The orthogonal projection of [tex]\vec{V}[/tex] =[−7−9] onto the line L through [26] and the origin is given by the vector [-69/10 -207/10].
What is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.
To find the orthogonal projection of a vector [tex]\vec{V}[/tex] onto a line L, we need to follow these steps:
Find a vector [tex]\vec{n}[/tex] that is orthogonal to the line L.
Find the projection of [tex]\vec{v}[/tex] onto [tex]\vec{n}[/tex] . This projection will be a scalar.
The orthogonal projection of [tex]\vec{v}[/tex] onto L is the vector that is obtained by multiplying the scalar projection of [tex]\vec{v}[/tex] onto [tex]\vec{n}[/tex] by the unit vector in the direction of L.
Let's apply these steps to the problem at hand:
Step 1: Find a vector [tex]\vec{n}[/tex] that is orthogonal to the line L.
The line L passes through [2 6] and the origin, so we can find the direction vector of the line by subtracting the two points:
[tex]\vec{d}[/tex] = [2 6]−[0 0]=[2 6].
To find a vector that is orthogonal to [tex]\vec{d}[/tex], we can take the cross product of [tex]\vec{d}[/tex]with the vector [0 0 1]:
[tex]\vec{n}[/tex] = [tex]\vec{d}[/tex] × [0 0 1] = [−6 2 0].
Step 2: Find the projection of [tex]\vec{v}[/tex]onto [tex]\vec{n}[/tex] .
The projection of [tex]\vec{v}[/tex] onto [tex]\vec{n}[/tex] is given by the formula:
proj n v = ( [tex]\vec{v}[/tex] · [tex]\vec{n}[/tex] ) / || [tex]\vec{n}[/tex] ||² * [tex]\vec{n}[/tex]
where · denotes the dot product and || [tex]\vec{n}[/tex] || is the magnitude of [tex]\vec{n}[/tex] .
Substituting the values we have:
proj n v = ([-7 -9] · [-6 2 0]) / ||[-6 2 0]||² * [-6 2 0]
= (-54 + (-18)) / (36 + 4) × [-6 2 0]
= -72/40 × [-6 2 0]
= [-27 9 0]/5
Step 3: The orthogonal projection [tex]\vec{v}[/tex] onto L is given by:
proj L v = (proj n v · [tex]\vec{d}[/tex] / || [tex]\vec{d}[/tex] ||²) × [tex]\vec{d}[/tex] / || [tex]\vec{d}[/tex] ||
where || [tex]\vec{d}[/tex] || is the magnitude of [tex]\vec{d}[/tex] .
Substituting the values we have:
proj L v = ([−27 9 0]/5 · [2 6]/(2² + 6²)) * [2 6]/(2² + 6²)
= -207/40 * [2 6]
= [-69/10 -207/10]
Therefore, the orthogonal projection of [tex]\vec{v}[/tex] =[−7−9] onto the line L through [26] and the origin is given by the vector [-69/10 -207/10].
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1/2(2x squared + 17x + 30)
Answer: 14
Step-by-step explanation:
Answer: x^2 + 17x/2 + 15
Step-by-step explanation:
i promise this is right
convert 180⁰ in to grades
Answer: 9/10
Step-by-step explanation:
Evaluate the expression for = 0. 6. Write your answer as a decimal or whole number. –20 + 18. 5u =
The expression -20 + 18.5u, when u is 0.6, in a decimal or whole number is equal to -8.9.
To evaluate the expression -20 + 18.5u when u = 0.6, we simply substitute 0.6 in place of u and simplify using the order of operations (PEMDAS).
-20 + 18.5u = -20 + 18.5(0.6) (substitute 0.6 for u)
-20 + 11.1 = -8.9 (simplify using multiplication first and then addition/subtraction)
Therefore, the value of the expression when u = 0.6 is -8.9.
The order of operations is a set of rules that dictate the order in which mathematical operations should be performed to avoid ambiguity and ensure that calculations are carried out correctly. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (performed from left to right), and Addition and Subtraction (also performed from left to right).
In this case, we first multiply 18.5 and 0.6, giving us 11.1. Then, we subtract 20 from 11.1, resulting in -8.9.
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6)
The value of Tony's investment was $1140 on January 1st. On this date
three years later, his investment was worth $1824. The average rate of
change for this investment was $19 per
(1) day
(2) month
(3) quarter
(4) year
Answer:
Step-by-step explanation:
Average rate of change = (Ending value - Beginning value) / Time elapsed
Using the formula for the average rate of change, we get:
(1824 - 1140) / 1095 = $0.55 per day
(1824 - 1140) / 36 = $19 per month
(1824 - 1140) / 12 = $54 per quarter
(1824 - 1140) / 3 = $228 per year
Therefore, the average rate of change for Tony's investment was $19 per month.
Find the values of c that make f continuous everywhere: x² – ² f(x) CX + 9 smaller c = if < 15 if x > 15 larger c = Use at least 3 decimal places in your answers. Submit Question 2 -5 4 -3 -2 1 2 3 4 5 1 -2 3 -4 -5+ Use the graph of f(x) above to estimate the value of f'(-2) to one decimal place. f'(-2) = Question Help: P Viden 1 d. 6+ 5 4 3 2 1 -6 -5 -4 -3 -2 2 3 4 5 -Z -1 5 6 -2 ده -4 -5 -6+ a In the graph above the slope of the tangent at 2 is
To find the values of c that make f continuous everywhere, Finally, from the graph above, it looks like the slope of the tangent at x = 2 is around 1.
For x < 15, the function is given by x² - c*x + 9. To ensure continuity at x = 15, we need to find the limit of the function as x approaches 15 from both sides:
lim x→15- (x² - c*x + 9) = 15² - c*15 + 9 = 201 - 15c
lim x→15+ (x² - c*x + 9) = 15² - c*15 + 9 = 201 - 15c
For continuity at x = 15, we need these two limits to be equal, so we set them equal to each other:
201 - 15c = 201 - 15c
Solving for c, we get c = 13.4 (rounded to 3 decimal places).
For x > 15, the function is given by x² - c*x + 9. To ensure continuity at x = 15, we need to find the limit of the function as x approaches 15 from both sides:
lim x→15- (x² - c*x + 9) = 15² - c*15 + 9 = 201 - 15c
lim x→15+ (x² - c*x + 9) = 15² - c*15 + 9 = 201 - 15c
For continuity at x = 15, we need these two limits to be equal, so we set them equal to each other:
201 - 15c ≤ 15 Solving for c, we get c ≥ 12.9 (rounded to 3 decimal places).
Therefore, the values of c that make f continuous everywhere are 13.4 ≤ c ≤ 12.9.
To estimate the value of f'(-2), we can look at the slope of the tangent line at x = -2 on the graph. From the graph, it looks like the slope of the tangent at x = -2 is around -2.5. Rounding to one decimal place, we estimate f'(-2) to be -2.5.
Finally, from the graph above, it looks like the slope of the tangent at x = 2 is around 1.
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in a sample of 178 students at an australian university that introduced the use of plagiarism-detection software in a number of courses, 53 students indicated a belief that such software unfairly targets students. does this suggest that a majority of students at the university do not share this belief? test appropriate hypotheses at level 0.05.
a) The appropriate hypothesis testing are states as [tex]H_0 : p = 0.50[/tex]
[tex]H_a : p > 0. 50 [/tex]
b) The p-value for z-test is equals to the 0.000. Also, p-value < α.
c) Conclusion: Null hypothesis is rejected and there is evidence to support that more than 50% do not belief that such software unfairly targets students.
We have a sample of at an australian university that introduced the use of plagiarism-detection software.
Sample size = 178
Number of students who belief that such software unfairly targets student = 53
a) Null and alternative hypothesis are stated here as for right tailed t test.
[tex]H_0 : p = 0.05 [/tex]
[tex]H_a : p > 0.05[/tex]
sample proportion for students who does not belief that such software unfairly targets student [tex]\hat p = \frac {178- 53 }{178} [/tex] = 0.71
Now, test-statistic : [tex]t = \frac { \hat p - p} {\sqrt{ \frac{ p( 1- p)}{n}}}[/tex]
Substitute all the known values in above formula, [tex]= \frac {0.71 - 0.05} {\sqrt{ \frac{ 0.05( 1- 0.05)}{178}}}[/tex]
=> t = 41.25
b) Now, using Excel, the p-value for z
= 41.25 is 0.000. So, p-value < 0.05
Therefore, the Null hypothesis is rejected here.
c) Conclusion: there is evidence to support the claim that more than 50% do not belief that such software unfairly targets students.
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Complete question:
in a sample of 178 students at an australian university that introduced the use of plagiarism-detection software in a number of courses, 53 students indicated a belief that such software unfairly targets students. does this suggest that a majority of students at the university do not share this belief? test appropriate hypotheses at level 0.05.
a) State appropriate hypothesis
b) find p-value
c) draw conclusion
using definition of derivative:lim as h approaches 0f(a+h) - f(a) / h
Using the definition of the derivative, we have:
f'(a) = lim (h -> 0) [(f(a+h) - f(a)) / h]
We're asked to use the definition of the derivative, which includes the terms:
limit, h, f(a+h), f(a), and the fraction f(a+h) - f(a) / h.
The definition of the derivative of a function f(x) at a specific point x=a is given by:
f'(a) = lim (h -> 0) [(f(a+h) - f(a)) / h]
f(a+h) represents the value of the function f(x) at the point (a+h).
f(a) represents the value of the function f(x) at the point a.
f(a+h) - f(a) calculates the difference in the function values at these two points.
h is the small change in the x-coordinate (x-axis) between these two points, and we let h approach 0 to ensure we're finding the instantaneous rate of change.
(f(a+h) - f(a)) / h represents the average rate of change between the points (a, f(a)) and (a+h, f(a+h)).
By taking the limit as h approaches 0, we find the instantaneous rate of change at the point x=a, which is the derivative of the function f(x) at x=a.
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How many teaspoons are there in 6 milliliters?
Hint: 1mL≈0.2tsp
Round your answer to the nearest tenth.
Answer: 1.2
Step-by-step explanation:
0.2 times 6 is 1.2
Prueba de unidad Stacia necesita3 9bombillas para cada3candelabros que ella hace Completa la tabla usando razones equivalentes. Número de bombillas Número de candelabros 39 3 4 10 Informar d
The simplified ratio is 3 light bulbs for every 1 chandelier.
How to explain the ratioIt should be noted that to find equivalent ratios, we need to multiply or divide both the numerator and denominator of the ratio by the same number.
In this case, the ratio is 9 light bulbs for every 3 chandeliers, which can be simplified by dividing both the numerator and denominator by 3:
9 light bulbs ÷ 3 = 3 light bulbs
3 chandeliers ÷ 3 = 1 chandelier
So the simplified ratio is 3 light bulbs for every 1 chandelier.
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Stacia needs 9 light bulbs for every 3 chandeliers she makes Complete the table using equivalent ratios.
SOMEONE PLEASE HELP I NEED THE ANSWER NOW AND RIGHT NOW PLEASEEEEE!!!!!!
Answer:
B
Step-by-step explanation:
Its easy
Find the exact value of cos (2theta), given tan A = -8/15, and theta lies in Quadrant II.
Please show steps and thank you in advance!
The value of cos (2tetha) is 161/289
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
sin(tetha) = opp/hyp
cos(tetha) = adj/hyp
tan(tetha) = opp/adj
Therefore if tan(tetha) = -8/15, therefore opposite is 8 and adj is 15
hyp = √8²+15²
= √ 64+225
= √ 289
= 17
therefore cos (tetha) = 8/17 and since theta is in second quadrant, cos tetha will be negative
cos (tetha) = -15/17
cos²(tetha) = 225/289
sin(tetha) = 8/17
sin²(tetha) = 64/289
cos(2tetha) = cos²(tetha) -sin²(tetha)
= 225/289 - 64/289
= 161/289
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Quiz Active
Does anyone know the answer
Answer:c the third one
Step-by-step explanation: because i did it!
What is the area of this polygon? Enter your answer in the box. units?
The area of the polygon containing the given triangle and rectangle is 45 square units.
What exactly is a rectangle?
A rectangle is a quadrilateral having four straight sides, four right angles, and parallel and equal-length opposing sides. A rectangle's opposing sides are also congruent, which implies they have the same length.
The formula A = lw gives the area of a rectangle, where A is the area, l is the length, and w is the width. A rectangle's perimeter is determined by the formula P = 2l + 2w, where P is the perimeter.
Now,
To find the area of the polygon containing the triangle and rectangle, we need to find the individual areas of the triangle and rectangle, and then add them together.
The area of a triangle
A = (1/2)bh
where b= base and h = height. Substituting the given values, we get:
A_triangle = (1/2)(9)(6) = 27 square units
The area of a rectangle is
A = lw
where l = length and w = width. Substituting the given values, we get:
A_rectangle = (9)(2) = 18 square units
Therefore, the total area of the polygon is:
A_polygon = A_triangle + A_rectangle
A_polygon = 27 + 18
A_polygon = 45 square units
Therefore, the area of the polygon containing the given triangle and rectangle is 45 square units.
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what is the measure of one exterior angle of a polygon with 26 number of sides? round to one decimal place
Answer: The sum of the exterior angles of any polygon is 360 degrees.
The measure of one exterior angle of a regular polygon with n sides is given by the formula:
360/n
For a polygon with 26 sides, the measure of one exterior angle is:
360/26 = 13.8 degrees (rounded to one decimal place)
Step-by-step explanation:
in testing hypotheses, which of the following would tend to be evidence in favor of the alternative hypothesis? a. a large p -value. b. a large level of significance. c. a small level of significance. d. a small p -value.
In testing hypotheses, when p-value ≤ alpha (not is significant region) would be evidence in favor of the alternative hypothesis. So, option( a) is right answer.
Hypothesis testing is a statistical procedure for deciding whether the results of a research study support a particular theory which applies to a population. Steps to do hypothesis testing are
Specify the Null Hypothesis.Specify the Alternative Hypothesis.Set the Significance Level (a)Calculate the Test Statistic and Corresponding P-Value.Drawing a Conclusion.Now, we have to draw condition where the conclusion in favour of alternative hypotheses.
If the p-value is lower than or equal to significance level ( a) then reject the null hypothesis, and make the conclusion that supports the potential change. If the p-value is greater than significance level(a) then we fail to reject the null hypothesis, and the conclusion is that we have to support the null hypothesis.Hence, option(a) is right answer for favour alternative hypothesis.
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5x+3(8-1)=30 help me lol
Answer:
1.8
Step-by-step explanation:
5x+3(8-1)=30
5x+24-3=30
5x+21=30
5x=9
x=9/5 or 1 4/5 or 1.8
if we want to estimate the population mean time for previews at movie theaters with a margin of error of minute, what sample size should be used? assume confidence.
The recommended sample size for estimating the population mean time for previews at movie theaters with a margin of error of one minute and a confidence level of 95% would be n = 1.
To determine the sample size needed to estimate the population mean time for previews at movie theaters with a margin of error of one minute, we would need to know the confidence level desired. The confidence level is the level of certainty we want to have in our estimate.
Let's assume a confidence level of 95%, which is commonly used in many statistical analyses. This corresponds to a Z-score of 1.96, which is the critical value for a 95% confidence level in a standard normal distribution.
The formula for calculating the sample size needed for estimating a population mean with a given margin of error and confidence level is:
n = ( [tex]Z^2[/tex] * [tex]σ^2[/tex] ) / [tex]E^2[/tex]
where:
n = sample size
Z = Z-score for the appropriate level of confidence
σ = standard deviation of the population (if known)
E = margin of error
Since the population standard deviation (σ) is not given, we will assume it is unknown and use a conservative estimate of 0.5 as a typical standard deviation for movie theater preview times.
Plugging in the values into the formula:
n = ( [tex]1.96^2[/tex] * [tex]0.5^2[/tex] ) / [tex]1^2[/tex]
n = (3.8416 * 0.25) / 1
n = 0.9604 / 1
n ≈ 0.9604
As sample sizes must be whole numbers, we round up to the nearest whole number to ensure we have enough sample size to meet the desired margin of error and confidence level.
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To estimate the population mean time for previews at movie theaters with a margin of error of one minute and a certain confidence level, we need to use the formula for sample size calculation.
To estimate the population mean time for previews at movie theaters with a margin of error of 1 minute, you'll need to calculate the sample size. Assuming you want a certain confidence level, you'll use the following formula:
n = (Z^2 * σ^2) / E^2
Where:
- n is the sample size
- Z is the Z-score, which depends on the desired confidence level (e.g., 1.96 for 95% confidence)
- σ is the population standard deviation (you'll need to have an estimate of this value)
- E is the margin of error (1 minute in this case)
Once you have the estimated standard deviation, you can plug the values into the formula and calculate the sample size required to achieve the desired margin of error and confidence level.
Since we do not know the standard deviation of the population, we can use a conservative estimate of 5 minutes as the standard deviation. For a 95% confidence level, the z-score is 1.96. Substituting these values into the formula, we get:
n = (1.96^2 * 5^2) / (1^2) = 96.04
Rounding up, we can say that a sample size of at least 97 previews would be needed to estimate the population mean time for previews at movie theaters with a margin of error of one minute and a 95% confidence level.
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Your Stats teacher tells you your test score was the 3rd quartile for the class. Which is true?
I. You got 75% on the test.
II. Youcan'treallytellwhatthismeanswithoutknowingthestandarddeviation.
III. You can't really tell what this means unless the class distribution is nearly Normal.
A store is having a sale, so an employee marks down some coats from $86.88 to $65.16. What is the discount (as a percent)?
Answer:The discount would be 25%.
Step-by-Step explanation:
1.In order for us to find out the discount we need to find how much the original price got cut off.Let’s use 86.88-65.16 the answer would be 21.72.
2.Now for us to find the discount we need to find out what part of a hundred is the discount.Let’s use 86.88/21.72 the answer would be 4.
3.So now we have a fourth of a hundred and a fourth of a hundred would be 25%.
Discount given=25%=21.72
Solve the quadratic equation x² +9x = 0 by
factoring the GCF.
Answer: x=0 and x=-9
Step-by-step explanation:
4 thumb drives and 1 compact disk have a total capacity of 18 gigabytes. 3 compact disks and 4 thumb drives have a total capacity of 22 gigabytes. Find the capacity of 1 thumb drive (x) and the capacity of 1 compact disk (y)
The capacity of 1 thumb drive is 4 gigabytes and the capacity of 1 compact disk is 2 gigabytes.
What is the capacity of 1 thumb drive and 1 compact disk?The first step is to form the system of equations that represent the information in the question:
4x + y = 18 equation 1
4x + 3y = 22 equation 2
The elimination method would be used to determined the required values.
Subtract equation 1 from equation 2
2y = 4
y = 4/2
y = 2
Substitute for y in equation 1: 4x + 2 = 18
4x = 18 - 2
4x = 16
x = 16/4
x = 4
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Help on both problems pls
Answer:
DE = √21
x = 10
Step-by-step explanation:
4)
AC is bisected by BX
AC/2 = 8/2 = 4 = AB
BX² + AB² = AX²
3² + 4² = AX²
AX = 5 = radius of the circle
DE² = DX² - EX²
DE² = 5² - 2² = 25 - 4 = 21
DE = √21
6)
x² = (11-5)² + 8² = 36 + 64 = 100
x = √100 = 10
x = 10
Paula comió un tercio de una pizza, Sofia un cuarto y Isabella el sexto. ¿Cuánto queda de pizza para Nicole?
3. How are the areas of the shaded
triangle and the rectangle related?
Select all that apply.
10 in.
4 in.
A The area of the rectangle is twice
the area of the shaded triangle.
The area of the shaded triangle is
twice the area of the rectangle.
The area of the rectangle is
one-half the area of the shaded
triangle.
The area of the shaded triangle is
one-half the area of the rectangle.
The area of the shaded triangle
is the same as the area of the
rectangle.
Based on the given information, the correct statement is: The area of the rectangle is twice the area of the shaded triangle.
What is the rectangle about?The shaded triangle is a part of the rectangle, as indicated by the given dimensions of 10 in. and 4 in. The shaded triangle is formed by one of the shorter sides of the rectangle and a diagonal line connecting the opposite corner of the rectangle to the midpoint of that shorter side.
Since the area of the rectangle is given by the formula length × width, the area of the rectangle is 10 in. × 4 in. = 40 square inches.
On the other hand, the area of the shaded triangle is given by the formula 1/2 × base × height, where the base is the length of the shorter side of the rectangle (4 in.) and the height is the length of the longer side of the rectangle (10 in.) divided by 2, since the triangle only occupies half of the height of the rectangle.
So, the area of the shaded triangle is 1/2 × 4 in. × (10 in./2) = 1/2 × 4 in. × 5 in. = 10 square inches.
Comparing the area of the rectangle (40 square inches) to the area of the shaded triangle (10 square inches), we can see that the area of the rectangle is indeed twice the area of the shaded triangle. Therefore, the correct statement is "The area of the rectangle is twice the area of the shaded triangle."
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The scale factor is applies ____ for linear quantities, _____ for two-dimensional quantities, and ___________ for 3-dimensional quantities.
The scale factor is applied uniformly for linear quantities, quadratically for two-dimensional quantities, and cubically for three-dimensional quantities.
The scale factor is a term used in geometry to describe a number or conversion factor that is used to increase or decrease a figure's size without altering its shape1. It is used to increase or decrease the size of an object1. The scale factor can be calculated if the dimensions of the original figure and the dimensions of the dilated (increased or decreased) figure are known1.
The scale factor is applied uniformly for linear quantities, quadratically for two-dimensional quantities, and cubically for three-dimensional quantities.
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1/ 3 is the difference in the gierls that have blue eyes and brown eyes
How to solve for the differenceLet's first find the difference in fractions between the number of girls with brown eyes and the number of girls with blue eyes.
Brown eyes: 7/12
Blue eyes: 1/4
To subtract these fractions, we need to find a common denominator, which in this case is 12. So, we'll convert the fractions to have the same denominator:
7/12 - (3/3)*(1/4) = 7/12 - 3/12
Now, subtract the fractions:
(7 - 3)/12 = 4/12
Simplify the fraction:
4/12 = (1/3)*(4/4) = 1/3
So, 1/3 more girls have brown eyes than blue eyes.
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Help I don't understand.
Using the given percentage we can see that the minimum and maximum numbers are:
N- = 967
N+ = 1,150
How to get the minimum and maximum amounts?The total number of students is 3,650, and we know that the average percentage is 29% ± 2.5%
The minimum value is what we get when we use the minus sign:
29% - 2.5% = 26.5%
The 26.5% of 3,650 is:
N- = (0.265)* 3,650 = 967
The maximum value is what we get when we use the plus sign:
29% + 2.5% = 31.5%
The 31.5% of 3,650 is:
N+ = (0.315)*3,650 = 1,150
These are the two values.
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25% off original price! The original price of a trampoline is $68. What is the sale price?
Answer: To find the sale price of the trampoline, you have to subtract 25% or a quarter of the original price ($68) from the original price ($68)
Step-by-step explanation:
To find a quarter of 68, you can simply divide this by 4 and now you have a quarter of the original price, $68. 68/4 = 17
Then you subtract a quarter of the original price from the original price.
68-17= sales price
68-17= 51
Sales Price = $51
Hope this helps :D
Please help me area parallelograms
The required area of the given parallelogram is 9yd² respectively.
What is Parallelogram?A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry.
A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.
If one of the angles in a parallelogram is a right angle, then all four angles must also be right angles.
A four-sided figure is a trapezoid if it has at least one angle of a different measure in addition to at least one right angle.
So, the formula for the area of a parallelogram is:
A=bh
Now, insert values as follows:
A = bh
A = 9/2 * 2
A = 4.5*2
A = 9yd²
Therefore, the required area of the given parallelogram is 9yd² respectively.
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low securitymedium securitymaximum securitytotalatlanta7016070300los angeles100150150400detroit155100245500total3254104651,200what is the appropriate degrees of freedom for this test?
Using the given data, we have r = 4 and c = 3. Therefore, the degrees of freedom would be (4-1)(3-1) = 6.
Explanation
The given data is in the form of a table, which represents the number of facilities in different locations with varying levels of security. To determine the appropriate degrees of freedom for this test, we need to know the type of statistical analysis that is being performed.
Since the question does not provide any context or information about the statistical analysis, we cannot determine the appropriate degrees of freedom. It is possible that the degrees of freedom may not even be relevant to the analysis being performed.
However, if we assume that a chi-square test is being conducted to determine whether there is a significant association between the location and the security level of facilities, then the appropriate degrees of freedom would be (r-1)(c-1), where r is the number of rows and c is the number of columns in the table.
In summary, the appropriate degrees of freedom for this test would be 6 if a chi-square test is being conducted to determine the association between the location and the security level of facilities.
To learn more about of chi-square test: brainly.com/question/31136907
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