The diameter of a circle is 22 feet. What is the circle's area?
Use 3.14 for ​.

Answer:

Step-by-step explanation:

(2x + 3)(3x - 2) + (3 - 4x)(2x + 3) - 4x² + 9     FOIL the first and second set of parentheses.

6x² - 4x + 9x - 6 + 6x + 9 - 8x² - 12x - 4x² + 9   Combine like terms

-6x² - x + 12     Factor.

(-3x + 4)(2x + 3)

The equation that can be used to find x, the number of jerseys is 82.49 = 15.70x + 3.99

The other three equations are incorrect because the equation should be represented by total cost equals cost of each shirt multiplied by number of jerseys plus shipping cost.

Ms Chen purchased 15 jerseys.

Cost of x jerseys including shipping = $82.49

Cost of shipping = $3.99

Cost of each jersey = $15.70

82.49 = 15.70x + 3.99

82.49 - 3.99 = 15.70x

78.50 = 15.70x

x = 78.50 / 5

x = 5

In conclusion, the number of jerseys bought is 5.

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The height of the tower is 17.32 meters

Height is the measurement of an item in the vertical direction, whereas distance is the measurement of an object in the horizontal direction from a certain location.

Given that, Ical is 10 meters away from a tower [since angle is not given let the angle of the top of the tower be 60°], we need to find the height of the tower, [see the figure attached]

The whole scene is making a right triangle, so using the concept of trigonometric ratios,

We get,

Tan 60° = height of the tower / distance of Ical from the tower

Tan 60° = height of the tower / 10

Height of the tower = 10 × Tan 60°

Height of the tower = 10 × √3

Height of the tower = 10√3

Height of the tower = 10 × 1.73

Height of the tower = 17.32

Hence, the height of the tower is 17.32 meters

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Answer:

To stretch the graph of f(x) horizontally by a factor of 6, we can multiply the x-values of each point on the graph by 1/6. This will make the curve wider and flatter. The equation of the transformed function will be of the form:

g(x) = cos((1/6)x)

To shift the graph of g(x) 5 units down, we can subtract 5 from the y-values of each point on the graph. The final equation of the transformed function will be:

g(x) = cos((1/6)x) - 5

So, the equation of the new function g(x) is g(x) = cos((1/6)x) - 5.

Therefore, the rational function whose graph has an x-intercept at x=2.

In mathematics, a function is a rule that assigns to each input value from a set (called the domain) exactly one output value from another set (called the range). In other words, a function is a relationship between two sets of numbers, such that for each input value there is a unique output value. Functions are commonly denoted by an equation that defines the relationship between the input and output variables. For example, the equation y = f(x) defines a function f, where x is the input variable and y is the output variable.

Here,

To identify the rational function whose graph is given below, we need to determine its equation. We know that the graph has an x-intercept at x=2 and a y-intercept at y=−2/3.

We also know that the function is a rational function, which means it can be written as a ratio of two polynomials. The general form of a rational function is:

f(x) = p(x)/q(x)

where p(x) and q(x) are polynomials, and q(x) cannot be zero.

To find the specific equation of the function whose graph is shown, we can use the information about the intercepts to write down two points that are on the graph. We can use these points to set up a system of equations that we can solve for the coefficients of the polynomials p(x) and q(x).

Using the x-intercept, we know that the point (2,0) is on the graph. Using the y-intercept, we know that the point (0,-2/3) is on the graph. So we can set up the following system of equations:

p(2)/q(2) = 0

p(0)/q(0) = -2/3

Since the denominator of a rational function cannot be zero, we know that q(2) and q(0) cannot be zero. This allows us to set up a third equation:

q(x) ≠ 0

Now we can use algebra to solve for the coefficients of p(x) and q(x). We can start by writing the rational function in general form:

f(x) = p(x)/q(x)

and then multiplying both sides by q(x):

f(x)q(x) = p(x)

We can now substitute x=2 and x=0 to get two equations:

f(2)q(2) = p(2) = 0

f(0)q(0) = p(0) = -2/3

We also have the equation q(x) ≠ 0. This means that the denominator cannot have any factors that would make it equal to zero, so we can assume that q(x) has a linear factor of (x - 2), since we know that the graph has an x-intercept at x=2. We can then write:

q(x) = a(x - 2)

where a is some constant.

Now we can substitute this expression for q(x) into the equation f(x)q(x) = p(x) and simplify:

f(x)q(x) = p(x)

f(x)a(x - 2) = p(x)

We can now substitute x=0 and use the equation we found for p(0):

f(0)a(-2) = -2/3

f(0) = 1/3a

Next, we can substitute x=2 and use the equation we found for p(2):

f(2)a(0) = 0

f(2) = 0

Finally, we can substitute these values for f(0) and f(2) into the general form of the rational function and simplify:

f(x) = p(x)/q(x)

f(x) = p(x)/(a(x - 2))

We know that p(x) = f(x)q(x) from the equation we derived earlier, so we can substitute this into the equation above:

f(x) = f(x)(x - 2)/a(x - 2)

We can now cancel the f(x) terms from both sides and simplify:

1 = (x - 2)/a

a = x - 2

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Answer:

f = 648

Step-by-step explanation:

[tex]\frac{f}{24} =27[/tex]

Multiply both sides by 24

[tex]f=648[/tex]

The triangle whose sides are √13, 6, and 7, is a right triangle.

What is the right triangle?

A right triangle is defined as a triangle with one right angle or two perpendicular sides. The longest side of a right triangle is called the hypotenuse.

Pythagorean Theorem :

The square on the hypotenuse is equal to the total of the squares on the legs of a right triangle.

Mathematically, let r be the length of the hypotenuse of a right triangle. Again let p, q be the lengths of other sides of this triangle. By the Pythagorean Theorem,

r² = p² + q².

How to solve this problem?

We just check which triangle's sides follow the above theorem.

Option A (Triangle with sides √13, 6, and 7 ):

13 + 36 = 49

i.e. (√13)² + 6² = 7²

This triangle's sides follow the Pythagorean Theorem.

So, the triangle with sides √13, 6, and 7 is a right triangle.

Option B (Triangle with sides 7, 8, and 13 ):

49 + 64 ≠ 169

i.e. 7² + 8² ≠ 13²

This triangle's sides do not follow the Pythagorean Theorem.

So, the triangle with sides 7, 8, and 13 is not a right triangle.

Option C (Triangle with sides 10, 11, and 12 ):

100 + 121 ≠ 144

i.e. 10² + 11² ≠ 12²

This triangle's sides do not follow the Pythagorean Theorem.

So, the triangle with sides 10, 11, and 12 is not a right triangle.

Option D (Triangle with sides √10, 9, and 8 ):

10 + 64 ≠ 81

i.e. (√10)² + 8² ≠ 9²

This triangle's sides do not follow the Pythagorean Theorem.

So, the triangle with sides √10, 9, and 8 is not a right triangle.

Therefore the triangle whose sides are √13, 6, and 7, is a right triangle. So, option A is correct.

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Let's call the position of the plane "P", and the positions of clearing A and clearing B "A" and "B", respectively. We want to find the distance from the plane to clearing A.

First, draw a diagram. The angle of depression to clearing A means that the line from the plane to clearing A makes a 32 degree angle with the horizontal. Similarly, the angle of depression to clearing B means that the line from the plane to clearing B makes a 56 degree angle with the horizontal. We know that the distance between clearings A and B is 5.7 km.

Now, we can use trigonometry to find the distance from the plane to clearing A. Let's call this distance "d". We can set up the following equation:

tan(32) = d/x

where x is the horizontal distance from the plane to clearing A. We can rearrange this equation to solve for d:

d = x tan(32)

Similarly, we can set up an equation for the distance from the plane to clearing B:

tan(56) = (x + 5.7) / d

We can rearrange this equation to solve for d:

d = (x + 5.7) / tan(56)

Now we can set the two expressions for d equal to each other and solve for x:

x tan(32) = (x + 5.7) / tan(56)

x tan(32) tan(56) = x + 5.7

x (0.6561) = x + 5.7

0.6561 x = x + 5.7

-0.3439 x = 5.7

x = -5.7 / 0.3439

x ≈ -16.57

Since the distance from the plane to clearing A is a positive distance, we can ignore the negative solution. Therefore, the distance from the plane to clearing A is approximately:

d = x tan(32) ≈ (-16.57) tan(32) ≈ 9.18 km

Rounding this to the nearest hundredth of a kilometer gives:

d ≈ 9.18 km

Therefore, the distance from the plane to clearing A is approximately 9.18 km.

:)?

The cost of gasoline if the truck uses 5 gallons to drive 60 miles is $18.70

To calculate the cost of gasoline for the old truck, we can use the following formula:

Cost of gasoline = Price per gallon × Number of gallons used

Given that

Price per gallon = 3.74

Number of gallons used = 5 gallons

We have

Cost of gasoline = $3.74/gallon × 5 gallons

Evaluate

Cost = $18.70

Hence, the cost is $18.70

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Complete question

An old truck has a fuel efficiency of 12 mpg. What is the cost of gasoline if the truck uses 5 gallons to drive 60 miles if the gasoline costs $3.74 per gallon

Note that where you have a square with a side of 20dm is inscribed in a circle, the area of the shaded region is At = [tex]\approx[/tex] 257.08dm²

A square is a geometrical shape with four equal sides and four equal angles, each measuring 90 degrees.

In the figure we will determine the area of the shade:

The formula is given as follows:

1/2(Area of the Square) + ∡AB + ∡DC

Note that the above equation subsists because:

i)  the shaded region comprises of two congruent or similar triangles since the diagonals of a Square will bisect each other equally creating 4 congruent triangles.

ii) A square in a circle will always create 4 equal Chords.

Thus, imputing the figures we have:
(20dm)²/2 + [π ((20√2)/2)² - (20dm)²]/4

= 200 + [200π -400]/4
= 200 + (50π -100)
= 100 + 50π

= 257.079632679

[tex]\approx[/tex] 257.08dm²

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Full Question:

A square with a side of 20 dm is inscribed in a circle. Determine the shaded area shown in the figure.

If a = 9 and c = 9, the length of b is 3√18.

Pythagoras theorem states that for a right angled triangle, the square of the hypotenuse is the sum of the squares of base and altitude.

Given is a right angled triangle with the given length of base and altitude.

Length of base = 9

Length of altitude = 9

We have to find b, which is the hypotenuse.

Using Pythagoras theorem,

Hypotenuse² = Base² + Altitude²

b² = a² + c²

b² = 9² + 9²

b² = 81 + 81

b² = 162

b = √162 = √(18×9) = 3√18

Hence the length of hypotenuse is 3√18.

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Your question is incomplete. Probably the correct question is as follows.

Given a right angled triangle.

a is marked the base, c is marked the altitude and b is marked the hypotenuse.

Find b: If a = 9 and c = 9

The 800 readers have a newspaper if the local newspaper has letters to the editor for 40 people if this is the number represents 5%.

What is the percentage?

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

It is given that:

The local newspaper has letters to the editor for 40 people if this is the number represents 5% of all the newspaper readers.

Let x be the total number of newspaper readers.

The value of x can be found as follows:

5 % of x = 40

(5/100)x = 40

x = 40/0.05

x = 800

Thus, the 800 readers have a newspaper if the local newspaper has letters to the editor for 40 people if this is the number represents 5%.

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Complete question:

The local newspaper has letters to the editor for 40 people if this is the number represents 5% of all the newspaper readers how many readers does the newspaper have

The solution is, the total surface area is 92 sq. inches.

Total surface area refers to the area including the base(s) and the curved part. It is the total area covered by the surface of the object. If the shape has a curved surface and base, then the total area will be the sum of the two areas.

here, we have,

Total paper required = total surface area

Surface area of a cuboid = 2[(l×b) + (l×h) + (b×h)],

Where 'l' is the length, 'b' is the breadth and 'h' is the height

For the box, total surface area = 2[(8×3) + (3×2) + (8×2)]

=2[24 + 6 + 16]

=2[46]

= 92 sq. inches

Hence, The solution is, the total surface area is 92 sq. inches.

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The area of the shaded region of the rectangle is 0.23 cm², and option 2 is the correct answer.

The combined shapes of one or more simple polygons and circles make up the area of the composite shapes. We can add or subtract the areas of all the fundamental shapes together to determine the area of the composite shapes. Simply calculate the area of each individual form to obtain the area of composite shapes.

The length of the rectangle is 0.9 cm.

The width of the rectangle is 0.4 cm.

The diameter of the circle us 0.4 cm, thus the radius = 0.4/2 = 0.2 cm.

The area of the rectangle is:

A = (l)(b)

Substituting the values:

A = (0.9)(0.4)

A = 0.36 sq. cm.

The area of the circle is:

A = πr²

A = (3.14)(0.2)²

A = 0.1256 sq. cm.

The area of the shaded portion is:

Area of shaded portion = area of rectangle - area of circle

Area of shaded portion = 0.36 - 0.1256 = 0.2344 sq. cm

Hence, the area of the shaded region of the rectangle is 0.23 cm², and option 2 is the correct answer.

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The number of coins Mark have is 48.

Joey has 25 collectible coins which is 9 more than 1/3 the number Mark has. Therefore, the number of coins Mark have can be calculated as follows:

Let's write the equation for the word problem before solving.

Hence,

let

x = number of coins Mark has

Therefore,

Number of coins Joey have = 9 + 1  /3 x

Hence,

25 = 9 + 1  / 3 x

25 - 9 = 1 / 3 x

16 = 1 / 3 x

cross multiply

x = 16 × 3

x = 48 coins

Therefore,

number of coins Mark have = 48 coins

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Answer:

slope = 4

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (6, 24 ) and (x₂, y₂ ) = (0, 0 )

m = [tex]\frac{0-24}{0-6}[/tex] = [tex]\frac{-24}{-6}[/tex] = 4

Answer:

Δ JKE

Step-by-step explanation:

the figure is a triangle and is named using its vertices.

the vertices are J, K, E

to name the triangle start with any vertex , then in clockwise/ anticlockwise order the other 2 vertices. in this case starting with J , then clockwise for K and E.

in this case then the figure is Δ JKE

The missing term in the sequence 5, 11, 17, ?, 31, 41 is B. 23.

We have been given the series 5, 11, 17, ?, 31, 41. We need to find the missing number out of the given sequence.

Let us write the prime numbers upto 50.

2, 3, 5, 7, 11, 13, 19, 23, 29, 31, 37, 41, 43, 47.

By looking into the above prime numbers we can make out our sequence. The series is formed by the alternate prime numbers. Thus we can complete the given sequence as,

5, 11, 17, 23, 31, 41.

Thus we got the missing number as 23 in the sequence 5, 11, 17, 23, 31, 41.

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Find the missing term in the sequence 5, 11, 17, ?, 31, 41.

The amount paid with discount for the laptop is $ 660.

Discount is the amount of money removed from the price of an object being sold.

Amount paid is the total cost of an item.

Since laptop computer that you want to purchase was originally priced at $750. You will receive a 20% student discount, and the sales tax rate is 8%.

First, we need to know how much discount is given.

Since there is a 20 % discount, the amount of discount removed is 20% × $750 = 0.2 × % 750 = $ 150

Also, there is a sales tax rate of 8%. So, the amount of sales tax added is 8% × $750 = 0.08 × $ 750 = $ 60

So, the total amount paid is T =  price - discount + tax

= $ 750 - $ 150 + $ 60

=  $ 660

So, the amount paid is $ 660.

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Answer:

x es igual a 8.

Step-by-step explanation:

Answer:

When using the number line, you represent subtraction of a negative number with an arrow going to the right. The direction of the arrow indicates the movement of the number line towards the positive side, which is the opposite of the direction of a negative number. Subtraction of a negative number is equivalent to addition of a positive number, so the arrow going to the right represents the addition of the absolute value of the negative number. For example, if you are subtracting -5 from 10, you can represent this on a number line by starting at 10 and drawing an arrow to the right that goes 5 units, ending at 15.

Answer:

When using the number line to represent subtraction of a negative number, you would represent it with an arrow going to the right (or in the positive direction).

For example, let's say you want to represent the following subtraction on a number line:

5 - (-3)

You can start at 5 on the number line and then move to the left by 3 units, since you are subtracting a negative number. However, instead of leaving the arrow pointing to the left to represent the subtraction, you can turn it around and point it to the right, which is the positive direction. This means that you end up at a point that is 8 units to the right of 0 on the number line, which represents the answer of 8.

So, the arrow would go to the right to show the subtraction of a negative number on the number line.

Therefore, Sam wrote a total of 38,789 digits. Therefore, the probability that Sam chooses a 0 is approximately 0.026. So the sum of all the digits in the numbers from 1000 to 9999 is: 4500.

In mathematics, probability is a measure of the likelihood or chance of an event occurring. It is a way of quantifying uncertainty and expressing how likely it is that a particular outcome will occur. Probability is calculated by dividing the number of outcomes that satisfy a certain condition (such as rolling a six) by the total number of possible outcomes. Probability theory is used in a wide range of fields, including mathematics, statistics, physics, engineering, economics, and social sciences. It is used to model and analyze random phenomena, make predictions, and estimate the likelihood of certain outcomes.

Here,

(a) Sam writes down all the positive integers from 1 to 9999, inclusive. To find the total number of digits Sam wrote, we can count the number of digits in each number and add them up.

Numbers from 1 to 9 have one digit each, so there are 9 numbers with one digit, for a total of 9 digits.

Numbers from 10 to 99 have two digits each, so there are 90 numbers with two digits, for a total of 180 digits.

Numbers from 100 to 999 have three digits each, so there are 900 numbers with three digits, for a total of 2700 digits.

Numbers from 1000 to 9999 have four digits each, so there are 9000 numbers with four digits, for a total of 36000 digits.

Adding up these totals gives:

9 + 180 + 2700 + 36000 = 38789

Therefore, Sam wrote a total of 38,789 digits.

(b) Since Sam chose the digits 1 to 9999, there are 4 digits (0, 1, 2, and 3) that can appear in the thousands place, and 10 digits (0 to 9) that can appear in each of the other three places.

Therefore, the probability of choosing a 0 at random is the number of times 0 appears in the numbers divided by the total number of digits written down.

0 appears as the last digit in 1000 numbers (from 10 to 9990), and as the first digit in 9 numbers (1000, 10000, 2000, 20000, 3000, 30000, 4000, 40000, and 5000). So the total number of times 0 appears is 1000 + 9 = 1009.

The total number of digits Sam wrote is 38,789, so the probability of choosing a 0 at random is:

1009/38789 ≈ 0.026

Therefore, the probability that Sam chooses a 0 is approximately 0.026.

(c) We can find the sum of all the digits Sam wrote by adding up the sum of the digits in each number from 1 to 9999.

The sum of the digits in the numbers from 1 to 9 is 1+2+3+4+5+6+7+8+9=45.

The sum of the digits in the numbers from 10 to 99 can be found by observing that each of the digits from 0 to 9 appears in the tens place the same number of times (that is, 10 times each). Since there are 90 two-digit numbers, each digit appears a total of 10 x 90 = 900 times in the tens place. So the sum of the digits in the tens place is:

900(0+1+2+3+4+5+6+7+8+9) = 45,000

Similarly, each of the digits from 0 to 9 appears in the hundreds place the same number of times (that is, 100 times each). So the sum of the digits in the hundreds place is:

100(0+1+2+3+4+5+6+7+8+9) = 4500

Finally, each of the digits from 0 to 9 appears in each of the four places (thousands, hundreds, tens, and ones) the same number of times (that is, 1000 times each). So the sum of all the digits in the numbers from 1000 to 9999 is: 4500.

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Answer:

3

Step-by-step explanation:

∠LMN = ∠BMN + ∠LMB (linear angles)

59x + 3 = 160 + (-1 + 7x)

59x - 7x = 160 - 1 - 3

52x = 156

x = 156/52 = 3

The stem and leaf for the split between hundreds place and the tens place is 74 and 5 respectively.

A stem and leaf plot also called a stem and leaf diagram is a way of organizing data into a form that makes it easy to observe the frequency of different types of values. It is a graph that shows numerical data arranged in order. Each data value is broken into a stem and a leaf.

Given that, 600, 600, 600, 610, 610, 610, 610, 610, 610, 610, 610, 610, 610, 610, 612, 620, 620, 625, 629, 631, 635, 638, 640, 640, 645, 646, 650, 651, 660, 660, 665, 671, 671, 674, 680, 693, 700, 705, 706, 707, 707, 715, 715, 719,  720,  725, 727, 732, 738, 739 and 745.

a) Split between hundreds place and the tens place.

60|  0   0   0

61|  1    1    1    1    1    1    1    1    1    1    1    2

62|  0   0   5   9

63|   1    5   8  

64|  0    0   5   6

65|  0    1

66|  0    0   5

67|   1     1    4

68|  0

69|  3

70|  0  5   6   7   7

71 |   5  5  9

72|   0  5  7

73|   2  8  9

74|   5

b) Split between the tens place and the ones place.

6|   00  00   00  10   10  10   10   10   10  10  10  10  10  10   12   20   20   25 29   31   35   38   40   40   45   46   50   51   60   60   65   71   71   74   80   93

7|    00   05   06   07   07   15   15   19  20  25  27  32  38  39  45

Therefore, stem and leaf for the split between hundreds place and the tens place is 74 and 5 respectively.

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Answer:

C

Step-by-step explanation:

If you start by picking a point to plug in you can check easily to see what works.

Lets start with x=pi. If we plug that into all the answer choices,

A. sec(pi/2)+2 = does not exist

B. 1/2sec(2pi) = 1/2

C. 2sec(pi/2) = does not exist

D. 2csc(pi/2) = 1

So, since at pi there is a vertical asymptote it should not exist. So, A or C.

Then pick x = 0, y must be 2.

A. sec(0) +2 = 1+2 = 3

C. 2sec(0) = 2

So, C must be the answer.

Answer:

Step-by-step explanation:

The number of partitions possible for a set A with n elements is given by the Bell number, denoted as Bn.

For a set A = {a, s, i, m, o, v} with 6 elements, the number of partitions possible is given by the 6th Bell number, which can be computed as follows:

B6 = ∑k=1 to 6 {6 choose k} * Sk

where Sk is the Stirling number of the second kind, which counts the number of ways to partition a set of n elements into k non-empty subsets.

Using this formula, we can compute the Bell number for n = 6 as follows:

B6 = {6 choose 1} * S1 + {6 choose 2} * S2 + {6 choose 3} * S3 + {6 choose 4} * S4 + {6 choose 5} * S5 + {6 choose 6} * S6

S1 = 1, S2 = 15, S3 = 25, S4 = 10, S5 = 1, S6 = 0 (using a table of Stirling numbers)

B6 = (6 choose 1) * 1 + (6 choose 2) * 15 + (6 choose 3) * 25 + (6 choose 4) * 10 + (6 choose 5) * 1 + (6 choose 6) * 0

= 1 + 90 + 200 + 150 + 6 + 1

= 448

Therefore, there are 448 possible partitions of the set A = {a, s, i, m, o, v}.

Since the graph is constant, the function is not changing within any interval. Therefore, there are no intervals where the function is changing.

In mathematics, a graph is a visual representation of a set of objects and the relationships between them. Graphs are widely used in many areas, including mathematics, computer science, engineering, social sciences, and more.

A graph consists of two main components: vertices (also known as nodes) and edges. The vertices represent the objects, and the edges represent the connections or relationships between them. The edges can be directed or undirected, meaning they can be one-way or two-way relationships.

There are many types of graphs, including:

Undirected graphs: Graphs in which edges have no direction.

Directed graphs: Graphs in which edges have a direction, often represented by arrows.

Weighted graphs: Graphs in which edges have weights or values, representing some kind of numerical data.

Bipartite graphs: Graphs in which the vertices can be divided into two distinct sets, with edges only connecting vertices in different sets.

Complete graphs: Graphs in which every vertex is connected to every other vertex by an edge.

Graphs are used to model and analyze various kinds of data, such as social networks, transportation systems, financial transactions, and more. They are also used in algorithms and data structures, such as shortest path algorithms and tree data structures. In addition, graphs are often visualized using software tools to help people better understand complex relationships and patterns in data.

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In preparing to construct a one-sample t interval for a population mean, suppose we are not sure if the population distribution is Normal. In option (c) A boxplot of the data has a large outlier, we would not be safe constructing the interval based on an SRS of size 24 from the population.

What is a sample?

A sample is characterised as a more manageable and compact version of a bigger group. A smaller population that possesses the traits of a bigger group. When the population size is too big to include all participants or observations in the test, a sample is utilised in statistical analysis.

Constructing a one-sample t interval for a population mean is generally safe when the population is not Normal, as long as the sample size is large enough (usually at least 30) or the sample is taken from a population that is not too skewed or has outliers.

Therefore, options (a), (b), and (e) suggest that the sample may come from a population that is roughly Normal or can be transformed to be Normal, and so constructing the interval based on an SRS of size 24 would be safe.

Option (d) suggests that the sample standard deviation is large, but this does not necessarily mean that constructing the interval would not be safe.

It may reduce the precision of the interval, but as long as the sample size is sufficient, the interval can still be constructed.

Option (c) suggests that the sample has a large outlier, which may significantly affect the distribution of the sample and the calculation of the interval.

Therefore, in this circumstance, constructing the interval based on an SRS of size 24 would not be safe.

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The probability that the individual must stop at at least one light that is 0.45.

Probability is the mathematical tool or procedure of predicting how likely a given event is going to happen.

Given is that there are two traffic lights on the route used by a certain individual to go from home to work. Let {E} denote the event that the individual must stop at the first light, and define the event {F} in a similar manner for the second light. Suppose that -

We can write -

P{E ∪ F} = P{E} + P{F} - P{E ∩ F}

P{E ∪ F} = 0.4 + 0.2 - 0.15

P{E ∪ F} = 0.6 - 0.15

P{E ∪ F} = 0.45

Therefore, the probability that the individual must stop at at least one light that is 0.45.

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