The CEO of a company wants to determine if taking the employees to a company retreat would boost their morale. He decides to use a random number table to survey a simple random sample of 50 of the 250 employees. Which of the following correctly labels the population of employees?

A. 000–250
B. 001–250
C. 0–250
D. 1–250

Answer:

a. The probability of completing the exam in one hour or less is 0.0783

b. The probability that student will complete the exam in more than 60 minutes but less than 75 minutes is 0.3555

c. The number of students will be unable to complete the exam in the allotted time is 8

Step-by-step explanation:

a. According to the given we have the following:

The time for completing the final exam in a particular college is distributed normally with mean (μ) is 77 minutes and standard deviation (σ) is 12 minutes

Hence, For X = 60, the Z- scores is obtained as follows:

Z=  X−μ /σ

Z=60−77 /12

Z=−1.4167

Using the standard normal table, the probability P(Z≤−1.4167) is approximately 0.0783.

P(Z≤−1.4167)=0.0783

Therefore, The probability of completing the exam in one hour or less is 0.0783.

b. In this case For X = 75, the Z- scores is obtained as follows:

Z=  X−μ /σ

Z=75−77 /12

Z=−0.1667

Using the standard normal table, the probability P(Z≤−0.1667) is approximately 0.4338.

Therefore, The probability that student will complete the exam in more than 60 minutes but less than 75 minutes is obtained as follows:

P(60<X<75)=P(Z≤−0.1667)−P(Z≤−1.4167)

=0.4338−0.0783

=0.3555

​

Therefore, The probability that student will complete the exam in more than 60 minutes but less than 75 minutes is 0.3555

c. In order to compute  how many students you expect will be unable to complete the exam in the allotted time we have to first compute the Z−score of the critical value (X=90) as follows:

Z=  X−μ /σ

Z=90−77 /12

Z​=1.0833

UsING the standard normal table, the probability P(Z≤1.0833) is approximately 0.8599.

Therefore P(Z>1.0833)=1−P(Z≤1.0833)

=1−0.8599

=0.1401

​

Therefore, The number of students will be unable to complete the exam in the allotted time is= 60×0.1401=8.406

The number of students will be unable to complete the exam in the allotted time is 8

When 'a' is 10, 'c' is approximately 142.97. You can repeat this process for different values of 'a' to find corresponding values of 'c'. Keep in mind that there are infinitely many solutions to this equation

To use the elimination method to solve the equation 2a + c = 162.97, we need another equation with the same variables. However, as there is only one equation given, we cannot apply the elimination method directly.

The elimination method typically involves adding or subtracting equations to eliminate one of the variables, resulting in a new equation with only one variable. Since we have only one equation, we don't have the opportunity to eliminate variables using another equation.

In this case, we can solve the given equation directly by isolating one variable in terms of the other. Let's solve for 'c':

2a + c = 162.97

Rearrange the equation to isolate 'c':

c = 162.97 - 2a

Now, we have an expression for 'c' in terms of 'a'. This equation represents a line in the 'a-c' coordinate plane. We can choose any value for 'a', substitute it into the equation, and calculate the corresponding 'c' value.

For example, let's say we choose 'a' = 10:

c = 162.97 - 2(10)

c = 162.97 - 20

c = 142.97

So, when 'a' is 10, 'c' is approximately 142.97.

You can repeat this process for different values of 'a' to find corresponding values of 'c'. Keep in mind that there are infinitely many solutions to this equation since we have one equation and two variables.

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Solve for x:

Answer:

C. x = 11.21

Step-by-step explanation:

The series of numbers that meets the 

requirements is 5+6+8+9+4+6+7+3+9+2+8+9+1.

How to check that the series meets the requirements?

To verify that the series meets the requirements, we must establish what the requirements are:

●Every 3 consecutive numbers must add up to 19.

●In total there must be 14 numbers.

●The total sum of all the numbers must be 77

To verify that every 3 consecutive numbers add  up to 19, we separate them into 4 groups of 3 and one number is left over.

5 + 6 + 8 = 19

9 + 4 + 6 = 19

7 + 3 + 9 = 19

2 + 8 + 9 = 19

In total there must be 14 numbers and they must add up to 77.

5+6+8+9+4+6+7+3+9+2+8+9+1 = 77

Given:

There are given the height, length, and width.

Where,

Explanation:

According to the question:

We need to find the surface area of the box:

Then,

To find the value, we need to use the surface area of a rectangular box:

So,

From the formula of the surface area of the rectangle box:

Then,

Put the height, width, and length into the given formula:

Then,

Final answer:

Hence, the correct option A.

Answer:

144

Step-by-step explanation:

48 ÷ 4 (which is how many sides a square has) is 12

So 12x12 because l×w (length and width) and all sides of a square are equal

So the answer would be 144

The perimeter of a square is 48 inches. What is the area, in square inches, of the square?

The perimeter of a square is 48 inches.

= 48 inches ÷ 4

= 12 inches

= (12 inches)^2

= (12×12) square inches

= 132 square inches

The area of the square is 132 square inches.

Answer:

y = x ^2 − 99 x + 81

Step-by-step explanation:

Work backwards to find the factors from the roots, then multiply the factors together.

Answer:

d , It’s the use of precise, rich, and colorful language to convey ideas.

Step-by-step explanation:

on edge .

Answer:

( D ) It’s the use of precise, rich, and colorful language to convey ideas.

Step-by-step explanation:

just took the test on edge. mark brainliesst

The graph that represents the given piecewise function has a range of

R: (-∞, 0) ∪ (0,2] ∪ (4, ∞).

A piecewise function is a combination of subfunctions that are defined with different intervals in the domain.

The range of the piecewise function is the union of all the ranges of the subfunctions.

The given piecewise function is

g(x) = x², x < 0

      = 1/2 x, 0 < x ≤ 4

      = x, x > 4

The domain and range for the subfunctions in the given piecewise function are:

for g(x) = x²; Domain is {x < 0} and Range is (-∞, 0)

for g(x) = 1/2 x; Domain is {0 < x ≤ 4} and Range is (0, 2]

for g(x) = x; Domain is {x > 4} and Range is (4, ∞)

Then, the range of the given piecewise function is

Range: (-∞, 0) ∪ (0, 2] ∪ (4, ∞)

Thus, the graph shown in the question is the correct one.

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Answer: c, its da 3rd graph

Step-by-step explanation:

The critical values, the intervals of increasing or decreasing and the maximum and minimum points of the f(x) is (-1.5, -16), x < -1.5 and x = -1.5 and for b (4,6) and (2,10), (2,4).

A) Critical values

We will find out the critical value by solving for f ' (x) = 0

therefore, taking the derivative of given function we get,

f ' (x) = 4(2x) + 12 = 0

        = 8x + 12 = 0

therefore, 8x = -12

                 x = -12/8

                 x= -1.5

x = -1.5 is the only critical value in x-coordinate. Now to determine the y-coordinate, simply put the value of x in the function f(x) = 4x2 + 12x - 7

we get, f(-1.5) = 4(-1.5)2 + 12 (-1.5) - 7

                      = 4(2.25) - 18 - 7

                      = 9 - 25 = -16  

therefore, the critical value of the function f(x) = 4x2 + 12x - 7 is (-1.5, -16)

f(x) =x3 - 9x2 + 24x - 10.

Intervals of increasing and decreasing function is i.e. f decreases for

x < -1.5.

Therefore, f has minimum value at x = -1.5.

B) Critical values

We will find out the critical value by solving for f ' (x) = 0

therefore, taking the derivative of given function we get,

f '(x) = 3x2 - 9(2x) + 24

       = 3x2 - 18x + 24 = 0

therefore, 3 ( x2 - 6x + 8) = 0

   i.e x2 - 6x + 8 = 0

        (x-4) (x-2) = 0

So, x = 4 or x = 2 are the two critical values in x-coordinate. Now to determine the y-coordinate, simply put the values of x in the function f(x) =x3 - 9x2 + 24x - 10

we get, Substituting x = 4

f(4) = 43 - 9 (4)2 +24 (4) -10

     = 64 - 144 + 96 - 10

     = 6

Now, Substituting x = 2

f(2) = 23 - 9(2)2 + 24(2) - 10

     = 8 - 36 + 48 - 10

     = 10

Therefore, the critical values of the function f(x) =x3 - 9x2 + 24x - 10 are (4,6) and (2,10).

Intervals of increasing and decreasing functions is f decreases in (2,4).

therefore, f has minimum at x = 4 and maximum at x = 2.

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Complete question:

For each function determine: i) the critical values ii) the intervals of increasing or decreasing iii) the maximum and minimum points.

a. f(x) = 4x²+12x–7 (3 marks)

b. F(x) = x°-9x²+24x-10 (3 marks)

Answer:

8

Step-by-step explanation:

16/5 equals 3.2

10/4 equals 2.5

Multiply them together and you get 8

Could you plz give me a crown I'm really close to leveling up!

The area of the rectangle that measures 16/5 inches by 10/4 inches is 8 inches².

A rectangle is a 2-dimensional quadrilateral with four right angles. A rectangle has two diagonals of equal length which bisect each other.

Area of a rectangle = length x width

16/5 x 10/4 = 160 / 20 = 8 inches²

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Answer:

1

Step-by-step explanation:

120 - 14 = 106

1/5 = 0.2

106 x ≈21

21 - 20 = 1

1

Answer

Step-by-step explanation:

Answer:

22222

Step-by-step explanation

Answer:

a

Step-by-step explanation:

Answer:

y = x/2 + 4

Step-by-step explanation:

x = 2y + 4

divide 2 + 4 on both sides in order to isolate y by its self.

x/2 + 4 = 2y + 4/2 + 4

x/2 + 4 = y

y = x/2 + 4

Answer:

I think its t+u

don't take my word for it preciate the points

Step-by-step explanation:

Answer:

jzjzhsjoqhzjs I I shxaoaas

Answer:

Step by step explanation:

To solve the following equation, we need to use inverse operations to solve equations.

Addition and subtraction are inverse operations, multiplication, and division too.

Then,

As a first step, apply the distributive property of multiplication:

Apply inverse operations:

\(\huge \bf༆ Answer ༄\)

Let's solve ~

The number of lights L that are on after t minutes of the stage shows is,

A. L = (1/2)t + 10.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, When the show starts, 10 lights are on which is a constant in out function.

Every 30 seconds or (1/2) a minute 1 more light comes on.

∴  The function best models the number of lights that are on after t minutes of the stage shows is,

L = (1/2)t + 10.

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Answer:

Step-by-step explanation:

Rewrite the expression y^2/3 as a radical expression.

if n is a positive integer that is greater than x and a is a real number or a factor, then aˣ/ⁿ = \(\sqrt[n]{a^x}\)

use the rule to convert y²/₃ to a radical

where a =, x =, and n =.

therefore, the radical expression is \(\sqrt[3]{y^2}\)

The graph shows four separate equations all representing the line, but written out in different ways. The easiest way to determine which does not represent the line is by assigning values for x and y, and this chosen ordered pair must satisfy only the correct equations.

Therefore, using the value of x to be equal to 2,

When x = 2,

y = 7/2(2 + 6)

y = 7/2(8)

y = 28

For equation B, when x = 2

y = 7/2 (2) + 21

y = 7 + 21

y = 28

For equation C, when x = 2,

y - 7 = 7/2 (2 + 4)

y - 7 = 7/2 (6)

y - 7 = 21

y = 21 + 7

y = 28

For equation D, when x = 2

y + 5 = 7/2 (2 + 8)

y + 5 = 7/2 (10)

y + 8 = 35

y = 35-8

y = 27

Only equation D does not satisfy the ordered pair (2, 28), hence the line is not represented by equation D

To prove that there are only these five regular polyhedra, we can consider Euler's polyhedron formula, which states that for any convex polyhedron, the number of vertices (V), edges (E), and faces (F) satisfy the equation V - E + F = 2.

The five regular polyhedra, also known as the Platonic solids, are the only convex polyhedra where all faces are congruent regular polygons, and the same number of polygons meet at each vertex.

The five regular polyhedra are:

1. Tetrahedron: It has four triangular faces, and three triangles meet at each vertex.

2. Cube: It has six square faces, and three squares meet at each vertex.

3. Octahedron: It has eight triangular faces, and four triangles meet at each vertex.

4. Dodecahedron: It has twelve pentagonal faces, and three pentagons meet at each vertex.

5. Icosahedron: It has twenty triangular faces, and five triangles meet at each vertex.

To prove that there are only these five regular polyhedra, we can consider Euler's polyhedron formula, which states that:

"for any convex polyhedron, the number of vertices (V), edges (E), and faces (F) satisfy the equation V - E + F = 2".

For regular polyhedra, each face has the same number of sides (n) and each vertex is the meeting point of the same number of edges (k). Therefore, we can rewrite Euler's formula for regular polyhedra as:

V - E + F = 2  

=>  kV/2 - kE/2 + F = 2  

=>  k(V/2 - E/2) + F = 2

Since each face has n sides, the total number of edges can be calculated as E = (nF)/2, as each edge is shared by two faces. Substituting this into the equation:

k(V/2 - (nF)/2) + F = 2  

=>  (kV - knF + 2F)/2 = 2  

=>  kV - knF + 2F = 4

Now, we need to consider the conditions for a valid polyhedron:

1. The number of faces (F), edges (E), and vertices (V) must be positive integers.

2. The number of sides on each face (n) and the number of edges meeting at each vertex (k) must be positive integers.

Given these conditions, we can analyze the possibilities for different values of n and k. By exploring various combinations, it can be proven that the only valid solutions satisfying the conditions are:

(n, k) pairs:

(3, 3) - Tetrahedron

(4, 3) - Cube

(3, 4) - Octahedron

(5, 3) - Dodecahedron

(3, 5) - Icosahedron

Therefore, there exist only five regular polyhedra.

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Answer:

(a) How many are there to select 2 pairs of gloves?

10 ways

(b) How many ways are there to select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.)

130 ways

Step-by-step explanation:

We solve the above questions using Combination

Combination = C(n, r) = nCr

= n!/n! ×(n - r)!

(a) How many are there to select 2 pairs of gloves?

We have 5 pairs of gloves. Therefore, the number of ways to select 2 gloves =5C2

= 5!/2! × (5 - 2)!

= 5!/2! × 3!

= 5 × 4 × 3 × 2 × 1/(2 × 1) × (3 × 2 × 1)!

= 10 ways.

(b) How many ways are there to select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.)

We are told to select 4 gloves out of the 10 gloves = 10C4

We have 5 pairs, we need to make sure that two out of the selected 4 make a pair = 5 × 2⁴

= 80

Hence,

10C4 - 5C4

= [10!/4! × (10 - 4)!] - 80

= 210 - 80

= 130 ways

Answer:

216 cm cube

Step-by-step explanation:

length of an side is known to be 6 cm, then the volume of the cube will be 6 × 6 × 6 = 216 and the unit will be cm3 ; here, the volume of the cube is 216 cm3.

The expression for the total amount of sales the store makes will be:25s + 28.8p

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

From the information, the shoe store stocks x pair of sneakers and y pairs of sandals. During a promotion, a pair of sneakers is priced at $50 and a pair of sandals at $36. The shop manages to sell half the sneakers and 80% of the sandal.

Let sneakers = s

Let sandals = p

An expression for the total amount of sales the store makes will be: 1/2(50s) + 0.8(36p).

= 25s + 28.8p

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The calculated measure of the angle D is (c) 32 degrees

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

The triangles ABC and DEF

The triangles are similar triangles

This means that the corresponding angles are equal

Given that

A = 32 degrees

And the corresponding angle is D

We have

D = 32 degrees

Hence, the measure of the angle is (c) 32 degrees

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Answer:

x = 2

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × breadth

given the rectangles have equal areas then equating the two areas gives

4x × 9 = 4(6x + 6) , that is

36x = 24x + 24 ( subtract 24x from both sides )

12x = 24 ( divide both sides by 12 )

x = 2