5)
Answer:
the formula represent the correct way is π(4)^2 (5)
Step-by-step explanation:
The formula that represent the correct way to calculate is given below:
As we know that
Volume = πr^2 h
where
r denotes the radius i.e. 4 inches
And, h denotes the height i.e. 5 inches
Now placed these values to the above formula
So,
= π(4)^2 × 5
= 80π in^3
Hence, the formula represent the correct way is π(4)^2 (5)
Answer: the answer is D.
Step-by-step explanation:
If there is 0.25 probability that a child in New York gets the flu and a 0.30 probability that a child in Los Angeles gets the flu, what is the probability that both will get the flu?If there is 0.25 probability that a child in New York gets the file and a 0.30 probability that a child in Los Angeles gets the flu, what is the probability that both will get the flu? O 0.075 O 0.275 O 0.25 O 0.55
Answer:
(.25)(.30) = .075 probability that both children will get the flu
The probability that both a youngster in New York and a kid in Los Angeles will get this season's virus can be determined by duplicating the singular probabilities. Consequently, the likelihood that both will get influenza is 0.075.
To find the probability of the two occasions happening, we duplicate the probabilities of every occasion. Considering that the probability of a kid in New York getting this season's virus is 0.25 (or 25%) and the probability of a youngster in Los Angeles getting influenza is 0.30 (or 30%), we multiply these probabilities: 0.25 * 0.30 = 0.075. This implies there is a 0.075 probability, or 7.5%, that both a youngster in New York and a kid in Los Angeles will get influenza.
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