(a) Express 386.71 correct to two significant figures

Express a vector A = [24, -15] as a linear combination of vectors in S, we solve the system of equations formed by equating A to the linear combination of S's vectors and find the coefficients.

i) To show that S = {[8, 2, 5], [H, H², H³]} is linearly independent, we set up the equation:

a * [8, 2, 5] + b * [H, H², H³] = [0, 0, 0]

Expanding this equation gives us the following system of equations:

8a + bH = 0

2a + bH² = 0

5a + bH³ = 0

To prove that S is linearly independent, we need to show that the only solution to this system is a = b = 0. Solving these equations will confirm the linear independence of S.

ii) Since S is linearly independent and contains two vectors, it forms a basis for a two-dimensional space, which we'll denote as Maz.

iii) To express vector A = [24, -15] as a linear combination of the vectors in S, we set up the equation:

[24, -15] = c * [8, 2, 5] + d * [H, H², H³]

Expanding this equation gives us the following system of equations:

8c + dH = 24

2c + dH² = -15

5c + dH³ = 0

By solving this system, we find the coefficients c and d that represent the linear combination of vectors in S that equals A.

Finally, substituting the values of c and d, we obtain the vector (4)s.

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Answer:

yes because if you factor you get (x-1)^2(x+1), and then if you solve that for the roots you get 1, 1, and -1

Answer: Is true

Step-by-step explanation:

The answer is -16

Step by step explanation:

the expression of this equation is √4x=-32, so first, we would find the square root of 4, which is 2. so now we have 2x=-32. Next we want to divide 2 from both sides, which gives us our final result: x=-16. So our answer is -16.

Answer:

Step-by-step explanation:

B : E and A

W : X

Answer:

x = 10

Step-by-step explanation

The exterior angle = the sum of the 2 interior angles (which is the other way to solve the other problem you just posted.)

-10 + 14x = 60 + 7x            Add 10 to both sides

-10+10+14x =60+10+7x     Combine

14x = 70 + 7x                     Subtract 7x from both sides

14x-7x = 70+7x-7x             Combine

7x = 70                              Divide by 7

7x/7 = 70/7

x = 10

Answer:

24 + 2n = 40

Step-by-step explanation:

let the number be n , then two times the number is 2n

This is then added to 24 and equal to 40

24 + 2n = 40 ← in equation form

Step-by-step explanation:

Let the two numbers be X and Y respectively.

We know that :

(a) X = 6Y + 5

(b) X + Y = 75

7Y + 5 = 75

X = 65

Y = 10

Answer:

y= 10         x = 65

Step-by-step explanation

did the same assignment lol

- mark me brainliest !

Answer:

Step-by-step explanation:

this addition uses the associative property

[tex]a + (b + c) = (a + b) + c[/tex]

[tex]12 + (17 + 1) = (12 + 17) + 1[/tex]

[tex]12 + 18 = 29 + 1[/tex]

[tex]30 = 30[/tex]

[tex] \red { \green {\boxed {\boxed{\star True \star}}}}[/tex]

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The implicit solution to the given differential equation Dx/dt = 4x² + (9t/√(6²+x²)) / (4tx) using the method for solving homogeneous equations is F(t,x) = C, where C is an arbitrary constant.

To solve the given differential equation, we can separate the variables and integrate both sides. Rearranging the equation, we have:

(4tx) Dx = (4x² + (9t/√(6²+x²))) dt. Next, we integrate both sides. Integrating the left side with respect to x and the right side with respect to t, we get:

∫(4tx) Dx = ∫(4x² + (9t/√(6²+x²))) dt. Integrating both sides will result in a function F(t,x) on the left side and the integral on the right side. Since we are looking for an implicit solution in the form F(t,x) = C, we can write the equation as:

F(t,x) = C. cccThis represents the general solution to the given differential equation, where C is an arbitrary constant. The specific form of the function F(t,x) will depend on the integration process and the initial conditions, if provided.

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Answer:

1 and 2

Step-by-step explanation:

Answer:

1 and 2

Step-by-step explanation:

Because 1.5 (1 1/2) is in between 1 and 2

Answer:

[tex]c = 5[/tex]

Step-by-step explanation:

You use the Pythagorean theorem: [tex]a^2 + b^2 = c^2[/tex].

Since we have the value of [tex]a = 3[/tex] and [tex]b = 4[/tex]..

Then we know that:

[tex]a^2 + b^2 = 3^2 + 4^2 = 9 + 16 = 25 = c^2[/tex]

Since we know that [tex]c^2[/tex] is now, we take square root of that to get value of [tex]c[/tex].

[tex]\sqrt{c^2}=\sqrt{25}\\\\c = 5[/tex]

Answer:

1/2

Step-by-step explanation:

2/3 - 1/6

Get a common denominator of 6

2/3 *2/2 - 1/6

4/6 - 1/6

3/6

Simplify

1/2

Answer:

5/6

Step-by-step explanation:

2/3 - 1/6

Find common denominators.

4/6 - 1/6

Subtract.

5/6

Best of Luck!

Answer:

g=-3

Step-by-step explanation:

7+3(2g-6)=-29

7+6g-18=-29

6g=-29+18-7

6g=-18

g=-3

I think this is the right answer :D hope this helps ;)

Answer:

Step-by-step explanation:

[tex]7+3(2g-6)= -29\\\\\mathrm{Subtract\:}7\mathrm{\:from\:both\:sides}\\\\7+3\left(2g-6\right)-7=-29-7\\\\Simplify\\\\3\left(2g-6\right)=-36\\\\\mathrm{Divide\:both\:sides\:by\:}3\\\\\frac{3\left(2g-6\right)}{3}=\frac{-36}{3}\\\\Simplify\\\\2g-6=-12\\\\\mathrm{Add\:}6\mathrm{\:to\:both\:sides}\\\\2g-6+6=-12+6\\\\Simplify\\\\2g =-6\\\\\mathrm{Divide\:both\:sides\:by\:}2\\\\\frac{2g}{2}=\frac{-6}{2}\\\\Simplify\\\\g =-3[/tex]

The minimum time for completing the project, based on the critical path analysis, is 18 weeks. The critical path, which consists of activities with zero slack time, includes activities A, B, C, F, G, and H. By summing up the durations of these critical activities, we find that the minimum time for completing the project is 18 weeks.


To calculate the minimum time for completing the project, we need to identify the critical path, which consists of activities with zero slack time. Here are the step-by-step calculations:

1. Assign forward and backward pass values:

  Start by assigning the project start time as Early Start (ES) = 0 for Activity A. Then, calculate the Early Finish (EF) for each activity by adding the duration to the ES. The backward pass starts from the project completion time, which is the Late Finish (LF) for Activity I, initially set at 26 weeks. Calculate the Late Start (LS) for each activity by subtracting the duration from the LF.

  Activity A: ES = 0, EF = ES + 4 = 4, LS = LF - 4 = 26 - 4 = 22, LF = 26

  Activity B: ES = 4, EF = ES + 3 = 4 + 3 = 7, LS = LF - 3 = 26 - 3 = 23, LF = 26

  Activity C: ES = 7, EF = ES + 2 = 7 + 2 = 9, LS = LF - 2 = 26 - 2 = 24, LF = 26

  Activity D: ES = 7, EF = ES + 6 = 7 + 6 = 13, LS = LF - 6 = 26 - 6 = 20, LF = 26

  Activity E: ES = 13, EF = ES + 5 = 13 + 5 = 18, LS = LF - 5 = 26 - 5 = 21, LF = 26

  Activity F: ES = 13, EF = ES + 4 = 13 + 4 = 17, LS = LF - 4 = 26 - 4 = 22, LF = 26

  Activity G: ES = 18, EF = ES + 2 = 18 + 2 = 20, LS = LF - 2 = 26 - 2 = 24, LF = 26

  Activity H: ES = 20, EF = ES + 3 = 20 + 3 = 23, LS = LF - 3 = 26 - 3 = 23, LF = 26

  Activity I: ES = 9, EF = ES + 5 = 9 + 5 = 14, LS = LF - 5 = 26 - 5 = 21, LF = 26

2. Calculate slack time:

  Slack time (ST) can be calculated by subtracting the EF from the LS or the ES from the LF for each activity.

  Activity A: ST = LS - EF = 22 - 4 = 18

  Activity B: ST = LS - EF = 23 - 7 = 16

  Activity C: ST = LS - EF = 24 - 9 = 15

  Activity D: ST = LS - EF = 20 - 13 = 7

  Activity E: ST = LS - EF = 21 - 18 = 3

  Activity F: ST = LS - EF = 22 - 17 = 5

  Activity G: ST = LS - EF = 24 - 20 = 4

  Activity H: ST = LS - EF = 23 - 23 = 0

  Activity I: ST = LS - EF = 21 - 14 = 7

3. Identify the critical path:

  The critical path consists of activities with zero slack time. In this case, the critical path includes activities A, B, C, F, G, and H.

4. Calculate the minimum project completion time:

  Sum up the durations of the activities on the critical path to find the minimum time for completing the project.

 Minimum Time = Duration of Activity A + Duration of Activity B + Duration of Activity C + Duration of Activity F + Duration of Activity G + Duration of Activity H

              = 4 + 3 + 2 + 4 + 2 + 3

              = 18 weeks

Therefore, the minimum time for completing the project is 18 weeks.

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After one year of compounding at a 6% interest rate, you would have approximately $3,180 in your savings account.

To calculate the amount of money you will have in the savings account after one year with compound interest, we can use the formula:

A = P(1 + r/n)^(nt)

Where:

A is the final amount

P is the principal amount (initial deposit)

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the number of years

Let's solve it step by step:

Given:

P = $3,000 (principal amount)

r = 6% = 0.06 (annual interest rate as a decimal)

n = 1 (compounded annually)

t = 1 (one year)

Using the formula:

A = 3000 * (1 + 0.06/1)^(1*1)

A = 3000 * (1 + 0.06)^1

A = 3000 * (1.06)^1

A ≈ $3180

So, after one year of compounding at a 6% interest rate, you would have approximately $3,180 in your savings account.

It seems there was a discrepancy in the answer provided. Based on the given information, the correct calculation yields $3,180, not $5,372.54.

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Answer:

70 miles per hour.

Step-by-step explanation:

MPH = Miles/(Hours + (Minutes/60))

Answer:

Step-by-step explanation:

the answer is 9.789 x 10^5

The upper bound of the 90% confidence interval for the recovery time is approximately 23.696 days.

It takes more than approximately 21.257 minutes to find a parking space 90% of the time.

To find the probability that it will take more than 11 days to recover from the surgical procedure, we need to calculate the area under the normal distribution curve to the right of 11 days.

Mean (μ) = 7 days

Standard deviation (σ) = 7.92 days

We can standardize the value of 11 days using the z-score formula:

z = (x - μ) / σ

z = (11 - 7) / 7.92

z = 0.506

Using a standard normal distribution table or a calculator, we can find the probability corresponding to the z-score of 0.506. The probability is approximately 0.3051.

Therefore, the probability that it will take more than 11 days to recover is approximately 0.3051 or 30.51%.

Question 8:

To find the upper bound of the 90% confidence interval for the number of days needed to recover from the surgical procedure, we need to calculate the z-score corresponding to the desired confidence level and then find the corresponding value using the standard deviation.

Given:

Mean (μ) = 20 days

Standard deviation (σ) = 2.24 days

For a 90% confidence interval, the z-score corresponding to the upper tail probability of 0.10 (1 - 0.90) is approximately 1.645.

Using the formula for the upper bound of the confidence interval:

Upper bound = μ + (z * σ)

Upper bound = 20 + (1.645 * 2.24)

Upper bound ≈ 23.696

Therefore, the upper bound of the 90% confidence interval for the recovery time is approximately 23.696 days.

Question 9:

To find the time it takes more than 90% of the time to find a parking space, we need to calculate the z-score corresponding to the desired upper tail probability and then find the corresponding value using the standard deviation.

Mean (μ) = 15 minutes

Standard deviation (σ) = 4.89 minutes

For a probability of 90%, the upper tail probability is 1 - 0.90 = 0.10.

Using a standard normal distribution table or a calculator, we can find the z-score corresponding to the upper tail probability of 0.10, which is approximately 1.282.

Using the formula for the upper bound:

Upper bound = μ + (z * σ)

Upper bound = 15 + (1.282 * 4.89)

Upper bound ≈ 21.257

Therefore, it takes more than approximately 21.257 minutes to find a parking space 90% of the time.

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Answer:

y=n(2)

Step-by-step explanation:

Answer:

x ≈ 19.7

Step-by-step explanation:

Using the sine ratio in the right triangle.

sin66° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{18}{x}[/tex] ( multiply both sides by x )

x × sin66° = 18 ( divide both sides by sin66° )

x = [tex]\frac{18}{sin66}[/tex] ≈ 19.7 ( to the nearest tenth )

Answer:

$85.50 dollars

Step-by-step explanation:

Becky bought a $14.50 and $20 dress, and a $8.25 pair of flipflops. That is $42.75 . Barbara bought differernt things but still spent the same amount of $42.75 . So if you add those up, it would be $85.50 that they have spent together. Hope this helps :)

s = (-38 ± √(-6556)) / 32

Since the term inside the square root is negative, the equation has no real solutions. This means that the ball will not hit the ground.

To determine how long it will take for the ball to hit the ground, we need to find the value of s when the height h(s) equals zero. In other words, we need to solve the equation:

16s^2 + 38s + 1250 = 0

We can use the quadratic formula to solve this equation. The quadratic formula states that for an equation in the form of ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 16, b = 38, and c = 1250. Plugging these values into the quadratic formula, we have:

s = (-38 ± √(38^2 - 4(16)(1250))) / (2(16))

Simplifying further, we get:

s = (-38 ± √(1444 - 8000)) / 32

s = (-38 ± √(-6556)) / 32

Since the term inside the square root is negative, the equation has no real solutions. This means that the ball will not hit the ground.

This result does not reflect reality. In reality, the ball would eventually hit the ground due to factors such as air resistance. The given equation does not take these factors into account.

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The concept of consumer surplus refers to the satisfaction that consumers get from purchasing a good or service for a price lower than their maximum willingness to pay. The difference between what they are willing to pay and what they actually pay is the consumer surplus.

Therefore, the consumer surplus that Frances gets for the iPhone she bought for $150 is $200, which means that her willingness to pay for an iPhone is $350. ($150 + $200 = $350)If Frances had bought the iPhone on sale for $100, her consumer surplus would have been $250. ($350 - $100 = $250)If the price of the iPhone had been $400, Frances would not have bought it because her willingness to pay is $350, and the price is more than that.

To summarize, Frances' willingness to pay for an iPhone is $350. If she had bought the iPhone on sale for $100, her consumer surplus would have been $250. If the price of the iPhone had been $400, her consumer surplus would have been zero because she would not have bought the iPhone.

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Answer:

= -1031/8

Step-by-step explanation:

Hope I get brainliest

Answer:

-123

Step-by-step explanation:

Answer:

-123

Step-by-step explanation:

-(29+1+4+89)

-(30+4+89)

-(34+89)

-123

hope this helps good luck at school :))

Answer:

-3×+5

Step-by-step explanation:

y=mx+b

m= y2-y1÷x2-x1

= -10+1÷5-2

= -9÷3

= -3

now,

y= -3×+b

-10 = -3(5)+b

-10 = -15+b

-10+15 = b

b= 5

therefore, y= -3×+5

The equation of the line passing through the points (2, -1) and (5, -10) in slope-intercept form is y= -3x+ 5.

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 the points as (5, -10) and (2, -1).

So, the slope of line

slope = (-1 + 10) / (2 -5)

slope = 9/ (-3)

Slope= -3

Now, using the slope intercept form

y= mx+ b

y= -3x + b

and, the line passes through (2, -1)

-1 = -3(2) + b

-1 + 6 = b

b= 5

Then, the equation of line is

y= -3x + 5

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Answer:

D

Step-by-step explanation:

Answer:

its a :)

Step-by-step explanation:

have a good day!!

Answer:

Range of the function f(x) = 3x² +18x is [-27,∞).What is the range of a function?The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.Here, we have f(x) = 3x² +18x.Let f(x) = y⇒ y = 3x² +18x⇒ y = 3(x²+6x)⇒ y/3 = x²+6x⇒ y/3 = x²+ 6x + 9 - 9⇒ y/3 = (x+3)² - 9⇒ y/3 + 9 = (x+3)² ⇒ (y+27)/3 = (x+3)² Taking square root on both sides, we get⇒  = x+ 3⇒   = xNow since f(x) = y ⇒ x = f⁻¹(y)⇒ f⁻¹(y) = ⇒ range = [-27,∞).Therefore, range of the function f(x) = 3x² +18x was found to be [-27,∞).

Step-by-step explanation: