A 10-speed bike changes gears by moving the chain to different size sprockets on the front and back. The speed at which the bike goes varies directly with the number of revolutions per minute (rpm) you turn the pedals, directly with the number of teeth on the front sprocket, and inversely with the number of teeth on the back sprocket. A standard bike with 70 cm diameter wheels will go about 7.4 kilometers per hour if you pedal 40 rpm in the lowest gear (39-tooth front sprocket, 28-tooth back one). Write an equation expressing km/h in terms of the three independent variables.

Answer:

p = 7

Step-by-step explanation:

(x² + px - 3)(3x - 5)

each term in the second factor is multiplied by each term in the first factor, that is

x²(3x - 5) + px(3x - 5) - 3(3x - 5) ← distribute parenthesis

= 3x³ - 5x² + 3px² - 5px - 9x + 15 ← collect like terms

= 3x³ +x²(3p - 5) - x(5p + 9) + 15

given the coefficient of the x- term is - 44 , then

-(5p + 9) = - 44 ← - (5p + 9) is th coefficient of x in the expansion

- 5p - 9 = - 44 ( add 9 to both sides )

- 5p = - 35 ( divide both sides by - 5 )

p = 7

Answer:

Step-by-step explanation:

What is the equation?

You need to replace all A with 3 and all c with 12. If I had the equation, I'd be glad to help further.

For the given values a=3 and c=12 the required expression is 4a-c=0.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

Given that,

The value of a = 3         (1)

And the value of c = 12       (2)

To determine the expression,

divide equation (1) and equation (2),

a/c = (3/12)

⇒a/c = 1/4

⇒4a=c

⇒4a-c = 0

The required expression is 4a-c=0.

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Answer: 1960

Step-by-step explanation:

Simple percentage. We have 1,400 as a base. To increase by a fraction divide the fraction by 100, add 1 and then multiply by the base. We have 40, and 40/100 = 0.4. We add one to get 1.4 and multiply 1,400 by it to get 1960

This represents adding 17 to the additive inverse of 19. By doing so, we effectively subtract 19 from 17.

To rewrite the subtraction expression "17 - 19" using addition without changing the digits, we can use the concept of additive inverse. The additive inverse of a number is the number that, when added to the original number, yields zero.

In this case, we want to rewrite the expression "17 - 19" using addition. We can think of it as finding the additive inverse of 19 and adding it to 17.

An additive inverse of a number is defined as the value, which on adding with the original number results in zero value. It is the value we add to a number to yield zero. Suppose, a is the original number, then its additive inverse will be minus of a i.e.,-a, such that; a+(-a) = a – a = 0.

The additive inverse of 19 is -19, since 19 + (-19) equals zero. Therefore, we can rewrite the subtraction expression as follows:

17 + (-19)

This represents adding 17 to the additive inverse of 19. By doing so, we effectively subtract 19 from 17.

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The subtraction expression 17 - 19 can be rewritten as an addition expression as 17 + (-19) using the concept of negative numbers.

In mathematics, subtraction can be rewritten as addition by using the concept of negative numbers. The subtraction expression 17 - 19 can be rewritten as an addition expression, without changing the digits, by considering -19 as a negative number to be added. Hence, 17 - 19 can be rewritten as 17 + (-19).

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The surface area of that part of the plane 10x+7y+z=4 that lies inside the elliptic cylinder \(\frac{x^2}{25} +\frac{y^2}{9}\) is 15π√150 and this can be determined by using the given data.

We are given the two equations are:

10x + 7y + z = 4---------(1)

\(\frac{x^2}{25} +\frac{y^2}{9} =1-------------(2)\)

equation(1) is written as

z = 4 - 10x - 7y-----------(3)

The surface area is given by the equation:

A(S) = ∫∫√[(∂f/∂x)² + (∂f/∂y)² + 1]dA------------(4)

compare equation(4) with equation(3) we get the values of ∂f/∂x and

∂f/∂y

∂f/∂x = -10

∂f/∂y = -7

substitute these values in equation(4)

A(S) = ∫∫√[(-10)² + (-7)² + 1]dA

A(S) = ∫∫√[100 + 49 + 1]dA

A(S) = ∫∫√[150]dA

A(S) = √150 ∫∫dA

Where ∫∫dA is the elliptical cylinder

From the general form of an area enclosed by an ellipse with the formula;

comparing x²/a² + y²/b² = 1  with x²/25 + y²/9 = 1, from that we get the values of a and b

a = 5 and b = 3

So, the area of the elliptical cylinder = πab

Thus;

A(S) = √150 × π(5 × 3)

A(S) = 15π√150

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The answers to all the subparts are:

So, (A) To make the same shade of green:

Then, cups of yellow paint when blue paint is just 1 cup:
10/2 = 5/1 = 5

Therefore, 5 cups of yellow paint will be needed with 1 cup of blue paint to make the same green shade.

(B) New pair of numbers to make the same green shade:

Old pair:

Another pair:

The new pair would be:

Therefore, the new pair to make the same shade of green will be 4 cups of blue paint and 20 cups of yellow paint.

(C) Proportional relationship:

Old pair:

Proportional relationship will be:

Therefore, the proportional relationship of the table will be x : 5y.

(D) Constant of proportionality:

According to part (C), the Constant of proportionality will be x : 5y.

Therefore, the answers to all the subparts are:

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Answer:B

Step-by-step explanation:

To find the correct equations for the missing boxes, we need more information about the relationships between the different activities in Jake's Gems. However, based on the given context, we can make some assumptions and suggest potential equations:

Mining and Cutting activities produce diamonds, rubies, and other gems. Let's assume that the production of each gem type is represented by a variable: D (diamonds), R (rubies), and G (other gems).

Maintenance supports the Mining and Cutting activities. We can assume that the maintenance effort required for each activity is represented by the variable M (maintenance).Since the question mentions five missing boxes, we can suggest additional equations to represent relationships between these variables, such as:

Mining + Cutting = D + R + G (the sum of all gem types produced equals the total production from Mining and Cutting activities).

Maintenance = M (maintenance effort required).

The relationships between these variables might include equations like D = f(M), R = g(M), G = h(M), where f, g, and h represent some functions or formulas that relate gem production to maintenance effort.

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An experiment can be assumed to have internal validity if random assignment and experimental control is employed. So the option c is correct.

The degree to which a study reliably establishes a cause-and-effect link is a sign of its internal validity. The procedures used in the study and the level of care done have a significant impact on this type of validity.

Internal validity is essential because, if proven, it enables alternate explanations for a discovery to be disregarded.

An experiment can be assumed to have internal validity if  random assignment and experimental control is employed. So the option c is correct.

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The right question is:

An experiment can be assumed to have internal validity if:

A. the dependent variable is valid.

B. there is a strong manipulation of the independent variable.

C. random assignment and experimental control is employed.

D. confounding variables are present.

The moment of inertia about the z-axis of a solid ball bounded by the sphere r = a with variable density proportional to the radius is:

I = (3/5) k a^5.

To find the moment of inertia about the z-axis of a solid ball bounded by the sphere r = a with variable density, we can use the formula:

I = ∫∫∫ r^2 ρ(r) sin^2θ dV

Where r is the distance from the z-axis, ρ(r) is the density at that distance, θ is the angle between the radius vector and the z-axis, and dV is the differential volume element.

Since the ball is symmetric about the z-axis, we can simplify this integral by only considering the volume element in the x-y plane. We can express this volume element as:

dV = r sinθ dr dθ dz

where r ranges from 0 to a, θ ranges from 0 to π, and z ranges from -√(a^2 - r^2) to √(a^2 - r^2).

Thus, the moment of inertia about the z-axis becomes:

I = ∫∫∫ r^2 ρ(r) sin^3θ dr dθ dz

We can further simplify this by assuming that the density is proportional to the radius. That is, ρ(r) = k r, where k is a constant. Therefore, the moment of inertia becomes:

I = k ∫∫∫ r^4 sin^3θ dr dθ dz

Integrating with respect to r first, we get:

I = k ∫∫ (1/5) a^5 sin^3θ dθ dz

Integrating with respect to θ next, we get:

I = (2/15) k a^5 ∫ sin^3θ dθ

Using the half-angle formula for sin^3θ, we get:

I = (2/15) k a^5 [(3/4)θ - (1/4)sinθcosθ] from 0 to π

Simplifying this expression, we get:

I = (2/15) k a^5 [(3/4)π]

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Answer:

200.96cm^2

Step-by-step explanation:

the circle's diameter is 16cm --> the radius is 8cm

the area of the circle is 8^2 x 3.14 = 200.96 cm^2

The height of the tree is 16 feet if it casts a 24 feet shadow at the same time of the day when 4 feet wall casts a 6-foot shadow.

The shadows at the same time of the day can be compared for the garden wall and a tree as follows;

tree shadow / tree height = wall shadow / wall height

As the height of the wall is given to be 4 feet and it has a 6-foot shadow, and the tree casts a 24-foot shadow, substituting these values in the equation;

24 / x = 6 / 4

Here x represents the height of the tree

Solving for x;

24 / x = 1.5

24 = 1.5 x

x = 24 / 1.5

x = 16

Therefore the height of the tree is calculated to be 16 feet.

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The height of the tree is 16 feet when it casts a 24 feet shadow at the same time of the day when 4 feet wall casts a 6-foot shadow.

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

The shadows at the same time of the day can be compared for the garden wall and a tree is given by;

tree shadow / tree height = wall shadow / wall height

Since we know that the height of the wall is given to be 4 feet and it has a 6-foot shadow, and the tree casts a 24-foot shadow, substituting these values in the equation;

24 / x = 6 / 4

Here x represents the height of the tree

Solving for x,

24 / x = 1.5

24 = 1.5 x

x = 24 / 1.5

x = 16

Therefore, the height of the tree is calculated to be 16 feet.

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Answer:

350 hours

Step-by-step explanation:

Answer:

1. the company C used 10 drivers2.      6 + 7 + 8 + 9 + 10 + 10 + 10 + 12 + 14 + 14 = 100/10. The Mean = 10  (6- 10) + (7- 10) + (8- 10) + (9- 10) + (10- 10) + (10- 10) + (10- 10) + (12- 10) + (14- 10)4 + 3 + 2 + 1 + 0 + 0 + 0 + 2 + 4  = 16/10 = 1 6/103. The groups that had the most deliveries where group A and B4. So if there are 6 deliveries of group A and 14 deliveries from group B i think the MAD would be 4

Step-by-step explanation:

Answer:

2.44

Step-by-step explanation:

Answer: ß

Step-by-step explanation:

The cost for a year is cheaper in the Gym A than Gym B. The value of k for the cheaper membership would be; $10.

An equation is an expression that shows the relationship between two or more numbers and variables. A linear equation is an equation that increases at a constant rate.

An equation in the form y = kx is called a linear equation.

In the equation of form y = kx

y = dependent variable which is the total cost

x = number of months

k = constant of proportion / cost per month

Thus k = y/x

The Cost per month at Gym A = $50 / 5 = $10

The Cost per month at Gym B = $40 / 3 = $13.33

The Membership cost at Gym A for a year = $10 x 12 = $120

The Membership cost at Gym B for a year = $13.33 x 12 = $160

Hence, The cost for a year is cheaper in the Gym A than Gym B. The value of k for the cheaper membership would be; $10.

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_____________________________________

AnswerS :

1. Tan Z = p / b = 21/28

2. Cos C = b / h = 16 / 34 = 8/17

3. Sin C = p/ h = 28/35

4. Tan X = p / b = 32/24 = 16 / 12

5. cos A = b / h = 30/34 = 15 / 17

6. Sin A = p / h = 32/40 = 16/20

7. sin Z = p / h = 24 / 40 = 12 / 20

8. sin C = p / h = 14 / 50 = 7 / 25

RemembeR :

- HappY LearninG (≧▽≦)

__________________________________

SOHCAHTOA is an acronym for the formula

Sin= Opposite/hypothenuse

cos= adjusent/ hypothenuse

tan=opposite/adjusent

After u found the ratio u use inverse- put it in ur calculator then u get the answer

i answered one question- so u see how to solve

In the trigonometric function, f(x) = 7cos[2π(x + 9)/7] + 1, the direction and how many units is is shifted vertically is 1 unit up

A trigonometric function is an equation containing a trigonometric ratio

Given the trigonometric function f(x) = 7cos[2π(x + 9)/7] + 1, we want to compare it with the trigonometric equation f(x) = acos[2π(x + c)/b] + d, to find the vertical shift of the graph. We proceed as follows

Since we know that the general equation of a trigonometric function is  f(x) = acos[2π(x + c)/b] + d where

Comaring both equations, we have that

So, we see that since d = + 1, we see that the function f(x) = 7cos[2π(x + 9)/7] + 1 is shifted vertically upwards by 1 unit.

So, the direction and how many units is is shifted vertically is 1 unit up

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He spent $200 on 0 tickets for children, 10 tickets for adults, and 20 tickets for seniors.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here,

Total number of tickets brought=30

Total amount paid=$200

Cost of kid ticket=$3.5

Cost of adult ticket=$8

Cost of senior ticket=$6

Let x, y, z be the number of tickets brought for kid, adult, senior.

x+y+z=30

3.5x+8y+6z=200

2y=x+z

x+y+z=30

3y=30

y=10

x+z=20

z=20-x

3.5x+80+6(20-x)=200

3.5x+80+120-6x=200

2.5x=0

x=0

z=20

He bought 0 tickets for kid, 10 tickets for adult and 20 tickets for senior with an amount of $200.

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Answer:

a = 50

50*2=100

Step-by-step explanation:

Answer:

13 Rungs

Step-by-step explanation:

According to the Question,

The plan recommends that the rungs of the ladder be spaced at 8-inch intervals.

Thus, the rungs Cover on 108 -(6+6) = 96 inches with 8-inch gaping between each rung.

Based on the information given, it should be noted that the equation that will given the value of 44 include n + 38, 2n + 32, etc.

It should be noted that your information is incomplete. Therefore, an overview of an equation will be given.

To solve this question, you simply have to replace n by 6. For example, let's say the equation given is:

= n + 38

= 6 + 38

= 44.

Also, 2n + 32

= 2(6) + 32

= 12 + 32

= 44

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We have to find out such expressions for the value of n which equals to 6 i.e (n = 6) and their sum tends to 44. So let's basically consider or form any expression of your choice it may be of multiplication, division, Subtraction it either addition. For example, 3n + 26, 5n + 14 gives their final value equal to = 4.

#1) 3n + 26

=> 3 × 6 + 26

=> 18 + 26

=> 44

#2) 5n + 14

=> 5 × 6 + 14

=> 30 + 14

=> 44

#3) 8n - 4

=> 8 × 6 - 4

=> 48 - 4

=> 44

#4) 7n + 2

=> 7 × 6 + 2

=> 42 + 2

=> 44

#5) 10n - 16

=> 10 × 6 - 16

=> 60 - 16

=> 44

Answer:

C

Step-by-step explanation:

Answer:

\(\sf M=\left(-\dfrac{1}{2},0\right)\)

Step-by-step explanation:

Let (x₁, y₁) = Point A = (-2, 1)

Let (x₂, y₂) = Point B = (1, -1)

\(\sf Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)\)

\(\implies \sf Midpoint=\left(\dfrac{-2+1}{2},\dfrac{1+(-1)}{2}\right)\)

\(\implies \sf Midpoint=\left(-\dfrac{1}{2},0\right)\)

Answer:

77

Step-by-step explanation:

To find the median marks, we first need to arrange the scores in ascending order:

55, 60, 65, 77, 80, 82, 85

Since there are 8 students, the middle value will be the 4th value in the ordered set. In this case, the median marks will be 77

Therefore, the median marks for the 8 students in maths is 77.

The importance of group discussion, to determine if a potential employee is qualified for the position, in order to determine if the candidate is a strong team player.

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The maximum value of f(x,y) = 43 - x^2 - y^2 on the line x + 6y = 37 is 6.

To find the maximum value of f(x,y) = 43 - x^2 - y^2 on the line x + 6y = 37, we need to use the equation of the line to eliminate one of the variables in the function.

First, we can solve the equation of the line for x: x = 37 - 6y

Then, we can substitute this expression for x into the function:

f(x,y) = 43 - (37 - 6y)^2 - y^2

Next, we can expand the squared term and simplify:

f(x,y) = 43 - (1369 - 444y + 36y^2) - y^2

f(x,y) = -1326 + 444y - 37y^2

Now, we can take the derivative of this function with respect to y to find the critical points:

f'(y) = 444 - 74y

Setting the derivative equal to zero and solving for y gives us:

444 - 74y = 0

74y = 444

y = 6

Substituting this value of y back into the equation of the line gives us:

x = 37 - 6(6) = 1

So the maximum value of the function occurs at the point (1,6). Plugging these values back into the original function gives us:

f(1,6) = 43 - 1^2 - 6^2 = 43 - 1 - 36 = 6

Therefore, the maximum value of f(x,y) = 43 - x^2 - y^2 on the line x + 6y = 37 is 6.

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The amount of money available for the project after 1 year will be $262,407.25.

We can use the formula for compound interest to find the amount of money that will be available for the project:

A = P(1 + r/n)^(na)

where A is the amount of money, P is the principal (initial investment), r is the annual interest rate, n is the number of times the interest is compounded per year, and a is the time in years.

In this case, P = $250,000, r = 4.5% = 0.045 (as a decimal), n = 12 (since the interest is compounded monthly), and t = 1 (since we want to find the amount after 1 year).

Plugging in these values, we get:

A = $250,000(1 + 0.045/12)¹² ˣ¹

= $262,407.25

As a result, $262,407.25 will be the amount of money left over for the project after a year.

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