consider the system of differential equations y′ 1 = −4y1 2y2, y′ 2 = −5y1 2y2. (1) rewrite this system as a matrix equation ~y′ = a~y. ~y′ = [ ] ~y

Answer:

conditional

Step-by-step explanation:

A camera has a listed price of 867.98 before tax. If the sales tax rate is 8.75%, the total cost of the camera with sales tax included is

$948.08.

To find the total cost of the camera including sales tax, you must use the formula price+(price*tax rate). In this case 867.98 + (867.98 * 0.0875) = 948.08.

To calculate the total cost with sales tax included, you must first determine the tax rate. In this case, the tax rate is 8.75%. To find the total cost, you must first multiply the price of the camera by the tax rate. This number will represent the amount of tax due to the purchase.

Then, you must add the price of the camera to the amount of tax for a total cost of 948.08. finally, to round to the nearest cent it is 948.08.

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Answer:

18

Step-by-step explanation:

The arrows on lines AB and CD indicate that these 2 shapes are similar and these 2 lines are corresponding so :

Linear scale factor :

12 ÷ 10 = 1.2 or 6/5

Let's use the fraction form

Using the linear scale factor we can make an equation to solve for x :

2x+4 = 6/5(x+8)

Expand the brackets :

2x+4 = 6/5x + 9.6

Subtract 4 from both sides :

2x = 6/5x + 5.6

Subtract 6/5x from both sides :

4/5x = 5.6

Divide both sides by 4/5 :

x = 7

Now substitute this value into the expression for the length of AE :

AE = 2(7) + 4

AE = 14 + 4

AE = 18

Hope this helped and have a good day

Answer:

116 units

Step-by-step explanation:

AE + ED = 180 because they make a straight angle and a straight angle is 180 degrees or half of a circle 360/2.

AE = 2x + 4 and ED = x +8 added together they equal 180

2x + 4 + x + 8 = 180  Combine the like terms

3x + 12 = 180  Subtract 12 from both sides of the equation

3x = 168  Divide both sides by 3

x = 56

Now that we know that x is 56 we can plug that in for AE to find its length

2x + 4

2(56) + 4

112 + 4

116

Step-by-step explanation:

1)  Total rectangle area =  W x H = 12 x 8 = 96 cm^2

 area of triangle (shaded portion) = 1/2 base * height = 1/2 * 7 x 8 = 28 cm^2

              Nonshaded portion = 96 - 28 cm^2 = 68 cm^2

          ratio shaded:nonshaded is then   28 : 68 = 7:17

2)   Look at the two middle triangles :  Height of each = 8 cm

       then reading across the diagram  height + base + height = 21 cm

            so base = 5 cm

   area of ONE triangle = 1/2 * base * height = 1/2 * 5 * 8 = 20 cm^2

        total area for FOUR of them  = 80 cm^2

Answer:

-2/3 then -7, 4

The probability to the statement to be true is 1/5.

Probability:

Probability refers the chance of an event occurring.

The formula of the probability is,

Probability = the number of ways of achieving success / the total number of possible outcomes.

Given,

The inhabitants of an island tell

the truth with probability 1/3 and

lie with probability 2/3, independently of each other.

One islander makes a statement. a second islander says that the first islander told the truth.

Here we need to find the probability of the statement.

Let us assuming the two islanders statements are independent, the probability they both told the truth is

=> 1/3 x 1/3 = 1/6

If the probability of the second guy backing up the first statement is the probability they both lied or they both told the truth

=> (2/3 x 2/3) + (1/3 x 1/3)

=> 4/9 + 1/6

=> 5/9

So, the probability of the first guy telling the truth, given that the second guy claiming it was true

=> P(A|B) = P(AB)/P(B)

=>  (1/9) / (5/9) = 1/5.

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Therefore, there are 4 x 1128 = 4512 possible 5 card poker hands with at least 3 aces that can be dealt from a standard deck of 52 cards.

1. There are 4 aces in a standard deck of 52 cards, so the maximum number of aces in a 5-card poker hand is 3.

2. There are C(4,3) = 4 ways to choose 3 aces out of the 4 aces in the deck.

3. For the remaining 2 cards, there are C(48,2) = 1128 ways to choose them from the 48 non-ace cards.

4. Therefore, there are 4 x 1128 = 4512 possible 5 card poker hands with at least 3 aces that can be dealt from a standard deck of 52 cards.

There are 4 aces in a standard deck of 52 cards, so the maximum number of aces in a 5-card poker hand is 3. There are C(4,3) = 4 ways to choose 3 aces out of the 4 aces in the deck. For the remaining 2 cards, there are C(48,2) = 1128 ways to choose them from the 48 non-ace cards.

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Answer: D. \(8\sqrt{2}\)

Step-by-step explanation:

Because the angles are the same we know the legs are the same length and we can use the formula a squared plus b squared equals c squared, and we know both legs are 8, and 8 squared is 64 so a squared plus b squared is 128. So h= \(\sqrt{128}\) and that is 11.313, and the only equation equal to that is D.

Answer:

The answer to your problem is D. 8√2

Step-by-step explanation:

Using the sine ratio in the right triangle

noting that sin45° = \(\frac{1}{sq root2}\) = exact value of it

sin45° = \(\frac{opposite}{hypotenuse}\) = \(\frac{8}{h}\)

Multiply both sides by h, then

h x \(\frac{1}{x, sq root2}\) = 8

Multiply both sides by, √2​

h = 8√2​ or D

Thus the answer to your problem is, D. 8√2​

Answer:

2 dollars.

Step-by-step explanation:

1 meter costs 3 dollars

2/3 meter costs 2/3 * 3

2/3 * 3 = 2

So you would pay 2 dollars for 2/3 of a meter.

Answer:

-------------------

Given three interior angle measures of a triangle:

Use the triangle sum theorem to find the missing angle:

So the missing angle is 67°.

(a) The center of the sphere is in the first octant and is tangent to the xz-plane and to the yz-plane. This means that the center of the sphere is at a point of the form (a,b,5) where a,b≥0. The distance from the origin to the center of the sphere is  \(\sqrt{43}\), so we have \(x^{2} +x^{2} +(5-0)^{2} =43\) This gives us \(a^{2} +b^{2} =38\)

The radius of the sphere is the distance from the center of the sphere to the point where the sphere touches the xz-plane. This distance is equal to the length of the hypotenuse of a right triangle with legs of length a and b. Therefore, the radius of the sphere is \(\sqrt{a^{2}+ b^{2} } =\sqrt{38}\)

The equation of the sphere is \((x-a)^{2}+ (y-b)^{2}+ (z-5)^{2} =38\)

(b) The point where the sphere touches the xz-plane is (a,0,5). The distance between the origin and this point is \(\sqrt{a} ^{2}+\sqrt(5-0)^{2} =\sqrt{a^{2} +25}\)

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Answer:

14.5 hours/14 hours 30 minutes

Step-by-step explanation:

The value of x when solving the equation 2x + 1 = -x + 4 using the algebra tiles is x = -1.

In the given model, 2 green long tiles and 1 green square tile represent the left side of the equation, and 1 long red tile and 4 square green tiles represent the right side of the equation. We are asked to find the value of x when solving the equation 2x + 1 = -x + 4 using the algebra tiles.

In the model, the green long tiles represent the positive term 2x, and the green square tile represents the positive constant term 1. The long red tile represents the negative term -x, and the square green tiles represent the positive constant term 4.

To balance the equation using algebra tiles, we need to ensure that both sides of the equation have the same number and type of tiles. In this case, we can see that the left side has 2 green long tiles and 1 green square tile, while the right side has 1 long red tile and 4 square green tiles.

To balance the equation, we need to eliminate the tiles on one side until we have the same number and type of tiles on both sides.

Here, we can remove one green long tile and add one long red tile to both sides. This will give us:

1 green long tile + 1 green square tile = 1 long red tile + 4 square green tiles

Now, we can see that both sides have 1 green long tile and 1 long red tile, as well as 1 green square tile and 4 square green tiles. The equation is balanced.

Since we have 1 green long tile representing the variable term, it corresponds to the value of x. Therefore, x = -1.

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Answer:

y = 2x

Step-by-step explanation:

quickest way : find the slope

which answer has that slope

(y2 - y1) ÷ (x2 - x1)

(10 - 8) ÷ (5 - 4)

2 ÷ 1 = 2

slope should be 2x

Answer:

\(\Huge\boxed{D}\)

Step-by-step explanation:

Hello There!

A is not true because overall 22% had trucks of the 100 people while only 9% overall had a van. So more people overall had trucks then vans meaning that vans has the lowest percentage of type of vehicle driven therefore we can eliminate answer choice A

B is also incorrect because from ages 41-50, a total of 14 people drive a van or sedan. Also from ages 41-50, a total of 14 people drive a SUV or truck. Because the total of people that drive each of the grouped vehicles is the same neither of the percentages would be lower or higher therefore we eliminate answer choice B

C is also incorrect because the same amount of people in the age group 31-40 drive trucks as the amount of people in the age group 41-50. Because the same amount of people from the different age groups drive trucks the percentage would be neither higher nor lower therefore C is incorrect

D is the correct answer choice because the total amount of people that drive trucks from the age range 21-30 is the same as the amount of people that drive a truck from other age groups. Or to be more specific the sum of the people who drive a truck from ages 31-40, 41-50 and over 50 is 11 (3+4+4=11) This meaning that the same percentage of people in the age range from 21-30 that drive a truck is the same as the percentage of people that drive a truck from the sum of the other age ranges. Hence the correct answer choice is D

Answer:

No the point (20,15) is not on line j.

Answer:

B and D

Step-by-step explanation:

quadrilaterals only have 4 sides hence the prefix quad

Answer:

B and D

Step-by-step explanation:

C has five sides and A has three sides with a curve, curve doesn't count as a side

The equation of the degree 6 polynomial with a root at 3, a double root at 2, and a triple root at -1, and y-intercept at y = 5 is given as follows:

y = -5/12(x - 3)(x - 2)²(x + 1)³.

The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.

The zeros of the function, along with their multiplicities, are given as follows:

Then the linear factors of the function are given as follows:

The function is then defined as:

y = a(x - 3)(x - 2)²(x + 1)³.

In which a is the leading coefficient.

When x = 0, y = 5, due to the y-intercept, hence the leading coefficient a is obtained as follows:

5 = -12a

a = -5/12

Hence the polynomial is:

y = -5/12(x - 3)(x - 2)²(x + 1)³.

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The measure of the central angle m ∠JIK is 160°.

Given that the circle I, in which IJ is the radius of 9 units, the area of shaded sector = 36π, we need to find the m ∠JIK, the central angle.

Area of the sector = central angle / 360° × π × radius²

∴ 36π = m ∠JIK / 360° × π × 9²

m ∠JIK = 360° × 4 / 9

m ∠JIK = 160°

Hence, the measure of the central angle m ∠JIK is 160°.

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Answer:

These are the estimates:

Polar Bear: 96

Reindeer: 72

Seal: 24

Walrus: 48

Step-by-step explanation:

240/30=8

Multiply the amount of people that like each animal by 8 to estimate how many out of 240 like that animal.

12*8=96

9*8=72

3*8=24

6*8=48

Answer:

It's quite easy

Step-by-step explanation:

people less than 30 years = frequency of people 0 to 15 + 15 to 30 = 8+15 =23

Therefore there are 23 people less than 30 years old.

pls mark me as brainliest pls.

Answer:

Let ac=ab=5

With this, bc= 5√2

Step-by-step explanation:

So to find ad, Let ad be x

5√2=(2)(x)

(5√2/2)= x

This proves that bc=2ad

The volume of e8.1.23 is 50/3 cubic units, and the centroid is at a height of y from the top. To find the centroid, divide the figure into two parts: the triangular part and the rectangular part. The total volume is V = (2/3)² (2/3+1) + 2(4/3)²/3V, which is 50/9 cubic units. The centroid is located at point O, with the height of O being y.

Given e8.1.23, we have to calculate the volume and the location of the centroid of the volume. Below are the steps:

Step 1: Calculation of volumeWe have to find the volume of the given e8.1.23, given as:In the above figure, let's consider a small element dx at a distance x from the top of the container. Its cross-section will be (2x+1)2. Let's now find the volume of this element. It will be:

Volume of the element = area × heightdx

= (2x + 1)² dx

Further integrating the above equation with limits from 0 to 2:

V = ∫02 (2x + 1)² dxV

= ∫02 (4x² + 4x + 1) dxV

= [4/3 x³ + 2x² + x]02V

= (4/3 × 2³ + 2 × 2² + 2) − 0V

= (32/3 + 8 + 2) − 0V

= 50/3 cubic units

Step 2: Calculation of CentroidThe centroid of the volume will be at a height y from the top. Let's divide the figure into two parts, one part will be the triangular part and the other part will be the rectangular part.Let the height of the rectangular part be a.Let the height of the triangular part be b.  Using the above figure,we know that b + a = 2 ⇒ b = 2 - aFor finding the location of the centroid of the volume, we have to use the formulae:where A1, A2, y1, and y2 are as follows:

A1 = a(2x+1)A2

= (2/3) b² y1

= a/2 y2

= b/3

For rectangular part:  

A1 = a(2x+1) y1

= a/2V1

= ∫02 a(2x + 1) (a/2) dxV1

= a/2 ∫02 (2ax + a) dxV1

= a/2 [ax² + ax]02V1

= a/2 (2a² + 2a)V1

= a² (a+1) cubic units

For triangular part:

A2 = (2/3) b²y2

= b/3V2

= ∫02 (2x + 1) (2/3) b² (x/3) dxV2

= 4b²/27 ∫02 x² dx + 2b²/9 ∫02 x dx + b²/3 ∫02 dxV2

= 4b²/27 [x³/3]02 + 2b²/9 [x²/2]02 + b²/3 [x]02V2

= 2b²/27 [8 + 4] + b²/3 [2]V2

= 2b²/3 cubic units

Therefore, the total volume is:

V = V1 + V2= a² (a+1) + 2b²/3 cubic units

Let's now find a and b:From the figure, b = 2 - a

Therefore, 2 - a + a = 2

⇒ a = 2/3

Therefore, b = 4/3

Therefore, the total volume is:

V = (2/3)² (2/3+1) + 2(4/3)²/3V

= 50/9 cubic units

Location of the centroid: Let's consider a point O as shown in the figure. The height of the point O will be y. For finding the value of y, let's first find the moments of each part with respect to O.

Using the formula M = Ay and M1 = A1 y1 + A2 y2 M = M1 = Ay

⇒ a(2x+1) [a/2] = [(2/3) b²] [b/3] (2x+1)/2

= b²/9 (2x+1)

= 2b²/9x

= (2b²/9 - 1)/2

For rectangular part:  

A1 = a(2x+1)

= (2/3)(2/3 + 1) (2x + 1)

= 2/3 (2x+1) = 4/9

For triangular part:

A2 = (2/3) b²

= (2/3) (4/3)²

= 32/27y2

= b/3

= 4/9

Let's now find y = M/Vy

= M1/V

= (A1 y1 + A2 y2)/V

= (A1 y1)/V + (A2 y2)/V

= M1/V

= 4/3 + 32/81y

= 50/27

Thus, the volume of the given e8.1.23 is 50/3 cubic units and the location of the centroid is 50/27 units from the top.

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The probability density function is f(x)=0.25.

What do you mean by probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

According to the given question,

We have he continuous random variable x, which has a uniform distribution over the interval from 20 to 28. refer to exhibit 6-1. We calculate the probability density function has what value in the interval between 21 and 25.  

We use the formula:

\(f(x)=\frac{1}{b-a}\)

We have a=21 and b=25, we get

\(f(x)=\frac{1}{25-21}\\ f(x)=\frac{1}{4} \\f(x)=0.25\)

Therefore, the probability density function is f(x)=0.25.

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The magnetic field B at a distance of 2 cm, 10 cm, and 20 cm away from the axis of a solid wire of radius 10 cm carrying a current of 5.0 A uniformly distributed over its cross-section is 0.01 T, 1.0 x 10^-5 T, and 2.5 x 10^-6 T respectively, and a graph of B versus x for 0 < x < 20 cm shows a peak value of 0.01 T at x = 0 and a rapid decrease to approach zero as x approaches the radius of the wire.

To find the magnetic field B at a point at a distance r from the axis of the wire, we can use the formula:

B = μ₀I/(2πr)

where B is the magnetic field, I is the current, r is the distance from the axis, and μ₀ is the permeability of free space (4π x 10^-7 T m/A).

(a) At a distance of 2 cm from the axis, the magnetic field is:

B = μ₀I/(2πr)

= (4π x 10^-7 T m/A) x (5.0 A)/(2π x 0.02 m)

= 0.01 T

(b) At a distance of 10 cm from the axis, the magnetic field is:

B = μ₀I/(2πr)

= (4π x 10^-7 T m/A) x (5.0 A)/(2π x 0.10 m)

= 1.0 x 10^-5 T

(c) At a distance of 20 cm from the axis, the magnetic field is:

B = μ₀I/(2πr)

= (4π x 10^-7 T m/A) x (5.0 A)/(2π x 0.20 m)

= 2.5 x 10^-6 T

To sketch a graph of B versus x for 0 < x < 20 cm, we can use the formula for B and plot it for different values of x. Since the current is distributed uniformly over the cross-section of the wire, the magnetic field will also be symmetric around the axis of the wire. Therefore, the graph will have a maximum at x=0 and will decrease as x increases.

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the probability that the diameter of a elected bearing is greater than 85 millimeter P(diameter > 85) = P(z > (85-81)/4) = P(z > 1) = 0.1587

The diameter of ball bearings is normally distributed, with a mean of 81 millimeters and a variance of 16.

To calculate the probability that a selected bearing has a diameter greater than 85 millimeters, we first calculate the z-score for 85 millimeters.

We subtract 81 from 85 to get 4, and divide by 4 to get 1 for the z-score.

We the look up the probability for a value of 1 in the z-table, which is 0.1587.

This is the probability that a selected bearing has a diameter greater than 85 millimeters, rounded to four decimal places.

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Answer:

The answer should be D, 2,839 millimeters.

If you multiply 96 by 29.574, you get 2,839.

Answer:

66 percentage of people are on the sand.