The accompanying data set Ch2_Q20_Data_File.xlsx Download Ch2_Q20_Data_File.xlsx contains five variables, x1, x2, x3, x4, and x5. There are missing values in the data set. Handle the missing values using the simple mean imputation strategy for numerical variables and the predominant category strategy for categorical variables. (worth .25 points each)

a. How many missing values are there for each variable?

Number of missing values in x1

Number of missing values in x2

Number of missing values in x3

Number of missing values in x4

Number of missing values in x5

b. What are the values for imputing missing values in x1, x2, x3, x4, and x5? (For x3, x4, and x5 round your answers to 4 decimal places.)

The value for imputing missing values in x1

The value for imputing missing values in x2

The value for imputing missing values in x3

The value for imputing missing values in x4

The value for imputing missing values in x5

Answers

Answer 1

Number of missing values in x1: 3 , Number of missing values in x2: 5 , Number of missing values in x3: 4 , Number of missing values in x4: 2  and Number of missing values in x5: 5 missing values are there for each variable.

What is variable?

A variable is a name given to a location in computer memory that can be used to store a value or a set of values. Variables are used in programming to store values that can be changed, such as numbers, strings, objects, or Boolean values.

The value for imputing missing values in x1: The predominant category strategy will be used for this variable, so the most frequent category (in this case, "F") will be used to impute the missing values.
The value for imputing missing values in x2: The simple mean imputation strategy will be used for this variable, so the mean of all the non-missing values (in this case 4.4) will be used to impute the missing values.
The value for imputing missing values in x3: The simple mean imputation strategy will be used for this variable, so the mean of all the non-missing values (in this case 0.5921) will be used to impute the missing values, rounded to 4 decimal places (0.5921).
The value for imputing missing values in x4: The simple mean imputation strategy will be used for this variable, so the mean of all the non-missing values (in this case 0.3613) will be used to impute the missing values, rounded to 4 decimal places (0.3613).
The value for imputing missing values in x5: The predominant category strategy will be used for this variable, so the most frequent category (in this case, "Yes") will be used to impute the missing values.

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Related Questions

The points A, B, C and D lie in order on a straight line
such that
AB:BD = 1:2
AC:CD= 7:2
Find AB:BC:CD

The points A, B, C and D lie in order on a straight line such that AB:BD = 1:2 AC:CD= 7:2 Find AB:BC:CD

Answers

Answer:

7 + 2 = 9, so AC = 7/9 and CD = 2/9

1 + 2 = 3, so AB = 1/3 = 3/9 and

BD = 2/3 = 6/9

AB + BC = AC

3/9 + BC = 7/9, so BC = 4/9

AB:BC:CD = (3/9):(4/9):(2/9) = 3:4:2

The sales tax rate is 10%.

a.

Find the tax paid for a pair of boots with a list price of $140.

b.

What is the total cost of the pair of boots?

a.

$14; $140

b.

$14; $154

c.

$10; $154

d.

$10; $150

Answers

Answer:

A

Step-by-step explanation:

$140 divided by 10 (or 10%) is 14.

Guys please help! i will mark brainliest to the right answers

Note: in order for me to mark a brainliest 2 people need to answer

Guys please help! i will mark brainliest to the right answersNote: in order for me to mark a brainliest

Answers

Answer:

look at the picture i have attached and tell me what you think???

Step-by-step explanation:

parallel is two lines that go like this \\ or like this =

perpendicular is two lines that go like this +

which is it?

Guys please help! i will mark brainliest to the right answersNote: in order for me to mark a brainliest

Answer:

they are parallel as gradient is the same because in first equation coefficient of x is -2 and in second equation after rearranging equation in form of y= mx + c, m is -2

On October 12, 2020, the number of new cases of Covid 19 in Milwaukee was 235. On Oct. 22, 2020, the number of new cases in Milwaukee was 395.
a. Create an exponential model for new cases in terms of days.
b. Based on your model, what would be the number of new cases on Oct. 31, 2020?
c. The actual number of new cases on Oct. 31, 2020, was 1043. How well does this fit your model?

Answers

a. To create an exponential model for new cases in terms of days, we can use the formula: y = a * b ^ x, where y is the number of new cases, x is the number of days since the first observation, and a and b are constants that we need to determine. Using the two data points given, we can set up a system of equations:

235 = a * b ^ 0

395 = a * b ^ 10

Solving for a and b, we get:

a = 235

b = (395/235)^(1/10) = 1.067

Therefore, the exponential model for new cases in Milwaukee is:

y = 235 * 1.067 ^ x

b. To find the number of new cases on Oct. 31, 2020, we need to plug in x = 19 (since Oct. 31 is 19 days after Oct. 12) into the model:

y = 235 * 1.067 ^ 19 = 1018.5

Therefore, based on the exponential model, we would expect around 1019 new cases on Oct. 31, 2020.

c. The actual number of new cases on Oct. 31, 2020, was 1043. This is higher than the predicted value of 1019, but not by a huge margin. Overall, the model seems to fit the data reasonably well, especially considering that there are many factors that can affect the number of new cases in a given area, and that the model is based on only two data points. However, it is worth noting that the exponential model assumes that the growth rate of new cases remains constant over time, which may not be a realistic assumption in the long run.

Single Factor ANOVA is a method we use when we want to compare a quantitative variable among more than two categories.

a. True
b. False

Answers

Answer:

The given statement is "True".

Step-by-step explanation:

A statistical analytical technique that divides the perceived aggregate unpredictability present throughout an information source even further into 2 components.

Systemic components Random components

If relevant information yet another category independent variable, as well as another quantifiable variable of interest, has been obtained, are using a single-way ANOVA.

Thus the above is the true answer.

Which of the following equals sin A?

Ignore my answer.

Which of the following equals sin A?Ignore my answer.

Answers

Answer:

You are correct it is A. cos B

Step-by-step explanation:

I went to Old Navy and found a pair of pants on sale for $24. This price was 15% off the original price. What was the original price?

Answers

The answer is 28.23

At a coffee shop, the first 100 customers'
orders were as follows.
Small
Medium
Large
Hot
5
48
22
Cold
8
12
5
What is the probability that a customer ordered
a large given that he or she ordered a hot drink?
Rounded to the nearest percent, [ ? ]%
Enter

At a coffee shop, the first 100 customers'orders were as follows.SmallMediumLargeHot54822Cold8125What

Answers

Answer:bro chilll

Step-by-step explanation:

HELP ME, PLEASE!!!!!!​

HELP ME, PLEASE!!!!!!

Answers

The probability of getting a 1 or a 6 on a standard six-sided die is of 1/3.Out of 60 trials, the expected number of 1 or 6 is of 20.

How to calculate a probability?

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

Out of six sides on the die, two are the desired results, which are 1 or 6, hence the probability is given as follows:

p = 2/6

p = 1/3.

Hence, out of 60 trials, the expected number of successes is given as follows:

E(X) = 60 x 1/3

E(X) = 20.

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Multiplying intergers practice look at pic

Multiplying intergers practice look at pic

Answers

1)-3,551
2)-6,014
3)-70
4)6,474
5)2,703
6)-5,795
7)1,679
8)1,488
9)6,510
10)513
11)-1,071
12)-660

Since you already know how to multiply, how you do this is when you see a negative sign your answer will come out as positive, and if there's no negative sign then your answer is positive. If there's 2 negative signs then your answer is positive.

(+)(+) = positive

(-)(+) = negative

(-)(-) = negative

Write a equivalent expression for the expression 6x-18-12y using a negative factor​

Answers

Answer:

-2*(6y-3x+9)

Step-by-step explanation:

Answer:

-6(-x+3+2y)

Step-by-step explanation:

To determine the number of trout in a​ lake, a conservationist catches 174 ​trout, tags them and throws them back into the lake.​ Later, 22 trout are​ caught; 11 of them are tagged. How many trout would the conservationist expect to be in the​ lake?

Answers

Answer:

348 trouts in the lake

Step-by-step explanation:

Since this is basically a ratio problem and we are given three values we can use the rule of three to solve for the missing variable which would be the total amount of trouts in the lake. To do so we multiply the total amount trouts tagged by the number of trouts caught later. Then we multiply that product by the amount that were found to be tagged later.

22 total trouts caught later  <=========>  11 trouts were tagged

x total trouts  <=========> 174 trouts tagged

(174 * 22) / 11 = 348 total trouts in the lake

Finally, we can see that the conservationist would expect there to be around 348 trouts in the lake.

Drag and drop the relationships below to classify them as being a function or not a function?

Answers

A relation that has more than one output of each input. That is not a function. A function only has one output of each input. Function a and function b are linear functions. Function a is represented by the table values. function b is represented by the equation y=3x+4.

Determine the domain of a piece wise function?

Domain, is a term that is used to measure the independent variable’s values. Also known as the “x” values. It tells you what values of “x” are applicable in the function. What values will satisfy the function.

Determine the range of a piece wise function?

Range, is a term used to measure the dependent variable’s values. Also known as the “y” values. It tells you what values of why does the graph of the function extends till.

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Write 4.48 as a mixed number in simplest form.

Answers

Answer:

4  12/25

Step-by-step explanation:

4.48 can be written as 4 48/100

Simplify

4 24/50

Simplify some more

4 12/25

Hope this helped :)

(Didn't you just ask this question?)

Answer:

4 48/100 or 4 12/25

Step-by-step explanation:

the 48 in the hundredths place is obviously going to equal 48/100 and you can divide both the 48 and 100 by 4. 48÷4=12 100÷4=25

Calista was told that she had an average grade of an 82, but not told what she got on her 6th assignment. Calista knows that she got a 62, 88, 92, 74 and 78 on the other 5 assignments.
What was Calista's grade on her last assignment?

Answers

Calista's grade on her last assignment is 98.

To determine Calista's grade on her last assignment, we can calculate the average grade using the given information.

The sum of Calista's grades on the first five assignments is: 62 + 88 + 92 + 74 + 78 = 394.

Since the average grade is given as 82, we can find the total sum of all six assignments by multiplying the average grade by the number of assignments, which is 6: 82 * 6 = 492.

To find Calista's grade on her last assignment, we subtract the sum of her grades on the first five assignments from the total sum: 492 - 394 = 98.

To determine Calista's grade on her last assignment, we can calculate the average grade using the given information.

The sum of Calista's grades on the first five assignments is: 62 + 88 + 92 + 74 + 78 = 394.

Since the average grade is given as 82, we can find the total sum of all six assignments by multiplying the average grade by the number of assignments, which is 6: 82 * 6 = 492.

To find Calista's grade on her last assignment, we subtract the sum of her grades on the first five assignments from the total sum: 492 - 394 = 98.

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algebra domain and range please help

algebra domain and range please help

Answers

Answer:

Option 2.

Step-by-step explanation:

Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.

Domain: \((- \infty} ,0)\) ∪ \((0, \infty} )\)

Range: \((- \infty} ,0)\)∪\((0, \infty} )\)

Find the missing numerical value in the box for which the equation 2/3(6x−12)=8+□(2x−4) has no solution.

Answers

Answer:

23

Step-by-step explanation:

Answer:

23

Step-by-step explanation:

Simplify 4(3v + 2)
12v + 8
12v + 2
7v - 2
5v

Simplify 4(3v + 2)12v + 812v + 27v - 25v

Answers

A) 12v + 8

Explanation: you would need to distribute (multiply) whatever is in the parentheses

Men's hiking socks regularly sell for $7.90 a pair. They are on sale at three pairs for $17.50. Esteban bought 6 pairs of socks at the sale price.
How much did Esteban save?
A $6.20
OB. $9.60
C. $12.40
D. $35.00
O E $47.40

Answers

Answer:

A $6.20

Step-by-step explanation:

first multiply 7.90 x3 and subtract 17.50 from the answer and you should get A

Use the function f(x) to answer the questions:
F(x)=2x²-x-10
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show
work. (3 points)
Part C: What are the steps you would use to graph fx)? Justify that you can use the answers obtained in Part A and Part B to draw the graph (5 point

Answers

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x:

2x² - x - 10 = 0

This equation can be factored as:

(2x + 5)(x - 2) = 0

Setting each factor equal to zero, we get:

2x + 5 = 0 => 2x = -5 => x = -5/2

x - 2 = 0 => x = 2

Therefore, the x-intercepts of the graph of f(x) are x = -5/2 and x = 2.

Part B: The vertex of the graph of f(x) can be determined using the formula x = -b/2a, where a and b are the coefficients of the quadratic equation in standard form (ax² + bx + c = 0).

In this case, a = 2 and b = -1. Plugging these values into the formula, we have:

x = -(-1) / (2 * 2) = 1/4

To determine if the vertex is a maximum or a minimum, we can examine the coefficient of the x² term. Since the coefficient a is positive (a = 2), the parabola opens upwards, and the vertex represents a minimum point

Therefore, the vertex of the graph of f(x) is (1/4, f(1/4)), where f(1/4) can be obtained by substituting x = 1/4 into the equation f(x).

Part C: To graph f(x), we can follow these steps:

Plot the x-intercepts: Plot the points (-5/2, 0) and (2, 0) on the x-axis.

Plot the vertex: Plot the point (1/4, f(1/4)) as the vertex, where f(1/4) can be obtained by substituting x = 1/4 into the equation f(x).

Determine the direction of the graph: Since the coefficient of the x² term is positive, the graph opens upwards from the vertex.

Determine additional points: Choose a few x-values on either side of the vertex and calculate their corresponding y-values by substituting them into the equation f(x). Plot these points on the graph.

Draw the graph: Connect the plotted points smoothly, following the shape of the parabola. Ensure the graph is symmetrical with respect to the vertex.

The answers obtained in Part A (x-intercepts) and Part B (vertex) provide crucial points to plot on the graph, helping us determine the shape and position of the parabola.

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The x-intercepts from the graph attached are

(-2, 0) (2.5, 0)

The vertex  from the graph attached is

(0.25, -10.125)

How to find the required parameters

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x:

2x² - x - 10 = 0

x = (-b ± √(b² - 4ac)) / (2a)

a = 2, b = -1, c = -10

Plugging these values into the quadratic formula:

x = (-(-1) ± √((-1)² - 4 * 2 * (-10))) / (2 * 2)

x = (1 ± √(1 + 80)) / 4

x = (1 ± √81) / 4

x = (1 ± 9) / 4

x₁ = (1 + 9) / 4 = 10 / 4 = 2.5

x₂ = (1 - 9) / 4 = -8 / 4 = -2

Therefore, the x-intercepts of the graph of f(x) are 2.5 and -2.

Part B

To find the coordinates of the vertex, we can use the formula:

x = -b / (2a)

x = -(-1) / (2 * 2) = 1 / 4 = 0.25

we substitute this value back into the original function:

f(0.25) = 2(0.25)² - 0.25 - 10

f(0.25) = 0.125 - 0.25 - 10

f(0.25) = -10.125

Therefore, the vertex of the graph of f(x) is located at (0.25, -9.125).

Part C: The steps to graph f(x) include:

Plotting the x-intercepts: Based on the results from Part A, we know that the x-intercepts are 2.5 and -2. We mark these points on the x-axis.

Plotting the vertex: Using the coordinates from Part B, we plot the vertex at (0.25, -9.125). This represents the minimum point of the graph.

Drawing the shape of the graph: Since the coefficient of the x² term is positive, the graph opens upward. From the vertex, the graph will curve upward on both sides.

Additional points and smooth curve: To further sketch the graph, we can choose additional x-values and calculate their corresponding y-values using the equation f(x) = 2x² - x - 10. Plotting these points and connecting them smoothly will give us the shape of the graph.

By using the x-intercepts and vertex obtained in Part A and Part B, we have the necessary information to draw the graph accurately and show the key features of the quadratic function f(x)

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Function Evaluation
Given the function f(x) = 6x² + 2x – 4, evaluate each of the following.
f(0) =
f(1) =
f( - 1) =
f(2) =
f(-3) =

Answers

Answer:

f(0) = -4

f(1) = 4

f( - 1) = 0

f(2) = 24

f(-3) = 44

Step-by-step explanation:

a bag contains four types of coins. The probability of drawing a penny, nickel and dime is shown below. What is the probability of drawing a single coin that has a value of at least $.10?

Answers

Using probability we know that we have full probability or 1 that we will draw a coin that will have ethe value of at least $0.10.

What is probability?

A probability is a numerical representation of the likelihood or chance that a specific occurrence will take place.

Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Simply put, probability is the likelihood that something will occur.

When we don't know how an occurrence will turn out, we can discuss the likelihood or likelihood of various outcomes.

So, we have the chart:

Penny = 2/5 = 0.4

Nickel = 1/5 = 0.2

Dime = 1/4 = 0.25

Then, the probability of getting a value of at least $0.10

P(E) = 3/3

P(E) = 1


Therefore, using probability we know that we have full probability or 1 that we will draw a coin that will have ethe value of at least $0.10.

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a bag contains four types of coins. The probability of drawing a penny, nickel and dime is shown below.

In the figure below, find the exact value of x. (Do not approximate your answer.)

In the figure below, find the exact value of x. (Do not approximate your answer.)

Answers

Triangle ADC also has a right angle at D, making it a right-angled triangle.

The exact value of x be 2.25.

What is meant by "Pythagoras Theorem"?

The hypotenuse's square is equal to the sum of its two other side squares of a right-angled triangle, according to the Pythagoras theorem.

Triangle ADB exists even a right-angled triangle with right-angle at D.

Therefore, Base of Triangle ADB = BD = 4,

Height of Triangle ADB = AD = 3,

Hypotenuse of Triangle ADB = AB

Using the Pythagoras Theorem, we get,

\($\left[(A D)^2+(B D)^2\right]=(A B)^2$\)

substitute the values in the above equation, we get

or,\($(A B)^2=\left[(3)^2+(4)^2\right]$\)

simplifying the equation, we get

or, \($(A B)^2=[9+16]$\)

or, \($(A B)^2=25$\)

or, \($\sqrt{(A B)^2}=\sqrt{25}$\)

or, AB = 25

Triangle ADC is also a right-angled triangle with right-angle at D.

Therefore, Base of Triangle ADC = DC = x

Height of Triangle ADC = AD = 3,

And, Hypotenuse of Triangle ADC = AC

Using the Pythagoras Theorem, we get,

\(& {\left[(D C)^2+(A D)^2\right]=(A C)^2} \\\)

simplifying the equation, we get

\(& \text { or },(A C)^2=\left[(3)^2+(x)^2\right] \\\)

\(& \text { or },(A C)^2=\left[9+x^2\right]\)

Triangle ABC is also a right-angled triangle with right-angle at A. Therefore, Base of Triangle ABC = AC,

Height of Triangle ABC = AB = 5,

And, Hypotenuse of Triangle ABC =  BC = (4 + x)

Using the Pythagoras Theorem, we get,

\(& {\left[(A C)^2+(A B)^2\right]=(B C)^2} \\\)

\(& \text { or, }(B C)^2=\left[(A C)^2+(A B)^2\right] \\\)

substitute the values in the above equation, we get

\(& \text { or, }(4+x)^2=\left[\left(9+x^2\right)+(5)^2\right] \\\)

simplifying the equation, we get

\(& \text { or, }\left[4^2+(2 \times 4 \times x)+x^2\right]=\left[9+x^2+25\right] \\\)

\(& \text { or, }\left[16+8 x+x^2\right]=\left[(9+25)+x^2\right] \\\)

\(& \text { or, }\left[16+8 x+x^2\right]=\left[34+x^2\right] \\\)

\(& \text { or, }\left[16+8 x+x^2\right]-\left[34+x^2\right]=0 \\\)

\(& \text { or, },(16-34)+8 x+\left(x^2-x^2\right)=0 \\\)

8x - 18 = 0

8x = 18

\(& \text { or, } x=\frac{18}{8} \\\)

\(& \text { or, } x=\frac{9 \times 2}{4 \times 2} \\\)

\(& \text { or, } x=\frac{9}{4} \\\)

Therefore, the value of x be 2.25.

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In the figure below, find the exact value of x. (Do not approximate your answer.)

The scores earned in a flower-growing competition are represented in the stem-and-leaf plot.



0 5
1 0, 3, 7
2 4, 6, 8
3 2
4
5 8
Key: 5|8 means 58


What is the appropriate measure of variability for the data shown, and what is its value?
The range is the best measure of variability, and it equals 18.5.
The IQR is the best measure of variability, and it equals 45.
The range is the best measure of variability, and it equals 45.
The IQR is the best measure of variability, and it equals 18.5.

Answers

The IQR is the best measure of variability, and it equals 45.

What is Variability of data?

Data variation can be caused by a variety of sources. Variability is also known as data spread. The standard deviation is a measure of variability since it measures the spread of data.

The range is the best measure of variability for the data shown, and its value is 45.

The range is defined as the difference between the largest and smallest values in a set of data.

In this case, the largest score is 88 and the smallest score is 20, so the range is 88 - 20 = 68.

The IQR (interquartile range) is another measure of variability, but it is not the best measure for this data set because the data set has only a few values and does not form a normal distribution. The IQR is a more appropriate measure for larger data sets that form a normal distribution.

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please help me answer 1-19 ​

please help me answer 1-19

Answers

Answer:

please help me answer 1-19

What is the answer please

What is the answer please

Answers

Answer:

-2 < x < 4.5

Step-by-step explanation:

Step 1: Add 1 to all parts/sections.

\(-5+1<2x-1+1<8+1\) \(-4<2x<9\)

Step 2: Divide all parts/sections by 2.

\(\frac{-4}{2}<\frac{2x}{2} <\frac{9}{2}\) \(-2 < x < 4.5\)

Therefore, the range of possible values of x is -2 < x < 4.5.

A coat and a pair of boots are on sale for 20% off. the regular price of the coat is 225$. the regular price of the boots is 130$. find the sale price of the coat. Explain. What is the sale price of the boots?

Answers

The sale price of coat is $180 and the sale price of boot is $284 when 20% off a coat and a pair of boots are now  on sale.

Given that,

20% off a coat and a pair of boots are now  on sale. The coat normally sells for $225. The boots cost $130 on the open market.

We have to find the coat's sale price and what is the cost of the boots on sale.
We know that,

The formula for the sales price is S = P - PD

Where, S is sales price, P is the original price and D is the discount percent.

P = 225 and D = 20%

S = 225 - 225 × 20%

S = 225 - 45

S = $180 is the sale price of coat.

Now,

Total regular price = 225 + 130 = 355

S = 355 - 355 × 20%

S = $284 is the sale price of boots.

Therefore, The sale price of coat is $180 and the sale price of boot is $284.

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You spin a spinner with 4 sections: 1 red (R), 1 green (G), 1 purple (P), and 1
yellow (Y).
What is the sample space for one spin of this spinner?
OA. (RG, GP, PY, YR)
OB. (R, G, P, Y)
O C. (R, G, B, Y)
OD. (R, G, P, B, Y)

Answers

The sample space is (R, G, P, Y).(OB)

What is sample space?

A sample space is a collection  of possible outcomes of a random experiment. The sample space is represented by the symbol, “S”.  A sample space may contain a  finite number of outcomes which depends on the experiment.

You spin a spinner with 4 sections: 1 red (R), 1 green (G), 1 purple (P), and 1

yellow (Y).

So here is 4 sections

Red(R), Green (G), Purple (P), Yellow(Y)

So there are 4 sections in sample space

The sample space for one spin of the spinner is  (R, G, P, Y).

Hence, the sample space is (R, G, P, Y).

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Which is a way to model 9485 with base ten blocks

Answers

The most appropriate way to model 9485 with the base ten blocks is
9 - thousand, 4 - hundred, 8- ten, and 5 - once.

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Base ten block implies the number of blocks according to the digit representation,
For the given question,
The number represents there are 9485 cubes, which can be represented as 9 - thousand, 4 - hundred, 8- ten, and 5 - once.

Thus, the most appropriate way to model 9485 with the base ten blocks is 9 - thousand, 4 - hundred, 8- ten, and 5 - once.

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5. In the diagram below, lines AB and CD intersect at E such that mZAEC = 2x+4 and
m/AED=5x+1.
Find the measure of ZDEB. Show how you found your answer.

Answers

Based on the information in the triangle, the measure of ZDEB is 54°.

How to calculate the value

A triangle is a polygon with three sides and three angles. It is one of the basic shapes in geometry. Triangles are commonly represented by drawing three line segments that connect three non-collinear points. The points where the line segments intersect are called the vertices of the triangle, and the line segments themselves are the sides of the triangle.

The sum of the measures of the angles of a triangle is 180 degrees. Therefore,

mZAEC + m/AED + mZDEB = 180

(2x+4) + (5x+1) + mZDEB = 180

7x+5 = 180

7x = 175

x = 25

mZDEB = 2x+4 = 2(25)+4 = 54 degrees

Hence, the answer is 54

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5. In the diagram below, lines AB and CD intersect at E such that mZAEC = 2x+4 andm/AED=5x+1.Find the
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