can you please solve this fast
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The given subset satisfies all three conditions of a subspace, we can conclude that it is a subspace of ℙ2.

To prove this, we need to show that the set satisfies the three conditions of a subspace: closure under addition, closure under scalar multiplication, and contains the zero vector.

Let p(t) and q(t) be two polynomials of the form \(p(t) = at²\)and \(q(t) = bt²\), where a and b are real numbers. Then, the sum of these two polynomials is:

\(p(t) + q(t) = at² + bt²\)

\(= (a+b)t²\)

Since a+b is a real number, the sum of p(t) and q(t) is still of the form at² and thus belongs to the given set. Therefore, the set is closed under addition.

Now, let p(t) be a polynomial of the form \(p(t) = at²\) and c be a real number. Then, the scalar multiple of p(t) by c is:

\(c p(t) = c(at²) = (ca)t²\)

Since ca is a real number, the scalar multiple of p(t) by c is still of the form at² and thus belongs to the given set. Therefore, the set is closed under scalar multiplication.

Finally, the zero vector is the polynomial of the form \(p(t) = 0t² = 0\), which clearly belongs to the given set. Therefore, the set contains the zero vector.

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Answer:

(x, y) → (x - 8, y + 4)

Step-by-step explanation:

The answer is c (x,y)->(x-8,y+4)

(1) Using the Black/Scholes Option Pricing Model, the value of the call option is $7.70.

(2) The intrinsic value of the call is the difference between the stock price and the strike price of the option. Therefore, it is $4.

(3) The stock price required to break-even is the sum of the strike price and the option premium. Therefore, it is $74.

(4) If volatility were to decrease, the value of the call would decrease.

(5) If the exercise price would increase, the value of the call would decrease.

(6) If the time to maturity were 3-months, the value of the call would decrease.

(7) If the stock price were $62, the value of the call would be zero.

(8) The maximum value that a call option can take is unlimited.

In the Black/Scholes option pricing model, the value of a call option can be calculated using the formula:

C = S*N(d1) - X*e^(-rT)*N(d2)

where S is the stock price, X is the exercise price, r is the risk-free rate, T is the time to maturity, and σ2 is the variance of the stock's return.

Using the given values, we can calculate d1 and d2:

d1 = [ln(S/X) + (r + σ2/2)T]/(σ2T^(1/2))

   = [ln(74/70) + (0.10 + 0.50/2)*0.5]/(0.50*0.5^(1/2))

   = 0.9827

d2 = d1 - σ2T^(1/2) = 0.7327

Using these values, we can calculate the value of the call option:

C = S*N(d1) - X*e^(-rT)*N(d2)

= 74*N(0.9827) - 70*e^(-0.10*0.5)*N(0.7327)

= $7.70

The intrinsic value of the call is the difference between the stock price and the strike price of the option. Therefore, it is $4.

The stock price required to break-even is the sum of the strike price and the option premium. Therefore, it is $74.If volatility were to decrease, the value of the call would decrease. This is because the option's value is directly proportional to the volatility of the stock.

If the exercise price would increase, the value of the call would decrease. This is because the option's value is inversely proportional to the exercise price of the option.

If the time to maturity were 3-months, the value of the call would decrease. This is because the option's value is inversely proportional to the time to maturity of the option.If the stock price were $62, the value of the call would be zero. This is because the intrinsic value of the call is zero when the stock price is less than the strike price.

The maximum value that a call option can take is unlimited. This is because the value of a call option is directly proportional to the stock price. As the stock price increases, the value of the call option also increases.

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Answer: 67/100

Step-by-step explanation: 0.67 is in the hundredths place not the tenths so it cant be 67/99 its 67/100

Answer:

a = 1/2 (b) (h)

Step-by-step explanation:

Use Pythagorean theorem for sub triangle on the left: 8^2 + h^2 = 22^2

Use Pythagorean again for sub triangle on the right: x^2 + h^2= 31^2

Find your base: 8+x=b

Find entire area: a = 1/2 (b) (h)

The rank-nullity theorem states that the rank of a matrix plus the dimension of its null space equals the number of columns.

Thus, if the null space of a 4 x 5 matrix is three-dimensional, then the rank of the matrix is 5 - 3 = 2.

Answer to Question 2:

The dimension of the solution space of A x = 0 is 6 - 2 = 4, since the number of columns of A is 6 and its rank is 2. The solution space of A x = 0 is the null space of A, which has dimension 4 by the rank-nullity theorem.

Answer to Question 3:

No, the columns of A do not necessarily have to be linearly independent. The column space of A is the span of its columns, which has dimension p. However, the columns of A may be linearly dependent, which means that some columns can be expressed as linear combinations of the others.

Answer to Question 4:

To prove that H + K is a subspace of V, we need to show that it satisfies three conditions:

It contains the zero vector: 0 = 0 + 0 belongs to H + K, since it can be expressed as the sum of the zero vectors in H and K.

It is closed under vector addition: if w1 and w2 belong to H + K, then there exist h1 and k1 in H and K such that w1 = h1 + k1, and there exist h2 and k2 in H and K such that w2 = h2 + k2. Therefore, w1 + w2 = (h1 + h2) + (k1 + k2) belongs to H + K, since it can be expressed as the sum of vectors in H and K.

It is closed under scalar multiplication: if w belongs to H + K and c is a scalar, then there exist h and k in H and K such that w = h + k. Therefore, c w = c h + c k belongs to H + K, since it can be expressed as the sum of vectors in H and K.

Since H + K satisfies these three conditions, it is a subspace of V.

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Answer:

Area of the composite figure = 42 in²

Step-by-step explanation:

Composite area of the given figure = Area of the rectangle + Area of the right triangle

Area of the rectangle = Length × Width

                                    = 6 × 5

                                    = 30 in²

Area of the right triangle = \(\frac{1}{2}(\text{Base})(\text{Height})\)

                                         = \(\frac{1}{2}(4)(6)\)

                                         = 12 in²

Area of the composite figure = 30 + 12

                                                  = 42 in²

Exponential kind of function best models the set of data points (-3, 18), (-2, 6), (-1, 2), (0, 11), and (1,27).

To figure out which sort of capability best models the given arrangement of pieces of information, we can plot them on a chart and outwardly review the state of the bend that interfaces them.

After plotting the given pieces of information, we can see that the bend that best fits them is certainly not a straight line (direct) or a parabola (quadratic), as it seems to bend all the more steeply. The bend that best fits these focuses is likewise not a steady capability (nothing unless there are other options), as the upsides of y change concerning x.

Consequently, the capability that best models the given arrangement of information focuses is a dramatic capability, which has a bend that increments or diminishes at a speeding up rate. An overall condition for a dramatic capability is:

y =\(ab^x\)

where an and b are constants. We can utilize the given focuses to track down the upsides of an and b, and in this manner get the particular condition that models the data of interest.

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Answer:

x² + y² = 4

Step-by-step explanation:

We need to write the standard equation of circle with , centre (0,0) and radius 2 unit . The Standard equation of the circle ⭕ is ,

=> ( x - h)² + (y -k)² = r²

=> ( x -0)² + (y-0)² = 2²

=> x² + y² = 4 .

The correct option is option A: 2d = 12.

I apologize if this is incorrect. I hope you have a lovely day! :)

Answer:

\( \sf \: a) \: 2d = 12\)

Step-by-step explanation:

Given information,

→ Jorge is taking a trip with Bruce.

→ Bruce eats 2 cups of food a day.

Now we have to,

→ Find the required equation.

Let us assume that,

→ d = Number of days

The equation will be,

→ 2d = 12

=> As Bruce eats 2 cups in a day.

Then the value of d will be,

→ 2d = 12

→ d = 12 ÷ 2

→ [ d = 6 ]

Hence, option (a) is correct.

Answer:

It will take 7.46 minutes for the tank to drain completely

Step-by-step explanation:

The first thing we need to do is to find the rate at which the tank empties.

The rate can be found easily by dividing the amount of water leaving the tank by the time the water takes to leave the tank.

Jada notices 2 gallons of water leave the tank in three minutes.  ( The two gallons was obtained from 7-5 = 2).

The rate at which the tank is being emptied is  2 gallons ÷ 3 minutes = 0.67 gallons per minute.

The next step is to use this rate to estimate the amount of time it will take for the tank to be empty.

For the tank to be empty, it has to lose all 5 gallons of water it has.

it loses this 5 gallons at the rate of 0.67 gallons per minute.

We can set up a simple relation as shown below:

1 minute 0.67 gallons are lost

x minutes 5 gallons are lost

By cross multiplying, we have that

x = 5/0.67 = 7.46 minutes

It will take 7.46 minutes for the tank to drain completely

Categorical data is data that can be divided into different categories. Examples of categorical data include hair color, number of suitcases on a plane, tree height, and amount of rainfall.

Hair color would be classified as categorical data because it can be divided into categories such as black, brown, blonde, and red. Number of suitcases on a plane would also be classified as categorical data because the amount of suitcases can be divided into categories such as 0, 1, 2, 3, etc. Tree height would be classified as categorical data as it can be divided into categories such as small, medium, and large. Amount of rainfall would also be classified as categorical data as it can be divided into categories such as light rainfall, moderate rainfall, and heavy rainfall.

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Answer:

B.) You don't really have to worry about finding the slope. You just have to look for the y intercept, which is (0, -2)

Hope this helps! :)

a)The x co-ordinates of P and Q satisfy the equation x² + 4x - 5 = 0.

b)The co-ordinates of P and Q are (-5, -1) and Q = (1, 5).

The given equation of the circle is;

x² + y² = 26.

Th circle satisfies the line y = x + 4.

Thus, Put the value of y in the main equation.

x² + (x + 4)² = 26.

Simplify the equation;

x² + x² + 16 + 8x = 26

2x² + 8x - 10  = 0

Divide the equation by 2.

x² + 4x - 5  = 0  

Part a: This shows that x co-ordinates of P and Q satisfy the equation x² + 4x - 5 = 0.

Part b: Now, do the factorization of x² + 4x - 5  = 0.

(x + 5)(x - 1) = 0

x = -5 and 1.

For x = -5; y = -1

Point P = (-5, -1)

For x = 1; y = 5

Point Q = (1, 5)

Thus, the requires points P and Q are obtained.

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Answer:

\(9^{3/2}-3\times 5^0-(\dfrac{1}{81})^{-1/2}=15\)

Step-by-step explanation:

The given expression is :

\(9^{3/2}-3\times 5^0-(\dfrac{1}{81})^{-1/2}=15\)

We need to prove that LHS is equal to RHS.

Taking LHS,

\(=9^{3/2}-3\times 5^0-(\dfrac{1}{81})^{-1/2}\)

\(=(3)^{2\times\dfrac{3}{2}}-3-(\dfrac{1}{9})^{2\times \dfrac{-1}{2}}\\\\=27-3-9\\\\=15\\\\=RHS\)

Hence, LHS = RHS.

(a) The set of vectors forms a plane in ℝ³.

(b) The set of vectors forms a plane in ℝ³.

(c) The set of vectors forms all of ℝ³.

To determine whether the set of all linear combinations of a given set of vectors in ℝ³ forms a line, a plane, or all of ℝ³, examine the linear independence of the vectors.

(a) {(-2, 5, -3), (6, -15, 9), (-10, 25, -15)}:

To determine the linear independence, form a matrix using these vectors as rows and perform row reduction. If the row-reduced echelon form contains a row of zeros, it indicates linear dependence.

Creating a matrix and performing row reduction:

-2 5 -3

6 -15 9

-10 25 -15

After row reduction, we obtain the following row-reduced echelon form:

1 -5/2 3/2

0 0 0

0 0 0

Since the row-reduced echelon form contains a row of zeros, the vectors are linearly dependent. Therefore, the set of all linear combinations of these vectors forms a plane in ℝ³.

(b) {(1, 2, 0), (1, 1, 1), (4, 5, 3)}:

Performing the same process, we create a matrix and perform row reduction:

1 2 0

1 1 1

4 5 3

After row reduction, we obtain the following row-reduced echelon form:

1 0 -2

0 1 2

0 0 0

Since the row-reduced echelon form does not contain a row of zeros, the vectors are linearly independent. Thus, the set of all linear combinations of these vectors forms a plane in ℝ³.

(c) {(0, 0, 3), (0, 1, 2), (1, 1, 0)}:

Creating a matrix and performing row reduction:

0 0 3

0 1 2

1 1 0

After row reduction, we obtain the following row-reduced echelon form:

1 1 0

0 1 2

0 0 3

Since the row-reduced echelon form does not contain a row of zeros, the vectors are linearly independent. Therefore, the set of all linear combinations of these vectors forms all of ℝ³.

In summary:

(a) The set of vectors forms a plane in ℝ³.

(b) The set of vectors forms a plane in ℝ³.

(c) The set of vectors forms all of ℝ³.

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The complete question goes thus:

Determine whether the set of all linear combinations of the following set of vector in R3 is a line or a plane or all of R3. Justify, your answer. (a) {(-2,5,-3), (6, -15,9),(-10, 25, -15)} (b) {(1,2,0), (1,1,1),(4,5,3)} (c) {(0,0,3), (0,1,2), (1,1,0)}

Refer to the attachment

The 90% confidence interval for the proportion of district residents in favor of starting the school day 15 minutes later is (0.392, 0.548). The true proportion is estimated to lie within this interval with 90% confidence.

To calculate the 90% confidence interval for the true proportion of district residents who are in favor of starting the school day 15 minutes later, we can use the following formula:

CI = p ± z*(√(p*(1-p)/n))

where:

CI: confidence interval

p: proportion of residents in favor of starting the day later

z: z- score based on the confidence level (90% in this case)

n: sample size

First, we need to calculate the sample proportion:

p = 94/200 = 0.47

Next, we need to find the z- score corresponding to the 90% confidence level. Since we want a two-tailed test, we need to find the z- score that cuts off 5% of the area in each tail of the standard normal distribution. Using a z-table, we find that the z- score is 1.645.

Substituting the values into the formula, we get:

CI = 0.47 ± 1.645*(√(0.47*(1-0.47)/200))

Simplifying this expression gives:

CI = 0.47 ± 0.078

Therefore, the 90% confidence interval for the true proportion of district residents who are in favor of starting the school day 15 minutes later is (0.392, 0.548). We can be 90% confident that the true proportion lies within this interval.

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The effective interest on £2000 at a 3% interest rate compounded quarterly over a period of 4 years is approximately £245.15.

To calculate the effective interest, we need to use the formula for compound interest:

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

Where:

A = the future value of the investment (including interest)

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

n = the number of compounding periods per year

t = the number of years

In this case, the principal amount (P) is £2000, the annual interest rate (r) is 3% (or 0.03 as a decimal), the compounding is done quarterly (n = 4), and the investment period (t) is 4 years.

Plugging the values into the formula:

A = £2000(1 + 0.03/4)^(4*4)

= £2000(1 + 0.0075)^16

= £2000(1.0075)^16

≈ £2000(1.126825)

Calculating the future value:

A ≈ £2253.65

To find the effective interest, we subtract the principal amount from the future value:

Effective Interest = £2253.65 - £2000

≈ £253.65

Therefore, the effective interest on £2000 at a 3% interest rate compounded quarterly after 4 years is approximately £253.65.

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Answer:

y = -2x - 3

Step-by-step explanation:

Slope: (5 - - 5)/(-4 -1) = 10/-5 = -2

y-intercept= 5 - (-2)(-4) = 5 - 8 = -3

Answer:

1.75 or about 1 cup of ice cream

Step-by-step explanation:

Well, we first have to figure out how many cups of ice cream are in a quart. (There are 4 cups in a quart) So know we have to divide 4 into 7 that will give you 1.75 so each family would get approximatley 1.75 cups of ice cream. That is if it is talking about specifically  how much ice cream but you could also say about a cup

The area of the region enclosed by the petal of a rose curve r = sin2θ in the first quadrant is π/8 square units

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

We know the area in the polar coordinates is given by:

\(\rm A =\int\limits^a_b {\dfrac{1}{2}r^2} \, d\theta\)

We have r = sin2θ

Here the quadrant is not given, so we are assuming we need to find the area in the first quadrant.

Put this value in the above integration and limit 0 to π/2

\(\rm A =\int\limits^{\dfrac{\pi}{2}}_0 {\dfrac{1}{2}(sin^22\theta)} \, d\theta\)

After solving the above integration, we get:

\(\rm A = \dfrac{\pi}{8}\)

Thus, the area of the region enclosed by the petal of a rose curve r = sin2θ in the first quadrant is π/8 square units

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The cost per second to power such a circuit during the peak usage period is approximately \(2.376 x 10^-6\)$/s. The cost per second to power the circuit during the peak usage period can be calculated using the following steps:

Calculate the power consumption of the device-The power consumption of the device can be calculated using the formula: Power = Voltage x Current. P = V x I, Substituting the given values:

P = 110V x 0.12A

= 13.2 W

Calculate the cost per second-The cost per second can be calculated using the formula:

Cost per second = Power x Cost per Joule

C = P x CC

= 13.2 W x 1.8 x \(10^-7\) $/J

≈ 2.376 x 10^-6 $/s

Therefore, the cost per second to power such a circuit during the peak usage period is approximately 2.376 x\(10^-6\) $/s.

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Answer:

Josie because 25 miles in 5 hours is 5 miles every hour and Greta runs 4.5 miles evry hour

Step-by-step explanation:

Josie runs  25 / 5 = 5 mils per hour

Greta 18 / 4 = 4,5 miles per hour

Josie is FASTER

The annual effective rate is 15.87%.

The annual effective rate can be calculated using the following formula:

(1 + i)^n - 1

where

i is the quarterly interest rate and

n is the number of quarters in a year. In this case, we have

i=0.15 and

n=4. Therefore, the annual effective rate is

(1 + 0.15)^4 - 1 = 15.87%

The quarterly interest rate is 15%. This means that if you invest $100, you will have $115 at the end of the quarter. If you compound the interest quarterly for 60 quarters, you will have $D_a = $296.78 at the end of 60 quarters. The annual effective rate is the rate that would give you $296.78 if you invested $100 at a simple annual interest rate.

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Answer:

y = -3.325x + 88.5

Step-by-step explanation:

The equation for slope-intercept form is y = mx + b

m = slope

b = y intercept value

Answer:

Elena made 10 batches.

Step-by-step explanation:

1 batch uses 2/3 cup

Elena used 6 2/3 cup

The number of batches is the quotient of 6 2/3 and 2/3.

We need to divide 6 2/3 by 2/3. First, we convert 6 2/3 into a fraction.

6 2/3 ÷ 2/3 = 20/3 ÷ 2/3 = 20/3 × 3/2 = 10

Answer: Elena made 10 batches.

Answer:

10

Step-by-step explanation:

2/3 for 1 cup if he used 6 2/3 of sugar then its 10.

if you times 2/3 by 10 its 6.66 and 6.66 is 2/3

1/3=33

2/3=66

3/3=100

Answer:

74=ab/c

Step-by-step explanation:

a=7c/4b

b=7c/4a

c=4ab/7

Answer:

320

Step-by-step explanation:

cheerleaders =1

football team members=2

2+1=3

football team members= 480 ×2/3

=320