Question 3(Multiple Choice Worth 2 points)
Write the equation 4x – 3y = 12 in the form y = mx + b.
Oy = t - 4
o
y = 3x – 12
o
IN
Y
ft +4
Oy = -x - 4

Answer:

$5.50

Step-by-step explanation:

You need to divide $2,673 by 486.

we are given data on bear transplants in Glacier National Park over a 10-year period and are asked to calculate probabilities related to the bears' characteristics and outcomes.

a) To find the probability of selecting a male bear that became a nuisance after relocation, we divide the number of male bears that became nuisances by the total number of bears in the sample.

b) To find the probability of selecting a female bear or a bear that was successfully transplanted, we add the number of female bears to the number of successfully transplanted bears and divide by the total number of bears in the sample.

c) To find the probability of a randomly selected bear being a female and returning to the capture area, we divide the number of female bears that returned to the capture area by the total number of female bears in the sample.

d) To find the probability of a randomly selected male bear being enough of a nuisance to be transplanted, we multiply the proportion of nuisance bears that are male by the overall proportion of bears that become nuisances.

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The equation for the linear function f(- 1 / 2) = 1 and f(0) = -4  is f(x) = - 10x - 4

A linear function is a function that represents a straight line on the coordinate plane.

Therefore, the linear function of f(- 1 / 2) = 1 and f(0) = -4 can be represented as follows:

y = mx + b

where

Hence, using (- 1 / 2, 1)(0, -4)

m = -4 - 1 / 0 + 1  / 2

m = - 5 / 0.5

m = - 10

Therefore, using (0, -4)

y = - 10x + b

-4 = - 10(0) + b

b = -4

Hence, the linear function is f(x) = - 10x - 4

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The product of the volume and total surface area of the given right conical frustum is approximately 146520π². To find the product of the volume and total surface area of a right conical frustum, we first need to determine the individual values of volume and surface area.

The volume of a frustum can be calculated using the formula:

V = (1/3)πh(r₁² + r₂² + r₁r₂),

where h is the height of the frustum, r₁ and r₂ are the radii of the larger and smaller bases, respectively.

In this case, we are given that the radii of the larger and smaller bases are 12 and 9 units, respectively. We also know that the two bases are 4 units apart, which means the height of the frustum is 4 units.

Substituting the given values into the formula, we have:

V = (1/3)π(4)(12² + 9² + 12*9)

 = (1/3)π(4)(144 + 81 + 108)

 = (1/3)π(4)(333)

 = (4/3)π(333)

 ≈ 444π cubic units

Now, let's move on to calculating the total surface area of the frustum. The formula for the total surface area is:

A = π(r₁ + r₂)ℓ + πr₁² + πr₂²,

where ℓ is the slant height of the frustum.

Since the frustum is a right frustum, the slant height ℓ can be found using the Pythagorean theorem:

ℓ = √(h² + (r₁ - r₂)²)

Substituting the given values, we have:

ℓ = √(4² + (12 - 9)²)

 = √(16 + 9)

 = √25

 = 5

Now we can calculate the total surface area:

A = π(12 + 9)(5) + π(12²) + π(9²)

 = π(21)(5) + π(144) + π(81)

 = 105π + 144π + 81π

 = 330π square units

Finally, to find the product of the volume and total surface area, we multiply the two values:

VA = (444π)(330π)

  ≈ 146520π²

Therefore, the product of the volume and total surface area of the given right conical frustum is approximately 146520π².

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Answer:

300

Step-by-step explanation:

We divide the distance by time to get the rate. 1,200 is our distance, and 4 is our time.

1,200/4=300

Using Trigonometry, the BC is 4-√2.

The following trigonometric calculations are performed on a right-angled triangle: To go against the grain or hypotenuse. opposing side/hypotenuse = cos. The word "tan" is short for the bordering or adversarial side. Calculating height and distance is one of the most crucial applications for trigonometry in daily life. The principles of trigonometry are frequently applied in a variety of disciplines, such as criminology, marine biology, aviation, and navigation.

The relationship is represented by the sides' ratio, which is a trigonometric ratio. There are six trigonometric ratios: sine, cosine, tangent, cotangent, secant, and cosecant.

In right angle triangle ABGC by trigonometry

\(sin B = \frac{GC}{ BC}\)

⇒\(sin 45 = \frac{4}{ BC}\)

\(BC = 4\sqrt{2 }\) units

Hence, BC = 4√2

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Answer:

11 inch dummy

Step-by-step explanation:

4 + 7=11

Answer:

The answer is B, or the second one.

90 Adult tickets and 18 Children's tickets

Step-by-step explanation:

(90 x 15) + (18 x 9)

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The number of children's tickets sold is 18.

The number of adult tickets sold is 90.

Option B is the correct answer.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 - 9 is an equation.

We have,

Number of children tickets = x

Number of adults tickets = 5x

Cost of each children ticket = $9

Cost of each adult ticket = $15

Total  sales = $1512

Now,

9x + 5x(15) = 1512

9x + 75x = 1512

84x = 1512

x = 18

Thus,

The number of children's tickets sold is 18.

The number of adult tickets sold is 90.

Option B is the correct answer.

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True. A hashing algorithm is a mathematical routine used to generate a hash value from a primary key value.

A relative record number that may be used to retrieve the required record in a data structure is created using this hash value.

In order to facilitate quick access to the data, the hashing algorithm makes sure that the same hash value is generated for every primary key. How quickly the requested record can be found depends on how effective the hashing method is.

Also, it must be safe enough to prevent two main key values from producing the same hash value, as doing so might result in accessing the wrong records.

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The code snippet provided is a simple example of a mutual exclusion solution using the flag variables as a way to ensure that only one process can access the critical section (cs1) at a time.

The prefix1 and suffix1 are placeholders that do not have any significance to the functionality of the code.

In this implementation, the while loop keeps checking the value of flag[0] until it becomes false. Once flag[0] is false, the process can proceed to the critical section and execute the code within the curly braces.

Before exiting the critical section, the flag[1] variable is set to true to indicate that the process has entered the critical section. This is necessary because another process may be waiting to access the critical section, and the flag[1] variable serves as a signal to indicate that the critical section is currently being used.

After executing the code within the critical section, flag[1] is set to false to indicate that the process has finished accessing the critical section, and another process can now enter it.

Overall, this implementation is a basic form of mutual exclusion, and more complex algorithms exist to prevent deadlocks and other issues that may arise in concurrent systems.

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Answer:

A = 1

B = 2

C = 10

Step-by-step explanation:

slope intercept form is

y = mx + b

m is the slope

b is the y-intercept

The slopes of parallel lines are negative reciprocals

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

y = 2x + 7

slope  = 2

slope of perpendicular line is the negative reciprocal of 2

slope = -1/2

y = 5x - 5

y-intercept is -5

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

slope intercept form of perpendicular line

using slope = -1/2 and y-intercept  = -5

y = -(1/2)x - 5

Change to standard form:

multiply both sides by 2

2y = -x - 10

Add x + 10 to both sides

x + 2y + 10 = 0

Therefor

A = 1

B = 2

C = 10

Answer:

So, the prime factorization of 828 can be written as 2^2 × 3^2 × 23 where 2, 3, and 23 are prime.

Step-by-step explanation:

828 / 2 = 414

414 / 3 = 138

138 / 2 = 69

69 / 23 = 3

3 / 3 = 1

Answer to question 18:The differential equation is given by y′′+100y=0, we have to find the values of k for which y=Asinkt+Bcoskt is the solution.

Asinkt+Bcoskt can be written as

Rsin(kt+θ), where R=√(A2+B2),k=±√(k2),θ=tan−1(BA), for A and B not both 0.Then,

y′=kRcos(kt+θ), y′′=−k2

Rsin(kt+θ).

Therefore,

y′′+100y=(100−k2)R

sin(kt+θ).For this to be zero for all values of A and B, we must have

k=±10.Therefore, the answer is

k=±10. The given differential equation is

dtdy​=y4−y3+6y2

We need to find the constant solutions of the equation. The constant solutions are those solutions for which

y'=0 and y"=0.

We know that, dtdy​=0, when

y=0,y4−y3+6y2=0⇒y2(y2−y+6)=0y2−y+6>0 for all real y

Therefore, the only constant solutions are y(t)=0.Therefore, the answer is

d. y(t)=0 Answer to question 20:Given differential equation is

y′′+16y′+64y=0If we substitute

y=e^(mt), then the equation becomes

m²e^(mt)+16me^(mt)+64e^(mt)=0⇒(m+8)²e^(mt)=0⇒m=-8

Since the characteristic equation has a repeated root of -8, then the general solution of the differential equation is

y=(C1+C2t)e^(-8t)

Therefore, the answer is y=te^(−8t).

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A = …?

A = ½ (a + b) × h

A = ½ (6 + 2) × 3

A = ½ (8) × 3

A = 4 × 3

A = 12 square units.

Answer:

no solution

Step-by-step explanation:

The solution to a system of equations is at the point of intersection of the 2 lines.

Since the 2 lines are parallel they never intersect.

Thus there is no solution

The calculated measure of the angle CTZ is 38 degrees

From the question, we have the following parameters that can be used in our computation:

This means that

YTA + BTC = 90

So, we have

4y + 6 + 7y - 4 = 90

So, we have

11y = 88

Divide

y = 8

Next, we have

CTZ = 90 - BTC

So, we have

CTZ = 90 - (7y – 4)

This gives

CTZ = 90 - (7 * 8 – 4)

Evaluate

CTZ = 38

Hence, the measure of CTZ is 38 degrees

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The expression that can be used to represent the total price is 3(p - $0.75) + 5(p - $1).

The expression that can be used to determine the total amount spent in store A is:

5(p - $1)

The expression that can be used to determine the total amount spent in store B is:

3(p - $0.75)

Total price = 3(p - $0.75) + 5(p - $1)

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Answer:

0

Step-by-step explanation:

Answer:

x=20

x= -20

Step-by-step explanation:

(a) To show that W1 and W2 are orthogonal subspaces, we need to show that the dot product of any vector in W1 with any vector in W2 is zero. We can do this by showing that the dot product of each pair of basis vectors from W1 and W2 is zero.

(b) We can write y as a linear combination of the basis vectors, then solve for the coefficients using a system of equations. We get y = (-5/8)*v1 + (19/8)*v2 + (11/4)*v3 + (5/4)*v4. We can then take the appropriate linear combinations of v1, v2, v3, and v4 to get a vector in W1 and a vector in W2 that add up to y.

(a) To show that the subspaces W1 and W2 are orthogonal to each other, we need to show that every vector in W1 is orthogonal to every vector in W2. In other words, we need to show that the dot product of any vector in W1 with any vector in W2 is zero.

Let's take an arbitrary vector w1 in W1, which can be written as a linear combination of v1 and v2:

w1 = a1v1 + a2v2

Similarly, let's take an arbitrary vector w2 in W2, which can be written as a linear combination of v3 and v4:

w2 = b1v3 + b2v4

Now we can take the dot product of w1 and w2:

w1 · w2 = (a1v1 + a2v2) · (b1v3 + b2v4)

= a1b1(v1 · v3) + a1b2(v1 · v4) + a2b1(v2 · v3) + a2b2(v2 · v4)

We know that v1 · v3 = v1 · v4 = v2 · v3 = 0, because these pairs of vectors are not in the same subspace. Therefore, the dot product simplifies to:

w1 · w2 = a2b2(v2 · v4)

Since v2 · v4 is a scalar, we can pull it out of the dot product:

w1 · w2 = (v2 · v4) * (a2*b2)

Since a2 and b2 are just constants, we can say that w1 · w2 is proportional to v2 · v4. But we know that v2 · v4 = 0, because the dot product of orthogonal vectors is always zero. Therefore, w1 · w2 must be zero as well. This holds for any choice of w1 in W1 and w2 in W2, so we have shown that W1 and W2 are orthogonal subspaces.

(b) To find a vector in W1 that adds up to y, we can take the projection of y onto the subspace spanned by v1 and v2. Similarly, to find a vector in W2 that adds up to y, we can take the projection of y onto the subspace spanned by v3 and v4.

The projection of y onto W1 is given by proj_W1(y) = (-5/8)*v1 + (19/8)*v2.

The projection of y onto W2 is given by proj_W2(y) = (11/4)*v3 + (5/4)*v4.

Therefore, a vector in W1 that adds up to y is (-5/8)*v1 + (19/8)*v2, and a vector in W2 that adds up to y is (11/4)*v3 + (5/4)*v4.

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Answer:

25.82 is my answer in two decimal places

numbers above 4 are rounded to add 1

while numbers below 4 are rounded to add zero

from the last 5... round to add 1 to 2 before it

then the 2 +1 becomes 3

the 3 is rounded to add zero to 1, before it

then 1 +0 is still 1

then 1 is rounded to add zero to 6

then 6+0 is still 6

6 is then rounded to add 1 to 1

then 1+1 becomes 2, which is rounded to add zero to 9

then 9 is rounded to add 1 to 8

the the 8+1 becomes 9, which is rounded to add 1 to 3

then 3+1 becomes 4, which is rounded to add zero to 2.

stops here, since it's to two decimal places

answer is 25.82

Answer:

HIIiiiiiiiiiiiiiiiiiiIIIIIIIIIIIIIiiiiiiiiiiiiIIIIIIIIIIIIIIII

Step-by-step explanation:

Let:

x = number we want to find

the sum of a number and 6 is multiplied by 5:

(x + 6)*5

the result is the same as 7 times the number increased by 16. So:

(x + 6)*5 = 7x + 16

Let's solve for x:

Use distributive property on the left hand side:

5x + 30 = 7x + 16

Subtract 5x from both sides:

5x + 30 - 5x = 7x + 16 - 5x

30 = 2x + 16

Subtract 16 from both sides:

30 - 16 = 2x + 16 - 16

14 = 2x

Divide both sides by 2:

14/2 = 2x/2

7 = x

Answer:

I dont know

Step-by-step explanation:

Answer:

All real numbers

Step-by-step explanation:

The answers based on the given information:

1. Output per worker (Y/L) is given as 100. Capital per worker (K/L) is given as 40,000.

2. Investment per worker (I/L) can be calculated using the savings rate (s). I/L = s * (Y/L). Since the savings rate is 20% (0.20), I/L = 0.20 * 100 = 20.

3. Depreciation per worker can be calculated using the depreciation rate (d) and capital per worker (K/L). Depreciation per worker = d * (K/L). Since the depreciation rate is 4% (0.04), Depreciation per worker = 0.04 * 40,000 = 1,600.

4. Net investment per worker can be calculated by subtracting depreciation per worker from investment per worker. Net investment per worker = (I/L) - Depreciation per worker = 20 - 1,600 = -1,580.

5. Since the net investment per worker is negative, capital per worker is decreasing.

7. If capital per worker is 360,000, net investment can be calculated by multiplying the savings rate by the new output per worker (assuming it stays the same) and then subtracting the depreciation. Net investment = (s * (Y/L)) - (d * 360,000) = (0.20 * 100) - (0.04 * 360,000) = 20 - 14,400 = -14,380.

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The image point for the given rule and preimage is (6 - 8)

When we apply a rule T<a, b> to a preimage point (x, y) we get the image (x + a, y + b), so this is like a translation.

So if we apply the rule T<4, -1> to the preimage point (2, -7), the image will be:

(2 + 4, - 7 + (-1)) = (6 - 8)

Concluding, the image point is (6 - 8)

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Answer:

A) The 4 and (-4) are 0s.

B) 0 points after the second round

C) 4+(-4) is 0

The 4 and the (-4) are the zero pairs in the model

Andrew has 4 + (-4) = 0 points after the second round.

4 + (-4) = 0