All the probabilities are solved and are mentioned below.
What is probability mass function?In probability and statistics, a probability mass function is a function that gives the probability that a discrete random variable is exactly equal to some value
Given is that there is a chance that a bit transmitted through a digital transmission channel is received in error. Let X denote the number of bits in error in the next four bits transmitted. Suppose the probability mass function is given by -
Pr(X = 0) = 0.55
Pr{X = 1) = 0.22
Pr(X = 2) = 0.13
Pr(X = 3) = 0.08
Pr(X = 4) = 0.02
We can find the probabilities as -
{ 1 } - the probability that two or fewer bits are transmitted in error :
P{E} = P(0) + P(1) + P(2)/∑P{n}
P{E} = 0.9/1
P{E} = 0.9
{ 2 } - the probability that at least one bit is transmitted in error -
P{E} = P(1) + P(2) + P(3) + P(4)/∑P{n}
P{E} = 0.45/1
P{E} = 0.45
{ 4 } - the expected value of the number of bits transmitted in error -
n = 0 + 1 + 2 + 3 + 4
n = 10
{ 4 } - the standard deviation of the number of bits transmitted in error -
σ = 1.0677
Therefore, all the probabilities are solved and are mentioned above.
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Determine the set of x-values where f(x) =
The set of x-values where f(x) is continuous is all real numbers except x=1, interval notation is (-∞, 1) U (1, ∞).
What are the set of x-values?
The function f(x) is a rational function, which is continuous for all x-values except those that make the denominator 0.
Thus, to find the set of x-values where f(x) is continuous, we need to find the values that make the denominator x-1 equal to 0:
x - 1 = 0
x = 1
Therefore, the set of x-values where f(x) is continuous is all real numbers except x=1. We can write this set in interval notation as:
(-∞, 1) U (1, ∞)
which means the set of all x-values less than 1, combined with the set of all x-values greater than 1.
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A 16ft pipe has been cut into two parts, one 3 times as long as the other. How long (in ft) is each part?
Answer:
12 feet
Step-by-step explanation:
Let x be the length of the shorter part of the pipe.
According to the problem, the longer part is three times as long as the shorter part. Therefore, the length of the longer part is 3x.
We also know that the sum of the lengths of the two parts is equal to the original length of the pipe, which is 16 feet.
So we can write an equation:
x + 3x = 16
Simplifying this equation, we get:
4x = 16
Dividing both sides by 4, we get:
x = 4
So the length of the shorter part is 4 feet, and the length of the longer part is 3 times as long, or 3 × 4 = 12 feet.
In a company, 90% of the workers are men. If 410 people work for the company who aren't men, how many workers are there in all? Use pencil and paper. Show two different ways that you can solve this problem.
The total number of workers if, In a company, 90% of the workers are women, If 440 people work for the company who aren't women is 4400.
What is percentage?
As it is clear from the term per-cent means measuring anything per hundred. For example, you get marks per 100 marks, so you get the percentage.
Given:
In a company, 90% of the workers are women,
If 440 people work for the company who aren't women,
Calculate the percentage of people who aren't women as shown below,
The percentage of people who aren't women = 100% - the percentage of women
The percentage of people who aren't women = 100% - 90%
The percentage of people who aren't women = 10%
Assume that there are a total of x workers then according to the statement,
10% of x = 440
10 / 100 × x = 440
x = 440 × 100 / 10
x = 4400
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CAN SOMEONE HELP WITH THIS QUESTION?✨
The marginal revenue is 909 dollars per unit.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
R(q) = -2q² + 1000q _____(1)
Where q is the unit sold.
Now,
Substitute q = 91 in (1).
R(q) = -2q² + 1000q
R(q) = -2 x 91² + 1000 x 91
R(q) = -8281 + 91000
R(q) = $82719
Now,
91 units = $82719
1 unit = 82719/91
1 unit = $909
Thus,
909 dollars per unit is the marginal revenue.
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What is the slope of the line on the graph?
C)2
The slope of the line on the given graph in the image below is: 2.
How to Find the Slope of a Line on a Graph?To find the slope of the line in a graph, use any two points on the line and plug in the coordinates of the two points in the slope formula which is given as:
Slope (m) = change in y / change in x = rise/run = y2 - y1 / x2 - x1
Picking two points on the line, (0, 1) and (1, 3):
Slope (m) = change in y / change in x = (3 - 1) / (1 - 0)
Slope (m) = 2/1
m = 2
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Austin runs 7 miles in 51 minutes.How many minutes does he take per mile?
Answer:
7 min 48 sec / mile
Step-by-step explanation:
51 min ÷ 7 miles = 7.2857142857142
Rounds to 7
If the area of a rectangle with width x can be represented with the expression A(x) = x(14 – x), what is the perimeter of the rectangle?
A
28
B
56
C
56 – 4x
D
4x + 28
Answer: D
Step-by-step explanation:
To find the perimeter of the rectangle, we need to know both the length and width of the rectangle. Since we are given the expression for the area, which is A(x) = x(14 – x), we can use this expression to find the length of the rectangle that corresponds to a given width x.
The area of a rectangle is equal to its length multiplied by its width. So we have:
A(x) = x(14 – x)
We can rewrite this equation as a quadratic equation in standard form:
A(x) = -x^2 + 14x
To find the maximum value of A(x), we can use the formula for the x-coordinate of the vertex of a quadratic function:
x = -b / 2a
where a = -1 and b = 14 in this case.
x = -14 / 2(-1) = 7
So the maximum area occurs when the width of the rectangle is 7.
To find the length of the rectangle, we can substitute x = 7 into the expression for the area:
A(7) = 7(14 – 7) = 49
So the length of the rectangle is 49/7 = 7.
Now we can find the perimeter of the rectangle by using the formula:
P = 2(l + w)
where l is the length and w is the width.
Substituting l = 7 and w = x, we get:
P = 2(7 + x)
So the correct answer is (D) 4x + 28.
The total price of 3 mangoes and 6 apples is $42. If the price of a mango is $2 less than 2 times that of an apple, find the price of an apple.
Answer:
$4
Step-by-step explanation:
Let's denote the price of an apple by "a" and the price of a mango by "m". Then we can set up two equations based on the information given in the problem:
"The total price of 3 mangoes and 6 apples is $42"
mangoes are three times apples in this case.
3m + 6a = 42
"The price of a mango is $2 less than 2 times that of an apple"
m = 2a - 2
Now we can substitute equation 2 into equation 1 and solve for "a":
3(2a - 2) + 6a = 42
6a - 6 + 6a = 42
12a = 48
a = 4
Therefore, the price of an apple is $4.
꧁༒αηѕωєяє∂ ву gσ∂кєу༒꧂
The scrap value of a machine at the end of its useful life is given by S(n)=C(1-r), where C is the original cost, n is the useful life
of the machine in years, and r is the constant annual percentage of value lost. Find the scrap value of the following machine.
Original cost, $41,000; life, 10 years; annual rate of value lost, 13%
Answer:
$ 2,484.23
Step-by-step explanation:
The formula for scrap value is
S(n) = C( 1- r)ⁿ
where
S(n) = scrap value after n years
C = original cost
r = rate of value lost in decimal
n = number of years
First convert r to a decimal by dividing by 100
r = 13/100 = 0.13
S(10) = 10,000(1 - 0.13)¹⁰
= 10,000 x (0.87)¹⁰
= 10000 x 0.248423
= $ 2,484.23
Find the equation of the line through the points (−2,−10)
and (−2,−5).
Answer:
x = -2
Step-by-step explanation:
The line passing through the points (-2, -10) and (-2, -5) is a vertical line because both points have the same x-coordinate (-2).
Therefore, the equation of the line is simple:
x = -2
This means that for any value of y, the corresponding value of x is always -2. Visually, this line looks like a straight vertical line passing through the point (-2, -10) and (-2, -5) on the coordinate plane.
Answer:
Step-by-step explanation:
how do you solve a 3 collumn table
The way to solve a 3 column table depends on the information in the table but there are general steps to follow shown below.
How to work with a three column table ?First, identify the headings for each column. Then, determine the type of data being presented in each column because the data may be numerical (such as measurements or quantities), categorical (such as types or classifications), or a combination of both.
Analyze the data in each column and use mathematical operations or formulas to calculate or analyze the data, if necessary. Finally, draw conclusions or make inferences based on the data in the table.
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100 POINTS HELP A company buys equipment for $625 to help increase sales. What is the shareholder's equity if $450 was put on credit?
A. $450
B. $1075
C. $625
D. $175
The shareholder's equity if $450 was put on credit is $175. Option D
How to find the shareholder's equityThe purchase of equipment for $625 represents a decrease in the company's shareholder equity, since assets have increased while the equity has not changed.
If $450 was put on credit, this means that the company has only paid $625 - $450 = $175 towards the equipment.
The shareholder's equity is reduced by this amount, so the new shareholder's equity is:
Shareholder's equity = Initial equity - Decrease in equity
Shareholder's equity = 0 - $175
Shareholder's equity = -$175
Since the shareholder's equity is negative, it means that the company owes more than it owns. Therefore, the answer $175.
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The sum of four times a number and seven is 27. Find the number.
Provide your answer below:
Answer:
Look at the screenshot.
what is the y intercept when the coordinate is -3,-3 and the slope is -1!! quick answers needed
When the coordinate is (-3, -3) and the slope is -1, the y-intercept is -4.
What is slope?Slope is a measure of the stainless of a line what is surface and it represent by the letter m. It is calculated by dividing the vertical change in the line or surface by the horizontal change in the line or surface. Slope is used in mathematics engineering and other science to measure the rate of change between two point.
The y-intercept is the point at which a line crosses the y-axis when plotting coordinates on a graph. To find the y-intercept, you need to use the equation y = mx + b, where m is the slope and b is the y-intercept. In this case, the equation would be y = -1x - 4. This equation can be used to solve for the y-intercept when the coordinate is (-3, -3). By substituting -3 for x and -3 for y, the equation can be rearranged to -3 = -1(-3) - b, which simplifies to -4 = -b. Therefore, the y-intercept is -4.
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Question content area top
Part 1
The line models the cost of renting a kayak. Write an equation in slope-intercept form for the line, where x is the number of hours the kayak is rented and y is the total cost of renting the kayak.
The equation of the line that models the cost of renting a kayak in slope-intercept form is: y = 5x + 10
The slope and y-intercept of the line that predicts the price of renting a kayak must be identified in order to formulate the equation for the line.
We can observe from the provided graph that the line traverses points (0, 10) and (6, 40). We may determine the slope of the line using these two points:
Slope = (Y Change/X Change) = (40 - 10)/(6 - 0) = 30/6 = 5
The equation of a line can also be expressed in the slope-intercept form, which is as follows:
y = mx + b
where m denotes the line's slope and b its y-intercept.
The slope of the line is previously known to be 5. One of the points the line passes through can be used to determine the y-intercept, for instance (0, 10). When we enter these numbers into the equation, we obtain:
10 = 5(0) + b
If we simplify, we get:
b = 10
Thus, the slope-intercept form equation of the line that represents the cost of renting a kayak is as follows:
y = 5x + 10
where x represents the duration of the kayak rental and y represents the entire cost.
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given a set of data that is skewed-right, there is at least % of the data within 3 standard deviations. use either chebyshev's theorem or the empirical rule to fill in the blank with the best answer:
The set of data that is skewed-right, there is at least 99.7% of the data within 3 standard deviations.
What Is the Empirical Rule?A statistical principle known as the empirical rule, also known as the three-sigma rule or 68-95-99.7 rule, holds that with a normal distribution, almost all observed data will lie within three standard deviations (denoted by ) of the mean or average (denoted by ).
Some points about standard deviation using Empirical Formula:
In accordance with the Empirical Rule, 99.7% of data that are found to have a normal distribution fall within 3 standard deviations of the mean.According to this formula, 68% of the data are within one standard deviation of the mean, 95% are within two standard deviations, and 99.7% are within three standard deviations.Learn more about Empirical Formula here:
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Aldo and Lena are standing on a riverbank 220 meters apart at points A and B respectively (see the figure below). They want to know the distance from Aldo to a house located across the river at point C. Aldo measures angle A to be 51 and Lena measures angle B to be 65. What is the distance from Aldo to the house? Round your answer to the nearest tenth of a meter.
When Aldo and Lena are standing on a riverside 220 meters apart at certain points, the distance between Lena and the home is 240.8 meters.
what is distance ?Displacement is the overall, purposeless movement of an object. Speed can be characterized as the amount of area an object has covered, disregarding of the origin or ending location. Distance has characterized by the extent or size of the distance between two places. The gap between adjacent positions and the distance moved between them are not exactly the same thing, it should be emphasized. The travelled is the entire length of a path that join different places. Distance is the average trip distance of a body. It is also known as distance. For instance, OP = 360 m would indicate the length of the path for an object traveling from 0 ° to point P.
given
BC/sin 53 = 250/sin 56
BC = 250 * sin 53 /sin 56
=240.8 m
When Aldo and Lena are standing on a riverside 220 meters apart at certain points, the distance between Lena and the home is 240.8 meters.
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The point A ( 3 , − 2 ) is reflected over the point ( 4 , 0 ) and its image is point B . What are the coordinates of point B ?
The coordinates of point B are (1,2).
How to find Reflection of a point?
When a point is reflected across the X-axis, the x-coordinates remain the same. But the Y-coordinates are transformed into their opposite signs. Therefore, the reflection of the point (x, y) across X-axis is (x, -y).
The reflected point will be equidistant from the point over which it is reflected as the original point and in the same line as the original point and the reflected point.
Find the difference between the x and y values of the given points and add that value (distance) to the reflection point.
x-values: 4-3 = 1 y-values: 0-(-2) = 2
Add to reflection point x: 4-3 = 1 y: 0 -(-2)= 2
Hence, The coordinates of point B are (1,2).
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Pls answer and show me how you got that answer
The mass of the radioactive sample at the beginning of the 13th day of the experiment will be around 424.7 grams.
What does one gramme represent?A metric weight measurement unit. A gramme is one thousandth of a kilogramme, or about 30 times smaller than an ounce. Leave a space between the word "gramme" (or the symbol "g") and the number that comes before it when a specific number is provided. In technical and scientific writing, the unit name and the number are either written together in full (for example, ten grammes) or a numeral is used with the sign ( e.g. 10 g ).
When we find the mass of radioactive, we obtain:
m₀=initial mass=1500 grams, r = 13% and n =12 days
⇒m = m₀ x [tex](1 - \frac{r}{100} )^{n}[/tex]
⇒m =1500×[tex](1-\frac{13}{100}) ^{12}[/tex]
⇒m=424.7 grams.
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2 A representative sample of 60 students from a high school is surveyed
which elective he or she is taking. The table shows the respons Elective Dance Music Art Photography Electronics Number of Stud 19 7 15 11 8
The Accurate Prediction of the data:
In a group of 120 students, it is expected that 16 of them are taking electronics.
About 25% of the students in the school are taking art.
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. With the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
Total students = 60
let x% of students chose Arts
So, x% of 60 = 15
x/ 100 (60) = 15
x = 1500 / 60
x = 25%
and, if there 120 students then number of students choose electronics
= 8/60 x 120
= 16
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find derivative of f(x) = 4x³ using first Principre and F(x) = 2x²-3x
Answer:
12x^2.
Step-by-step explanation:
let y = 4x^3
If y is increased by a small amount Δy then x is increased by a small amount Δx, so we write:
y + Δy = 4(x + Δx)^3
y + Δy = 4(x^3 + 3x^2 Δx + 3x(Δx)^2 + (Δx)^3)
y + Δy = 4x^3 + 12x^2 Δx + 12x(Δx)^2 + 4(Δx)^3
Δy = 4x^3 + 12x^2 Δx + 12x(Δx)^2 + 4(Δx)^3 - y
= 4x^3 + 12x^2 Δx + 12x(Δx)^3 + 4(Δx)^2 - 4x^3
Δy/Δx = (4x^3 + 12x^2 Δx + 12x(Δx)^3 + 4(Δx)^2- 4x^3 ) / Δx
= (12x^2 Δx + 12x(Δx)^3 + 4(Δx)^2) / Δx
= 12x^2 + 12x(Δx)^2 + 4Δx
Now as Δx approaches zero, the limit ( that is the derivative) of f(x)
= 12x^2
- as we can neglect the last 2 terms.
The second part can be solved by the same process.
Roger will pour concrete to make a sidewalk with the dimensions, in feet, shown in the figure below. He will pour the concrete to a depth of 4 inches. One bag of concrete mix makes 0.6 cubic feet of concrete. What is the least whole number of bags of concrete mix that Roger needs in order to make the sidewalk?
F. 16
G. 44
H. 50
J. 58
K. 67
Answer:
The least whole number of bags of concrete mix that Roger needs in order to make the sidewalk is G, 44. To calculate this, we must first convert the cubic feet of the sidewalk into cubic inches, which would be 345,600 cubic inches. Then, we need to divide this by the amount of cubic inches in one bag (0.6 cubic feet = 630 cubic inches). This gives us 550 bags of concrete mix, but since Roger will be using a whole number, the closest he can get is 44 bags.
Can somebody help..? The question is down below
The required measures of the angles are the following: ∠J = 135°, ∠F = 45°, ∠B = 135°, and ∠C = 22°.
What are supplementary angles?The supplementary angles are illustrated as when pairing of angles addendum to 180° then they are called supplementary angles.
The measure of the angles are given as follows:
∠I = 22°
∠A = 23°
∠J = 180° - ∠I - ∠A (sum of interior angles in a triangle)
∠J = 180° - 22° - 23° = 135°
∠F = 180° - ∠J (supplementary angles)
∠F = 180° - 135° = 45°
∠B = 360° - 90° - 90° - 45° (sum of interior angles in the quadrilateral)
∠B = 135°
∠C = 180° - ∠A - ∠B (sum of interior angles in a triangle)
∠C = 180° - 23° - 135° = 22°
Thus, the required measures of the angles are the following: ∠J = 135°, ∠F = 45°, ∠B = 135°, and ∠C = 22°.
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A basketball player makes 39% of her shots from the free throw line. Suppose that each of her shots can be considered independent and that she throws 5 shots. Let x = the number of shots that he makes. What is the sample space for x?.
The sample space for x, where x is the number of shots the basketball player makes out of 5 free throws, is,{SSSSS, FSSSS, SFSSS, SSFSS, SSSF S, SSSSF, FSSF S, FSFSS, FSSSF, SFFSS, SFSSF, SSFFS, FSSFS, FSFSS, FFSSS, SFFSF, SFSSF, SSFSF, FSSSF, FSFSS, SFSFS, FSSFS, FSSSF, SFFFS, SSFFS, FFSFS, FFSFF, FSFFS, SFSFF, SFSSS}There are 32 possible outcomes in the sample space.
The sample space for x is the set of all possible outcomes of the experiment of shooting 5 free throws. Since each shot can either be made or missed, there are 2 possible outcomes for each shot. Therefore, there are 2^5 = 32 possible outcomes for the experiment.
To enumerate the sample space, we can use the notation S for made shots and F for missed shots. Then, each outcome of the experiment can be represented by a string of 5 letters, where each letter represents the outcome of a single shot.
Using this notation, the sample space for x is:
{SSSSS, FSSSS, SFSSS, SSFSS, SSSF S, SSSSF, FSSF S, FSFSS, FSSSF, SFFSS, SFSSF, SSFFS, FSSFS, FSFSS, FFSSS, SFFSF, SFSSF, SSFSF, FSSSF, FSFSS, SFSFS, FSSFS, FSSSF, SFFFS, SSFFS, FFSFS, FFSFF, FSFFS, SFSFF, SFSSS}
Note that there are 6 outcomes where the player makes 0 shots, 5 outcomes where the player makes 1 shot, 10 outcomes where the player makes 2 shots, 10 outcomes where the player makes 3 shots, 5 outcomes where the player makes 4 shots, and 1 outcome where the player makes all 5 shots.
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Find the perimeter of the triangle whose vertices are (−1,−14)
, (7,1)
, and (−1,7)
. Write the exact answer. Do not round.
To find the perimeter of the triangle, we need to calculate the length of each of its sides and then add them up.
Let's start by finding the length of the side between (-1, -14) and (7, 1). We can use the distance formula for this:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the coordinates, we get:
distance = sqrt((7 - (-1))^2 + (1 - (-14))^2)
= sqrt(8^2 + 15^2)
= sqrt(289)
= 17
So the length of the first side is 17.
Now let's find the length of the side between (-1, -14) and (-1, 7):
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the coordinates, we get:
distance = sqrt((-1 - (-1))^2 + (7 - (-14))^2)
= sqrt(0^2 + 21^2)
= 21
So the length of the second side is 21.
Finally, let's find the length of the side between (7, 1) and (-1, 7):
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the coordinates, we get:
distance = sqrt((-1 - 7)^2 + (7 - 1)^2)
= sqrt((-8)^2 + 6^2)
= sqrt(100)
= 10
So the length of the third side is 10.
Now we can add up the lengths of all three sides to get the perimeter:
perimeter = 17 + 21 + 10
= 48
Therefore, the perimeter of the triangle is 48.
is this problem a one solution,no solution or all real numbers
The equation is true for all real numbers, and therefore the solution set is (C) all real numbers.
What is the solution to the equation?In arithmetic, a solution to the equation expresses can be replaced for the variable to provide a piece of real number information.
We can start simplifying the equation using the distributive property:
4(6x - 4) = 8(3x - 2)
24x - 16 = 24x - 16
We can see that both sides of the equation are identical, so the equation is an identity. This means that the equation is true for all real numbers, and therefore the solution set is all real numbers.
In other words, any value we choose for x will make the equation true.
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The complete question would be as:
How many solutions have the below equation?
4(6x - 4) = 8(3x - 2)
A. one solution.
B. no solution.
C. all real numbers.
Nikki is going to use SSS to prove that PQR SQR.
Which of these is a necessary step in Nikki's proof?
A.
Prove that PQR SQR by vertical angles.
B.
Prove that PQ QR by CPCTC.
C.
Prove that QR QR by the reflexive property.
D.
Prove that QPR QSR by the transitive property.
Prove that QR QR by the reflexive property.
The triangles are congruent by reflexive property of SSS
What are Congruent Triangles?Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape
The three sides are equal (SSS: side, side, side)
Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)
A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)
Given data ,
Let the first triangle be ΔPQR
Let the second triangle be ΔQRS
And , the side QR is the common side
Now , measure of side PQ = measure of side QS
And , measure of side PR = measure of side RS
So , the three sides are equal (SSS: side, side, side) and they are congruent triangles
And , QR ≈ QR by the reflexive property.
Hence , the triangles are congruent by SSS
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The complete question is attached below :
Nikki is going to use SSS to prove that PQR SQR.
Which of these is a necessary step in Nikki's proof?
A.
Prove that PQR SQR by vertical angles.
B.
Prove that PQ QR by CPCTC.
C.
Prove that QR QR by the reflexive property.
D.
Prove that QPR QSR by the transitive property.
which of the following is equal to 9•6 divided by long division?
The solution to the expression 9•6 is 54
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
9•6 divided by long division
The above expression is a product expression
This means that it cannot be evaluated using long division
When the expression is evaluated. we have
9 * 6 = 54
Hence, the solution is 54
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The correct matching of the fractions
0.1 - 1/10
0.01 - 1/100
100% - 1
What is a fraction?A fraction is a way of representing a part of a whole or a quantity that is less than one. Fractions consist of two numbers separated by a horizontal or diagonal line, with the number above the line being called the numerator and the number below the line being called the denominator.
The numerator represents how many parts of the whole are being considered, while the denominator represents the total number of equal parts that the whole is divided into.
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At the Crown Interior Pizza Hat location in Faridabad, a report showed that 431 out of 778 orders were for delivery. What is the minimum sample size needed to have a 4 percentage point error for the proportion of orders that were carry-out?
*If you used a program on the graphing calculator or formula can you specify which ones please?
Answer:
Step-by-step explanation:
To determine the minimum sample size needed to have a 4 percentage point error for the proportion of orders that were carry-out, we can use the following formula:
n = (Z^2 * p * q) / E^2
where:
n is the sample size we want to determine
Z is the z-score associated with the desired level of confidence (let's assume a 95% confidence level, so Z = 1.96)
p is the estimated proportion of orders that were carry-out (we don't know this yet, so we'll use 0.5 as a conservative estimate)
q is 1 - p (i.e., the estimated proportion of orders that were delivery)
E is the desired margin of error (in this case, 0.04)
Using the given information, we can estimate that the proportion of orders that were carry-out is:
p = 1 - 431/778 = 0.446
Then, plugging in the values into the formula, we get:
n = (1.96^2 * 0.446 * 0.554) / 0.04^2 ≈ 602.25
Rounding up to the nearest whole number, the minimum sample size needed is 603.
Note that I used the formula for sample size calculation based on a finite population, since the total number of orders is known (778). If we used the formula for an infinite population, the result would be very similar (around 604). I calculated this by hand, without using any calculator program, but you could use a calculator or a spreadsheet to perform the calculations more efficiently.