There is a bag filled with 4 blue and 5 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting exactly 1 blue?

A. In equation form: Revenue = 9x1 + 12x2 + 4x3 + 5x4 + 8x5

B. Non-negativity constraint: x1, x2, x3, x4, x5 ≥ 0

To solve this problem using E x c e l Solver, set up the revenue function and the constraints. Here's how you can do it:

a. Revenue Function:

Let's denote the number of cakes baked for each type as x1, x2, x3, x4, and x5 respectively.

The revenue function can be formulated as:

Revenue = (Selling Price of Cake 1 × Number of Cake 1) + (Selling Price of Cake 2 × Number of Cake 2) + (Selling Price of Cake 3 × Number of Cake 3) + (Selling Price of Cake 4 × Number of Cake 4) + (Selling Price of Cake 5 × Number of Cake 5)

In equation form:

Revenue = 9x1 + 12x2 + 4x3 + 5x4 + 8x5

b. Constraints:

The constraints for the availability of ingredients can be formulated as follows:

Milk constraint: 4x1 + 3x2 + x3 + 5x4 + 4x5 ≤ 280

Sugar constraint: 7x1 + 4x2 + 5x3 ≤ 300

Egg constraint: x1 + 2x2 + 3x3 + 4x4 + 5x5 ≤ 80

Flour constraint: 3x1 + 4x2 + 2x3 + 4x4 + 6x5 ≤ 250

Cream constraint: 4x1 + 5x3 + x4 + 3x5 ≤ 190

Non-negativity constraint: x1, x2, x3, x4, x5 ≥ 0

c. Solve the system of linear inequalities using E x c e l Solver:

To solve the system of linear inequalities using E x c e l Solver, follow these steps:

1. Open M i c r o s o f t E x c e l and enter the following data in a new sheet:

| | A | B |

|-----|-----------|-----------------|

| 1 | Cakes | Selling Price |

| 2 | Cake 1 | $9 |

| 3 | Cake 2 | $12 |

| 4 | Cake 3 | $4 |

| 5 | Cake 4 | $5 |

| 6 | Cake 5 | $8 |

| | | |

| | | Formula |

| 9 | Milk | 280 |

| 10 | Sugar | 300 |

| 11 | Eggs | 80 |

| 12 | Flour | 250 |

| 13 | Cream | 190 |

2. In cell B16, enter the formula for the revenue:

=B2×B7 + B3×B8 + B4×B9 + B5×B10 + B6×B11

3. In cell B18, enter the formula for the milk constraint:

=4×B2 + 3×B3 + B4 + 5×B5 + 4×B6

4. In cell B19, enter the formula for the sugar constraint:

=7×B2 + 4×B3 + 5×B4

5. In cell B20, enter the formula for the egg constraint:

=B2 + 2×B3 + 3×B4 + 4×B5 + 5×B6

6. In cell B21, enter the formula for the flour constraint:

=3×B2 + 4×B3 + 2×B4 + 4×B5 + 6×B6

7. In cell B22, enter the formula for the cream constraint:

=4×B2 + 5×B4 + B5 + 3×B6

8. In cell B24, enter the formula for the non-negativity constraint for Cake 1:

=B2

9. Repeat step 8 for the remaining cakes, entering the formulas in cells B25, B26, B27, and B28:

=B3

=B4

=B5

=B6

10. Now, select cells B16 to B28 and click on the "Solver" button in the "Data" tab.

11. In the Solver Parameters window, set the objective to maximize the cell B16 (Revenue).

12. Set the By Changing Variable Cells to B24:B28 (the number of cakes baked).

13. Click on the "Add" button in the "Subject to the Constraints" section.

14. In the Constraint window, select the range B18:B22 for the constraint cells.

15. In the Solver Parameters window, click on the "Add" button again and select the range B24:B28 for the non-negativity constraints.

16. Set the Solver options as desired, and click on the "Solve" button.

E x c e l Solver will calculate the optimal values for the number of cakes to be baked for each type that maximize the revenue, while satisfying the given constraints on ingredient availability. The solution will be displayed in cells B24:B28, indicating the number of cakes to be baked for each type.

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Answer:

25:36

Step-by-step explanation:

the number of hours on weekdays which is 25, and the total hours she worked is 25+11 which is 36, so it is 25:36

a. The graph represents a proportional relationship.

b. The graph does not represent a proportional relationship.

c. The graph does not represent a proportional relationship.

d. The graph represents a proportional relationship.

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable exists.

The equation that defines the proportional relationship is a linear function with slope k and intercept zero presented as follows:

y = kx.

Hence graphs a and d represent proportional relationship, as they have intercepts at the origin.

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Answer:

the iqr is 42

Step-by-step explanation:

Based on the given information, the average annual salary for all US teachers is $48,000 with a standard deviation of $5,700. So, you should feel good about your $52,000 offer, as it is above the average salary for US teachers and places you in a relatively higher earning position compared to your peers.

If you apply for a teaching position and were offered $52,000, let's determine your relative position in the salary distribution using a z-score.

The z-score is calculated as (X - μ) / σ, where X is your salary, μ is the mean salary, and σ is the standard deviation. Plugging in the values, we have:
Z = ($52,000 - $48,000) / $5,700 = $4,000 / $5,700 ≈ 0.70
A z-score of 0.70 indicates that your salary is 0.70 standard deviations above the mean salary. Based on a normal distribution table, about 24% of teachers would earn more than you, and 76% would earn less.

Considering the probability result, you should feel good about your $52,000 offer, as it is above the average salary for US teachers and places you in a relatively higher earning position compared to your peers.

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All the solutions are,

⇒ x = 1/2 (w- v)

⇒ x = (b - 9)/(a - 2)

⇒ x = (4 + w) / (7 - v)

⇒ x = 2 / (v + w)

⇒ x = 7v/(3w - 4)

Given that;

Expressions are,

⇒ 6x + v = 4x + w

⇒ ax + 9 = 2x + b

⇒ 7x - w = vx+4

⇒ 6 - wx = vx + 4

⇒ 3(wx - v) = 4(x + v)

We can simplify as;

⇒ 6x + v = 4x + w

⇒ 6x - 4x = w - v

⇒ 2x = w - v

⇒ x = 1/2 (w- v)

⇒ ax + 9 = 2x + b

⇒ ax - 2x = b - 9

⇒ (a - 2)x = b - 9

⇒ x = (b - 9)/(a - 2)

⇒ 7x - w = vx+4

⇒ 7x - vx = 4 + w

⇒ (7 - v) x = 4 + w

⇒ x = (4 + w) / (7 - v)

⇒ 6 - wx = vx + 4

⇒ vx + wx = 6 - 4

⇒ (v + w)x = 2

⇒ x = 2 / (v + w)

⇒ 3(wx - v) = 4(x + v)

⇒ 3wx - 3v = 4x + 4v

⇒ 3wx - 4x = 7v

⇒ (3w - 4)x = 7v

⇒ x = 7v/(3w - 4)

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(1 , -5) satisfy the inequality y ≤ 3x + 2  but not to y > –2x – 3

According to the question,

It is Given : y ≤ 3x + 2  

y > –2x – 3

We have to find the relationship between the point (1, –5) and the given system of inequalities.

Substituting the point (1,5) in our inequality y ≤ 3x + 2  

=> x = 1

=> y ≤ 3(1) + 2  

=> y ≤  5

=> - 5 ≤ 5

Which is true

Hence point (1, –5)  satisfy y ≤ 3x + 2  

Substituting the point (1,5) in our inequality  y > –2x – 3

x = 1

=> y > -2(1) - 3

=> y > - 5

but - 5 = -5

Hence  point (1, –5)   does not satisfy y > –2x – 3

I've answered the question in general as the given question is incomplete

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The value of q is 0.35.

The value of p is 0.16.

The value of r is 0.27.

The value of P(A given NOT B) is approximately 0.4211.

To calculate the values of p, q, and r, we can use the information provided in the Venn diagram and the probabilities of events A and B.

Given:

P(A) = 0.43

P(B) = 0.62

P(A∩B) = 0.27

Calculating the value of p:

The value of p represents the probability of event A occurring without event B. In the Venn diagram, p corresponds to the region inside A but outside B.

We can calculate p by subtracting the probability of the intersection of A and B from the probability of A:

p = P(A) - P(A∩B)

= 0.43 - 0.27

= 0.16

Therefore, the value of p is 0.16.

Calculating the value of q:

The value of q represents the probability of event B occurring without event A. In the Venn diagram, q corresponds to the region inside B but outside A.

We can calculate q by subtracting the probability of the intersection of A and B from the probability of B:

q = P(B) - P(A∩B)

= 0.62 - 0.27

= 0.35

Therefore, the value of q is 0.35.

Calculating the value of r:

The value of r represents the probability of both event A and event B occurring. In the Venn diagram, r corresponds to the intersection of A and B.

We are given that P(A∩B) = 0.27, so the value of r is 0.27.

Therefore, the value of r is 0.27.

Finding the value of P(A given NOT B):

P(A given NOT B) represents the probability of event A occurring given that event B does not occur. In other words, it represents the probability of A happening when B is not happening.

To calculate this, we need to find the probability of A without B and divide it by the probability of NOT B.

P(A given NOT B) = P(A∩(NOT B)) / P(NOT B)

We can calculate the value of P(A given NOT B) using the provided probabilities:

P(A given NOT B) = P(A) - P(A∩B) / (1 - P(B))

= 0.43 - 0.27 / (1 - 0.62)

= 0.16 / 0.38

≈ 0.4211

Therefore, the value of P(A given NOT B) is approximately 0.4211.

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The inequality which represents the number of jeans and sweater which he must purchase is; $17x + $9y >= $75.

It follows from the task content that, to receive free shipping, $75 or more must be spent on the pieces of clothing to receive free shipping.

On this note, it follows that the required inequality is; $17x + $9y >= $75.

This follows from the fact that jeans are $17 each and sweaters are $9 each.

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When you activate a prepaid device with equipment, you may have the opportunity to earn money through various means.

Firstly, as a retailer or reseller, you can make a profit by selling the prepaid device and associated equipment at a higher price than your purchase cost. This markup allows you to earn a margin on each sale.

Additionally, some service providers or retailers offer commission-based programs where you earn a commission or referral fee for each prepaid device activation. By promoting and selling these devices, you can earn a percentage of the total sale value or a fixed amount per activation.

Furthermore, you might have the chance to upsell customers on additional accessories or services during the activation process. By offering relevant accessories like cases, screen protectors, or headphones, you can increase the overall sale value and earn extra income.

It's worth noting that the specific earning potential can vary depending on factors such as the popularity of the device, the commission structure, and the competitiveness of the market. It's advisable to research and understand the terms and conditions of any commission or referral programs before engaging in such activities.

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Let's draw the triangles:

Since the lines with the red arrow are parallel, the angles in blue must be congruent because the triangles share the yellow angle (and the lines are parallel). Therefore, the angles in green are congruent too:

So from here we can clear x:

x = 30

And now we can find the measures of the labeled angles and verify that they are the same:

The labeled angles are 85º

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Since the cannonball is fired at an angle of 45°, it will have the same horizontal and vertical velocities.

Let x be the distance it travels before it is 600 feet above ground. At this point, its vertical displacement will be 600 feet, and we can use the formula for vertical displacement:

y = v0*t + (1/2)at^2

Since there is no initial vertical velocity and we are ignoring gravity, a = 0 and the equation simplifies to:

y = 0*t + 0 = 600

Solving for t, we get:

t = sqrt(2y/a) = sqrt(2*600/0) = undefined

This means that the cannonball will never be 600 feet above ground if we ignore gravity. Since this is not realistic, we cannot answer this question without additional information or by assuming that gravity is acting on the cannonball.

The number of bees that visit a plant is 100 times the number of years the plant is alive, then 100t is the total number of bees that will visit the plant in its lifetime

Answer:

d

Step-by-step explanation:

You are asking a question trying to suggest whether it can be done later

The coordinate of point P is (7/2, -13)

The formula for calculating the midpoint of coordinates is expressed as shown below:

M(x, y) = {(mx₁+nx₂)/2, (my₁+ny₂)/2}

Given the coordinate points A(-4, 2) and B(3, -6) divided in the ratio 2:5, then;

M(x, y) = {(2(-4)+5(3))/2, (2(2)+5(-6))/2}

M(x, y) = {-8+15)/2, (4-30)/2}

M(x, y) = {7/2, (-26)/2}

M(x, y) = (7/2, -13)

Hence the coordinate of point P is (7/2, -13)

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Answer:

C and E

Step-by-step explanation:

23 > 16 and \(23\geq 16\) are both true statements since the quantity of 23 is greater than that of 16.

C

that's the answer

enjoy

\(\boxed{\underline{\bf \: ANSWER}}\)⇨

\( \sf \frac{x}{27} = \frac{4}{9} \\ \)

Use the cross-multiplication method. Then,..

\( \sf \frac{x}{27} = \frac{4}{9} \\ \sf 4 \times 27 = 9x \\ \sf 108 = 9x \\ \sf 108 \div 9 = x \\ \boxed{ \bf \: 12 = x}\)

So, the correct value of x is 12 (option C.)

_____

Hope it helps.

It may be 1^4 ............................

Answer:

Rhombus

Step-by-step explanation:

This could be a rhombus since in a square, the lines are congruent and perpendicular, so we move on to a broader shape, rectangles. the diagonals are congruent but not perpendicular, so we go to rhombus, and in a rhombus the diagonals are not congruent but they are perpendicular.

(a) To meet the desired 20g protein and 80g carbohydrate intake, prepare 4 servings of Pork & Beans and combine with 15 slices of "lite" rye bread.

(b) Bread: A/4 slices, Beans: B/21 - (A/4) * (12/21) servings.

(a) To prepare a meal of "beans-on-toast" that supplies 20 grams of protein and 80 grams of carbohydrates, you can use the following combination:

- Servings of Campbell's Pork & Beans: 4 servings.

- Slices of "lite" rye bread: 15 slices.

By using 4 servings of Campbell's Pork & Beans, you will obtain a total of 20 grams of protein (5 grams per serving) and 84 grams of carbohydrates (21 grams per serving).

Combining this with 15 slices of "lite" rye bread will contribute an additional 60 grams of carbohydrates (12 grams per slice) and 4 grams of protein (4 grams per slice). Thus, your meal will meet the desired nutritional requirements of 20 grams of protein and 80 grams of carbohydrates.

(b) The formula to determine the number of slices of bread and servings of Pork & Beans needed to meet specific protein and carbohydrate requirements is as follows:

- Number of slices of bread (Bread): A divided by 4.

- Number of servings of Pork & Beans (Beans): (B divided by 21) minus ((A divided by 4) multiplied by (12 divided by 21)).

Using this formula, you can calculate the appropriate quantities of bread and beans based on the desired protein (A) and carbohydrate (B) values.

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Answer:

98.2

Step-by-step explanation:

100 x 0.982 = 98.2

98.2 / 100 = 0.982

Answer:

6

Step-by-step explanation:

Answer:

y = 3/2x + 7

Step-by-step explanation:

The slops is rise over run, so in this case the slope is 3/2 because it goes up 3 units while going 2 units to the right.

The points (0,7) is on the y axis. This means that 7 is the y intercept

With this information, we can follow the format of the slope intercept equation: y = mx + b

m stands for the slope and b stands for the y intercept. Plugging the information in, our equation is:

y = 3/2x + 7

Answer:

The rate of change of Function A is less than the rate of change of function B.

Other than that, everything else you put is correct.

Step-by-step explanation:

None.

Answer:

Option A, B and D are correct options.

Step-by-step explanation:

First we will find rate of change of function A and function B

Rate of Change of Function A

The formula used to calculate rate of change is: \(Rate\:of\:Change=\frac{y_2-y_1}{x_2-x_1}\)

We have x_1=1, y_1=5, x_2=2, y_2=7

Putting values in formula and finding rate of change

\(Rate\:of\:Change=\frac{y_2-y_1}{x_2-x_1}\\Rate\:of\:Change=\frac{7-5}{2-1}\\Rate\:of\:Change=\frac{2}{1}\\Rate\:of\:Change=2\)

So, Rate of change of Function A = 2

Now, finding y-intercept.

y-intercept is found by putting x =0

Looking at the function, we can write the equation: y=2x+3

Now, put x =0

y=2(0)+3

y=3

So, when x =0, y=3

So, y-intercept is 3 for function A.

Rate of Change of Function A

The formula used to calculate rate of change is: \(Rate\:of\:Change=\frac{y_2-y_1}{x_2-x_1}\)

We have x_1=1, y_1=1, x_2=2, y_2=4

Putting values in formula and finding rate of change

\(Rate\:of\:Change=\frac{y_2-y_1}{x_2-x_1}\\Rate\:of\:Change=\frac{4-1}{2-1}\\Rate\:of\:Change=\frac{3}{1}\\Rate\:of\:Change=3\)

So, Rate of change of Function B = 3

Now, finding y-intercept.

y-intercept is found by putting x =0

Looking at the graph, when x=0, y is -2

So, y-intercept is -2 for function B.

We get following answers:

Rate of change of Function A = 2

Rate of change of Function B = 3

y-intercept is 3 for function A.

y-intercept is -2 for function B.

So, The correct options are:

The rate of change of function A and B are positive

The rate of change of function A is less than the rate of change of function B. (Because 2 is less than 3)

The y-intercept of function A is positive, while y-intercept of function B is negative.

So, Option A, B and D are correct options.

This is an inequality.

This is what the statement should look like: \(57 > x - 8\)

Now, you can actually "properly" reverse these meaning the equality sign changes too. So basically you can mirror them.

The "mirrored" inequality expression would look like this: \(x - 8 < 57\)

Now just like normal algebra, you can transpose these terms from 1 side to another and so, -8 would transpose to the right hand side and the operation would be the inverse or in this case, addition. The expression would look something like this: \(x < 57 + 8\)

Add them up and you get: \(x < 65\) :D

Answer: look up triangle perimeter calculator

Step-by-step explanation: