Verify that the points are the vertices of a parallelogram and find its area. (2,-1,1), (5, 1,4), (0,1,1), (3,3,4)
Answers
Answer:
Verified
Area = 13.12 square units.
Step-by-step explanation:
Let the given points / vertices of the parallelogram be represented as follows:
A(2,-1,1),
B(5, 1,4),
C(0,1,1),
D(3,3,4)
In vector notation, we can have;
A = 2i - j + k
B = 5i + j + 4k
C = 0i + j + k
D = 3i + 3j +4k
One of the ways to prove that a quadrilateral is a parallelogram is to show that both pairs of opposite sides are parallel.
(i) Now, let's find the various sides of the assumed parallelogram. These sides are:
AB = B - A = [5i + j + 4k] - [2i - j + k] open the brackets
AB = 5i + j + 4k - 2i + j - k collect like terms and solve
AB = 5i - 2i + j + j - k + 4k
AB = 3i + 2j+ 3k
BC = C - B = [0i + j + k] - [5i + j + 4k] open the brackets
BC = 0i + j + k - 5i - j - 4k collect like terms and solve
BC = 0i - 5i + j - j + k - 4k
BC = -5i + 0j - 3k
CD = D - C = [3i + 3j +4k] - [0i + j + k] open the brackets
CD = 3i + 3j + 4k - 0i - j - k collect like terms and solve
CD = 3i - 0i + 3j - j + 4k - k
CD = 3i + 2j + 3k
DA = A - D = [2i - j + k] - [3i + 3j +4k] open the brackets
DA = 2i - j + k - 3i - 3j - 4k collect like terms and solve
DA = 2i - 3i - j - 3j + k - 4k
DA = - i - 4j - 3k
AC = C - A = [0i + j + k] - [2i - j + k] open the brackets
AC = 0i + j + k - 2i + j - k collect like terms and solve
AC = 0i - 2i + j + j + k - k
AC = - 2i + 2j +0k
BD = D - B = [3i + 3j + 4k] - [5i + j + 4k] open the brackets
BD = 3i + 3j + 4k - 5i - j - 4k collect like terms and solve
BD = 3i - 5i + 3j - j + 4k - 4k
BD = - 2i + 2j + 0k
(ii) From the results in (i) above, it has been shown that;
AB is equal to CD, and that implies that AB is parallel to CD. i.e
AB = CD => AB || CD
Also,
AC is equal to BD, and that implies that AC is parallel to BD. i.e
AC = BD => AC || BD
(iii) Therefore, ABDC is a parallelogram since its opposite sides are equal and parallel.
(B) Now let's calculate the area of the parallelogram.
To calculate the area, we find the magnitude of the cross product between any two adjacent sides.
In this case, we choose sides AC and AB.
Area = | AC x AB |
Where;
[tex]AC X AB = \left[\begin{array}{ccc}i&j&k\\-2&2&0\\3&2&3\end{array}\right][/tex]
AC X AB = i(6 - 0) - j(-6 - 0) + k(-4 -6)
AC X AB = 6i + 6j - 10k
|AC X AB| = [tex]\sqrt{6^2 + 6^2 + (-10)^2} \\[/tex]
|AC X AB| = [tex]\sqrt{36 + 36 + 100} \\[/tex]
|AC X AB| = [tex]\sqrt{172} \\[/tex]
|AC X AB| = 13.12
Therefore the area is 13.12 square units.
PS: The diagram showing this parallelogram has been attached to this response.
Related Questions
Need help with this can anyone help me?
Answers
Please mark as brainliest :)
An apartment complex rents an average of 2.3 new units per week. If the number of apartment rented each week Poisson distributed, then the probability of renting no more than 1 apartment in a week is:_________
Answers
Answer:
[tex]P(X\leq 1) = 0.331[/tex]
Step-by-step explanation:
Given
Poisson Distribution;
Average rent in a week = 2.3
Required
Determine the probability of renting no more than 1 apartment
A Poisson distribution is given as;
[tex]P(X = x) = \frac{y^xe^{-y}}{x!}[/tex]
Where y represents λ (average)
y = 2.3
Probability of renting no more than 1 apartment = Probability of renting no apartment + Probability of renting 1 apartment
Using probability notations;
[tex]P(X\leq 1) = P(X=0) + P(X =1)[/tex]
Solving for P(X = 0) [substitute 0 for x and 2.3 for y]
[tex]P(X = 0) = \frac{2.3^0 * e^{-2.3}}{0!}[/tex]
[tex]P(X = 0) = \frac{1 * e^{-2.3}}{1}[/tex]
[tex]P(X = 0) = e^{-2.3}[/tex]
[tex]P(X = 0) = 0.10025884372[/tex]
Solving for P(X = 1) [substitute 1 for x and 2.3 for y]
[tex]P(X = 1) = \frac{2.3^1 * e^{-2.3}}{1!}[/tex]
[tex]P(X = 1) = \frac{2.3 * e^{-2.3}}{1}[/tex]
[tex]P(X = 1) =2.3 * e^{-2.3}[/tex]
[tex]P(X = 1) = 2.3 * 0.10025884372[/tex]
[tex]P(X = 1) = 0.23059534055[/tex]
[tex]P(X\leq 1) = P(X=0) + P(X =1)[/tex]
[tex]P(X\leq 1) = 0.10025884372 + 0.23059534055[/tex]
[tex]P(X\leq 1) = 0.33085418427[/tex]
[tex]P(X\leq 1) = 0.331[/tex]
Hence, the required probability is 0.331
If segment XY = 5 and segment YZ = 10, what is the length of XZ?
Answers
Answer:
The length of segment XZ is 15 units
Step-by-step explanation:
Given
[tex]XY = 5[/tex]
[tex]YZ = 10[/tex]
Required
Determine XZ
Assuming XY and YZ are on the same plane such that
[tex]XZ = XY + YZ[/tex]
Substitute values for XY and YZ
[tex]XZ = 5 + 10[/tex]
[tex]XZ = 15[/tex]
Hence, the length of segment XZ is 15 units
Sheila_____ her case ,look(had pickrd, have, picked
Answers
Answer:
Had Picked
Step-by-step explanation:
Solves the following equation for a. Show steps for full credit.
4a + 10 = 2a + 26
Answers
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{a = 8}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{4a + 10 = 2a + 26}[/tex]
Move 2a to left hand side and change it's sign
Similarly, move 10 to right hand side and change it's sign
⇒[tex] \sf{4a - 2a =26 - 10}[/tex]
Collect like terms
⇒[tex] \sf{2a = 26 - 10}[/tex]
Subtract 10 from 26
⇒[tex] \sf{2a = 16}[/tex]
Divide both sides of the equation by 2
⇒[tex] \sf{ \frac{2a}{2} = \frac{16}{2} }[/tex]
Calculate
⇒[tex] \sf{a = 8}[/tex]
Hope I helped!
Best regards!!
Ella has 164 ounces of lemonade. She fills glasses with
8 ounces of lemonade each until all the lemonade is gone.
The last glass is not full. How much lemonade is in the
last glass?
Answers
Answer:
4 ounces
Step-by-step explanation:
If you divide the 164 ounces by the 8 ounces per glass, you get 20.5 glasses filled. So, half of the last glass would be 4.
Answer:
4 ounces
Step-by-step explanation:
We're looking for the remainder of ounces.
To find how many FULL glasses will be made, we divide 8 by 164 and look at the integer part of the number.
[tex]164\div8=20.5[/tex]
So 2 full glasses were made.
To find the remainder, we multiply 20 by 8 and subtract from 164.
[tex]20\cdot8=160\\\\164-160=4[/tex]
Hope this helped!
A unit of electricity costs 13.2 pence. On average, Tanya uses 90 units of electricity per week. She pays for her bill in 12 weeks. How much will her electricity bill be then? £
Answers
Answer:
90*12=1080
1080*13.2=14256
14256:100=142,56pounds
What is 4^6 times 2^3=??
Answers
Answer:
32,768
Step-by-step explanation:
Remember to follow PEMDAS.
First, solve for the exponents for both terms:
[tex]4^6 = 4 * 4 * 4 * 4 * 4 * 4 = 4096[/tex]
[tex]2^3 = 2 * 2 * 2 = 8[/tex]
Multiply the two terms together:
[tex]4096 * 8 = 32768[/tex]
32,768 is your answer.
~
Darius filled up his gas tank with 24 gallons of gas. For each mile that he drives, he uses 0.06 gallons of gas.
Answers
a
n
=−0,06n+24
mark me a brainlist
Imagine that * represents a new operation so that a * b means to double a, and then add b. For example, 2 * 10 = 14. What is -3 * 8 ?
A. 14
B 17
C 2
D 48
Answers
Answer:
C 2
Step-by-step explanation:
-3 doubled = -6
-6 +8 = 2 so C 2
Answer:
C. 2
Step-by-step explanation:
-3(2) = -6
-6+8 = 2
Evaluate (64×1/2-125×1/3)×(64×1/2-125×1/3)
Answers
Explanation:
(64x1/2-125x1/3)(64x1/2-125x1/3)
= (64*1/2-125*1/3)^2
= (32 - 125/3)^2
= (96/3 - 125/3)^2
= (-29/3)^2
= 841/9
Find the arc length of ABC .
Answers
Answer:
C.
Step-by-step explanation:
Since the radius of the circle is 12 units, we can calculate the circumference.
2 * pi * r = 2 * pi * 12 = 24 * pi = 24pi.
The arc angle is 240 degrees, and the whole circle would be 360 degrees. So, we can set up an equation.
[tex]\frac{24\pi }{360} =\frac{x}{240}[/tex]
[tex]\frac{24\pi }{6} =\frac{x}{4}[/tex]
[tex]\frac{4\pi }{1} =\frac{x}{4}[/tex]
1 * x = 4 * 4 * pi
x = 16pi
So, your answer is C.
Hope this helps!
Listed below are the amounts (dollars) it costs for marriage proposal packages at different baseball stadiums. Find the range, variance, and standard deviation for the given sample data. Include appropriate units in the results. Are there any outliers, and are they likely to have much of an effect on the measures of variation?
38, 50, 50, 55, 55, 95, 95, 130, 180, 213, 250, 350, 450, 1750, 3000
Answers
Answer:
Question 1
a) Range
= $2962
b) Variance
= $680557.4954
c) Standard Deviation
= $824.9590871
Question 2
Are there any outliers, and are they likely to have much of an effect on the measures of variation?
Yes, there are outliers present I the given sample data.
These outliers are the larger cost for marriage proposals which are: 1750, 3000
These largest costs are much bigger than the rest of the sample data, and they would likely have much of an effect on the measures of variation
Step-by-step explanation:
We are given the following sample data in dollars
38, 50, 50, 55, 55, 95, 95, 130, 180, 213, 250, 350, 450, 1750, 3000
Question 1
a) Range
This is the difference between the maximum cost and the minimum cost
The minimum cost = $38
The maximum cost = $3000
Range = $3000 - $38
= $2962
b) Variance
Reading the question, we are given sample data.
Hence, we use the formula for Variance of a sample
= (Mean - x)²/N - 1
Step 1
We find the Mean
Mean = Sum of terms/Number of terms
Number of terms = 15
Mean = 38 + 50 + 50 + 55 + 55 + 95 + 95 + 130 + 180 + 213 + 250 + 350 + 450+ 1750 + 3000/15
= $6761/15
= $450.7333333
Step 2
(x - Mean)²/N - 1
N = 15
= $[(38 - 450.7333333)²+ (50 + 450.7333333)²+( 50 +450.7333333)² + (55 +450.7333333)² + (55 +450.7333333)² + (95 + 450.7333333)²+ (95 +450.7333333)²+ (130 +450.7333333)²+ (180 +450.7333333)² + (213 + 450.7333333)²+ (250 +450.7333333)² + (350 + 450.7333333)² + (450 +450.7333333)²+ (1750 +450.7333333)² + (3000 +450.7333333)²]/15 - 1
=$ (- 412.7333333² + -400.7333333² + -400.7333333² + -395.7333333² + -395.7333333² + -355.7333333² + -355.7333333² + -320.7333333² + -270.7333333² + -237.7333333² + -200.7333333² + -100.7333333² + -0.7333333333² + 1299.266667² + 2549.266667²)/15 - 1
= $( 170348.8044+ 160587.2044, 160587.2044+ 156604.8711, 156604.8711+ 126546.2044, 126546.2044+ 102869.8711, 73296.53776+ 56517.13776, 40293.8711+ 10147.20444+ 0.5377777777+ 1688093.872, 6498760.539)/14
= $9527804.935/14
Variance = $680557.4954
c) Standard deviation = √Variance
Standard deviation = √$680557.4954
= $824.9590871
Question 2
Are there any outliers, and are they likely to have much of an effect on the measures of variation?
Yes, there are outliers present in the given sample data.
These outliers are the largest cost for marriage proposals which are: $1750 and $3000
These largest costs are much bigger than the rest of the sample data, and they would likely have much of an effect on the measures of variation.
I am in confusion ❤️
Answers
Answer:
The Brain
Step-by-step explanation:
It goes down 3 and moves to the right 2
so its -3/2 =- 1.5
you slope is -1.5❤✔ hope I helped!
The number of credits being taken by a sample of 13 full-time college students are listed below. Find the mean, median, and mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why. Find the mean. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The mean is nothing. (Type an integer or decimal rounded to one decimal place as needed.) B. The data set does not have a mean. Does the mean represent the center of the data? A. The mean represents the center. B. The mean does not represent the center because it is not a data value. C. The mean does not represent the center because it is the smallest data value. D. The mean does not represent the center because it is the largest data value. E. The data set does not have a mean. Find the median. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The median is nothing. (Type an integer or decimal rounded to one decimal place as needed.) B. The data set does not have a median. Does the median represent the center of the data?
Answers
Answer:
The data is missing in the question, below is the complete question:
The number of credits being taken by a sample of 13 full-time college students are listed below. Find the mean, median, and mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why. 9 9 12 12 9 10 8 8 8 8 8 8 11 Find the mean. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The mean is nothing . (Type an integer or decimal rounded to one decimal place as needed.) B. The data set does not have a mean. Does the mean represent the center of the data? A. The mean represents the center. B. The mean does not represent the center because it is the smallest data value. C. The mean does not represent the center because it is not a data value. D. The mean does not represent the center because it is the largest data value. E. The data set does not have a mean. Find the median. Select the correct choice below and, ifnecessary, fill in the answer box to complete your choice. A. The median is nothing . (Type an integer or decimal rounded to one decimal place as needed.) B. The data set does not have a median. Does the median represent the center of the data? A. The median represents the center. B. The median does not represent the center because it is the largest data value. C. The median does not represent the center because it is not a data value. D. The median does not represent the center because it is the smallest data value. E. The data set does not have a median. Find the mode. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The mode(s) is/are nothing . (Type an integer or decimal rounded to one decimal place as needed. Use a comma to separate answers as needed.) B. The data set does not have a mode. Does (Do) the mode(s) represent the center of the data? A. The mode(s) represent(s) the center. B. The mode(s) does (do) not represent the center because it (they) is (are) not a data value. C. The mode(s) does (do) not represent the center because it (one) is the largest data value. D. The mode(s) does (do) not represent the center because it(one) is the smallest data value. E. The data set does not have a mode.
Answer:
a.) mean = 9.23
ii) The mean represents the centre (A)
b) Median = 9
ii) The median represents the centre (A)
c) Mode = 8
ii) The mode(s) does (do) not represent the center because it(one) is the smallest data value. (D)
Step-by-step explanation:
Arranging the data in ascending order:
8 8 8 8 8 8 9 9 9 10 11 12 12
a) calculating for mean
[tex]\bar x = \frac{sum\ of\ data}{number\ of\ data}\\ \bar x = \frac{8+8+8+8+8+8+9+9+9+10+11+12+12}{13} \\\bar x =\frac{120}{13} \\\bar x = 9.23[/tex]
ii) does the mean represent the centre of the data?
The measure of central tendency/location is a statistical tool used to accurately depict values that are at the central location of the data set
Yes, the mean represents the centre of the data, because there are no outliers in the data set. Outliers are unusual values compared to the rest of the values in the dataset.
b) calculating the median (M)
[tex]M =( \frac{n\ +\ 1}{2})th\ term\\ \\where:\\n = number\ of\ data\ in\ the\ dataset = 13\\\\\therefore M = \frac{13+1}{2}\\ M = \frac{14}{2} \\M= 7th\ term[/tex]
The 7th term after arranging in ascending or descening order, is the median term
8 8 8 8 8 8 9 9 9 10 11 12 12
∴ Median = 9
ii) Yes, the Median represents the center of the data, because it litterally tells the data at the middle of the distribution
c) The mode is the data with the highest number of occurrence in the dataset (highest frequency); 8 8 8 8 8 8 9 9 9 10 11 12 12
The data with the highest number of occurrence is 8, which occurred 6 times.
Mode = 8
ii) The mode does not represent the centre of the data because it is the smallest value in the dataset, hence it doesn't tell the value that is the middle term.
I DON'T UNDERSTAND! Use a system of equations to solve a word problem.
A. The sum of two numbers is -2, and their difference is 4. Find the two numbers.
B. One number is 2 less than a second number. Twice the second number is 14 less than 5 times the first. Find the two numbers.
C. A flat rectangular piece of aluminum has a perimeter of 64 inches. The length is 8 inches longer than the width. Find the width. Select one: A) 20 in. B) 32 in. C) 28 in. D) 12 in.
Answers
Answer:
A) 1 and -3
B) 8 and 6
C) D) 12 in.
Step-by-step explanation:
A) 1 and -3
B) x-2 = first number
x = second number
2x=5(x-2)-14
2x=5x-10-14
2x=5x-24
2x+24=5x
24=5x-2x
24=3x
8=x
So the two numbers are 8 and 6
C) width=x
length=x+8
x+x+x+8+x+8=64
4x+16=64
4x=48
x=12
Find the missing side length using pythagorean theorem. simplify radicals if necessary* PLEASE HELP!!
Answers
Answer:
15
Step-by-step explanation:
a^2 + b^2 = c^2
9=a
12-b
Plug in the numbers
Write the equation of the line that passes through the points (8,0)(8,0) and (-9,-9)(−9,−9). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.
Answers
Answer:
Hence, the equation of the line that passes through the points (8,0) and (-9,-9) is [tex]y =\frac{9x}{17} - \frac{72}{17}[/tex].
Step-by-step explanation:
We have to find the equation of the line that passes through the points (8,0) and (-9,-9).
Let the two points be ([tex]x_1,y_1[/tex]) = (8, 0) and ([tex]x_2, y_2[/tex]) = (-9, -9).
Now, we will find the two-point slope using the above two points, i.e;
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{-9-0}{-9-8}[/tex] = [tex]\frac{9}{17}[/tex]
Now, the equation of the line using one of the point, let's say ([tex]x_1,y_1[/tex]) = (8, 0) is given by;
[tex]y - y_1 = \text{Slope} \times (x - x_1)[/tex]
[tex]y - 0 =\frac{9}{17} \times (x - 8)[/tex]
[tex]y =\frac{9x}{17} - \frac{72}{17}[/tex]
Hence, the equation of the line that passes through the points (8,0) and (-9,-9) is [tex]y =\frac{9x}{17} - \frac{72}{17}[/tex].
Find y using the Angle Sum Theorem
Answers
Explanation:
In a triangle the angle sums up to 180 degree.
Find x:
87 + 33 + x = 180
130 + x = 180
x = 50
Find y:
x + y = 180 (straight angle)
But x = 50
=> 50 + y = 180
=> y = 130
The measure of the angle y is 120°.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
The Sum of the three angles is 180 degrees.
33 + 87 + x = 180
x = 180 - 120
x = 60
Now,
x + y = 180
60 + y = 180
y = 180 - 60
y = 120
Thus,
The value of y is 120°.
Learn more about triangles here:
https://brainly.com/question/25950519
#SPJ2
Write an equation for a line parallel to the line y=1/3x-4 through (-3,2)
Answers
Answer:
(-4,-1)
Step-by-step explanation:
If a line must be parallel, then its slope must be the same.
Their points can be different, the slope should be same.
So, y = 1/3x - 4
=> We find the slope of the equation:
=> Slope = the number with which "x" is multiplied
=> Slope of this equation = 1/3
So, we need to find the point that makes a slope of 1/3 from (-3, 2)
=> Slope = y/x - y1/x1
=> 1/3 = -3/2 - y1/x1
=> y1/x1 = -3/2 - 1/3
=> y1/x1 = -3-1 / 2-3
=> y1/x1 = -4/-1
So, the point is (-4,-1)
Troll Inc. has an outstanding issue of perpetual preferred stock with an annual dividend of $9.50 per share. If the required return on this preferred stock is 6.5%, at what price should the stock sell? * a) $104.27 b) $106.95 c) $109.69 d) $146.15 e) None of the above
Answers
Answer:
d) $146.15
Step-by-step explanation:
From the above Question, we are given the following values:
The annual dividend per share of a perpetual preferred stock = $9.50
The required return rate on this preferred stock = 6.5% = 0.06
The selling price of the stock = ??
The formula to calculate the Selling price of the stock =
Annual dividend per share / Required return rate
= $9.5/ 0.065
= $146.15384615
Approximately $146.15
Therefore, the price at which the stock should sell is $146.15.
7 apples and 11 bananas cost $1.47. how much do 2 apples and a banana cost?
Answers
Answer: $0.27
Step-by-step explanation:
7a + 11b = 1.47
7a = 1.47 - 11b
[tex]a=\dfrac{1.47-11b}{7}[/tex]
Make a table. Choose values for b starting at $0.01 and solve for "a".
The value of "a" must terminate at the hundredths place since we are working with money.
You will discover that a = 0.10 and b = 0.07
The cost of 2 apples and 1 banana is:
2a + b
= 2(0.10) + (0.07)
= 0.20 + 0.07
= 0.27
Among the four northwestern states, Washington has 51% of the total population, Oregon has 30%, Idaho has 11%, and Montana has 8%. A market researcher selects a sample of 1000 subjects, with 450 in Washington, 340 in Oregon, 150 in Idaho, and 60 in Montana. At the 0.05 significance level, test the claim that the sample of 100 subjects has a distribution that agrees with the distribution of state populations.
Answers
Answer:
Step-by-step explanation:
From the given information:
the null hypothesis and the alternative hypothesis can be computed as follows:
[tex]\mathbf{H_o:}[/tex] The sample have a distribution that agrees with the distribution of state populations.
[tex]\mathbf{H_1:}[/tex] The sample have a distribution that does not agrees with the distribution of state populations.
The Chi-Square test statistics [tex]\mathbf{X^2 = \dfrac{(Observed \ value - Expected \ value )}{(Expected \ value ) ^2 }}[/tex]
Among the four northwestern states, Washington has 51% of the total population, Oregon has 30%, Idaho has 11%, and Montana has 8%. A market researcher selects a sample of 1000 subjects, with 450 in Washington, 340 in Oregon, 150 in Idaho, and 60 in Montana.
The observed and the expected value can be computed as follows:
States Observed Expected [tex]X^2 = \dfrac{(O- E)^2}{E}[/tex]
Washington 450 0.51 × 1000 = 510
Oregon 340 0.30 × 1000 = 300
Idaho 150 0.11 × 1000 = 110
Montana 60 0.08 × 1000 = 80
Total 1000 1000
For washington :
[tex]X^2 = \dfrac{(O- E)^2}{E}[/tex]
[tex]X^2 = \dfrac{(450 -510)^2}{510}[/tex]
[tex]X^2 = \dfrac{3600}{510}[/tex]
[tex]X^{2}=[/tex] 7.06
For Oregon
[tex]X^2 = \dfrac{(O- E)^2}{E}[/tex]
[tex]X^2 = \dfrac{(340- 300)^2}{300}[/tex]
[tex]X^2 = \dfrac{1600}{300}[/tex]
[tex]X^{2}=[/tex] 5.33
For Idaho
[tex]X^2 = \dfrac{(O- E)^2}{E}[/tex]
[tex]X^2 = \dfrac{(150- 110)^2}{110}[/tex]
[tex]X^2 = \dfrac{1600}{110}[/tex]
[tex]X^2 =14.55[/tex]
For Montana
[tex]X^2 = \dfrac{(O- E)^2}{E}[/tex]
[tex]X^2 = \dfrac{(60- 80)^2}{80}[/tex]
[tex]X^2 = \dfrac{400}{80}[/tex]
[tex]X^2 = 5[/tex].00
The Chi-square test statistics for the observed and the expected value can be computed as follows:
States Observed Expected [tex]X^2 = \dfrac{(O- E)^2}{E}[/tex]
Washington 450 0.51 × 1000 = 510 7.06
Oregon 340 0.30 × 1000 = 300 5.33
Idaho 150 0.11 × 1000 = 110 14.55
Montana 60 0.08 × 1000 = 80 5.00
Total 1000 1000 31.94
The Chi-square Statistics Test [tex]\mathbf{X^2 = 31.94}[/tex]
Degree of freedom = n - 1
Degree of freedom = 4 - 1
Degree of freedom = 3
At 0.05 level of significance, the critical value of :
[tex]X^2_{(df, \alpha) }=X^2_{(3, 0.05)[/tex] = 7.815
Decision Rule: To reject null hypothesis if the test statistics is greater than the critical value
Conclusion: We reject the null hypothesis since test statistics is greater than critical value, therefore, we conclude that there is sufficient information to say that the sample has a distribution that does not agrees with the distribution of state populations.
Jerry has reached 39% of his weekly exercise time goal so far this week if he has exercise for a total of 78 minutes this week. What is his weekly exercise time goal in minutes?
Answers
Answer:
his weekly exercise time goal in minutes = 200 minutes
Step-by-step explanation:
Jerry has reached 39% of his weekly exercise time goal.
so far this week ,he has exercise for a total of 78 minutes this week.
39% of total = 78 minutes
100%= x
X=100*78/39
X=100*2
X= 200 minutes
his weekly exercise time goal in minutes = 200 minutes
What is the length ok a bus if the scale is 0.5 inches to 5 feet and the length of the bus is 4.5 inches
Answers
Answer:
4.5 divided by 0.5=9
9 times 5=45
45 feet
Step-by-step explanation:
Answer:
45 feet
Step-by-step explanation:
Set up a proportion:
[tex]\frac{0.5}{5}[/tex] = [tex]\frac{4.5}{x}[/tex]
Cross multiply:
0.5x = 22.5
x = 45
= 45 feet
The length of the base of a right-angle triangle ABC is 6 cm and the length of the hypotenuse is 10 cm find the area of the triangle
Answers
Answer:
The area of the triangle is 24 [tex]\text{cm}^{2}[/tex].
Step-by-step explanation:
We are given that the length of the base of a right-angle triangle ABC is 6 cm and the length of the hypotenuse is 10 cm.
And we have to find the area of the triangle.
As we know that the area of the triangle is given by the following formula;
Area of the triangle = [tex]\frac{1}{2}\times \text{Base} \times \text{Height}[/tex]
Firstly, we will find the height (perpendicular) of the triangle ABC bu using the Pythagoras Theorem.
[tex]\text{Hypotenuse}^{2} =\text{Perpendicular}^{2} +\text{Base}^{2}[/tex]
[tex]\text{10}^{2} =\text{Perpendicular}^{2} +\text{6}^{2}[/tex]
[tex]100=\text{Perpendicular}^{2} +36[/tex]
[tex]\text{Perpendicular}^{2} =100-36[/tex]
[tex]\text{Perpendicular}^{2} =64[/tex]
[tex]\text{Perpendicular} =\sqrt{64}[/tex] = 8 cm.
Now, the area of the triangle = [tex]\frac{1}{2}\times \text{Base} \times \text{Height}[/tex]
= [tex]\frac{1}{2}\times \text{6} \times \text{8}[/tex]
= 24 [tex]\text{cm}^{2}[/tex]
Hence, the area of the triangle is 24 [tex]\text{cm}^{2}[/tex].
A man drove 12 mi directly east from his home, made a left turn at an intersection, and then traveled 7 mi north to his place of work. If a road was made directly from his home to his place of work, what would its distance be to the nearest tenth of a mile?
Answers
Answer:
13.9 miles
Step-by-step explanation:
If we draw out the way he drove, the drive from his home to the intersection represents the long leg of a right triangle and the short leg can be represented by his drive from the intersection to the workplace.
A road from his home to work would represent the hypotenuse.
Since we know the distances of the legs, we can use the pythagorean theorem to find the hypotenuse, or the distance of the new road.
Plug in the values:
a² + b² = c²
12² + 7² = c²
193 = c²
13.9 = c
= 13.9 miles
Gessenia is having trouble interpreting how the constants within each expression can be represented in the given scenario. Draw a model or write an expression that explains this term.
Answers
Answer:
The height and width of the interior tile = 3·x + 4 - 4 = 3·x and 2·x + 4 - 4= 2·x
Please see attached diagram
Step-by-step explanation:
The given parameters are;
The given rectangular floor tile with width = 3·x + 4 and height = 2·x + 4
Where, x is in centimetres
The interior tile maintains a height to width ration of 2:3
The dimension of the trim border = 2 cm
Therefore;
The relationship between the width and height of the interior and exterior tiles is given as follows
Width of exterior tile = Width of interior tile + 2 × The dimension of the trim border
Which gives;
Width of exterior tile = Width of interior tile + 2 × 2 = Width of interior tile + 4
Height of exterior tile = Height of interior tile + 2 × The dimension of the trim border
Height of exterior tile = Height of interior tile + 2 × 2 = Height of interior tile + 4
Where the interior tile maintains a height to width ration of 2:3, we have;
For a unit length x, The height and the width of the interior tiles are 2·x:3·x
Therefore, for a given height 2·x, the width will be 3·x
Given the width of the exterior tile = 3·x + 4
The height of the exterior tile will then be 2·x + 4 and the width of the exterior tile will be 3·x + 4
The sides ratio of the interior tiles remain 2·x:3·x = 2/3
- 4(-5h-4)=2(10h+8) *
Answers
Answer:
0
Step-by-step explanation:
We need to solve the given expression for the value of h.
- 4(-5h-4)=2(10h+8)
Opening brackets on both sides of the above equation
+20h+4=20h+16
Taking h terms on the one side and the constants on the another side
20h-20h=16-4
0=20
It means that the value of - 4(-5h-4)=2(10h+8) is equal to 0.
find compound amount annually of p=4000,time=3/2 and rate =10% solve it step wise.
Answers
Step-by-step explanation:
Hey, there!!
Principal (p) = 4000
Time = 3/2= 1.5 yrs.
rate = 10%
Now, we have formula,
[tex]c.a = p \times {(1 + \frac{r}{100}) }^{t} [/tex]
Putting their values,
[tex]ca = 4000\times {(1 + \frac{10}{100} )}^{1.5} [/tex]
[tex]ca =4000 \times {(1 + 0.1)}^{1.5} [/tex]
[tex]ca = 4000 \times 1.153689[/tex]
Simplifying them we get,
C.A = 4614.75
Hope it helps...