If 7/2 litre petrol cost 2163/8 find the cost of 4 litre petrol

If MSwithin is smaller than MSbetween, then increasing MSwithin and/or decreasing MSbetween will lead to an increase in the F statistic.

The F statistic is calculated by dividing the variance between groups (MSbetween) by the variance within groups (MSwithin). Therefore, to increase the value of the F statistic, either the numerator (MSbetween) needs to increase, or the denominator (MSwithin) needs to decrease.

So, the answer is:

a. MSwithin > MSbetween

If the variance within groups (MSwithin) is reduced or the variance between groups (MSbetween) is increased, the F statistic will increase. Therefore, if MSwithin is smaller than MSbetween, then increasing MSwithin and/or decreasing MSbetween will lead to an increase in the F statistic.

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Answer:

1. (5·sin(A) - 3·cos(A)/(4·cos(A) + 5·sin(A))  = 1/8

2. θ = 30°

3. tan(θ) - cot(θ) = (2·sin²(θ) -1)/((cos(θ)×sin(θ))

from tan(θ) - 1/tan(θ) = sin(θ)/cos(θ) - cos(θ)/sin(θ) and sin²(θ) +  cos²(θ) = 1

4. tan10°·tan15°·tan75°·tan80°= 1 from;

sin(α)·sin(β) = 1/2[cos(α - β) - cos(α + β)]

cos(α)·cos(β) = 1/2[cos(α - β) + cos(α + β)]

5. x² + y² = a² + b² where x = a·cosθ - b·sinθ and y = a·sinθ + b·cosθ from;

cos²θ + sin²θ = 1

Step-by-step explanation:

1. Here we have 5·tan(A) = 5·sin(A)/cos(A) = 4

∴ 5·sin(A) = 4·cos(A)

Hence to find the value of (5·sin(A) - 3·cos(A)/(4·cos(A) + 5·sin(A)) we have;

Substituting the value for 5·sin(A) = 4·cos(A) into the above equation in both the numerator and denominator we have;

(4·cos(A) - 3·cos(A)/(4·cos(A) + 4·cos(A)) = cos(A)/(8·cos(A)) = 1/8

Therefore, (5·sin(A) - 3·cos(A)/(4·cos(A) + 5·sin(A)) = 1/8

2. For the equation as follows, we have

\(\frac{sin \theta}{1 + cos \theta} + \frac{1 + cos \theta}{sin \theta} = 4\) this gives

\(\frac{2sin (\theta/2) cos (\theta/2) }{2 cos^2 (\theta/2)} + \frac{2 cos^2 (\theta/2)}{2sin (\theta/2) cos (\theta/2) } = 4\)

\(tan\frac{\theta}{2} + \frac{1}{tan\frac{\theta}{2} } = 4\)

\(tan^2\frac{\theta}{2} + 1 = 4\times tan\frac{\theta}{2}\)

\(tan^2\frac{\theta}{2} - 4\cdot tan\frac{\theta}{2} + 1 = 0\)

We place;

\(tan\frac{\theta}{2} = x\)

∴ x² - 4·x + 1 = 0

Factorizing we have

(x - (2 - √3))·(x - (2 + √3))

Therefore, tan(θ/2) = (2 - √3) or (2 + √3)

Solving, we have;

θ/2 = tan⁻¹(2 - √3) or tan⁻¹(2 + √3)

Which gives, θ/2 = 15° or 75°

Hence, θ = 30° or 150°

Since 0° < θ < 90°, therefore, θ = 30°

3. We have tan(θ) - cot(θ) = tan(θ) - 1/tan(θ)

Hence, tan(θ) - 1/tan(θ) = sin(θ)/cos(θ) - cos(θ)/sin(θ)

∴  tan(θ) - 1/tan(θ) = (sin²(θ) -  cos²(θ))/(cos(θ)×sin(θ))...........(1)

From sin²(θ) +  cos²(θ) = 1, we have;

cos²(θ) = 1 - sin²(θ), substituting the value of sin²(θ) in the equation (1) above, we have;

(sin²(θ) -  (1 - sin²(θ)))/(cos(θ)×sin(θ)) = (2·sin²(θ) -1)/((cos(θ)×sin(θ))

Therefore;

tan(θ) - cot(θ) = (2·sin²(θ) -1)/((cos(θ)×sin(θ))

4. tan10°·tan15°·tan75°·tan80°= 1

Here we have since;

sin(α)·sin(β) = 1/2[cos(α - β) - cos(α + β)]

cos(α)·cos(β) = 1/2[cos(α - β) + cos(α + β)]

Then;

tan 10°·tan15°·tan75°·tan80° = tan 10°·tan80°·tan15°·tan75°

tan 10°·tan80°·tan15°·tan75° = \(\frac{sin(10^{\circ})}{cos(10^{\circ})} \times \frac{sin(80^{\circ})}{cos(80^{\circ})} \times \frac{sin(15^{\circ})}{cos(15^{\circ})} \times \frac{sin(75^{\circ})}{cos(75^{\circ})}\)

Which gives;

\(\frac{sin(10^{\circ}) \cdot sin(80^{\circ})}{cos(10^{\circ})\cdot cos(80^{\circ})} \times \frac{sin(15^{\circ}) \cdot sin(75^{\circ})}{cos(15^{\circ})\cdot cos(75^{\circ})}\)

\(=\frac{1/2[cos(80 - 10) - cos(80 + 10)]}{1/2[cos(80 - 10) + cos(80 + 10)]} \times \frac{1/2[cos(75 - 15) - cos(75 + 15)]}{1/2[cos(75 - 15) + cos(75 + 15)]}\)

\(=\frac{1/2[cos(70) - cos(90)]}{1/2[cos(70) + cos(90)]} \times \frac{1/2[cos(60) - cos(90)]}{1/2[cos(60) + cos(90)]}\)

\(=\frac{[cos(70)]}{[cos(70) ]} \times \frac{[cos(60)]}{[cos(60) ]} =1\)

5. If x = a·cosθ - b·sinθ and y = a·sinθ + b·cosθ

∴ x² + y² = (a·cosθ - b·sinθ)² + (a·sinθ + b·cosθ)²

= a²·cos²θ - 2·a·cosθ·b·sinθ +b²·sin²θ + a²·sin²θ + 2·a·sinθ·b·cosθ + b²·cos²θ

= a²·cos²θ + b²·sin²θ + a²·sin²θ + b²·cos²θ

= a²·cos²θ + b²·cos²θ + b²·sin²θ + a²·sin²θ

= (a² + b²)·cos²θ + (a² + b²)·sin²θ

= (a² + b²)·(cos²θ + sin²θ) since cos²θ + sin²θ = 1, we have

= (a² + b²)×1 = a² + b²

Answer:

74.25

Step-by-step explanation:

Answer:

nhgfdsazxcvb

Step-by-step explanation:

hfdcvbn

Answer:

V = hpi(r)^2

 =  20(3.14)(17)^2 = 18,149.20 cubic mm

More accurately,

V = 20(3.14159)(17)^2 = 18158.39 mm^3

Step-by-step explanation:

It will take 10 classes for YOGA FOR US & STRETCH LAND to have the same amount of money spent on yoga classes.

For Yoga For Us after 10 classes . You would have spent 50 dollars for the classes,plus our $30 fee is (50+30) which is $80

For Stretch Land after 10 classes.  You would have spent 20 dollars for the classes,plus our $60 fee is (60+20) which is $80.

Each yoga studio will have gathered $80 after 10 classes.

Hope this helps <3 & don't forget to drink water!!

Answer:

d) 2 tons plus 1,200 pounds.

Step-by-step explanation:

1 ton = 2000

2000 + 2000 = 4000

5200 - 4000

= 1200

hence, the answer is 2 tons plus 1,200 pounds.

hope this helps and is right :)

Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

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he required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

Let’s assume the general solution of the given differential equation is,

y=e^{mx}

By taking the derivative of this equation, we get

\(\frac{dy}{dx} = me^{mx}\\\frac{d^2y}{dx^2} = m^2e^{mx}\\\frac{d^3y}{dx^3} = m^3e^{mx}\\\frac{d^4y}{dx^4} = m^4e^{mx}\\\)

Now substitute these values in the given differential equation.

\(\frac{d^4y}{dx^4}-2\frac{d^2y}{dx^2}-8y\\=0m^4e^{mx}-2m^2e^{mx}-8e^{mx}\\=0e^{mx}(m^4-2m^2-8)=0\)

Therefore, \(m^4-2m^2-8=0\)

\((m^2-4)(m^2+2)=0\)

Therefore, the roots are, \(m = ±\sqrt{2} and m=±2\)

By applying the formula for the general solution of a differential equation, we get

General solution is, \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

Hence, the required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

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If the volunteer enrolls 80 new members, there is only a 0.029% chance that she can achieve her goal of having an average donation of at least $100 from those members.

At the museum, one of our phone volunteers has set a personal goal of getting an average donation of at least $100 from the new members she enrolls during the membership drive.

If she enrolls 80 new members, which can be considered a random sample of all the museum's members, what is the probability that she can achieve her goal?

To answer this question, we can use the binomial probability formula. The formula takes the probability of success (p) multiplied by the number of trials (n) to calculate the probability of success, given the number of successes (x).

In this case, the probability of success is 0.8 and the number of trials is 80.

The probability of success given the number of successes (x) is 0.029.

This means that if the volunteer enrolls 80 new members, there is only a 0.029% chance that she can achieve her goal of having an average donation of at least $100 from those members.

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Answer:

a.) Money left = $1

b) No

Step-by-step explanation:

Given - You have $15. It costs $ to ride each ride once,

To find - a. How much money do you have left if you ride each ride once?

              b. Do you have enough money to ride each ride twice? Explain.

Proof -

As it is not given in the question that, how much cost to ride each ride once.

Let us assume that,

The cost for each ride = $2

Total rides  = 7

Now,

Total money we have = $15

a.)

Given, cost for 1 ride = $2

⇒ Cost for 7 rides = 7×$2 = $14

∴ Money left =  $15 - $14 = $1

b.)

Given,

Cost for 1 ride = $2

Cost of 1 ride if we ride twice = 2×$2 = $4

Cost of 7 rides if we ride twice = 7×$4 = $28

As $28 > $15

So, we cannot ride each ride twice.

Answer:

Dis’ old bet you got help lolllllllllllllll *sings in gay ferret*

I might be better on my own

I hate you blowing up my phone

I wish I never met yo' a*s

Sometimes it be like that

But I'm not myself the nights you're gone

There ain't no way I'm moving on

I'm not afraid to need you bad

Sometimes it be like that

Explanation

the slope of a line is given by:

so

Step 1

let

P1(-18,12)

P2(6,4)

now, replace in the formula

therefore, the slope is

I hope this helps you

20 girls and 30 boys

A branch of mathematics that deals usually with the nonnegative real numbers including sometimes the transfinite cardinals and with the application of the operations of addition, subtraction, multiplication, and division to them

To make the new situation:

Suppose A classroom has 50 people.

The ratio of girls to boys is 2:3, so in other words, we need to find out how many boys and girls there are, and there are 2 girls for every three boys, So ,how many boys and girls are there?

The answer would be :

Let the two parts in which we divide 50 be 2x and 3x respectively

2x+3x=50

5x=50

x= \(\frac{50}{5}\)

x=10

Here,

2x= 2×10=20

3x =3*10=30

20 girls and 30 boys.

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Answer:-9

Step-by-step explanation:

Mode

2 x 5 = 10

6 x 5 = 30

5 x 5 = 25

3 x 5 = 15

7 x 5 = 35

8 x 5 = 40

9 x 5 = 45

2 x 5 = 10

4 x 5 = 20

7 x 5 = 35

4 x 5 = 20

7 x 5 = 35

The mode is 35 because it is repeated 3 times.

Answer:

32 inches

Step-by-step explanation:

1 trucks= 8 inches

4 truck= (4×8) 32 inches

The expression √180 * 2√30 is equivalent to the expression 60√6

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

The square root is a factor of a number that, when multiplied by itself, gives the original number.

Given the expression √180 * 2√30

Collecting like terms give:

= 2√(180 * 30)

Simplifying:

= 60√6

The expression √180 * 2√30 is equivalent to the expression 60√6

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The correct simplified expression is \(\rm 28x^3-33x^2-33x+18\).

Given

Polynomial; \(\rm (7x - 3)(4x^2 -3x - 6)\)

Multiplication is the process of calculating the product of two or more numbers. The multiplication of numbers say, ‘a’ and ‘b’, is stated as ‘a’ multiplied by ‘b’.

Then,

The correct simplification of the expression is;

\(\rm \rm (7x - 3)\times (4x^2 -3x - 6)\\\\7x(4x^2 -3x - 6)-3(4x^2 -3x - 6)\\\\ 28x^3-21x^2-42x-12x^2+9x+18\\\\28x^3-33x^2-33x+18\)

Hence, the correct simplified expression is \(\rm 28x^3-33x^2-33x+18\).

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Answer

The answer is climate

Answer:

It would most likely be climate because it sounds like it has something to do with the weather which it does.

Step-by-step explanation:

Determine the conditions for when a function has an inverse. Use the horizontal line test to recognize when a function is one-to-one. Find the inverse of a given function.

It is simple to establish whether the inverse of a function is also a function using the horizontal line test.

Because it fails the vertical line test, a function's inverse might not actually be a function.

Graph of the line

f\left( x \right) = - x + 2

f(x)=−x+2.

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Answer: 476 ft³

Step-by-step explanation:

Volume = width x hight x length

        V = 4 ft x 17 ft x 7 ft

        v  = 476 ft³

The evaluated probability for chances of  randomly selecting an employee who will  have a starting salary of at least $31,000 is 11.51%. Here, we have to depend on the principles of standard normal distribution to find the percentage of probability,


Let us take  z-score for a starting salary of $31,000 as

z = (31000 - 25000) / 5000
= 1.2

Now after using a standard normal distribution table , the probability of a z-score of 1.2 or greater is approximately 0.1151
Converting it into percentage
0.1151 x 100
= 11.51%
The evaluated probability for chances of  randomly selecting an employee who will  have a starting salary of at least $31,000 is 11.51%.

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Answer:

85

Step-by-step explanation:

115-30 = 85

ur looking for ILM which bisects KLM since KLM is 115 and the other piece that makes up KLM (KLI) is 30 all u have to do is subtract

12 collect comics and drawing

5 collect comics

7 drawing

x

30=12+75+x

x=6

Here any of the data are counting the same people because each one has a different description, so you can solve if like this

Answer:

Step-by-step explanation:

If f and g are inverse functions, then f (x) = y if and only if g (y) = x In trigonometry, the inverse sine function is used to find the measure of angle for which sine function generated the value. For example, sin-1(1) = sin-1(sin 90) = 90 degrees.

Answer:

\(\boxed{x = 30}\)

Step-by-step explanation:

x + 2x + 3x = 180 (Interior angles of a triangle add up to 180 degrees)

=> 6x = 180

Dividing both sides by 6

=> x = 180 / 6

=> x = 30

Answer:

x= 30

Step-by-step explanation:

3x + 2x + x = 180

6x= 180

x = 180/6

:• x = 30