Two tons of water is pumped into a tank 15 ft. high in 5 minutes. Determine the power output of the pump.

Answer:

I believe the answer is 3.    : )

Final Answer:

The volume of the box that will hold nine 9.425 cm³ cylindrical containers, each measuring 3 centimeters long, is approximately 108 cm³.

Explanation:

First, we need to find the radius of each cylindrical container since we have its volume and the length. The volume V of a cylinder is given by the formula:
[tex]\[ V = \pi r^2 h \][/tex]
where r is the radius and h is the height (or length) of the cylinder. We are given:
[tex]\[ V = 9.425 \text{ cm}^3 \\\\\[ h = 3 \text{ cm} \][/tex]

We need to solve for r:

[tex]\[ 9.425 = \pi r^2 (3) \\\\\[ r^2 = \frac{9.425}{3\pi} \\\\\[ r^2 = \frac{9.425}{3 \times 3.14159} \\\\\[ r^2 = \frac{9.425}{9.42477} \\\\\[ r^2 \approx 1 \\\\\[ r \approx 1 \text{ cm} \][/tex]

Now we know the radius of one cylindrical container is approximately 1 cm. Although this rounding might lead to a slightly inaccurate result, we'll proceed with this approximation for simplicity's sake.

Since each container is a cylinder with a radius of 1 cm, the diameter of each container is [tex]\( 2 \times 1 = 2 \)[/tex] cm. If we wanted to pack these containers without any wasted space in one layer, we would arrange them in a 3 by 3 grid, given there are 9 containers. The length and the width of the box would then each be 3 times the diameter of one container.

Hence:
Length of box = Width of box = [tex]\( 3 \times 2 \)[/tex] cm = 6 cm.
The height of the box would be equal to the length of one of the containers, which is 3 cm.

Now we can find the volume of the box:
Volume of box [tex]\( V_{\text{box}} \) = Length \( \times \) Width \( \times \) Height[/tex]
[tex]\[ V_{\text{box}} = 6 \text{ cm} \times 6 \text{ cm} \times 3 \text{ cm} \\\\\[ V_{\text{box}} = 36 \text{ cm}^2 \times 3 \text{ cm} \\\\\[ V_{\text{box}} = 108 \text{ cm}^3 \][/tex]
Rounding to the nearest whole number, the volume of the box that will hold nine 9.425 cm³ cylindrical containers, each measuring 3 centimeters long, is approximately 108 cm³.

Answer:

THE NUMERATOR OF THE RATIONAL EXPRESSION REPRESENTS THE  TOTAL COST OF GASOLINE PURCHASED.

THE DENOMINATOR OF THE RATIONAL EXPRESSION REPRESENTS THE TOTAL GALLONS OF GASOLINE PURCHASED

The complete problem is:

Annabella spends $2.25 per gallon on gas at the gas station. After driving a certain distance, she stops at a second gas station and spends $2.15 per gallon on gasoline.

Annabella can express her average cost per gallon of gasoline as [tex]y = \frac{(2.25x + 2.15(x+5))}{2x+5}[/tex]

What is the meaning of the parts of this rational expression in the context of the situation?

THE NUMERATOR OF THE RATIONAL EXPRESSION REPRESENTS THE __________.

(select one)

1. total cost of the gasoline purchased

2. total number of gallons of gasoline purchased

3. cost per gallon of gasoline

THE DENOMINATOR OF THE RATIONAL EXPRESSION REPRESENTS THE ________.

1. total cost of the gasoline purchased

2. total number of gallons of gasoline purchased

3. cost per gallon of gasoline

So, in this context and based on the given data, the numerator of the expression is referring to the total cost of gasoline purchased, and the denominator is expressing the total gallons of gasoline purchased.

You can deduct this because, the numerator contains the amounts of costs per gallon, being x gallons. On the other hand, you can see in the denominator that there's no costs multiplying the variable, it's just a quantity which refers to the amount of gasoline, not the cost.

Final answer:

The properties of real numbers include closure, commutative, associative, identity, and inverse properties. These properties govern how real numbers behave in addition and multiplication operations.

Explanation:

The properties of real numbers refer to the characteristics and behavior of numbers that belong to the real number system. The real number system includes all rational and irrational numbers, such as whole numbers, integers, fractions, decimals, and square roots.

The properties of real numbers include:

These properties of real numbers are fundamental in algebraic operations and calculations. They provide a basis for solving equations, simplifying expressions, and working with mathematical concepts.

Answer:

4)6,246

Step-by-step explanation:

First we will find the value of r.

The formula for circumference is C = 2πr:

280 = 2(3.14)r

280 = 6.28r

Divide each side by 6.28:

280/6.28 = 6.28r/6.28

44.6 ≈ r

The formula for the area of a circle is

A = πr²

Using our value for r, we have

A = 3.14(44.6)² = 6245.9624 ≈ 6246

Area of circle is,

⇒ 11493.2 cm²

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

Circumference of circle = 280 cm.

Now, We know that;

Circumference = 2πr

Hence, We get;

⇒2πr = 280

⇒ 2 × 3.14 r = 380

⇒ 6.28 r = 380

⇒ r = 380 / 6.28

⇒ r = 60.5

Hence, Area of circle is,

⇒ πr²

⇒ 3.14 × 60.5²

⇒ 11493.2 cm²

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Answer: The inequality that represents the condition based on the number of gallons of fuel will be:

[tex]3300P +5700S \geq94500[/tex]

The inequality that represents the condition based on the number of minutes will be:

[tex]75P +130S\geq2400[/tex]

Step-by-step explanation:

Let  P denote the number of round trips to Prague and S the number of round trips to Stockholm.

Since the plane requires 3300 gallons of fuel and 75 minutes to make a round trip to Prague and 5700 gallons of fuel and 130 minutes to make a round trip to Stockholm.

Then the inequality that represents the condition based on the number of gallons of fuel will be:

[tex]3300P +5700S \geq94500[/tex]

The inequality that represents the condition based on the number of minutes will be:

[tex]75P +130S\geq2400[/tex]

Here we want to write the quadratic function for the parabola shown in vertex form.

We will get the function: f(x) = 2*(x - 5)^2 + 3

So the general function of a parabola with vertex (h, k) and leading coefficient a is:

f(x) = a*(x - h)^2 + k

Here, we know the formula:

f(x) = a*(x - 5)^2 + 3

where:

So the vertex is the point (5, 3), and we only must find the value of a to completely determine the parabola's function

We also know that:

f(6) = 5

So we can solve:

5 = a*(6 - 5)^2 + 3

5 = a*(1)^2 + 3

5 = a + 3

5 - 3 = a = 2

So we just found the value of a, replacing this on the parabola's function we get:

f(x) = 2*(x - 5)^2 + 3

If you want to learn more about parabolas, you can read:

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In order to find which one of the given points is a solution to the equation, we need to plug each point in the equation and check which one fits in .

The equation is :

5x+2y=-9

a.(2,-4)

5x+2y=-9

LHS: 5x+2y

Plugging (2,-4) in this,

5(2) +2(-4) = 10-8 =2

RHS : -9

LHS ≠RHS

So (2,-4) is not the solution.

b.(-1,2)

5x+2y=-9

LHS: 5x+2y

Plugging (-1,2) in this,

5(-1) +2(2) = -5+4 =-1

RHS : -9

LHS ≠RHS

So (-1,2) is not the solution.

c.(-2,5)

5x+2y=-9

LHS: 5x+2y

Plugging (-2,5) in this,

5(-2) +2(5) = -10+10 =0

RHS : -9

LHS ≠RHS

So (-2,5) is not the solution.

d.(1,-3)

5x+2y=-9

LHS: 5x+2y

Plugging (1,-3) in this,

5(1) +2(-3) = 5-6=-1

RHS : -9

LHS ≠RHS

So (1,-3) is not the solution.

None of the given options is a solution to the given equation.

The thickness of a thin crust pizza is 4 times smaller than the thickness of a deep dish pizza.

The question asks us to compare the thickness of a deep dish pizza to that of a thin crust pizza and determine how many times smaller the thin crust is. The deep dish pizza has a thickness of 2 x 10⁻¹ feet and the thin crust pizza has a thickness of 5 x 10⁻² feet. To find how many times smaller the thin crust is, we divide the thickness of the thin crust by the thickness of the deep dish pizza:
(5 x 10⁻² feet) / (2 x 10⁻¹ feet) = 0.25

Answer:

(3,-8)

Step-by-step explanation:

In graph 2, the dots are scattered and also no association.

An association (relationship) between two numerical variables can be described by its form, direction, strength, and outliers. A scatter plot shows the association between two variables. A scatter plot matrix shows all pairwise scatter plots for many variables.

For the given situation,

There are four new consignments of t-shirts.

Each consignment contained t-shirts of five different sizes.

Graph is plotted as shown below between each of the t-shirt sizes and the profit earned on each new size.

If one variable increases as the other variable increases, there is said to be a positive association.

Two variables have a negative association when the values of one variable tend to decrease as the values of the other variable increase.

No association means that there is no line and all the dots are scattered.

From the graph shown, in graph 2 the dots are scattered. Thus no  association.

Hence we can conclude that in graph 2, the dots are scattered and also no association.

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9514 1404 393

Answer:

  x/4 +1

Step-by-step explanation:

The quotient of a number (x) and 4 is written ...

  x/4

One more than that is ...

  x/4 +1

The correct answer is:

B. TX and TL  

Explanation:

Opposite rays are rays that have the same endpoint and extend in opposite directions.  The ones in the diagram that fit this description are TX and TL.

Given is rectangle with perimeter = 54 centimeters and area = 176 squared centimeters.

Let's consider the length of rectangle = L and width of rectangle = W.

We know the following formulas for rectangle :-

Perimeter = 2 x (L + W)

Area = L x W

So we have 2 x (L + W) = 54 and L x W = 176.

L + W = 27 and L x W = 176

We need to find two positive integers such that their sum is 27 and product is 176.

Using trial and error, we have two such positive integers such that 11 + 16 = 27 and 11 x 16 = 176.

So, the dimensions of rectangle would be 11cm x 16cm.

Hence, option A is correct i.e. 11 cm by 16 cm.

Answer:

For this one the answer is b: 53 :)

Take Care

the answer can also be written as 1.3(3,1)

Answer:

Option D. [tex]7.1\ m[/tex]

Step-by-step explanation:

we know that

The area of a circle is equal to

[tex]A=\pi r^{2}[/tex]

In this problem we have

[tex]A=40\ m^{2}[/tex]

substitute and solve for r

[tex]40=\pi r^{2}[/tex]

[tex]r^{2}=40/( \pi)[/tex]

[tex]r=3.57\ m[/tex]

Multiply the radius by [tex]2[/tex] to obtain the diameter

so

[tex]3.57*2=7.14\ m[/tex]

According to apex, the answer is "Doubling the Square"