Show mathematically why the ratio 15:10 is not equal to 10:15

Answer:

from the graph we can see that

for 2 gallones - it can travell 70 miles

4 gallones - 140 miles

we will take the first case

2 gallones - 70 miles

17 gallones - ? miles

cross multiply

\( \frac{17 \times 70}{2} \)

= 595 miles

Answer:

Dollars per passenger would be $252.
The maximum revenue is $63,404.

Step-by-step explanation:

Let's define the number of passengers above 212 as x.

The revenue function is given by R(x) = (212 + x)(292 - x).

We can expand and simplify the revenue function:

\(R(x) = 212 * 292 + 212 * (-x) + x * 292 + x * (-x)\)

= \(61804 - 212x + 292x - x^2\)

= \(-x^2 + 80x + 61804\)

The revenue function is a quadratic function in the form\(R(x) = -x^2 + 80x + 61804\), representing a downward-opening parabola.

To find the x-coordinate of the vertex (which gives the number of passengers for maximum revenue), use the formula \(x = -b/2a\), where \(a = -1\) and \(b = 80\).

\(x=\frac{-80}{2*(-1)}\)

\(= \frac{80}{2}\)

\(= 40\)

Therefore, the number of passengers above 212 for maximum revenue is 40.

Substitute x = 40 into the revenue function to find the maximum revenue:

\(R(x) = -(40)^2 + 80(40) + 61804\)

\(= -1600 + 3200 + 61804\)

\(= 61804 + 1600\)

\(= 63404\)

Hence, the maximum revenue is $63,404.

To determine the fare per passenger, subtract x from the base fare of $292:

Fare per passenger = Base fare - x

\(= 292 - 40\)

\(= 252\) Dollars per passenger.

Answer:

The area of this triangle is (1/2)(9)(8) = 36.

Answer: 120 yds

Step-by-step explanation:

48+30+24+18+120 yds

Answer:

See below ~

Step-by-step explanation:

Question 1

⇒ The given angles are supplementary (add up to 180°)

⇒ 6x + 6 + 8x - 22 = 180

⇒ 14x - 16 = 180

⇒ 14x = 196

⇒ x = 14

============================================================

Question 2

⇒ The given angles are complementary (Add up to 90°)

⇒ 3x + 5 + 40 = 90

⇒ 3x + 45 = 90

⇒ 3x = 45

⇒ x = 15

Answer:

∠TRU is supplementary with ∠PQS as SQ║TR.

Supplementary angles add up to 180°.

Consider ΔRTU

∠RUV is exterior angle and therefore is sum of ∠TRU and ∠RTU:

<TRU

Sum of 2 interiors =exterior

<RTU

Answer:

2x=80º

x=40º

Step-by-step explanation:

180-60=3x

120=3x

40=x

Answer:

the approximate value of m is -0.12, indicating that the value of Ty's computer decreases by 0.12 (or 12%) each year.

Step-by-step explanation:

o express this depreciation rate as a slope in the equation y = mx + b, we need to determine how much the value changes (the "rise") for each year (the "run").

Since the value decreases by 12% per year, the slope (m) would be -12%. However, we need to express the slope as a decimal, so we divide -12% by 100 to convert it to a decimal:

m = -12% / 100 = -0.12

Answer: y = 5x-2

Step-by-step explanation:

Recall that for two vector x and y making an angle θ with each,

x • y = ||x|| ||y|| cos(θ)

If we replace y with x, we see that

x • x = ||x|| ||x|| cos(0) = ||x||²   ⇒   ||x|| = √(x • x)

Using the last identity, the magnitude of w is

||w|| = √(w • w)

but since w = u + v, we have

w • w = (u + v) • (u + v)

The dot product distributes over sums and is commutative, so

w • w = (u • u) + (u • v) + (v • u) + (v • v)

… = ||u||² + 2 (u • v) + ||v||²

… = ||u||² + 2 ||u|| ||v|| cos(θ) + ||v||²

If u has a direction of 45° with the positive x-axis, v has a direction of 150°, then the angle between u and v is |45° - 150°| = 105°. So,

||w|| = √(||u||² + 2 ||u|| ||v|| cos(150°) + ||v||²)

… = √(10² + 2 • 10 • 13 cos(150°) + 13²)

… ≈ 14.2

Using the parallelogram rule for vector addition (see attached sketch), the sum of the angle between w and u and 45° is equal to the direction of w.

If φ is the angle between w and u, then

w • u = ||w|| ||u|| cos(φ)

… = 14.2 • 10 • cos(φ)

but we also have

w • u = (u + v) • u

… = (u • u) + (v • u)

… = ||u||² + ||u|| ||v|| cos(105°)

… = 10² + 10 • 13 • cos(105°)

… ≈ 66.4

Then

14.2 • 10 • cos(φ) ≈ 66.4

cos(φ) ≈ 0.467

φ ≈ 62.1°

and so the direction of w is 62.1° + 45° ≈ 107.1°.

Number of days taken by \(9\) boys to cut the grass on the football field is equals to \(20\) days.

"Number is defined as the arithmetic value which help us to count the data as per the given situation."

According to the question,

Number of days taken by \(15\) boys to cut the grass on the football field

 \(=12\)days

As per the given condition we have,

Number of days taken by \(9\) boys to cut the grass on the football field

\(=\frac{(15)(12)}{9}\)

\(= 20\)days

Hence, number of days taken by \(9\) boys to cut the grass on the football field is equals to \(20\) days.

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The value of x from the venn diagram if P(T | V) = 1/5 is 16

From the question, we have the following parameters that can be used in our computation:

The venn diagram

From the venn diagram, we have the following probability values

P(T | V) = (x - 4)/(3x + x - 4)

Evaluate the like terms

So, we have

P(T | V) = (x - 4)/(4x - 4)

From the question, we have

P(T | V) = 1/5

This means that

(x - 4)/(4x - 4) = 1/5

When evaluated, we have

x = 16

Hence, the value of x is 16

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Answer:

  sin(θ) = -12/13

Step-by-step explanation:

You want the sine of the third-quadrant angle whose cosine is -5/13.

In the third quadrant, both the sine and the cosine are negative. The sine of the angle can be found from your knowledge of the {5, 12, 13} Pythagorean triple, or using the Pythagorean trig identity:

  sin(θ) = -√(1 -cos(θ)²)

  sin(θ) = -√(1 -(-5/13)²) = -√(144/169)

  sin(θ) = -12/13

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For the given equation, 1/x + 2/x+10 = 1/3,

1)The least common denominator is x+10. Option c is correct.

2)The equation will have 2 valid solutions. Option a is correct.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, the equation is,

1/x + 2/x+10 = 1/3

\(\frac{1}{x}+\frac{2}{x+10}=\frac{1}{3}\)

Cross-multiply the given equation,

\(3\left(x+10\right)+6x=x\left(x+10\right)\)

The obtained value of x after simplifying the equation is,

\(\\\ x=5,\:x=-6\)

Thus, for the given equation, 1/x + 2/x+10 = 1/3, the least common denominator is x+10. Option c is correct and the equation will have 2 valid solutions. Option a is correct.

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Question 1:

(a) The equation representing Elaine's total parking cost is:

C = x * t

(b) So the cost of parking for a full 24 hours would be 24 times the cost per hour.

Question 2:

The given system of equations is inconsistent and has no solution.

(a) To represent Elaine's total parking cost, C, in dollars for t hours, we need to know the cost per hour. Let's assume the cost per hour is $x.

(b) If Elaine wants to park her car for a full 24 hours, we can substitute t = 24 into the equation from part (a):

C = x * 24

Question 2:

To solve the linear system:

-x - 6y = 5

x + y = 10

We can use the elimination method.

Multiply the second equation by -1 to create opposites of the x terms:

-x - 6y = 5

-x - y = -10

Add the two equations together to eliminate the x term:

(-x - 6y) + (-x - y) = 5 + (-10)

-2x - 7y = -5

Now we have a new equation:

-2x - 7y = -5

To check the answer, we can substitute the values of x and y back into the original equations:

From the second equation:

x + y = 10

Substituting y = 3 into the equation:

x + 3 = 10

x = 10 - 3

x = 7

Checking the first equation:

-x - 6y = 5

Substituting x = 7 and y = 3:

-(7) - 6(3) = 5

-7 - 18 = 5

-25 = 5

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the unit rate is 1 inch to (5/3) feet.

The unit rate will be a constant K that relates the two given lengths.

First, we know that the length in the doll house is 6 inches, while the length of the dining table is 10ft.

Then k gives a relation between 1 inch and a number of ft.

Then we have the relation:

6in = 10ft

If we divide both sides by 6, we get:

1 inch = (10/6) ft

1 inch = (5/3) ft.

This means that the unit rate is 1 inch to (5/3) feet.

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Answer:

Step-by-step explanation:

“y” should be the first step of the system.

Answer:

800 books

problem solving steps：

adults:60%

young people:5%

children=100%-60%-5%

=35%

35%=280 books

1%=280÷35

=8

100%=800

so,there are 800 books

The values of the expressions are  7x - 5y = -1, 12z + 2y² = 6 and 2xy + 8z = 4

From the question, we have the following parameters that can be used in our computation:

x = 2, y = 3 and z = -1

Substitute the known values in the given equations, so, we have the following representation

7x - 5y = 7 * 2 - 5 * 3

7x - 5y = -1

12z + 2y² = 12 * -1 + 2 * 3²

12z + 2y² = 6

2xy + 8z = 2 * 2 * 3 + 8 * -1

2xy + 8z = 4

Hence, the expressions have their values to be -1, 6 and 4

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Complete question

Consider the following expressions:

7x-5y=

12z+2y²=

2xy+8z=

Determine the values when x = 2, y = 3 and z = -1

Answer:

17.6

Step-by-step explanation:

19sin(68) = 17.6

The negations of the given statements with the application of De Morgan's law and/or conditional law.

a) ∃x (¬P(x) ∨ ¬R(x))

De Morgan's law:

∃y ∀z(¬P(y) ∧ ¬Q(z))

b) ∃y ∀z(¬P(y) ∧ ¬Q(z))

The double negation:

∃y ¬∃z(P(y) ∨ Q(z))

c) ¬∃x (P(x) ∨ (∀z (¬R(z)) → (∀z ¬Q(z))))

The conditional law:

¬∃x (P(x) ∨ (∀z (¬R(z)) → (∀z ¬Q(z))))

Let's form the negation of the given statements and apply De Morgan's law and/or conditional law, when applicable:

a) ∀x (P(x) ∧ R(x))

The negation of this statement is:

∃x ¬(P(x) ∧ R(x))

Now let's apply De Morgan's law:

∃x (¬P(x) ∨ ¬R(x))

b) ∀y∃z(¬P(y) → Q(z))

The negation of this statement is:

∃y ¬∃z(¬P(y) → Q(z))

Using the conditional law, we can rewrite the negation as:

∃y ¬∃z(¬¬P(y) ∨ Q(z))

c) ∃x (P(x) ∨ (∀z (¬R(z) → ¬Q(z))))

The negation of this statement is:

¬∃x (P(x) ∨ (∀z (¬R(z) → ¬Q(z))))

Using the conditional law, we can rewrite the negation as:

¬∃x (P(x) ∨ (∀z (R(z) ∨ ¬Q(z))))

Applying De Morgan's law:

¬∃x (P(x) ∨ (∀z ¬(¬R(z) ∧ Q(z))))

Simplifying the double negation:

¬∃x (P(x) ∨ (∀z ¬(R(z) ∧ Q(z))))

Using De Morgan's law again:

¬∃x (P(x) ∨ (∀z (¬R(z) ∨ ¬Q(z))))

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Answer:

\(\huge\boxed{\sf d = 14.39\ cm}\)

Step-by-step explanation:

Given:

Circumference = c = 45.1846 cm

π = 3.14

Required:

Diameter = d = ?

Formula:

C = πd

Solution:

Rearrange formula

d = C / π

d = 45.1846 / 3.14

d = 14.39 cm

\(\rule[225]{225}{2}\)

Answer:

Step-by-step explanation:

y-12=-2(x+2)

y=-2x-2+12

y=-2x+8

Answer:

?you surrendering?

i have no idea what your talking about

Answer:

what? explain what the white flag is flag of surrender?

Answer:

First, we rearrange the equation to isolate the y-term on one side:

dy/dx + ytanx = secx

Then, we multiply both sides by the integrating factor, which is e^(∫tanx dx) = e^(ln|secx|) = |secx|: | secx| dy/dx + ysecx tanx = 1

Next, we can write this as the derivative of a product using the product rule: d/dx (y |secx|) = 1

Integrating both sides with respect to x, we get:  y |secx| = x + C

where C is the constant of integration. Solving for y, we have:

y = (x + C)/|secx|

Note that there is a singularity at x = (2n + 1)π/2, where the denominator |secx| is zero. At these points, the solution is not defined

Answer:

The answer is number 2