MATHEMATICS MIDDLE SCHOOL

Elia rode her bicycle from her house to the beach at a constant speed of 18 kilometers per hour, and then rode from the beach to the park at a constant speed of 15 kilometers per hour. The total duration of the rides was 1 hour and the distance she rode in each direction are equal. Let b be the number of hours it took Elia to ride from her house to the beach, and put p the number of hours it took her to ride from the beach to the park.

Answers

Answer 1

Answer:

Answer:

$\displaystyle b=0.45\ h$

$\displaystyle p=0.55\ h$

Step-by-step explanation:

Cinematics

When an object moves at a constant speed, it can be computed as

$\displaystyle v=(x)/(t)$

Where x is the distance traveled and t the time needed to complete it at the constant speed v

If we wanted to compute t from the equation above, then

$\displaystyle t=(x)/(v)$

Elia rode her bicycle from her house to the beach at 18 km/h and then from the beach to the park at 15 km/h, taking 1 hour in the whole travel, each distance being equal. If we call b as the number of hours it took Elia to ride from her house to the beach, and p the number of hours it took her to ride from the beach to the park, then we can compute

$\displaystyle b=(x)/(18)$

$\displaystyle p=(x)/(15)$

The question doesn't ask for something in particular, so I'm helping you by solving the complete problem. We know the total time is 1 hour, so

$\displaystyle b+p=1$

Replacing b and p

$\displaystyle (x)/(18)+(x)/(15)=1$

Multiplying by 90

$\displaystyle (90x)/(18)+(90x)/(15)=90$

Simplifying and solving for x

$\displaystyle 5x+6x=90$

$\displaystyle 11x=90$

$\displaystyle x=(90)/(11)=8.18\ km$

We finally compute b and p

$\displaystyle b=(8.18)/(18)=0.45\ h$

$\displaystyle p=(8.18)/(15)=0.55\ h$

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a mail truck picks up two boxes of mail from the post office. the total weigth of the boxes is 32 pounds. One box is 8 pounds heavier than the other box. How much does each box weigth?

A store owner is stocking shelves.he places 37 eight-ounce packages of cheese on a shelf then he puts 24 ounce cheese on the same shelf how many pounds of cheese does he put on the shelf

Answers

There are 37 eight ounce of cheese.
37 times 8 = 296 ounces of cheese.
There are 16 ounces in a pound, so divide.
296/16 = 18.5 pounds on the shelf.

Then he places 24 ounce of cheese on the shelf. Divide that by 16.
24/16 = 1.5 pounds.

Add the pounds together-
18.5 + 1.5 = 20 pounds (lbs)

Numbers like 10, 100, 1,000, and so on are called

Answers

Numbers like 10, 100, 1,000, and so on are called exponents.

What are exponents?

Exponentiation is a mathematical process that involves the base b and the exponent or power n. It is represented by the symbol bn and is spoken as "b raised to the power of n."

Numbers starting with a 1 and followed by only 0s (such as 10, 100, 1,000,10,000, and so forth) are called powers of ten, and they're easy to represent as "exponents". Powers of ten are the result of multiplying 10 times itself any number of times.

Exponents are also used to represent numbers in the form of scientific notations. Scientific notations are used to represent extremely large numbers or extremely small numbers.

Therefore, the numbers like 10, 100, 1,000, and so on are called exponents.

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#SPJ2

Numbers starting with a 1 and followed by only 0s (such 10, 100, 1,000,10,000, and so forth) are called powers of ten, and they're easy to represent as "exponents". Powers of ten are the result of multiplying 10 times itself any number of times.

The larger of two numbers is twice the smaller increased by five. Find the two numbers if three times the larger exceeds double the smaller by 31

Answers

Answer:

Larger number is 13 and Smaller number is 4.

Step-by-step explanation:

Let the larger number be x.

Also let the smaller number be y.

We need to find the two numbers.

Given:

The larger of two numbers is twice the smaller increased by five.

framing in equation form we get;

$x=2y+5$ ⇒equation 1

Also Given:

Three times the larger exceeds double the smaller by 31

$3x=2y+31$ ⇒equation 2

Now Substituting the value of x from equation 1 in equation 2 we get;

$3(2y+5) = 2y+31$

Now Using Distributive property we get;

$6y+15 = 2y +31$

Combining the like terms we get;

$6y-2y = 31-15$

Now Using Subtraction property we get;

$4y =16$

Now Using Division property we get;

$(4y)/(4)=(16)/(4)\n\ny =4$

Now Substituting value of y in equation 1 we will find the value of x.

$x=2y+5\n\nx = 2*4+5\n\nx=8+5\n\nx=13$

Hence Larger number is 13 and Smaller number is 4.

2.1 liters of coffee were equally distributed to 30 cups. How many milliliters of coffee were in each cup?

Answers

The amount of coffee in each cup is the average coffee in the cups.

The amount of coffee in each cup is 70mL

The given parameters are:

$\mathbf{Size = 2.1L}$

$\mathbf{Cup = 30}$

So, the amount in each cup is:

$\mathbf{Amount = (Size)/(Cup)}$

Substitute known values

$\mathbf{Amount = (2.1L)/(30)}$

$\mathbf{Amount = 0.07L}$

Convert liters to milliliters

$\mathbf{Amount = 0.07 * 1000mL}$

$\mathbf{Amount = 70mL}$

Hence, the amount of coffee in each cup is 70mL

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70 ml

Further explanation

Given:

2.1 liters of coffee were equally distributed to 30 cups.

Question:

How many milliliters of coffee were in each cup?

The Process:

Step-1: converting liters into milliliters

Recall $\boxed{ \ 1 \ liter = 1,000 \ milliliters \ }$

Let us change the 2.1 liters unit of coffee into milliliters.

$\boxed{ \ 2.1 \ liters * (1,000 \ mL)/(1 \ liter) = \ ? \ }$

$\boxed{ \ = 2.1 * 1,000 \ mL} \ }$

$\boxed{ \ = 21 * (1)/(10) * 1,000 \ mL} \ }$

$\boxed{ \ = 21 * 100 \ mL} \ }$

$\boxed{\boxed{ \ 2,100 \ mL \ }}$

Therefore, 2,100 mL of coffee are available for distribution.

Step-2: calculating how many milliliters of coffee were in each cup

$\boxed{ \ 30 \ cups = 2,100 \ mL \ }$

$\boxed{ \ 1 \ cups = \ ? \ mL \ }$

We have to divide the total amount of coffee by the number of cups.

$\boxed{ \ 1 \ cup * (2,100 \ mL)/(30 \ cups) * 1,000 \ mL = \ ? \ }}$

$\boxed{ \ = (2,100)/(30) \ }$

The numerator and denominator are equally divided by 10.

$\boxed{ \ = (210)/(3) \ }$

$\boxed{ \ = 210 / 3 \ }$

$\boxed{\boxed{ \ 70 \ }}$

Thus, 70 milliliters of coffee were in each cup.

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Keywords: 2.1 liters of coffee, were equally distributed, to 30 cups, how many, milliliters, in each cup, least common multiple, LCM, numerator, denominator

A cell phone company collected data if texting speed in words per minute according to time in minutes. explain why a scatter plot is used to represent the data, including the purpose of scatter plots

Answers

Answer:

Scatter plots resembles line graphs in that they are plotted on the x and y axis. The are used because they show how much one variable is affected by another.

Scatter diagrams are important since in statistics they can show the extent of correlation, if any, between the values of observed quantities or a behavior.

Answer:

A scatter plot is defined as a diagram which uses Cartesian coordinates to display values about two variables, one indepedent, the other one dependent.

This diagrams are used in statistics to display information about surveys to a certain sample in a population. The purpose of a scatter plot is to shows if the variables are related, that is, if they have any type of linear correlation between them. If they have linear correlation, then the data is represented by a line.

Now, in this case, the independent variable is time in minutes and the dependent variable is texting. Basically, with this data, the company will be able to stablish the relation between words written in a certain time, that is, the speed of texting actually.

With a scatter plot, they would find the relation that forms the speed of texting. It could be "the more time, more text is written", or "the less time, more text is written".

If we need to establish a possible relation, the most logical would be "the more time, more word are texted".

Can you explain how complex fractions can be used to solve problems involving ratios?

Answers

example: (1/5)/(4/13)=(1/5)*(13/4)=13/20

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