The total number of ordered pairs (A,B) such that |A|+|B|=4 is:
1x5 + 10x6 + 10x10 + 5x1 = 141
So the answer is 141.
The problem is asking for ordered pairs (A,B), where A and B are subsets of {1,2,3,4,5} such that the cardinality (number of elements) of set A plus the cardinality of set B equals 4.
We can approach this problem by counting the number of ways to choose subsets A and B with the given cardinality and then multiply the results.
First, let's count the number of subsets of {1,2,3,4,5} with cardinality k, for k=0,1,2,3,4,5.
k=0: there is only one subset with no elements, the empty set.
k=1: there are 5 subsets with one element, namely {1},{2},{3},{4},{5}.
k=2: there are 10 subsets with two elements, namely {1,2},{1,3},{1,4},{1,5},{2,3},{2,4},{2,5},{3,4},{3,5},{4,5}.
k=3: there are 10 subsets with three elements, namely {1,2,3},{1,2,4},{1,2,5},{1,3,4},{1,3,5},{1,4,5},{2,3,4},{2,3,5},{2,4,5},{3,4,5}.
k=4: there are 5 subsets with four elements, namely {1,2,3,4},{1,2,3,5},{1,2,4,5},{1,3,4,5},{2,3,4,5}.
k=5: there is only one subset with five elements, the whole set {1,2,3,4,5}.
Next, let's count the number of ordered pairs (A,B) such that |A|=k and |B|=4-k, for k=0,1,2,3,4.
k=0: there is only one subset A with no elements, and only one subset B with 4 elements, so there is only one possible ordered pair (A,B).
k=1: there are 5 possible subsets A and 1 possible subset B, so there are 5 possible ordered pairs (A,B).
k=2: there are 10 possible subsets A and 6 possible subsets B, so there are 60 possible ordered pairs (A,B).
k=3: there are 10 possible subsets A and 10 possible subsets B, so there are 100 possible ordered pairs (A,B).
k=4: there are 5 possible subsets A and 1 possible subset B, so there are 5 possible ordered pairs (A,B).
Therefore, the total number of ordered pairs (A,B) such that |A|+|B|=4 is:
1x5 + 10x6 + 10x10 + 5x1 = 141
So the answer is 141.
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Find all real solutions of this equation to answer the question.
(6 – 2x)(3 – 2x)x = 40
Yes. Because 3/2 is a root, you can cut squares with sides of 3/2 in. to make the box
No. This equation has no real solutions.
No. The only real solution is x = 4. It is not possible to cut squares of this size.
Answer:
Please mark me the brainliest
Step-by-step explanation:
To solve the equation (6 – 2x)(3 – 2x)x = 40, we can start by simplifying the left-hand side:
(6 – 2x)(3 – 2x)x = 40
(18x – 12x^2 – 6x + 4x^2)x = 40
(2x^3 – 8x^2 + 18x)x = 40
2x^4 – 8x^3 + 18x^2 = 40
2x^4 – 8x^3 + 18x^2 – 40 = 0
We can try to factor this equation by grouping terms:
2x^4 – 8x^3 + 18x^2 – 40 = 0
2(x^4 – 4x^3 + 9x^2 – 20) = 0
2((x^2 – 2x + 1)(x^2 – 2x – 20)) = 0
2(x – 1)^2(x – 5)(x + 4) = 0
Therefore, the real solutions of the equation are x = 1 (with multiplicity 2), x = 5, and x = -4.
Now, to answer the question, we need to determine whether it is possible to cut squares with sides of 3/2 in. to make a box. We can use the value of x = 3/2 to find the dimensions of the box:
length = 6 – 2x = 6 – 2(3/2) = 3 in.
width = 3 – 2x = 3 – 2(3/2) = 0 in.
height = x = 3/2 in.
Since the width is 0, it is not possible to cut squares with sides of 3/2 in. to make a box. Therefore, the correct answer is:
No. It is not possible to cut squares of this size.
b) Another larger triangle is made from smaller, similar triangles. The perimeter
of this larger triangle is 32 times larger than the perimeter of one of the smaller
triangles.
How many smaller triangles are used to form this larger triangle?
The number of smaller triangles used to fill the larger triangle is given as follows:
1024 triangles.
How to obtain the number of smaller triangles?The perimeter of the larger triangle is 32 times larger than the perimeter of one of the smaller triangles, which means that the ratio of the areas is given as follows:
32² = 1024.
The ratio of the areas is obtained squared as the perimeter is measured in units, while the area is measured in units squared.
This means that 1024 smaller triangles are needed to fill the larger triangle.
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gregor mendel is examining peas to try to understand how traits are passed from parents to offspring. today, gregor has 228 228228 peas to examine. the pods have 6 66 peas per pod. How many pods of peas are there?
The number of pods of peas would be 38. So there are 38.038 pods of peas for Gregor Mendel to examine.
To find out how many pods of peas there are, you simply need to divide the total number of peas by the number of peas per pod. In this case, Gregor Mendel has 228 peas, and each pod contains 6 peas.
Step 1: Divide the total number of peas by the number of peas per pod.
228 peas ÷ 6 peas/pod = 38 pods
Number of peas = 22.8228
Peas per pod = 6
Therefore, the number of pods of peas would be:
22.8228/6 = 38.038
So, there are 38 pods of peas for Gregor Mendel to examine in his study of traits passed from parents to offspring.
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GEOMETRY PLEASE HELP!! FOR 30 POINTS!!
A dart hits the circular dartboard shown below at a random point. Find the probability that the dart lands in the shaded circular region. The radius of the dartboard is 9 in, and the radius of the shaded region is 4 in.
Use the value 3.14 for pie. Round your answer to the nearest hundredth.
Mr victor had 100 computers for sale he sold w computers in the morning and (2w+3) computers in the afternoon. He had 7computers left. How many computers did he sell in the morning?
From the addition arithematic operation, the total number of sold computers by Mr victor is equals to ninty-three out of hundard computers .
Addition, subtraction, multiplication, and division are four basic arithmetic operations used in mathematics.
Total number of computers Mr victor has
= 100
Number of computers sold by him in morning = w
Number of computers sold by him in afternoon = 2w + 3
Number of computers left after selling = 7
We have to determine the number of computers he had to sell. We have total counts of computers so we equate all sold and unsold computers to total and will determine value of variable w. Using addition, w + 2w + 3 + 7 = 100
Simplify, 3w + 10 = 100
=> 3w = 90
Dividing by 3 both sides,
=> w = 30
So, Number of computers sold in morning = 30
Number of computers sold in afternoon = 2×30 + 3 = 63
So, total sold computers = 63 + 30 = 93.
Hence, required value is 93.
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Tam has $74. Then the following events happen, in order: Tam spends $5 on lunch. Tam's parents double the money she has left. Tam adds all the money to the $148 in her savings account. 2. Use the drop-down menus to answer the questions below. An expression that models this series of events is 148 + 2(74-5) C CLEAR Sarah also had some money. The amount she currently has is equal to 2 x 18 -9 + 50. A possible series of events that led to this amount would be: 1. starts with $18 O CHECK P
Answer:
Step-by-step explanation:
Tam's initial amount of money = $74
Tam spends $5 on lunch, so she has $74 - $5 = $69 left.
Tam's parents double the money she has left, so she now has $69 x 2 = $138.
Tam adds all the money to the $148 in her savings account, so her total amount of money becomes $138 + $148 = $286.Expression that models this series of events: 148 + 2(74-5)For Sarah:
Sarah starts with $18.
Sarah doubles her money, so she now has $18 x 2 = $36.
Sarah subtracts $9 from her current amount, so she now has $36 - $9 = $27.
Sarah adds $50 to her current amount, so she now has $27 + $50 = $77.A possible series of events that led to Sarah's current amount of money: Starts with $18, doubles it to $36, subtracts $9, and then adds $50.
PLEASE HELP ME TO SOLVE THIS QUESTION
3.Xavier's salary increases by 2% each year.
In 2010 , his salary was £40,100
i) Calculate his salary in 2015 and give your answer to the nearest pound.
ii) In which year did Xavier's salary first greater than £47,500
i) Based on exponential growth, Xavier's salary in 2015 is £44,274.
ii) The year that Xavier's salary first became greater than £47,500 would be 2019.
What is exponential function?Exponential functions show the relationship between two variables and a variable exponent with a periodic constant rate of growth or decay in the value of something
Annual increase in Xavier's salary = 2% or 0.02
Xavier's salary in 2010 = £40,100
The number of years between 2015 and 2010 = 5 years
Exponential Function:i) y = £40,100(1.02)^5
= £44,273.64
= £44,274
ii) £47,500 = £40,100(1.02)^t
t = 9 years
= 2019 (2010 + 9)
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Estimation (gcse maths)
Answer:
√(4.93 × 17.1) is about √(5 × 20) = √100 = 10. 0.209 is about 0.2, or 1/5.
So we have 10/0.2 = 100/2 = 50.
Place point D where it partitions
the segment into a 1:2 ratio.
1
+
2
3
D
+
4
5
6
Answer: Partitioning a Segment in a Given Ratio ; Find the coordinates of the point that divides the directed line segment · with the coordinates of endpoints at M(−4,0) ...
Step-by-step explanation:
What is the RACI matrix?
a. Resource Allocation & Cost Inventory matrix
b. Matrix of Responsible and Certified Individuals
c. Responsible, Accountable, Consult & Inform matrix
d. Recently Added Control Incident reporting matrix
The RACI matrix is the Responsible, Accountable, Consult & Inform matrix. It is a tool used in project management to clearly define the roles and responsibilities of team members in relation to a project.
c. Responsible, Accountable, Consult & Inform matrix
The RACI matrix is a tool used in project management to clearly define roles and responsibilities. It stands for Responsible, Accountable, Consulted, and Informed. Assigning these roles to individuals or teams, it ensures efficient allocation of resources and effective communication throughout the project.
The matrix identifies who is Responsible for a task, who is Accountable for its completion, who needs to be Consulted before decisions are made, and who needs to be Informed about progress. This helps to avoid confusion and ensure that resources are allocated appropriately, which can ultimately impact the cost of the project.
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It is estimated that the average smartphone owner used 606 megabytes of data per month with a standard deviation of 240 megabytes per month. A random sample of 64 smartphone users was selected a. What is the mean of the sample mean, my? b. What is the standard deviation (standard error) of the sample mean? C. What is the probability that the average amount of data used in this sample was greater than 632 megabytes (P(X > 632))? Show your work! >
Previous question
The probability that the average amount of data used in this sample was greater than 632 megabytes is approximately 0.1922 or 19.22%.
a. The mean of the sample mean (my) can be calculated using the formula:
my = population mean = 606 megabytes per month
b. The standard deviation (standard error) of the sample mean can be calculated using the formula:
standard error = [tex]\frac{standard deviation}{\sqrt{sample size} }[/tex]
standard error = [tex]\frac{240}{\sqrt{64} }[/tex]
standard error = 30
Therefore, the standard error of the sample mean is 30 megabytes per month.
c. To find the probability that the average amount of data used in this sample was greater than 632 megabytes, we need to use the formula for the z-score:
z = [tex]\frac{(x - my) }{standard error}[/tex]
where x is the sample mean, my is the population mean, and standard error is the standard error of the sample mean.
z = [tex]\frac{(632 - 606) }{30}[/tex]
z = 0.87
Using a z-table or calculator, we can find that the probability of getting a z-score of 0.87 or higher is 0.1922. Therefore, the probability that the average amount of data used in this sample was greater than 632 megabytes is approximately 0.1922 or 19.22%.
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In a random sample of 18 residents of the state of Montana, the mean waste recycled per person per day was 2.1 pounds with a standard deviation of 0.74 pounds. Determine the 80% confidence interval for the mean waste recycled per person per day for the population of Montana. Assume the population is approximately normal.
Construct the 80% confidence interval. Round to one decimal
Lower endpoint: ??
Upper endpoint: ??
The 80% confidence interval for the mean waste recycled per person per day for the population of Montana is given as follows:
(1.9, 2.3).
What is a t-distribution confidence interval?The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the variables of the equation are presented as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 80% confidence interval, with 18 - 1 = 17 df, is t = 1.33.
The parameters are given as follows:
[tex]\overline{x} = 2.1, s = 0.74, n = 18[/tex]
The lower bound of the interval is given as follows:
2.1 - 1.33 x 0.74/sqrt(18) = 1.9.
The upper bound of the interval is given as follows:
2.1 + 1.33 x 0.74/sqrt(18) = 2.3.
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the figure below is reflected over x axis. what are the coordinates of the image of point v after this transformation
Note that the coordinates of V after it has been reflected over the x-axis will be: V' (3, -5)
The coordinates given are
V (3, 5)
W(5,8)
X (9, 6)
y (3, 3)
When point is reflected over the x- ais, it's y - coordinate takes on a polarized sign that is it goes from positive to negative of vice versa while the x-cordinte remains the same
So after the image on point v hs been reflected, the new coordinates for V = V' = (3, -5)
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A person's muscle mass is expected to decrease with age. To explore this relationship in women, a nutritionist randomly selected 6 women. The results follow: X is age, and Y is a measure of muscle mass. X Y
43 106 47 97
41 106
47 92 48 92
46 113 Answer the following questions: 1. Fit a quadratic regression model, interpret the meaning of the regression coefficient. (2 Marks) [use R program to solve (X'X)^-1] 2. Test whether the quadratic term can be dropped from the regression model use a = 0.05. (2 Marks) [Hint: MSE = 47.086, SSR(x,x^2) = 230.74 and SSR(x) = 135.03] 3. Express the fitted regression function obtained in (1) in terms of the original variable X (1 Mark)
1. The quadratic regression model is [tex]Y = b0 + b1X + b2X^2[/tex] . The regression coefficient b2 represents the rate of change in muscle mass with respect to age squared. 2. The quadratic term can not be dropped from the regression model, since the calculated F-value is less than the critical value. 3. The fitted regression function in terms of the original variable X is [tex]Y = 87.017 + 0.241X - 0.002X^2[/tex].
To determine the quadratic regression model follow these steps:
1. Using R program, the quadratic regression model:
[tex]Y = b0 + b1X + b2X^2[/tex]
where Y is the muscle mass, X is the age.
The regression coefficients are:
b0 = 283.962
b1 = -14.501
b2 = 0.162
The regression coefficient b2 (quadratic term) represents the rate of change in muscle mass with respect to age squared. It measures the acceleration or deceleration of the change in muscle mass as the age increases.
2. Using the F-test.
[tex]F = [SSR(x,x^2) - SSR(x)] / [(k - 1) * MSE][/tex]
where k = number of coefficients = 3 (b0, b1, b2).
MSE = Mean Squared Error = 47.086
[tex]SSR(x,x^2), SSR(x) =[/tex] Sum of Squares due to Regression with both X and [tex]X^2[/tex] as predictors = 230.74, due to Regression with only X as predictor = 135.03
Therefore,
[tex]F = [230.74 - 135.03] / [(3 - 1) * 47.086] = 2.214[/tex]
Using a significance level the critical value for F-test is 5.143.
Since the calculated F-value (2.214) is less than the critical value (5.143), we fail to reject the null hypothesis. Therefore, there is not enough evidence that quadratic term can be dropped from regression model.
3. The fitted regression function in terms of the original variables:
[tex]Y = 87.017 + 0.241X - 0.002X^2[/tex]
where X is the age and Y is the measure of muscle mass.
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Any equation is given
40=x^2-3x
What is one solution to the equation?
The solution of the quadratic equation, 40 = x² - 3x is x = 8 or x = -5.
How to solve quadratic equation?Quadratic equation can be represented as follows:
ax²+ bx + c
where
a, b and c are constantTherefore, let's solve the quadratic equation as follows:
40 = x² - 3x
Hence,
x² - 3x - 40 = 0
x² + 5x - 8x - 40 = 0
x(x + 5) - 8(x + 5) = 0
(x - 8)(x + 5) = 0
x = 8 or x = -5
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Point A is reflected about the y-axis. Find A'.
Answer:(2, 3)
Step-by-step explanation:
Because we are reflecting the point across the y axis, we know that we are changing the X coordinate. Reflecting across in this case, since there is no other given rule means we are changing the current X coordinate to be the negative version of itself, since it is already negative, this makes the new point a positive one.
This can be explained as moving the point across the given axis at the same distance as the original point from the axis, but in the opposite direction. If it is on the left of the axis, we move it the same distance from the axis to the right, and vice-versa.
We do not change the y coordinate, because we are reflecting the point across the Y axis, which is the vertical line that has an x origin of 0.
All of this means that the new coordinate for our point will be (2, 3).
T/FThe area of descriptive statistics was developed to provide further detail to statisticians about population inferences.
Descriptive statistics is a branch of statistics that deals with the collection, analysis, interpretation, and presentation of data. It focuses on summarizing and describing the characteristics of a sample or population. The purpose of descriptive statistics is to provide a clear and concise summary of the data, including measures of central tendency, variability, and distribution.
True,This information can be used to make inferences about the population as a whole. Therefore, descriptive statistics helps statisticians to better understand and interpret the population data.
False, Descriptive statistics is a branch of statistics that focuses on summarizing and organizing data from a sample or population. It provides insights into the basic features of the data, such as the mean, median, and standard deviation, but does not make inferences about the population.
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an orange juice company sells a can of frozen orange juice that measures 9.4 centimeters in height and 8.5 centimeters in diameter. the company wants to design a new label for the can of juice. if the label will cover the area between the bases, what dimension will be available for the design?
The dimension available for the design is the lateral surface area of the can, which is approximately 251.33 square centimeters.
The area between the bases of the can is the lateral surface area of the can, which can be calculated using the formula:
Lateral surface area = 2 x π x r x h
where π is the mathematical constant pi (approximately 3.14159), r is the radius of the can (which is half of the diameter), and h is the height of the can.
In this case, the height of the can is given as 9.4 centimeters, and the diameter (and hence the radius) is given as 8.5/2 = 4.25 centimeters.
Plugging in these values, we get:
Lateral surface area = 2 x π x 4.25 cm x 9.4 cm
= 251.327 square centimeters
Therefore, the dimension available for the design is the lateral surface area of the can, which is approximately 251.33 square centimeters.
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For this activity, your task is to collect two 3-D items from your environment in order to
calculate their volumes and surface areas. One item will be either a prism or a pyramid,
the other item will be either a cone or a cylinder. Some items that will work for this
activity are canned goods, food storage containers, recyclable cardboard items, etc.
Make sure to show all work for your calculations and answer each reflection question in
two to three sentences.
Prism/Pyramid (Object 1) Cone/Cylinder (Object 2)
Object 1: Object 2:
3-D Shape: 3-D Shape:
Dimensions: Dimensions:
Base Area Calculations:
Base of Object 1: Base of Object 2:
Area Formula: Area Formula:
Base Area: Base Area:
Volume Calculations:
3-D Shape of Object 1: 3-D Shape of Object 2:
Volume Formula: Volume Formula:
Volume: Volume:
Surface Area Calculations:
3-D Shape of Object 1: 3-D Shape of Object 2:
Surface Area Formula: Surface Area Formula:
Surface Area: Surface Area:
It should be noted that to obtain measurements for the Prism or Pyramid:
- Identify prism or pyramid as 3-D shape
- Measure length, width, and height
- Calculate base area. For a prism: find the base's dimension (i.e., rectangle or triangle) and multiply it by height. For a pyramid: halve the calculation of the base and then multiply it by height.
- To calculate volume, obtain the product of the base area and height
- Compute surface area via summation of each face, including the base.
How to explain the informationAlso, to determine measurements for Cone or Cylinder:
- Recognize cone or cylinder as 3-D shape
- Take note of dimensions through measuring the radius and the height
- Compute for Area of Base. For a cone, use the formula πr^2; while for a cylinder, make use of 2πr^2 instead
- In order to measure volume of a cone, get the result of multiplying base area by height and dividing by 3. Meanwhile, the cylinder requires solely multiplying the base area by height.
- Tabulate surface area for cone after applying Pythagorean theorem to solve slant height divided by curved surface area with formula πrl. Do not neglect inclusion of base area in computation.
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Find the P-hate and E by using the given confidence
interval (0.444, 0.484)
p-hate=
E=
The true population proportion and the sample proportion, given the confidence level and sample size.
In statistics, P-hat represents the sample proportion and E represents the margin of error.
Given a confidence interval of (0.444, 0.484), we can find P-hat and E as follows:
P-hat = (lower limit + upper limit) / 2
P-hat = (0.444 + 0.484) / 2
P-hat = 0.464
Therefore, the sample proportion (P-hat) is 0.464.
To find E (the margin of error), we need to use the formula:
E = (upper limit - lower limit) / 2
E = (0.484 - 0.444) / 2
E = 0.02
Therefore, the margin of error (E) is 0.02.
Note that the margin of error indicates the maximum likely difference between the true population proportion and the sample proportion, given the confidence level and sample size.
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A drawing of William’s backyard is given.
If William plans to mow the yard, how much area will he have to mow?
Responses
48
yd2
48 yd, 2
96
yd2
96 yd, 2
112
yd2
112 yd, 2
144
yd2
Answer:48 yd2
Step-by-step explanation:
The area of the yard that William would have to mow would be C. 112 yards ²
How to find the area ?To find the area to be mowed, find the area of the entire yard including the porch, and then the area of the porch, and then subtract the area of the porch.
Area of yard :
= 12 x 12
= 144 yard ²
The area of the porch is:
= ( 12 - 8 ) x ( 12 - 4 )
= 4 x 8
= 32 yards ²
The area to be mowed is:
= 144 - 32
= 112 yards ²
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Darrien and his family are at a football game. Darrien’s dad gives him $22 to buy snacks. He finds that drinks cost $1.50 and a bowl of nachos cost $2.75. Write and graph an inequality that shows the amount of sodas and nachos that Darien can afford to buy.
Pete, the skateboarding penguin, practices on a ramp in the shape of a right triangular prism
as shown below.
I need help ASAP!!! please
Of course! I'm here to help. Please provide me with the details or information you need assistance with regarding Pete, the skateboarding penguin and the right triangular prism ramp. I'll do my best to provide you with prompt and accurate help.
Jaxon bought two boxes of eggs at a market and recorded the mass of each egg
in the stem-and-leaf diagram below.
a) Which of the boxes has the smaller range of masses?
b) What is the value of this range? Give your answer in grams (g).
Box A
9865 4 39
2 5
84 6
65321 7
Box A
Box B
Box B
4679
157
258
Key
25 represents a mass of 52 g
5/4 represents a mass of 54 g
The range of Box A is 31 grams which is smaller.
Given that, Jaxon bought two boxes of eggs at a market and recorded the mass of each egg in the stem-and-leaf diagram,
So, the ranges are ;
Box A = 76 - 45 = 31 grams
Box B = 78 - 43 = 35 grams
Therefore, we see that the range of the box A is smaller than the range of the box B.
Hence, the range of Box A is 31 grams which is smaller.
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Pleas help me I will give 50
Answer:
Stem | Leaf
1| 9
2| 5 9
3| 0 3 3 8
4| 0 7 9
5| 4 5
6| 1 5
7| 2 7
8| 1
Step-by-step explanation:
Minimum: 19
Maximum: 81
Range: 62
Count: 17
Sum: 808
Mean: 47.53
Median: 47
Mode: 33
Standard Deviation: 18.9
Variance: 357.3
3. Convert the given Infix expression "A+B* C + D" to Postfix expression using Stack. (2 marks)
The postfix expression for the given infix expression is "A B C * + D +".
To convert the infix expression "A+B*C+D" to postfix expression using a stack, we can follow these steps:
Create an empty stack and an empty output queue.
Process each symbol in the infix expression from left to right.
If the symbol is an operand (e.g. A, B, C, D), add it to the output queue.
If the symbol is an operator (e.g. +, *), then do the following:
a. While the stack is not empty and the top of the stack has greater precedence than or equal precedence to the current operator, pop the top of the stack and add it to the output queue.
b. Push the current operator onto the stack.
After processing all the symbols in the infix expression, pop any remaining operators from the stack and add them to the output queue.
Using this algorithm, we can convert the infix expression "A+B*C+D" to postfix expression as follows:
Symbol: A + B * C + D
Action: Push A Push + Push B Push * Push C Pop * Pop + Push D
Output: A B C * + D +
Therefore, the postfix expression for the given infix expression is "A B C * + D +".
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Help fast pls Geometry
Answer:
64.141 cm ^2
Step-by-step explanation:
Formula for solving this is Pi(7^2) (170/360)
170 being the angle in degrees.
an incomplete table of values for an exponential function is shown. the exponential function is of the form y=a*b^x, where a is a real number such as a does not equal 0 and b is a positive number not equal to 1. complete the table with possible values for the exponential function
The table showing the exponential function is completed and presented below
x y
0 96
1 192
2 384
3 768
How to complete the tableThe expression for the table is given as
y = a * b^x,
Point (0, 96) is on the table.
a = 96,
when b = 2, we have that
for x = 1
y = 96 x 2^x = 96 x 2^1 = 192
for x = 2
y = 96 x 2^x = 96 x 2^2 = 384
for x = 3
y = 96 x 2^x = 96 x 2^3 = 768
Therefore, The required exponential function will be
x y
0 96
1 192
2 384
3 768
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a construction worker is using the coordinate grid to show the length of the wall inside a house one end of the wall will be at 5,6 the wall will be 4 units long which point could be the location of the other end of the wall.
The point that could be the location of the other end of the wall will be (0, 5).
How to explain the pointBy using one or more elements or coordinates, a reference frame can properly pinpoint location alongside other mathematical components on such space, including Euclidean space.
A point or object in a two-dimensional plane can be found by utilizing its coordinates, which appear to be sets of integers. The y and x vectors can be used to identify the position of a point on a double surface. a group of photos used to identify certain areas.
In conclusion, the point that could be the location of the other end of the wall will be (0, 5).
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The following frequency table shows the observed high temperatures in Buffalo, New York, in May 2007. Which interval contains the median temperature? 50 - 59 60 - 69 70 - 79 80 - 89
The interval that contains the median temperature is 70-79 in the frequency table showing the observed high temperatures in Buffalo.
First, we need to calculate the total number of observations, which is 5+12+9+5=31.
The median is the middle value of the data set when arranged in ascending or descending order. Since there are 31 observations, the median will be the 16th value.
To determine which interval contains the median temperature, we need to calculate the cumulative frequency of each interval. The cumulative frequency for the first interval is 5, for the second interval it is 5+12=17, for the third interval it is 17+9=26, and for the fourth interval it is 26+5=31.
Since the median is the 16th value, it lies within the third interval, which is 70-79.
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The question is -
The following frequency table shows the observed high temperatures in Buffalo, New York, in May 2007. Which interval contains the median temperature?
temperature frequency
50-59 5
60-69 12
70-79 9
80-89 5