Evaluate the expression -4 4/5 - 1 4/7 and write the result in simplest form.

Answer: 122 degrees

Step-by-step explanation:

Don’t feel like explaining.

9990000 are 7 digit phone number combinations are possible.

what is permutation and combination?

Find every 7-digit phone number combination that exists first.

Given that the digit can be repeated, a total of 107 combinations are available.

The next step is to identify all conceivable combination of seven-digit numbers that begin with "911."

since it begins with "911" Therefore, there are just 4 digits left. 104 combinations are thus feasible in total.

The total number of potential combinations that begin with "911" is then subtracted.

We finally get

10⁷  - 10⁴

= ( 10³ - 1 ) ×  10⁴

= 999 × 10⁴

= 9990000

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Answer:

To solve this problem, we will use the following steps:

Step 1: Since a pair of dice are tossed, we have 36 possible outcomes (6 outcomes for each die).

Step 2: To find the probability that doubles are rolled, we can find the number of outcomes that result in doubles and divide that by the total number of possible outcomes.

Step 3: To find the probability that the sum on the two dice is less than 7, we can find the number of outcomes that result in a sum of less than 7 and divide that by the total number of possible outcomes.

Step 4: We will use this probability to find the conditional probability of rolling doubles, given that the sum on the two dice is less than 7.

Step 5: To find the number of outcomes that result in doubles, we can consider rolling (1,1), (2,2), (3,3), (4,4), (5,5), (6,6) which are 6 outcomes.

Step 6: To find the number of outcomes that result in a sum of less than 7, we can consider rolling (1,1), (1,2), (1,3), (1,4), (1,5), (2,1), (2,2), (2,3), (2,4), (2,5), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (5,1), (5,2) which are 18 outcomes.

Step 7: To find the conditional probability of rolling doubles, given that the sum on the two dice is less than 7, we can find the number of outcomes that result in doubles and sum less than 7 which are (1,1), (2,2), (3,3), (4,4), (5,5) which are 5 outcomes.

Step 8: We can calculate the probability by dividing the number of outcomes that result in doubles and sum less than 7 by the number of outcomes that result in a sum less than 7.

5/18 = 0.278

Final Answer: The probability of rolling doubles, given that the sum on the two dice is less than 7, is 0.278 or 27.8%.

Answer: Adult tickets were sold = 325

Step-by-step explanation:

Let, A = Number of adult tickets sold

S = Number of student tickets sold

Total number of tickets=599

Therefore:

                           A + S = 599

If, there were 51 fewer student tickets sold them adult tickets.

Since,

                            S=A-51

So, substitute A-51 for the value of the first equation.    

                            A+S=599    

                        A+(A-51)=599

Expanding to get:

                            2A-51=599

Solve to get:

                          2A=599+512

                          A=650A

                          A=325

So, A=325 adult tickets were sold.

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To solve the given linear programming (LP) problem using the graphical LP approach, we will plot the feasible region, identify the corner points, and determine the optimal solution.

Here are the steps:

Step 1: Plot the constraints:

- Plot the line 5x + y = 32, which represents the constraint 5x + y ≤ 32. To do this, find two points that lie on this line by assigning values to x and solving for y. For example, when x = 0, y = 32, and when x = 6, y = 2. Connect these points to draw the line.

- Plot the line x + 3y = 12, representing the constraint x + 3y ≥ 12. Again, find two points on this line and connect them. For instance, when x = 0, y = 4, and when x = 12, y = 0.

- Draw the lines representing x = 20 and y = 20 as vertical and horizontal lines passing through x = 20 and y = 20, respectively.

Step 2: Identify the feasible region:

- Shade the area that satisfies all the constraints. The feasible region is the intersection of the shaded regions.

Step 3: Identify the corner points:

- Find the coordinates of the corner points of the feasible region. These points are the intersections of the lines representing the constraints.

Step 4: Evaluate the objective function:

- Calculate the objective function Z = 3x + 12y for each corner point.

Step 5: Determine the optimal solution:

- Identify the corner point that gives the minimum value of the objective function Z. This point corresponds to the optimal solution of the LP problem.

Once you have completed these steps, you will have the complete solution to the LP problem using the graphical LP approach.

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Answer:

0,1/13,49/100,1/2,11/20,8/9,1

Step-by-step explanation:

We cannot say that the two events are independent since the probability of eating pizza and sushi together is not known. If the probability of eating both together is 0, then the events are mutually exclusive, and if the probability is greater than 0, then the events are dependent.

We cannot say that the events of Marco eating sushi and pizza are independent. Two events are independent if the occurrence of one does not affect the probability of the other. However, in this case, if Marco eats sushi for dinner, it reduces the probability that he will eat pizza for dinner since he never eats both together.

Similarly, if Marco eats pizza for dinner, it reduces the probability that he will eat sushi for dinner. Therefore, the events are not independent, and the occurrence of one event affects the probability of the other. In other words, the events are dependent.

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In this scenario, the marginal revenue for firefighting protective clothes is given as MR = 495 - 6x, and the marginal cost is MC = 4.5x + 12, with a fixed cost of $315. We need to find the number of units that will result in maximum profit, the revenue function, the cost function, and the maximum profit.

a) To find the number of units that will result in maximum profit, we need to set the marginal revenue equal to the marginal cost and solve for x. So, we have 495 - 6x = 4.5x + 12. By solving this equation, we can determine the value of x.

b) The revenue function R(x) can be obtained by integrating the marginal revenue function. Integrating MR = 495 - 6x with respect to x will give us the revenue function R(x).

c) The cost function C(x) is given as MC = 4.5x + 12. The cost function represents the total cost incurred for producing x units.

d) The maximum profit can be found by subtracting the cost function from the revenue function. We evaluate the profit function P(x) = R(x) - C(x) and determine the value of x that maximizes the profit.

For the second scenario, we are given the marginal revenue function MR = R'(x) = 3e^(10x). We need to find the revenue from having x = 80 in sales. To do this, we integrate the marginal revenue function with respect to x and evaluate it at x = 80 to find the revenue R(80). Using the given information R(0) = 0, we can determine the appropriate constant C in the antiderivative.

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Answer:

No solution

Step-by-step explanation:

x = -y

2x + 2y = 6

2(-y) + 2y = 6

0 = 6

To write the expression \(6 \frac{7}{12}\)  in radical form.

To express the radical form in simplest it just means simplifying the radical so that there are further no more square root, cube root etc.

Use the rule:

\(a\frac{x}{y}\) = \(\sqrt[y]{a^{2} }\)

Apply this rule on the the given expression:

\(6\frac{7}{12} = \sqrt[12]{6^{7} }\)

Therefore, the expression in radical form is \(\sqrt[12]{6^{7} }\)

Answer:

See below

Step-by-step explanation:

g (h(6))   :

   h (6) =  3 ( 6^2) + 2 = 110

   then g (110) =   sqrt (110)

h (g(5))

    g(5) = sqrt 5

        then h( sqrt5) = 3 ( sqrt5)^2 + 2 = 17

Step-by-step explanation:

parallel. both lines lines up beside eachother

Answer:

Q1 35,145 145 Q2 27,153,153

Step-by-step explanation:

As opposite angles are the same.So for example on Q1, 35+35= 70

360-70=290

290÷2= 145

The measure of angle are:

<X= 145

<Y= 35

<Z =145

<U= 153

<V= 27

<W= 153

An angle is formed when two straight lines or rays meet at a common endpoint.

Given:

angle <1 = 35

<Y = 35 (Vertically opposite angle)

<X + 35 = 180 (Linear pair)

<X = 145

<Z = <X = 145 (Vertically opposite angle)

Now,

<V = 27 (Vertically opposite angle)

<U + 27 = 180 (Linear pair)

<U = 153

<U= <W =153 (Vertically opposite angle)

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Answer:

B. (2, 4)

D. (10, -1)

Step-by-step explanation:

The solution sets must be in the shaded region of the systems of inequalities. It cannot be on either lines because both lines are dotted. In that case, only B and D work because they are inside the shaded regions while the other points are not.

Answer:

B. (2, 4)

D. (10, -1)

Step-by-step explanation:

To be a solution, a point must be in the shaded part of the graph.

Answer: (2, 4), (10, -1)

Answer:

06 + 10

Step-by-step explanation:

a2 + b2

(3x2) + (5 x 2)

6 + 10

therefore option A is the correct answer

Answer:

50

Step-by-step explanation:

if 50 degrees is the angle across from b, then 50 is b. 50 applies to b as well. whatever is across from it is the same thing. all of the angles should add up to 360 at an intersection.

Answer:

x<28

Step-by-step explanation:

Isolate x

First, subtract 4 on both sides

x/2+<14

Then, multiply both sides by 2 to get x alone

x<28

On a number line, there would be an open circle (not filled in dot) on 28, and the entire left side of the number line would be filled in

Answer:

x<28

Step-by-step explanation:

x/2+4<18

multiply the 2 on both sides to get rid of it

x+8<36

isolate the x

x<28

on the number line, it's an open circle with the arrow pointing to the left.

Answer:

1

Step-by-step explanation:

LOL

Answer:

1+1-1=1

Step-by-step explanation:

1+1=2

2-1=1

your answer is 1

The minimum distance you can park from a driveway leading from a fire department can vary depending on the local laws and regulations in your area.

However, it is important to keep in mind that fire departments need clear and unobstructed access to their driveways at all times, in case of an emergency.
In many areas, the law requires a minimum distance of 20 feet from the edge of a fire department driveway to the nearest parked vehicle. This distance allows fire trucks and emergency vehicles enough space to turn, enter, and exit the driveway without any obstruction or delay.
It is also important to note that blocking a fire department driveway can result in a hefty fine or even a vehicle being towed away. This is because obstructing the entrance and exit to a fire department can cause unnecessary delay, which can be dangerous or even fatal in emergency situations.
Overall, it is important to always be aware of your surroundings and the laws in your area when parking near a fire department or any other emergency service. By doing so, you can ensure the safety and accessibility of these essential services at all times.

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if your asking for the length of the shorter side the answer is 20in

Step-by-step explanation:

32 divided by 8 is 4

5 times 4 equals 20

Answer:

P = 2L + 2W

W = 5

P = 2L + 2(5) = 16

2L + 10 = 16

2L = 6

L = 3 ft

Step-by-step explanation:

So we know that the perimeter of a rectangle= 2 (length + width).

We set up the equation so it's 16= 2 (length+ 5)

Divide both sides by 2, so 8 = length + 5.

Subtract 5 from both sides and you get length = 3

Answer:

12 nickels and 9 dimes

Step-by-step explanation:

1/ We have: n + d = 21 <=> d = 21 - n or opposite (n = 21 - d)

2/ We have: 0.05n + 0.10d = 1.50 and then we will put 1/ into 2/

=> 0.05n + 0.10(21 - n) = 1.50

=> 0.05n + 2.1 - 0.1n = 1.5

=> -0.05n = -0.6

=> n = 12

Nevertheless, d = 21 - n = 21 - 12 = 9

Answer: The front row has 4 fixed seats (s1, s2, s3, s4) and 5 open seats. The back row has 6 fixed seats (s5, s6, s7, s8, s9, s10) and 3 open seats. The remaining students (s11, s12, s13, s14, s15) can be placed in the open seats in the front row or the open seats in the back row in any combination.

The open seats in the front row can be filled by the remaining 5 students in 5! ways.

The open seats in the back row can be filled by the remaining 5 students in 5! ways.

So the total number of ways the students can be seated is (5!)^2 = 54321 * 54321 = 14400

Step-by-step explanation:

The work done on a particle moving uniformly around the unit circle centered at the origin under a constant force field, f(x, y), is zero.

When a particle moves in a closed path, like a circle, the net work done by a conservative force field is always zero. In this case, the force field is constant, which means it does not change as the particle moves along the path. Since the work done by a constant force is given by the formula W = F * d * cos(θ), where F is the force, d is the displacement, and θ is the angle between the force and the displacement vectors, we can see that the cosine of the angle will always be zero when the particle moves along the unit circle centered at the origin. This implies that the work done is zero. Thus, the work done on the particle is zero.

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A 95% confidence interval for percent of american adults who believe in aliens:  (0.6578, 0.7822)

In this question we have been given that in a survey conducted on an srs of 200 american adults, 72% of them said they believed in aliens

We need to find the 95% confidence interval for percent of american adults who believe in aliens.

95% confidence interval = (p ± z√[p(1 - p)/n])

Here, n = 200

p = 72%

p = 0.72

And the z-score for 95% confidence interval is 1.960

The upper limit of interval would be,

(p + z√[p(1 - p)/n])

= 0.72 + 1.960 √[0.72(1 - 0.72)/200]

= 0.72 + 1.960 √[(0.72 * 0.28)/200]

= 0.72 + 1.960 √0.001008

= 0.72 + 0.0622

= 0.7822

The lower limit of interval would be,

(p - z√[p(1 - p)/n])

= 0.72 - 1.960 √[0.72(1 - 0.72)/200]

= 0.72 - 1.960 √[(0.72 * 0.28)/200]

= 0.72 - 1.960 √0.001008

= 0.72 - 0.0622

= 0.6578

Therefore, a 95% confidence interval = (0.6578, 0.7822)

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Solution:

Time taken to ring 12 customers = 9min

Time taken to ring 1 customer =9/12 min

=3/4 min

Time taken to ring 4 customer = 3×4/4

=3 min

We can conclude that the correct answer is:

she will take 3 minutes to ring 4 customers

Angle 0 is in the 1st quadrant, its reference angle is 0 radians, and it intersects the unit circle at the point (1, 0).

Define Angle ?

In mathematics, an angle is a geometric figure formed by two rays or lines that share a common endpoint, called the vertex.

a. The angle 0 is measured from the positive x-axis in a counterclockwise direction. In the Cartesian coordinate system, the positive x-axis lies on the right side of the coordinate plane. Since the angle 0 starts from this position, it falls within the 1st quadrant. The 1st quadrant is the region where both x and y coordinates are positive.

b. The reference angle is the positive acute angle between the terminal side of an angle and the x-axis. Since the angle 0 lies entirely on the positive x-axis, the terminal side coincides with the x-axis. In this case, the reference angle for 0 radians is 0 radians itself. The reference angle is always positive and its value is less than or equal to π/2 radians (90 degrees).

c. To find the point where 0 intersects the unit circle, we consider the trigonometric functions cosine and sine. The unit circle is a circle with a radius of 1 centered at the origin (0, 0) in the Cartesian coordinate system.

For angle 0, the cosine function gives the x-coordinate on the unit circle, and the sine function gives the y-coordinate. Since 0 lies on the positive x-axis, the x-coordinate is 1 (cos(0) = 1), and the y-coordinate is 0 (sin(0) = 0). Therefore, the point of intersection with the unit circle for angle 0 is (1, 0).

In summary, angle 0 is in the 1st quadrant, its reference angle is 0 radians, and it intersects the unit circle at the point (1, 0).

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Starting with the least likely event, the chances of a politician fulfilling all his or her campaign promises can be quite low due to the complexities of politics and the potential for unforeseen circumstances.

Next, while full moons are relatively common, they occur approximately once a month, making it more likely than the politician's scenario but less likely than the other events.

Rolling a die and getting a 6 has a higher likelihood as there is a 1 in 6 chance of rolling a 6 on a fair six-sided die. The safe arrival of a person in New York City from Chicago is more probable than the previous events but still has an element of uncertainty regarding the fate of their luggage.

Randomly selecting an ace from a regular deck of 52 playing cards has a higher probability compared to the previous events, as there are four aces in a deck. The likelihood increases further when randomly selecting the queen of hearts, which is only one specific card out of the 52-card deck.

Finally, selecting a black card from a regular deck has the highest probability among the listed events since there are 26 black cards in the deck, including all the clubs and spades.

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Answer:

A data type is an attribute associated with a piece of data that tells a computer system how to interpret its value

Step-by-step explanation:

Data types categorize data and specify its nature, amount characteristics, and behavior. It decides how data is handled within a computer system in terms of storage and manipulation.

Data types categorize data and specify its nature, characteristics, and behavior. It is a crucial part of every data structure and computer language. Primitive data types and complex data types are the two basic divisions of data types. Basic types like numbers, characters, booleans, and strings are examples of primitive data types. Arrays, objects, and records are examples of sophisticated data types that are more complex. Data types specify how information is handled and stored by computer systems. Size, precision, and range are a few examples of the unique qualities that each data type possesses. The arithmetic, comparison, and logic operations that can be carried out on the data are also determined by the data types.

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