MATHEMATICS
COLLEGE

Answer: Archimides' Principle states that any body immersed in a fluid receives a vertical pushing force upwards equal to the weight of the fluid displaced by the body.

Then, there are two forces acting on the body, its weight (vertical downwards) and the bouyancy (vertical push upwards).

There are three possibilities:

1) The buoyancy is greater than the weight of the body => the body will float (move upward, toward the surface if it is a liquid)

2) The buoyancy is equal than the weight of the boy => the body wll remain quite (also floating but not moving either upwards or downwards)

3) The buoyancy is less than the weight of the body => the body will sinkl.

So, a body will float on water when the buoyancy from the liquid is overcomes its weight.

Buoyancy is related with density because:

buoyancy = weight of the liquid displaced = mass o fliquid * g = density of the liquid * Volume of the liquid * g

Weight of the body = mass of the body * g = density of the body * Volumen of the body * g

When the body is completely immersed in the liquid its volume es equal to the volume of the liquid displaced =>

So we can compare the weight of the body and the buouancy force

density of liquid * volume of liquid * g vs density of body * volume of liquid * g

where the difference is the densities of liquid and body.

That is why it is deduced that the bodies float when their densities are smaller than the densities of the liquid where they are.

Then, there are two forces acting on the body, its weight (vertical downwards) and the bouyancy (vertical push upwards).

There are three possibilities:

1) The buoyancy is greater than the weight of the body => the body will float (move upward, toward the surface if it is a liquid)

2) The buoyancy is equal than the weight of the boy => the body wll remain quite (also floating but not moving either upwards or downwards)

3) The buoyancy is less than the weight of the body => the body will sinkl.

So, a body will float on water when the buoyancy from the liquid is overcomes its weight.

Buoyancy is related with density because:

buoyancy = weight of the liquid displaced = mass o fliquid * g = density of the liquid * Volume of the liquid * g

Weight of the body = mass of the body * g = density of the body * Volumen of the body * g

When the body is completely immersed in the liquid its volume es equal to the volume of the liquid displaced =>

So we can compare the weight of the body and the buouancy force

density of liquid * volume of liquid * g vs density of body * volume of liquid * g

where the difference is the densities of liquid and body.

That is why it is deduced that the bodies float when their densities are smaller than the densities of the liquid where they are.

Answer:

Answer:

If the weight is equal to the buoyant force, it will float. The same is true for if the weight is less than the buoyant force. However, if the weight is greater than the buoyant force, it will sink.

MIDDLE SCHOOL

Which of these represents the factorization of x4−256 ? A

(x−4)2(x+4)2

B

(x−4i)2(x+4i)2

C

(x−4)2(x+4i)2

D

(x−4)(x+4)(x−4i)(x+4i)

Answer:

(x+4)(x-4)(x+4i)(x-4i) (answer D)

Step-by-step explanation:

We can re-write the original binomial as a difference of squares noticing that and that

Then we have:

Then we can factor this out using the difference of squares factor form:

Now, , is itself a difference of squares which we can factor out further:

And we can also solve for the binomial: :

then we can write

Therefore, the final factor form of the original binomial is the product of all factors we found:

HIGH SCHOOL

Mac deposited $918.78 in a savings account that earns 2.1% simple interest. What is Mac's account balance after ten years?

MIDDLE SCHOOL

To make 1 1/2 dozen muffins a recipe uses 3 1/2 cups of flour how many cups of flour are needed for every dozen muffins made?

3 1/2 divided by 3= 1.1666

so 1/2 dozen muffins uses 1.1666 cups of flour.

1.1666 x 2= 2.3332

it takes 2.3332 cups of flour to make a dozen muffins

2.3332 = 2 1/3 cups of flour

2 1/3 cups of flour are needed for every dozen muffins made

so 1/2 dozen muffins uses 1.1666 cups of flour.

1.1666 x 2= 2.3332

it takes 2.3332 cups of flour to make a dozen muffins

2.3332 = 2 1/3 cups of flour

2 1/3 cups of flour are needed for every dozen muffins made

MIDDLE SCHOOL

What value of x makes f(x) = -2 if f(x) = 3.4x - 7.1 A. -13.9 B. -1.5

C. 1.5 D. 2.8

Option C

For x = 1.5 we get f(x) = -2

Solution:

Given function is:

We have to find the value of "x" so that f(x) = -2

Substitute f(x) = -2 in given function

Solve for "x" by moving the constants to one side and variables to other side

For x = 1.5 we get f(x) = -2

We can verify by substituting x = 1.5 in given function

Thus for x = 1.5 we get f(x) = -2

MIDDLE SCHOOL

A catalog company charges a shipping fee of $0.25 for each pound an order weighs. A $3 handling fee is also charged. Write an equation that represents the total fees for an order weighing p pounds.

Answer:

We get the following equation,

s =

[where s is in $ and p is in pound]

Step-by-step explanation:

The catalog company charges a shipping fee of $ 0.25 for each pound an order weighs. A $3 handling fee is also charged.

Let, s be the total fees for an order weighing p pounds.

Then, we get the following equation,

s =

[where s is in $ and p is in pound]

MIDDLE SCHOOL

Write the standard form for the scientific notation. please help fast!!! 2.32 x 10^3

4.2 x 10 ^4

4.2 x 10^(-2) 30 points

Multiplication by 10ⁿ → move decimal n places to the right.

Multiplication by 10⁻ⁿ → move decimal n places to the left.

For n ∈ N

MIDDLE SCHOOL

Which expression is equivalent to 60 – 3y - 9? 3(17 - y)

3(20 - y) - 3

17(3 - y)

S

pani

20(3 – 3y) - 9

An expression is defined as a set of numbers, variables, and mathematical operations. The expression that is equivalent to 60-3y-9 is 3(17-y).

What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The expression that is equivalent to 60-3y-9 can be written as,

Thus, the expression that is equivalent to 60-3y-9 is 3(17-y).

Learn more about Expression:

brainly.com/question/13947055

Answer:

3(17-y)

Step-by-step explanation:

If you distribute the 3 into the equation it would be 51 - 3y and if you use the commutative property it would be 60-9-3y and then if you solve would be 51-3y.

MIDDLE SCHOOL

How many solutions can be found for the linear equation? 6(x + 2) 2 = 12x 4 + 6 A) no solution Eliminate B) one solution C) two solutions D) infinitely many solutions

Answer:

Option D - Infinitely many solutions

Step-by-step explanation:

Given : Linear equation

To find : How many solutions can be found for the linear equation?

Solution :

Linear equation

Solve the linear equation,

Which means the equation has infinitely many solutions.

Therefore, Option D is correct.

I am pretty sure there is only one solution because when I solve it I got 8.

COLLEGE

The number x of bottles of garden plant fungicide sold by a garden center each day was recorded with the following results: x 0 1 2 3 4 5 6 7

P(x) .074 .135 .141 .150 .143 .134 .122 .101

The probability that at most two bottles will be sold on a randomly selected day is about:

.426 i am pretty sure