Please help!!! Rationalize the denominator and simplify the following expression:

The largest sum of three numbers that meet at a corner is 15

The number cube that completes the question is added as an attachment

The largest number in the number cube is 6.

On the number cube, the next largest numbers share the same corner with the number 6

So, the largest set of numbers on the cube are 6, 5, 4

Add the numbers:

Sum = 6 + 5 + 4

Evaluate

Sum = 15

Hence, the largest sum of three numbers that meet at a corner is 15

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To solve this exercise, we apply the rule of three:

Oranges......................Price

 8.................................$4.40

 9.......................................x

We solve as follows:

[tex]\boldsymbol{\sf{x=\dfrac{9\times4.40}{8}=\dfrac{39.6 }{8}=4.9 }}[/tex]

Therefore, 9 oranges would cost $4.9.

The required cost of the amount of 4.95 dollars would be for 9 oranges.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

We have been given that a grocery store sells a bag of 8 oranges for $4.40.

We have to determine the cost for 9 oranges.

Let's assume x dollars would it cost for 9 oranges.

As per the given condition, we can write the ratio as:

8 oranges : $4.40 = 9 oranges : x dollars

⇒ 8 / 4.40 = 9 / x

Cross multiplication and rearrange the terms of the above equation,

⇒ 8x = 4.40×9

Divide by 8 into both sides of the equation,

⇒ x = (4.40×9)/8

⇒ x = (39.6)/8

⇒ x = 4.95

Therefore, the cost of the amount of 4.95 dollars would for 9 oranges.

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There are 19958400 ways if 9 people are selected for positions and if Amy does not want to play then the number of ways will be 1814400 if done through permutations.

Given there are 11 people and nine positions.

We have to find the number of ways in which arrangement can be done if there are 11 people and 9 positions and the number of ways to arrange if Amy doe not want to play assuming the pitcher has already been chosen.

Permutations helps us to know the number of ways an object can be arranged. It is denoted by n[tex]P_{r}[/tex]=n!/(n-r)!

where n is the number of choices available,

r is the choices.

Given that the team has 11 players while there are only 9 positions available, the number of ways is 11[tex]P_{9}[/tex]=11!/(11-9)!

=11!/2!

=19958400

Now Amy does not want to play, therefore the number of ways the remaining people can be arranged in the place of pitcher is 10. Also the positions has also decreased from 9 to 8.

Thus the number of ways in which remaining people can be arranged are: 10[tex]P_{8}[/tex]=10!/(10-8)!

=10!/2!

=1814400

Hence the number of ways in which 11 people are arranged is 19958400 and the number of ways in which the remaining players are arranged is 1814400.

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Answer:

19,958,400

10

8

1,814,400

Step-by-step explanation:

Hope this helps

The solid 3D object that is produced by rotating the triangle about line m is a cone.

It should be noted that a triangle simply means a shape that has three sides and three angles.

In this case, the solid 3D object that is produced by rotating the triangle about line m is a cone.

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The required domain of the inverse function is x ≤ 0. Hence option D is correct.

f(x) = -x^2

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is independent variable while Y is dependent variable.

Inverse of function f(x) = -x^2
y = -x^2
x = √-y
Now,
Inverse function of f(x) is √-x
Its domain is define as less than or equal to zero.

Thus, the required domain of the inverse function is x ≤ 0.

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In accordance with the compound interest model, the future value if you invest $ 1200 at 5.25 % compounded quarterly for two years is $ 1807.

The compound interest model is based on the assumption that the initial capital obtain gains continuously in time. This model is represented by the following expression:

C' = C · (1 + r/100)ˣ     (1)

Where:

Please notice that a year consists in four quarters. If we know that C = 1200, r = 5.25 and x = 8, then the current capital is:

C' = 1200 · (1 + 5.25/100)⁸

C' = 1807

In accordance with the compound interest model, the future value if you invest $ 1200 at 5.25 % compounded quarterly for two years is $ 1807.

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Answer: 9

Step-by-step explanation:

    We will use the Order of Operations to solve.

 Given:

4 – 15 ÷ (30 – 33)

 Subtract 33 from 30:

4 – 15 ÷ (– 3)

 Divide -15 by -3:

4 + 5

 Add 4 to 5:

9

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{In order for you to solve for this}\\\huge\textbf{equation, you have to do PEMDAS.}\\\\\\\\\huge\textbf{PEMDAS simply means: }[/tex]

[tex]\bullet\large\textbf{ Parentheses}[/tex]

[tex]\bullet\large\textbf{ Exponents}[/tex]

[tex]\bullet\large\textbf{ Multiplication}[/tex]

[tex]\bullet\large\textbf{ Division}[/tex]

[tex]\bullet\large\textbf{ Addition}[/tex]

[tex]\bullet\large\textbf{ Subtraction}[/tex]

[tex]\huge\textbf{Now, let's answer the given equation.}[/tex]

[tex]\mathbf{4 - 15 \div (30 - 33)}[/tex]

[tex]\mathbf{= 4 - 15 \div 3}[/tex]

[tex]\mathbf{= 4 - (-5)}[/tex]

[tex]\mathbf{= 4 + 5}[/tex]

[tex]\mathbf{= 9}[/tex]

[tex]\huge\textbf{We got the \boxed{\bf +} because double negatives}\\\huge\textbf{equal a positive.}[/tex]

[tex]\huge\textbf{We have found the result to the question}[/tex]

[tex]\huge\textbf{Thus, your answer should be: \boxed{\mathsf{9}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

Regular Deal

Step-by-step explanation:

Pay as you go

Pay only $6 each time you work out

Regular Deal

Pay $50 a month and $2 each time you work out

All-in-one price!

Pay just $100 per month for unlimited use of our great facilities

1. Carlo thinks he will go to the gym about 20 times a month. Which of these options is the least expensive for Carlo? Show how you determined your answer.​

For 20 visits to the gym:

Pay as you go:

20 × $6 = $120

Regular Deal

$50 + 20 × $2 = $50 + $40 = $90

All-in-one price!

$100

Answer:

The best deal is for 20 visits per month is: Regular Deal

Answer:

17 gallons

Step-by-step explanation:

1 gallon has 16 cups

2 gallons have 32 cups

32-15=17

Answer:

17 cups

Step-by-step explanation:

1 gallon=16 cups

Since he made 2 gallons of soup, multiply 16 x 2 and you will get 32 cups of soup. If he served 15 cups of soup to his guests, he will have 17 cups of soup left over, because 32 - 15 = 17.

I hope i helped!!! :)

Answer:

∠ EGF = 64°

∠ DGE = 26°

Step-by-step explanation:

• ∠ EGF + 90° + 26° = 180°          [angles in a triangle add up to 180°]
⇒ ∠ EGF = 180° - 90° - 26°

⇒ ∠ EGF = 64°

• ∠ DGE + ∠ EGF = 90°                 [as shown in the diagram]

⇒ ∠ DGE + 64° = 90°

⇒ ∠ DGE = 90° - 64°

⇒ ∠ DGE = 26°

The length of the flagpole is x - 5  yards

The area of the flagpole is given as:

Area = x^2 - 10x + 25

Expand the expression

Area = x^2 - 5x -5x + 25

Factorize the expression

Area = (x - 5)(x - 5)

Express as squares

Area =(x - 5)^2

The area of a square is

Area = Length^2

So, we have:

Length = x - 5

Hence, the length of the flagpole is x - 5  yards

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The solution to the system of equations from the graph is x = 285.7 and y = 214.3

An equation is an expression that shows the relationship between two or more numbers and variables.

Let y represent the the volume of milk he uses and x the volume of whipping cream he uses. Hence:

x + y = 500   (1)

Also:

0.18x + 0.04y = 500(0.12)    (2)

From the graph:

x = 285.7 and y = 214.3

The solution to the system of equations from the graph is x = 285.7 and y = 214.3

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Answer:

B. 2.85

Step-by-step explanation:

to find the average of multiple numbers, we add them together and divide by the number of values we combined

for example: the average of 1, 2, and 3:

1 + 2 + 3 = 6

6 / 3 (because there were 3 numbers) = 2

so, this average would be 2.

Let's add the weights (I have changed these into a denominator of 20, so that they can be easily added. Let me know if you need clarification on how I did so)

1 1/2 pounds, 4 3/4 pounds, 2 3/10pounds

1 1/2 = 1  10/20

4 3/4 = 4  15/20

2  3/10 =  2   6/20

1 10/20 + 4 15/20 + 2 6/20 = 7  31/20

7 31/20 = 8 11/20

8 11/20 = 8.55

8.55 / 3 = 2.85

so, the average weight of these packages is 2.85 [pounds]

hope this helps! ^u^

Answer:

x = 23

Step-by-step explanation:

5x - 9 and 2x + 60 are corresponding angles and are congruent , so

5x - 9 = 2x + 60 ( subtract 2x from both sides )

3x - 9 = 60 ( add 9 to both sides )

3x = 69 ( divide both sides by 3 )

x = 23

Answer:

C

Step-by-step explanation:

Total Work hours = 3 1/2 hours

One routine physical routine requires: 1/3 hours.

Number of routines can be completed = Total work hours / Time required for one physical routine

= [tex]3\frac{1}{2} / \frac{1}{3}\\=\frac{7}{2} /\frac{1}{3} \\=\frac{7}{2} *3\\[/tex]

= 10.5 routines.

In this case, we are unable to complete half a routine (0.5), so we will choose the highest possible whole number, in this case, its 10 routines.

The percentage of data points that are above 27 are; 2.28%

We are given;

Mean; μ = 51

Standard deviation; σ = 12

Sample mean; x' = 27

Thus, formula for z-score is;

z = (x' - μ)/σ

z = (27 - 51)/12

z = -2

Now, from the empirical rule of normal distribution graph attached, we see that at z = -2, the percentage is 95.44%. However, we want to find the percentage that lie above 27. Thus, this is (100% - 95.44%)/2 = 2.28%

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The expected profit for the gambler is $4,621

The possible outcomes are:

Then the expected profit is:

P = ($6,500*0.81 + $200*0.08 - $6,000*0.11) = $4,621

The expected profit for the gambler is $4,621

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Step-by-step explanation:

tens place is 8 because the first number from the back is the unit

the tenth place is 2

For Marvin used the Quantitative Reasoning Process to build a budget while he is going to college. He worked hard over the summer and saved $2,595.9 to live on during the next two semesters of school. Marvin will receive a scholarship each semester for $958.35 money can Marvin spend each month, on average, for things like groceries, entertainment, and miscellaneous items is mathematically given as  

$4512.6

Savings with Marvin = $2,595.9

Scholarship amount  = $958.35

Total Scholarship amount received in 2 semesters = $958.35 X 2 = $ 1916.7

Now total money that Paolo have = (Savings with Marvin) + (Total Scholarship amount received in both semesters) = $2,595.9 + $1916.7 = $ 4512.6

Tuition & books cost  = $2000

Tuition & books cost for 2 semesters = $2000 X 2 = $4000

Housing cost for 2 semester contract =$1,000

Total expenses in books and housing = $4000+ $1000 = $5000

Money left with Marvin after Total expenses in books and housing = $ 4512.6 - $5000 = −487.4

This means he has overspent.

as no. of months in 2 semesters = 8

Amount that Marvin would be in debt each month = −487.4/8 = −$60.925

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Answer:

1.5

π/2

Step-by-step explanation:

√2 ≈ 1.41

√3 ≈ 1.73

1.5 is a rational number (15/10) that is in between.

π/2 ≈ 1.57 is an irrational number that is in between.

The triangle formed is a right triangle and the hypotenuse side is 6 ft.

The situation forms a right angle triangle.

A right triangle has one of its angles as 90 degrees.

Therefore, the triangle is represented below

The hypotenuse side of the right triangle is 6 foot, which is the length of the ladder.

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Answer:

30

Step-by-step explanation:

First Convert Mixed Number to Improper

[tex]6\frac{2}{3} = \frac{2+3*6}{3} = \frac{2+18}{3} = \frac{20}{3}\\\\\frac{20}{3} \div \frac{2}{9}\\[/tex]

Next, we know that when dividing fractions, there is a certain pattern to follow.

It goes like this:
[tex]\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{ad}{bc}\\\\[/tex]

A simple way to remember this is to know

KOR.

Keep, Opposite, Reciprocal

Keep:

[tex]\frac{a}{b}[/tex]

Opposite:

[tex]\div \rightarrow \times[/tex]

Reciprocal:

Basically Flip the Numerator and Denominator

[tex]\frac{c}{d}\rightarrow\frac{d}{c}[/tex]

And you can simply solve it then :)

WORK FOR SOLUTION

[tex]\frac{20}{3}\times\frac{9}{2} \\\\\frac{180}{6}\\\\\ =30[/tex]

Answer:

Hello! the answer to this question is 30.

Step-by-step explanation:

To solve for the quotient, we have to convert the mixed number to an improper fraction:

[tex]6\frac{2}{3} = \frac{6*3 + 2}{3} = \frac{20}{3}[/tex]

When dividing fractions, we have to flip the divisor to its reciprocal. When doing so, the divisor [tex]\frac{2}{9}[/tex] becomes [tex]\frac{9}{2}[/tex].

Now that we have the reciprocal, the operation will change from division to multiplication. We can take the final steps to solve the problem:

[tex]\frac{20}{3} * \frac{9}{2}[/tex]

This leaves you with a result [tex]\frac{180}{6}[/tex]. This can further be simplified by doing 180 ÷ 6 to get 30.

Therefore, the quotient is 30.

Answer:

1.08 Meters

Step-by-step explanation:

Simply, divide the length value by 100.

So in this case, the length value is 108.

So 108 ÷ 100 would be equal to 1.08.

This would mean moving the decimal points to places to the left would give you your answer.

Therefore, 108 centimeters is 1.08 meters.

[tex]\bf{Now \ \to \ \ 108\not{cm}*\dfrac{1 \ m}{100 \not{cm}}=1.08 \ m }[/tex]

if x is changed by 2 , the y changes by  +3, Option B is the correct answer.

The equation of a Linear Function is given by

y = mx +c

here m is the slope , c is the intercept on the y axis

The data is given in the table

To determine the relation , a function needs to be established between the variables.

m = ( y2 -y1 )/(x2-x1)

m = (-7 +10) /(-2+4)

m = 3 / 2

y = (3/2)x + c

at x = 0 , y= -4

-4 = 0 + c

c = -4

The function is

y = (3/2) x - 4

if x is changed by 2 , the y changes by  +3

Therefore Option B is the correct answer.

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Answer:

[tex]x \ = \ 10[/tex]

Step-by-step explanation:

Let point [tex]D[/tex] be the point where the straight line drawn from point [tex]A[/tex] meets the straight line [tex]BC[/tex], it is evident that [tex]\triangle ABD[/tex] and [tex]\triangle ACD[/tex] is similar given that both triangles share the same angle, [tex]\angle BAD \ = \ \angle DAC[/tex]. Hence, the ratio of the sides of each triangle is the same. Specifically,

                                              [tex]\displaystyle{\frac{x+4}{8} \ = \ \frac{2x+1}{12}}[/tex].

Performing cross multiplication yields

                                           [tex]12\left(x+4\right) \ = \ 8\left(2x+1\right) \\ \\ \rule{0.15cm}{0cm}12x+48 \ = \ 16x+8 \\ \\ \rule{1.1cm}{0cm} 4x \ = \ 40 \\ \\ \rule{1.3cm}{0cm} x \ = \ 10[/tex].

Answer:

40 feetI is the correct answer

Answer:  -9 , -3 , -2 , 6

Step-by-step explanation:

that should help

Answer:

the probability= 2/6=1/3