If "a", "b" and "c" vectors are in cyclic order then:

1. Sea level (0 m) - 100%

2. Mid-level elevation (4,500 m) - 57%

3. Peak (8,850 m) - 33%

Identify the elevation and the percentage of oxygen available at each elevation.

Elevation has a significant impact on the amount of oxygen in the atmosphere. The oxygen level increases with decreasing height and decreases with increasing elevation. Thus, we have a situation where the oxygen concentration is highest at sea level or 0 elevations. The oxygen level drops dramatically when we ascend to greater elevations, say 4,500 m, making breathing difficult. Even at higher altitudes, such as 8,850 m, the oxygen level will drop significantly, making it necessary for a person to undergo extensive training and carry oxygen to survive.

1. Sea level (0 m) - 100%

2. Mid-level elevation (4,500 m) - 57%

3. Peak (8,850 m) - 33%

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It looks like the function might be defined by

[tex]f(x) = \begin{cases} 3a{}x + b & \text{if } x > 1 \\ 11 & \text{if } x = 1 \\ 5a{}x - 2b & \text{if } x < 1 \end{cases}[/tex]

To ensure continuity at [tex]x=1[/tex], we need both one-sided limits to exist and have the same value.

[tex]\displaystyle \lim_{x\to1^-} f(x) = \lim_{x\to1} (5a{}x - 2b) = 5a - 2b[/tex]

[tex]\displaystyle \lim_{x\to1^+} f(x) = \lim_{x\to1} (3a{}x + b) = 3a + b[/tex]

Both limit values must be equal to [tex]f(1) = 11[/tex], so that

[tex]\begin{cases} 5a - 2b = 11 \\ 3a + b = 11 \end{cases}[/tex]

Eliminating [tex]b[/tex], we have

[tex](5a - 2b) + 2 (3a + b) = 11 + 2\cdot11 \implies 11a = 33 \implies \boxed{a=3}[/tex]

Solving for [tex]b[/tex], we get

[tex]5\cdot3 - 2b = 11 \implies -2b = -4 \implies \boxed{b=2}[/tex]

Answer:

5.5

Step-by-step explanation:

For the first fold, we cut the 11-inch side in half, resulting in an 8.5-by-5.5-inch piece. After the second fold, we have a 4.25 by 5.5 piece after halving the 8.5 inch side. The length is 5.5 inches.

Answer:

A. W

Step-by-step explanation:

Because their is a rhythm and pattern

The top of the escalator exists 9 feet far from the ground floor.

Let h denote the distance between the top of the escalator from the ground floor.

We have existed given that the angle of depression from the top of the escalator to the floor stands 36.84°, and the escalator exists 15 feet long.

The side h exists opposite side and 15 feet side exists hypotenuse of a right triangle.

[tex]$&\sin =\frac{\text { Opposite }}{\text { Hypotenuse }} \\[/tex]

[tex]$&\sin \left(36.84^{\circ}\right)=\frac{h}{15} \\[/tex]

[tex]$&\sin \left(36.84^{\circ}\right) * 15=\frac{h}{15} * 15 \\[/tex]

[tex]$&0.599582468446 * 15=h \\[/tex]

8.993737 = h

[tex]$&h \approx 9[/tex]

Therefore, the top of the escalator exists 9 feet far from the ground floor.

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The percentage of respondents who play only hockey is 27.24%.

According to the given question.

Total number of respondents = 2302

And, the number of reposdents who play only hockey = 627

Therefore,

The percentage of respondents said that they play only hockey

= (number of respondents who play only hockey/ total number of respondents)  × 100

[tex]= \frac{627}{2302} \times 100[/tex]

= 27.237 %

≈ 27.24%

Hence, the percentage of respondents who play only hockey is 27.24%.

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The percentage reduction of the price of the video game from 60 to 45 was 25%.

The percentage reduction refers to the fractional reduction in the price of the video game.

This implies that a percentage is a fraction of a value.  Percentages are calculated over 100.

A percentage is, therefore, a number or ratio expressed as a fraction of 100, often denoted using the "%" sign.

The old price of the video game = 60

The new price of the video game = 45

Reduction in price = 15 (60 - 45)

Percentage reduction = 25% (15/60 x 100)

Thus, the percentage reduction of the price of the video game from 60 to 45 was 25%.

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The answer is y - 3 = -1/2 (x - 2).

First, let's find the slope.

Then, the point slope form will be :

Answer: y=-0,5x+4.

Step-by-step explanation:

[tex]A(-4;6)\ \ \ \ B(2;3)\\Straight \ line\ equation\ is:\\\displaystyle\\\boxed {\frac{x-x_1}{x_2-x_1} =\frac{y-y_1}{y_2-y_1}} \\\frac{x-(-4)}{2-(-4)}=\frac{y-6}{3-6} \\ \frac{x+4}{2+4}=\frac{y-6}{-3} \\\frac{x+4}{6}=\frac{y-6}{-3} \\ Multiply\ the\ left\ and\ right\ sides\ of\ the\ equation \ by\ -3:\\\frac{-(x+4)}{2} =y-6\\-0,5x-2=y-6\\y=-0,5x+4.[/tex]

The number of hours spent repairing televisions. after how many hours does he break even is 7 hours

These are equations that contains several equations with unknowns. Given the function that modelled the revenue generated from television repair as;

y = 25 + 30x

where:

x is the number of hours spent repairing televisions.

If his overhead cost, in dollars, is modelled by the equation y=5x^2−10, the company breaks even when;

25 + 30x = 5x^2 -10

Divide through by 5

5 + 6x = x^2 - 2

Equate to zero to have:

x^2 - 6x  -2 - 5 = 0

x^2 - 6x - 7 = 0

x^2 - 7x + x - 7 = 0
x(x-7)+1(x-7) =0

x = -1 and 7

Hence the number of hours spent repairing televisions. after how many hours does he break even is 7 hours

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Answer:

1.8 tonne

Step-by-step explanation:

sum the parts of the ratio, 2 + 3 = 5 parts

divide the total mix by 5 to find the value of one part of the mix

3 tonne ÷ 5 = 0.6 tonne , then

3 parts = 3 × 0.6 = 1.8 tonne ← amount of gravel in the mix

Answer:50%

Step-by-step explanation:  It doesn't matter how many questions there are because for each question, you have a 50% chance of getting it right. So, the probability is 50%.

the location of the g point is 3.

Two ratios are set to be equal in an equation called a proportion. You might express the ratio as 1: 3 for instance, if there is 1 boy and 3 girls.

Point G Partition the directed line segment form d to f into a

5:4 ratio

so,

g - d = (5/9) x (f - d)

We have that d = -2 and f = 7, Therefore

g - d = (5/9) x (f - d)

g + 2 = (5/9) x (7 + 2)

g + 2 = 5

g = 3

Therefore the location of the g point is 3.

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Answer: OPTION D

Step-by-step explanation:

The value of a particular trigonometric expression that is cos 2θ under the third quadrant is -119/169

Given:

sin θ = -⁵/₁₃

This can be seen from the trigonometric identity.

cos 2θ = 1 - 2sin²θ

From trigonometric identities, we know that;

cos 2θ = 1 - 2sin²θ

Thus;

cos 2θ = 1 - 2(-⁵/₁₃)²

cos 2θ = 1 - 2(25/169)

cos 2θ = 119/169

since cos θ is negative in the third quadrant, then we have;

cos 2θ = -119/169

so; cos θ is negative in the third quadrant, so ;

cos 2θ = -119/169

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Inequalities help us to compare two unequal expressions. For all real numbers x such that x²<4, the interval which will satisfy the given inequality is (-2,2).

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

Given the inequality x²<4, whose solution can be calculated as shown below.

x² < 4

x² - 4 < 0

x² - 2² < 0

(x+2)(x-2)<0

x = (-2, 2)

Hence, for all real numbers x such that x²<4, the interval which will satisfy the given inequality is (-2,2).

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[tex]\bf{ (x^2-5x)(2x^2+x-3)}[/tex]

[tex]\bf{Distribute \ the \ sum \ group. }[/tex]

[tex]\bf{Expand \ the \ distribution \ of \ terms. }[/tex]

[tex]\bf{Remove \ parentheses. }[/tex]

[tex]\bf{Collect \ like \ terms. }[/tex]

[tex]\bf{Simplify}[/tex]

Answer:

He is 2 years old.

Step-by-step explanation:

She is 22, in 8 years she will be 30. 30 is 3×10. At that time, her brother will be 10; that is 8 years from now. So now, the little brother is 10-8 = 2 years old.

If you must show algebra work:

x = brother's age now.

x+8=brother's age in 8 years.

YingYu's age in 8 years = 3 × brother's age in 8 years

22+8 = 3(x+8)

30 = 3x +24

6 = 3x

2 = x

Answer:

y=[-4]x+[10]

Step-by-step explanation:

For a line to be perpendicular to another it must have the reverse reciprocal of the opposite line, to find the reverse reciprocal you take your slope, flip the numerator and denominator, and multiply it by -1.

The slope [tex]\frac{1}{4}[/tex] turns into [tex]\frac{4}{1}[/tex] and is then multiplied by -1 to become [tex]\frac{-4}{1}[/tex] which can be simplified down to: [tex]-4[/tex]

Now that we know the slope we need the line to pass through a point, so we will use point slope form:

[tex]y-y1=m(x-x1)[/tex]
Substitute in our slope and point values:

[tex]y-2=-4(x-2)[/tex]

Now solve for y:

[tex]y-2=-4(x-2)\\y-2=-4x+8\\y=-4x+10[/tex]

Then you will find that line [tex]y=-4x+10[/tex] runs perpendicular to [tex]y=\frac{1}{4}x-8[/tex] and intersects point (2,2).

The size around the circular edge of the plate is 37.68 inches

The circumference of a circle can be solved as follows:

The ant is standing at the centre of a perfectly circular plate and it walks to the edge of the plate .

The centre of the plate to the edges is 6 inches. Therefore, the radius of the circular plate is 6 inches.

Hence, the distance around the edge of the plate is the circumference of the plate.

Therefore,

circumference of the circular plate = 2πr

circumference of the circular plate = 2 × π × 6

circumference of the circular plate = 12π

circumference of the circular plate = 12 × 3.14

circumference of the circular plate = 37.68 inches

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Answer: 2

Step-by-step explanation:

1) substitute

2) calculate the difference before the absolute value

3) calculate the absolute value

4) convert into whole numbers/reduce

5) subtract the whole numbers

this is what i think might be wrong

The value of the function w(5) is 53

The function is given as:

w(x) = 9x + 8

The expression w(5) implies that the value of x is 5

i.e. x = 5

Substitute the known values in the above equation

w(5) = 9 * 5 + 8

Evaluate the product

w(5) = 45 + 8

Evaluate the sum

w(5) = 53

Hence, the value of the function w(5) is 53

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Answer:

B

Step-by-step explanation:

Answer:

36 units

Step-by-step explanation:

to find the distance take the absolute value of the difference, that is

| - 42 - (- 78) | = | - 42 + 78 | = | 36 | = 36

or

| - 78 - (- 42) | = | - 78 + 42 | = | - 36 | = 36

Answer:

-36

Step-by-step explanation:

-78 - (-42)

= -78 + 42

= -36

Anderson could provide 0.5x2 + 4x + 8 = 0 has exactly one real root if the discriminant is 0,

Any equation that can be rewritten in standard form as where x represents an unknown, a, b, and c represent known numbers, and where a 0 is true is a quadratic equation. As there is no ax2 term when a = 0, the equation is linear rather than quadratic.

A polynomial's discriminant is a quantity that depends on the coefficients and enables for some root attributes to be inferred without actually computing them. It is actually a polynomial function of the original polynomial's coefficients.

0.5x^2 + 4x + 8 = 0

The discriminant is computed utilizing:

d = b^2 - 4ac

Thus, we have:

d = 4^2 - 4 * 0.5 * 8

Evaluate

d = 0

The equation has only one real root since the discriminant is 0,

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The factorization of given cubic polynomial 6x³ - 11x² - 12x + 5 is:  

6x³ - 11x² - 12x + 5 = (x + 1)(x - [tex]\frac{5}{2}[/tex])(x - [tex]\frac{1}{3}[/tex])

For given question,

We have been given the cubic polynomial 6x³ - 11x² - 12x + 5

We need to factorize given cubic polynomial.

By the rational roots theorem, any rational zero of f(x) is expressible in the form ± [tex]\frac{p}{q}[/tex] for integers p, q with p a divisor of the constant term 5 and q a divisor of the coefficient 6 of the leading term.

Factors of p = 5: 1, 5

Factors of q = 6: 1, 2, 3, 6

That means that the only possible rational zeros are:

±{ [tex]\frac{1}{1} ,\frac{1}{2} ,\frac{1}{3} ,\frac{1}{6} ,\frac{5}{1} ,\frac{5}{2} ,\frac{5}{3} ,\frac{5}{6}[/tex] }

= ±{ [tex]1 ,\frac{1}{2} ,\frac{1}{3} ,\frac{1}{6} ,5 ,\frac{5}{2} ,\frac{5}{3} ,\frac{5}{6}[/tex] }

We need to find the exact zeros of given cubic polynomial.

For x = 1,

6(1)³ - 11(1)² - 12(1) + 5 = -12

This means, x = 1 is not a zero of given cubic polynomial.

For x = -1,

6(-1)³ - 11(-1)² - 12(-1) + 5 = 0

This means, x = -1 is a zero of given cubic polynomial and (x + 1) is a factor.

To factorize given cubic polynomial we use synthetic division.

The synthetic division (6x³ - 11x² - 12x + 5) ÷ (x + 1) is as shown in following image.

⇒ 6x³ - 11x² - 12x + 5 = (x + 1)(6x² - 17x + 5)

The factors of above quadratic polynomial 6x² - 17x + 5 are:

⇒ 6x² - 17x + 5 = (x - [tex]\frac{5}{2}[/tex])(x - [tex]\frac{1}{3}[/tex])

So, the factors of given cubic polynomial are:

⇒ 6x³ - 11x² - 12x + 5 = (x + 1)(x - [tex]\frac{5}{2}[/tex])(x - [tex]\frac{1}{3}[/tex])

Therefore, the factorization of given cubic polynomial 6x³ - 11x² - 12x + 5 is:  6x³ - 11x² - 12x + 5 = (x + 1)(x - [tex]\frac{5}{2}[/tex])(x - [tex]\frac{1}{3}[/tex])

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The idea that group work theories are appropriate for all clients all the time is a myth (Third option).

About Group Process:

The term "group process" describes how people collaborate within an organization to complete tasks. Typically, organizations invest a lot of time and effort into defining and achieving goals, but little thought is usually given to how those goals are affecting the most valuable resource of a group - its people.

Since different clients have different demands and priorities, group work might not be suitable for many, but not for all. Different types of clients require different types of collaboration, type of group or individuals, and working strategies that work for their goals the best.

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Answer:

The hand moved [tex]\bf \frac{3}{4}[/tex] of a complete turn.

Step-by-step explanation:

The hand moved from 3 to 12, that is, it moved:

12 - 3 = 9 hours

In a clock, 12 hours represent a complete turn.

∴ Using the unitary method:

12 hours    ⇒     1 turn

1 hour        ⇒     [tex]\frac{1}{12}[/tex] turns

9 hours     ⇒     [tex]\frac{1}{12}[/tex]  × 9 = [tex]\frac{9}{12}[/tex]

                                     = [tex]\bf \frac{3}{4}[/tex] turns    (simplified)

∴ The hand moved [tex]\bf \frac{3}{4}[/tex] of a complete turn.

The answer is  [tex]\boxed{\frac{3}{4}}[/tex].

To find the fraction of a complete turn it moved in this case, take the ratio between hours covered between 3 and 12, and the hours covered in a complete turn.

Answer: D. 5 choose 3

Step-by-step explanation:

The 'C' stands for Choose

and you read left to right, leaving you with "5 choose 3"

The quantity of meat and cheese sold by the deli according to the description accounts in the task content are; 4.5 and 2.5 pounds respectively.

The quantity of meat sold by the deli as represented by the variable X in the task content can be calculated by solving the systems of equations.

The quantity of cheese sold by the deli as represented by the variable y in the task content can be calculated by solving the systems of equations.

Consequently, solving the system of equations by means of substitution, we have;

y = (30.50-4x)/5

Hence, we have;

11x + 14((30.50-4x)/5) = 84.50

x = 4.5 pounds of meat and

y = 2.5 pounds of cheese.

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