Step-by-step explanation:
The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.
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Step-by-step explanation:
Certainly! "Mean," "median," and "mode" are three different measures of central tendency used in statistics to describe a dataset. They help provide insight into the typical or central value within a set of data points.
1. **Mean:**
- **Definition:** The mean, also known as the average, is calculated by adding up all the values in a dataset and then dividing by the total number of values.
- **Calculation:** Mean = (Sum of all values) / (Number of values)
- **Explanation:** The mean gives you the "typical" or "average" value in a dataset. It's the sum of all the values divided by the number of values. For example, if you have test scores of 80, 85, 90, 92, and 95, the mean score would be (80 + 85 + 90 + 92 + 95) / 5 = 88.4.
2. **Median:**
- **Definition:** The median is the middle value in a dataset when the values are arranged in ascending or descending order. If there is an even number of values, the median is the average of the two middle values.
- **Explanation:** The median is the middle value that separates the dataset into two equal halves. It is not influenced by extreme values (outliers) as much as the mean. For example, in the dataset 4, 7, 9, 12, 15, the median is 9 because it's the middle value.
3. **Mode:**
- **Definition:** The mode is the value that appears most frequently in a dataset. A dataset can have one mode (unimodal), more than one mode (multimodal), or no mode if all values occur with the same frequency.
- **Explanation:** The mode represents the most common value or values in a dataset. For example, in the dataset 2, 3, 3, 4, 4, 4, 5, the mode is 4 because it appears more frequently than any other value.
In summary, the mean is the average value, the median is the middle value, and the mode is the most frequently occurring value in a dataset. Each of these measures provides different insights into the central tendency of data and can be useful for various statistical analyses and interpretations.
What is the answer for y?
The linear function that models the data is y=3/5x - 2/5 which has the form y=mx+b, where m is the slope and b is the y-intercept.
What is linear function?This can be written in the form y = mx + b where m and b are constants and x is a variable. The graph of a linear function is a straight line that goes through the origin.
To calculate the linear function, we must first calculate the slope. The slope is the numerical change in y (rise) divided by the numerical change in x (run).
Subtracting the y-values for x=-9 and x=-8, we get
-29/5 - (-26/5) = -3/5.
Similarly, subtracting the x-values for x=-9 and x=-8, we get
-9 - (-8) = -1.
Now, -3/5 / -1, we get the slope, m, of 3/5.
Next, we must calculate the y-intercept, b.
To do this, we can use either of the points given.
Using the points (x=-9, y=-29/5), we can substitute the x and y values into the linear equation, y=mx+b.
-29/5 = 3/5(-9) + b, which can be simplified to
-29/5 = -27/5 + b.
Adding 27/5 to both sides, we get b = -2/5.
Therefore, the linear function that models the data is y=3/5x - 2/5.
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Arrange the steps to find an inverse of a modulo m for each of the following pairs of relatively prime integers using the Euclidean algorithm in the order. a = 2, m=17 Rank the options below. The ged in terms of 2 and 17 is written as 1 = 17-8.2. By using the Euclidean algorithm, 17 = 8.2 +1. The coefficient of 2 is same as 9 modulo 17. 9 is an inverse of 2 modulo 17. The Bézout coefficients of 17 and 2 are 1 and 8, respectively. a = 34, m= 89 Rank the options below. The steps to find ged(34,89) = 1 using the Euclidean algorithm is as follows. 89 = 2.34 + 21 34 = 21 + 13 21 = 13 + 8 13 = 8 + 5 8 = 5 + 3 5 = 3 + 2 3 = 2+1 Let 34s + 890= 1, where sis the inverse of 34 modulo 89. $=-34, so an inverse of 34 modulo 89 is -34, which can also be written as 55. The ged in terms of 34 and 89 is written as 1 = 3 - 2 = 3-(5-3) = 2.3-5 = 2. (8-5)- 5 = 2.8-3.5 = 2.8-3. (13-8)= 5.8-3.13 = 5. (21-13)-3.13 = 5.21-8. 13 = 5.21-8. (34-21) = 1321-8.34 = 13. (89-2.34) - 8.34 = 13.89-34. 34 a = 200, m= 1001 Rank the options below. By using the Euclidean algorithm, 1001 = 5.200 +1. Let 200s + 1001t= 1, where sis an inverse of 200 modulo 1001. The ged in terms of 1001 and 200 is written as 1 = 1001 - 5.200. s=-5, so an inverse of 200 modulo 1001 is -5.
We have that, using Euclid's algorithm, we find the inverse of 200 modules 1001 is -5 (or 1001+5).
How do we find the inverse of a modulus?To find the inverse of a module m using Euclid's algorithm, the steps are as follows:
1. Calculate the greatest common divisor (GCD) of a and m using the Euclidean algorithm.
2. Let a = GCD * s + m*t, where s is the inverse of a module m.
3. The GCD in terms of a and my is written as 1 = m-s*a.
4. Find s = -a, so the inverse of a module m is -a (or m+s).
For example, a = 2, m=17, so GCD = 1 = 17-8*2 and the inverse of 2 modulo 17 is -8 (or 17+8). Similarly, for a = 34, m= 89, the GCD = 1 = 89-34*2 and the inverse of 34 modulo 89 is -34 (or 89+34). Finally, for a = 200, m= 1001, the GCD = 1 = 1001-5*200 and the inverse of 200 modulo 1001 is -5 (or 1001+5).
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the car that Andrew used to UWC has a fuel consumption rate of 0,0052k /100km.The cost of petrol for the month of January is R11,90 /litre. calculate the cost of petrol for the trip to UWC.
The cost of petrol for the trip to UWC is R1.2384.
What is cost?In general, cost refers to the amount of resources (usually money) that must be expended to produce or acquire something. It can be thought of as the value of the resources that are given up in order to obtain something else.
According to the given information:To calculate the cost of petrol for the trip to UWC, we need to know the distance traveled and the amount of fuel consumed.
Let's assume that the distance from Andrew's home to UWC is 20 kilometers (km). Then, the amount of fuel consumed for the trip is:
[tex]Fuel consumed = (0.0052 k/100 km) * 20 km = 0.00104 k[/tex]
where k stands for liters of petrol.
To convert the amount of fuel consumed to liters, we need to multiply by 100, since the fuel consumption rate is given in liters per 100 km:
[tex]Fuel consumed = 0.00104 k * 100 = 0.104 liters\\Fuel consumed = 0.00104 k * 100 = 0.104 liters[/tex]
Now we can calculate the cost of petrol for the trip:
[tex]Cost of petrol = (0.104 liters) * (R11.90/liter) = R1.2384[/tex]
Therefore, the cost of petrol for the trip to UWC is R1.2384.
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The scatter plot shows the relationship between the test scores of a group of students and the number of hours they study in a week:
On a grid, Label Hours Studying on x axis and Test Scores on y axis. The title of the graph is Test Scores and Hours Studying. The scale on the x axis shows the numbers from 0 to 10 at increments of 1, and the scale on the y axis shows numbers from 0 to 100 at increments of 10. Dots are made at the ordered pairs 1.1, 10 and 2, 25 and 3.1, 10.1 and 4, 30 and 4, 45 and 5, 45 and 6, 25 and 6.5, 60 and 7, 45 and 7.5, 50 and 7.5, 75 and 8, 60 and 8.5, 75 and 9, 60. The ordered pair 1, 100 is circled and labeled as M. All the other points are put in an oval and labeled as N.
Part A: What is the group of points labeled N called? What is the point labeled M called? Give a possible reason for the presence of point M. (5 points)
Part B: Describe the association between students' test scores and the number of hours they study. (5 points)
Part A: The group of points labeled N is called a scatter plot. The point labeled M is an outlier.
Part B: The association between students' test scores and the number of hours they study is that as the number of hours students study increases, their test scores tend to increase as well.
What is scatter plot?A scatter plot is a type of graph that displays the relationship between two variables. It is often used to show how one variable is affected by another.
Part A: The presence of point M could be due to an error in recording data, or it could be due to an unusual event or circumstance that is not representative of the population.
Part B: This suggests that the more time students put into studying, the better their test scores will be. However, it is important to note that the graph does not necessarily imply that studying for more hours will necessarily lead to higher test scores, as the scatter plot also shows that there are other factors that could affect test scores.
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Part A: The group of points labeled N is called a scatter plot.
The point labeled M is called an outlier.
The presence of point M is likely due to the fact that the student studied for only one hour, yet achieved a perfect score
Part B: The association between students' test scores and the number of hours they study is that as the number of hours students study increases, their test scores tend to increase as well.
What is scatter plot?A scatter plot displays the relationship between two variables. It is often used to show how one variable is affected by another.
Part A: The group of points labeled N is called a scatter plot.
The point labeled M is called an outlier.
The presence of point M is likely due to the fact that the student studied for only one hour, yet achieved a perfect score.
Part B: The scatterplot shows a weak positive association between students' test scores and the number of hours they study.
As the number of hours studying increases, the test scores tend to increase, although there is considerable variability in this relationship. The outlier at 1, 100 indicates that there may be other factors other than study time that influence test scores.
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Two-ninths of h
algebraic expression translate
The algebraic expression "two-ninths of h" can be written as (2/9)h, where h is the variable being multiplied by the fraction 2/9.
"Two-ninths of h" is an algebraic expression that represents a quantity that is equal to two-ninths of the value of h. It can be written as 2h/9 or (2/9)h. In this expression, h represents an unknown value or variable, and 2/9 is a constant that specifies the fraction of h that is being considered. This expression can be used in mathematical equations to represent a specific portion or amount of h, depending on the context of the problem.
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This is the third part of a three-part problem. Consider the system of differential equations y_1' = 5y_1 + 3y_2, y_2' = 3y_1 + 5y_2, with solutions y_1(t) = c1 e^2t + c2 e^8t, y_2(t) = -c_1 e^2t + c_2 e^8t, for any constants c_1 and c_2. Rewrite the solution of the equations in vector form as y vector (t) = c_1 y_1 vector (t) + c_2 y_2 vector (t).
Solution is y(t) = ((c1e2t − c2e2t) (1 0) + (c1e8t + c2e8t) (0 1))
The differential equations of the given system are: y1′=5y1+3y2y2′=3y1+5y2 The solutions to these equations are:y1(t)=c1e2t+c2e8t y2(t)=−c1e2t+c2e8tNow,
let's rewrite the solution in the vector form y(t) = c1y1 vector(t) + c2y2 vector(t).The vector form of y1(t) and y2(t) is as follows: y1 vector(t) = (1 0) (c1e2t) + (0 1) (c2e8t)y2 vector(t) = (-1 0) (c1e2t) + (0 1) (c2e8t)
Therefore, the solution in the vector form y(t) = c1y1 vector(t) + c2y2 vector(t) is as follows: y(t) = c1((1 0) (c1e2t) + (0 1) (c2e8t)) + c2((-1 0) (c1e2t) + (0 1) (c2e8t))y(t) = (c1e2t − c2e2t) (1 0) + (c1e8t + c2e8t) (0 1)y(t) = ((c1e2t − c2e2t) (1 0) + (c1e8t + c2e8t) (0 1))
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I need to show my work please help
Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 15 people took the trip. She was able to purchase coach tickets for $220 and first class tickets for $910. She used her total budget for airfare for the trip, which was $8130. How many first class tickets did she buy? How many coach tickets did she buy?
Rose has less than $30 to spend on decorations for the school dance. She has already spent $5. Which number line shows how much money she could still spend on decorations
The correct answer is number line A. Number Line A shows that Rose has $25 remaining to spend on decorations. The number line shows that she has already spent $5, as indicated by the arrow pointing from 0 to 5.
What is Number Line?Number line is the visual representation of numbers on a straight line. These are often used to represent linear equations, as well as to learn basic mathematical concepts such as addition, subtraction, multiplication, and division.
The number line shows that she has a total of $30 available for decorations, as indicated by the arrow pointing from 0 to 30. Between the two arrows, it is clear that Rose has $25 remaining to spend on decorations.
Number Line B does not accurately represent Rose’s situation because the arrow pointing from 0 to 20 does not indicate that Rose has already spent $5. Number Line C does not accurately represent Rose’s situation because the arrow pointing from 0 to 25 does not indicate that Rose has a total of $30 available to spend.
To solve this problem, Rose needs to identify the total amount of money she has available to spend on decorations and the amount of money she has already spent. Once she has identified these two values, she can use a number line to represent her situation.
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mixed in a drawer are blue socks, white socks, and gray socks. you pull out two socks, one at a time, without looking. find the probability of getting 2 socks of the same color.
The probability of getting 2 socks of the same color given by the following solution is 65/132.
Beginning with the first sock, we have three options: blue, white, or grey. If we wanted to know the likelihood of drawing only one blue sock, we might divide the number of blue socks in the drawer by the total number of socks (2 / 12).
We have three options for the second sock: blue, white, or grey. Keep in mind that we are drawing without replacement, so there is now one fewer sock in the drawer. Thus, with three alternatives for the first sock and three options for the second sock, the total number of combinations is three times three, or nine. The following are all of the potential combinations: (blue, blue), (blue, white), (blue, grey), (white, blue), (white, white), (white, grey), (white, blue), (white, white), (white, grey), (grey, blue), (grey, white) (gray, gray).
So the probability of 2 socks of the same color is, in equation form:
P(2 socks of same color) = P(blue sock first) * P(blue sock second) + P(white sock first) * P(white sock second) + P(gray sock first) * P(gray sock second).
= 2/12*1/11 + 4/12*3/11 + 6/12*5/11
= 65/132
Therefore, the probability of getting 2 socks of the same color 65/132.
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Complete question:
Mixed in a drawer are 2 blue socks, 4 white socks, and 6 gray socks. You pull out two socks, one at a time, without looking. Find the probability of getting 2 socks of the same color.
Find the outer perimeter.
6 ft
4 ft
15 ft
10 ft
P = [?] ft
Round to the nearest
hundredth.
Answer:
P= 40 ft
Step-by-step explanation:
Perimeter is the sum of all the lengths
So,
Perimeter= 6+4+15+10ft
= 35ft
Nearest ten can be 40ft or 30ft
If you succeed In understanding then kindly mark my answer the brainliest. Thank you :)
Shanika bought 1 Notebook and 5 pencils at a cost of $10.00. Jules paid $14.90 for 1 Notebook and 12 pencils. How much did Jules pay for 1 pencil if both pay the similar prices?
ANSWER
Jules paid $0.70 for one pencil
STEPS
Cost of One Pencil.
Let's assume the cost of one notebook be x and one pencil be y.
According to the given information,
Shanika bought 1 notebook and 5 pencils at a cost of $10.00. Therefore,
1x + 5y = 10 --- equation 1
Jules paid $14.90 for 1 Notebook and 12 pencils. Therefore,
1x + 12y = 14.9 --- equation 2
We need to find the cost of one pencil, i.e., y.
We can solve the above equations simultaneously to find the value of y.
Multiplying equation 1 by 12 and equation 2 by 5, we get:
12x + 60y = 120 --- equation 3
5x + 60y = 74.5 --- equation 4
Subtracting equation 4 from equation 3, we get:
7x = 45.5
x = 6.5
Substituting the value of x in equation 1, we get:
1(6.5) + 5y = 10
5y = 3.5
y = 0.7
Therefore, Jules paid $0.70 for one pencil.
ChatGPT
Answer:
Jules pay:
$0.7
Step-by-step explanation:
1n + 5p = 10 Eq. 1
1n + 12p = 14.9 Eq. 2
n = cost of one notebook
p = cost of one pencil
From Eq. 1
n = 10 - 5p Eq. 3
From Eq. 2
n = 14.9 - 12p Eq. 4
Equalizing Eq. 3 and Eq. 4:
10 - 5p = 14.9 - 12p
12p - 5p = 14.9 - 10
7p = 4.9
p = 4.9 / 7
p = 0.7
From Eq. 3:
n = 10 - 5p
n = 10 - 5*0.7
n = 10 - 3.5
n = 6.5
Check:
From Eq. 2:
n + 12p = 14.9
6.5 + 12*0.7 = 14.9
6.5 + 8.4 = 14.9
Then:
1 pencil = $0.7
Find the dimensions of the rectangular box with largest volume if the total surface area is given as 4 cm2. (Let x, y, and z be the dimensions of the rectangular box.)
(x, y, z) =
Answer:
x = y = z = (√6)/3 cm ≈ 0.8165 cm
Step-by-step explanation:
You want the dimensions of the cuboid with the largest volume and a total surface area of 4 cm².
Largest volumeFor a fixed surface area, the figure with the largest volume is a regular figure. In this case, it is a regular cuboid, or cube.
AreaThe total surface area of a cube with edge length s is ...
A = 6s²
Then the edge length of the desired cube is found from ...
4 = 6s²
s² = 2/3 = 6/9 . . . . . . divide by 6; write with square denominator
s = √(6/9) = (√6)/3
The dimensions of the box are ...
x = y = z = (√6)/3 cm ≈ 0.8165 cm
A train travelling at 40km/h takes 3 hours for a journey. How long will it take the train to complete the same journey, travelling at 90km/h?
Answer: 1 hour and 20 minutes
Step-by-step explanation:
We can use the formula:
time = distance / speed
Let's call the distance of the journey "d".
When the train is travelling at 40 km/h, it takes 3 hours to complete the journey. So we have:
3 = d / 40
Solving for "d", we get:
d = 3 x 40 = 120 km
Now we want to know how long it will take for the train to complete the same journey at 90 km/h. We can use the formula again:
time = distance / speed
Plugging in the values we know:
time = 120 / 90
Simplifying, we get:
time = 4/3 hours or 1 hour and 20 minutes
Therefore, the train will take 1 hour and 20 minutes to complete the journey at 90 km/h.
Required answer :-
1 hour 20 minutesStep-by-step explanation:
A train travelling at 40km/h takes 3 hours for a journey. So, Speed will be 40 km/hr
Time will be 3 hours.
Speed = Distance/time
Distance = Speed × time
Distance = 40 × 3
Distance = 120 km.
Now, we have to find that how long will it take the train to complete the same journey, travelling at 90km/h.
Now, Speed will be 90 km/hr
Distance = Speed × time
Time = Distance/speed
Time = 120/90
Time = 4/3 hours
1 hour = 60 minutes
4/3 × 60
4 × 20
80 minutes
1 hour 20 minutes.
Therefore, The train will take 1 hour 20 minutes to complete the journey, travelling at 90km/h.
in pascal's triangle, each entry is the sum of the two entries above it. in which row of pascal's triangle do three consecutive entries occur that are in the ratio 3:4:5?
The three consecutive entries in Pascal's Triangle that are in the ratio 3:4:5 occur in the 14th row.
The ratio 3:4:5 can be expressed as 3x, 4x, and 5x, where x is a constant. Using this ratio, we can find the values of the entries in the 14th row of Pascal's Triangle.
Starting from the left, the entries in the 14th row are 1, 13, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13, and 1.
We can see that the ratio of the 5th, 6th, and 7th entries (715, 1287, and 1716) is 3:4:5. Therefore, the answer is the 14th row.
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If < C and < D are supplementary and < C = 5 0 °, find the measure of
< D = °
....
Answer:
<D = 130°
Step-by-step explanation:
Supplementary = 180°
<C = 50°
<D = ?
<C + <D = 180°
180° - 50° = 130°
<D = 130°
in an experiment, it takes you one hour to memorize all the terms on a list. two years later you relearn them in 45 minutes. the time difference of 15 minutes, or 25 percent (15 divided by 60 times 100), is called the
The time difference of 15 minutes, or 25 percent (15 divided by 60 times 100), is called the time saved.
What is an experiment?An experiment is a controlled study in which a scientist manipulates a variable in order to determine its effects. An experiment must have a testable hypothesis, be replicable, and produce empirical evidence.
Discussing the time difference in an experiment. In an experiment, it takes one hour to memorize all of the words on a list, and two years later, they are relearned in 45 minutes.
The time difference of 15 minutes, or 25 percent (15 divided by 60 times 100), is referred to as the time saved.
Time saved is the difference between the total time it takes to finish a process with a particular method and the total time it would take to complete the same process without that method.
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Solve the inequality.
Answer:
-4 >= x or x <= -4
Step-by-step explanation:
19 <= 7 - 3x
12 <= -3x
divide by negative flip the sign
-4 >=
Answer:
x ≤ -4
Step-by-step explanation:
Now we have to,
→ Find the required value of x.
The inequation is,
→ 19 ≤ 7 - 3x
Then the value of x will be,
→ 19 ≤ 7 - 3x
→ 7 - 3x ≥ 19
→ -3x ≥ 19 - 7
→ -3x ≥ 12
→ x ≤ 12/(-3)
→ x ≤ -12/3
→ [ x ≤ -4 ]
Hence, the answer is x ≤ -4.
Solve the equation 3/4x - 5 = x give your answers correct to 2 decimal places
The solution to the equation 3/4x - 5 = x, is equals to -20.00 (correct to 2 decimal places).
To solve the equation 3/4x - 5 = x for x, we can start by isolating the variable term on one side of the equation and the constant term on the other side. We can do this by adding 5 to both sides of the equation:
3/4x - 5 + 5 = x + 5
3/4x = x + 5
Next, we can isolate x on one side of the equation by subtracting x from both sides:
3/4x - x = x + 5 - x
-1/4x = 5
Finally, we can solve for x by dividing both sides of the equation by -1/4:
x = -20
Therefore, by using isolating the variable term and solving for x. we find the solution of 3/4x - 5 = x, correct to 2 decimal places, is x = -20.00.
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A restaurant bill of $3200 is paid with $500 and $1000 bills. If 16 bills were used, determine how many $1000 and $500 bills were used.
Let's use variables to represent the number of $1000 and $500 bills used.
Let x be the number of $1000 bills used.
Then 16 - x is the number of $500 bills used.
The total amount paid is the sum of the values of the bills used:
$1000(x) + $500(16 - x) = $3200
Simplifying and solving for x:
$1000x + $8000 - $500x = $3200
$500x = $4800
x = 9.6
We can't have a fraction of a bill, so we'll round down to 9 $1000 bills.
Then the number of $500 bills used is:
16 - x = 16 - 9 = 7
Therefore, 9 $1000 bills and 7 $500 bills were used to pay the $3200 restaurant bill.
Factor
[tex]25x^6 + 10x^3 + 12[/tex]
Answer:
Step-by-step explanation:
To factor 25x^6 + 10x^3 + 12, we can first factor out the greatest common factor of the three terms which is 1, then use a substitution:
Let's substitute y = x^3. Then, the expression becomes:
25y^2 + 10y + 12
We can now try to factor this quadratic expression. However, since the discriminant (b^2 - 4ac) of this quadratic equation is negative (10^2 - 4*25*12 = -440), this expression cannot be factored using real numbers.
Therefore, the final answer for the factoring is:
25x^6 + 10x^3 + 12 = (unfactorable)
4. Adults were randomly selected for a poll and asked if they favored or opposed federal tax dollars being used for foreign aid. Of the 882 polled, 415 were opposed. A politician claims that more than 50% c
are opposed to federal tax dollars being used for foreign aid. Use a 0.01 significance level to test the claim. State the final conclusion.
There is sufficient evidence to support the claim that more than 50% of adults are opposed to federal tax dollars being used for foreign aid.
There is not sufficient evidence to support the claim that less than 50% of adults are opposed to federal tax dollars being used for foreign aid.
There is not sufficient evidence to support the claim.
There is not sufficient evidence to support the claim that more than 50% of adults are opposed to federal tax dollars being used for foreign aid.
The conclusion (a) is correct i.e., There is sufficient evidence to support the claim that more than 50% of adults are opposed to federal tax dollars being used for foreign aid.
What is Federal tax?In USA, an obligation to pay a tax to the federal government rather than a state government
Sample Size (n) = 882
Number of Success ( X) = 415
The Hypothesis is given by :
[tex]H_{0}[/tex] : p = 0.50
H₁ : p > 0.50
The point estimate of the proportion is calculated by :
p^ = X/n
= 415/882
= 0.47
Therefore, a point estimate is 0.47 .
The test statics is calculated by :
[tex]Z = \frac{\vec{}p - p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]
= [tex]\frac{0.47 - 0.50 }{\sqrt{\frac{0.50(1-0.50)}{882} } }[/tex]
= - 1.781.
Therefore, the test statistics is -1.781.
The p-value is obtained from normal distribution at test statistic (-1.781).
The p-value is 0.037.
Since the p-value is less than level of significance (0.01) which means we reject the null hypothesis.
Therefore, The conclusion (a) is correct i.e., There is sufficient evidence to support the claim that more than 50% of adults are opposed to federal tax dollars being used for foreign aid.
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Write in the standard form of a conic if possible, and identify the conic section represented by r = 6/(cos x + 3sin x)
The standard form of a conic section represented by r = 6/(cos x + 3sin x) is r^2 = 6(x + 3y) and the represented equation is a line.
The equation r = 6/(cos x + 3sin x) is in polar form, where r represents the distance from the origin to a point (x, y) in the plane, and x is the angle that the line connecting the origin to (x, y) makes with the positive x-axis. To determine the standard form of the conic represented by this equation, we need to convert it to Cartesian coordinates.
Using the trigonometric identity cos x = x/r and sin x = y/r, we can rewrite the equation as:
r = 6/(x/r + 3y/r)
Multiplying both sides by r, we get:
r^2 = 6(x + 3y)
This is the standard form of a conic section in Cartesian coordinates, namely an equation of a line. Therefore, the conic represented by the equation r = 6/(cos x + 3sin x) is a line in the Cartesian coordinate system.
In summary, to determine the standard form of a conic represented by an equation given in polar form, we can use trigonometric identities to rewrite it in Cartesian coordinates.
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An aquarium can be modeled as a right rectangular prism. Its dimensions are 19 in by 15 in by 12 in. How many cubic inches of water are in it when it is full? Round your answer to the nearest tenth if necessary.
Answer:
The volume of the aquarium can be found by multiplying its length, width, and height:
Volume = length x width x height
Volume = 19 in x 15 in x 12 in
Volume = 3,420 cubic inches
Therefore, when the aquarium is full, it can hold 3,420 cubic inches of water.
Step-by-step explanation:
The tires on Mavis’ car will have to be replaced when they each have 160 000 km of wear on them. If new tires cost $140.00 each, what is the total cost of the wear on Mavis’ tires for a year in which she drives 25 000 km?
Answer:
If the tires on Mavis’ car have to be replaced when they each have 160 000 km of wear, then the total distance Mavis can drive on a set of tires is:
4 tires * 160,000 km = 640,000 km
If Mavis drives 25,000 km in a year, she will need to replace her tires after:
640,000 km ÷ 25,000 km/year = 25.6 years
Since Mavis will need to replace her tires once every 25.6 years, the cost of the wear on her tires for a single year is:
$140.00/tire * 4 tires = $560.00
So the total cost of the wear on Mavis’ tires for a year in which she drives 25,000 km is $560.00.
Step-by-step explanation:
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The box plot shows information
about the heights, in cm, of a Yr 10
group of Year 10 students.
Yr 7
130
a) The table shows information about
the heights, in cm, of a group
of Year 7 students.
Complete the boxplot for Year 7.
b) The heights distributions of Year 10
and Year 7 are compared.
140
height
(cm)
150
160
Height (cm)
median
170
least
upper
lower
quartile quartile
height
145 158 154 166
range
25
A- The median height is higher for Yr 7 than for Yr 10
Select the statements that apply. B-The interquartile range is higher for Yr 7 than for Yr 10
C - The data range is wider for Yr 7 than for Yr 10
D- The median height is lower for Yr 7 than for Yr 10
180
(3)
(2)
Total marks: 5
Answer:
The box plot shows information
about the heights, in cm, of a Yr 10
group of Year 10 students.
Yr 7
130
a) The table shows information about
the heights, in cm, of a group
of Year 7 students.
Complete the boxplot for Year 7.
b) The heights distributions of Year 10
and Year 7 are compared.
140
height
(cm)
150
160
Height (cm)
median
170
least
upper
lower
quartile quartile
height
145 158 154 166
range
25
A- The median height is higher for Yr 7 than for Yr 10
Select the statements that apply. B-The interquartile range is higher for Yr 7 than for Yr 10
C - The data range is wider for Yr 7 than for Yr 10
D- The median height is lower for Yr 7 than for Yr 10
180
(3)
(2)
Total marks: 5
Step-by-step explanation:
A - The median height is higher for Yr 7 than for Yr 10. (Incorrect)
B - The interquartile range is higher for Yr 7 than for Yr 10. (Correct)
C - The data range is wider for Yr 7 than for Yr 10. (Correct)
D - The median height is lower for Yr 7 than for Yr 10. (Incorrect)
Therefore, the correct statements are B and C.
What is the value of x in the triangle to the right? (7x+3) 85 50
Answer:
Step-by-step explanation:
We know that a triangle angles total equals 180 so we could use the numbers and the equation, add it up and then find the value of x
(7x + 3) + 85 + 50 = 180
7x + 138 = 180
7x = 180-138
7x = 42
x = 6
Now that we found the value of x we can know substitute the value into the equation to find the value of the angle.
7x+3
42+3
45
someone please help!!
Adela paints a mural of Mount Rushmore. She uses the scale 6 ft to 1 ft from the actual monument to the mural. On Adela's mural, how much wider is George Washington's mouth than his eye? Show your work,
7/6 is wider George Washington's mouth than his eye.
What is unitary method?"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."
We always count the unit or amount value first and then calculate the more or less amount value. For this reason, this procedure is called a unified procedure.
Many set values are found by multiplying the set value by the number of sets.
A set value is obtained by dividing many set values by the number of sets.
According to our question-
eye length = 11/6
difference= 3 - 11/6
7/6
Hence, 7/6 is wider George Washington's mouth than his eye.
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Mr. McCoy's new ice cream shop is doing great! Last month, he sold out of his Boldly Buttered Popcorn ice cream and his Lovely Lavender Lemon ice cream. He sold x pints of Boldly Buttered Popcorn and y pints of Lovely Lavender Lemon. Each pint cost him $4 to make, and he charged $10 for each
After selling x pints of Boldly Buttered Popcorn icecream and y pints of Lovely Lavender Lemon on the charged of $10 for each, his profit equation is written as P = 6x + 6y = 6( x + y).
We have, Mr. McCoy's new ice cream shop. He sold two flavors of icecream. He sold his Boldly Buttered Popcorn ice cream and his Lovely Lavender Lemon ice cream. The quantity of sold Boldly Buttered Popcorn ice cream = x pints
The quantity of sold Lavender Lemon ice cream = y pints
Cost of each pint of ice cream = $4
Selling price of each pint of ice cream
= $10
First, total pints of icecream he sold
= pints of Boldly Buttered Popcorn ice cream+ pints of Lavender Lemon ice cream = ( x + y) pints
Now, Cost of (x + y) pints of ice cream
= $4 ( x + y)
Similarly, selling price of ( x + y ) pints of icecream = $ 10 ( x + y)
As we know, when selling price is greater than cost price then profit will occur. Equation for profit P = selling price - cost price = $ 10 ( x + y) - $4 ( x + y)
= 10 x + 10y - 4x - 4y
P = 6(x + y)
Hence, required equation is 6x + 6y.
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Complete question:
Mr. McCoy's new ice cream shop is doing great! Last month, he sold out of his Boldly Buttered Popcorn ice cream and his Lovely Lavender Lemon ice cream. He sold x pints of Boldly Buttered Popcorn and y pints of Lovely Lavender Lemon. Each pint cost him $4 to make, and he charged $10 for each. Write an equation for his profit or loss on ice cream selling.
choose one of the two boxes at random and select one of the balls in this box at random. if a blue ball is selected, what is the probability that this ball is from the second box?
Assume that the first box has 4 red balls and 3 blue balls and the second box has 5 red balls and 4 blue balls. the probability that this ball is from the second box is 12/55.
How to determine probabilityGiven that we need to choose one of the two boxes at random and select one of the balls in this box at random.
Let us assume that the first box has 4 red balls and 3 blue balls and the second box has 5 red balls and 4 blue balls.
Let the probability of selecting a blue ball from the first box be P(A) = (3/7)
Let the probability of selecting a blue ball from the second box be P(B) = (4/9)
So, the probability of selecting a blue ball is:
P(A) + P(B) = (3/7) + (4/9)= (27+28)/63= 55/63
If we have chosen a blue ball, then the probability that it is from the second box will be:
P(B|A) = P(B∩A) / P(A)P(B∩A) = P(A) × P(B|A) = (3/7) × (4/9) = 12/63
So, the probability that the blue ball is from the second box is:
P(B|A) = P(B∩A) / P(A)= (12/63) / (55/63)= 12/55
Therefore, the probability that this ball is from the second box is 12/55.
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