Work out the values of a, b, c and d.
Justify each of your answers.

The solutions for the quadratic equations ax² + bx = 0 are:

a) x=0 or x=-2 for x²+2x=0;

x=0 or x=2 for x²-2x=0;

x=0 or x=2 for -x²+2x=0;

x=0 or x=-2 for -x²-2x=0.

b) x=0 or x=-5/3 for 3x²+5x=0;

x=0 or x=5/3 for 3x²-5x=0;

x=0 or x=5/3 for -3x²+5x=0;

x=0 or x=-5/3 for -3x²-5x=0.

a) To solve the quadratic equations ax² + bx = 0, we need to factor out the common variable x, and then solve for x:

a) x²+2x=0

x(x+2)=0

x=0 or x=-2

b) x²-2x=0

x(x-2)=0

x=0 or x=2

c) -x² + 2x = 0

-x(x-2)=0

x=0 or x=2

d) -x²-2x=0

-x(x+2)=0

x=0 or x=-2

b) To solve the quadratic equations 3x²+5x=0, 3x²-5x=0, -3x²+5x=0, and -3x²-5x=0, we factor out the common variable x and then solve for x:

b) 3x²+5x=0

x(3x+5)=0

x=0 or x=-5/3

b) 3x²-5x=0

x(3x-5)=0

x=0 or x=5/3

c) -3x²+5x=0

x(-3x+5)=0

x=0 or x=5/3

d) -3x²-5x=0

x(-3x-5)=0

x=0 or x=-5/3

Therefore, the solutions for the quadratic equations ax² + bx = 0 are:

a) x=0 or x=-2 for x²+2x=0;

x=0 or x=2 for x²-2x=0;

x=0 or x=2 for -x²+2x=0;

x=0 or x=-2 for -x²-2x=0.

b) x=0 or x=-5/3 for 3x²+5x=0;

x=0 or x=5/3 for 3x²-5x=0;

x=0 or x=5/3 for -3x²+5x=0;

x=0 or x=-5/3 for -3x²-5x=0.

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The English translation of the question in the picture:

75. Solve the quadratic equations ax² + bx = 0

a) x²+2x=0,

x²-2x=0,

-x² + 2x = 0.

-x²-2x=0;

b) 3x²+5x=0,

3x²-5x=0.

-3x²+5x=0,

-3x²-5x=0;

The statement that the f distribution is always a left-tailed test is false statement about the f distribution. So, the right choice for answer option (a).

The F distribution (Snedecor's F distribution) represents continuous probability distribution which occurs frequently as null distribution of test statistics. Let two independent

chi-square variables are x and y with n₁ and n₂ with degree of freedom respectively. So, F-distribution is defined as F = ( X/n₁)/ (Y/n₂)

Characteristics : The F random variable is non-negative variable and the distribution is skewed to the right.

The F for left tail test both right-tailed &left tailed. So, the false statement is option(a).

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Complete question:

which of the following statements about the f distribution is false? group of answer choices

a) the f distribution is always a left-tailed test.

b) the f distribution is skewed to the right.

c)the f statistic is greater than or equal to zero.

d) as the degrees of freedom of for the numerator or denominator get larger, the curves approximates the normal distribution.

Answer:

Therefore, -8(2x-4) simplifies to -16x + 32.

Step-by-step explanation:

-8 * 2x - (-8 * 4)

Simplifying this expression further gives:

-16x + 32

Therefore, -8(2x-4) simplifies to -16x + 32.

Answer:

Step-by-step explanation:

For the given statements the correct answer is B |6| > |−8| and C |−8| < |3|.

What is statement?

In mathematics, a statement is a declarative sentence that is either true or false, but not both. Statements are often expressed using variables, symbols, or mathematical notation, and they can describe mathematical objects, relationships, properties, or operations.

For the first question, the correct response is:

B |6| > |−8|

This is true because the absolute value of a number is always positive, and it represents the distance of that number from zero on the number line. So, the absolute value of 6 is greater than the absolute value of -8, because 6 is further away from zero than -8 on the number line.

For the second question, the correct response is:

C |−8| < |3|

This is true because the absolute value of -8 is greater than the absolute value of 3. Absolute values tell us the distance from zero on the number line, and the distance between -8 and 0 is greater than the distance between 3 and 0.

Therefore for the given statements the correct answer is B |6| > |−8| and C |−8| < |3|.

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The volume of the given pyramid is 86 in³ respectively.

A three-dimensional shape is a pyramid.

A pyramid's flat triangular faces unite at a common point known as the apex and have a polygonal base.

The bases are joined to the peak to create a pyramid.

The lateral face is a triangle face formed by the connection of each edge of the base to the apex.

A three-dimensional figure is a pyramid.

Its base is a flat polygon.

The remaining faces are all triangles and are referred to as lateral faces.

So, the formula for the volume of the pyramid is:

V = lwh/3

Now, insert values as follows:

V = lwh/3

V = 7.4*7*5/3

V = 86.33333

Rounding off: 86 in³

Therefore, the volume of the given pyramid is 86 in³ respectively.

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Answer: A=78

Step-by-step explanation: 936/12=78

936 eggs were produced last year by the sizable dairy farm. 78 dozen eggs are produced by this farm. The answer is option (A).

The study of symbols for math and the procedures for using them to solve equations and comprehend the relationships between variables is the subject of the branch of mathematics known as algebra. When representing quantities and their relationships using letters and symbols, algebra uses graphs, functions, and expression manipulation in addition to equation and inequalities solving.

Numerous branches of science, technology, economics, and other disciplines make considerable use of algebraic concepts and methods. It is a fundamental area of mathematics that is frequently studied as a pre-requisite for more difficult maths and science courses.

Algebraic concepts that are important to know include:

Addition, subtraction, multiplication, and division are operations using numbers and variables.

Using variables to solve equations and inequalities

Algebraic expressions manipulation and simplification

Knowing how to graph both linear and nonlinear functions

Utilising matrices and vectors

studying trigonometric, rational, and polynomial functions

We must divide the total number of eggs by 12 to determine the number of dozen eggs produced.

936/12 = 78

We must divide the total number of eggs by 12 to determine the number of dozen eggs produced.

The answer is A) 78.

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We can use polynomial long division to divide (4x^4 - 4x^2 - x - 3) by (2x^2 - 3):

         2x^2 + 0x - 1

    ---------------------

2x^2 - 3 | 4x^4 + 0x^3 - 4x^2 - x - 3

         4x^4 - 6x^2

         -----------

                 2x^2 - x

                 2x^2 - 3

                 -------

                      x - 3  

Therefore,

(4x^4 - 4x^2 - x - 3)/(2x^2 - 3) = 2x^2 + 0x - 1 with a remainder of (x - 3)/(2x^2 - 3).

So the final answer is

2x^2 - 1 + (x - 3)/(2x^2 - 3)

Answer:

x=21

Step-by-step explanation:

Ally will have 91.148 meters of tape in all if Ally needs 90 meters of tape for a project.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that can include numbers, variables, and operators (such as addition, subtraction, multiplication, and division), as well as grouping symbols like parentheses.

Ally needs a total of 90 meters of tape for her project. She bought three rolls of tape, one with 50 meters, another with 22.86 meters, and the last one with 18.288 meters. To find the total amount of tape she has, she needs to add the length of all three rolls together.

Adding the length of the first two rolls, we get:

50 meters + 22.86 meters = 72.86 meters

Then adding the length of the third roll to the sum above, we get:

72.86 meters + 18.288 meters = 91.148 meters

Therefore, Ally will have 91.148 meters of tape in all.

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The required probability of randomly selected people among 11% of left handed are,

Having some lefties (≥1) among the 5 people is 0.4416.

Having exactly 3 lefties in the group of 5 people is 0.01054.

Percentage of people left handed = 11%

Number of people selected at random = 5

Probability that there are some lefties (≥1) among the 5 people,

Probability of the complement event, which is that there are no lefties in the group.

Probability of selecting a right-handed person is

=1-0.11

=0.89.

Probability that all 5 people are right-handed is,

P(all right-handed)

= (0.89)^5

= 0.5584

Probability of there being some lefties (≥1) is the complement of this,

P(some lefties)

= 1 - P(all right-handed)

= 1 - 0.5584

= 0.4416

Probability of there being some lefties (≥1) among the 5 people is 0.4416.

Probability that there are exactly 3 lefties in the group of 5 people,

Use the binomial distribution formula,

P(X=3) = (⁵C₃) × (0.11)^3 × (1-0.11)^2

where X is the number of lefties in the group.

Using the binomial coefficient formula

ⁿCₐ= n! / (a! * (n-a)!)

P(X=3)

= (5!/(3!*(5-3)!)) × (0.11)^3×(0.89)^2

= 0.01054

Probability of there being exactly 3 lefties in the group of 5 people is 0.01054

Therefore, the probability of having some lefties ( ≥ 1) among the 5 people and  exactly 3 lefties in the group is equal to 0.4416 and 0.01054 respectively.

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The above question is incomplete, the complete question is:

Assume that 11% of people are left-handed. if we select 5 people at random, find the probability of each outcome described below, rounded to four decimal places:

a. There are some lefties ( ≥ 1) among the 5 people.

b. There are exactly 3 lefties in the group.

Answer:

Step-by-step explanation:

A = 2πrh

Find radius

Diagonal = 14 so radius 14 : 2 = 7

A = 2πrh

A = 2π×7×2

A = 2π x 14

A = 28π meters  or 87.92 meters

That we know that Mandy sells 12 tickets, we can use the first equation to find out how many tickets Alonzo sells: a = 3n - 5 = 3(12) - 5 = 31

Alonzo sells 31 tickets.

What is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas. It involves the study of variables, expressions, equations, and functions.

Let's use algebra to solve the problem:

Let's start by defining some variables:

Let n be the number of tickets Mandy sells.

Let a be the number of tickets Alonzo sells.

We know that:

Alonzo sells 5 tickets less than three times what Mandy sells. So we can write:

a = 3n - 5

Together they sell a total of 43 tickets. So we can write:

a + n = 43

We have two equations with two variables, so we can solve for a by substituting the first equation into the second equation:

(3n - 5) + n = 43

4n - 5 = 43

4n = 48

n = 12

Now that we know that Mandy sells 12 tickets, we can use the first equation to find out how many tickets Alonzo sells:

a = 3n - 5 = 3(12) - 5 = 31

Therefore, Alonzo sells 31 tickets.

So the answer is: Alonzo sells 31 tickets.

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The values of x, y, and z in the given rhombus are: x = -31, y = 20, z = -87.

An equation is a mathematical statement saying that two amounts or values are the same, for example 6 x4=12x

We know that the side of a rhombus are equal in length.therefore we can solve the given equation

4y + 8 = -3x - 5 = -z + 1 = 88

Solving each equation for the variables, we get:

4y + 8 = 88

4y = 80

y = 20

-3x - 5 = 88

-3x = 93

x = -31

-z + 1 = 88

-z = 87

z = -87

Heance , the values of x, y, and z in the given rhombus are:

x = -31, y = 20, z = -87.

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The number of books that had no damage or minor damage in the sample is:

722 + 75 = 797

To estimate the number of books in the entire collection that would have no damage or minor damage, we can assume that the proportion of books with no or minor damage in the sample is approximately equal to the proportion of books with no or minor damage in the entire collection.

The proportion of books with no or minor damage in the sample is:

797 / (722 + 75 + 29) = 0.9064

So we can estimate the number of books with no damage or minor damage in the entire collection as:

0.9064 x 70,500 = 63,912.6

Rounding to the nearest whole number, we get:

63,913

19 is the range and 14 is the IQR. So, "The range is 19, and the IQR is 14" is the appropriate response.

The range in statistics is the distinction between the greatest and lowest values within a set of data. It is a gauge of variation that reveals the degree to which values within a dataset are dispersed.

You simply take the difference between the two values to determine the range. The range is given by: When the dataset, for instance, has the values 2, 3, 5, 8, et 10, the lowest value is 2, and the highest is 10.

Range = Highest value – Lowest value = 10 – 2 = 8 .The range in this instance is hence 8.

given

The range is the discrepancy between the data set's maximum and minimum values.

The box plot shows that the range is between 40 and 59, with 40 being the smallest value and 59 being the maximum.

Maximum value - Minimum value equals 59 - 40, which equals 19.

You may determine the values of Q1 and Q3 to be roughly 45 and 59, respectively, using the box plot.

IQR = Q3 - Q1 = 59 - 45 = 14

When the IQR is 14 and the range is 19, the answer is:

19 is the range and 14 is the IQR. So, "The range is 19, and the IQR is 14" is the appropriate response.

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The number of toy cars to the number of trucks is 5/2,the number of toy trucks is 2/7 of the total number of toy cars and toy trucks and  the number of toy cars is 5/7 of the total number of toy cars and toy trucks.

Let's represent the number of toy cars as 'c' and the number of toy trucks as 't'.

From the problem, we know that:

t = 2/5c

Express the number of toy cars as a fraction of the number of toy trucks:

c = 5/2t

c/t = (5/2t)/t = 5/2

Therefore, the number of toy cars is 5/2 times the number of toy trucks.

The total number of toy cars and toy trucks is:

c + t

Substituting t = 2/5c, we get:

c + (2/5)c = 7/5c

So the ratio of the number of toy trucks to the total number of toy cars and toy trucks is:

t/(c + t) = (2/5c) / (7/5c) = 2/7

Therefore, the number of toy trucks is 2/7 of the total number of toy cars and toy trucks.

The fraction of the total number of toy cars and toy trucks that is the number of toy cars is:

c / (c + t)

Substituting t = 2/5c, we get:

c / (c + 2/5c) = c / (7/5c) = 5/7

Therefore, the number of toy cars is 5/7 of the total number of toy cars and toy trucks.

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After answering the presented question, we can conclude that Rounding this to the nearest whole number, we get a surface area of 91 sq. ft.

In geometry, the diameter of a circle is any straight line segment that has an endpoint on the circle and travels through its centre. Another way to put it is the longest chord of a circle. Either idea can be used to define the diameter of a sphere. The diameter is the length of the line that runs tangent to the two points at either end of the circle. If you take length to be the distance between two points, diameter equals length. The diameter of a circle is the distance between its two furthest points.

First, we need to find the radius of the cone:

[tex]radius = diameter/2 = 6.4/2 = 3.2 ft[/tex]

Now we can use the Pythagorean theorem to find the height of the cone:

[tex]height^2 = slant height^2 - radius^2[/tex]

[tex]height^2 = 5.8^2 - 3.2^2[/tex]

[tex]height^2 = 20.84[/tex]

height ≈ 4.56 ft

Next, we can find the surface area of the cone by adding the area of the base to the lateral surface area. The base is a circle with radius 3.2 ft, so its area is:

base area =[tex]\pi (radius)^2[/tex]

base area =[tex]\pi (3.2)^2[/tex]

base area ≈ 32.17 sq. ft.

The lateral surface area is the curved surface area of the cone, which can be found using the slant height and the radius:

lateral surface area = [tex]\pi (radius)(slant height)[/tex]

lateral surface area = [tex]\pi (3.2)(5.8)[/tex]

lateral surface area ≈ 58.92 sq. ft.

Therefore, the total surface area is:

total surface area ≈ base area + lateral surface area

total surface area ≈ [tex]32.17 + 58.92[/tex]

total surface area ≈ 91.09 sq. ft

Rounding this to the nearest whole number, we get a surface area of 91 sq. ft.

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Answer:

1 minute and 30 seconds.

Step-by-step explanation:

200 words in 1 minute

200/2=100

1minute/2=30 seconds

100+200=300 words

1 minute+ 30 seconds= 1 minute and 30 seconds.

The value of y is 10. we canget this answer by using  fact  ratios of the corresponding sides are equal. Using this fact, we can set up the proportion

what is corresponding sides?

In geometry, corresponding sides are sides in two or more figures that are in the same relative position or location. For example, if you have two triangles ABC and DEF, and AB is corresponding to DE, BC is corresponding to EF, and AC is corresponding to DF, then AB and DE are corresponding sides, BC and EF are corresponding sides, and AC and DF are corresponding sides.

In the given question,

To solve for y, we need to use the fact that line wt and line ye are parallel to each other. This means that the ratios of the corresponding sides are equal. Using this fact, we can set up the following proportion:

wt/ty = we/yc

Substituting the given values, we get:

(8 + x + 6)/16 = 10/y

Simplifying and solving for y, we get:

y = (160)/(14 + x)

Now we need to use the fact that the sum of the lengths of two sides of a triangle is always greater than the length of the third side. Using this fact for triangle ATY, we get:

AT + TY > AY

Substituting the given values, we get:

x + 6 + 16 > y

Simplifying and substituting y with its expression, we get:

x + 22 > (160)/(14 + x)

Multiplying both sides by (14 + x), we get:

x² + 22x + 14x + 352 > 160

Simplifying and rearranging, we get:

x² + 36x - 192 > 0

Now we can solve this quadratic inequality to get the range of possible values for x:

(x - 4)(x + 48) > 0

The solutions are x < -48 or x > 4. Since x represents a length, we can ignore the negative solution. Therefore, we have:

x > 4

Substituting this value into the expression we derived for y, we get:

y = (160)/(14 + x) = (160)/(14 + 4) = 10

Therefore, the value of y is 10.

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Step-by-step explanation:

When the diver hits the water at Height = 0 , the diver is no longer in the air .

0  -16t^2 + 10t + 26      Use Quadratic Formula  

                                       a = -16        b = 10        c= 26

   to find the positive value of t  = 1.625 s

The expression for the probability of getting at least one six in n throws of fair dice is 1 - (5/6)ⁿ.

The complement rule states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring.

In this problem, we use the complement rule to find the probability of getting at least one six in n throws of a fair dice by subtracting the probability of not getting any sixes in n throws from 1.

Here we have

A fair dice is thrown n times.

The probability of getting at least one six in n throws of a fair dice is equal to 1 minus the probability of not getting any sixes in n throws.

The probability of not getting a six on any one throw  = 5/6

[ Since there are 5 possible outcomes that are not six and 6 possible outcomes in total ]

Therefore,

The probability of not getting any sixes in n throws is (5/6)ⁿ.

So, the probability of getting at least one six in n throws is:

P(at least one six) = 1 - P(no sixes) = 1 - (5/6)ⁿ

Therefore,

The expression for the probability of getting at least one six in n throws of fair dice is 1 - (5/6)ⁿ.

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C. Angle bisector can be constructed by drawing an angle on tracing paper and then folding the paper so that the rays forming the angle lie upon each other. When you fold the paper, the crease that is formed will be the angle bisector of the original angle.

The half-life of Potassium-42 can be calculated using the following formula:

t1/2 = (ln 2) / λ

where t1/2 is the half-life, ln is the natural logarithm, and λ is the decay rate.

Substituting the values given, we get:

t1/2 = (ln 2) / 0.055

t1/2 ≈ 12.6 hours

Therefore, the original quantity of Potassium-42 will be halved in approximately 12.6 hours.

It will take approximately 13.51 hours for the original quantity of potassium 42 to be halved with a decay rate of 5.5% per hour.

To find the number of hours it takes for potassium 42 to be halved with a decay rate of 5.5% per hour, we can use the formula:

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A player would need to make a goal in approximately 18.85 minutes or faster to be sponsored by the puck company.

To determine how fast a player needs to make a goal to be sponsored by the puck company, we'll need to find the

time cutoff for the top 10% quickest goals.

Step 1: Determine the z-score for the 90th percentile (since we want the top 10%).

We can use a standard normal distribution table (or a calculator) to find that the z-score for the 90th percentile is

approximately 1.28.

Step 2: Use the z-score formula to find the time cutoff.

The formula is: Z = (X - μ) / σ

Where Z is the z-score, X is the time cutoff we're looking for, μ is the mean (12.56 minutes), and σ is the standard

deviation (4.91 minutes).

Step 3: Solve for X.

Rearrange the formula to solve for X: X = Z × σ + μ

Plug in the values: X = 1.28 × 4.91 + 12.56

X ≈ 6.29 + 12.56

X ≈ 18.85

So, a player would need to make a goal in approximately 18.85 minutes or faster to be sponsored by the puck company.

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Answer:

To multiply (3x - 4y) and (4x - 7y), we need to use the distributive property, which states that: a(b + c) = ab + ac Using this property, we can expand the given expression as: (3x - 4y)(4x - 7y) = 3x(4x) + 3x(-7y) - 4y(4x) - 4y(-7y) Simplifying each term, we get: = 12x^2 - 21xy - 16xy + 28y^2 = 12x^2 - 37xy + 28y^2 Therefore, the simplified answer is 12x^2 - 37xy + 28y^2.

Answer:

c ik this because I took the same question as you

The product of the given algebraic expression is [tex]\frac{4}{(x-1)}[/tex].

The given expression is [tex]\frac{8x+8}{x^2-2x+1} .\frac{x-1}{2x+2}[/tex].

Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.

Here, [tex]\frac{4(2x+2)}{x^2-1x-1x+1} \times \frac{x-1}{2x+2}[/tex]

= [tex]\frac{4(2x+2)}{x(x-1)-1(x-1)} \times \frac{x-1}{2x+2}[/tex]

= [tex]\frac{4(2x+2)}{(x-1)(x-1)} \times \frac{x-1}{2x+2}[/tex]

Cancel the same factors, that is

= [tex]\frac{4}{(x-1)} \times \frac{1}{1}[/tex]

= [tex]\frac{4}{(x-1)}[/tex]

Therefore, the product of the given algebraic expression is [tex]\frac{4}{(x-1)}[/tex].

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Answer: 1264.2857%

Step-by-step explanation:

Answer:

She earned 67.29% profit

Step-by-step explanation:

First let's find how much she spent on the coats.

50 x $28

$1400

So, her expense was $1400

Now, let's find how much she earned selling these coats.

We know she sold 38 of these coats at $49 each. Let's find how much she earned for these 38 coats.

38 x $49

$1862

She earned $1862 on these 38 coats.

Now, let's find how much she earned on the rest of the coats (50-38 which is 12). We know she sold the remaining for $40 each.

12 x $40

$480

She earned $480 on the rest of the coats.

The total she earned $2342

To find the profit:

Profit= $ Earned - Expenses

Profit= 2342-1400

Profit=$942

The question is asking for the percentage.

To find the percentage, we can use the percentage formula:

[tex]\frac{Profit}{Expense}[/tex] x 100

We know that the profit is $942 and the expense is $1400

(We want to find how much profit she made out of the expense)

[tex]\frac{942}{1400}[/tex] x [tex]\frac{100}{1}[/tex]

If you round your answer, you will get 67.29

Answer: She earned 67.29% profit

The percentage of measurements in a data set that are above and below each of the following percentiles are 68%, 95% and 99.7%.

We need to calculate the percentage of the measurements contained in each of the following intervals:

According to the empirical rule, approximately 68% of the measurements in a normally distributed data set will fall within one standard deviation of the mean. Therefore, approximately 68% of the measurements will fall within the interval (mean - s, mean + s).

Similarly, approximately 95% of the measurements in a normally distributed data set will fall within two standard deviations of the mean. Therefore, approximately 95% of the measurements will fall within the interval (mean - 2s, mean + 2s).

Likewise, approximately 99.7% of the measurements in a normally distributed data set will fall within three standard deviations of the mean. Therefore, approximately 99.7% of the measurements will fall within the interval (mean - 3s, mean + 3s).

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Answer:

where is the pic

Step-by-step explanation: