Answer: To prove that triangles △ABC and △DEF are similar, we would use the AA Similarity Postulate. This postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. In other words, if the corresponding angles of two triangles are congruent, then the triangles are similar.
Step-by-step explanation:
Look at the data under PURCHASE BEHAVIOR. How often do consumers in this segment purchase a backpack? Purchase behavior last quarter - 23% : a. Once every 6 years b. Once every 3 years c. Once every year d. Once every 2 years e. Once every 5 yrs
By looking at the data under PURCHASE BEHAVIOR, we can see that the consumers in this segment purchase a backpack at a range of purchase every five years. The Option E is correct.
What determines a Consumer purchase interval?We have several factors that can determine a consumer's purchase interval, including:
Product usage: How frequently a product is used or consumed can influence the consumer's purchase interval. If a product is used frequently, the consumer may need to purchase it more often.Product durability: The durability of a product can impact the purchase interval. If a product is durable and lasts a long time, the consumer may not need to purchase it as frequently.Price: The price of a product can also determine the purchase interval. If a product is expensive, the consumer may wait longer before making another purchase.Consumer behavior: Consumer behavior, such as brand loyalty or habit, can also influence the purchase interval. Consumers who are loyal to a particular brand may purchase that brand more frequently, while others may be more open to trying different brands and products etc.Read more about Consumer
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Answer:
Step-by-step explanation:
answer is c. once every year
I neeed Help pls im stuck on this question.
Answer:
x = 12
The sum of ∠A and ∠C is 90°.
Step-by-step explanation:
Interior angles of a triangle sum to 180°.
[tex]\implies m \angle A + m \angle B + m \angle C = 180^{\circ}[/tex]
From inspection of the given right triangle:
m∠A = (2x + 1)°m∠B = 90°m∠C = (5x + 5)°Substitute the given angles into the equation and solve for x:
[tex]\implies m \angle A + m \angle B + m \angle C = 180^{\circ}[/tex]
[tex]\implies (2x+1)^{\circ} + 90^{\circ} + (5x+5)^{\circ} = 180^{\circ}[/tex]
[tex]\implies (2x+1)^{\circ} + 90^{\circ} + (5x+5)^{\circ}-90^{\circ} = 180^{\circ}-90^{\circ}[/tex]
[tex]\implies (2x+1)^{\circ} + (5x+5)^{\circ} = 90^{\circ}[/tex]
[tex]\implies 2x+1 + 5x+5 = 90[/tex]
[tex]\implies 2x+ 5x+1 +5 = 90[/tex]
[tex]\implies 7x+6 = 90[/tex]
[tex]\implies 7x+6 -6= 90-6[/tex]
[tex]\implies 7x=84[/tex]
[tex]\implies 7x\div7=84\div7[/tex]
[tex]\implies x=12[/tex]
Therefore, the value of x is 12.
To find the measure of each angle, substitute the found value of x into the expression for each angle:
[tex]m \angle A=(2(12)+1)^{\circ}=25^{\circ}[/tex][tex]m \angle B=90^{\circ}[/tex][tex]m \angle C=(5(12)+5)^{\circ}=65^{\circ}[/tex]Answer:
[tex]x = 12[/tex]
Step-by-step explanation:
A right angled triangle is given to us and we need to find out the value of " x " . The two unknown angles are (2x + 1)° and (5x + 5)° .
We know that, the Angle sum property of a triangle is 180° . So the sum of all the given angles inside the triangle will be 180° .
And as per question one of the angle is 90° . So the sum of other two angles will be 90° .
Hence ,
2x + 1 + 5x + 5 + 90 = 180
7x + 96 = 180
7x = 180 - 96
7x = 84
x = 84/2
x = 12
Hence the value of x is 12 .
And we are done!
9 people on a bus in Seattle and the average of their yearly income is $65,000. At the next stop, the highest paid person on the bus (with an income of $120,000 per year) gets off and Bill Gates gets on. Mr. Gates makes 7.6 Billion dollars a year. What is the new average and median salary of people on the bus?
The new average salary of the people on the bus is $84,44,96,111.11 and the median salary will not change and will remain same.
Given, we know that average salary of the 9 people on the bus is $65,000.
Formula for Average = sum of salary of all people/ the number of people.
Let us say average salary of first 8 people is 'S'. Given, salary of the 9th guy on the bus is $120,000 Now, we can write it like this :
⇒$65,000 = (S + $120,000)/9
⇒585,000 = S + $120,000
⇒S = $465,000
Therefore, average salary of 8 people is $465,000 after the 9th guy gets off. Now Bill Gates enters the bus with a salary of $7,600,000,000. New average salary :
⇒ (S + $7,600,000,000) / 9
⇒$84,44,96,111.11
Median will not change since, The median of a set of numbers is the number in the middle when you list them in order. For example, the median of {1, 3, 6, 9, 13} is 6. If you replace the highest number with a different number, the median will not change. In this example, {1, 3, 6, 9, 100} still has a median of 6.
Therefore, the new average yearly income of the people on the bus along with Bill Gates is $84,44,96,111.1111.
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PLEASE HELP ME!
Question in image. Thank you
The correct options for the given polynomial are:
NEG/EVENas x goes to ∞, f(x) goes to -∞as x goes to -∞, f(x) goes to -∞How to identify the end behavior of the polynomial?To analyze the end behavior of a polynomial we need to look at the degree and the sign of the leading coefficient.
Remember that the degree is the largest exponent of the polynomial.
Here we can see that the degree is 12, so it is even.
And the leading coefficient (the coefficient in the term with the largest exponent) is -10, so it is negative.
Then the first correct option is:
NEG/EVEN
That means that in both ends the polynomial tends to negative infinity, so:
as x goes to ∞, f(x) goes to -∞as x goes to -∞, f(x) goes to -∞Learn more about end behavior at:
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Look at the diagram in the image attached.
What is the measure of LLMN?
A. 67°
B. 71°
C. 109°
D. 113°
Answer:
67°
Step-by-step explanation:
Sum of the interior angles of a triangle = 180
To find x, set the sum of the supplementary angles to the 3 shown angles (x-6, x+9, x) equal to 180:
180 = (180-x+6) + (180-x-9) + (180-x)
180 = 536 - 3x
-357 = -3x
x = 119
119 - 6 = 113 this is the angle supplementary to ∠LMN, therefore:
m∠LMN = 180 - 113 = 67°
The graph of f(x)=x² was translated 4 units to the right and horizontally compressed by a factor of 5 to create the graph of function g. Write an equation in vertex form to represent function g.
The vertex form of the quadratic equation g is:
g(x) = 25*(x - 4)²
How to find the equation for function g?We start with the parent quadratic function:
f(x) = x²
We know that first we apply a translation of 4 units to the right, so we will get:
g(x) = f(x - 4)
And then we compress it horizontally by a factor of 5, then we can write:
g(x) =f( 5(x - 4))
Replacing the actual function we will get:
g(x) = ( 5*(x - 4))²
Distributing the exponent we will get:
g(x) = 5² *(x - 4)²
g(x) = 25*(x - 4)²
That is the quadratic equation in vertex form.
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HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
A cone with height h and radius r has volume V = 13πr2h. If a certain cone with a height of 9 inches has volume V = 3πx2 + 42πx + 147π, what is the cone’s radius r in terms of x?
Equations with roots that are whole numbers and fractions
The quadratic equations with roots that are whole numbers and fractions are listed below:
Case 2: 9 · x² - 78 · x - 27 = 0
Case 3: 7 · x² - 26 · x - 8 = 0
Case 4: 4 · x² + 2 · x - 32 · x - 16 = 0
Case 6: 4 · x² - 5 · x - 6 = 0
Case 7: 7 · x² + 38 · x - 24 = 0
How to factor a quadratic equation
In this problem we find eight cases of quadratic equations of the form a · x² + b · x + c = 0, where a, b, c are real coefficients. All roots can be found by means of algebra properties:
Case 1
5 · x² + 8 · x + 4 = 0
5 · [x² + (8 / 5) · x + 4 / 5] = 0
5 · (x + 4 / 5 - i 2 / 5) · (x + 4 / 5 + i 2 / 5)
Case 2
9 · x² - 78 · x - 27 = 0
9 · [x² - (26 / 3) · x - 3] = 0
9 · (x - 9) · (x + 1 / 3) = 0
Case 3
7 · x² - 26 · x - 8 = 0
7 · [x² - (26 / 7) · x - 8 / 7] = 0
7 · (x - 4) · (x + 2 / 7) = 0
Case 4
4 · x² + 2 · x - 32 · x - 16 = 0
4 · x² - 30 · x - 16 = 0
4 · [x² - (15 / 2) · x - 4] = 0
4 · (x - 8) · (x + 1 / 2) = 0
Case 5
2 · x² - 20 · x + 32 = 0
2 · (x² - 10 · x + 16) = 0
2 · (x - 8) · (x - 2) = 0
Case 6
4 · x² - 5 · x - 6 = 0
4 · [x² - (5 / 4) · x - 3 / 2] = 0
4 · (x - 2) · (x + 3 / 4) = 0
Case 7
7 · x² + 38 · x - 24 = 0
7 · [x² + (38 / 7) · x - 24 / 7] = 0
7 · (x - 4 / 7) · (x + 6) = 0
Case 8
x² - 5 · x - 6 = 0
(x - 6) · (x + 1) = 0
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Find (p•q)(x).
p(x) = x + 4
q(x) = 3x² + 2x
Answer:
(p • q)(x) = 3x² + 2x + 4
Step-by-step explanation:
(p • q)(x) same as p(q(x)) is the composite function obtained by applying the expression for q(x) in place of x in p(x)
We have
p(x) = x + 4
q(x) = 3x² + 2x
To find (p • q)(x)
wherever there is an x in p(x) substitute with 3x² + 2x
(p • q)(x) = x + 4
= (3x² + 2x) + 4
= 3x² + 2x + 4
Jim is 4 more than twice the age of his
cousin Mark. If the sum of their ages is
34. How old is Jim?
Answer:
24 years old
Step-by-step explanation:
Jim = 2x + 4
Mark = x
Sum of their ages = 34
2x + 4 + x = 34
2x + x = 34 - 4
3x = 30
3x / 3 = 30 / 3
x = 10
Mark = 10 years old
Jim = 2x + 4
= 2 ( 10 ) + 4
= 20 + 4
= 24
Therefore, Jim is 24 years old
The table shows the possible outcomes of spinning the given
spinner and flipping a fair coin. Find the probability of the coin
landing heads up and the pointer landing on either 1, 2, or 4.
The table mentioned in the question is not provided. However, we can use the following formula to find the probability of two independent events occurring together:
P(A and B) = P(A) x P(B)
Here, A represents the event of the coin landing heads up, and B represents the event of the pointer landing on either 1, 2, or 4.
Assuming that the spinner has equal sections, the probability of the pointer landing on either 1, 2, or 4 is 3/8 (since there are three out of eight possible sections on the spinner).
The probability of flipping a fair coin and getting heads is 1/2.
Therefore, the probability of the coin landing heads up and the pointer landing on either 1, 2, or 4 is:
P(A and B) = P(A) x P(B) = (1/2) x (3/8) = 3/16
So, the probability of the coin landing heads up and the pointer landing on either 1, 2, or 4 is 3/16.
The probability of the coin landing heads up and the pointer landing on either 1, 2, or 4 is 3/16.
What is probability?Probability denotes the possibility of the outcome of any random event. The meaning of this term is to check the extent to which any event is likely to happen.
Given that, a spinner is spined and coin is flipped,
P(A and B) = P(A) x P(B)
Here, A represents the event of the coin landing heads up, and B represents the event of the pointer landing on either 1, 2, or 4.
Assuming that the spinner has equal sections, the probability of the pointer landing on either 1, 2, or 4 is 3/8 (since there are three out of eight possible sections on the spinner).
The probability of flipping a fair coin and getting heads is 1/2.
Therefore, the probability of the coin landing heads up and the pointer landing on either 1, 2, or 4 is:
P(A and B) = P(A) x P(B) = (1/2) x (3/8) = 3/16
So, the probability of the coin landing heads up and the pointer landing on either 1, 2, or 4 is 3/16.
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which of the following statements are equivalent to the statement "the price increased by 1/2 of what it was before"
Answer: The price is now 1.5 of what it was before is the correct answer.
Step-by-step explanation:For the given situation,
The statement is given as price increased by 1/2.
Let us assume, we have an item costs 1$.
Now the price is increased by 1/2, so we need to add the fraction to 1.
1. The sum of two numbers is 72. If one number is 3 times the other, what is the largest number?
2. How many hours are there between 6:30am and 1:30pm on the same day?
3. Find the value of x
4. At $22.50 per metre, what is the price of 1 1/2 metres of cloth?
5. How many millilitres are there in half a litre?
Answer:
See below
Step-by-step explanation:
1. The sum of two numbers is 72. Lets say the two numbers are x and y:
x + y = 72
If one number is 3 times the other,
x = 3y
what is the largest number?
Substitute the second into the first expression
x + y = 72
3y + y = 72
4y = 72
y = 18
2. From 6:30am to noon is 5 1/2 hours. From noon to 1:30 is another 1 1/2 hours. The sum is (5.5 + 1.5) = 7 hours
3. I'm assuming the bottom two angles are the same (diffiuclt to read). If so, we know that the sum of the interior angles of a triangle is 180 degrees.
2x + x + x = 180
4x = 180
x = 45 degrees
4. (1.5 meters)*($22.50/meter) = $33.75
5. (0.5 L)*(1000 ml/L) = 500 ml
The Central Limit Theorem says that a histogram of the sample means will have a bell shape, even if the population is skewed and the sample is small. True or False
The statement "The Central Limit Theorem says that a histogram of the sample means will have a bell shape, even if the population is skewed and the sample is small. " is false.
What is meant by the central limit theorem?
According to the central limit theorem, a statistical theory, samples with large sample size and a finite variance will have a normal distribution and a mean that is about equal to the mean of the entire population. The central limit theorem proves that, in many circumstances, given identically distributed independent samples, the standardised sample mean tends towards the conventional normal distribution even though the original variables themselves are not normally distributed.
Since the given sample is small, the histogram will not have a bell shape.
This is because according to central limit theorem, the normal approximation may not be very accurate when the sample size is small, Yet, the normal approximation gets better as the sample size increases.
Therefore the statement "The Central Limit Theorem says that a histogram of the sample means will have a bell shape, even if the population is skewed and the sample is small. " is false.
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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar.
In the model above, the 8 that the arrow points to is
times the 8 to the left of the arrow and
times the 8 to the right of the arrow.
In the model above, the 8 that the arrow points to is 1/10 times the 8 to the left of the arrow and 10 times the 8 to the right of the arrow.
What is a place value?In Mathematics, a place value can be defined as a numerical value (number) which denotes a digit based on its position in a given number and it includes the following:
TenthsHundredthsThousandthsUnitTensHundredsThousands.Generally speaking, the place value of the 8 that the arrow points to is tens and as such, we have the following:
8 = 80 × 1/10
8 = 0.8 × 10
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Answer these 2 pls there are math questions
Answer:
x = 50°
d = 40°
Step-by-step explanation:
Angle sum property of quadrilateral:Quadrilaterals are four-sided polygon and the sum of all the interior angles is 360°
Sum of all angles of quadrilateral = 360°
60° + x + 3x + 2x = 360
60 + 6x = 360
Subtract 60 from both sides,
6x = 360 - 60
6x = 300
Divide both sides by 6
x = 300 ÷ 6
x = 50°
b) 120° + 110° + 90° + d= 360°
320 + d = 360
Subtract 320 from both sides,
d = 360 - 320
d = 40°
A pole 5 feet tall is used to support a guy wire for a tower, which runs from the tower
to a metal stake in the ground. After placing the pole, Liam measures the distance
from the pole to the stake and from the pole to the tower, as shown in the diagram
below. Find the length of the guy wire, to the nearest foot.
The length of the guy wire is approximately 21 feet
Calculating the length of the guy wireFrom the question, we are to calculate the length of the guy wire.
To calculate the length of the guy wire,
First, we will determine the height of the tower.
Let the height of the tower be h
From the given diagram, we can write that
h/(9 +4) = 5/4
h/13 = 5/4
h = (13×5)/4
h = 65/4
h = 16.25 feet
Let the length of the guy wire be l
Then,
From the Pythagorean's theorem we can write that
l² = 16.25² + (9+4)²
l² = 264.0625 + 13²
l² = 264.0625 + 169
l² = 433.0625
l = √433.0625
l = 20.81015
l ≈ 21 feet
Hence, the length is approximately 21 feet
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Bob has a box of chocolates containing 6 chocolate covered almonds, 4 chocolate covered peanuts, and 8 plain chocolates. If the chocolates look identical, what is the probability that the first two chocolates Bob eats will have almonds?
Answer:
The probability that the first two chocolates Bob eats will have almonds is 5/51 or 9.8% (nearest tenth).
Step-by-step explanation:
Given that Bob has a box of chocolates containing 6 chocolate covered almonds, 4 chocolate covered peanuts, and 8 plain chocolates, the total number of chocolates in the box is:
[tex]\implies \sf Total=6 + 4 + 8 = 18[/tex]
Probability Formula[tex]\boxed{\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}}[/tex]
Therefore, the probability that the first chocolate Bob eats will have almonds is:
[tex]\implies \sf P(first\;almond)=\dfrac{6}{18}[/tex]
As Bob has eaten one almond chocolate there are now 5 chocolate covered almonds left and a total of 17 chocolates. Therefore, the probability that the next chocolate Bob eats will have almonds is:
[tex]\implies \sf P(second\;almond)=\dfrac{5}{17}[/tex]
To find the total probability for two or more events, multiply the probabilities. Therefore, the probability that the first two chocolates Bob eats will have almonds is:
[tex]\begin{aligned}\implies \sf P(first\;almond)\;and\;P(second\;almond) & =\dfrac{6}{18} \times \dfrac{5}{17}\\\\ &=\dfrac{30}{306}\\\\&=\dfrac{5}{51}\\\\&=0.0980392...\\\\&=9.80392...\%\end{aligned}[/tex]
Therefore, the probability that the first two chocolates Bob eats will have almonds is 5/51 or 9.8% (nearest tenth).
3. Jamie thinks the probability of spinning a number less than or equal to 3 is 3. Is this correct?
Answer:
B. Jamie is incorrect. Since spinning a number from 1-3 is certain, the probability is 1.
Step-by-step explanation:
Probability is on a scale of 0 to 1, with 0 being impossible, and 1 being certain.
As the possibility of spinning and landing on a number less than or equal to 3 is 100%, as all numbers on there are less than or equal to 3, the probability would be 1, not 3.
F
00
Which mapping does not represent a function?
5
10
15.
20-
5-
10:
15
20
5-
10-
15
20-
5.
101
15
20
25
30
35
40
25
30
35
40
25
30
35
40
25
30
35
40
The relation can be a function is discussed below.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range.
Given:
We Know that in a function a input have only one output.
There no input value whose have the two distinct output at a same time.
We have attached question is not understood.
let us take example
Is A = {(1, 5), (1, 5), (3, -8), (3, -8), (3, -8)} a function?
We write the above data in table format then
x y
1 5
1 5
3 -8
3 -8
3 -8
Here we have input value 1 have two outputs but same value 5.
Thus, the Given relation A is a function
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Describe the signs of two rational numbers when (a) their sum is positive, (b) their product is positive, and (c) their quotient is positive. Give examples to support your answers
Answer:
here are signs for (A), (B) and (C) hope this helps :)
Step-by-step explanation:
(a) The signs of two rational numbers whose sum is positive can be either both positive or both negative. If the signs are different, the absolute value of one number is greater than the absolute value of the other.
Example:
1/2 + 3/4 = 1/4 (positive sum, both numbers are positive)
-2/3 + 4/5 = 2/15 (positive sum, both numbers are negative)
(b) The signs of two rational numbers whose product is positive can be either both positive or both negative.
Example:
1/3 * 4/5 = 4/15 (positive product, both numbers are positive)
-2/7 * -3/4 = 3/14 (positive product, both numbers are negative)
(c) The signs of two rational numbers whose quotient is positive can be either both positive or both negative.
Example:
2/3 ÷ 1/4 = 8/3 (positive quotient, both numbers are positive)
-5/6 ÷ -2/3 = 5/4 (positive quotient, both numbers are negative)
The median number of points scored by
players in a basketball game is
The range of the numbers of points scored by the same basketball players in the same game is
The possibility of any other range other than 13-6 through 17-10 with several recurring values (mode) is not possible because mean 12 is the median. Hence, I went with 16 and 9.
What is mean?The mean of a dataset, sometimes referred to as the arithmetic mean, is the sum of all results multiplied by the number of values . This is the most popular way to measure central tendency and is sometimes refereed to as the "mean." This is obtained by dividing the total total of values within the dataset by the sum of the values. Calculations may be performed using both raw data and information that has been compiled into frequency tables. The average of a number is referred to as average. Calculating the following is easy: After adding all the digits, divide by the number of digits. the sum split by the count.
The query is not complete. It would still be 9 and 16 if the question asked for the two numbers that may represent the lowest and highest scores.
9 numbers in total. List them in descending order. Your Median is the middle number. The gap between the greatest and the lowest number called the range. The probabilities are therefore 8-1, 9-2, 10-3, 11-4, 12-5, 13-6, 14-7, 15-8, 16-9, 17-10, 18-11, and 19-12. The possibility of any other range other than 13-6 through 17-10 with several recurring values (mode) is not possible because 12 is the median. Hence, I went with 16 and 9.
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Answer these in true or false
Answer: True, False, False
Step-by-step explanation:
Answer:
8. true
9. false
10. false
I got this from Khan academy.
Rewright the equation by completing the square. x^2 −14x+33=0
(x+_)^2
HELP!
how to convert ml to quarts
Answer:
1 milliliter = 0.00105669 liquid quart
Step-by-step explanation:
What are units?A unit can be used for measurement, and is commonly found in mathematics to describe length, size, etc.
Converting these units:
1 milliliter = 0.00105669 liquid quart1 quart = 946.353 mlTherefore, for every 1 milliliter it is equivalent to 0.00105669 liquid quart.
pls help with this homework question
Answer:
h = 12 feet
Step-by-step explanation:
using the right triangle shown in the diagram.
the base of the triangle is half the measure of the base of the square side.
then base of triangle = [tex]\frac{1}{2}[/tex] × 32 = 16 feet and hypotenuse = 20 feet
using Pythagoras' identity in the right triangle.
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
h² + 16² = 20²
h² + 256 = 400 ( subtract 256 from both sides )
h² = 144 ( take square root of both sides )
h = [tex]\sqrt{144}[/tex] = 12
the height h of the pyramid is 12 feet
solve this absolute value:
l3x+7l= -15
Answer:l^3x+28l=-6
or 0
Step-by-step explanation:
How many ways can two names be chosen from 76 in a raffle if only one entry per person is allowed
The number of ways two names can be chosen from 76 in a raffle where only one entry is allowed is 3,025.
This can be calculated by using the combination formula: nCr = n!/(r!(n-r)!), where n is the total number of names (76) and r is the number of names to be chosen (2). The calculation for the same is written out below:
nCr = 76!/(2!(76-2)!)
= 76!/(2!*74!)
= 3,025.
This means that there are 3,025 possible combinations of two names that can be chosen from the 76 names if only one entry is allowed per person.
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what is p value two tailed calculator
A p-value two-tailed calculator is a statistical tool used to calculate the p-value for a two-tailed test of a population mean or proportion.
A p-value two-tailed calculator is an online tool used in statistical analysis to determine the probability value of a two-tailed hypothesis test. This calculator helps researchers and analysts to determine if there is a significant difference between two population means or proportions. It calculates the p-value, which is the probability of obtaining results as extreme or more extreme than the observed results under the null hypothesis.
Users input sample data, population parameters, significance level, and type of test to obtain the calculated p-value. This tool is essential in hypothesis testing in fields such as psychology, medicine, and economics.
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what is 124 lbs to kg?
Answer: 56.2455
Step-by-step explanation: