Replace x and y with the corresponding components of r(t), where
[tex]\mathbf r(t)=\langle x(t),y(t)\rangle=\langlet+3,4-2t\rangle[/tex]
We have
[tex]\displaystyle\int_Cf(x,y)\,\mathrm ds=\int_1^2f(x(t),y(t))\sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2}\,\mathrm dt[/tex]
[tex]=\displaystyle\int_1^2(2(t+3)+4(4-2t))\sqrt{1^2+(-2)^2}\,\mathrm dt[/tex]
[tex]=\displaystyle\sqrt5\int_1^2(22-6t)\,\mathrm dt[/tex]
[tex]=\sqrt5(22t-3t^2)\bigg|_1^2=\boxed{13\sqrt5}[/tex]
I'm tempted to say the answer is B, but it doesn't seem to match up exactly. It's possible that choice contains a typo.
What single transformation maps Triangle ABC onto A’B’C’
Answer:
Your answer is B
Step-by-step explanation:
rotating about/around the origin taking a shape and rotating it with the same values but around the point (0,0). so rotating your shape ABC around (0,0) with the same value would give you the shape A'B'C'
The speed of light is 186,000 miles per second. About how many miles does light travel in an hour? 5.2 × 10^1 miles 3.1 × 10^3 miles 1.1 × 10^7 miles 6.7 × 10^8 miles
Hey there! I'm happy to help!
We see that light travels 186,000 miles per second. How many miles is this per minute. Well, there are 60 seconds a minute, so we multiply by 60!
186,000×60=11160000
And there are 60 minutes in an hour, so we multiply by sixty again!
11160000×60=669600000
Now, we need to write this in scientific notation. To do this, we move the decimal back enough places to have a one digit number, and we multiply that one digit number by 10 to the power of how many places you moved the decimal back.
In the number 669600000 we can move the decimal point back 8 times which gives us 6.696 (we don't need the zeroes after a decimal) multiplied by 10 to the 8th power because we moved the decimal back eight places.
This can be written as 6.696×10^8, which is closest to the answer option 6.7×10^8 miles.
Have a wonderful day! :D
The Hudson Record Store is having a going-out-of-business sale. CDs normally sell for $18.00. During the first week of the sale, all CDs will sell for $15.00. Written as a fraction, what is the rate of discount? What is this rate expressed as a percent? Round your answer to the nearest hundredth of a percent. During the second week of the sale, the same CDs will be on sale for 25% off the original price. What is the price of a CD during the second week of the sale?What is this rate expressed as a percent? Round your answer to the nearest hundredth of a percent. During the second week of the sale, the same CDs will be on sale for 25% off the original price. What is the price of a CD during the second week of the sale?
Answer:
The Hudson Record Store
1. As a fraction, discount rate = $3/$18 = 0.167
2. As a percentage, discount rate = 16.67%
3. Selling price during 2nd week = $13.50
4. The rate of the new selling price to the old is $13.50/$18 = 75%
Step-by-step explanation:
Selling price of CDs = $18
1st Week, sold CDs at $15
Discount = $3 ($18 - $15)
As a fraction, discount rate = $3/$18 = 0.167
As a percentage, discount rate = 16.67%
2nd Week, sold CDs at $13.50 ($18 - (25% of $18))
Discount = $4.50 ($18 - $13.50)
Price during the second week of the sale = $13.50
The rate of discount = $4.50/$18 = 25%
Nitrates are groundwater contaminants derived from fertilizer, septic tank seepage and other sewage. Nitrate poisoning is particularly hazardous to infants under the age of 6 months. The maximum contaminant level (MCL) is the highest level of a contaminant the government allows in drinking water. For nitrates, the MCL is 10mg/L. The health department wants to know what proportion of wells in Madison Count that have nitrate levels above the MCL. A worker has been assigned to take a simple random sample of wells in the county, measure the nitrate levels, and assess compliance. What sample size should the health department obtain if the estimate is desired to be within 2% with 95% confidence if: (hint: there are two different methods)There is no prior information available?
Answer:
The sample size is [tex]n = 2401[/tex]
Step-by-step explanation:
From the question we are told that
The margin of error is [tex]E = 0.02[/tex]
Given that the confidence level is 95% then the level of significance can be mathematically evaluated as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5\%[/tex]
[tex]\alpha = 0.05[/tex]
Next we would obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the z-table , the values is
[tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.05 }{2} } = 1.96[/tex]
The reason we are obtaining critical value of [tex]\frac{\alpha }{2}[/tex] instead of [tex]\alpha[/tex] is because
[tex]\alpha[/tex] represents the area under the normal curve where the confidence level interval ( [tex]1-\alpha[/tex] ) did not cover which include both the left and right tail while
[tex]\frac{\alpha }{2}[/tex] is just the area of one tail which what we required to calculate the sample size
NOTE: We can also obtain the value using critical value calculator (math dot armstrong dot edu)
Generally the sample size is mathematically evaluated as
[tex]n = [ \frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \r p (1- \r p)[/tex]
Where [tex]\r p[/tex] is the proportion of sample taken which we will assume to be [tex]\r p = 0.5[/tex]
substituting values
[tex]n = [\frac{ 1.96}{0.02} ]^2 *( 0.5 (1- 0.5)[/tex]
[tex]n = 2401[/tex]
The state of CT claims that the average time on death row is 15 years. A random survey of 75 death row inmates revealed that the average length of time on death row is 17.8 years with a standard deviation of 5.9 years. Conduct a hypothesis to test the state of CT's claim. What type of test should be run? t-test of a mean z-test of a proportion The alternative hypothesis indicates a right-tailed test left-tailed test two-tailed test Calculate the p-value. What is the decision? We reject the claim that the average time on death row is 15 years We fail to reject the claim that the average time on death row is 15 years
Answer:
a)The calculated value t = 4.111 > 1.9925 at 5 % level of significance
Null hypothesis is rejected
The claim that the average time on death row is not 15 years
b) The p-value is 0.000101<0.05
we reject Null hypothesis
The claim that the average time on death row is not 15 years
Step-by-step explanation:
Step(i):-
Sample size 'n' =75
Mean of the sample x⁻ = 17.8
standard deviation of the sample (S) = 5.9
Mean of the Population = 15
Null hypothesis:H₀:μ = 15 years
Alternative Hypothesis :H₁:μ≠15 years
Step(ii):-
Test statistic
[tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }[/tex]
[tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }=\frac{17.8-15}{\frac{5.9}{\sqrt{75} } }[/tex]
t = 4.111
Degrees of freedom
ν = n-1 = 75-1=74
t₀.₀₂₅ = 1.9925
The calculated value t = 4.111 > 1.9925 at 5 % level of significance
Null hypothesis is rejected
The claim that the average time on death row is not 15 years
P-value:-
The p-value is 0.000101<0.05
we reject Null hypothesis
The claim that the average time on death row is not 15 years
Find the solution to the system of equations.
Answer:
x = - 4, y = 7
Step-by-step explanation:
Given the 2 equations
- 7x - 2y = 14 → (1)
6x + 6y = 18 → (2)
Multiplying (1) by 3 and adding to (2) will eliminate the y- term
- 21x - 6y = 42 → (3)
Add (2) and (3) term by term to eliminate y
- 15x = 60 ( divide both sides by 15 )
x = - 4
Substitute x = - 4 into either of the 2 equations and evaluate for y
Substituting into (2)
6(- 4) + 6y = 18
- 24 + 6y = 18 ( add 24 to both sides )
6y = 42 ( divide both sides by 6 )
y = 7
Find the volume of each cone.
Answer: 6 cm, V=48π or V=150.8 cm³
It appears the question is asking for the radius, but below I have shown how to find the volume.
Step-by-step explanation:
The radius is half of the diameter. The diameter of the cone of 12 cm. Half of 12 is 6. Therefore, the radius is 6 cm.
The formula to find the volume of a cone is [tex]V=\pi r^2\frac{h}{3}[/tex]. Now that we have the radius from above, we can use that to plug into the equation along with the given height.
[tex]V=\pi (6^2)\frac{4}{3}[/tex] [expand the exponent]
[tex]V=36\pi \frac{4}{3}[/tex] [combine like terms]
[tex]V=48\pi[/tex] or [tex]V=150.8 cm^3[/tex]
A statement which checks to see if the value of the expression on the left side is the same as the value of the expression on the right side is an example of the use of the
Answer:
A relational statementStep-by-step explanation:
In computer programming relational operators are used to check conditions, that is if one conditions matches another and returns true if the condition is met or satisfied.
Find the exact value of sin 5x/6
Answer:
1/2
Step-by-step explanation:
i think sin 5 pi/6
[tex]sin \frac{5 \pi}{6} =sin (\frac{\pi}{2} +\frac{\pi}{3} )=cos \frac{\pi}{3} =\frac{1}{2} \\or\\sin\frac{5 \pi}{6} =sin (\pi-\frac{\pi}{6} )=sin \frac{\pi}{6} =\frac{1}{2}[/tex]
The exact Value of sin 5x/6 is 1/2.
What is Trigonometry?The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).
Given:
sin 5x/6
We can Split it as
sin (5π / 6) = sin (π/2 + π/3)
= cos π/3
= 1/2
Also, sin (5π / 6) = sin (π - π/6)
= sin π/6
= 1/2
Hence, the exact value is 1/2.
Learn more about Trigonometry here:
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You are selling your product at a three-day event. Each day, there is a 60% chance that you will make money. What is the probability that you will make money on the first two days and lose money on the third day
Answer:
The required probability = 0.144
Step-by-step explanation:
Since the probability of making money is 60%, then the probability of losing money will be 100-60% = 40%
Now the probability we want to calculate is the probability of making money in the first two days and losing money on the third day.
That would be;
P(making money) * P(making money) * P(losing money)
Kindly recollect;
P(making money) = 60% = 60/100 = 0.6
P(losing money) = 40% = 40/100 = 0.4
The probability we want to calculate is thus;
0.6 * 0.6 * 0.4 = 0.144
David says he has 2/3 of a pipe length left, while Don says he has 11/16 of a length left. Which person has the longest section left?
Answer:
Don
Step-by-step explanation:
1. We make the fractions have common denominators so it is easier to compare them. We can do this buy multiplying 2/3 by a factor of 16, so it becomes 32/48. For 11/16, we multiply by a factor of 3 so it becomes 33/48. It is now apparent that Don has the longer pipe.
Don has the longest section of pipe because the fraction number 11/16 is greater than the fraction number 2/3.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The decimal number is the sum of a whole number and part of a fraction number. The fraction number is greater than zero but less than one.
David says he has 2/3 of a line length left, while Wear says he has 11/16 of a length left.
Convert the fraction numbers 2/3 and 11/16 into the decimal number. Then we have
2/3 = 0.6667
11/16 = 0.6875
The decimal number 0.6875 is greater than 0.6667. Then the fraction number 11/16 is greater than the fraction number 2/3.
Don has the longest section of pipe because the fraction number 11/16 is greater than the fraction number 2/3.
More about the Algebra link is given below.
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The temperature, T^0Celcius, of an object, t minutes after it is removed from a head source, is given byT=55e^((-0.1t) )+15. Find the temperature of the object at the instant it is removed from the heat source.
Answer:
60°C
Step-by-step explanation:
This is a great example of a problem that looks really complicated, but can be broken down and easily understood!
First, we want to know the temperature the instant it is removed from the heat source. In that case, the time that has elapsed after it has been removed is 0, so we're looking for:
[tex]T(0)=55e^{-0.1(0))}+15=55e^{0}+15[/tex]
Now, any number raised to to the power of zero is 1, so this becomes:
[tex]T(0)=55(1)+15=60[/tex]
For more information on why any number raised to the zero power is 1, I highly recommend researching if it interests you. One of the most intuitive ways is to think of the pattern of exponents:
[tex]3^{3}=3*3*3=27[/tex]
[tex]3^{2}=3*3=9[/tex]
[tex]3^{1}=3[/tex]
You might notice that with each decrease in power, it can be read as dividing the expression by three, so following that pattern gives:
[tex]3^{0}=\frac{3}{3}=1[/tex]
And if we follow the division pattern, we do end up going into negative exponents correctly:
[tex]3^{-1}=\frac{1}{3^{1}}[/tex]
[tex]3^{-2}=\frac{1}{3^{2}}=\frac{1}{9}[/tex]
[tex]3^{-3}=\frac{1}{3^3}=\frac{1}{27}[/tex]
If C(x) is the cost of producing x units of a commodity, then the average cost per unit is c(x) = C(x)/x. Consider the cost function C(x) given below. C(x) = 54,000 + 130x + 4x3/2 (a) Find the total cost at a production level of 1000 units. (Round your answer to the nearest cent.) $ (b) Find the average cost at a production level of 1000 units. (Round your answer to the nearest cent.) $ per unit (c) Find the marginal cost at a production level of 1000 units. (Round your answer to the nearest cent.) $ per unit (d) Find the production level that will minimize the average cost. (Round your answer to the nearest whole number.) units (e) What is the minimum average cost? (Round your answer to the nearest dollar.) $ per unit
Answer:
Step-by-step explanation:
Given that:
If C(x) = the cost of producing x units of a commodity
Then;
then the average cost per unit is c(x) = [tex]\dfrac{C(x)}{x}[/tex]
We are to consider a given function:
[tex]C(x) = 54,000 + 130x + 4x^{3/2}[/tex]
And the objectives are to determine the following:
a) the total cost at a production level of 1000 units.
So;
If C(1000) = the cost of producing 1000 units of a commodity
[tex]C(1000) = 54,000 + 130(1000) + 4(1000)^{3/2}[/tex]
[tex]C(1000) = 54,000 + 130000 + 4( \sqrt[2]{1000^3} )[/tex]
[tex]C(1000) = 54,000 + 130000 + 4(31622.7766)[/tex]
[tex]C(1000) = 54,000 + 130000 + 126491.1064[/tex]
[tex]C(1000) = $310491.1064[/tex]
[tex]\mathbf{C(1000) \approx $310491.11 }[/tex]
(b) Find the average cost at a production level of 1000 units.
Recall that :
the average cost per unit is c(x) = [tex]\dfrac{C(x)}{x}[/tex]
SO;
[tex]c(x) =\dfrac{(54,000 + 130x + 4x^{3/2})}{x}[/tex]
Using the law of indices
[tex]c(x) =\dfrac{54000}{x} + 130 + 4x^{1/2}[/tex]
[tex]c(1000) = \dfrac{54000}{1000}+ 130 + {4(1000)^{1/2}}[/tex]
c(1000) =$ 310.49 per unit
(c) Find the marginal cost at a production level of 1000 units.
The marginal cost is C'(x)
Differentiating C(x) = 54,000 + 130x + 4x^{3/2} to get C'(x) ; we Have:
[tex]C'(x) = 0 + 130 + 4 \times \dfrac{3}{2} \ x^{\dfrac{3}{2}-1}[/tex]
[tex]C'(x) = 0 + 130 + 2 \times \ {3} \ x^{\frac{1}{2}}[/tex]
[tex]C'(x) = 0 + 130 + \ {6}\ x^{\frac{1}{2}}[/tex]
[tex]C'(1000) = 0 + 130 + \ {6} \ (1000)^{\frac{1}{2}}[/tex]
[tex]C'(1000) = 319.7366596[/tex]
[tex]\mathbf{C'(1000) = \$319.74 \ per \ unit}[/tex]
(d) Find the production level that will minimize the average cost.
the average cost per unit is c(x) = [tex]\dfrac{C(x)}{x}[/tex]
[tex]c(x) =\dfrac{54000}{x} + 130 + 4x^{1/2}[/tex]
the production level that will minimize the average cost is c'(x)
differentiating [tex]c(x) =\dfrac{54000}{x} + 130 + 4x^{1/2}[/tex] to get c'(x); we have
[tex]c'(x)= \dfrac{54000}{x^2} + 0+ \dfrac{4}{2 \sqrt{x} }[/tex]
[tex]c'(x)= \dfrac{54000}{x^2} + 0+ \dfrac{2}{ \sqrt{x} }[/tex]
Also
[tex]c''(x)= \dfrac{108000}{x^3} -x^{-3/2}[/tex]
[tex]c'(x)= \dfrac{54000}{x^2} + \dfrac{4}{2 \sqrt{x} } = 0[/tex]
[tex]x^2 = 27000\sqrt{x}[/tex]
[tex]\sqrt{x} (x^{3/2} - 27000) =0[/tex]
x= 0; or [tex]x= (27000)^{2/3}[/tex] = [tex]\sqrt[3]{27000^2}[/tex] = 30² = 900
Since production cost can never be zero; then the production cost = 900 units
(e) What is the minimum average cost?
the minimum average cost of c(900) is
[tex]c(900) =\dfrac{54000}{900} + 130 + 4(900)^{1/2}[/tex]
c(900) = 60 + 130 + 4(30)
c(900) = 60 +130 + 120
c(900) = $310 per unit
Identify the value of the CRITICAL VALUE(S) used in a hypothesis test of the following claim and sample data:
Claim: "The average battery life (between charges) of this model of tablet is at least 12 hours."
A random sample of 80 of these tablets is selected, and it is found that their average battery life is 11.58 hours with a standard deviation of 1.93 hours. Test the claim at the 0.05 significance level.
a. -0.218
b. -1.645
c. -1.946
d. -1.667
Answer:
C
Step-by-step explanation:
The critical value we are asked to state in this question is the value of the z statistic
Mathematically;
z-score = (x- mean)/SD/√n
From the question
x = 11.58
mean = 12
SD = 1.93
n = 80
Substituting this value, we have
z= (11.58-12)/1.93/√80 = -1.946
Dr. Denscombe randomly assigned 10 participants to drink a caffeinated beverage and another 10 participants to drink a noncaffeinated beverage. He then recorded their average driving speed over a 10-minute period. Caffeinated drivers averaged 50 mph with a variance of 20 and noncaffeinated drivers averaged 30 mph with a variance of 20. What is t
Answer: t = 10
Step-by-step explanation:m
Given that; n₁ = 10, n₂ = 10
ж₁ = 50, ж₂ = 30
Sˣ₁ = 20, Sˣ₂ = 20
Now using TEST STATISTICS
t = (ж₁ - ж₂) / √ ( Sˣ₁/n₁ + Sˣ₂/n₂ )
so we substitute our figures
t = ( 50 - 30 ) / √ ( 20/10 + 20/10 )
t = 20 / √4
t = 10
Simba Travel Agency arranges trips for climbing Mount Kilimanjaro. For each trip, they charge an initial fee of $100 in addition to a constant fee for each vertical meter climbed. For instance, the total fee for climbing to the Shira Volcanic Cone, which is 3000 meters above the base of the mountain, is $400.Let y represent the total fee (in dollars) of a trip where they climbed x vertical meters.Complete the equation for the relationship between the total fee and vertical distance.
Answer:
[tex]y(x)=100+0.1x[/tex]
Step-by-step explanation:
Let y represent the total fee (in dollars) of a trip where they climbed x vertical meters.
We know that there is an initial fee of $100, so we know that if we climb x=0 meters, we have a fee of y(0)=100.
[tex]y(0)=100[/tex]
As there is a constant fee (lets called it m) for each vertical meter climbed, we have a linear relationship as:
[tex]y(x)-y(0)=m(x-0)\\\\\\y(x)-100=mx\\\\\\y(x)=100+mx[/tex]
We know that for x=3000, we have a fee of $400, so if we replace this in the linear equation, we have:
[tex]y(3000)=100+m(3000)=400\\\\\\100+3000m=400\\\\3000m=400-100=300\\\\m=300/3000=0.1[/tex]
Then, we have the equation for the total fee in function of the vertical distance:
[tex]y(x)=100+0.1x[/tex]
Which statement must be true if ?
A.
B.
C.
D.
Answer:
D
Step-by-step explanation:
D because they are congruent try measuring it.
Answer:
[tex]\boxed{\mathrm{D}}[/tex]
Step-by-step explanation:
The triangles are congruent.
The angles that are corresponding on both triangles must be congruent.
Angle Q in triangle PQR must be congruent to angle T in triangle STU.
How to do this? what is the answer??
Answer:
I think that is the C
Step-by-step explanation:
Answer:
Option B is the correct answer.
Step-by-step explanation:
here, arc RT =162°
as in question given that the value of arc RT is 162° the value of angle RST is 1/2 of 162°.
so, its value must be 81°only.
hope it helps..
If y varies directly as x, and y is 6 when x is 72, what is the value of y when x is 8?
NO
54
оо
96
Answer:
2/3
Step-by-step explanation:
The equation for direct variation is: y = kx, where k is a constant.
Here, we see that y varies directly with x when y = 6 and x = 72, so let's plug these values into the formula to find k:
y = kx
6 = k * 72
k = 6/72 = 1/12
So, k = 1/12. Now our formula is y = (1/12)x. Plug in 8 for x to find y:
y = (1/12)x
y = (1/12) * 8 = 8/12 = 2/3
Thus, y = 2/3.
~ an aesthetics lover
Answer:
Step-by-step explanation: I hope i'm right
[tex]y \alpha x\\y=kx....(1)\\6=72k\\\frac{6}{72} =\frac{72k}{72} \\\\1/12 =k\\y = 1/12x=relationship-between;x-and;y\\x =8 , y =?\\y = \frac{8}{12} \\Cross-Multiply\\12y =8\\12y/12 = 8/12\\\\y = 2/3[/tex]
The Highway Safety Department wants to study the driving habits of individuals. A sample of 121 cars traveling on the highway revealed an average speed of 60 miles per hour with a standard deviation of 11 miles per hour. Determine a 95% confidence interval estimate for the speed of all cars.
Answer:
{58.02007 , 61.97993]
Step-by-step explanation:
Data are given in the question
Sample of cars = n = 121
Average speed = sample mean = 60
Standard deviation = sd = 11
And we assume
95% confidence t-score = 1.97993
Therefore
Confidence interval is
[tex]= [60 - \frac{1.97993 \times 11}{\sqrt{121} }] , [60 + \frac{1.97993 \times 11}{\sqrt{121} }][/tex]
= {58.02007 , 61.97993]
Basically we applied the above formula to determine the confidence interval
Global Airlines operates two types of jet planes: jumbo and ordinary. On jumbo jets, 25% of the passengers are on business while on ordinary jets 30% of the passengers are on business. Of Global's air fleet, 40% of its capacity is provided on jumbo jets. (Hint: The 25% and 30% values are conditional probabilities stated as percentages.) What is the probability a randomly chosen business customer flying with Global is on a jumbo jet?
Answer:
Answer:
The probability is [tex]P(J|B) = 0.36[/tex]
Step-by-step explanation:
B =business
J=jumbo
Or =ordinary
From the question we are told that
The proportion of the passenger on business in the ordinary jet is [tex]P(B| Or) = 0.25[/tex]
The proportion of the passenger on business in the jumbo jet is [tex]P(B|J) = 0.30[/tex]
The proportion of the passenger on jumbo jets is [tex]P(j) = 0.40[/tex]
The proportion of the passenger on ordinary jets is evaluated as
[tex]1 - P(J) = 1- 0.40 = 0.60[/tex]
According to Bayer's theorem the probability a randomly chosen business customer flying with Global is on a jumbo jet is mathematically represented as
[tex]P(J|B) = \frac{P(J) * P(B|J)}{P(J ) * P(B|J) + P(Or ) * P(B|Or)}[/tex]
substituting values
[tex]P(J|B) = \frac{ 0.4 * 0.25}{0.4 * 0.25 + 0.6 * 0.3}[/tex]
[tex]P(J|B) = 0.36[/tex]
Step-by-step explanation:
When using the Distance Formula, the solution is the perimeter of a polygon.
true or false?
Answer:
false
Step-by-step explanation:
When solving the distance formula it is the distance from one point to another. If you had a rectangle and used the distance formula from each point then you would have a perimeter
A square matrix N is called nilpotent if there exists some positive integer k such that Nk = 0. Prove that if N is a nilpotent matrix, then the system Nx = 0 has nontrivial solutions.
Answer:
Nx = λx
Nx = 0, with x≠0
if N is nilpotent matrix, then the system Nx = 0 has non-trivial solutions
Step-by-step explanation:
given that
let N be a square matrix in order of n
note: N is nilpotent matrix with [tex]N^{k} = 0[/tex], k ∈ N
let λ be eigenvalue of N and let x be eigenvector corresponding to eigenvalue λ
Nx = λx (x≠0)
N²x = λNx = λ²x
∴[tex]N^{k}x[/tex] = (λ^k)x
[tex]N^{k}[/tex] = 0, (λ^k)x = [tex]0_{n}[/tex], where n is dimensional vector
where x = 0, (λ^k) = 0
λ = 0
therefore, Nx = λx
Nx = 0, with x≠0
note: if N is nilpotent matrix, then the system Nx = 0 has non-trivial solution
Let T:V→W be a linear transformation from a vector space V into a vector space W. Prove that the range of T is a subspace of W.
Answer:
The range of T is a subspace of W.
Step-by-step explanation:
we have T:V→W
This is a linear transformation from V to W
we are required to prove that the range of T is a subspace of W
0 is a vector in range , u and v are two vectors in range T
T = T(V) = {T(v)║v∈V}
{w∈W≡v∈V such that T(w) = V}
T(0) = T(0ⁿ)
0 is Zero in V
0ⁿ is zero vector in W
T(V) is not an empty subset of W
w₁, w₂ ∈ T(v)
(v₁, v₂ ∈V)
from here we have that
T(v₁) = w₁
T(v₂) = w₂
t(v₁) + t(v₂) = w₁+w₂
v₁,v₂∈V
v₁+v₂∈V
with a scalar ∝
T(∝v) = ∝T(v)
such that
T(∝v) ∈T(v)
so we have that T(v) is a subspace of W. The range of T is a subspace of W.
You will note the wheel has 38 slots. There are two green slots (labeled
0,00) and 36 slots which alternate red/black and are numbered 01-36. A
player participates by tossing a small ball around the wheel as the wheel
spins, and the ball lands in one of the 38 slots. The goal is for the ball to
land in a slot that the player predicted it would, and bet money on
happening. Define the following events:
E = The ball lands in an even numbered slot
M = The ball lands in a slot that is numbered a multiple of three (3,6,9,
12, etc...)
Use the given information to calculate the conditional probability M|E.
Round your answer to four decimal places.
Answer:
~0.3158
Step-by-step explanation:
Number of even numbers in the range of 1 - 38 is 38/2 = 19
=> P(E) = 19/38 = 1/2
Having: 38 = 3 x 12 + 2, then the number of numbers that is a multiple of 3 in the range of 1 - 38 is 12
=> P(M) = 12/38 = 6/19
Having: 38 = 6 x 6 + 2, then the number of numbers that is a multiple of 6 (or multiple of 2 and 3) is 6
=> P(E and M) = 6/38 = 3/19
Applying the conditional probability formula:
P(M|E) = P(E and M)/P(E) = (3/19)/(1/2) = 6/19 = ~0.3158
Look at the parallelogram ABCD shown below. The table below shows the steps to prove that if the quadrilateral ABCD is a parallelogram, then its opposite sides are congruent. Statement Reasons 1 . AB is parallel to DC and AD is parallel to BC - definition of parallelogram 2 . angle 1 = angle 2, angle 3 = angle 4 - if two parallel lines are cut by a transversal then the corresponding angles are congruent 3 . BD = BD - Reflexive Property 4 . triangles ADB and CBD are congruent - if two sides and the included angle of a triangle are congruent to the corresponding sides and angle of another triangle , then the triangles are congruent by SAS postulate 5 . AB = DC, AD = BC - corresponding parts of congruent triangles are congruent Which statement is true about the table? 1. It is not correct because it provides incorrect sequence of statement 2 and statement 4. 2. It is not correct because it does not provide correct reasons for statement 2 and statement 4. 3. It is accurate because it provides the correct sequence of statements. 4. It is accurate because it provides the correct reasons for the statements.
Answer:
2
Step-by-step explanation:
The original price of a burrito was $8. The price was increased by 10%. What is the new price?
Answer:
The new price is 8.80
Step-by-step explanation:
First find the increase
8 * 10%
8 * .10
.80
Add this to the original price
8 + .80
8.80
The new price is 8.80
Answer:
the answer is $8.80 :))
how could you correctly rewrite the equation 4(5+3)=2(22-6) using the distributive property?
We can correctly rewrite the equation: 4(5+3) = 2(22-6) by distributing each side.
4(5+3) = 2(22-6)
4(8) = 2(16)
32 = 32
Once you finish distributing each side, you can check to see if it is equal on both sides.
In our case it is since they both equal 32 after distributing the terms.
A cylinder with a base diameter of x units has a volume
of sex cubic units.
Which statements about the cylinder are true? Select
two options.
The radius of the cylinder is 2x units.
The area of the cylinder's base is 2-ox? square units.
The area of the cylinder's base is nexsquare units.
The height of the cylinder is 2x units.
The height of the cylinder is 4x units.
Answer:
(C) The area of the cylinder's base is [tex]\dfrac{1}{4} \pi x^2[/tex] square units.
(E)The height of the cylinder is 4x units.
Step-by-step explanation:
If the Base Diameter = x
Therefore: Base radius = x/2
Area of the Base
[tex]=\pi (x/2)^2\\=\dfrac{ \pi x^2}{4} $ square units[/tex]
Next, we know that:
The volume of a cylinder = Base Area X Height
[tex]\pi x^3=\dfrac{ \pi x^2}{4} \times Height\\Height =\pi x^3 \div \dfrac{ \pi x^2}{4}\\=\pi x^3 \times \dfrac{ 4}{\pi x^2}\\\\Height=4x$ units[/tex]
Therefore, the correct options are: C and E.
Learn more: https://brainly.com/question/16856757
Given that (-7,-7) is on the graph of f(x), find the corresponding point for the function f(x-5)
Answer: (-2,-7)
Step-by-step explanation:
A function f(x-c) , where c>0 , represents the horizontal shift of original function to the right c units.
The function f(x-c) is going to add c to the x value, while keeping the y value the same.
Similarly,
The function f(x-5) is going to add 5 to the x value, while keeping the y value the same.
So, the corresponding point to (-7,-7) on f(x-5) = (-7+5,-7)
= (-2,-7)
hence, the corresponding point to (-7,-7) on f(x-5) = (-2,-7)