Somebody helppppp me pleassse

Mark and Don are planning to sell each other their marble collections at a garage sale. If Don has 1 more than 3 times the numbe

Volgvan

Answer: Mark has 28 marbles while Don has 85 marbles.

Step-by-step explanation:

Let x represent the number of marbles that Mark has.

Let y represent the number of marbles that Don has.

If Don has 1 more than 3 times the number of marbles Mark has, it means that

y = 3x + 1

The total number of marbles is 113. It means that

x + y = 113- - - - - - - - - - - - 1

Substituting y = 3x + 1 into equation 1, it becomes

x + 3x + 1 = 113

4x + 1 = 113

4x = 113 - 1 = 112

x = 112/4

x = 28

y = 3x + 1 = 3 × 28 + 1

y = 85

4 0

3 years ago

Both the La Plata river dolphin (Pontoporia blainvillei) and

Citrus2011 [14]

Answer:

1. A sperm whale is 3 orders of magnitude heavier than a La Plata river dolphin; 2. The radius of the larger ball is one (1) order of magnitude bigger than the radius of the smaller ball; 3. The volume of the larger ball is 3 orders of magnitude bigger than the volume of the smaller ball.

Step-by-step explanation:

If we expressed a number as:

$\\ N = a * 10^{b}$ (1)

Where

$\\ \frac{1}{\sqrt{10}} \leq a < \sqrt{10}$ (2)

or

$\\ 1 \leq a < 10$ (3)

Then, b represents the order of magnitude of such a number (Order of magnitude (2020), in Wikipedia).

The order of magnitude can be defined as "...the smallest power of ten needed to represent a quantity" (Weisstein, Eric W. "Order of Magnitude". From MathWorld--A Wolfram Web Resource).

Having gathered all this information, we can proceed as follows:

<h3>First case</h3>

The La Plata river dolphin weighs between 30 and 50kg and the sperm whale weighs between 35,000 and 40,000kg.

Then, considering (1) and (3) to express the dolphin and whale's weight (since in this way the order of magnitude is the same as the exponent part in the scientific notation):

$\\ 30kg \leq Dolphin_{weight} \leq 50kg$

$\\ 3*10^{1}kg \leq Dolphin_{weight} \leq 5*10^{1}kg$

$\\ 35000kg \leq Whale_{weight} \leq 40000kg$

$\\ 3.5*10^{4}kg \leq Whale_{weight} \leq 4.0*10^{4}kg$

Since the range for the weights are in the same order of magnitude for both dolphin and whale (considering the definition above):

$\\ Dolphin_{weight} = 10^{1}\;(order\;of\;magnitude=1)$

$\\ Whale_{weight} = 10^{4}\;(order\;of\;magnitude=4)$

Then

$\\ \frac{Whale_{weight} = 10^{4}}{Dolphin_{weight} = 10^{1}}$

$\\ \frac{Whale_{weight}}{Dolphin_{weight}} = \frac{10^{4}}{10^{1}}$

$\\ \frac{Whale_{weight}}{Dolphin_{weight}} = 10^{4-1}$

$\\ \frac{Whale_{weight}}{Dolphin_{weight}} = 10^{3}$

Thus

A sperm whale is 3 orders of magnitude heavier than a La Plata river dolphin.

<h3>Second case</h3>

Following the same reasoning, we can conclude that the radius of the larger ball is one (1) order of magnitude bigger than the radius of the smaller ball:

$\\ \frac{Larger\;ball_{radius}}{Smaller\;ball_{radius}} = \frac{10^{1}}{10^{0}}$

$\\ \frac{Larger\;ball_{radius}}{Smaller\;ball_{radius}} = 10^{1-0} = 10^{1}$

<h3>Third case</h3>

For this case, we need to calculate the volume of a sphere for both radii (1cm and 10cm).

The volume of a sphere is

$\\ V_{sphere} = \frac{4}{3}*\pi*R^{3}$

Then, the volume of the ball of radius 1cm is:

$\\ V_{radius=1} = \frac{4}{3}*\pi*(1cm)^{3}$

$\\ V_{radius=1} \approx 4.19*10^{0}cm^{3}$

And, the volume of the ball of radius 10cm is:

$\\ V_{radius=10} = \frac{4}{3}*\pi*(10cm)^{3}$

$\\ V_{radius=10} \approx 4.19*10^{3}cm^{3}$

Thus

$\\ \frac{10^{3}}{10^{0}} = 10^{3}$

As a result, the volume of the larger ball is 3 orders of magnitude bigger than the volume of the smaller ball.

4 0

3 years ago

A graph in which the frequency for each category of a quantitative variable is represented as a vertical column that touches the

Arturiano [62]

Answer:

Histogram.

Step-by-step explanation:

Such a Graph is called Histogram.

A histogram can be defined as a visual representation of data in form of bars of different heights. In histogram, each and every bar groups numbers into ranges. The greater the height of the bar, the larger the data falls into its range. It basically represents shape and spread of continuous data sample.

3 0

2 years ago

A baker bakes 752 muffins in a weekend. she sells the muffins in packs of 12. how many packs of muffins did she sell, how many d

eduard

752/12 = 62.66 and since she can't sell a portion of a 12 pack, she sold 62 whole packages and had 2/3 of one remaining, 2/3 of 12 is 8 remaining.

8 0

3 years ago

To prepare for a bake-off, Lee used 640 grams of flour each day for 4 weeks. How many kilograms did Lee use in those 4 weeks?

dangina [55]

1week = 7days so
4weeks = 28 days
So 28 x 640 = 17920

1000grams = 1kg

17920 divide 1000 =17.92

Lee uses 17.92kg in those 4weeks

8 0

2 years ago