An urn contains n balls, one of which one is special. If k of these balls are withdrawn one at a time, with each selection being equally likely to be any of the balls that remain at the time, what is the probability that the special ball is chosen

The expressions that are equivalent to 3^8 are:

We have to solve these out

3^8. = 6561

From the options

A. 3^2x3^4

= 9 x 81

= 729

B  3²x3^6

= 9 x 729

= 6561

C.  3^16/3^2

= 43046721/9

= 4782969

d. 3^12/3^4

= 531441 / 81

= 6561

E.  (3^4)²

= 3⁴ x 3⁴

= 3⁴⁺⁴

= 3⁸

= 6561

F. (3¹)^7

= 3⁷

= 2187

The expressions that are equivalent to 3^8 are:

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Answer: A) 2 and a half B) 5 pints

Step-by-step explanation:

in 1 cup there are 16 table spoons.

a) 4tbsp (2 servings) times 10 (to reach 20 servings) =40 tbsp

40/16 =2.5

ANSWER A= 2 and a half cups of lemon juice.

in 1 pint there are 2 cups.

b)

1 cup = 1/2 a pint,

1/2 pint (2 servings) times 10 (to reach 20 servings) = 5 pints

ANSWER B= 5 pints of olive oil

Answer:

The answer to your problem is, D. The range is the best measure of variability, and it equals 32.

Step-by-step explanation:

We know the scores earned in a flower-growing competition are represented in the stem-and-leaf plot.

The key will equal 2|1 means 21

Which we conclude to 17, 19, 21, 25, 29, 30, 31, 32, 46, 49.

Quartile:

Median, Minimum, Maximum, & Range:

Thus the answer to your problem is, D. The range is the best measure of variability, and it equals 32.

Based on the information provided, the inference that a significant number of students in the homeroom class plan to become soldiers is valid.

The teacher surveyed his homeroom class about their post-graduation plans. He found out that most of his students plan to become soldiers.

An inference is a conclusion that can be drawn from a given set of data. In this case, the inference that can be made is that a significant number of students in the homeroom class plan to become soldiers.Therefore, the inference is valid based on the data provided.

However, it is essential to keep in mind that the sample size in the homeroom class is relatively small and may not be representative of the entire population. If the teacher had surveyed a more extensive and diverse population, the results might have been different.

In conclusion, based on the information provided, the inference that a significant number of students in the homeroom class plan to become soldiers is valid. However, this may not apply to the entire population, and it is crucial to consider the sample size when drawing inferences.

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The equation 2-3cos(x) = 5+3cos(x) has no solution in the range of 0° to 180°.

1. Start with the given equation: 2-3cos(x) = 5+3cos(x).

2. Subtract 3cos(x) from both sides to isolate the constant term: 2-3cos(x) - 3cos(x) = 5.

3. Combine like terms: 2-6cos(x) = 5.

4. Subtract 2 from both sides: -6cos(x) = 3.

5. Divide both sides by -6: cos(x) = -1/2.

6. To find the solutions for cos(x) = -1/2 in the range of 0° to 180°, we need to determine the angles where cos(x) equals -1/2.

7. These angles are 120° and 240°, as cos(120°) = cos(240°) = -1/2.

8. However, the given equation states that 2-3cos(x) equals 5+3cos(x), which is not satisfied by cos(x) = -1/2.

9. Therefore, the equation 2-3cos(x) = 5+3cos(x) has no solution in the range of 0° to 180°.

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Answer:

15: 58 degrees. 16: Answer D

Step-by-step explanation:

Question 15

All you have to do for this one is to add the angle measures of 22 and 36 degrees together to get the answer of 58 degrees.

Question 16

The interior angles of a triangle will always add up to 180 degrees.

Therefore, 180 - 53 - 21 is the answer, which totals 106 degrees.

Answer:

V=πr2h

3=π·102·7

3≈733.03829

Step-by-step explanation:

Answer:

  a) 10

  b) 7.5

  c) 8

  d) 75

Step-by-step explanation:

Pick's theorem tells you the area of a figure drawn on grid points is ...

  A = i +b/2 -1

where i is the number of interior grid points, b is the number of boundary grid points.

__

a) b = 12 (The verticals cross a grid point, but the diagonals don't. The number of boundary points is the number of vertices +2.)

  i = 5

  Area = 5 +12/2 -1 = 10 . . . square units

__

b) b = 5 (The horizontal crosses a grid point, but none of the diagonals do. The number of boundary points is the number of vertices +1.)

  i = 6

  Area = 6 +5/2 -1 = 7.5 . . . square units

__

c) b = 8 (The upper left diagonal crosses 2 grid points, so the number of boundary points is the number of vertices +2.)

  i = 5

  Area = 5 +8/2 -1 = 8 . . . square units

__

d) b = 3, i = 6

  Area = 6 +3/2 -1 = 7.5 . . . square units

_____

Additional comment

The first figure can be divided by vertical lines into 4 congruent trapezoids with bases 3 and 2. Then the area is (4)(1/2(3+2)(1) = 10.

The remaining figures can be considered as the area of the bounding box less the areas of triangles discarded when the figure is cut out. (No additional lines need be drawn.) The areas figured this way agree with the area values shown above. The area of a triangle is A=1/2bh, so is not difficult to figure mentally.

The football is approximately 96.4 feet from the base of the goal post.

The tangent function in trigonometry is used to determine the proportion between the lengths of the adjacent and opposite sides in a right triangle. Where theta is the angle of interest, the tangent function is defined as:

tan(theta) = opposing / adjacent.

When the lengths of one side and one acute angle are known, the tangent function is used to solve for the unknown lengths or angles in right triangles. In order to utilise the tangent function, we must first determine the angle of interest, name the triangle's adjacent and opposite sides in relation to that angle, and then calculate the ratio of those sides using the tangent function.

Given, the angle of elevation is 16 degrees 42'.

That is,

Angle of elevation = 16 degrees 42' = 16 + 42/60 = 16.7 degrees

Using tangent function we have:

tan(16.7) = 30/x

x = 30 / tan(16.7)

x = 96.4 feet

Hence, the football is approximately 96.4 feet from the base of the goal post.

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Answer:

Cost for each pound of jelly beans:  $2.75

Cost for each pound of almonds:  $3.75

Step-by-step explanation:

Let J be the cost of one pound of jelly beans.

Let A be the cost of one pound of almonds.

Using the given information, we can create a system of equations.

Given 3 pounds of jelly beans and 5 pounds of almonds cost $27:

\(\implies 3J + 5A = 27\)

Given 9 pounds of jelly beans and 7 pounds of almonds cost $51:

\(\implies 9J + 7A = 51\)

Therefore, the system of equations is:

\(\begin{cases}3J+5A=27\\9J+7A=51\end{cases}\)

To solve the system of equations, multiply the first equation by 3 to create a third equation:

\(3J \cdot 3+5A \cdot 3=27 \cdot 3\)

\(9J+15A=81\)

Subtract the second equation from the third equation to eliminate the J term.

\(\begin{array}{crcrcl}&9J & + & 15A & = & 81\\\vphantom{\dfrac12}- & (9J & + & 7A & = & 51)\\\cline{2-6}\vphantom{\dfrac12} &&&8A&=&30\end{array}\)

Solve the equation for A by dividing both sides by 8:

\(\dfrac{8A}{8}=\dfrac{30}{8}\)

\(A=3.75\)

Therefore, the cost of one pound of almonds is $3.75.

Now that we know the cost of one pound of almonds, we can substitute this value into one of the original equations to solve for J.

Using the first equation:

\(3J+5(3.75)=27\)

\(3J+18.75=27\)

\(3J+18.75-18/75=27-18.75\)

\(3J=8.25\)

\(\dfrac{3J}{3}=\dfrac{8.25}{3}\)

\(J=2.75\)

Therefore, the cost of one pound of jelly beans is $2.75.

No, the relationship on the table is not proportional

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

x   y

____ ____

6 -2

7 -1

8 0

9  1

On the table of values, we can see that:

Using the above as a guide, we have the following:

The relationship is not a proportional relationship

This is so because it does not have a constant rate (addition of 1 to x and y does not represent proportional relationship)

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Answer:

\(\huge\boxed{\text{Numbers: 3, 18}}\)

Step-by-step explanation:

We can create two equations and solve the system of equations to find both the numbers. Let's represent the numbers as a and b.

We can create two equations:

\(a+b=21\)

\(b=6a\)

We can now substitute the value of b (6a) into the first equation.

\(a + (6a) = 21\)

Combine like terms:

\(7a=21\)

Divide both sides by 7:

\(a=3\)

Now we know the first number is 3. We can plug this value into one of the equations to find b. Let's plug it into \(b=6a\).

\(b = 6 \cdot 3\\\\b = 18\)

So our numbers are 3 and 18.

Hope this helped!

Step-by-step explanation:

We can create two equations and solve the system of equations to find both the numbers. Let's represent the numbers as a and b.

We can create two equations:

a+b=21a+b=21

b=6ab=6a

We can now substitute the value of b (6a) into the first equation.

a + (6a) = 21a+(6a)=21

Combine like terms:

7a=217a=21

Divide both sides by 7:

a=3a=3

Now we know the first number is 3. We can plug this value into one of the equations to find b. Let's plug it into b=6ab=6a .

b=6⋅3

b=18

So our numbers are 3 and 18.

Hope this helped!

When x is equal to 1, the Function f(x) = -4x - 5 yields a value of -9.

The find ƒ(1) for the function f(x) = -4x - 5, we need to substitute x = 1 into the function and evaluate the expression.

Replacing x with 1, we have:

ƒ(1) = -4(1) - 5

Simplifying further:

ƒ(1) = -4 - 5

ƒ(1) = -9

Therefore, when x is equal to 1, the value of the function f(x) = -4x - 5 is ƒ(1) = -9.

Let's break down the steps taken to arrive at the solution:

1. Start with the function f(x) = -4x - 5.

2. Replace x with 1 in the function.

3. Evaluate the expression by performing the necessary operations.

4. Simplify the expression to obtain the final result.

In this case, substituting x = 1 into the function f(x) = -4x - 5 gives us ƒ(1) = -9 as the output.

It is essential to note that the notation ƒ(1) represents the value of the function ƒ(x) when x is equal to 1. It signifies evaluating the function at a specific input value, which, in this case, is 1.

Thus, when x is equal to 1, the function f(x) = -4x - 5 yields a value of -9.

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Answer:

Each tile would be 8.5 in

Step-by-step explanation:

Area of parallelogram is A=bh, so 4.25*2= 8.5

The total amount the man had = 52,200 rupees. Out of this, he gave 21,750 rupees to his son, 13,050 rupees to his daughter, and 17,400 rupees to his wife , the total amount given away by the man = 21,750 + 13,050 + 17,400 = 52,200 rupees.

A man gave 5/12 of his money to his son, 3/7 of the remainder to his daughter, and the remaining to his wife. If his wife gets Rs. 8,700, what is the total amount?

The given problem can be solved using the concept of ratios and fractions. Let us solve the problem step-by-step.Assume the man had x rupees with him.The man gave 5/12 of his money to his son.

The remaining amount left with the man = x - 5x/12= (12x/12) - (5x/12) = (7x/12)The man gave 3/7 of the remainder to his daughter.'

Amount left with the man after giving it to his son = (7x/12)The amount given to the daughter = (3/7) x (7x/12)= (3x/4)The remaining amount left with the man = (7x/12) - (3x/4)= (7x/12) - (9x/12) = - (2x/12) = - (x/6) (As the man has given more money than what he had with him).

Therefore, the daughter's amount is (3x/4) and the remaining amount left with the man is (x/6).The man gave all the remaining amount to his wife.

Therefore, the amount given to the wife is (x/6) = 8700Let us find the value of x.x/6 = 8700 x = 6 x 8700 = 52,200

Therefore, the man had 52,200 rupees with him.He gave 5/12 of his money to his son. Therefore, the amount given to his son is (5/12) x 52,200 = 21,750 rupees.

The remaining amount left with the man = (7/12) x 52,200 = 30,450 rupees.He gave 3/7 of the remainder to his daughter. Therefore, the amount given to his daughter is (3/7) x 30,450 = 13,050 rupees.

The amount left with the man = (4/7) x 30,450 = 17,400 rupees.The man gave 17,400 rupees to his wife.
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Answer:

y=2x+3 and y=-2x-3

Step-by-step explanation:

First situation:

2x-y=3

making y subject

y=2x+3

Second situation:

2x+y=-3

making y subject

y=-2x-3

Answer:

\(Area = 153.938040026m^2\)

\(Circumference= 43.9822971503m\)

Step-by-step explanation:

Area

\(Area = \pi r^2\\Area = \pi *7^2\\Area = 49\pi\\Area = 153.938040026\)

Circumference

\(C = 2\pi r\\C = 2\pi*7\\C= 14\pi\\C=43.9822971503\)

The domain restrictions for (f/g)(x) are (c) x = 0, 6

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

f(x) = x² - 5x - 6

g(x) = x² - 6x

The composite function (f/g)(x) is calculated as

(f/g)(x) = f(x)/g(x)

substitute the known values in the above equation, so, we have the following representation

(f/g)(x) = (x² - 5x - 6 )/(x² - 6x)

For the domain restriction, we have

x² - 6x = 0

When solved, we have

x =  6 or x = 0

Hence, the domain restrictions for (f/g)(x) are (c) x = 0, 6

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Question

Given f(x) = x² - 5x - 6 and g(x) = x² - 6x, what are the domain restrictions

for (f/g)(x)?

A) x = +6

B) x = 0

C) x = 0,6

D) x = -2,6

Answer:The acceleration that an objects gains is given by the mass of the object.

If the acceleration of the object becomes 5 m/s² the force is 15 N.

Reason:

The given parameters are;

The acting force ∝ The acceleration of the object.

The acceleration given by an amount of force, F, of 18 N = 6 m/s²

Required:

The force acting on the object acceleration, a, is 5 m/s².

Solution:

According to Newton's Second Law of motion, we have;

F = m·a

Where;

m = The mass of the object

Therefore, we have;

From the conditions, F = 18 N, when a = 6 m/s², we have, the mass of the

given object is given as follows;

The force acting when the the acceleration, a = 5 m/s², is therefore;

F = 3 kg × 5 m/s² = 15 N

If the acceleration of the object becomes 5 m/s² the force is 15 N.

Step-by-step explanation:

Answer:

x/7

Step-by-step explanatio

Answer:

7 ÷ 8

Step-by-step explanation:

It is 7 ÷ 8 because

a fraction is really a

division sign

Answer:7 divided by 8

Step-by-step explanation:

The time it will take after 17 repetitions with the learning curve having a rate of 80% is of:

6.19 seconds.

The learning curve formula is an exponential function defined as follows:

\(y = ab^x\)

In which the parameters are listed as follows:

Then y gives the time it takes to make the xth object.

In the context of this problem, the values of the parameters are given as follows:

Then the time needed for the 17th repetition is of:

y = 275 x (0.8)^17 = 6.19 seconds.

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Answer:

14

Step-by-step explanation:

100% - 30%= 70% (the times they've won)

0.7x20=14

Answer:

46/3

Step-by-step explanation:

|2a| - b/3

Plug in the values and evaluate.

|2(7)| - (-4)/3

|14| + 4/3

Apply | a | = a

14 + 4/3

42/3 + 4/3

= 46/3

Answer: The answer would be 6!

Answer:

4x^2+3x-6

Step-by-step explanation:

Answer:

4x^2+3x-2

Step-by-step explanation:

I hope this helps

Answer: 12 different ways.

Step-by-step explanation:

For a set of M elements, the number of combinations of N elements (N ≤ M) is given by:

\(C(M, N) = \frac{M!}{(M - N)!*N!}\)

In this case we know that there is a room that can hold two of the girls, then the number of combinations of the two girls that can be in that room is:

\(C(4, 2) = \frac{4!}{2!*2!} = \frac{4*3}{2} = 6\)

So these are the different combinations for the larger room.

So we assume that two girls already have a room, then we have two girls left and two rooms left.

For the first room, there are two possible girls that can be in, let's choose one of them.

For the last room, whe have only one girl left, so we have one option.

The total number of combinations will be equal to the product between the number of options for each event (where the events are assigning the girls to the rooms)

Then the number of different outcomes is:

C = 6*2*1 = 12

There are 12 different ways.

Answer:

24

Step-by-step explanation:

56/7=8

8x3=24

Answer:

The first angle is \(70^{o}\).

Step-by-step explanation:

Let the measure of the second angle be represented by \(x^{o}\).

Thus, the first angle = \((3x+10)^{o}\)

Third angle = \(90^{o}\)

Sum of angles in a triangle = \(180^{o}\)

So that;

\(x^{o}\) + \((3x+10)^{o}\) + 90 = \(180^{o}\)

\(x^{o}\) + \(3x^{o}\) + \(100^{o}\) = \(180^{o}\)

\(4x^{o}\) = \(180^{o}\) - \(100^{o}\)

\(4x^{o}\) = \(80^{o}\)

divide both sides by 4 to have;

\(x^{o}\) = \(20^{o}\)

The first angle = \((3x+10)^{o}\)

                        = ( 3 x 20 + 10)

                        = 60 + 10

                        = \(70^{o}\)

Therefore, the first angle is \(70^{o}\).