Tina is selling tickets for a fundraiser.


She wants to sell more than $300 worth


of tickets. The inequality 12t> 300 can


be used to determine the number of


tickets, t, she must sell in order to meet


her goal. Which number line represents


the solution to this inequality? (6. 9B |


6. 1A, 6. 1B, 6. 10, 6. 1F)


10


20


30


B


to


10


20


30


+


С


+o


+


10


20


30


D


+


10


O


20


30

Therefore, After 20 minutes, there are approximately 11.9 kg (rounded to one decimal place) of salt in the tank.

To solve this problem, we need to consider the rate of change of the amount of salt in the tank over time.

(a) Let's denote the amount of salt in the tank after t minutes as y (in kg). We can set up a differential equation to represent the rate of change of salt:

dy/dt = (rate of salt in) - (rate of salt out)

The rate of salt in is given by the concentration of salt in the incoming water (0 kg/L) multiplied by the rate at which water enters the tank (90 L/min). Therefore, the rate of salt in is 0 kg/L * 90 L/min = 0 kg/min.

The rate of salt out is given by the concentration of salt in the tank (y kg/9000 L) multiplied by the rate at which water leaves the tank (90 L/min). Therefore, the rate of salt out is (y/9000) kg/min.

Setting up the differential equation:

dy/dt = 0 - (y/9000)

dy/dt + (1/9000)y = 0

This is a first-order linear homogeneous differential equation. We can solve it by separation of variables:

dy/y = -(1/9000)dt

Integrating both sides:

ln|y| = -(1/9000)t + C

Solving for y:

y = Ce^(-t/9000)

To find the particular solution, we need an initial condition. We know that at t = 0, y = 12 kg (the initial amount of salt in the tank). Substituting these values into the equation:

12 = Ce^(0/9000)

12 = Ce^0

12 = C

Therefore, the particular solution is:

y = 12e^(-t/9000)

(b) To find the amount of salt in the tank after 20 minutes, we substitute t = 20 into the particular solution:

y = 12e^(-20/9000)

y ≈ 11.8767 kg (rounded to one decimal place)

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Step-by-step explanation:

this creates 2 similar triangles.

that means all angles are the same. and all the side lengths of one triangle correlate to the corresponding side lengths of the other triangle by the same multiplication factor.

2 × f = 12

f = 12/2 = 6

now the same factor also applies to the relation of the heights :

6 × 6 = 36 ft

the tree is 36 ft tall.

In this case, the experimental probability is D. 0.860

First, note that Experimental probability, also known as Empirical probability, is founded on real experiments and adequate documentation of events.

In the table we can see that he rolled the cube 1000 times, and he recorded that 140 of those times he rolled a 5.

Then, the probability of rolling a 5 will be equal to:

P1 = 140/1000 = 0.14

Now, the probabilty of NOT rolling a 5, is equal to the rest of the probabilities, this is:

P2 = 1 - 0.14 = 0.86

then the correct option is D

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Jimmy rolls a number cube multiple times and records the data in the table above. At the end of the experiment, he counts that he had rolled 140 fives. Find the experimental probability of not rolling a five, based in Jimmy’s experiment. Round the answer to the nearest thousandth.

A. 0.140

B. 0.167

C. 0.667

D. 0.860

Three different vectors are [-8, 14],  [-6, 16], and [15, -18].

To find three different vectors that are in the span of the given vectors \(u_1\) = [-3, 8] and \(u_2\) = [-5, 6], we can use linear combinations of these vectors.

Let's call the three different vectors \(v_1\), \(v_2\), and \(v_3\). We can express them as follows:

\(v_1\) = \(u_1\) + \(u_2\) = [-3, 8] + [-5, 6] = [-3 + (-5), 8 + 6] = [-8, 14]

\(v_2\) = 2\(u_1\) = 2[-3, 8] = [-6, 16]

\(v_3\) = -3\(u_2\) = -3[-5, 6] = [15, -18]

Therefore, three different vectors that are in the span of \(u_1\) and \(u_2\) are \(v_1\) = [-8, 14], \(v_2\) = [-6, 16], and \(v_3\) = [15, -18].

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The factor that has a multiplicity of 3 is x - 2, and the polynomial has 7 roots.

The polynomial is given as:

\(P(x) = (x + 7)(x - 2)\²(x^2 - 4)(x + 1)^2\)

Express 4 as 2^2. So, the polynomial becomes

\(P(x) = (x + 7)(x - 2)\²(x^2 - 2^2)(x + 1)^2\)

Apply the difference of two squares on (x^2 - 2^2).

So, we have:

\(P(x) = (x + 7)(x - 2)\²(x - 2)(x + 2)(x + 1)^2\)

Group the common factors

\(P(x) = (x + 7)(x - 2)^3(x + 2)(x + 1)^2\)

For a factor to have a multiplicity of 3, it means that the exponent (i.e. power) is 3.

This means that x - 2 has a multiplicity of 3.

Next, we add the multiplicities of each factor, to get the number of roots.

\(n = 1 + 3 + 1 + 2\)

\(n = 7\)

Hence, the polynomial has 7 roots

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Answer: 64x^2

Step-by-step explanation:

Answer:

Step-by-step explanation:

The loop will run an infinite number of times

Answer:

-2x=30y-6

2x+30y-6=0

Step-by-step explanation:

The bearing of Town B from Danielle is

If Danielle is initially facing towards Town A at a bearing of 300 degrees, and she turns 135 degrees clockwise, we can determine the bearing of Town B from Danielle.

To calculate the new bearing, we add the initial bearing and the clockwise turn.

Initial bearing: 300 degrees

Clockwise turn: 135 degrees

Bearing of Town B = Initial bearing + Clockwise turn

Bearing of Town B = 300 degrees + 135 degrees

Bearing of Town B = 435 degrees

Therefore, the bearing of Town B from Danielle is 435 degrees.

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Answer: 2(x^2-7)

Step-by-step explanation:

Answer:

bx-3=2x+a

comparing the coefficient of x^1

b=2

comparing the coefficient of x^0

a= -3

a). To maximize production within the budget, 600 units of labor and 100 units of capital should be purchased. b). The maximum production under the budgetary constraint is approximately 8,366 units.

a). To maximize production, we need to allocate the budget efficiently between labor and capital. We can calculate the number of units of labor and capital by dividing the budgeted amount by the cost per unit. The budget of $576,000 divided by the cost of labor per unit ($400) gives us 1,440 units of labor. Similarly, dividing the budget by the cost of capital per unit ($2,400) gives us 240 units of capital. However, this allocation does not maximize production within the budgetary constraint.

b). To find the optimal allocation, we can use the partial derivatives of the production function with respect to L and K. Taking the partial derivative of the production function with respect to L, we get 37.5L^(-0.25)K^0.25. Equating this to the budgeted amount of labor (600 units), we can solve for K, which comes out to be 100 units. Similarly, by taking the partial derivative of the production function with respect to K, we get 12.5L^0.75K^(-0.75). Equating this to the budgeted amount of capital (100 units), we can solve for L, which comes out to be 600 units.

By substituting these values into the production function, we can calculate the maximum number of units of production, which is approximately 8,366 units.

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The conditional probability P(B|A) represents the probability of event B occurring given that event A has already occurred.

Using the provided probabilities, we can calculate P(B|A) by dividing the probability of both A and B occurring (P(A and B)) by the probability of A occurring (P(A)). The resulting value will provide the conditional probability of B given A.

To calculate P(B|A), we divide the probability of both A and B occurring (P(A and B)) by the probability of A occurring (P(A)). Given the provided probabilities:

P(A) = 0.76

P(B) = 0.19

P(A and B) = 0.05

We can substitute these values into the formula for conditional probability:

P(B|A) = P(A and B) / P(A)

Substituting the values:

P(B|A) = 0.05 / 0.76

Calculating this division:

P(B|A) ≈ 0.0658

Therefore, the conditional probability P(B|A) is approximately 0.0658. This means that given event A has occurred, there is a probability of approximately 0.0658 for event B to also occur.

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Answer:

12

Step-by-step explanation:

=40*3/10

=120/10

=12

Answer:

The two numbers are 4 and -6. Since -6 is less than 4, the lesser of these two numbers is -6.

The lesser number is -6.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Let's call the two numbers x and y. We know that:

We can solve this system of equations using substitution. Solving the first equation for x, we get:

x = -2 - y

We can substitute this expression for x in the second equation:

-2 - y + 2y = -8

Simplifying this equation, we get:

y = -6

Now we can use the first equation to find x:

x + y = -2

x + (-6) = -2

x = 4

So the two numbers are -6 and 4, and the lesser of the two numbers is -6.

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Answer:

15%

Step-by-step explanation:

0.15 x 100 = 15%

you just find the surface area for each rectangle/square and then add them together

5x8=40

5x8=40

25x5=125

8x25=200

5x25=125

8x25=200

add those numbers and you get 730 :)

The derivative of the inverse of the following function at the specified point on the graph of the inverse function is 1/2

Let's have further explanation:

The derivative of the inverse function (f⁻¹) at point '9', can be obtained by following these steps:

1: Express the given function 'f' in terms of x and y.

Let us assume, y=f(x).

2: Solve for x as a function of y.

In this case, we know that f(8) = 9, thus 8=f⁻¹(9).

Thus, from this, we can rewrite the equation as x=f⁻¹(y).

3: Differentiate f⁻¹(y) with respect to y.

We can differentiate y = f⁻¹(y) with respect to y using the chain rule and get:

                     y'= 1/f'(8).

4: Substitute f'(8) = 2 in the equation.

Substituting f'(8) = 2, we get y'= 1/2.

Thus, (f⁻¹)'(9) = 1/2.

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Answer:

y = 5x + 16

Step-by-step explanation:

5y + x = 20

5y = -x + 20

y = \(-\frac{1}{5}\)x + 20

Points: (-2, 7)

Slope (m⊥): = 5

y = 5x + b

7 = 5 ( -2 ) + b

6 = -10 + b

b = 16

y = 5x + 16

We have that the 80% of this type of seeds germinate, if we plant 90 seeds, the 80% is: 90 * 80/100 = 72

Then we know that 72 seeds will germinate.

a) The probability that fewer than 75 seeds germinate is 1 or 100%, having in count that at least 72 seeds will germinate.

Then the correct answer is 1 (100%)

b) The probability of 80 or more seeds germinating is 0, again, having in mind the percent of seeds that germinate. In other words, as just 72 of 90 seeds will germinate, it's impossible that 80 or more seeds will germinate.

Then the correct answer is 0 (0%).

c) To approximate the probability that the number of seeds germinated is between 67 and 75 is the average of the probability that 67 seeds have been germinated and the maximum probability because 72 are the seed that will germinate.

Then the correct answer is 0.965

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The total probability of a girl having a "K-name" is 3/8. The total probability of there being a girl in the club is 5/8.

Therefore, the conditional probability of having a girl with a "K-name" given that there is a girl in the club can be calculated as follows:

P (Girl | K-name) = P (K-name | Girl) × P (Girl) / P (K-name) = 2/5 * 5/8 / 3/8 = 2/3

Therefore, the probability of a girl with a K-name given that there is a girl in the club is 2/3.

In a club consisting of 5 girls (Kirsten, Sarah, Suzie, Monica, and Katie) and 3 boys (Kevin, Steve, and Samuel), we are asked to find P(Girl | K-name).

We can use Bayes' theorem to calculate the conditional probability of this event. This theorem states that the probability of an event given another event can be calculated as the product of the probability of the second event Therefore, the probability of a girl having a "K-name" given that there is a girl in the club is 2/3.

The conditional probability of there being a girl in the club given that a girl has a K-name is 2/3.

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Vector w can be expressed as w=1u-2v as linear combination of vector u and v.

Vector equation would be w=Au + Bv

[1,1]=A[5,7] + B[2,3]

Here A and B are constants and we are trying to find their values.

We can split two equations as

1=5A+2B → equation a

1=7A+3B → equation b

Solving these equations by elimination method . Multiplying equation a with 3 and equation b with 2.

3=15A+6B

2=14A+6B

1=A → A=1

Putting value of A in equation b:

1=7+3B

1-7=3B

-6=3B

B=-6/3=-2

A = 1 and B = -2 . It means we can write w as 1u - 2v. We can recheck by plugging the values in any of the vector to confirm if the values are correct or not.

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Height = Volume / area of base

Area of base = 3.5 x 4 = 14 sq. inches.

Height = 84 / 14

Height = 6 inches.

Answer:

False

Step-by-step explanation:

Horizontal goes from left to right. Therefore, the horizontal axis would be the x-axis because it shows the shifts from left to right. The y-axis would be up and down, which is vertical.

Answer:

d (or V in the picture) = 16

Step-by-step explanation:

Because the two triangle are similar, the ratios of each of the side lengths should be equal.  Therefore, 8/1 should be equal to d/2.

1.) Set up equality of ratios: 8/1 = d/2

2.) Cross multiply: 8*2 = d*1

3.) 16 = d

Therefore , the solution of the given problem of mean comes out to be one team's data values are closer to the median mean than that of the other.

The result from a set, also known as the arithmetic mean, is the sum of all values split by all of the values. It is frequently referred to as "mean" and is thought to be among the most commonly employed primary trend average. To obtain this answer, multiply the total number of numbers in the collection by the total number of values present.

Here,

The closer the data values are to the mean, the less variable they are, and the smaller the MAD.

A higher MAD shows that the data values are more variable and dispersed from the mean.

In this instance, the Bears' MAD of the amount of victories is 1, while the Saints' MAD is unspecified.

We cannot compare the distinctions of the two teams based solely on MAD since the Saints' MAD is not stated.

Since we cannot tell which team has a larger or smaller MAD, we cannot draw the conclusion that one team's data values are closer to the median mean than that of the other.

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(a) The dot product of A and B is given by: A · B = (2î + 3ĵ + 4k) · (î - 2ĵ + 3k)= 2(1) + 3(-2) + 4(3)= 2 - 6 + 12 = 8

Therefore, A · B = 8.

(b) The angle between two vectors A and B is given by:

θ = cos^(-1)((A · B) / (|A| |B|))

In this case, |A| is the magnitude of vector A and |B| is the magnitude of vector B. The magnitude of a vector is given by the square root of the sum of the squares of its components.

|A| = √(2² + 3² + 4²) = √(4 + 9 + 16) = √29

|B| = √(1² + (-2)² + 3²) = √(1 + 4 + 9) = √14

Plugging in the values:

θ = cos^(-1)(8 / (√29 √14))

(c) The scalar component of vector A in the direction of vector B is given by:

A_B = (A · B) / |B|

Plugging in the values:

A_B = 8 / √14

(d) The cross product of vectors A and B is given by:

A x B = (2î + 3ĵ + 4k) x (î - 2ĵ + 3k)

= (3(3) - 4(-2))î + (4(1) - 2(3))ĵ + (2(-2) - 3(3))k

= 17î - 2ĵ - 13k

Therefore,AXB = 17î - 2ĵ - 13k.

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(a) The dot product of A and B is given by: A · B = (2î + 3ĵ + 4k) · (î - 2ĵ + 3k)= 2(1) + 3(-2) + 4(3)= 2 - 6 + 12 = 8

Therefore, A · B = 8.

(b) The angle between two vectors A and B is given by:

θ = cos^(-1)((A · B) / (|A| |B|))

In this case, |A| is the magnitude of vector A and |B| is the magnitude of vector B. The magnitude of a vector is given by the square root of the sum of the squares of its components.

|A| = √(2² + 3² + 4²) = √(4 + 9 + 16) = √29

|B| = √(1² + (-2)² + 3²) = √(1 + 4 + 9) = √14

Plugging in the values:

θ = cos^(-1)(8 / (√29 √14))

(c) The scalar component of vector A in the direction of vector B is given by:

A_B = (A · B) / |B|

Plugging in the values:

A_B = 8 / √14

(d) The cross product of vectors A and B is given by:

A x B = (2î + 3ĵ + 4k) x (î - 2ĵ + 3k)

= (3(3) - 4(-2))î + (4(1) - 2(3))ĵ + (2(-2) - 3(3))k

= 17î - 2ĵ - 13k

Therefore,AXB = 17î - 2ĵ - 13k.

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