Evalúe the limit. Show steps

The approximate probability that a randomly selected 10-year-old child will be more than 51.75 inches tall is 0.6915.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. From the information, the heights of 10-year-old children have a normal probability distribution with a mean of 54.6 inches and standard deviation of 5.7 inches.

Based on this, the probability that a randomly selected 10-year old child will be more than 51.75 inches tall will be:

P(X > 51.75)

= P(Z > [(number - mean) / standard deviation)]

= P(Z > [(51.75 - 54.6) / 5.7)]

= P(Z > -0.5)

= 1 - P(Z = -0.5)

This will be looked at in the z table.

= 1 - 0.3805

= 0.6915

Therefore, the probability is 0.6915.

Learn more about probability on:

brainly.com/question/25870256

#SPJ1

We are given the following two numbers to compare

Let us simplify them

So, we can compare them as

The quantity on the left side is greater than the quantity on the right side.

To know how much each message sent costs, knowing that 75 messages cost $6.75, we only have to divide the cost of the total of 75 text messages by the total number of the cost of the message,

So that:

We say, that the cost of each text message is $0.09.

The slope of the line that passes through points (10,4) and (7, 3) is 1/3

Here we are dealing with a slope of a line where a slope of a line is the change in the y coordinate with regard to the change in the x coordinate. If P(x1,y1) and Q(x2,y2) are the two points on a straight line, at that point the slope formula is given by:

m = Change in y-coordinates/Change in x-coordinates

m = (y₂– y₁)/(x₂ – x₁)

Since we are given two points (10,4) and (7, 3),  where x₁ and x₂ are 10, 7 whereas y₁ and y₂ are 4, 3

From  the formula we get,

m = (y₂-y₁)/(x₂-x₁)

 = ( 3-4)/(7 - 10)

 = -1/-3

 =1/3

To know more about the slope of a line refer to the link https://brainly.com/question/14511992?referrer=searchResults.

#SPJ1

Answer: 100

Step-by-step explanation:

First, we need to know how many workers must be hired to pave one mile.
Which is 5 workers per 1 mile ( 150 / 30 )

Then you can either do
(5 + 5 +5 +5 + 5) + (5 + 5 +5 +5 + 5) + (5 + 5 +5 +5 + 5) + (5 + 5 +5 +5 + 5)
OR
5 x 20 = 100

( if I'm wrong it's like 3 am so I'm a bit slow but I hope I helped )

The diameter of the outer circle = 12.907 ft

The thickness of the circular pipe = 2.983 ft

The diameter of the inner circle = q = The diameter of the outer circle - The thickness of the circular pipe

⇒ The diameter of the inner circle = 12.907 - 2.983 ft

⇒ The diameter of the inner circle = q = 9.924 ft

To learn more about Circles, refer to:

https://brainly.com/question/11833983

#SPJ13

Answer:

6, because anything inside | | are positive so -3 will now be 3.

3 minus -3 = 6

Step-by-step explanation:

Hope it helps! =D

The probability of four coworkers  having different birth months is 0.572 or 55/96

Given there are four coworkers and the condition is they should have different birth months.

As we know probability is the ratio of favorable out comes to the total number of outputs

Favorable outcomes are

For first person 12 months

For second person 11 months

For third person 10 months

For Fourth person 9 months

Total outcomes

For each and every person total outcomes are 12 months which add up to 12 x 12 x 12 x 12 =  [tex]12^{4}[/tex]

Now probability will be

Probability = [tex]\frac{(12)(11)(10)(9)}{12^{4} }[/tex]

Probability = 55/96

Hence the probability of four coworkers having different birth months is 55/96

Learn more about Probability at

https://brainly.com/question/11234923?referrer=searchResults

#SPJ1

The parent functions are defined with all coefficients with value 1.

They can be linear, quadratic, cubic, absolute, reciprocal, exponential, logarithmic, square root, sine, cosine, tangent...

Then we can pick a function and transform it in order to include the point (-1,5) in the function definition.

We will use the quadratic parent function:

We will adjust the coefficient a of the quadratic function in order to include (-1,5)

Then, our transformed function is:

The largest five-digit multiple of 15 whose digits are all distinct and nonzero is 12345.

Suppose that the number is abcd.efg and belongs to the decimal numerical system. Remember one thing that the place on the left of decimal point is called ones. Move one-one places to right, and divide by 10 and 10 more and more. Move one-one places to left, and multiply (un-divide) by 10 and 10 more and more. We will call d as ones digit, c as tens digit (it get multiplied by 10), b as hundreds digit etc.

WE need to find the five-digit multiple of 15 whose digits are all distinct and nonzero.

Thus, we can see that the largest five-digit multiple of 15 could be ;

12345

Since it must be all distinct and nonzero. so the correct digit is 12345.

Hence, the largest five-digit multiple of 15 whose digits are all distinct and nonzero is 12345.

Learn more about place value here:

https://brainly.com/question/17983725

#SPJ1

The missing integer that makes the following addition statement true is -1.

The commutative law of addition is also known as the law of cumulative addition and it states that when two numbers are added together, then, the outcome is equal to the addition of their interchanged position because addition is considered as a binary operation.

Mathematically, the commutative law of addition can be represented using the following formula:

A + B = B + A.

An integer can be defined as a whole number that may either be positive, negative, or zero such as -1, 0, 1, 2, 3, etc.

Now, we would determine the missing number:

x + 3 = 2

x = 2 - 3

x = -1.

Read more on missing numbers here: https://brainly.com/question/603901

#SPJ1

Complete Question:

Find the missing integer that makes the following addition statement true.

+ 3 = 2

Answer:

[tex]x = - 8[/tex]

Step-by-step explanation:

[tex]8x = 4x - 32 \\ 8x - 4x = - 32 \\ 4x = - 32 \\ x = - 8[/tex]

The value of a that makes the solution of the equation is 1/2.

Given,

The equation: 3(2x - 4) = 4(ax - 2)

Solve,

3(2x - 4) = 4(ax - 2),

Open the bracket and multiply:

6x - 12 = 4ax - 8

Add 12 to both sides

6x -12 + 12 = 4ax + 12 - 8

We get,

6x = 4ax + 4

Add - 4ax to both sides:

6x - 4ax = 4ax - 4ax + 4

We get,

6x - 4ax = 4

Take x = 1

Then,

6 × 1 - 4a × 1 = 4

6 - 4a = 4

Now,

Add - 6 to both sides

6 - 6 - 4a = 4 - 6

We get,

-4a = -2

That is,

4a = 2

a = 2/4 = 1/2

That is,

The value of a that makes the solution of the equation is 1/2.

Learn more about solutions here:

https://brainly.com/question/25812462

#SPJ1

The distance from city C to city D is 5435 miles

The area of mathematics known as algebra aids in the representation of issues or circumstances into mathematical statements. To create a meaningful mathematical expression, it requires variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in all areas of mathematics, including coordinate geometry, calculus, and trigonometry. 2x + 4 = 8 is a basic algebraic expression.When operations like addition, subtraction, multiplication, division, etc. are performed on variables and constants, we obtain algebraic expressions as the mathematical statement.

The distance from city A to city B is 3001 miles Let distance from city A to city B x and distance from city C to city D y

The distance from city A to city B is 3001 miles

x= y - 3001....(i)

x+ y = 7869....(ii)

y- 3001 +y = 7869

2y = 10870

y=5435

The distance from city C to city D is 5435

To learn more about basic alegbra visit:

brainly.com/question/15167098

#SPJ9

The value of x that makes m parallel to n is 90 degrees.

The value of x that makes m and n parallel is 15.

How to find the angles in parallel lines?

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, vertically opposite angles etc.

The value of x that makes the line ma and n parallel can be calculated as follows:

180 - x  = x (alternate exterior angle)

180  = 2x

x = 180 / 2

x = 90 degrees

2.

3x - 15 + 150 = 180(supplementary angles)

3x = 180 - 150 + 15

3x = 45

x = 45 / 3

x = 15

learn more on  parallel lines and angles here: https://brainly.com/question/26121822

#SPJ1

Answer:  −8x − 12y − 18q − 42p

Step-by-step explanation:

i did the exam xD

Given

A right angle triangle is removed from the rectangle to create the shaded region.

That is,

To find: The area of the shaded region.

Explanation:

It is given that,

That implies,

The area of the shaded region is,

Hence, the area of the shaded region is 39ft^2.

After evaluating the limit we have came to find that the limit of  [tex]\lim_{x\rightarrow -\infty }\frac{x^2}{x^2\ +4}[/tex] as x approaches ∞- is 1

The value that a function, sequence, or index approaches as an input, or an index, approaches a particular value is known as a limit in mathematics. Limits, which are essential to calculus and mathematical analysis, are required by the definitions of continuity, derivatives, and integrals.

In addition to being closely related to the concepts of limit and direct limit in category theory, the idea of a limit of a sequence is further generalised to encompass the idea of a limit of a topological network.

A limit of a function is typically expressed in formulas as

[tex]{\displaystyle \lim _{x\to c}f(x)=L,}[/tex]

To find the limit we will use L'Hôpital's Rule

Find the derivative

⇒ [tex]\lim_{x\rightarrow -\infty }\frac{x^2}{x^2\ +4}[/tex]

⇒ [tex]\lim_{x\rightarrow -\infty }\frac{2x}{2x +0}[/tex]

⇒ [tex]\lim_{x\rightarrow -\infty }\frac{2x}{2x }[/tex]

Evalue -∞ as x

⇒ [tex]\frac{2(-\infty)}{2(-\infty)} }[/tex]

⇒ 1

Learn more about Limit

brainly.com/question/23935467
#SPJ10

length of a cylinder of volume 2 litres and radius 10 cm is 0.0064cm and  the radius of a cylinder of volume 45 cm³ and length 4 cm is 1.8928cm.

PART A

Volume of Cylinder = 2 Litres

Radius of cylinder = r = 10 cm

We need to find the length of a cylinder .

We know , Volume of Cylinder = π[tex]r^{2} h\\[/tex]

On substituting the values of Volume of Cylinder and r , we get

2 = π( [tex]10^{2}[/tex])h

h = 2 / 100π = 0.0064 cm

Here h = length of a cylinder

The length of a cylinder is  0.0064cm .

PART B

radius of a cylinder = r

volume of cylinder = 45 cm³

length of cylinder = h = 4 cm

Volume of Cylinder = π[tex]r^{2} h\\[/tex]

45 = 3.14 [tex]r^{2}[/tex] (4)

[tex]r^{2}[/tex] = 3.5828

r = 1.8928

Radius of a cylinder is 1.8928cm.

To know more about volume of cylinder refer to the link:

https://brainly.com/question/9554871

#SPJ9

Answer:

The answer to your question is: B

Explanation:
based on the statistics given, this answer best fits the Queston.

the shape of the curved surface is the sphere

So, as a part of the shape is flat

The block may represents a semi sphere

Answer:

Step-by-step explanation:

Answer:

x > 6 with an open point

Hope this helps!

Step-by-step explanation:

-2 ( x + 6 ) > -4x

-2x - 12 > -4x

-(-4x) - 2x > -(-12)

4x - 2x > 12

2x > 12

x > 6

Answer:

4y + 5 = 2

Step-by-step explanation:

4y + 5 = 2  Subtract 5 from both sides

4y = -3  Divide both sides by 4

y = [tex]\frac{-3}{4}[/tex]

Answer:

4y+5=2

Step-by-step explanation:

First, replace "a number" with "y"
The sentence becomes: "The sum of 4 times y and 5 is 2"
Replace "is" with the equals sign, "="
The sentence becomes: "The sum of 4 times y and 5 = 2"
Replace "times" with the multiply symbol, " * "
The sentence becomes: "The sum of 4 * y and 5 = 2"
Replace "the sum of ___ and ___" with " ___ + ___"

The sentence becomes: "4*y + 5 = 2".
the " * " isn't needed since 4y implies multiplication already, so you can optionally remove the *

To be able to get the expected value of Z, we will be using the following formula:

We get,

Therefore, the expected value of Z is -12.29.

Answer:

Step-by-step explanation:

Normally we use the symbols U for set union corresponding to or and ∩ for set intersection corresponding to and.

But here i will use and and or

By the rules of probability

P(A or  B) = P(A) + P(B) - P( A and  B)  
So P(A or b ) = 0.45 + 0.65 - 0.35 = 0.75

The complement of a set A is all the elements not in A
P(A') = 1 - P(A)

If we denote the complement of a set A as A' then your second expression is asking What is the complement of A or B or P(A or B)'
P(A and  B)' = 1 - P(A or B) = 1- 0.75 = 0.25

P(A|B)  = P(A and  B)/P(B) = 0.35/0.65 = 0.54

P(B|A) = P(A and B)/P(A) = 0.35/0.45 = 0.78

Based on the given parameters, the amount of the investment after 2 years is $3123

The given parameters about the compound interest are

Principal Amount, P = $3000

Interest Rate, R = 2%

Time, t = 2

Number of times, n = 4 i.e quarterly

Compound interests are different from simple interest, and they are calculated using the following compound interest formula

CI = P(1 + R/n)^nt - P

To calculate the amount, we have:

A = P + CI

So, the equation becomes

A = P + P(1 + R/n)^nt - P

Evaluate the like terms

A = P(1 + R/n)^nt

Substitute the known values in the above equation

A = 3000 * (1 + 2%/4)^(2 * 4)

Express 2% as decimal

A = 3000 * (1 + 0.02/4)^(2 * 4)

Evaluate the sum

A = 3000 * (1.005)^8

Evaluate the exponent

A = 3000 * 1.041

Evaluate the product

A = 3123

Hence, the value of the investment is $3123

Read more about compound interest at:

https://brainly.com/question/24924853

#SPJ1

Answer:

1.4 Relations and Functions

A relation is a correspondence between two sets. If x and y are two

elements in these sets and if a relation exists between x and y, then x

corresponds to y, or y depends on x.

DEFINITION OF A FUNCTION:

Let X and Y two nonempty sets. A function from X into Y is a relation that

associates with each element of X, exactly one element of Y.

However, an element of Y may have more than one elements of X

associated with it.

That is for each ordered pair (x,y), there is exactly one y value for each x,

but there may be multiple x values for each y. The variable x is called the

independent variable (also sometimes called the argument of the

function), and the variable y is called dependent variable (also

sometimes called the image of the function.) x = y2 is not a function from X into Y, because there

is not exactly one y value for each x.

Solving for y, you get y =

which means there are two possible values for y

Step-by-step explanation:

After substituting x = -1/2 in f(x), the value of the function f(-1/2) is found to be 5.333.

A function from a set X to a set Y assigns exactly one element of Y to each element of X.

The set X is known as the function's domain, and the set Y is known as the function's codomain.

The given function is f(x) = -2/3x +5.

To obtain f(-1/2), we must substitute the value of x with -(1/2).

f(x) = -2/3x +5

f(-1/2) = -2/3×(-1/2) + 5

f(-1/2) = (2/6) + 5

f(-1/2) = 0.333 + 5

∴ f(-1/2) = 5.3333

Therefore, the value of the function f(-1/2) obtained after substituting        x = -1/2 is 5.333.

Learn more about problems based on domain and codomain here:

https://brainly.com/question/2264373

#SPJ9