Scores on an exam follow an approximately normal distribution with a mean of 76. 4 and a standard deviation of 6. 1 points. What is the minimum score you would need to be in the top 2%?.

The value of the expression after rationalizing [tex]\frac{3+\sqrt{18} }{1+\sqrt{8} }[/tex] the denominator is [tex]\frac{3\sqrt{2}+9 }{7}[/tex].

A finite collection of symbols that is well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.

Rationalizing the denominator is the process of shifting a root, such as a square root or a cube root, from the fraction's denominator to its numerator (numerator).

The numerator is the part of a fraction that comes before the vinculum.

The denominator of a fraction is the phrase that comes before the vinculum.

Consider the expression,

[tex]\frac{3+\sqrt{18} }{1+\sqrt{8} }[/tex]

Now, let [tex]y=\frac{3+\sqrt{18} }{1+\sqrt{8} }[/tex]

To rationalize the denominator we multiply and divide the expression by the conjugate 1 - √8.

[tex]y=\frac{3+\sqrt{18} }{1+\sqrt{8} } \times \frac{1-\sqrt{8} }{1-\sqrt{8} }[/tex]

[tex]y=\frac{(3+\sqrt{18})(1-\sqrt{8}) }{(1+\sqrt{8})(1-\sqrt{8}) }[/tex]

[tex]y=\frac{3-3\sqrt{8} +\sqrt{18}-(\sqrt{18} )(\sqrt{8} ) }{1-8}[/tex]

[tex]y=\frac{3-6\sqrt{2}+3\sqrt{2}-(3\sqrt{2})(2\sqrt{2}) }{-7}[/tex]

[tex]y=\frac{3-3\sqrt{2}-12 }{-7}[/tex]

[tex]y=\frac{-3\sqrt{2}-9 }{-7}[/tex]

[tex]y=\frac{3\sqrt{2} +9}{7}[/tex]

The value of the expression when rationalized [tex]\frac{3+\sqrt{18} }{1+\sqrt{8} }[/tex] is [tex]\frac{3\sqrt{2}+9 }{7}[/tex].

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Answer:

2.043

Step-by-step explanation:

A real world situation that can be modeled by the equation. 19.25x =17.25x +26.77 is that a company charges 19.25 per hour and another company charges 17.25 per hour plus a one time fee of 26.77. What number of hours they have the same price?

It should be noted that an equation is used to show the relationship between the variables that are illustrated.

In this case, a real world situation that can be modeled by the equation. 19.25x =17.25x +26.77 is that a company charges 19.25 per hour and another company charges 17.25 per hour plus a one time fee of 26.77. What number of hours they have the same price?

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1) the mathematical model for given situation is f(t) = 2t + t, where t is the time in minutes

2) the amount of water in the pool after 50 minutes = 105 gallons

3) and the amount of time required to fill the pool =  12 hours 46 minutes

In this question,

a small pool hold 1500 gallons of water.

When there's is 5 gallons of water in the pool, the person decided

that not to stand outside and watch the pool fill.

This means, from the time he had decided, the amount of water in the pool = 5 gallons.

the water was filling the pool at a rate of 2.

Let t be the time in minutes.

So, the amount of water in the pool after 't' minutes would be,

f(t) = 2t + 5

We get an mathematical model for given situation,

f(t) = 2t + 5, where t is the time in minutes

We need to find the amount of water in the pool after 50 minutes

For t = 50 minutes

f(50) = 2(50) + 5

f(50) = 100 + 5

f(50) = 105 gallons

Also, we need to find the amount of time required to fill the pool.

1500 = 2t + 5

1495 = 2t

t = 747.5 minutes

t = 12 hours 46 minutes

Therefore, 1) the mathematical model for given situation is f(t) = 2t + t, where t is the time in minutes

2) the amount of water in the pool after 50 minutes = 105 gallons

3) and the amount of time required to fill the pool =  12 hours 46 minutes

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The value of 6300 kg in grams written in standard form will be 6.3 × 10^6.

It should be noted that the value of 6300 kg in grams will be:

1000 grams = 1 kilogram

= 6300 × 1000

= 6300000

= 6.3 × 10^6

Therefore, the value of 6300 kg in grams written in standard form will be 6.3 × 10^6.

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Answer: 1

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the number =x

So, x*12*2=144

=12x=144/2

=12x=72

=x=72/12

=x=6

So the answer is 6 because 6*12=72 and doubling 72 gives us 144.

Have a great day!!!

The inverse function returns the original value for which the output of a function was given.

The inverse of this function is [tex]f^{-1[/tex](x) = -(x - 4/3)

The inverse function returns the original value for which the output of a function was given. When it comes to functions, f and g are inverse, with f(g(x)) = g(f(x)) = x. A function that is made up of its inverse returns the original value.

A function's inverse is not always a function! To ensure that the inverse function is also a function, the original function must be a one-to-one function. A one-to-one function is one in which each second element corresponds to exactly one first element. (Each x and y value is only used once).

The inverse of a function is thought to be a reflection of the original function along the line y = x. Simply put; the inverse function is obtained by swapping the original function's (x, y) values.

Let the function be y = 4 - 3x

f(x) = 4 - 3x

y = 4 - 3x

simplifying the value of x, we get

x = 4 - 3y

x - 4 = -3y

x - 4/-3 = y

[tex]f^{-1[/tex]= - (x - 4/3)

The inverse of this function is [tex]f^{-1[/tex](x) = -(x - 4/3).

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The answer is g= -3x+6

The g function can be obtained from the graph using two points, the first (0,6) and the second (2,0).

Remember, a line has the following equation:

y=mx=b, where 'm' is the slope and 'b' the interception with 'y' axis

b=6, since x=0 and y=6.

Now to find the slope, lets use the following equation:

With the previously obtained point.

We have m=-3

Hence our function g has the following

g= -3x+6

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Answer:look below

Step-by-step explaination

22X8=?

The solution for equation ln (3 x+5)²=4 is 0.796.

ln (3 x+5)²=4

2 ln (3x + 5)= 4

3x + 5 = [tex]e^{2}[/tex]

3x = 7.389-5

x = 0.796

A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign.

Two expressions joined by the equals symbol ("=") form an equation. The "left hand side" and "right hand side" of the equation are the expressions on either side of the equals sign. The right side of an equation is frequently considered to be zero.

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Answer:

44

Step-by-step explanation:

6(8)-4

48-4

44

Answer:The answer is 44

Step-by-step explanation:6 times 8 would be 48.48-4 is 44.

An absolute value equation that has the given solution is  mathematically given as

I3 + xI - 7 = 0 where the solutions (or roots) are in X= 4 and X= -10

This is further explained below.

Generally, in this case, we want an absolute value equation that has the solutions x = 4 and x= -10.

A cheap way to do this is to look for a number N that:

N + 4 = -(N - 10)

then, isolating N we get:

2N = 6 + 10 = 6

N = 6/2 = 3

then

=N +4  

= 3 + 4

= -8

and

=N - 10

= 3 - 10

= -7

In conclusion,  we know that I-7I = I7I = 7

now we can write our equation as:

I3 + xI - 7 = 0

where the solutions (or roots) are in X= 4 and X= -10

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Answer:

mean is the sum of all the values divided by the total values.

Step-by-step explanation:

so total values are 6, and the sum of all the values is: 1+29+27+28+30+27

                                                                                         = 142

so now the mean is 142÷6=   23.67

Answer:

y=6x-3

Step-by-step explanation:

6 is the slope bur (0,-3) is the y-intercept. Therefore, you just need to plug in the y-intercept and slope into y=mx+b which will give you y=6x-3.

Answer:

The solution to this equation is (9t)^(12) / (4a)^(6).

Step-by-step explanation:

It is given that [(4a³t²)/(9at^6)]^-3 which is to be simplified and solved to get the final answer.

Now,

let us have a look at the equation and observe the powers given;

=> [(4a³t²)/(9at^6)]^-3

So, let us convert the powers using the rules;

=> [(4a²)/(9t^4)]^-3

Further, we will apply the rule known as product of powers and we get an equation that is;

=> (4a)^(-6) / (9t)^(-12)

Now, after reciprocating both the powers as per the rules we get;

=> (9t)^(12) / (4a)^(6)

Therefore, the solution to this equation is (9t)^(12) / (4a)^(6).

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The value of x for the equation 2 x=1/2 is 0.25

A linear equation with one variable is one that has just one variable. It has the formula Ax + B = 0, with A and B being any two real integers and x being an ambiguous variable with just one possible value. One such linear equation in one variable is 9x + 78 = 18.

One method for expressing a linear equation is in the slope-intercept form (the equation of a line). Y = mx+b, where m is the slope and b is the y-intercept, is the formula for the slope-intercept form (the point where the line crosses the y-axis). Using y=mx+b to graph a line is often simple.

Given,

2x = 1/2

x= 1/4

x = 0.25

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Classification of each of the listed as rational or irrational are done below

What is a rational numbers?

This is a term used in mathematics to refer to some set of numbers that are fractions where the numerator and the denominator are non zero digits. Rational numbers can be expressed as fractions.

Irrational numbers refers to numbers that cannot form a fraction

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The given equation in logarithmic form is 7^5 =16807

As given to us, the function is log₇16807=5

Let us write this function in exponential form using the definition of logarithm

logₐx=b

a^b=x

here the logarithm is log₇16807=5

thus 7^5=16807

hence the given equation in logarithmic form is 7^5 =16807

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The equation to find the nth term of the sequence is aₙ = 4n - 17

The equation of the sequence can be represented as follows;

a₃ = - 5, a₄ = - 1, a₅ = 3, a₆ = 7, a₇ = 11

Therefore, let's find the equation of the nth term.

Using arithmetic formula,

aₙ = a + (n - 1)d

where

Therefore,

d = 11 - 7 = 4

Hence, let's find the first term using 7th term

11 = a + 6(d)

11 = a + 6(4)

11 - 24 = a

a = - 13

Therefore, the equation to find the nth term of the sequence is as follows:

aₙ = -13 + (n - 1)4

aₙ = - 13 + 4n - 4

aₙ = - 13 - 4 + 4n

aₙ = 4n - 17

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The simplest form of the expression is 81 x⁴y⁸

We have given an expression (√9 x y²)⁴ .

On simplifying , we get

(√9 x y²)⁴ = (3 x  y²)⁴

                 = 3⁴x⁴y⁸              

                 = 81 x⁴y⁸

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Answer:

x = 15 , ∠ B = 108°

Step-by-step explanation:

∠ A and ∠ Bare alternate exterior angles and are congruent

∠ A = ∠ B , that is

6x + 18 = x + 93 ( subtract x from both sides )

5x + 18 = 93 ( subtract 18 from both sides )

5x = 75 ( divide both sides by 5 )

x = 15

Then

∠ B = x + 93 = 15 + 93 = 108°

Answer:7 and a half

Step-by-step explanation:

Simple enough, if it seven inches and grows half an inch a week than after a week it grows half an inch, so its just 7 + a half, your awnser is 7 and a half

The completely factorised form of the expression given in the task content as given is; (3x +6) (x+b).

In order words, when the above given polynomial expression is being factorized, it gives (3x +6) (x+b) as its complete factorized form.

It follows from the task content that the expression which is required to be factorized completely is given below as;

3x² + 3bx + 6a + 6b

So therefore, the mathematics expression can be factored completely as follows step by step:

(3x² + 3bx) + (6x + 6b)

3x(x + b) + 6(x+b)

Ultimately, the completely factorized form of the mathematical expression as indicated in the given expression above is therefore represented as thus;

(3x +6) (x+b)

Therefore, The completely factorised form of the expression given in the task content as given is; (3x +6) (x+b).

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Answer:

3(x – 2)(x + b)

Step-by-step explanation:

I got it right on the test.

Answer:since the bottom is 10cm and both tops are the same length that means its 5cm

Step-by-step explanation:YOU can divide 10 by 2

Answer:

12%

Step-by-step explanation:

Odds in favor means number of favorable outcomes : number of unfavorable outcomes

Here favorable outcome is selecting a left-handed person

So odds of 3:22 means that the ratio of selecting  left-handed person to right-handed person is [tex]\frac{3}{22}[/tex]

P(left) = [tex]\frac{3}{3+22} = \frac{3}{25}[/tex]

P(left) as percent = [tex]\frac{3}{25}\cdot100[/tex] = 12%