In graphing a trigonometric function, how does one establish which are the EXTREMUM coordinates and which are the MIDLINE INTERCEPTION coordinates. I can find the x values and the y values but do not know which X goes with which Y and the graphs end up incorrect! It is EXTREMELY frustrating. How do I discern which is which!!!!! Thank You.
Answers
Answer:
If I getting the question correctly, your doubt is the order of the values you get after doing the math. I mean, you can do the calculations, but in the end, you don't form the coordinate pairs correctly, that's why I understand from your question. So, here is what you need to do.
One way to graph is by using the definitions of those kinds of functions. For example, let's say we want to find the points to draw the function: [tex]y=sin(x)[/tex]
Remember that trigonometric functions have a specific period, that means, their drawing repeats over and over again after a certain number. That period is [tex]2 \pi[/tex], that means this number represents a cycle.
So, the main thing you need to do is to pick a starting point to then, draw the curve according to the [tex]2 \pi[/tex] period.
Now, we know that sine functions intercept the origin of the coordinate system, as you can observe in the image attached, there you can see that from the origin you draw those waves making sure you intercept the x-axis at every [tex]\pi[/tex] number. In the end, you will have a sine function.
On the other hand, if you want to have a chart with all x-values and y-values. First, you need to set x-values: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5. Then, you need to find each y-values for each of them.
Now, you have to draw a chart value, to keep in other the coordinate pairs, that way, you'll have the correct pairs at the end.
For example, for [tex]x=-5[/tex], we get [tex]y=-0.09[/tex], that means in the chart value, you are gonna form the pair [tex](-5, -0.09)[/tex], and now you have your first point of the drawing. Then, you keep repeating the process until you complete all the chart values.
As you can imagine, you're going to get really small decimal numbers, that's why I explained to you the first method, it's faster and easier.
Related Questions
amanda teaches the art of quilling to 4 students. These students each teach art of quilling to 4 other students. If this process continues for 5 generation after amanda, BLANK people other than amanda will know the art of qiulling
Answers
Answer:
1024
Step-by-step explanation:
4 * 4 * 4 * 4 * 4
NEED HELP ASAP!!
What is the equation of the line that is parallel to the
given line and has an x-intercept of -3?
O y = x + 3
O y = ?X + 2
Oy=-3x + 3
y=-3x+2
Answers
Answer:
B
Step-by-step explanation:
The equation of the line that is parallel to the given line and has an x-intercept of -3 is y= 2/3x + 2.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
We have a graph.
So, slope of line in graph is
= (-1-1)/ (0.-3)
= -2/ (-3)
= 2/3
and, we know that two parallel line have same slope.
so, the slope of parallel line is 2/3 and the x intercept is -3.
So, the Equation line is y= 2/3 x + b
0 = 2/3 (-3) +b
b= 2
Thus, the required equation is y= 2/3x + 2.
Learn more about Slope here:
https://brainly.com/question/2863474
#SPJ5
Construct a frequency distribution and a frequency histogram for the given data set using the indicated number of classes. Describe any patterns.
Number of classes: 8
Data set: Reaction times (in milliseconds) of 30 adult females to an auditory stimulus.
430 386 352 301 450 291 429 467 454 385 380
373 386 307 321 336 310 413 306 357 514 443
442 326 508 424 386 429 412 418
Answers
Answer:
The histogram for the data is attached below.
Step-by-step explanation:
Arrange the data in ascending order as follows:
S = {291 , 301 , 306 , 307 , 310 , 321 , 326 , 336 , 352 , 357 , 373 , 380 , 385 , 386 , 386 , 386 , 412 , 413 , 418 , 424 , 429 , 429 , 430 , 442 , 443 , 450 , 454 , 467 , 508 , 514}
Compute the range:
[tex]Range=Max.-Min.\\=514-291\\=223[/tex]
Compute the class width:
[tex]Class\ Width =\frac{Range}{No.\ of\ classes}=\frac{223}{8}=27.875\approx 28[/tex]
The classes are as follows:
290 - 318
319 - 347
348 - 376
377 - 405
406 - 434
435 - 463
464 - 492
493 - 521
Compute the frequency distribution as follows:
Class Interval Frequency
290 - 318 5
319 - 347 3
348 - 376 3
377 - 405 5
406 - 434 7
435 - 463 4
464 - 492 1
493 - 521 2
The histogram for the data is attached below.
Help!! It’s much appreciated in this time
Answers
Answer: D. y = (x - 3)² + 2
Step-by-step explanation:
Inverse is when you swap the x's and y's and solve for y.
y = [tex]\sqrt{x-2}[/tex] + 3
Swap: x = [tex]\sqrt{y-2}[/tex] + 3
Solve: x - 3 = [tex]\sqrt{y-2}[/tex]
(x - 3)² = [tex](\sqrt{y-2})^2[/tex]
(x - 3)² = y - 2
(x - 3)² + 2 = y
Please help, much needed. A lot of points
Answers
Answer:
A. -9
Step-by-step explanation:
If one of the variables were negative than, it would not be able to equal 2/7.
Gravel is being dumped from a conveyor belt at a rate of 20 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 11 ft high
Answers
Answer:
0.0526ft/minStep-by-step explanation:
Since the gravel being dumped is in the shape of a cone, we will use the formula for calculating the volume of a cone.
Volume of a cone V = πr²h/3
If the diameter and the height are equal, then r = h
V = πh²h/3
V = πh³/3
If the gravel is being dumped from a conveyor belt at a rate of 20 ft³/min, then dV/dt = 20ft³/min
Using chain rule to get the expression for dV/dt;
dV/dt = dV/dh * dh/dt
From the formula above, dV/dh = 3πh²/3
dV/dh = πh²
dV/dt = πh²dh/dt
20 = πh²dh/dt
To calculate how fast the height of the pile is increasing when the pile is 11 ft high, we will substitute h = 11 into the resulting expression and solve for dh/dt.
20 = π(11)²dh/dt
20 = 121πdh/dt
dh/dt = 20/121π
dh/dt = 20/380.133
dh/dt = 0.0526ft/min
This means that the height of the pile is increasing at 0.0526ft/min
If jimmy has 15 apples and give 7 to gohn how many does jimmy have?
Answers
Answer:
Hey there!
Jimmy has 15-7, or 8 apples left.
Hope this helps :)
At what point does the line
Y = -1/2 X + 2 intercept the Y-axis?
A. - 1
B. -1/2
C. 1
D. 2
E. -2
Answers
Answer:
D. 2
Step-by-step explanation:
The y-intercept is when the graph crosses the y-axis when x = 0. In that case, simply plug in x as 0:
y = -1/2(0) + 2
y = 2
Therefore, the graph crosses the y-axis at 2.
Answer:
D
Step-by-step explanation:
our equation is y= [tex]\frac{-1}{2}[/tex] x +2
-1/2 is the slope 2 is the y-interceptso the answer is 2
if we want to verify our answer we can follow these steps
the y-intercept is given by calculating the image of 0
y= -1/2*0+2 = 2so it's right
A rectangle has a width of 3/4 inches and a length of 9/10 inches. Another rectangle
is larger but still proportional to the first rectangle. It has a width of 30 inches and a length of 36 what proportion could model this situation
Answers
Answer:
Bigger size / smaller size = 40
Step-by-step explanation:
Notice that we
36 / (9/10) = 30 / (3/4) = 40
Therefore the proportion model would be
Bigger size / smaller size = 40
50 points + brainliest!
Answers
Answer:
( x+2) ^2 = 11
x =1.32,-5.32
Step-by-step explanation:
x^2 + 4x -7 = 0
Add the constant to each side
x^2 + 4x -7+7 = 0+7
x^2 + 4x = 7
Take the coefficient of the x term
4
Divide by 2
4/2 =2
Square it
2^2 = 4
Add this to each side
x^2 + 4x +4 = 7+4
Take the 4/2 as the term inside the parentheses
( x+2) ^2 = 11
Take the square root of each side
sqrt( ( x+2) ^2) =±sqrt( 11)
x+2 = ±sqrt( 11)
Subtract 2 from each side
x = -2 ±sqrt( 11)
To the nearest hundredth
x =1.32
x=-5.32
Answer:
[tex](x+2)^2=11[/tex]
[tex]x=-2 \pm \sqrt{11}[/tex]
Step-by-step explanation:
[tex]x^2+4x-7=0[/tex]
[tex]x^2+4x=7[/tex]
[tex]x^2+4x+4=7+4[/tex]
[tex](x+2)^2=11[/tex]
[tex]x+2=\pm\sqrt{11}[/tex]
[tex]x=-2 \pm \sqrt{11}[/tex]
Check whether these statements are wff or not:(a) (p˅q) ∧∼r
Answers
Answer:
It is a well formed formula
Step-by-step explanation:
1 - p,q,r are well formed formulas.
2 - [tex]p \ \lor \ q[/tex] is a well formed formula as well.
3 - [tex]\neg r[/tex] is a well formula as well
4 - [tex](\ p \ \lor \ q) \ \land \ \neg r[/tex] is a well formula as well.
Data was collected for a sample of organic snacks. The amount of sugar (in mg) in each snack is summarized in the histogram below. 2 4 6 8 10 amount of sugar (mg) 180 182 184 186 188 190 192 194 Frequency What is the sample size for this data set?
Answers
Answer:
The sample size is 30.
Step-by-step explanation:
The sample size of a histogram can be calculated by summing up all the frequencies of all the occurrences in the data set
From the question the frequency is given as
Frequency = 2 4 6 8 10
The sample size n =
2 + 4 + 6 + 8 + 10
= 30
Therefore the sample size n of the data set = 30
Identify an equation in point-slope form for the line perpendicular to
y= - 1/3x - 6 that passes through (-1,5).
O A. y + 1 = 3(x - 5)
O B. y + 5 = 1/3(x - 1)
O C. y - 5 = 3(x + 1)
O D. y - 5 = - 1/3(x + 1)
Answers
Answer:
hope you get it....sorry for any mistake calculations
Construct the confidence interval for the population mean mu. c = 0.90, x = 16.9, s = 9.0, and n = 45. A 90% confidence interval for mu is:______.
Answers
Answer:
The 90% confidence interval for population mean is [tex]14.7 < \mu < 19.1[/tex]
Step-by-step explanation:
From the question we are told that
The sample mean is [tex]\= x = 16.9[/tex]
The confidence level is [tex]C = 0.90[/tex]
The sample size is [tex]n = 45[/tex]
The standard deviation
Now given that the confidence level is 0.90 the level of significance is mathematically evaluated as
[tex]\alpha = 1-0.90[/tex]
[tex]\alpha = 0.10[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the standardized normal distribution table. The values is [tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]
The reason we are obtaining critical values for [tex]\frac{\alpha }{2}[/tex] instead of that of [tex]\alpha[/tex] is because [tex]\alpha[/tex] represents the area under the normal curve where the confidence level 1 - [tex]\alpha[/tex] (90%) did not cover which include both the left and right tail while [tex]\frac{\alpha }{2}[/tex] is just considering the area of one tail which is what we required calculate the margin of error
Generally the margin of error is mathematically evaluated as
[tex]MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]MOE = 1.645* \frac{ 9 }{\sqrt{45} }[/tex]
[tex]MOE = 2.207[/tex]
The 90% confidence level interval is mathematically represented as
[tex]\= x - MOE < \mu < \= x + MOE[/tex]
substituting values
[tex]16.9 - 2.207 < \mu < 16.9 + 2.207[/tex]
[tex]16.9 - 2.207 < \mu < 16.9 + 2.207[/tex]
[tex]14.7 < \mu < 19.1[/tex]
QUESTION 4 (10 MARKS)
A retired couple requires an annual return of $2,000 from investment of $20,000. There are 3
options available:
(A) Treasury Bills yielding 9%;
(B) Corporate bonds 11%;
Junk Bonds. 130%
How much should be invested in each to achieve their goal? Give 3 sets of options that can
achieve their goal.[10 Marks]
Answers
Answer:
(T, C, J) = (in dollars)
(10000, 10000, 0),
(15000, 4915.97, 84.03),
(18181.82, 1680.67, 137.51)
Step-by-step explanation:
There are a number of ways to approach this question. We have chosen an approach that determines the investments required to achieve interest rate targets.
__
For an overall interest rate of I, the proportion that must be invested at rate I1 < I < I2 is ...
proportion at I1 = (I2 -I)/(I2 -I1)
Similarly, the proportion that must be invested at I2 is what's left over. It can be computed similarly:
proportion at I2 = (I -I1)/(I2 -I1)
__
We want an overall interest rate of $2000/$20000 = 10%.
Given available interest rates of 9%, 11%, and 130%, we need to have investments at a rate lower than 10% and at a rate higher than 10%.
If we use only the options for 9% and 11% (no junk bonds), then we can compute ...
proportion at 9% = (11 -10)/(11 -9) = 1/2
proportion at 11% = (10 -9)/(11 -9) = 1/2
1st Option:
$10,000 in treasury bills; $10,000 in corporate bonds
__
Suppose we want to achieve a 13% return on our investments at 11% and 130%. Then the proportion invested at 9% will use this value for I2:
proportion at 9% = (13 -10)/(13 -9) = 3/4
Of the remaining 1/4 of the money, we can achieve a 13% return by mixing the investments like this:
proportion at 11% = (130 -13)/(130 -11) = 117/119
proportion at 130% = (13 -11)/(130 -11) = 2/119
2nd option:
$20,000 × 3/4 = $15,000 in treasury bills
$5000 × 117/119 = $4,915.97 in corporate bonds
The remaining amount, $84.03 in junk bonds
__
Let's suppose we want a 20% return on our investment in junk bonds and corporate bonds. Then the proportion of the money invested at 9% will be ...
proportion at 9% = (20 -10)/(20 -9) = 10/11
And the proportion at 11% will be ...
proportion at 11% = (130 -20)/(130 -11) = 110/119 . . . (of the remaining 1/11 of the funds)
3rd option:
$20,000 × 10/11 = $18,181.82 in treasury bills
$1,818.18 × 110/119 = $1,680.67 in corporate bonds
The remaining amount, $137.51 in junk bonds
_____
Additional comment
The most that could be invested in Junk Bonds is $165.29. If the remainder is invested in Treasury Bills, then the overall return will be $2000. (You could consider this to be a 4th option.)
Help ASAP it’s Math I need this rightnow 31 points
Answers
Answer:
AC (b)
Step-by-step explanation:
Since 10 is half of 20, you have to find the variable closest to the middle. Which in this case, is C. So, your awnser is B. (AC)
Answer:
[tex]\boxed{\sf C}[/tex]
Step-by-step explanation:
The whole segment is [tex]\sf \sqrt {20}[/tex], we can see that AD is approximately 75% of the segment AE.
[tex]75\%*\sqrt{20} = 3.354102[/tex]
[tex]\sqrt{10}= 3.162278[/tex]
AC is almost half of AE.
[tex]\frac{\sqrt{20} }{2} = 2.2360679775[/tex]
[tex]\sqrt{10} = 3.16227766017[/tex]
It isn’t close to the option C.
Determine the t critical value(s) that will capture the desired t-curve area in each of the following cases.
a. Central area = 0.95, df = 10
b. Central area = 0.95, df = 20
c. Central area = 0.99, df = 20
d. Central area = 0.99, df = 60
e. Upper-tail area = 0.01, df = 30
f. Lower-tail area = 0.025, df = 5
Answers
Answer:
a) Central area = 0.95, df = 10 t = (-2.228, 2.228)
(b) Central area = 0.95, df = 20 t= (-2.086, 2.086)
(c) Central area = 0.99, df = 20 t= ( -2.845, 2.845)
(d) Central area = 0.99, df = 60 t= (-2.660, 2.660)
(e) Upper-tail area = 0.01, df = 30 t= 2.457
(f) Lower-tail area = 0.025, df = 5 t= -2.571
Step-by-step explanation:
In this question, we are to determine the t critical value that will capture the t-curve area in the cases below;
We can use the t-table for this by using the appropriate confidence interval with the corresponding degree of freedom.
The following are the answers obtained from the table;
a) Central area = 0.95, df = 10 t = (-2.228, 2.228)
(b) Central area = 0.95, df = 20 t= (-2.086, 2.086)
(c) Central area = 0.99, df = 20 t= ( -2.845, 2.845)
(d) Central area = 0.99, df = 60 t= (-2.660, 2.660)
(e) Upper-tail area = 0.01, df = 30 t= 2.457
(f) Lower-tail area = 0.025, df = 5 t= -2.571
when a stone falls freely, the time taken to hit the ground varies as the square root of the distance fallen. If it takes four seconds th fall 78.4m, find how long would it takefor a stone to fall 500m
Answers
Answer:
The stone would take approximately 10.107 seconds to fall 500 meters.
Step-by-step explanation:
According to the statement of the problem, the following relationship of direct proportionality is built:
[tex]t \propto y^{1/2}[/tex]
[tex]t = k\cdot t^{1/2}[/tex]
Where:
[tex]t[/tex] - Time spent by the stone, measured in seconds.
[tex]y[/tex] - Height change experimented by the stone, measured in meters.
[tex]k[/tex] - Proportionality constant, measured in [tex]\frac{s}{m^{1/2}}[/tex].
First, the proportionality constant is determined by clearing the respective variable and replacing all known variables:
[tex]k = \frac{t}{y^{1/2}}[/tex]
If [tex]t = 4\,s[/tex] and [tex]y=78.4\,m[/tex], then:
[tex]k = \frac{4\,s}{(78.4\,m)^{1/2}}[/tex]
[tex]k \approx 0.452\,\frac{s}{m^{1/2}}[/tex]
Then, the expression is [tex]t = 0.452\cdot y^{1/2}[/tex]. Finally, if [tex]y = 500\,m[/tex], then the time is:
[tex]t = 0.452\cdot (500\,m)^{1/2}[/tex]
[tex]t \approx 10.107\,s[/tex]
The stone would take approximately 10.107 seconds to fall 500 meters.
Evan wants to build a rectangular enclosure for his animals. One side of the pen will be against the barn, so he needs no fence on that side. The other three sides will be enclosed with wire fencing. If Evan has 1000 feet of fencing, you can find the dimensions that maximize the area of the enclosure. a) Let w be the width of the enclosure (perpendicular to the barn) and let l be the length of the enclosure (parallel to the barn). Write an function for the area A of the enclosure in terms of w . (HINT first write two equations with w and l and A . Solve for l in one equation and substitute for l in the other). A(w) = ___________ b) What width would maximize the area? w = __________ c) What is the maximum area? A = _________ square feet
Answers
Answer: A. A=(1000-2w)*w B. 250 feet
C. 125 000 square feet
Step-by-step explanation:
The area of rectangular is A=l*w (1)
From another hand the length of the fence is 2*w+l=1000 (2)
L is not multiplied by 2, because the opposite side of the l is the barn,- we don't need in fence on that side.
Express l from (2):
l=1000-2w
Substitude l in (1) by 1000-2w
A=(1000-2w)*w (3) ( Part A. is done !)
Part B.
To find the width w (Wmax) that corresponds to max of area A we have to dind the roots of equation (1000-2w)w=0 ( we get it from (3))
w1=0 1000-2*w2=0
w2=500
Wmax= (w1+w2)/2=(0+500)/2=250 feet
The width that maximize area A is Wmax=250 feet
Part C. Using (3) and the value of Wmax=250 we can write the following:
A(Wmax)=250*(1000-2*250)=250*500=125 000 square feets
6th grade math help me, please :))
Answers
Answer:
[tex]\sf a) \ 2.5\\b) \ 7.5[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{250}{100}[/tex]
[tex]\sf Express \ as \ a \ decimal.[/tex]
[tex]=2.5[/tex]
[tex]\sf Multiply \ 3\% \ with \ 250.[/tex]
[tex]\displaystyle 250 \times \frac{3}{100}[/tex]
[tex]\displaystyle \frac{750}{100}=7.5[/tex]
Simplify the expression . 39*x / 13
Answers
Answer:
3x
Step-by-step explanation:
39*x / 13
39/13 * x
3*x
3x
Answer:
3x
Step-by-step explanation:
We are given the expression:
39*x /13
We want to simplify this expression. It can be simplified because both the numerator (top number) and denominator (bottom number) can be evenly divided by 13.
(39*x /13) / (13/13)
(39x/13) / 1
3x / 1
When the denominator is 1, we can simply eliminate the denominator and leave the numerator as our answer.
3x
The expression 39*x/13 can be simplified to 3x
A candy store called "Sugar" built a giant hollow sugar cube out of wood to hang above the entrance to their store. It took 13.5\text{ m}^213.5 m 2 13, point, 5, start text, space, m, end text, squared of material to build the cube. What is the volume inside the giant sugar cube?
Answers
Answer:
3.375
Step-by-step explanation:
Answer:
3.375
Step-by-step explanation:
Had it on Khan
please help me ☣️☢️☢️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️▫️
Answers
Answer:
acute isosceles triangle
vertex angle, y = 44.0 degrees. (smallest angle)
Step-by-step explanation:
If the sides are in the ratio 4:4:3,
two of the sides have equal lengths, so it is an isosceles triangle.
Also, the sum of square of the two shorter sides is greater than the square of the longest side, so it is an acute triangle.
To find the smallest angle, we draw the perpendicular bisector of the base (side length 3) and form two right triangles.
The base angle x is given by the ratio
cos(x) = 1.5/4 = 3/8
Consequently the base angle is arccos(3/8) = 68.0 degrees.
The vertex angle equals twice the complement of 68.0
vertex angle, y = 2 (90-68.0) = 44.0 degrees. (smallest angle)
Tosh. Inc.'s bonds currently sell for $980 and have a par value of $1,000. They pay a $95 annual coupon and have a 12-year maturity, but they can be called in 3 years at $1,150. What is their yield to call (YTC)?
Answers
Answer:
14.24%
Step-by-step explanation:
We have found that the yield to call (YTC) formula is:
YTC = [C + (F-P) / N] / [(F + P) / 2]
Where:
C = Periodic coupon amount = 95
P = Current Price = 980
F = Redemption amount = 1150
N = time left to redemption = 3
We replace:
YTC = [95 + (1150-980) / 3] / [(1150 + 980) / 2]
YTC = 0.1424
In other words, the yield to call (YTC) is equal to 14.24%
At a deli counter, there are sandwiches with meat and vegetarian sandwiches. Kira is at the counter buying sandwiches for a picnic. In how many ways can she choose sandwiches if fewer than must be vegetarian sandwiches
Answers
Answer:
The number ways to choose between meat and vegetarian sandwiches can be computed using computation technique.
Step-by-step explanation:
There are two types of sandwiches available at the deli counter. The possibility of combinations can be found by computation technique of statistic. It is assumed that order does not matter and sandwiches will be selected at random. The sandwiches can be arranged in any order and number ways can be found by 2Cn.
Find the value of annuity if the periodic deposit is $400 at 4% compounded monthly for 18 years
Answers
Answer:
~820.8$
Step-by-step explanation:
The total money (M) after 18 years could be calculated by:
M = principal x (1 + rate)^time
with
principal = 400$
rate = 4% compounded monthly = 0.04/12
time = 18 years = 18 x 12 = 216 months (because of compounded monthly rate)
=> M = 400 x (1 + 0.04/12)^216 = ~820.8$
Please HELP best answer will receive a BRAINLIEST. Given the probability density function f ( x ) = 1/3 over the interval [ 4 , 7 ] , find the expected value, the mean, the variance and the standard deviation.
Answers
Answer:
[tex] E(X) =\int_{4}^7 \frac{1}{3} x[/tex]
[tex] E(X) = \frac{1}{6} (7^2 -4^2) = 5.5[/tex]
Now we can find the second moment with this formula:
[tex] E(X^2) =\int_{4}^7 \frac{1}{3} x^2[/tex]
[tex] E(X^2) = \frac{1}{9} (7^3 -4^3) = 31[/tex]
And the variance for this case would be:
[tex] Var(X)= E(X^2) -[E(X)]^2 = 31 -(5.5)^2 = 0.75[/tex]
And the standard deviation is:
[tex] Sd(X)= \sqrt{0.75}= 0.866[/tex]
Step-by-step explanation:
For this case we have the following probability density function
[tex] f(x)= \frac{1}{3}, 4 \leq x \leq 7[/tex]
And for this case we can find the expected value with this formula:
[tex] E(X) =\int_{4}^7 \frac{1}{3} x[/tex]
[tex] E(X) = \frac{1}{6} (7^2 -4^2) = 5.5[/tex]
Now we can find the second moment with this formula:
[tex] E(X^2) =\int_{4}^7 \frac{1}{3} x^2[/tex]
[tex] E(X^2) = \frac{1}{9} (7^3 -4^3) = 31[/tex]
And the variance for this case would be:
[tex] Var(X)= E(X^2) -[E(X)]^2 = 31 -(5.5)^2 = 0.75[/tex]
And the standard deviation is:
[tex] Sd(X)= \sqrt{0.75}= 0.866[/tex]
A crew clears brush at a rate 2/3 acre in 2 days. How long will it take the same crew to clear the entire plot of 4 acres?
Answers
Answer:
It takes the crew 12 days to clear the bush.
Step-by-step explanation:
Given clears 2/3 acres / 2 days, or 1/3 acre per day
Time to clear 4 acres
= 4 / (1/3)
= 4 * (3/1)
= 12 days
A table of values of a linear function is shown below. Find the output when the input is N. Type your answer in the space provide
Answers
Answer:
[tex] -3n - 7 [/tex]
Step-by-step explanation:
Considering the linear function represented in the table above, to find what output an input "n" would give, we need to first find an equation that defines the linear function.
Using the slope-intercept formula, y = mx + b, let's find the equation.
Where,
m = the increase in output ÷ increase in input = [tex] \frac{-13 - (-10)}{2 - 1} [/tex]
[tex] m = \frac{-13 + 10}{1} [/tex]
[tex] m = \frac{-3}{1} [/tex]
[tex] m = -3 [/tex]
Using any if the given pairs, i.e., (1, -10), plug in the values as x and y in the equation formula to solve for b, which is the y-intercept
[tex] y = mx + b [/tex]
[tex] -10 = -3(1) + b [/tex]
[tex] -10 = -3 + b [/tex]
Add 3 to both sides:
[tex] -10 + 3 = -3 + b + 3 [/tex]
[tex] -7 = b [/tex]
[tex] b = -7 [/tex]
The equation of the given linear function can be written as:
[tex] y = -3x - 7 [/tex]
Or
[tex] f(x) = -3x - 7 [/tex]
Therefore, if the input is n, the output would be:
[tex] f(n) = -3n - 7 [/tex]
Solve the given systems of equations:
x-y+z=1
-3x+2y+z=1
2x-3y+4z=3
Answers
Answer:
x = 3/2
y = 2
z = 3/2
Step-by-step explanation:
There are multiple methods to solve these. Message me for the method you need to see step by step.