A band wants to enter a contest that requires traveling expenses. They need at least $1,150 to cover all of the expenses. They have already saved $700. They are selling shirts with a profit of $7. 00 per shirt to earn the remaining money Part Which inequality represents the minimum number of shirts, n, the band must sell to earn the remaining money 1, 150​

Answers

Answer 1

the number of shirts has to be an integer (you can not sell "part" of a shirt) n >= 65

They need at least $1,150

They have already saved $700

They are selling shirts with a profit of $7.00 per shirt

If they sell n number of shirts, they will earn n times $7.00

Since they have already 700, they will earn a total of 700 + 7n

If this quantity has to be equal or greater to 1,150, we can write:

1150 <= 700 + 7n

if we solve this inequality for n:

1150 <= 700 + 7n

1150 - 700 <= 7n

450 <= 7n

450/7 <= n

64.28 <= n

Since the number of shirts has to be an integer (you can not sell "part" of a shirt)

n >= 65

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Related Questions

How do you graph log functions with transformations?

Answers

required transformed function will be y = parent function+5⇒y=logx+5.

Since, given function y= logx

According to the graph, the transformed function is getting after shifting  the function by 5 unit upward.

Thus, transformed function must be equals to parent function+5.

Therefore, required transformed function will be y = parent function+5⇒y=logx+5.

How to do logarithmic transformations?

Image result for How do you graph log functions with transformations?

Recall the general form of a logarithmic function is: f ( x ) = k + a log b ⁡ where a, b, k, and h are real numbers such that b is a positive number ≠ 1, and x - h > 0. A logarithmic function is transformed into the equation: f ( x ) = 4 + 3 log ⁡

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Find the perimeter of the rectangle

A. 46
B. 136
C. 23
D. 25

Answers

Answer:

A.46

Step-by-step explanation:

rectangle divided in two by the diagonal, we find the missing side (x) with Pythagoras

x² = 17² - 8²

x² = 289 - 64

x² = 225

x = √225

x = 15in

now we have all the sides and we add them to find the perimeter

8 + 15 + 8 + 15 =

46in

Is the simplified form of 2 square foot 3. Square Foot 12 rational

Answers

The simplified form of the given radical expression is rational.

What is exponent  ?

Exponent can be defined as the method of expressing large numbers in terms of powers. Exponent refers to how many times a number multiplied by itself. For example, 6 is multiplied by itself 4 times, i.e. 6 × 6 × 6 × 6.

We are asked to determine whether the simplified form of  2√3.√12

To solve our given problem we will use exponent property for radicals

           √m.√n = a√m.n

          2√3.√12=2√3.12

            2√3.√12=2√36

             2√3.√12=2×6

              2√√3.√12=12

The simplified form of the given radical expression is rational.

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Since our given radical expression simplifies to a rational, therefore, our answer is yes

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Which fraction is equivalent to -3/2

A) 3/-2

b) -(3/-2)

C) -3/-2

D) -(-3/2


HELP ASAP PLS

Answers

Answer: A

Step-by-step explanation: The other answer choices have 2 negatives which cancel and make a positive number.

Your colleague’s computer stops working, and no one from the IT department is available to fix it. You have basic knowledge of computer hardware. Which action should you take as an ethical employee?
A.
Initiate help by offering to check the computer.
B.
Start a conversation with your colleague and provide a distraction.
C.
Take a quick break and offer your computer for a short time.
D.
Ignore it because it is beyond your designated scope of work.

Answers

Since you have basic knowledge of computer hardware, an action which you should take as an ethical employee include the following: A. Initiate help by offering to check the computer.

What is a computer hardware?

A computer hardware can be defined as a physical component of a computer system or an information technology (IT) that can be seen, touched and replaced.

In Computer technology, there are various examples of a computer hardware and these include the following:

Power supply unit (PSU).Hard-disk driveKeyboardMonitor (screen)MouseMotherboardCentral processing unit (CPU).Network interface card (NIC).Memory module

Based on ethical principles, we can reasonably infer and logically conclude that an ethical employee should initiate help by offering to help check the colleague’s computer since he or she has basic knowledge of computer hardware.

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holy has $125. she spends $35 on gas for her car. which model represents how much money holy has left

Answers

Holy has $90 left over

Answer:

Holy has $85 dollars remaining.

Step-by-step explanation:

(There is no model given in the question, so I'll tell you what the model should be equal to)

If she has $125 to spend, and she spends $35 of that money on gas, she will have $85 left.

$125 - $35 = $85

PLEASE HELP FAST I WILL GIVE BRAINLIEST, Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

Using the properties of integer exponents, match each expression with its equivalent expression.

Answers

The 5⁻³ is equivalent to 1/125, - 5⁻³ is equivalent to -1/125,  (-5⁻³)⁻¹ is equivalent to -125 and (-5⁻³)⁰ is equivalent to 1

What is Expression?

An expression is combination of variables, numbers and operators.

Equivalent expressions are expressions that work the same even though they look different.

5⁻³

This can be written as 1/5³ which is equal to 1/125

-5⁻³

This can be written as -1/5³ which is equal to -1/125

(-5⁻³)⁻¹

We have an exponential property

[tex](x^{a} )^{b} =x^{ab}[/tex]

So (-5⁻³)⁻¹=(-5)³=-125

(-5⁻³)⁻¹  equivalent expression is -125

(-5⁻³)⁰

=(-5)⁰=1

Hence, the 5⁻³ is equivalent to 1/125, - 5⁻³ is equivalent to -1/125,  (-5⁻³)⁻¹ is equivalent to -125 and (-5⁻³)⁰ is equivalent to 1

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Brigid has a 25-foot ladder she will use to paint the side of her house. What angle does the ladder need to make with house so she can reach 18 feet up the side of her house

Answers

The ladder needs to make an angle of approximately 54.7 degrees with the house in order for Brigid to reach 18 feet up the side of the house.

To determine the angle the ladder needs to make with the house, we can use the tangent function.

First, we'll need to determine the opposite side (the height that the ladder needs to reach) and the adjacent side (the distance from the base of the ladder to the house) of the triangle formed by the ladder and the house.

Opposite side = 18 feet

Adjacent side = 25 feet

We can then use the tangent function to find the angle:

tan(angle) = opposite / adjacent

Solving for the angle, we get:

angle = arctan(18/25) = approximately 54.7 degrees

Therefore, the ladder needs to make an angle of approximately 54.7 degrees with the house in order for Brigid to reach 18 feet up the side of the house.

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How do you find the two missing sides of an acute triangle?

Answers

Using the Pythagorean Theorem (a2 + b2 = c2), plug in the known side lengths to solve for the two unknown sides of an acute triangle.

1. Identify the two known side lengths of the triangle.

2. Plug the known side lengths into the Pythagorean Theorem equation (a2 + b2 = c2).

3. Solve for the two unknown sides of the triangle.

4. The two unknown sides are the lengths of the missing sides of the triangle.

5. To solve for the unknown side lengths, first, calculate the hypotenuse (the longest side) by finding the square root of the sum of the squares of the two shorter sides.

6. Then, calculate the shorter sides by subtracting the square of the hypotenuse from the sum of the squares of the two shorter sides.

7. Finally, use the Pythagorean Theorem to calculate the missing side lengths.

8. The two missing side lengths will be the unknown side lengths of the triangle.

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f(n) = 2n-1 find the arithmetic sequence ?

Answers

An arithmetic sequence is a sequence of numbers in which the difference between any two successive members of the sequence is a constant value. The general form of an arithmetic sequence is:

a, a + d, a + 2d, a + 3d, ...

where "a" is the first term of the sequence, and "d" is the common difference between successive terms.

Given the function f(n) = 2n - 1, we can see that the function outputs a sequence of integers, with a common difference of 2. So f(n) is not an arithmetic sequence.

Arithmetic sequence is a list of numbers in which each number is the sum of the previous number and a constant number.

Example: 1,3,5,7,9 is an arithmetic sequence because the constant difference is 2.

If you have any other question feel free to ask.

What is the smallest positive multiple of $13$ that is greater than $500?$

Answers

507

500 divided by 13 is a little over 38 so multiplying 13 by 38 will give you 494 and multiplying 13 by 39 will give you 507

Answer:

Step-by-step explanation:

The smallest possible multiple of 13 dollars greater than 500 dollars would be 507 which is 13*39 (i assume you mean whole numbers when you say positive numbers, if not the other answer would be 13*38.461)

We need to assume the sample was randomly selected because we are making inferences about ___________. a)unknown statistic b) unknown parameter c) means

Answers

We need to assume the sample was randomly selected because we are making inferences about means. Means refers to the average of a sample of data points, which can be used to estimate the value of an unknown population parameter.

If the sample was not randomly selected, then our estimates of the population parameter could be biased or inaccurate. This is because the sample may not be representative of the population as a whole, which could lead to incorrect estimates of the population parameter.

In order to make valid inferences about a population, it is essential to use random sampling. This is because random sampling ensures that the sample is representative of the population as a whole, meaning that the estimates of the population parameter that you obtain from the sample will be unbiased and accurate. If the sample is not randomly selected, then there is a risk that the sample is not representative of the population, which could lead to incorrect estimates of the population parameter.

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Quadrilateral FGHI is similar to quadrilateral JKLM. Find the measure of side JK. Figures are not drawn to scale.

Answers

The measure of side KL in the given quadrilateral is 31.88 units.

What is a Quadrilateral?

A quadrilateral is a four-sided polygon with four edges and four corners that is used in geometry.

The Latin words Quadri, a variation of four, and latus, meaning "side," are the source of the name.

A two-dimensional shape with four sides, four vertices, and four angles is referred to as a quadrilateral.

Convex and concave are the two main forms.

Convex quadrilaterals can also be divided into a number of subgroups, including trapezoids, parallelograms, rectangles, rhombus, and squares.

So, according to the given figure of FGHI and JKLM:

FG/JK = GH/KL = HI/LM = FI/JM

GH/KL = HI/LM

7/KL = 9/41

KL = 7*41/9 = 31.888

Therefore, the measure of side KL in the given quadrilateral is 31.88 units.

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Correct question with a diagram:

Quadrilateral FGHI is similar to quadrilateral JKLM. Find the measure of side KL. Round your answer to the nearest tenth.

What type of lines will be presented by the system of equations 2x 3y 6 and 4x 6y 11?

Answers

The system of equations 2x+3y=6 and 4x+6y=11 will present two lines in the coordinate plane.

The linear equation is a mathematical expression that describes a straight line in a coordinate plane. It is of the form y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept (the point where the line crosses the y-axis). Linear equations can also be expressed in other forms, such as ax + by = c, where a, b, and c are constants.

Since each equation represents a line, and the system has two equations, it will have two lines. The lines will be in slope-intercept form (y = mx + b), with different slopes and y-intercepts. The lines will intersect at one point, which is the solution to the system of equations.

The system of equation will present the unique straight line as the solution in two-dimensional coordinate plane.

Two lines in the coordinate plane will present the system of equations 2x+3y=6 and 4x+6y=11 .

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What is the volume of Hannah's suitcase in cubic inches?

Answers

The volume of Hannah's suitcase in cubic inches is: C: 7938.

How to find the volume?

The volume can be determine using this formula

Volume = Length × Width × Depth

Where:

Length = 27 inches

Width = 21 inches

Depth = 14 inches

Let plug in the formula

Volume = 27 inches × 21 inches × 14 inches

Volume = 7,938

Therefore we can conclude that the volume is 7,938.

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For triangle ABC use the Triangle Proportionality Theorem to solve for x

1. what is the value of x?

2. What is the perimeter of triangle ABC?

show ALL work-- PLEASE HELP!

Answers

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here's the solution ~

The two triangles in the shown figure are similar, therefore conclusion can be made that :

Ratio of its it's corresponding sides is equal.

[tex]\qquad \sf  \dashrightarrow \: \dfrac{2x - 4 + 6}{6} = \dfrac{24}{4} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{2x + 2}{6} = 6[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2x + 2 = 6 \times 6[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2x + 2 = 36[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2x = 36 - 2[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2x = 34[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 17[/tex]

Therefore, The value of x is " 17 "

Now, the measure of side BC is :

[tex]\qquad \sf  \dashrightarrow \: 2x - 4[/tex]

[tex]\qquad \sf  \dashrightarrow \:2 (17) - 4[/tex]

[tex]\qquad \sf  \dashrightarrow \: 34 - 4[/tex]

[tex]\qquad \sf  \dashrightarrow \: 30 \: \: units[/tex]

So, its perimeter will be :

[tex]\qquad \sf  \dashrightarrow \: p = AB + AB + BC [/tex]

[tex]\qquad \sf  \dashrightarrow \: p = 24 + 26 + 30[/tex]

[tex]\qquad \sf  \dashrightarrow \: p = 80 \: \: units[/tex]

Answer:

1) x = 17,2) P = 86 units.

------------------------------------

Part 1

According to Triangle Proportionality Theorem we have the following equal proportions:

(24 - 4)/4 = (2x - 4)/620/4 = (x - 2)/35 = (x - 2)/3x - 2 = 5*3x - 2 = 15x = 17

Part 2

The missing side is:

BC = 6 + 5*6 = 6 + 30 = 36 units

The perimeter is:

P = 24 + 36 + 26 = 86 units

What do you get when you subtract 3xy from 5 by?

Answers

When we subtract 3xy from 5 we will get 3xy - 5.Both are different 3xy is a polynomial in xy and 5 is a constant we can not simplify further.

First, let's try to learn subtraction in the case of polynomials.

3xy is a polynomial.

5 is a constant.

Polynomials can be subtracted using a method that involves changing the signs to the opposite sign. The process resembles adding polynomials. Depending on the specific equation, we transform the sign while subtracting polynomials to either positive or negative. Learn more about subtracting polynomials, their techniques, procedures, and examples by reading on.

For instance, subtract 5x + 8y - 20z from 4x - 10y + 15z.

The polynomials should first be arranged in standard form. In this illustration, it has already been set up.

Place them horizontally in step two.

(4x - 10y + 15z) - (5x + 8y - 20z)

Step 3: By using parenthesis, modify the second polynomial's sign.

4x-10y-15z, and 5x+8y 20z

Step 4: Group terms that are similar together.

4x - 5x - 10y - 8y + 15z + 20z

Step 5: Resolve the problem

-x - 18y + 35z

As a result, we get -x - 18y + 35z when we subtract 4x - 10y + 15z from 5x + 8y - 20z.

In the same way, if we subtract 3xy from 5 we will get 3xy - 5.

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Suppose a historian wants to estimate the true mean number of children per household in New York City in 1900. The historian randomly selects 200 household census records from New York City. She records the number of children residing in each household. The historian then computes the mean number of children per household among these 200 households.

Answers

The data which is given by the historian is used to find the population, variable, parameter, sample, data, and statistic. He estimated the mean number of children per household in New York City in 1900.

Population - all of the households in New York City in 1900.

Variable - a quantity equivalent to the number of children in a randomly selected household

Parameter -  the mean number of children per household in New York City in 1900

Sample - the 200 households selected by the historian

Data - the 200 records collected by the historian

Statistic -  the mean number of children per household in the historian's sample.

Complete question:

Suppose a historian wants to estimate the true mean number of children per household in New York City in 1900. The historian randomly selects 200 household census records from New York City. She records the number of children residing in each household. The historian then computes the mean number of children per household among these 200 households. Classify each description as one of a parameter, variable, population, sample, data, or statistic.

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Which of the following is equivalent to 5 a) ²/3 + 2/1/1/0 4 b) 1/2 x 1/1/20 c) / x4 d) / x4 ÷ 4 ? Show your thinking.​

Answers

The answer is d) / x4 ÷ 4.

To show my thinking, I will use the distributive property to simplify the expression.

5 = (1/2 x 1/1/20) + (²/3 + 2/1/1/0 4)

= (1/2 x 1/1/20) + (1/2 x 4)

= (1/2 x 1/1/20) + (1/2 x 4/1)

= (1/2 x 1/1/20) + (1/2 x 4/1) ÷ 4

= (1/2 x 1/1/20 ÷ 4) + (1/2 x 4/1 ÷ 4)

= (1/2 x 1/4/80) + (1/2 x 1/4)

= (1/8 x 1/80) + (1/8)

= 1/8 + 1/8

= / x4 ÷ 4

Find the ratio of the volume of the cone to the volume of the cylinder. Express your answer as a common fraction.

Answers

The ratio of the volume of the cone to the cylinder is 1:3.

A cone has a circular base and the base is made of a radius and diameter.

The volume of a cone is defined as the amount of space a cone occupies. The formula of the volume of a cone is given as one-third the product of the area of the circular base and the height of the cone. If the radius of the cone is "r" and the height is "h", the volume of a cone is given as V = (1/3)πr²h.

A cylinder is a three-dimensional solid shape that makes of two parallel bases linked by a curved surface.

Thus, the volume (V1) of a right circular cylinder, using the above formula, is,

                   V1=  πr²h

Here,

'r' is the radius of the cylinder

'h' is the height of the cylinder

π is a constant whose value is 22/7.

The ratio of the volume of the cone to the cylinder is

=  (1/3)πr²h :  πr²h

= 1 : 3

So, the ratio is - 1:3.

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Please help asap people kept giving me wrong answers. Due tonight in a couple hours +25pts

ES = ___ units


Round your answer to the nearest tenth.

Answers

The value of ES will be;

⇒ ES = 10.63 units

What is Line segment?

Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.

Given that;

The coordinate of E = (- 3, - 4)

The coordinate of S = (4,  4)

Now,

Since, The coordinate of E = (- 3, - 4)

The coordinate of S = (4,  4)

Hence, The value of ES is find as;

⇒ ES = √ (4 - (-3))² + (4 - (-4))²

         = √ 7² + 8²

         = √ 49 + 64

         = √ 113

         = 10.63

Thus, The value of ES = 10.63 units

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which system of equations has only one solution
4x+2y=8 -4x-2y=3

Answers

Answer is this system of equations has NO solution

Step by step

4x + 2y = 8
Arrange in y intercept form
2y = -4x + 8
Divide all by 2 to solve
y = -2x + 4

-4x -2y = 3
Arrange in y intercept form
2y = -4x -3
Divide all by 2 to solve
y = -2x -3/2

These equations have the same slope (2) with different y intercepts, so they are parallel lines. Parallel lines never intersect so there is no solution.

How do you find the asymptotes and zeros of a function?

Answers

The process to find the asymptote and zeros of the function is explained below.

The term asymptote is referred as a horizontal/vertical/slant line to which the curve is very close to but the curve doesn't touch the asymptote.

Here we need to find the way to identify the asymptotes and zeros of a function.

The process of finding the asymptote is defined as,

If you want to find the horizontal asymptotes, then apply the limit x→∞ or x→ -∞.

Where as if you want to find the vertical asymptotes, then apply the limit y→∞ or y→ -∞.

Finally, if you want to find the slant asymptote, then divide the numerator by the denominator.

The process of finding the zero of the function is defined as the way to find the values of x where f(x) = 0.

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How do you know if a graph is wider or narrower than the parent function?

Answers

The parabola narrows as the quadratic coefficient increases. The parabola's width increases as the quadratic coefficient decreases.

Define the condition for wider graph of the parent function?

The graphs' width and whether or not they slant upward or downward depend on the quadratic term's coefficient, a for the parent function.

The parabola ends point up when the quadratic coefficient is positive.The parabola's ends point down when the quadratic coefficient is negative.The parabola narrows as the quadratic coefficient increases.The parabola's width increases as the quadratic coefficient decreases.The axis of symmetry is moved away from the y-axis by the linear-term coefficient b. The quadratic coefficient's sign and the linear coefficient's sign both affect the shift's direction.The y-intercept is impacted by the constant term c. The intercept point just on y-axis increases higher the higher the number is.

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Radicals help please

Answers

Consequently, the answer to the above fraction problem comes out to be 1/2 .

What is fraction?

An element of a fraction or ratio is a piece of a whole. The number of equally sized pieces into which the whole has been divided is represented by the denominator b, and the number of parts that are included is represented by the numerator a. The LCM of two fractions' denominators is the least common multiple (LCD) of those denominators.

Here,

Given here is: (4√(2) - √(2)) × √(2) /  (2) (2) × √(18) (18)

The radical is then simplified in order to determine its value.

=> 3√(2) × √(2) / 2√(2) × 3√(2)

=> 3(2) / 6(2)

=> 3/6

=> 1/2 or 0.5

so,

after simplification, the answer is 1/2.

Consequently, the answer to the above fractional problem comes out to be 1/2 .

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I
need to show work please help me its due tomorrow

Answers

Answer:

#1

Step-by-step explanation:

boxes   apples

3            6

6           12

9          18

10         20

ratio of apples to boxes is 2:1.   2 apples each box.  Divide the number of apples by 2 to get the number of boxes.  multiply boxes by 2 to get apples.

#2

boxes    cherries

3             12

5           20

6            24

7            28

if you divide cherrie by 4 you get the number of boxes.

Multiply boxes by 4 to get cherries.

Ratio of cherries to boxes is 4 to 1.

16. A large waffle cone has a diameter of 3 inches and a height of 8 inches. Two scoops of
✓ ice cream have been stacked on top of the cone, after it was filled. The scoops are
completely round and have a diameter the same as the cone.

Find the volume of the two scoops of ice cream combined with the ice cream inside the
cone.

Answers

The volume is 23 inches long.

Answer:

(1/3) (44.5)π cm3.

Step-by-step explanation:

The volume of the two scoops of ice cream combined with the ice cream inside the cone can be calculated as follows:

Volume of cone = (1/3) π (3/2)2h = (1/3) π (4.5)8 = (1/3) (35.5)π

Volume of scoop = (1/6) π d3 = (1/6) (3)π

Total volume = (1/3) (35.5)π + 2(1/6) (3)π = (1/3) (44.5)π cm3.

jacks meeting stared at 2:45 pm and ended at 5:25 pm how long did the meeting last

Answers

Jacks meeting lasted for 160 min or 2 hrs 40 min.

What is Time?

Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future.

Given is that jacks meeting stared at 2:45 pm and ended at 5:25 pm.

The time for which the meeting lasted can be written as -

{i} = 2:45 pm

{i + 60 minutes} = 3:45 pm

{i + (2 x 60) minutes} = 4:45 pm

{i + (2 x 60 + 40) minutes} = 5:25 pm

{f} = 5 : 25 pm

The meeting lasted for -

2 x 60 + 40

160 minutes

or

2 hours 40 minutes

Therefore, Jacks meeting lasted for 160 min or 2 hrs 40 min.

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If a coin is tossed 4 times, the odds of it coming up either heads every time or tails every time are 1:7.
What is the probability the coin comes up all heads or all tails after 4 tosses?

Answers

The probability the coin comes up all heads or all tails after 4 tosses is 12.5%.

What is probability?

Probability refers to the ratio, chance, likelihood, or odds that an expected outcome is achieved when there are many possible outcomes.

Probability is a fractional value, especially when the odds of the occurrence of the expected event are not 100% uncertain or certain.

In this case, probability lies between zero and one.

Odds of a coin coming up either heads or tails every time = 1:7

The sum of ratios = 8 (1 + 7)

Thus, the probability of the coin coming up with all heads or all tails = 12.5% (1/8 x 100)

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Individual bottles of water are filled by a machine at a factory with an amount of water that is approximately normal with a mean of 505 mL and a standard deviation of 10 mL. A random sample of 16 bottles is selected for a quality inspection What is the probability that the mean amount of water in these 16 bottles is within 5 mL of the population mean? Choose 1 answer: P(500 < < 510) 0.38 B P(500 < t <510) 0.45 P(500 < & <510) 0.88 P(500 <<510) 0.95 We cannot calculate this probability because the sampling distribution is not normal.

Answers

The probability of the event that the mean amount of water in the 16 bottles is within 5 mL of the population mean is approximately 0.9544, which is closest to 0.95.

The correct answer is: D. P(500 <<510) 0.95.

Here, we have to find the probability that the mean amount of water in the 16 bottles is within 5 mL of the population mean (505 mL), we need to calculate the probability P(500 <x < 510), where x is the sample mean.

Given that the sample size (n) is 16 and the population standard deviation (σ) is 10 mL, we can use the Central Limit Theorem to approximate the sampling distribution of the sample mean.

The Central Limit Theorem states that for a sufficiently large sample size (n ≥ 30), the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution.

The mean of the sampling distribution of the sample mean is equal to the population mean (μ) and the standard deviation of the sampling distribution (standard error) is given by σ/√n, where σ is the population standard deviation and n is the sample size.

In this case:

μ = 505 mL (population mean)

σ = 10 mL (population standard deviation)

n = 16 (sample size)

The standard error (SE) of the sample mean is:

SE = σ/√n = 10/√16 = 10/4 = 2.5 mL

Now, we need to find the z-scores for 500 mL and 510 mL:

z₁ = (500 - μ) / SE = (500 - 505) / 2.5 = -2

z₂ = (510 - μ) / SE = (510 - 505) / 2.5 = 2

Using the z-table or a statistical calculator, we can find the probabilities corresponding to these z-scores:

P(z < -2) ≈ 0.0228

P(z < 2) ≈ 0.9772

Now, to find the probability that the sample mean is within 5 mL of the population mean (P(500 <x < 510)), we subtract the probability corresponding to the lower z-score from the probability corresponding to the higher z-score:

P(500 < x < 510) ≈ P(z < 2) - P(z < -2) ≈ 0.9772 - 0.0228 ≈ 0.9544

So, the probability of the event that the mean amount of water in the 16 bottles is within 5 mL of the population mean is approximately 0.9544, which is closest to 0.95.

The correct answer is: D. P(500 <<510) 0.95

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