Points P(6, –8) and Q(–18, 2) are plotted on the coordinate plane.
Enter the distance, in units, between points P and Q.
What are the new coordinates of L if parallelogram LMNO is translated down 20 units?
Answer:
The answer is [tex](-4,-19)[/tex]
Step-by-step explanation:
Firstly, we have to determine the coordinates of L before the translation.
If we see the graph, we can see that the coordinate "x" is -4 and the coordinate "y" is 1. So, the original coordinates of L are [tex](4,1)[/tex]
Then, we have to determine the vector of translation. We know that the parallelogram LMNO is translated down 20 units, so it means that it moved only in the negative vertical direction. Then the coordinate of the vector is [tex](0,-20)[/tex]
Finally, in order to determine the new coordinates of L, we have to add the original coordinates of L with the coordinates of the vector of translation, that is:
[tex](-4+0,1-20)\\(-4,-19)[/tex]
So, the new coordinates of L is [tex](-4,-19)[/tex]
Solve for x. x/4 = 3/8 A) 2/3 B) 3/2 C) 3/32 D) 7/8
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The table below shows the number of cars sold each month for 5 months at two dealerships.
Cars Sold
Month Admiral Autos Countywide Cars
Jan 4 9
Feb 19 17
Mar 15 14
Apr 10 10
May 17 15
Which statements are supported by the data in the table? Check all that apply.
The mean number of cars sold in a month is the same at both dealerships.
The median number of cars sold in a month is the same at both dealerships.
The total number of cars sold is the same at both dealerships.
The range of the number of cars sold is the same for both dealerships.
The data for Admiral Autos shows greater variability.
Answer:
1st, 3rd and 5th statements are true.
Step-by-step explanation:
We have been given a table that hows the number of cars sold each month for 5 months at two dealerships. We are asked to choose the correct statement from the given choices.
1. The mean number of cars sold in a month is the same at both dealerships.
Let us find mean sales for both dealerships.
[tex]\text{Mean}=\frac{\text{Sum of all number of data set}}{\text{Total number in data set}}[/tex]
[tex]\text{Mean sales for Admiral autos}=\frac{4+19+15+10+17}{5}[/tex]
[tex]\text{Mean sales for Admiral autos}=\frac{65}{5}[/tex]
[tex]\text{Mean sales for Admiral autos}=13[/tex]
[tex]\text{Mean sales for Countywide Cars}=\frac{9+17+14+10+15}{5}[/tex]
[tex]\text{Mean sales for Countywide Cars}=\frac{65}{5}[/tex]
[tex]\text{Mean sales for Countywide Cars}=13[/tex]
We can see that mean number of cars sold at both dealerships, therefore, statement 1st is true.
2. The median number of cars sold in a month is the same at both dealerships.
Let us arrange our given data set from least to greatest.
Median sales for Admiral autos: 4, 10, 15, 17, 19.
As our data set have 5 data points, therefore, the median will be the value of 3rd data point that is 15.
Median sales for Countywide Cars: 9, 10, 14, 15, 17.
As our data set have 5 data points, therefore, the median will be the value of 3rd data point that is 14.
Since the median number of cars sold at both dealerships is different, therefore, 2nd statement is false.
3. The total number of cars sold is the same at both dealerships.
We have already seen that both dealerships sold 65 cars, therefore, 3rd statement is true.
4. The range of the number of cars sold is the same for both dealerships.
[tex]\text{Range}=\text{The highest value- The Lowest value}[/tex]
[tex]\text{Range of Admiral Autos}=19-4[/tex]
[tex]\text{Range of Admiral Autos}=15[/tex]
[tex]\text{Range of Countywide Cars}=17-9[/tex]
[tex]\text{Range of Countywide Cars}=8[/tex]
Since the ranges of both dealerships are different, therefore, 4th statement is false.
5. The data for Admiral Autos shows greater variability.
Let us find standard deviation of both data sets.
[tex]\sigma=\sqrt{\frac{\sum(x-\overline x)^2 }{n-1}}[/tex]
[tex]\text{SD of Admiral Autos}=\sqrt{\frac{(4-13)^2+(19-13)^2+(15-13)^2+(10-13)^2+(17-13)^2}{5-1}}[/tex]
[tex]\text{SD of Admiral Autos}=\sqrt{\frac{(-9)^2+(6)^2+(2)^2+(-3)^2+(4)^2}{4}}[/tex]
[tex]\text{SD of Admiral Autos}=\sqrt{\frac{81+36+4+9+16}{4}}[/tex]
[tex]\text{SD of Admiral Autos}=\sqrt{\frac{146}{4}}[/tex]
[tex]\text{SD of Admiral Autos}=\sqrt{36.5}\approx 6.04[/tex]
[tex]\text{SD of Countywide Cars}=\sqrt{\frac{(9-13)^2+(17-13)^2+(14-13)^2+(10-13)^2+(15-13)^2}{5-1}}[/tex]
[tex]\text{SD of Countywide Cars}=\sqrt{\frac{(-4)^2+(4)^2+(1)^2+(-3)^2+(2)^2}{4}}[/tex]
[tex]\text{SD of Countywide Cars}=\sqrt{\frac{16+16+1+9+4}{4}}[/tex]
[tex]\text{SD of Countywide Cars}=\sqrt{\frac{46}{4}}[/tex]
[tex]\text{SD of Countywide Cars}=\sqrt{11.5}\approx 3.39[/tex]
Since SD for Admiral Autos is 6.04 and SD for Countywide Cars is 3.39, therefore, 5th statement is true indeed.
Final answer:
The mean number of cars sold per month is the same at both dealerships, with both having a mean of 13 cars. The total number of cars sold over the five months is also the same at 65 cars for each dealership. Admiral Autos shows greater variability, with a range of 15 cars, compared to Countywide Cars, with a range of 8 cars.
Explanation:
You are looking at the sales data for two dealerships over five months. To analyze the data, let's calculate the mean (average), median, total cars sold, and the range for both dealerships.
Admiral Autos
Mean: (4 + 19 + 15 + 10 + 17) / 5 = 65 / 5 = 13 cars per month
Median: The middle value when data is ordered which here is 15.
Total: 4 + 19 + 15 + 10 + 17 = 65 cars
Range: The difference between the highest and lowest values is 19 - 4 = 15 cars
Countywide Cars
Mean: (9 + 17 + 14 + 10 + 15) / 5 = 65 / 5 = 13 cars per month
Median: The middle value when data is ordered which here is 14.
Total: 9 + 17 + 14 + 10 + 15 = 65 cars
Range: The difference between the highest and lowest values is 17 - 9 = 8 cars
Based on the calculations:
The mean number of cars sold in a month is the same at both dealerships.
The total number of cars sold is the same at both dealerships.
The data for Admiral Autos shows greater variability because it has a higher range.
the length of one side of a square field is represented by the expression 3 - 7 x what is an expression for the perimeter of the field of expressed as a product
Ken has 8 toy trains Ron has 3 toy trains how many fewer toy trains does Ron have than ken ?
What is the range of the middle 50% of the data
Answer:it’s c on edge
Step-by-step explanation:
None
The dimensions of triangle A are four times the dimensions of triangle B. The area of triangle B is 15cm 2. what is the area of triangle A
Is it necessary to use the formulas for special products of binomials to multiply these binomials? Complete the explanation. Yes/no. Special products of binomials can/cannot be found by using FOIL instead of their formulas. In any case, the formulas would likely be faster to use.
According to the statement, the answer is no. Foil method is used to solve the special product of binomials.
What is Foil method?To combine binomials, utilize the FOIL Method.
An abbreviation is F O I L. First, Outside, Inside, and Last are represented by the letters, denoting the sequence of multiplying terms. For your solution, multiply the first word, an outside term, the inside term, the very last term, and then join like terms.
FOIL specifies the specific terms to multiply and their order.
First - multiply the first termsOutside - multiply the outside/outer termsInside - multiply the inside/inner termsLast - multiply the last termsTo know more about foil method:
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the weather report says there is a 30% chance of rain. what is the possibility that it does not rain?
The possibility that it does not rain is,
⇒ 70%
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Given that;
The weather report says there is a 30% chance of rain.
Hence, The possibility that it does not rain is,
⇒ 1 - 30%
⇒ 1 - 30/100
⇒ 70 / 100
⇒ 70%
Thus, The possibility that it does not rain is,
⇒ 70%
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Samir knows that the volume of prism is 40 cubic units . He also knows that the width can of the prism is 2 units and the height is 5 units. What is the length of the prism?
Final answer:
The length of the prism is 4 units, which is determined by dividing the volume of the prism (40 cubic units) by the product of its width (2 units) and height (5 units).
Explanation:
Samir knows that the volume of a prism is 40 cubic units, the width is 2 units, and the height is 5 units. To find the length of the prism, we can use the formula for the volume of a prism: V = lwh, where V is the volume, l is the length, w is the width, and h is the height. Plugging in the known values, we get 40 = l × 2 × 5. To solve for l, we divide both sides of the equation by the product of the width and height (2 × 5), yielding l = 40 / (2 × 5) = 40 / 10 = 4 units. Thus, the length of the prism is 4 units.
Lauren's scores on her math tests are 93,91,98,100,95,92,and 96. What score does Lauren need to get on her next math test test so that the mean and the mediam stay the same?
Lauren needs to get a mean/median score in order to keep from changing either of those values. She needs a 95.
_____
In order, the scores are
... 91, 92, 93, 95, 96, 98, 100
The median is the middle of these, 95, and the problem statement tells us the mean is the same (which it is).
=====
If Lauren were to get a higher score, it would raise the mean. The median would shift to halfway between 95 and 96. The score that makes the new mean be 95.5 is 99. The mean and median would be the same (again), but they wouldn't stay the same value they are now.
Likewise, if Lauren were to get a lower score, it would reduce the mean. The median would shift to halfway between 93 and 95. The score that makes the new mean be 94 is 87. The mean and median would be the same (again), but they wouldn't be the same value they are now.
If Lauren got 87, 95, or 99 on her test, her mean and median scores would be the same. They would only stay the same if she got a 95.
Solve this quadratic word problem
What is the overlap of Data Set 1 and Data Set 2? high moderate low none Two line plots aligned vertically so that their labels match. The first line plot is from 20 to 60, is labeled Data Set 1, and shows the following values that appear as x marks above the line. One x mark above 20. Three x marks above 25. Three x marks above 30. Two x marks above 35. One x mark above 40. The second line plot is also from 20 to 60, is labeled Data Set 2, and shows the following values that appear as x marks above the line. One x mark above 35. Two x marks above 40. Three x marks above 45. Two x marks above 50. One x mark above 55. One x mark above 60. Image: Do not include the blue squiggly lines under the Xs.
The overlap of data set 1 and data set 2 is low.
What is Overlap of Data Sets?Overlap of two or more data sets is defined as the measure of the intersection between the given data sets.
Given two data sets.
Both are marked from 20 to 60.
Both data set has 10 data points which is explained in the question.
Overlapping happens once at the point 35 and once at the point 40.
That is out of the 10 data points from each, only 2 overlapped.
This means that the overlap is low.
Hence the overlap of data set 1 and data set 2 is low.
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The perimeter of a rectangle is 126 ft. The ratio of its length to its width is 5 : 4. What are the dimensions of the rectangle? 30 ft by 33 ft 35 ft by 28 ft 6 ft by 60 ft 3 ft by 60 ft
The length and width of the given rectangle will be 35 and 28 feet respectively.
What is a rectangle?A rectangle is a geometrical figure in which opposite sides are equal.
The angle between any two consecutive sides will be 90 degrees.
Area of rectangle = length × width.
The perimeter of the rectangle = 2( length + width).
It is known that,
The perimeter of the rectangle = 2( length + width).
2(L + W) = 126
L + W = 63
The ratio of length to width,
L/W = 5/4
L = 5/4 W
(5/4 )W + W = 63
W(1 + 5/4) = 63
W = 63(4/9)
W = 7 x 4 = 28
And, L = 63 - 28 = 35
Hence "The length and width of the given rectangle will be 35 and 28 feet respectively".
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Anthony has added a line of best fit to the scatterplot at right. Do you agree with where he put the line? Explain your reasoning