Need helppp........!!!!!!!!!!

The value of determinant of the matrix det (AB) is 15.

Given matrices A and B are 3 by 3 matrices with

det (A) = 3 and

det (b) = 5.

We need to find the value of det (AB).

Writing the given matrices into the augmented matrix form gives [A | I] and [B | I] respectively.

By multiplying A and B, we get AB. Similarly, by multiplying I and I, we get I. We can then write AB into an augmented matrix form as [AB | I].

Therefore, we can solve the augmented matrix [AB | I] by row reducing [A | I] and [B | I] simultaneously using elementary row operations as shown below.


The determinant of AB can be calculated as det(AB) = det(A) × det(B)

= 3 × 5

= 15.

Conclusion: The value of det (AB) is 15.

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We need to find the value of determinant det(AB), using the formula: det(AB) = det(A)det(B)

=> det(AB) = 3 × 5

=> det(AB) = 15.

Hence, the value of det(AB) is 15.

The given matrices are A and B. Here, we need to determine the value of det(AB). To calculate the determinant of the product of two matrices, we can follow this rule:

det(AB) = det(A)det(B).

Given that: det(A) = 3

det(B) = 5

Now, let C = AB be the matrix product. Then,

det(C) = det(AB).

To evaluate det(C), we have to compute C first. We can use the following method to solve the augmented matrix by elementary row operations.

Given matrices A and B are: Matrix A and B:

[A|B] = [3 0 0|1 0 1] [0 3 0|0 1 1] [0 0 3|1 1 0][A|B]

= [3 0 0|1 0 1] [0 3 0|0 1 1] [0 0 3|1 1 0].

We can see that the coefficient matrix is an identity matrix. So, we can directly evaluate the determinant of A to be 3.

det(A) = 3.

Therefore, det(AB) = det(A)det(B)

= 3 × 5

= 15.

Conclusion: Therefore, the value of det(AB) is 15.

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Answer:

x = 68°

Step-by-step explanation:

This is an isosceles triangle, which means the two base angles will be the same. (56° and 56°)

All triangles angles must add up to 180, so if we take 180-56-56 we will find the missing angle (x).

180-56-56 = 68

x = 68°

Answer:

x=\(\sqrt{55}\) or about 7.4

Step-by-step explanation:

Use the Pythagorean Theorem:

8^2=3^2+x^2

64=9+x^2

55=x^2

x=\(\sqrt{55}\) or about 7.4

Answer:

7.42 feet

Step-by-step explanation:

.

Answer: Choice B

Two imaginary solutions

=======================================================

Explanation:

The given equation is

4x^2 - 3x + 1 = 0

Compare this to the general quadratic

ax^2 + bx + c = 0

to find that a = 4, b = -3, c = 1.

Plug those values into the discriminant formula below.

d = b^2 - 4ac

d = (-3)^2 - 4*4*1

d = 9 - 16

d = -7

Then recall that...

We see that d = -7 fits with the third option highlighted above.

4x2 – 3x + 1 =

Answer:

i don't know I just like my personality

The differential equation concerning the given question is Q' = -2.5Q Q(0) = 0 . Therefore the required correct answer for the question is Option A.

a) The differential equation expressing the quantity Q(t)  of warfarin in the body, at t hours later when a patient who is suffering from Warfarin  is given a pill containing 2.5 mg of Warfarin then,

dQ/dt = -kQ
here Q(0) = 2.5

b) The differential equation the expressing the quantity Q(t)  of warfarin in the body, at t hours later when a patient who is not suffering from Warfarin  is given a pill containing 0.5 mg/hr then,

dQ/dt = -kQ + r
where Q(0) = 0
Here
k = rate constant
r = rate of administration
The differential equation concerning the given question is Q' = -2.5Q Q(0) = 0 . Therefore the required correct answer for the question is Option A.

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The rate at which Warfarin leaves the body should be proportional to the amount still in the body, not a constant rate of 2.5. So the correct differential equation for part (b) is:

Q' = 0.5 - kQ, where Q(0) = 0

Where k is the proportionality constant for the rate of elimination.

Explanation

(a) Let's denote the rate of elimination as k, where k > 0. Since the elimination rate is proportional to the amount of warfarin, we can write the differential equation as:

Q'(t) = -kQ(t)

Given that the initial condition is a 2.5 mg pill, the initial condition should be:

Q(0) = 2.5

So the differential equation for part (a) is:

Q'(t) = -kQ(t), Q(0) = 2.5

(b) In this case, the patient receives warfarin intravenously at a rate of 0.5 mg/hour. Thus, we should add the rate of administration to our equation:

Q'(t) = 0.5 - kQ(t)

The initial condition is still that the patient has no warfarin in her system:

Q(0) = 0

So the differential equation for part (b) is:

Q'(t) = 0.5 - kQ(t), Q(0) = 0

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First of all we have to find the cost of a book then multiply it by 5 :

$ 11.20 ÷ 8 = $ 1.4

$ 1.4 × 5 = $ 7

Thus 5 books have a cost of $ 7 .

Answer:

The cost of 5 books is $7

Step-by-step explanation:

If there are 8 books and you need to find the cost of 5, you need to first find the cost for one book.

If 8 books cost 11.20.

11.20 ÷ 8 = 1.40

1.40 is the cost of one book

1.40 x 5 = 7

So the cost of 5 books is $7

I tried my best to explain

Answer:

Quadrilateral ABCD is a SQUARE

Step-by-step explanation:

When we are given coordinates (x1, x2) and (y1 , y2) for a Quadrilateral, we solve for the sides using this formula.

√(x2 - x1)² + (y2 - y1)²

A (3, 1), B (4, 4), C (7, 5), D (6, 2)

Side AB = A (3, 1), B (4, 4)

√(x2 - x1)² + (y2 - y1)²

= √(4 - 3)² + (4 - 1)²

= √1² + 3²

= √1 + 9

= √10

Side BC = B (4, 4), C (7, 5)

√(x2 - x1)² + (y2 - y1)²

= √(7 - 4)² + (5 - 4)²

= √3² + 1²

= √9 + 1

= √10

Side CD = C (7, 5), D (6, 2)

√(x2 - x1)² + (y2 - y1)²

= √(6 - 7)² + (2 - 5)²

= √(-1) ² + (-3)²

= √1 + 9

= √10

Side AD = A (3, 1), D (6, 2)

√(x2 - x1)² + (y2 - y1)²

= √(6 - 3)² + (2 - 1)²

= √3² + 1²

= √9 + 1

= √10

From the above calculation,

Side AB = √10

Side BC = √10

Side CD = √10

Side AD = √10

Hence, AB = BC = CD = AD

When all the side of a Quadrilateral are the same or equal to each other, it means the Quadrilateral is a square.

Therefore, Quadrilateral ABCD is a SQUARE

The Trapezoidal rule and Simpson's rule are two methods used to approximate the value of a definite integral. The Trapezoidal rule approximates the integral by dividing the region between the lower and upper limits of the integral into n trapezoids, each with a width h. The approximate value of the integral is then calculated as the sum of the areas of the trapezoids. The Simpson's rule is similar, except the region is divided into n/2 trapezoids and then the integral is approximated using the weighted sum of the area of the trapezoids.

For the given integral 4 x x2 1 0 dx, with n = 200, the Trapezoidal rule and Simpson's rule approximate the integral to be 7.4528 and 7.4485 respectively, rounded to four decimal places. The exact value of the integral is 7.4527. The difference between the exact and approximate values is very small, thus indicating that both the Trapezoidal rule and Simpson's rule are accurate approximations.

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The probability that exactly 8 peas are green, from the random selection would be 22. 56 %.

This is a binomial probability problem as the probability of an exact likelihood from an event needs to be found.

The relevant formula is:

P ( X = k ) = C ( n , k) x p^ k x q ^( n - k)

Solving for the probability, that exactly 8 peas are green gives:

P ( X = 8 ) = C( 12, 8) x ( 3 / 4 ) ^8 x ( 1 / 4 )^4

P ( X = 8 ) = (12! / ( 8 ! ( 12 - 8 )!) ) x ( 3/4 ) ^8 x ( 1 / 4 ) ^4

P ( X = 8 ) = 0. 2256

P ( X = 8 ) = 22. 56 %

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Answer: 4/10 = look below for explanation

Step-by-step explanation:

Transform 2/5 into the same demononator

= 2/5 becomes 4/10 because you've multiplied 2x2 and 5x2

which becomes 4/10 and 1/10

to solve: 4/10 - 1/10 = 3/10

Answer:

(2xy)²

Step-by-step explanation:

please mark me as brainliest

x²/21 + y²/25 = 1 is the equation of the ellipse

Given: the length of the major axis = 10 and foci = (0, ± 2)

Since the foci are on the y-axis, the major axis will be along the y-axis. Thus, the equation of the ellipse is:

x²/b² + y²/a² = 1

Since the length of the major axis = 2a. Thus:

2a = 10

a = 10/2 = 5

a² = 5² = 25

c = 2

c² = a² - b²

2² = 5² - b²

4 = 25 - b²

b² = 25 - 4 = 21

Substitute a² = 25 and b² = 21 into the equation:

x²/b² + y²/a² = 1

x²/21 + y²/25 = 1

Therefore,  the equation of the ellipse is x²/21 + y²/25 = 1

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The average rate energy is 3.99 W and  the energy per cycle of the wave is 0.996 J.

Given equation of wave is: y(x,t) = 0.370sin(8πt − 3πx + 4π)

where x and y are in meters,

t is in seconds, and μ of the wire is 77.5 g/m.

- The wave equation for the given wave can be represented as :

y(x,t) = A sin(kx - ωt)

where A is the amplitude

k is the wave number

ω is the angular frequency

a) The average rate at which energy is conveyed along the wire is given by

Pavg = ½μω²A²v

Pavg = ½(0.0775 kg/m)(8π/T)²(0.370 m)²v

= 0.17 m/s

Therefore, Pavg = 3.99 W.

b) The energy per cycle of the wave is given by

E = PavgT / 2πE

= (3.99 W)(2π / 8π)E

= 0.996 J

Therefore, the energy per cycle of the wave is 0.996 J.

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Answer:

6,2

Step-by-step explanation:

The fourth point of the parallelogram will be (-6,1) so option (C) will be correct.

A basic quadrilateral with two sets of parallel sides is known as a parallelogram.

A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.

There are 4 types of parallelograms, including 3 special types. The four types are parallelograms, squares, rectangles, and rhombuses.

The slope of the green lines and red line should be same for being it a parallelogram.

Slope of green line = (7-2)/(3-1) = 2.5

So the only coordinate is matching the slope 2.5 of red line is (-6,1).

Slope = (6-1)/(-4+6) = 2.5

Hence "The fourth point of the parallelogram will be (-6,1)".

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As OP bisects ∠AOR, ∠AOP = ∠POR = 55°

So, ∠AOR = ∠AOP + ∠POR = 55° + 55° = 110°

As OS bisects ∠ROB, ∠ROS = ∠SOB = x

As total angle on a line is 180°,

110° + x + x = 180°

=> 2x = 70

=> x = 35°

∠POS = ∠POR + ∠ROS = 55° + x = 55° + 35°

=> ∠POS = 90°

The values of b and a for the logarithmic function in this problem are given as follows:

The logarithmic function in the context of this problem has the format given as follows:

\(y = b\log_3{x + a}\)

The vertical asymptote is at x = -4, hence:

\(y = b\log_3{x - 4}\)

When x = 5, y = -1, hence the parameter b is obtained as follows:

\(-1 = b\log_3{5 - 4}\)

0.477b = -1

b = -1/0.477

b = -2.1.

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Answer:

\(y = \frac{5}{2}x +\frac{1}{2}\)

Step-by-step explanation:

in this graph we know two points whose values are certain which are, (1,3) and (-1,-2) we can find the equation of this line from these two points.

first we need to find slop which is m.

y2-y1/x2-x1 = m

y2 = 3( highest y value will always be y2) and y1 = -2

x2 = 1( counterpart of y2) and x1 = -1

3--2/1--1 = 5/2 ( -- is +)

so m = 5/2

now we can find the equation of line.

choose any of the two points from above to find the equation. ill choose (1,3)

y-3/x-1 = 5/2

\(y-3 = \frac{5}{2} (x-1)\\\\y = \frac{5}{2}x -\frac{5}{2} +3\\\\y = \frac{5}{2}x +\frac{1}{2}\)

Answer: The Philadelphia Eagles tried to blow a 19-point lead to the Chicago Bears, but managed to hold on for a 22-14 victory in a rematch of the NFC Wild Card Game to move to 5-4 on the year. Philadelphia allowed the Bears to score 14 unanswered points after taking a 19-0 lead in the third quarter, but put together one of their most impressive drives of the season in taking 8:14 off the clock in the fourth quarter, converting four consecutive third downs in the most critical junction of the game.

Chicago never got the ball back after Jake Elliott hit a 38-yard field goal with 26 seconds left to make it 22-14. Bears tight end Adam Shaheen muffed the catch on the kickoff and the Eagles recovered to deny Chicago a last ditch effort for a Hail Mary and an attempt to tie the game with a two-point conversion.

Jordan Howard scored a touchdown in his first game against his former team, finishing with 19 carries for 82 yards and a touchdown. Zach Ertz had his best game of the season as the Eagles tight end had nine catches for 103 yards and a touchdown, a 25-yard catch for his second score of 2019.

The Bears had just nine total yards in the first half, but rallied back in this game with two scoring drives in three possessions between the third and fourth quarter. Chicago's offense had no turnovers, but finished with just 164 yards of offense. Mitchell Trubisky went 10 of 21 for 125 yards with no touchdowns and a 66.6 passer rating. The Bears have lost their fourth consecutive game after a 3-1 start to the season, falling to 3-5 and remaining in last place in the NFC North.

Step-by-step explanation:

The number of points scored by the eagles is 19 points.

Suppose the points scored by the bears, eagles, and cowboys are x, x+2, x+4 respectively.

It is given the product of the points scored by the bears and cowboys was 37 more than the 8 times the sum of the points scored by the eagles and cowboys.

This means, x(x+4) =37+8(x+2+x+4)

x(x+4) =37+8(2x+6)

\(x^{2} +4x = 37+16x+48\)

\(x^{2} -12x-85=0\), which is a quadratic equation.

Any equation in the form \(ax^{2} +bx+c=0\) is called a quadratic equation where \(a\neq 0\).

\(x^{2} -17x+5x-85=0\)

\(x(x-17)+5(x-17)=0\)

\((x-17)(x+5)=0\)

\(x=17\)

So, eagles scored x+2 = 17+2 =19 points.

Therefore, The number of points scored by the eagles is 19 points.

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The value of the postfix expression 6 3 2 4 + - * is 18, which falls between 15 and 100. Therefore, the correct answer is d) Something between 15 and 100.

Here is the step-by-step  of how to evaluate the postfix expression:

1. Start with the first two numbers, 6 and 3, and the first operator, *. Multiply 6 and 3 to get 18.
2. Move on to the next two numbers, 2 and 4, and the next operator, +. Add 2 and 4 to get 6.
3. Now you have 18 and 6, and the last operator, -. Subtract 6 from 18 to get 12.
4. The final result is 12.

Therefore, the value of the postfix expression 6 3 2 4 + - * is 12, which falls between 15 and 100. The correct answer is d) Something between 15 and 100.

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Answer: Therefore, the length of a blue bead is 2.5 cm, and the length of a green bead is 1.2 cm. And the length of the bracelet is:

10 × (2.5 + 1.2) = 37 cm.

Step-by-step explanation:

To represent the length of the bracelet, we need to determine the length of each repetition of the basic pattern and then multiply it by the number of times the pattern is repeated.

The length of each repetition of the basic pattern is the sum of the length of one blue bead and one green bead, which is:

B + 1.2 cm

Since the basic pattern is repeated 10 times, the total length of the bracelet is:

10 × (B + 1.2) cm

And we know that the total length of the bracelet is 37 cm, so we can set up an equation:

10 × (B + 1.2) = 37

Simplifying the equation, we can divide both sides by 10:

B + 1.2 = 3.7

Subtracting 1.2 from both sides, we get:

B = 2.5

Therefore, the length of a blue bead is 2.5 cm, and the length of a green bead is 1.2 cm. And the length of the bracelet is:

10 × (2.5 + 1.2) = 37 cm.

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The dimension of subspace a is 2 and the dimension of subspace b is 1.

To find the dimensions of subspaces, we need to find a basis for each subspace and then count the number of vectors in the basis.

a. The representative vector (d, c - d, c) can be written as (d, -d, 0) + (0, c, c) = d(1, -1, 0) + c(0, 1, 1). This shows that W is spanned by the set S = {(1, -1, 0), (0, 1, 1)}. To show that S is linearly independent, we can set the linear combination equal to zero:
a(1, -1, 0) + b(0, 1, 1) = (a, -a, b) + (0, b, b) = (0, 0, 0)
This implies a = -b and b = 0, which means a = b = 0. Therefore, S is linearly independent and a basis for W. The dimension of W is the number of vectors in the basis, which is 2.

b. The representative vector (2b, b, 0) can be written as b(2, 1, 0). This shows that W is spanned by the set S = {(2, 1, 0)}. To show that S is linearly independent, we can set the linear combination equal to zero:
a(2, 1, 0) = (0, 0, 0)
This implies a = 0. Therefore, S is linearly independent and a basis for W. The dimension of W is the number of vectors in the basis, which is 1.

In summary, the dimension of subspace a is 2 and the dimension of subspace b is 1.

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a) The null hypothesis (H0): The air bag hospitalization rate for midsize cars is equal to or higher than 7.8%.

  The alternative hypothesis (Ha): The air bag hospitalization rate for midsize cars is lower than 7.8%.

b) The critical value is -2.33.

c) The p value is 0.0085.

a. The null hypothesis (H0): The air bag hospitalization rate for midsize cars is equal to or higher than 7.8%.

  The alternative hypothesis (Ha): The air bag hospitalization rate for midsize cars is lower than 7.8%.

b. Since we are testing if the air bag hospitalization rate is lower than 7.8%, it is a one-tailed test. We will use a significance level of 0.01.

Now, the critical value is -2.33 (corresponding to a one-tailed test with a significance level of 0.01).

c. The proportion of hospitalizations in the sample is: p = 46/821 = 0.056

  The expected proportion under the null hypothesis is: p0 = 0.078 (7.8% expressed as a decimal)

  The standard error of the proportion is: SE(p) = √((p0 * (1 - p0)) / n)

= √((0.078 * (1 - 0.078)) / 821)

= 0.0091

and, the test statistic (z-value) is:

z = (p - p0) / SE(p)

= (0.056 - 0.078) / 0.0091

= -2.418

So, the p-value is approximately 0.0085.

d. The decision and conclusion:

  Since the computed test statistic (z-value) of -2.418 is smaller than the critical value of -2.33, we reject the null hypothesis.

  Therefore, there is evidence to support the claim that the air bag hospitalization rate is lower than 7.8% for midsize cars with air bags at a 0.01 level of significance.

  In conclusion, based on the given data, we have sufficient evidence to suggest that the air bag hospitalization rate for midsize cars is lower than 7.8%.

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The ranking is like, D (next to the end of the wrench, B=E (middle of the wrench), F next to the top of the wrench, A (top of the wrench), C (bottom of the wrench)

Given,

Forces;

D > B=E > F > A > C

We have to rank these forces (a through f) on the basis of the magnitude of the torque they apply to the wrench, measured about an axis centered on the bolt

Magnitude of torque;

The ratio of the force's and the lever arm's magnitudes yields the torque's magnitude. Force has a dimensional formula of [M1L1T2], whereas a lever arm has [L]. Consequently, [M1L2T]2 is the dimensional formula for torque.

Here,

The ranking is;

D (next to the end of the wrench, B=E (middle of the wrench), F next to the top of the wrench, A (top of the wrench), C (bottom of the wrench)

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Answer:

Its EFBGCAHDI

The upper and lower quartiles of the discounts are £45 and £20 respectively.

The interquartile range of the discounts is £25.

Based on the information provided about the discount on sale items shown in the graph (line plot) attached below, the upper and lower quartiles of the discounts can be calculated by using the following mathematical expressions;

Upper quartile, P₇₅ = 80 × 75/100

Upper quartile, P₇₅ = 60, which corresponds to £45.

Lower quartile, P₂₅ = 80 × 25/100

Lower quartile, P₂₅ = 20, which corresponds to £20.

Mathematically, interquartile range (IQR) of a data set is typically calculated as the difference between the first quartile (Q₁) and third quartile (Q₃):

Interquartile range (IQR) = Q₃ - Q₁ = P₇₅ - P₂₅

Interquartile range (IQR) = 45 - 20

Interquartile range (IQR) = £25.

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Complete Question:

A shop has an event where 80 items are on sale. Each item is discounted by u to £60.

a. Find the upper and lower quartiles of the discounts.

b. Find the interquartile range of the discounts.

The first four points of the pattern are (3, 0), (5, 4), (7, 8) and (9, 12).

Coordinates are the set of points in a geometrical plane or space, which is used to denote the exact point in the coordinate plane or space.

Given that,

Maddy wrote a pattern for all the x coordinates starting at 3 and followed the rule "add 2".

The first x coordinate is 3.

Then comes 5, 7, 9, 11, .........

Ted wrote a pattern for all the y coordinates starting at 0 and followed the rule "add 4".

The first y coordinate is 0.

Then comes 4, 8, 12, 16, ........

So the points are (3, 0), (5, 4), (7, 8), (9, 12), (11, 16), .........

Hence the points are going in the form as (3, 0), (5, 4), (7, 8), (9, 12), (11, 16), .........

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