Complete Question:
In P2, find the change-of-coordinates matrix from the basis B = {1 − 3t² , 2+t− 5t² , 1 + 2t} to the standard basis C = {1, t, t²}. Then, write t² as a linear combination of the polynomials in B.
Answer:
The change of coordinate matrix is :
[tex]M = \left[\begin{array}{ccc}1&2&1\\0&1&2\\-3&-5&0\end{array}\right][/tex]
U = t² = 3 [1 − 3t²] - 2 [2+t− 5t²] + [1 + 2t]
Step-by-step explanation:
Let U = {D, E, F} be any vector with respect to Basis B
U = D [1 − 3t²] + E [2+t− 5t²] + F[1 + 2t]..............(*)
U = [D+2E+F]+ t[E+2F] + t²[-3D-5E]...................(**)
In Matrix form;
[tex]\left[\begin{array}{ccc}1&2&1\\0&1&2\\-3&-5&0\end{array}\right] \left[\begin{array}{ccc}D\\E\\F\end{array}\right] = \left[\begin{array}{ccc}D+2E+F\\E+2F\\-3D-5E\end{array}\right][/tex]
The change of coordinate matrix is therefore,
[tex]M = \left[\begin{array}{ccc}1&2&1\\0&1&2\\-3&-5&0\end{array}\right][/tex]
To find D, E, F in (**) such that U = t²
D + 2E + F = 0.................(1)
E + 2F = 0.........................(2)
-3D -5E = 1........................(3)
Substituting eqn (2) into eqn (1 )
D=3F...................................(4)
Substituting equations (2) and (4) into eqn (3)
-9F+10F=1
F = 1
Put the value of F into equations (2) and (4)
E = -2(1) = -2
D = 3(1) = 3
Substituting the values of D, E, and F into (*)
U = t² = 3 [1 − 3t²] - 2 [2+t− 5t²] + [1 + 2t]
6th grade math, help me please :)
Answer:
(14,4) (21, 6) (28,8) If they had six losses, they would have 21 wins
Step-by-step explanation:
According to the information given, for every 7 wins, they lose 2 games. That means in order to finish the table, we have to find multiples of 7 and 2. If they won 14 games, they would have 4 losses. This is because since 14 is twice the value of 7, they would have lost twice the number of games.
The next would be 21 wins since 7x3 is 21 and 6 losses since 2x3 is 6
The last one would be 28 wins (7x4) and 8 losses (2x4)
If they had six losses, they would have 21 wins
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Mandeep Sharma: Attempt 1
Question 1 (2 points)
A scientist records the internal temperature of a kiln that has been turned off for maintenance after
a limestone calcination reaction as 794 °C. He then leaves the room to allow the kiln cool further.
The room temperature is 25°C. An equation that models the temperature of the cooling kiln (T in °C,
t in min) is as follows:
T(t) = 1.0.73l/3.7 + 25
How fast is the reaction cooling rate (%T lost/min) to the nearest whole number?
Your Answer:
Answer
Answer:
c and I will talk to you later today or tomorrow morning and then I will
Step-by-step explanation:
email to you later today to see you and the kids are doing well and that you
In a large school, it was found that 69% of students are taking a math class, 70% of student are taking an English class, and 50% of students are taking both.
A. True
B. False
Answer:
P(Math or English) = 0.89
Step-by-step explanation: This solution will only be applicable if finding the probability that a randomly selected student is taking a math class or an English class.
Lets study the meaning of or , and on probability. The use of the word or means that you are calculating the probability
that either event A or event B happened
Both events do not have to happen
The use of the word and, means that both event A and B have to happened
The addition rules are: # P(A or B) = P(A) + P(B) ⇒ mutually exclusive (events cannot happen
at the same time)
P(A or B) = P(A) + P(B) - P(A and B) ⇒ non-mutually exclusive (if they
have at least one outcome in common)
The union is written as A ∪ B or “A or B”.
The Both is written as A ∩ B or “A and B”
Lets solve the question
The probability of taking Math class 69%
The probability of taking English class 70%
The probability of taking both classes is 50%
P(Math) = 69% = 0.69
P(English) = 70% = 0.70
P(Math and English) = 50% = 0.50
To find P(Math or English) use the rule of non-mutually exclusive
P(A or B) = P(A) + P(B) - P(A and B)
P(Math or English) = P(Math) + P(English) - P(Math and English)
Lets substitute the values of P(Math) , P(English) , P(Math and English)
in the rule P(Math or English) = 0.69 + 0.70 - 0.50 = 0.89
P(Math or English) = 0.89
P(Math or English) = 0.89
This solution will only be applicable if we are to find the probability that a randomly selected student is taking a math class or an English class.
A political scientist wants to prove that a candidate is currently carrying more than 60% of the vote in the state. She has her assistants randomly sample 200 eligible voters in the state by telephone and only 90 declare that they support her candidate. The observed z value for this problem is _______. 4.33 2.33 0.45 -.31 -4.33
Answer:
Z= -4.33
Step-by-step explanation:
Hello!
The study variable is:
X: number of voters that support the candidate out of 200 surveyed voters.
This variable has a binomial distribution, where the "success" is that the voter supports the candidate and the "failure" is that the voter doesn't support the candidate. X~Bi(n;p)
Considering the sample size is large enough, you can apply the Central Limit Theorem and approximate the distribution of the sample proportion to normal: ^p ≈ N(p;[tex]\frac{p(1-p)}{n}[/tex])
Using this distribution you can an approximation to the standard normal distribution: [tex]Z= \frac{p'-p}{\sqrt{\frac{p(1-p)}{n} }}[/tex]≈N(0;1)
Where the sample proportion is ^p= p'= [tex]\frac{x}{n} = \frac{90}{200} = 0.45[/tex]
x= number of successes
n= sample size
The population proportion is p= 0.60
[tex]Z= \frac{0.45-0.60}{\sqrt{\frac{0.60*0.40}{200} }}= -4.33[/tex]
I hope this helps!
Determine the sum of the arithmetic series 6 + 11 + 16 +......
91.
Answer:
873
Step-by-step explanation:
so the equation is: 5x+1
sum is:
[tex] \frac{first \: one \: + \: last \: one}{2} \times quantity \: of \: terms \\ [/tex]
we have 6( 5×1+1) to 91 (5×18+1)
so we have 18 terms
then:
[tex] \frac{91 + 6}{2} \times 18 = 873[/tex]
Identify which quadrant of the coordinate plane the point (−3, 15) lies in.
Answer:
Quadrant II.
Step-by-step explanation:
Quadrant | has positive x and y coordinates.
Quadrant || has negative x and positive y coordinates.
Quadrant ||| has negative x and y coordinates.
Quadrant |V has positive x and negative y coordinates.
Since -3 is negative and 15 is positive, the answer is Quadrant II.
Choose the name of this figure.
A.
line
B.
angle
c.
line segment
D.
ray
Answer:
we dont see aa figure
Step-by-step explanation:
If sin t=0.29 and sin w = 0.43, both t and w are positive, and the angles determined by t and w are in quadrant 2, then which of the following statements is true? Explain your selection
a. t>w
b. w>t
c. cannot be determined
Answer:
a. t>w
Step-by-step explanation:
Sin t= 0.29
t = sin^-1(0.29)
t= 16.86°
Sin w= 0.43
W = sin^-1(0.43)
W= 25.47°
Angles in the second quadrant are positive in sine and they are generally determined by subtracting the initial value from 180°
For t= 180°-16.86°
t = 163.14°
For w = 180°-25.47°
W= 154.53°
163.14°>154.53°
t>w
i need help please!!!
Answer:
1 = 95
2 = 77
3 = 85
4 = 103
Step-by-step explanation:
Inscribed angles are half their arc that their 2 lines intersect.
A line with points (-4.0) and (-3.1)
has a slope of?
Slope is the change in y over the change in x
Slope = (1-0) /( -3 - -4)
Slope = 1/1
Slope = 1
the linear equation y=2x represents the cost y of x pounds of pears. which order pair lies on the graph of the equation? A. (2,4) B. (1,0) C.(10,5) D. (4,12)
Answer:
A. (2, 4)
Step-by-step explanation:
The ordered pairs represent (x, y). Since you have y =2x, this is the same as ...
(x, 2x)
That is, the second number in the pair needs to be twice the first number in the pair. Since you know your times tables, you know that this is not the case for (1, 0), (10, 5) or (4, 12). Those values of x would give (1, 2), (10, 20), (4, 8).
It is the case that you have (x, 2x) for (2, 4).
The point (2, 4) lies on the graph of y = 2x.
The Gold Bar has a trapezium cross-sectional area Gold has a density of 19.3 grams per
Answer: 22.3 quarter
Step-by-step explanation:
Answer:
13.896 kg
Step-by-step explanation:
What is the value of x?
Answer:
x=98°
Step-by-step explanation:
The angles of a triangle must equal 180°.
To get the third angle (G) you must do: 180°-53°-45°
That will give you 82°
Anglr G and angle x create a straight line which is 180°.
so to get the answer you must do 180°-G=x
180°-82°=98°
Therefore x=98°
At what point does the line
Y = 2X + 6 intercept the Y-axis?
A. 2.
B. 8
C. -2
D. 1/6
E. 6
Answer:
E. 6
Step-by-step explanation:
The y-intercept is where the graph crosses the y-axis when x = 0. In that case, simply plug in x as 0:
y = 2(0) + 6
y = 6
Therefore, our graph crosses the y-axis at 6.
Answer: 6
Step-by-step explanation: The equation of this line is written in slope-intercept form which is more commonly known as y = mx + b form.
In this form, the m or the coefficient of the x term represents the slope
of the line and the b or the constant term represents the y-intercept.
We can see that the y-intercept is 6.
A boat that can travel 18 mph in still water can travel 21 miles downstream in the same amount of time that it can travel 15 miles upstream. Find the speed (in mph) of the current in the river.
Hey there! I'm happy to help!
We see that if the river isn't moving at all the boat can move at 18 mph (most likely because it has an engine propelling it.)
We want to set up a proportion where our 21 miles downstream time is equal to our 15 miles upstream time so we can find the speed. A proportion is basically showing that two ratios are equal. Since our downstream distance and upstream distance can be done in the same amount of time, we will write it as a proportion.
We want to find the speed of the river. We will use r to represent the speed of the river. When going downstream, the boat will go faster, so it will have a higher mph. So, our speed going down is 18+r. When you are going upstream, it's the opposite, so it will be 18-r.
[tex]\frac{distance}{speed} =\frac{21}{18+r} = \frac{15}{18-r}[/tex]
So, how do we figure out what r is now? Well, one nice thing to know about proportions is that the product of the items diagonal from each other equals the product of the other items. Basically, that means that 15(18+r) is equal to 21(18-r). This is a very nice trick to solve proportions quickly. We see that we have made an equation and now we can solve it!
15(18+r)=21(18-r)
We use the distributive property to undo the parentheses.
270+15r=378-21r
We subtract 270 from both sides.
15r=108-21
We add 21 to both sides.
36r=108
We divide both sides by 36.
r=3
Therefore, the speed of the river is 3 mph.
You also could have noticed that 18mph to 21 mph is +3, and 18mph to 15 mph -3 in -3 mph, so the speed of the river is 3 mph. That would have been a quicker way to solve it XD!
Have a wonderful day!
Which functions have an axis of symmetry of x = -2? Check all that apply. A. f(x) = x^2 + 4x + 3 B. f(x) = x^2 - 4x - 5 C. f(x) = x^2 + 6x + 2 D. f(x) = -2x^2 - 8x + 1 E. f(x) = -2x^2 + 8x - 2
Answer:
A. f(x) = x^2 + 4x + 3
D. f(x) = -2x^2 - 8x + 1
Step-by-step explanation:
The axis of symmetry is found by h = -b/2a where ax^2 +bx +c
A. f(x) = x^2 + 4x + 3
h = -4/2*1 = -2 x=-2
B. f(x) = x^2 - 4x - 5
h = - -4/2*1 = 4/2 =2 x=2 not -2
C. f(x) = x^2 + 6x + 2
h = -6/2*1 = -3/2 = x=-3/2 not -2
D. f(x) = -2x^2 - 8x + 1
h = - -8/2*-2 = 8/-4 =-2 x=-2
E. f(x) = -2x^2 + 8x - 2
h = - 8/2*-2 = -8/-4 =2 x=2 not -2
Answer:
Hey there! The answer to this question is
A. f(x) = x^2 + 4x + 3
D. f(x) = -2x^2 - 8x + 1
Betty can mow a lawn in 60 minutes. Melissa can mow the same lawn in 30 minutes. How long does it take for both Betty and Melissa to mow the lawn if they are working together? Express your answer as a reduced fraction.
Answer:
20 minutes
Step-by-step explanation:
Melissa works as fast as two Bettys, so working together, they get the job done at the rate 3 Bettys could do it. That time is (60 minutes)/3 = 20 minutes.
Working together, Betty and Melissa can mow the lawn in 20 minutes.
_____
You can also think in terms of mowing rates as lawns per minute. The total mowing rate is ...
Betty's rate + Melissa's rate = (1/60 lawns/min) +(1/30 lawns/min)
= (1/60 +2/60) lawns/min = 1/20 lawns/min
The inverse rate is then ...
20/1 min/lawn
Together, they take 20 minutes to mow 1 lawn.
The Social Justice Club is going to rent a mammoth barbeque to cook the hot dogs for the hot dog sale. After contacting three rental companies in town, you have found out that each one will deliver and pick up their barbeque. The cost of propane is included in the rental. The rental costs are indicated below.
Rental A: $15/h
Rental B: $5/h + 50
Rental C: $9/h + 20
Student selling hot dogs at a table.
Write an equation that models the rental cost, C, for each company.
Graph all three models onto the same set of coordinate axis.
Which rental company should be chosen if you use the barbeque during lunch (11:05 - 12:30) and keep the barbeque to continue sales during the football game that will end about 4:30? Justify your answer.
Which rental company should be chosen if your school lunch hours run from 11:05 - 12:30? Justify your answer.
Which rental company should be chosen if your school returned the barbeque the following day? Justify your answer.
Answer:
(A)Cost of Rental A, C= 15h
Cost of Rental B, C=5h+50
Cost of Rental C, C=9h+20
(B)
i. Rental C
ii. Rental A
iii. Rental B
Step-by-step explanation:
Let h be the number of hours for which the barbeque will be rented.
Rental A: $15/h
Cost of Rental A, C= 15hRental B: $5/h + 50
Cost of Rental B, C=5h+50Rental C: $9/h + 20
Cost of Rental C, C=9h+20The graph of the three models is attached below
(b)11.05-4.30
When you keep the barbecue from 11.05 to 4.30 when the football match ends.
Number of Hours = 4.30 -11.05 =4 hours 25 Minutes = 4.42 Hours
Cost of Rental A, C= 15h=15(4.42)=$66.30 Cost of Rental B, C=5h+50 =5(4.42)+50=$72.10 Cost of Rental C, C=9h+20=9(4.42)+20=$59.78Rental C should be chosen as it offers the lowest cost.
(c)11.05-12.30
Number of Hours = 12.30 -11.05 =1 hour 25 Minutes = 1.42 Hours
Cost of Rental A, C= 15h=15(1.42)=$21.30 Cost of Rental B, C=5h+50 =5(4.42)+50=$57.10 Cost of Rental C, C=9h+20=9(4.42)+20=$32.78Rental A should be chosen as it offers the lowest cost.
(d)If the barbecue is returned the next day, say after 24 hours
Cost of Rental A, C= 15h=15(24)=$360 Cost of Rental B, C=5h+50 =5(24)+50=$170 Cost of Rental C, C=9h+20=9(24)+20=$236Rental B should be chosen as it offers the lowest cost.
I NEED HELP ASAP PLEASE! :)
Answer:
option 1
Step-by-step explanation:
[tex]r=\sqrt{(5\sqrt{2})^{2}+(-5\sqrt{2})^{2} } \\\\=\sqrt{25*2+25*2}\\\\ =\sqrt{50+50}\\\\=\sqrt{100}\\\\=10[/tex]
[tex]x=tan^{-1}(\frac{-5\sqrt{2}}{5\sqrt{2}})\\\\x=tan^{-1} (-1)\\x=\frac{7\pi}{4}[/tex]
[tex]re^{ix}=10e^{i\frac{7\pi}{4}}[/tex]
Please answer this correctly
A sample of 17 patients in a hospital had these hemoglobin readings 112 120 98 55 71 35 99 142 64 150 150 55 100 132 20 70 93 find a 95% confidence interval for the hemoglobin reading for all the patienta in the hospital
Answer:
The 95% confidence interval for the hemoglobin reading for all the patients in the hospital is (72, 112).
Step-by-step explanation:
The (1 - α)% confidence interval for the population mean, when the population standard deviation is not provided is:
[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\cdot \frac{s}{\sqrt{n}}[/tex]
The data provided is:
S = {112, 120, 98, 55, 71, 35, 99, 142, 64, 150, 150, 55, 100, 132, 20, 70, 93}
Compute the sample mean and sample standard deviation as follows:
[tex]\bar x=\frac{1}{n}\sum X=\frac{1}{17}\times[112+120+98+...+93]=92.1176\\\\s=\sqrt{\frac{1}{n-1}\sum (x-\bar x)^{2}}=\sqrt{\frac{1}{17-1}\times 25041.7647}=39.56[/tex]
The critical value of t for 95% confidence level and n - 1 = 16 degrees of freedom is:
[tex]t_{\alpha/2, (n-1)}=t_{0.05/2, 16}=2.120[/tex]
*Use a t-table.
Compute the 95% confidence interval for the hemoglobin reading for all the patients in the hospital as follows:
[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\cdot \frac{s}{\sqrt{n}}[/tex]
[tex]=92.1176\pm 2.120\times\frac{39.56}{\sqrt{17}}\\\\=92.1176\pm 20.3408\\\\=(71.7768, 112.4584)\\\\\approx (72, 112)[/tex]
Thus, the 95% confidence interval for the hemoglobin reading for all the patients in the hospital is (72, 112).
given that 3*6=12 and 2*5=9, then a*b may be defined as
Answer:
I noticed a pattern:
3 * 2 + 6 = 12 and 2 * 2 + 5 = 9
This means that a*b = 2a + b.
As Devine rides her bike, she picks up a nail in her front tire. The height, h, of the nail from the ground as she rides her bike over time, t, in seconds, is modelled by the equation below: As Devine rides her bike, she picks up a nail in her front tire. The height, h, of the nail from the ground as she rides her bike over time, t, in seconds, is modelled by the equation below:f(x)=-14 cos(720(t-10))+14
Using the equation, determine the following. Show your work for part marks.
a) What is the diameter of the bike wheel?
b) How long does it take the tire to rotate 3 times?
c) What is the minimum height of the nail? Does this height make sense? Why?
Step-by-step explanation:
a) The diameter of the wheel is the distance between the minimum and maximum. In other words, it's double the amplitude.
d = 2 × 14 = 28.
b) The period of the wave is:
720 = 2π / T
T = π/360
So the time for 3 revolution is:
3T = π/120
3T = 0.026 seconds
c) The minimum here is when cosine = 1.
h(t) = -14(1) + 14
h(t) = 0
This makes sense, since the minimum height is when the nail is at the bottom of the wheel, or at the ground.
Please answer this correctly without making mistakes
Answer:
A digit that makes this sentence true is 4.
Step-by-step explanation:
Since the first digit in the number to the left is 3, you simply have to find a digit greater than 3. Here are the possibilities:
4
5
6
7
8
and
9
Out of any of these you can choose, I chose 4.
9514 1404 393
Answer:
3, or any greater digit
Step-by-step explanation:
Suppose the digit is 'd'. Then the value on the right is ...
69.436 +100d
Subtracting the value on the left, we want the difference greater than 0.
69.436 +100d - 352.934 > 0
100d -293.498 > 0 . . . . simplify
100d > 293.498 . . . . . . . add 293.498
d > 2.93498 . . . . . . . . . . divide by 100
That is d is any single digit greater than 2.9. Those digits are ...
d ∈ {3, 4, 5, 6, 7, 8, 9}
Any digit 3 or greater makes the sentence true.
I need help asap I don't understand this
Answer:
[tex]\boxed{\sf \ \ \ a=-2, \ b = 1 \ \ \ }[/tex]
Step-by-step explanation:
Hello,
saying that the function is continuous means that you cannot have a "jump" in the graph of the function
so we want
a*(-3)+b=7 and a*4+b=-7
it comes
(1) -3a + b = 7
(2) 4a + b = -7
(2)-(1) gives 4a + b + 3a - b =7a = -7-7 = -14
so a = -14/7 = -2
we replace in (1)
b = 7 + 3*(-2) = 7 - 6 = 1
hope this helps
Point p is the centroid of jkl. Kr=72 and Pq=30 what is kp?
Answer:
B (48)
Step-by-step explanation:
One particular property of medians is the 2/3 ratio. Basically, the centroid separates the median into two line segments, and the longer line segment is 2/3 of the median length. So, 72 x 2/3 is 48.
Which of the following is not an example of a quadratic function?
1. f(x)= (3x-2)(4x +7) 2. f(x) = (2x-1)2
3. f(x)= -7x²+8X
4. f(x)= 8x4–3x+5x2
Answer:
4. f(x) = 8x^4 – 3x + 5x^2
Step-by-step explanation:
In choices 1., 2., and 3., each function is a 2nd degree function since the term with the highest degree has an exponent of 2 on x. In choice 4., the function is a 4th degree function since there is a term with x^4, and that is the highest exponent on x.
Answer: 4. f(x) = 8x^4 – 3x + 5x^2
An article reported that for a sample of 52 kitchens with gas cooking appliances monitored during a one-week period, the sample mean CO2 level (ppm) was 654.16, and the sample standard deviation was 165.4.
Required:
a. Calculate and interpret a 9596 (two-sided) confidence interval for true average C02 level in the population of all homes from which the sample was selected.
b. Suppose the investigators had made a rough guess of 175 for the value of s before collecting data. What sample size would be necessary to obtain an interval width of 50 ppm for a confidence level of 95%?
Answer:
a) [tex]654.16-2.01\frac{165.4}{\sqrt{52}}=608.06[/tex]
[tex]654.16+2.01\frac{165.4}{\sqrt{52}}=700.26[/tex]
b) [tex]n=(\frac{1.960(175)}{25})^2 =188.23 \approx 189[/tex]
So the answer for this case would be n=189 rounded up to the nearest integer
Step-by-step explanation:
Part a
[tex]\bar X=654.16[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
s=165.4 represent the sample standard deviation
n =52represent the sample size
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom aregiven by:
[tex]df=n-1=52-1=51[/tex]
Since the Confidence is 0.95 or 95%, the significance [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and the critical value would be [tex]t_{\alpha/2}=2.01[/tex]
Now we have everything in order to replace into formula (1):
[tex]654.16-2.01\frac{165.4}{\sqrt{52}}=608.06[/tex]
[tex]654.16+2.01\frac{165.4}{\sqrt{52}}=700.26[/tex]
Part b
The margin of error is given by this formula:
[tex] ME=z_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (a)
And on this case we have that ME =25 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=(\frac{z_{\alpha/2} s}{ME})^2[/tex] (b)
The critical value for this case wuld be [tex]z_{\alpha/2}=1.960[/tex], replacing into formula (b) we got:
[tex]n=(\frac{1.960(175)}{25})^2 =188.23 \approx 189[/tex]
So the answer for this case would be n=189 rounded up to the nearest integer
Calculate sales tax using the following information: Taxable amount of the sale: $ 142 Sales tax percentage: 7 % What is the amount of the sales tax? Round the answer to the nearest cent (hundredths).
Answer:
Step-by-step explanation:
142(.07)= 9.94 amount of the sales tax
$142+9.94= $151.94
What is the volume of this aquarium?
Answer:
4,224 in ^3
Step-by-step explanation:
5184-960 (subtract the cut-out from the entire shape)