Which number line shows the solution the inequality

Answer:

[tex]\sqrt{(-\frac{806}{94}+8)^2+(-\frac{215}{94}-9)^2+ (-\frac{251}{94}-8)^2}[/tex] Whatever this number may be

Step-by-step explanation:

The distance will be on the plane containing the point, and perpendicular to the line - which exists as long as the point doesn't sit on the line, but in that case our distance will simply be zero. Good news, since the line is given in parametric equation, the equation of the plane is easy to write by simply computing the dot product between the vector generating the line - or any multiple of it! - and the vector joining a random point x y z of the space with our given point, and setting it equal to zero. The equation of our plane is thus

[tex]6(x-(-8)) + 3(y-9) -7(z-8) = 0\\6(x+8)+3(y-9)-7(z-8)=0[/tex]

We could multiply now or later, doesn't matter, so let's wait. Now, we need to know when the line passes through the plane, so let's plug the (parametric) coordinate of the line and let's see for which value of t that happens:

[tex]6(-2-6t+8) +3(1-3t -9) -7(-5+7t-8) =0\\6(6-6t) -3(8+3t)+7(13-7t)=0\\36-36t-24-9t+91-49t = 0\\t=103/94[/tex]

Found this value of t, we can use it to find the coordinate of the point in common between the line and the plane:

[tex](-2-6\frac {103}{94};1-3\frac {103}{94}; -5+7\frac {103}{94}) = (-\frac{806}{94};-\frac{215}{94};-\frac{251}{94})[/tex]

At this point it's simply a matter of calculating the distance between two points in 3D space, given by the usual [tex]\sqrt{\Delta x^2+\Delta y^2+\Delta z^2}[/tex], whatever abomination of a number it might become:

[tex]\sqrt{(-\frac{806}{94}+8)^2+(-\frac{215}{94}-9)^2+ (-\frac{251}{94}-8)^2}[/tex]

At this point is a simple exercise in number crunching which I refuse to entertain more - but please double check all calculation above in case I didn't notice something.

The amount the she had in her savings before the trip was $825

From the question, we are to calculate how much Imani has in her savings before the trip

Let the amount she has in her savings before the trip be x

From the given information,

"Imani spent a third of her savings on airfare for a vacation"

That is,

She spent (1/3)x

The amount remaining after this time will be x - (1/3)x = (2/3)x

"She then spent another $300 on hotels"

The amount remaining after this time will be (2/3)x - $300

"If she has $250 left for meals and souvenirs"

That is,

(2/3)x - $300 = $250

Now, solve for x

(2/3)x - $300 = $250

(2/3)x = $250 + $300

(2/3)x = $550

x = $550 × 3/2

x = $825

Hence, the amount the she had in her savings before the trip was $825

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Answer:

x=2

Step-by-step explanation:

3x+4=2x+6

3x=2x+2

x=2

Mean = 0.5545, Median =0.57, Mode = 0.79  of the following data.

What is mean median and mode?

For the given data 0.29, 0.3, 0.34, 0.35, 0.37, 0.46, 0.51, 0.51, 0.52, 0.57, 0.57, 0.58, 0.62, 0.63, 0.65, 0.68, 0.77, 0.79, 0.79, 0.79.

The mean is calculated as:

Mean = (0.29 + 0.3 + 0.34 + 0.35 + 0.37 + 0.46 + 0.51 + 0.51 + 0.52 + 0.57 + 0.57 + 0.58 + 0.62 + 0.63 + 0.65 + 0.68 + 0.77 + 0.79 + 0.79 + 0.79)/20

= 11.09/20

Mean = 0.5545

Median is the middle value of the data set and since the sample size is even which is 20 hence the median is found between n/2 and n/2 +1 which is 10th value and 11th value when the data set is arrange in ascending order.

so, the 10th value is 0.57 and 11th value is also 0.57 so, the median is (0.57 + 0.57)/2 = 0.57

Median:

The median is the most occuring value in the dataset and as we can see that 0.79 appeared 3 times hence 0.79 is Mode.

So, finally:

Mean = 0.5545

Median =0.57

Mode = 0.79

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Neon (Ne), hydrogen (H), helium (He), and Carbon (C) are examples of; C: elements you can tell because they can be found on the periodic table

Elements are pure substances which are composed of only one type of atom. Compound are substances which are formed by two or more different types of elements that are united chemically in fixed proportions.

Now, Neon (Ne), hydrogen (H), helium (He), and Carbon (C) are examples of elements. This is because they are all composed of only one type of atom and they can as well be found in the periodic table that contains only elements.

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According to the solving the non of the quadratic equations equivalent.

4X² + 5x - 3.

A quadratic equation seems to be a second-order polynomial equation in a variable, x ax2+bx+c=0, with a 0 as the coefficient. The fundamental theorem of algebra ensures that it has at least one solution as it is a second-order polynomial problem. The solution could be straightforward or difficult.

Equivalent equations are those that have the same solutions or roots. An equivalent equation is produced by adding or subtracting the identical number or expression from both sides of an equation. Equivalent equations are produced by multiplying and dividing both sides of such an equation by the same non-zero value.

3 ⁢X² + 5 x − 7 ⁢+ ( X² + 4 ).

Simplifying this equation:

3 ⁢X² + 5 x − 7 +  X² + 4

= 4X² + 5x - 3

According to the solving the non of the quadratic equations equivalent.

4X² + 5x - 3.

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I understand that the question you are looking for is:

Which expression is equivalent to the given expression?

3 ⁢X² + 5 x − 7 ⁢+ ( X² + 4 ).

A. - 4X² + 5X − 4

B. X² + 4

C. X² + 28

D. - 4 ⁢X² + 5x − 28

Answer:

18

Step-by-step explanation:

5*(6)-10(2)+8 = 18

Substitute k = 6 and c = 2 into the equation and solve it.

Answer:

Step-by-step explanation:

You want to know the number of outcomes in the sample space when 3 marbles are chosen from 7. If four are red marbles, you want to know the number of outcomes when all chosen are red.

There are C(7,3) = 7!/(4!·3!) = 35 ways to choose 3 marbles from 7. Given that there are different colored marbles involved, not all of these outcomes are unique.

There are 35 possible outcomes.

There are C(4, 3) = 4 ways to choose 3 red marbles from 4 red marbles.

There are 4 possible outcomes with all red marbles.

__

Additional comment

The 35 possible outcomes are ...

  (RRR) - 4, (RRG) - 12, (RRY) - 6, (RGG) - 4, (RGY) - 8, (GGY) - 1

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The meaning of |-36| is  the absolute value of negative 36.

We know that, the absolute value of any real number m is the positive value of m.

For any ±m ∈ R,

| ±m | = m

The absolute value of a number is also know as modulus of number.

In this question we have been given an absolute value |-36|

|-36| = 36

So, the meaning of |-36| would be,

- the absolute value of negative 36

Therefore, the meaning of |-36| is  the absolute value of negative 36.

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The length of each side of the tank is 9 feet.

Height = 8

Volume = 648

Let y be the cross sectional area

Therefore, 648 = 8y

y² = 648/8

y² = 81

Therefore, y = ✓81

y = 9

The length of each side of the tank is 9 feet.

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Answer: $4.10*0.08%=0.33

Step-by-step explanation:

The step which is included in the graph of the function is Option(a)  

y=-5 for -4≤ x <-3.

From the properties of the greatest integer function y = [x], we know that

y = 0 for, 0 ≤ x < 1

y = -1 for, - 1 ≤ x < 0

y = -2 for, - 2 ≤ x < -1

Here,we are given a greatest integer function f(x) or y =[x-1]

Hence, the step which is included in the graph of the function is  

y=-5 for -4 ≤ x <-3.

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880 oz

Step-by-step explanation:

The height of the building is 23.09m.

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Answer:

No, I do not agree with Simon's reasoning.

Step-by-step explanation:

7*2=14

8*1=8

BUT

7+2=9

8+1=9

YET

Simon isn't properly solving the equation with the right basic operation of arithmetic. He must multiply, not use addition.

Hope this helps.

Answer:

10.6 ounces

Step-by-step explanation:

1. Divide the total spent by the cost per ounce to get number of ounces bought.

2.65 ÷ 0.25 = 10.6 ounces

Using proportions, it is found that Jen planned to spend 19/4 hours paddleboarding.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

In this problem, we have that:

4 + 3/4 = 4.75 hours = 19/4.

Jen planned to spent 19/4 hours paddleboarding.

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Answer:

2.3(2.99)=$6.877

Step-by-step explanation:

Multiply the pounds (2.3) by the price of apples per pound.

Hope this helps! :)

Answer:

2.3(2.99)=$6.877

Step-by-step explanation:

Hope this helps!

The value of m is $25 and value of b is $100, the cost is $300 and the number of students is 12.

As per the given relation in the question, we see that b is calculated once and m is calculated based on the variable value x, which is the number of students. Hence, for correct calculation, value of m is $25 and value of b is $100.

The cost if 8 students are passengers will be calculated by keeping the value of x and other constants as per the above answer.

Cost = 25×8 + 100

Cost = 200 + 100

Cost = $300

Number of students will again be found as the value of x, by keeping the values as specified above.

400 = 25x + 100

25x = 400 - 100

25x = 300

x = 300 ÷ 25

x = 12

Hence, value of m is $25 and value of b is $100, the cost is $300 and the number of students is 12.

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The complete question is attached in figure.

The number of students who will be going on the trip is B. 40 students.

A mathematical expression is a rule-based set of numbers, variables, and mathematical operations performed to compute the output value.

The mathematical operations used to solve mathematical expressions include additions, subtractions, divisions, and multiplications.

The total of the weekend trip = $4,030

The cost of cleaning for the bus = $30

The cost of food and lodging per student = $60

The bus charge per student = $40

Total cost per student = $100 ($60 + $40)

The total cost, y = 4,030 - 30 - 100x

The number of students = x

x= (4,030 - 30)/100

= (4,000/100)

= 40.

Thus, the number of students who will be going on the trip is B. 40 students.

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The linear functions for this problem are given as follows:

13. y = 2x/3 + 8/3.

14. y = -3x + 5.

15. y = -1/3x - 2.

16. y = 5/4x - 1/4.

17. y = 7/4x + 19/2.

A linear function is modeled by the following rule:

y = mx + b

In which:

The slope is also related with parallel and perpendicular lines, as follows:

In item 13, the line in slope-intercept form is:

y = 2x/3.

The line we want to find is parallel, hence it has the same slope, that is:

y = 2x/3 + b.

When x = -1, y = 2, hence:

2 = -2/3 + b

b = 8/3.

Hence the line is:

y = 2x/3 + 8/3.

For item 14, the line is perpendicular to:

y = 1/3x + 4.

Hence the slope is found as follows:

1/3m = -1

m = -3.

Then:

y = -3x + b.

When x = 0, y = 5, hence b = 5 and the line is:

y = -3x + 5.

For item 15, the line is perpendicular to:

y = 3x + 4.

Then the slope is found as follows:

3m = -1

m = -1/3.

Then:

y = -1/3x + b.

When x = 0, y = -2, hence b = -2 and the line is:

y = -1/3x - 2.

For item 16, the line is perpendicular to:

y = 4 - 4/5x.

Then the slope is found as follows:

-4m/5 = -1

m = 5/4.

Hence:

y = 5/4x + b.

When x = 1, y = 1, hence:

1 = 5/4 + b

b = -1/4.

Then the line is:

y = 5/4x - 1/4.

For item 17, the line is perpendicular to:

y = 13/7 - 4/7x

Then the slope is found as follows:

-4m/7 = -1

m = 7/4.

Hence:

y = 7/4x + b.

When x = -2, y = 6, hence:

6 = -14/4 + b

b = 19/2.

Hence the line is given by:

y = 7/4x + 19/2.

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The 3 consecutive odd integers are -3, -5 and -7

Let the 3 consecutive odd integers be 2x-1,  2x+1 and 2x+3

If the sum of 2 times the first and the last term is equal to 5 times the middle integer, then;

2(2x-1)+2x+3 = 5(2x+1)

Expand

4x-2 + 2x +3 = 10x+5

6x +1 = 10x + 5

6x - 10x = 5 - 1

-4x = 4

x = -1

Determine the numbers

First number = 2(-1) - 1 = -3

Second number = -5

Third number = -7

Hence the 3 consecutive odd integers are -3, -5 and -7

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Given that

To find

So, according to the question

We have,

∵ From figure m∠1 and m∠2 divided 90° into two parts

∴       m∠1 + m∠2  = 90° ----------------------(1)

Now putting the values of m∠1 and m∠2 in equation (1)

        m∠1 + m∠2  = 90° ----------------------(1)

       (x+38)° + 3x° =  90°

       x°+38° + 3x° =  90°

                     4x° =  90° - 38°

                     4x° =  52°

                     x° =  (52/4)°

                     x° =  13°

So,

                m∠1 = (x+38)°

                        = (13+38)°

               m∠1 = 51°  

And

                m∠2 = 3x°

                        = (3 × 13)°

                m∠2 = 39°

The angles are

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Answer:

Step-by-step explanation:

The minimum is the smallest value in a data set.

Ordering the data from least to greatest, we get:

1  2   3   5   6   7   9   11   12   13   14   16   17   19   20  

So the minimum is 1

The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.

Quartile 1 is 5,        

1   2   3   5   6   7   9  11   12   13   14   16   17   19   20  

The first half is

1   2   3   5   6   7   9, the median of these numbers is 5 so Quartile 1 = 5

The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

The median is 7,     1   2   3   5   6   7  9   11   12   13   14   16   17   19  20

The third quartile (or upper quartile or 75th percentile) is the median of the second half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.

Quartile 3 is 16,

1   2   3   5   6   7   9   11   12   13   14   16   17   19   20  

The upper half is

12   13   14   16   17   19   20, the median of these numbers is 16 so Quartile 3 = 16

The maximum is the greatest value in a data set.

Ordering the data from least to greatest, we get:

1   2   3   5   6   7   9   11   12   13   14   16   17   19   20  

So, the maximum is 20.

Answer: 5/(5+n)

Step-by-step explanation:

Let "a number" be represented by "n"

[tex]5/(5+n)[/tex]