You have a list of 600 random, normally distributed numbers with a mean of 10 and a standard deviation of 2. Which of these statements is true?.

Answers

Answer 1

About 285 numbers lie between the values 10 and 14. (option C).

A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or a Gaussian distribution. In statistics and the natural and social sciences, normal distributions are crucial concepts.

There are 600 numbers and their mean is 10 where the standard deviation is 2.

47.5% of the numbers should fall between 10 and 14, as expected. In a normal distribution, 47.5% of the sample size will fall between the mean and two standard deviations on either side of it.

By doing calculation on option C, we got that = [tex]\frac{285}{600}*100=47.5[/tex]

Hence, option C is correct, i.e., about 285 numbers would lie between the values 10 and 14.

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Related Questions

make x the subject of the formula 13x=6y

Answers

The formula which represents the solution of the given equations; 13x = 6y for variable, x is; x = 6y / 13.

What is the solution of the given equation for x?

It follows from the task content that the solution of the given equation for variable, x is to be determined.

Since the given equation is; 13x = 6y.

It follows that the equation can be solved as follows;

13x = 6y

Divide both sides of the equation by 13 so that we have;

x = 6y / 13.

Ultimately, the formula for x is; x = 6y / 13.

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find the solution set x^2 -8x+ 7=0

Answers

Step-by-step explanation:

x²-8x+7=0

x²-7x-x+7=0

x(x-7) -1(x-7)=0

(x-7) (x-1)=0

Either, x-7=0 i.e x=7

or, x-1=0 i.e x=1

A family ha two car. During one particular week, the firt car conumed 30 gallon of ga and the econd conumed 40 gallon of ga. The two car drove a combined total of 1850 mile, and the um of their fuel efficiencie wa 55 mile per gallon. What were the fuel efficiencie of each of the car that week?

Answers

The fuel efficiency of the first car was 40.72 miles per gallon and the fuel efficiency of the second car was 14.28 miles per gallon.

The problem can be solved by using a system of equations.

We can call the fuel efficiency of the first car x and the fuel efficiency of the second car y.

From the problem, we know:

x + y = 55 (the combined fuel efficiency of the two cars is 55 miles per gallon)

We can also use the information about the amount of gas consumed and the distance has driven to set up another equation:

(30 gallons) * (x miles per gallon) + (40 gallons) * (y miles per gallon) = 1850 miles

Now we have a system of two equations with two variables (x and y):

x + y = 55

(30)x + (40)y = 1850

We can solve this system of equations using any method of solving such as substitution or elimination.

x = 55 - y

and substitute it in the second equation

(30)(55-y) + (40)y = 1850

1650 - 30y + 40y = 1850

-14y = -200

y = 14.28

x = 55 - 14.28 = 40.72

So the fuel efficiency of the first car was 40.72 miles per gallon and the fuel efficiency of the second car was 14.28 miles per gallon.

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ASAP!! Please help me answer all of these questions! No links or files please! I will report!



Thank you have a good day!

Answers

The questions 18, 19, and 20 have the values of x for the bisected angle to be 6, 15, and 8 respectively.

How to derive values of x for the bisected angles

If line UW bisects m∠TUV then;

m∠TUW = m∠WUV

13x - 5 = 7x + 31

13x - 7x = 31 + 5 {collect like terms}

6x = 36

x = 36/6 {divide through by 6}

x = 6

If line MO bisects m∠PMN then;

2(m∠OMN) = m∠PMN

2(2x + 7) = 74 {divide through by 2}

2x + 7 = 37

x = (37 - 7)/2 {make x the subject}

x = 15

If line EF bisects m∠CEB then;

m∠FEB = m∠CEF

10x - 3 = 7x + 21

10x - 7x = 21 + 3 {collect like terms}

3x = 24

x = 24/3 {divide through by 3}

x = 8

Therefore 6, 15, and 8 are the values of x for questions 18, 19, and 20 respectively for the bisected angles.

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Which value of x is the solution to this equation 5x^2 -3x+45

Answers

This means that the solution to the equation x is 6.

What is equation?

An equation is a mathematical statement that expresses the relationship between two values. It typically consists of an equal sign (=) and two expressions that are related to each other. Equations are used to describe how one value depends on another, or how two values are related to each other.

To solve this equation, use the Quadratic Formula,
which states that for an equation of the form ax2 + bx + c = 0,
the solution is x = [-b ± √(b2 - 4ac)] / 2a.
Plugging in the given equation,
we have a = 5, b = -3, and c = 45.
This means that the solution to the equation is x = [-(-3) ± √((-3)2 - 4*5*45)] / 2*5, or x = 6.

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What is a 1 in 3 angle?.

Answers

1 in 3 angle of slope in degree is 18.435°.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located.

The inverse tangent function is called arctangent, often known as arctan or tan-1. Tangent only has a limited domain for its inverse function.

So to find the 1 in 3 angle we have to put the value 1/3 in arctan function

∴ arctan (1/3) = 18.43494882° ≈ 18.435.

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Kim went to the store and bought 4 items: $32.45, $46.78, $12.91, and $52.38. How much did Kim spend if the sales tax is 8%?

Answers

To find out how much Kim spent in total with the 8% sales tax included, we first need to add up the cost of all 4 items: $32.45 + $46.78 + $12.91 + $52.38 = $144.52

Next, we'll multiply that total cost by the sales tax rate as a decimal (8% expressed as 0.08) to find out how much tax Kim had to pay: $144.52 x 0.08 = $11.56

Finally, we'll add the total cost of the items and the tax to find out how much Kim spent in total: $144.52 + $11.56 = $156.08

help pls mathematics ​

Answers

Therefore , the solution of the given problem of inequality comes out to be 13 and 17 is the number of hikers.

What does inequality really mean?

In mathematics, an inequality is a linear connection or a collection of numbers even when there is no equal sign. Equity always comes after equilibrium. When two numbers are not equal, inequality exists. Between equality and inequality, there exist differences. The most common symbol was chosen because when parameters aren't the same or comparable (). Values can be compared using a variety of disparities, no matter how few or numerous they are.

Here,

Given :

a) The minimum number of hikers

who walks between 8 miles and 19 miles :

=> 8 < x < 19

=> 7 +6

=> 13

b) The maximum number of hikers

who walks between 8 miles and 19 miles :

=> 8 < x < 19

=> 7+6+4

=> 17

Therefore , the solution of the given problem of inequality comes out to be 13 and 17 is the number of hikers.

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If Ellen is X years old.in thirteen years she will be twenty-four years old why’s the answer to that

Answers

Should be 11



24-13=11
answer: 11

step by step explanation:
the equation x+13=24 can represent this situation
subtract 13 on each side to get 11
hope this helps lab

Plssss help!!!! I need to finish this and it is really difficult:

Answers

The result of addition and subtraction is

5 (2/3) - 1 (1/4) = 58 (5/12) + 31 (1/6) = 393 (1/4) + 3 (3/5) = 79 (1/10) - 6 (7/10) = 27 (5/8) + 2 (1/7) = 1020 (9/11) - 18 (3/10) = 310 (3/7) + 22 (2/9) = 321 (5/6) + 5 (1/6) = 7113 (1/13) + 86 (9/11) = 20065 (17/20) + 19 (3/25) = 8571 (41/50) + 25 (5/24) = 9712 (13/15) + 18 (2/5) = 31

The directions to solve these problems are to round each fraction to the nearest whole number and then add or subtract. We have to round each fraction into the nearest whole number.

If the fraction is more than 1/2 we round it up to 1.If the fraction is less than 1/2 we round it down to 0.

1. 5 (2/3) - 1 (1/4) = (5 + 1) - 1 = 6 - 1 = 5

2/3  = 4/6
1/2 = 3/6
2/3 > 1/21/4  
1/2 = 2/4
1/4 < 1/2

2. 8 (5/12) + 31 (1/6) = 8 + 31 = 39

5/12
1/2 = 6/12
5/12 < 1/21/6
1/2 = 3/6
1/6 < 1/2

3. 3 (1/4) + 3 (3/5) = 3 + (3 + 1) = 3 + 4 = 7

1/4
1/2 = 2/4
1/4 < 1/23/5 = 6/10
1/2 = 5/10
3/5 > 1/2

4. 9 (1/10) - 6 (7/10) = 9 - (6 + 1) = 9 - 7 = 2

1/10
1/2 = 5/10
1/10 < 1/27/10
1/2 = 5/10
7/10 > 1/2

5. 7 (5/8) + 2 (1/7) = (7 + 1) + 2 = 8 + 2 = 10

5/8
1/2 = 4/8
5/8 > 1/21/7 = 2/14
1/2 = 7/14
1/7 < 1/2

6. 20 (9/11) - 18 (3/10) = (20 + 1) - 18 = 21 - 18 = 3

9/11 = 18/22
1/2 = 11/22
9/11 > 1/23/10
1/2 = 5/10
3/10 < 1/2

7. 10 (3/7) + 22 (2/9) = 10 + 22 = 32

3/7 = 6/14
1/2 = 7/14
3/7 < 1/22/9 = 4/18
1/2 = 9/18
2/9 < 1/2

8. 1 (5/6) + 5 (1/6) = (1 + 1) + 5 = 2 + 5 = 7

5/6
1/2 = 3/6
5/6 > 1/21/6
1/2 = 3/6
1/6 < 1/2

9. 113 (1/13) + 86 (9/11) = 113 + (86 + 1) = 113 + 87 = 200

1/13 = 2/26
1/2 = 13/26
1/13 < 1/29/11 = 18/22
1/2 = 11/22
9/11 > 1/2

10. 65 (17/20) + 19 (3/25) = (65 + 1) + 19 = 66 + 19 = 85

17/20
1/2 = 10/20
17/20 > 1/23/25 = 6/50
1/2 = 25/50
3/25 < 1/2

11. 71 (41/50) + 25 (5/24) = (71 + 1) + 25 = 72 + 25 = 97

41/50
1/2 = 25/50
41/50 > 1/25/24
1/2 = 12/24
5/24 < 1/2

12. 12 (13/15) + 18 (2/5) = (12 + 1) + 18 = 13 + 18 = 31

13/15 = 26/30
1/2 = 15/30
13/15 > 1/22/5 = 4/10
1/2 = 5/10
2/5 < 1/2

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What is the value of x in the triangle?

Answers

Subtract the sum of the two angles from 180 degrees. The sum of all the angles of a triangle always equals 180 degrees. Write down the difference you found when subtracting the sum of the two angles from 180 degrees. This is the value of X

n + 3 = -6
pls solve for n :)

Answers

N + 3 = -6
-3 -3
N= -9
n + 3 = -6
Step 1: get n alone by itself on one side, so subtract 3 to both sides to remove the 3 next to n.
n = -9
That’s your answer

If
CE
and
FH
are parallel lines and mCDB= 65°, what is mEDB?

Answers

Answer:

65° or 115°

Step-by-step explanation:

there is no picture but if

mEDB looks like mCDB then its 65°

but if they dont look alike then

180-65=115

straight line is 180°

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What are the two types of indirect proof in geometry?.

Answers

There are two methods of indirect proof:

Proof of the contrapositive and proof by contradiction.

Now, According to the question:

Let's know:

An indirect proof, also called a proof by contradiction, is a roundabout way of proving that a theory is true. When we use the indirect proof method, we assume the opposite of our theory to be true. In other words, we assume our theory is false.

Hence, There are two methods of indirect proof:

Proof of the contrapositive and proof by contradiction.

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What is the product of 7x 6 2?.

Answers

The product of (7x - 6)² is  49x² - 84x + 36.

Equation is (7x - 6)²,

⇒ We will solve the given problem using the algebraic identity

(a - b)² = a² + b² - 2ab

Here a = 7x and b = 6

⇒ (7x - 6)² = (7x)² + 6² - 2(7x)(6)

⇒ (7x - 6)² = 49x² + 36 - 84x

⇒ 49x² - 84x + 36

The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x+3=8 only has one variable.

A product is the outcome of multiplication in mathematics, or an expression that specifies the factors (numbers or variables) to be multiplied.

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For each graph, determine the y-intercept using the slope formula. Write the y-intercept in coordinate form.

Answers

y = 8/3x + 100 exists the equation of the line in slope-intercept form.

What is meant by Slope of Line?

The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line.

A line's slope and y intercept are represented in the slope intercept form as y = mx + b.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) contains

m = y₂-y₁/x₂-x₁

At two of the points the line passes through in the accompanying graph.

Let the two points be (0, 100) and (42, 148)

Let the equation be m = y₂-y₁/x₂-x₁

substitute the values in the above equation, we get

Slope = 148-100/42

= 48/42 = 8/3

To find y intercept, we get

100 = 8/3(0) + b

b = 100

So slope intercept form exists y = 8/3x + 100

Therefore, y = 8/3x + 100 exists the equation of the line in slope-intercept form.

The complete question is:

Examine the linear graph. Determine the y-intercept and write the y-intercept in coordinate form. Then write the equation of the line in slope-intercept form.

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How to determine if a differential equation is linear?

Answers

It is linear if and only if the coefficients of y (the dependent variable) and all order derivatives of y are functions of t or constant terms.

What is equation?

An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the relationship between two expressions on opposite sides of the sign. It mostly consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.

Here,

It is linear if and only if all order derivatives of y (the dependent variable) are functions of t or constant terms.

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4 A popular board game includes a five-section
spinner to determine the number of spaces a
player moves during a turn. The results of
10 spins are shown.
Spin
Spaces
Moved
1 2 3
F 0.1
G 0.6
5 4
4 5 6 7 8 9 10
2 5 1 3 5 4 5 2
What is the experimental probability a player
will move 2 spaces and 5 spaces during a
game?
H 0.08
J Not here

Answers

In an experiment, there is a H 0.08 probability that a player will move both two and five spaces during a game.

What is the simple definition of probability?

Player movement during a turn is determined by a spinner. It displays the outcomes of 10 spins.The likelihood or chance that a specific event will occur is represented by a probability. Both proportions between 0 and 1 and percentages between 0% and 100% can be used to describe probabilities. chances in multiples.

A (1): the probability that a particular occurrence will take place. (2): the proportion of the number of outcomes in a comprehensive set of equally likely options that result in a specific event to the total number of conceivable outcomes. How likely something is to occur is known as its probability. when we are unsure of how an event will turn out.

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what is the following product? Assume x>0 3root x^2 times 4 root x ^3

Answers

The product is 3x * 4x^(3/2) = 12x^(5/2)

How to do the product of root?

When multiplying two terms with the same base and different exponents, you can add their exponents.

For example, √(a^m) * √(a^n) = √(a^m * a^n) = √(a^(m+n)) = a^((m+n)/2)

The product of 3√(x^2) * 4√(x^3) is equal to:

12x^(5/2)

This is because when you multiply two terms with the same base, you can add their exponents:

3√(x^2) * 4√(x^3) = (3*4)√(x^(2+3/2)) = 12x^(5/2)

This is because

√(x^2) = x^(2/2) = x

√(x^3) = x^(3/2) = x^(3/2)

so we can write 3root x^2 = 3x and 4root x^3 = 4x^(3/2)

Hence, the product is 3x * 4x^(3/2) = 12x^(5/2)

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How do you change improper fractions to mixed numbers for kids?.

Answers

The way to change improper fractions to mixed numbers for kids is solved by using the division operation.

In math the term called fraction is defined as a part of a whole number, and a way to split up a number into equal parts

Here we need to identify the way to change improper fractions to mixed numbers for kids.

As from the definition of fraction we have identified that the way to solve the improper fraction into mixed fraction is written as follows:

Here we have to convert an improper fraction to a mixed number,

Then we have to work out how many whole numbers there are by dividing the numerator by the denominator.

And then we have to make the remainder the new numerator and leave the denominator as it was.

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Solve this equation for the given domain.
cos(2x + 45°) = 0.8 for 0° ≤ x ≤ 180°

Answers

The solution to the equation cos(2x + 45°) = 0.8 in the domain of 0° to 180° is x = 15° and X=139° or X=176 °

How to find the solution?

Because Cos (±37° +360k) = 0.8

0≤2X ≤ 360°

0+45°=2x+45° 360°+45° 45°≤ 2x+45°< 405°

50 2x+45° = 360°-37° or 2x+45° = 360° + 37°

{list the equation} 397° -45°=2X = 323-45°

2X = 323-45°. 2x=397° -45°

2x= 278°.         2x= 352°

X = 139°.          X=176°

So , x = 139° or x = 176°

To discover the solution set of an equation with a particular domain, first insert each domain value into the equation to obtain the associated range values. Make ordered pairs out of these values and put them down as a set. That set is your solution!

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what is the highest fraction that is reduced to 1/2
I WILL MARK U BRAINLIST

Answers

Answer:

I think its two

Step-by-step explanation:

If I am wrong sorry

Is 999 a cube number?.

Answers

=> 999 is not a perfect cube.

Because cube root of 999 is 3 [tex]\sqrt[3]{37}[/tex] .

Now, According to the question:

A cube number is the result when a number has been multiplied by itself twice. The symbol for cubed is 3. For example, 8 is a cube number because it's 2 x 2 x 2 (2 multiplied by itself twice); this is also written as [tex]2^3[/tex] (“two cubed”).

It is the real solution of the equation [tex]x^3[/tex] = 999.

The cube root of 999 is expressed as [tex]\sqrt[3]{999}[/tex] or 3 [tex]\sqrt[3]{37}[/tex] in the radical form and as[tex](999)^\frac{1}{3}[/tex] or [tex](999)^0^.^3^3[/tex] in the exponent form.

The prime factorization of 999 is 3 × 3 × 3 × 37, hence, the cube root of 999 in its lowest radical form is expressed as 3 [tex]\sqrt[3]{37}[/tex].

Cube root of 999: 9.996665555Cube root of 999 in Exponential Form: [tex](999)^\frac{1}{3}[/tex]Cube root of 999 in Radical Form:  [tex]\sqrt[3]{999}[/tex] or 3 [tex]\sqrt[3]{37}[/tex] .

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Uie buy 3 piece of pizza and 2 cookie for a total of 6. 50. The next day he buy 1 piece of pizza and 1 cookie for 2. 50. How much doe a cookie cot

Answers

The cost of one cookie is 1. This value can be determine from the eliminate methods or substitution methods.

How to determine the cookie cost?

As per data given is a two different formula of pizza and cookie, we can determine it by elimination methods or substitution methods. Let do it by elimination methods. As per formula given are first buy 3 pizza + 2 cookie =  6.50 and the second buy 1 pizza + 1 cookie = 2.50. The calculation will be:

3 pizza + 2 cookie =  6.50

1 pizza + 1 cookie = 2.50     multiply with 3 because we want eliminate pizza

3 pizza + 2 cookie =  6.50

3 pizza + 3 cookie = 7.50       -

0 pizza - 1 cookie = - 1

1 cookie = 1

Hence the price of one cookie will cost you 1.

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What is the slope of 3x 4y =- 12?.

Answers

The slope of the equation 3x + 4y = -12 is -3/4

Slope in math is defined as the ratio of the amount that y increases as x increases some amount

Here we have given the equation 3x + 4y = -12.

As we all know that the general form of the equation of the line is written as,

y = mx + c

here m refers the slope of the line and c refers the y intercept of the line.

Now, we have to convert the given equation into the general form then it can be look like the following,

=> 4y = -12 - 3x

=> y = -12/4 - 3x/4

It can be rewritten as,

=> y = -3x/4 - 12/4

Then the resulting slope is -3/4.

Complete Question:

What is the slope of the equation 3x + 4y = -12?

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How do you find the opposite side of a triangle?.

Answers

Multiply the hypotenuse of triangle by sinθ to determine the length of the side opposite the angle (θ). Alternatively, to obtain the side next to the angle, multiply the hypotenuse by cos(θ).

Scalene triangles are typically described as triangles with no two sides that are equal. Isosceles triangles are those triangles whose two sides are equal. An equilateral triangle is one with equal lengths on each of its three sides. Clearly, all equilateral triangles are isosceles, but not the opposite.

The side across from the right angle is always the hypotenuse of a right triangle. The opposite and neighboring sides are the other two sides.  

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Dennis and Gail Schultz are looking over the repayment schedule for their $5,500 loan for lake house remodeling at 15% interest for 42 months with a monthly payment of $168.85. They note that the balance after payment 18 is $3,493.39, after 24 is $2,718.43, and after 30 is $1,883.50. How much would they save by paying off the loan earlv at payment (a) 19, (b) 25, or (c) 31?

Answers

Answer:

c)31

Step-by-step explanation:

The goal of this exercise is to determine the total savings by paying the debt early at

)

a)

19

19th payments

)

b)

25

25th payments and

)

c)

31

31st payments.

Two hiker walk on a trail in the direction of increaing mile marker number. Mandy tart at mile marker 1 and hike at a rate of 2. 5 mile per hour. At the ame time, Rita tart at mile marker2 and hike at a rate of 3 mile per hour. The equation 2. 5h1= 3h 2 repreent the number of hour h it will take Mandy to catch up with Rita

Answers

Mandy will catch up Rita at 0.5 hour after they start walking.

When will Mandy catch up Rita?

As per data given are Mandy start = 1, Rita start = 2, Mandy speed = 5 and Rita speed = 2. Based on this explanation we can determine the formula for Mandy time to catch up Rita as follow

s1 = s2

Rita start + Rita speed x t = Mandy start + Mandy speed x t

2 +3 x t = 1 + 5 x t

2 + 3t = 1 + 5t

2 - 1 = 5t - 3t

1 =  2t

t = 0.5 h

Hence, Mandi will catch up with Rita at 0.5h after start.

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y= x^2-4
find the zeros.

Answers

The zeros of the given function y = x²-4 are 2 and -2.

What is zero of a function?

The zeros of a function are defined as the values of the variable of the function such that the function equals 0.

Given is a function, y = x²-4

To find the zeros, equate the function to 0,

x²-4 = 0

x² = 4

x = ±2

Hence, the zeros of the function are 2 and -2.

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How do you find the nth sum?.

Answers

The nth partial sum of a geometric sequence can be calculated using the first term a1 and common ratio r as follows: Sn=a1(1−rn)1−r. The infinite sum of a geometric sequence can be calculated if the common ratio is a fraction between −1 and 1 (that is |r|<1) as follows: S∞=a11−r.

In arithmetic, a chain is an enumerated series of gadgets in which repetitions are allowed and order matters. Like a hard and fast, it consists of contributors (additionally referred to as elements, or terms). The quantity of elements (possibly endless) is called the duration of the series.

Unlike a fixed, the same factors can appear a couple of times at distinct positions in a chain, and unlike a fixed, the order does be counted. formally, a chain can be described as a function from herbal numbers (the positions of elements inside the collection) to the factors at each position. The belief of a sequence may be generalized to a listed family, defined as a character from an arbitrary index set.

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