There is 0.17% of the time is Judy idle.
It will take 25 minutes on average, does a student spend waiting in line.
The waiting line on average is 4.1 customers.
The probability that an arriving student will find at least one other student waiting in line is 0.68.
Given students arrive at the Administrative Services Office at an average of one every 6 minutes, and their requests take on average 5 minutes to be processed.
The service counter is staffed by only one clerk, Judy gumshoes, who works eight hours per day.
Assume Poisson arrivals and exponential service times.
ProbabilityIt was said in the question Students arrive at the Administrative Services Office at an average of one every 15 minutes which means that:
λ = 60/6 = 10customers/hr
μ = average of 5 minutes = 60/5 = 12customers/hr
1) What percentage of time is Judy idle?
The percentage when Judy was idle = 1- λ/μ = 1- 0.83= 0.17
%Service time = 0.83
%idle time = 0.17
There is 0.17% of time is Judy idle.
2) How much time, on average, does a student spend waiting in line?
A student spends waiting in line then we make use of the formula below:
λ /μ(λ-μ )
= 0.41 × 60
= 25 minutes
It will take 25 minutes on average, does a student spend waiting in line.
3) How long is the waiting line on average?
To calculate How long the waiting line is on average;
average waiting time x arrival rate = 0.41hrs x 10 customers/hr = 4.1 customers
The waiting line on average is 4.1 customers.
What is the probability that an arriving student will find at least one other student waiting in line?
P1( Probability of having a customer to attend to) = 0.17 x 0.83 = 0.141
P2( Probability of having 2 customer to attend to) = 0.17 x 0.83 x 0.83 = 0.117
The probability of finding at least one customer = 1 -[ po + p1]
= 1 - 0.17 - 0.141 = 0.68
The probability that an arriving student will find at least one other student waiting in line is 0.68.
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Select the graph that matches the system of inequalities. 2x – y ≤ 3 x – 2y ≥ –2
Answer:
Step-by-step explanation:
Graph A
out of 139 7th graders, 86 voted math as their favorite subject. what percent is this?
Answer:
61.9%
Step-by-step explanation:
percent = part/whole × 100%
part = 86
whole = 139
percent = 86/139 × 100%
percent = 61.9%
Answer:
The percent is:
61.87%
Step-by-step explanation:
86 / 139 = 0.6187
0.6187 * 100 = 61.87%
3. RETIREMENT Mr. Ram has $410,000 in a
retirement account that earns 3.85%
simple interest each year.
Find the amount
of interest earned after 5 years.
Lets turn 3.85% into a decimal first. Multiply 0.0385 with 410,000 which gives you 15785. Add that to 410,000 which gives you 425785. Multiply 3.85 by 425785. Repeat that process 5 times until you get the amount of interest earned after 5 years.
16. 21) Thex- andy-axes are the asymptotes of a hyperbola that passes through the point(2,2). Its equation is a) x2−y2=0
b) xy=4
c) y2−x2=0
d) x2+y2=4
The equation of the hyperbola with given x and y axes will be x² + y² = 4 that is option D is correct.
The hyperbola x² + y² = 4 is a standard form of the equation for a hyperbola centered at the origin, which means that the hyperbola passes through the point (0,0). However, the given information states that the hyperbola passes through the point (2,2). This can be achieved by shifting the hyperbola to the right and up by 2 units, resulting in the equation (x-2)² + (y-2)² = 4.
The asymptotes of a hyperbola are the lines that the hyperbola approaches but never touches as it extends to infinity. The asymptotes of a hyperbola centered at the origin are the x-axis and y-axis. Since this hyperbola has been shifted to the right and up by 2 units, the asymptotes are the x-axis and y-axis shifted by 2 units in the same direction. Therefore, the x- and y-axes are the asymptotes of this hyperbola.
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Anthony the anteater requires 1800 calories each day. He gets 1 calorie from every
50 ants that he eats. If he sticks his tongue out 150 times per minute and averages 2
ants per lick, how many hours will it take for him to get 1800 calories?
Answer: 5 hours
Step-by-step explanation:
1800cal/day
a= ants
50a= 1 cal
150 licks per minute, 2 ants per lick--- 2*150 = 300 ants per minute
6*50a= 1 cal*6
-- 300a = 6cal
The anteater can get a avg of 6 calories per minute.
6*60 = 360
We can make a equation:
x =calories
360x = 1800
360/360x = 1800/360
x = 5
It would take the anteater a total of 5 hours to withdraw 1800 calories from ants. This is 300*60*5 ants!
To check:
360(5)=1800
1800=1800
Please help!! Determine the measure of the exterior angle.
Answer:
[tex]92.05^{\circ}[/tex]
Step-by-step explanation:
By the exterior angle theorem, the answer is [tex]m\angle Y+m\angle Z=92.05^{\circ}[/tex].
Answer:
A
Step-by-step explanation:
exterior angle = sum of the other two angles
63.25 + 28.8
92.05°
The cost of fountain drinks at Hot Dog
Hut.
volume
(fluid ounces)
16
20
30
Double Jeop-
cost
($)
$1.49
$1.59
$1.89
Eraser
No
x2
Does this scenario represent a proportional
relationship?
1
Yes
2
Answer:
No (not a proportional relationship)
Step-by-step explanation:
The cost of fountain drinks at Hot Dog Hut:
[tex]\begin{array}{|c|c|}\cline{1-2} \sf Volume & \sf Cost \\\sf \sf (fluid\;ounces) & \sf(\$) \\\cline{1-2} \vphantom{\dfrac12}16& 1.49\\\cline{1-2} \vphantom{\dfrac12}20&1.59 \\\cline{1-2} \vphantom{\dfrac12}30& 1.89\\\cline{1-2} \end{array}[/tex]
A proportional relationship is one in which two quantities vary directly with each other.
Calculate the rate of change of the ordered pairs.
Rate of change between (30, 1.89) and (20, 1.59):
[tex]\implies \dfrac{1.89-1.59}{30-20}=\dfrac{0.3}{10}=0.03[/tex]
Rate of change between (20, 1.59) and (16, 1.49):
[tex]\implies \dfrac{1.59-1.49}{20-16}=\dfrac{0.1}{4}=0.025[/tex]
As the rates of change are different (not constant), the relationship is not proportional.
Note: The graph of a proportional linear relationship is a line that passes through the origin (0, 0).
A bus is going 44 miles an hour from one town to another. The bus arrives 7 minutes late. How many miles apart are the two towns?
Answer:
Step-by-step explanation:
let the distance be x miles
the difference in time taken between two towns = 7 minutes
44 - x = 49
x = 49 - 44
x = 5 miles
Therefore , the distance between two towns is 5 miles .
You go to a party with 500 guests. What is the probability that exactly one other guest has the same birthday as you? Calculate this exactly and also approximate by using the Poisson PMF.
The probability that exactly one other guest has the same birthday as you is 0.3483.
How does one determine probability?The number of possible outcomes is divided by the total number of possible outcomes to determine probability. Odds are not the same as probability. Odds are calculated by dividing the chance of a given event by the probability that it won't.
How do probability and an example work?The likelihood of success is a measure of probability. the number of potential outcomes. For instance, the chance of flipping a coin and obtaining heads is 1 in 2, as there is only one way to acquire a head and there are a total of 2 possible outcomes (a head or tail). We express P(heads) = 12.
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Find the sum of 6.34 × 1019 and 2.246 × 1017.
8.586 × 1019
6.36246 × 1036
6.36246 × 1019
8.586 × 1036
The correct answer would be C, 6.36246 × 1019
pLEASE!
a) If 3/5 of the 595 students are seventh graders, and 5/8 of them participated in the
competition, about how many seventh graders participated in the competition?
Describe the process you used to find your answer. (2 points)
b) If 2/5 of the 595 students are eighth graders, and 7/8 of them participated in the
competition, about how many eighth graders participated in the competition?
Describe the process you used to find your answer. (2 points).
c) About how many total students participated? Describe the process you used to
find your answer. (2 points)
3/5 of 595 students are 7th graders:
3/5*595 = 3*(595/5) = 3*119 = 357 students5/8 of them participated in the competition:
5/8*357 = 5*357/8 = 1785/8 = 223 1/8 ≈ 223 studentsPart B2/5 of the 595 students are 8th graders:
2/5*595 = 2*(595/5) = 2*119 = 238 students7/8 of them participated in the competition:
7/8*238 = 7*238/8 = 1666/8 = 208 2/8 ≈ 208 studentsPart CAbout how many total students participated?
Find the sum of participated students from parts A and B:
223 + 208 = 431 studentsHelp quick!! What is the sum of the interior angles of a regular polygon with 5 sides? I think it’s D but I’m still confused.
Answer:
D) 540
Step-by-step explanation:
he sum of the interior angles of a polygon can be found using the formula (n - 2) * 180 degrees, where n is the number of sides in the polygon. In this case, we are given that the polygon has 5 sides, so we can plug this into the formula to find the sum of its interior angles:
(5 - 2) * 180 degrees = 3 * 180 degrees = 540 degrees
Therefore, the sum of the interior angles of a regular polygon with 5 sides is 540 degrees.
The library has 65400 art books and 9600 science books. What part of all the books are science books.
Answer: it should be 12.8 percent
Step-by-step explanation:
Let f(x)=8-2x. Find f(-4)
Answer:
f(-4)=16
Step-by-step explanation:
since f(x)=8-2x and we are asked to find f(-4),
we plug -4 in for x and we get
[tex]f(-4)=8-2(-4)[/tex]
[tex]2*-4=-8[/tex]
[tex]8-(-8)=8+8[/tex]
[tex]8+8=16[/tex]
[tex]f(-4)=16[/tex]
Determine which integer in the solution set will make the equation true
Answer:
s= 2
Step-by-step explanation:
4s - 14 = -6 Add 14 to both sides
4s - 14 + 14 = -6 + 14 Simplify
4s = 8 Divide both sides by 4
s = 2
Check
4x - 14 = -6
4(2) - 14 = -6
8 - 14 = -6
-6 = -6
First, we should the leave the variable [tex]s[/tex] on the left side of the equation.
[tex]4s-14=-6[/tex][tex]4s=-6+14[/tex][tex]4s=8[/tex]Divide both sides by [tex]4.[/tex]
[tex]\frac{4s}{4}=\frac{8}{4}[/tex][tex]s=2[/tex]Conclusion:
Consequently, the element [tex]2[/tex] in the given set is the only real solution of this equation. What we need to do in such questions is to leave the unknown alone. Since the power of the variable [tex]s[/tex] of our unknown is [tex]1[/tex] we can only find [tex]1[/tex] root, respectively.
0=-16r^2-50
algebra question
[tex]r=\frac{5i\sqrt{2} }{4}, -\frac{5i\sqrt{2} }{4}[/tex] or simply just say ± [tex]\frac{5i\sqrt{2} }{4}[/tex].
Hope this helps!
Answer:
[tex]r=\dfrac{5\sqrt{2}}{4}}\:i\:,\quad \;\;r=-\dfrac{5\sqrt{2}}{4}}\:i[/tex]
Step-by-step explanation:
To solve the given equation, rearrange the equation to isolate r.
Given equation:
[tex]0=-16r^2-50[/tex]
Add 16r² to both sides of the equation:
[tex]0+16r^2=-16r^2-50+16r^2[/tex]
[tex]16r^2=-50[/tex]
Divide both sides of the equation by 16:
[tex]\dfrac{16r^2}{16}=\dfrac{-50}{16}[/tex]
[tex]r^2=-\dfrac{25}{8}[/tex]
[tex]\textsf{For\;\:}x^2=f\left(a\right)\textsf{\:the\:solutions\:are\:\:}x=\pm\sqrt{f\left(a\right)}[/tex]
[tex]r=\pm\sqrt{-\dfrac{25}{8}}[/tex]
[tex]\textsf{Apply\;the\:radical\:rule:}\;\:\sqrt{-a}=\sqrt{a}\sqrt{-1}[/tex]
[tex]r=\pm\sqrt{\dfrac{25}{8}}\sqrt{ -1}[/tex]
[tex]\textsf{Apply\;the\:imaginary\:number\:rule:}\;\:\sqrt{-1}=i[/tex]
[tex]r=\pm\sqrt{\dfrac{25}{8}}\:i[/tex]
[tex]\textsf{Apply\;the\:radical\:rule:}\:\:\sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}},\:\quad \:a\ge 0,\:b\ge 0[/tex]
[tex]r=\pm\dfrac{\sqrt{25}}{\sqrt{8}}\:i[/tex]
Simplify the numerator and denominator of the fraction:
[tex]r=\pm\dfrac{5}{2\sqrt{2}}\:i[/tex]
Rationalise the denominator by multiply the numerator and denominator by √2:
[tex]r=\pm\dfrac{5\cdot\sqrt{2}}{2\sqrt{2}\cdot \sqrt{2}}\:i[/tex]
[tex]r=\pm\dfrac{5\sqrt{2}}{4}}\:i[/tex]
Therefore, the solutions to the given equation are:
[tex]r=\dfrac{5\sqrt{2}}{4}}\:i\:,\quad \;\;r=-\dfrac{5\sqrt{2}}{4}}\:i[/tex]
What is 3 1/5 divided by 5/8
Answer:
128/25
Step-by-step explanation:
(3 1/5) / (5/8) =
(3 + 1/5) / (5/8) =
(15/5 + 1/5) / (5/8) =
(15+1)/5 / (5/8) =
16/5 / (5/8) =
16/5 * 8/5 = ==> dividing by a number is equaled to multiplying by its
reciprocal: the reciprocal of 5/8 is 8/5.
(16 * 8) / (5*5) = 128/25
A music teacher had noticed that some students went to pieces during exams. He wanted to test whether this performance anxiety was different for people playing different instruments. He took groups of guitarists. drummers and pianists (variable = 'Instru') and measured their anxiety (variable = 'Anxiety') during the exam. He also noted the type of exam they were performing (in the UK, musical instrument exams are known as 'grades' and range from 1 to 8 ). He wanted to see whether the type of instrument played affected performance anxiety when accounting for the grade of the exam. Which of the following statements best reflects what the effect of GRADE in the table tells us? Tests of Between-Subjects Effects a.
R
Squared
=.466
(Adjusted
R
Squared
=.438)
The grade of exam had a significant relationship with the level of anxiety experienced. The grade of exam did not have a significant relationship with the level of anxiety experienced. The type of instrument played had a significant relationship with the grade of exam that was being taken. The type of instrument played did not have a significant relationship with the grade of exam that was being taken.
The statement that best reflects the grade is "The variances of anxiety scores were roughly the same in the different groups of musicians."
The term variances refers the mean squared difference between each data point and the center of the distribution measured by the mean
Here we have given that a music teacher had noticed that some students went to pieces during exams and he wanted to test whether this performance anxiety was different for people playing different instruments. While he took groups of guitarists. drummers and pianists (variable = 'Instru') and measured their anxiety (variable = 'Anxiety') during the exam. Here he also noted the type of exam they were performing (in the UK, musical instrument exams are known as 'grades' and range from 1 to 8 ).
Now, we need to find the statements best reflects what the effect of GRADE in the table tells us.
While we looking into he given question we have identified that this performance anxiety was different for people playing different instruments.
So, based on this concept the correct statement id option (c).
Because, here the variances of anxiety scores were roughly the same in the different groups of musicians where if Levine's test of equality of error variances is non-significant (sig > .05) then there is equality of variances.
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Please complete this table:
Answer:
Solutions: (0,2) and (3,1)
Not a solution (6,4)
Step-by-step explanation:
x + 3y = 6
0 + 3y = 6
3y = 6
y = 2
(0,2)
x + 3y = 6
3 + 3y = 6
3y = 3
y = 1
(3,1)
x + 3y = 6
6 + 3(4) = 6
6 + 12 = 12
18≠12
(6,4)
How many integers are solutions of the inequality |x|<4
Answer:
Infinite number of integers that satisfy the inequality |x|<4.
Step-by-step explanation:
The absolute value of a number indicates its distance from 0 on the number line. Therefore, the inequality |x|<4 indicates that x is less than 4 units away from 0 on the number line. Because there are an infinite number of integers on the number line, there are an infinite number of integers that satisfy the inequality |x|<4.
5. A table of values and the plot of the residuals for the line of best fit are shown.
x
The point that the line estimate best fits is the point x = 6 with a residual of 0.18
How to interpret the residuals of the line of best fit?
We are given a table which displays the point and then their residual values are also added from the graph to get;
The table is as follows:
x y Residual Absolute Residual value
1 10 0.4 0.4
2 8 -1.125 1.125
2.5 9.5 0.625 0.625
4 8 -0.25 0.25
5 8 0.2 0.2
6 7.5 0.18 0.18
7.2 7 0.19 0.19
8.5 6 -0.25 0.25
The residual value is negative if the point on the scatter plot lies below the regression line and it is positive if the point on the scatter plot lies above the regression line.
Formula for the residual value is;
Residual value = Actual y-value(i.e. on scatter plot) - Observed y-value
Now, the residual value is farthest from the line if the absolute value of the residual value is highest.
Hence, the highest absolute residual value is: 1.125
The point that it best fits is the lowest absolute value which is 0.18
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An article in Optical Engineering reported on use of an optical correlator to perform an experiment by varying brightness and contrast. The useful range of gray levels characterizes the resulting modulation. The data are shown below:
Brightness (%): 54 61 65 100 100 100 50 57 54
Contrast (%): 56 80 70 50 65 80 25 35 26
Useful range (ng): 96 50 50 112 96 80 155 144 255
USE MINITAB TO CARRY OUT THE FOLLOWING:
Fit a multiple linear regression model to these data.
Estimate σ2.
Predict the useful range when brightness = 80 and contrast = 75.
Test for significance of regression using α = 0.05. What is the p-value for this test?
Find a 95% confidence interval and prediction interval when brightness = 80 and contrast = 75.
Analyze R2.
Analyze the residuals.
Analyze using Best Subsets.
On analyzing the data given in question we get to know that the sensitivity is negative.
Our function is 40 + 24 x 2.4 /1 + 4x to the point.
For the time being, our first task is to determine the sensitivity, which is the derivative of our discovery. The quotient rule, whose derivative we shall be utilizing, says that the derivative of F org equals G f prime minus f g prime all over g squared.
The bottom function is one plus four times the top function's derivative, or 40.4 times. 40 has a derivative of zero.
When a light source is x cm away from a light probe, the light's intensity is measured as y microwatts per square cm. The outcomes are displayed as ordered pairs( x , y).
So we just need to multiply 24 x240.4.
Using the power rule, we can reduce the 0.4 point to 9.6 x to the minus 0.6.
We subtract one from the initial exponents minus the top function 40 + 24 x to the point for times the bottom function's derivative 10 So we have the derivative of four additional 40.4 by the power rule,
we bring down the 0.4 multiplied by four against 1.6 next to the minus 0.6, and we divide all of that by one plus four x to the 40.4 squared.
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You wish to buy a home for $315,000. You have a 30 year mortgage at 3.75% annual interest rate. If you put 10% down, what will be the monthly payment you make to the bank?
0.9(315 000) * 30(0.0375)
= 283 500 * 1.125
= 318 937.5 (total amount of 30 year mortgage)
= 318 937.5 / 360
= $885.94 (monthly payment)
CHECKING:315 00 * 0.1 = 31 500 (amount of down)
315 000 - 31 500 = 283 500 (balance without interest)
283 500 * 30(0.0375) = 318 937.5 (balance with interest)
318 937.5 / 30(12) = 885.94
Therefore, the monthly payment will be $885.94
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The scale on a map states that 1 cm represents 8 miles. How many miles would be represented by 32cm on the map?
Answer:
256 miles
Step-by-step explanation:
1 cm = 8 miles
32 cm = x miles
32 * 8 = 256 miles
A group of hikers park their car at a trail head and hike into the forest to a campsite. The next morning, they head out on a hike from their campsite walking at a steady rate. The graph shows their distance in miles, d, from the car on the day of their hike after h hours.
The campers will be 40 miles from their car after 12 hours.
Given :
A group of hikers park their car at a trail head and hike into the forest to a campsite. The next morning, they head out on a hike from their campsite walking at a steady rate. The graph shows their distance in miles, d, from the car on the day of their hike after h hours .
We can pick two points on the line graphed and substitute the coordinates into this formula to find the slope:
slope m = y2 - y1 / x2 - x1
Choosing the points (0,4) and (2,10), we get:
m = 4 - 10 / 0 - 2
= -6 / -2
= 6 / 2
= 3
We can substitute the point (0,4) and the slope into y = mx + b and solve for "b":
4 = 3 * 0 + b
b = 4
Then, the equation of this line is:
y = 3x + 4
Since the distance in miles is represented on the y-axis and the time in hours is represented on the x-axis. we can rewrite the equation as:
d = 3h + 4
if h = 12
d = 3 * 12 + 4
= 36 + 4
= 40 miles
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Full question :
A group of hikers park their car at a trail head and hike into the forest to a campsite. The next morning, they head out on a hike from their campsite walking at a steady rate. The graph shows their distance in miles, d, from the car on the day of their hike after h hours.How many miles will the campers be from their car after 12 hours?
Can someone explain how to do this? Normally i’d know how to do it but I’m clueless. HELP!!!
The value of the missing sides assuming both triangles are similar will be 18 inches.
What is the similarity?Similar figures are those figures which are identical in shape, but not necessarily in size.
Two squares with sides of 10 and 5 are similar because their shape is exact but the size is different.
As per the given two triangle,
Suppose the length of missing side is x inches.
Suppoes both triangles are similar by AAA rule.
The ratio of corresponding sides will be same thus,
x/6 = 12/4
x = 3 x 6 = 18 inches
Hence "If both triangles are comparable, the value of the missing sides will be 18 inches".
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MATHEMATICAL CONNECTIONS Graph the lines on the same coordinate plane.
Answer:
see attached for a graphcentroid: (0, 2)Step-by-step explanation:
You want the graphs of the given lines, and the centroid of the triangle they form.
y1 = 3x -4y2 = 3/4x +5y3 = -3/2x -4GraphIt works well to start by plotting the y-intercept of each equation, then using the slope to identify the "rise" and "run" to another point on the line. Then the line can be drawn through the points.
y1: y-intercept = (0, -4); additional point 3 up and 1 over: (1, -1).y2: y-intercept = (0, 5); additional point 3 up and 4 over: (4, 8).y3: y-intercept = (0, -4); additional point 3 down and 2 over: (2, -7). This one is more easily plotted in the reverse direction, 3 up and 2 to the left: (-2, -1).VerticesThe graph shows you the points of intersection of the lines are ...
(-4, 2), (4, 8), (0, -4) . . . . . . . . . the last is the y-intercepts of y1 and y3
CentroidThe centroid coordinates are the average of the vertex coordinates, their sum divided by 3.
centroid = ((-4, 2) +(4, 8) +(0, -4))/3 = (-4+4+0, 2+8-4)/3 = (0, 6)/3
centroid = (0, 2)
__
Additional comment
The slope of each line is the x-coefficient in the equation. That slope is the ratio of "rise" (change in y) to "run" (change in x) for the line. It is often convenient to draw a graph by finding points on the line counting the grid squares for rise and run.
A sample of 60 account balances of a credit company showed an average balance of $1151. The sample standard deviation was $112. You want to determine if the mean of all account balances is significantly different from $1120. Use a 0.01 level of significance. Choose the t-statistic and the appropriate conclusion.
Group of answer choices
t = 2.144 ; fail to reject the null hypothesis
t = 2.019 ; fail to reject the null hypothesis
t = 2.019 ; reject the null hypothesis
t = 2.144 ; reject the null hypothesis
Find the p value also and explain how to get it.
The t-statistic for this hypothesis test is 2.019 and the appropriate conclusion is that we fail to reject the null hypothesis.
To find the p-value, we can use the t-distribution calculator and enter in the degrees of freedom (df = 59), the t-statistic (t = 2.019), and the significance level (alpha = 0.01). The resulting p-value is 0.055, which is greater than the significance level of 0.01. Therefore, we are unable to reject the null hypothesis.
The formula for the t-statistic can be used to calculate the t-statistic for this hypothesis test:
t = (1151 - 1120) / (112 / √60)
t = 2.019
Therefore, the t-statistic for this hypothesis test is 2.019 and the appropriate conclusion is that we fail to reject the null hypothesis.
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find all values of the scalar k for which the two vectors are orthogonal. (enter your answers as a comma-separated list.) u
Therefore, the value of the scalar k for which the two vectors are orthogonal is k =1/5.
What is vector ?In physics and mathematics, the term "vector" is used to refer, informally, to certain quantities that cannot be described by a single number or to certain constituents of vector spaces.
Here,
When the dot product of two vectors is zero, those two vectors are said to be orthogonal.
Dot product:
Let's assume we have the two vectors a and b.
a = (1,2) (1,2)
b = (2,3) (2,3)
Their dot item is:
a.b = (1,2). (1,2).
(2,3) = 1*2 + 2*3 = 8
Regarding this issue:
u = (2,3) (2,3)
(k + 1, k - 1) = v
So
u.v = (2,3). (2,3).
(k + 1, k - 1) = 2k + 1, 3k - 1, or 2k + 2, 3k - 3, or 5k - 1
The vectors must be orthogonal for the dot product to equal 0.
So:
=> 5k -1 =0
=> 5k =1
=> k =1/5
Therefore , the value of the scalar k for which the two vectors are orthogonal is k =1/5.
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can someone pleaseee help me with this math question
Answer:
(a) To find the range of the function f(x), we need to consider all possible values of x in the range -7 ≤ x ≤ 7 and x ≠ -5. For each value of x, we can evaluate the function to find the corresponding value of f(x). Then, we can find the minimum and maximum values of f(x) in this range to determine the range of the function.
For example, if x = -7, then the function will return a value of 2 - 12/(-7) + 5 = 2 + 2 + 5 = 9. If x = 7, then the function will return a value of 2 - 12/7 + 5 = 2 - 1 + 5 = 6.
We can see that the minimum value of the function is 6, which is achieved when x = 7, and the maximum value of the function is 9, which is achieved when x = -7. Therefore, the range of the function is {6, 9}.
(b) To find the inverse of the function f(x), we need to switch the x and y values in the function definition to obtain a new function g(y) such that g(f(x)) = x for all values of x in the domain of the original function.
In this case, the inverse of the function f(x) is given by g(y) = (2 - y + 5)/(-12). This inverse function is defined for all values of y in the range {6, 9}, which is the range of the original function.
To find the value of f^-1(0), we can plug in 0 for y in the inverse function g(y) to obtain g(0) = (2 - 0 + 5)/(-12) = -1/12. Therefore, f^-1(0) = -1/12.