Suppose a balloon is filled with 5000 cm³ of helium. It then loses one fourth of its helium each day. How much helium will be left in the balloon at the start of the tenth day?c. How can you write a formula for this sequence?

Answers

Answer 1

The sequence can be expressed by the formula: v(n) = 5000 . (3/4)ⁿ⁻¹. Helium left at the start of the 10th day is 375.42 cm³

1st day:

Helium is filled with 5000 cm³ of helium.

We can write v(1) = 5000 cm³

2nd day:

The balloon losses 1/4 of helium volume. In other word, the remaining volume of helium is:

(1 - 1/4) = 3/4 of its initial volume.

We can write:

v(2) = 3/4 . 5000 = 3750  cm³

We can continue this process:

v(3) = 3/4 . 3750 = 2812.5

Notice that each day remaining volume of helium forms a geometric sequence, with v(1) = 5000 and a common ratio (r) = 3/4.

Recall the formula for the nth term of a geometric sequence:

v(n) = v(1) . rⁿ⁻¹

To find the explicit formula, substitute v(1) = 5000 and (r) = 3/4:

v(n) = 5000 . (3/4)ⁿ⁻¹

Tenth day means n = 10. Substitute these parameters into the formula:

v(10) = 5000 . (3/4)¹⁰⁻¹

v(10) = 5000 . (3/4)⁹

        = 375.42 cm³

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Related Questions

7 x 10-8 in standard form

Answers

Answer:

7×10= 70

70-8= 62

Answer62

help pls id help u too

Answers

Answer:

x = 1

y = -4

but I am not sure about z

Step-by-step explanation:

please check with your calculator first

What else is needed to prove these triangles congruent using the SAA postulate? I NEED THE ANSWER

Answers

To prove triangles ACB and ECD to be congruent using SAA we need

A. Both ∠B and ∠D need to be congruent and ∠A and ∠E need to be congruent.

As given in the question,

In the triangle ACB and ECD,

Given : AC ≅ EC

            ∠ACB ≅∠ECD

To prove triangles to be congruent using SAA.

Two angles need to be congruent.

∠B ≅ ∠D

∠A ≅ ∠E

Therefore, to prove triangles ACB and ECD to be congruent using SAA we need

A. Both ∠B and ∠D need to be congruent and ∠A and ∠E need to be congruent.

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Silver gym costs $75 to join their gym plus $25 per training session, world fitness costs $100 to join and only $20 per training session. How many sessions will it take for the cost to be the same?

Answers

Answer:

5 Sessions

Step-by-step explanation:

$75+$25. $100+20 | Prices

125. 140. | + Cost of Session

150. 160

175. 180

200. 200

225. 220

Reflect ABC over the x axis translate by <-3,-1>, and rotate 180 degrees around the origin

Answers

Following a 180-degree rotation, the new points are (3,1)

The size of the image will either rise or decrease depending on the answer to the question. And there are two ways to rotate: clockwise and counterclockwise. The coordinate values will vary depending on the quadrant.

Consequently, the new points upon rotation are (3,1).

What do translation, rotation, and reflection mean?

The word "reflection" flips or creates a mirror image of the object. An picture is rotated by rotating it either clockwise or anticlockwise. Finally, translation moves certain parts of the picture.

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What is the vertical change?
What is the horizontal change?
Write the slope as a fraction or decimal.

Answers

A line is seen on the graph. The horizontal displacement is 2 units, and the graph's rate of change is 0.5.

Point A's coordinates are: (2,1).

Point B's coordinates are: (4,2).

The coordinates of the point change from (2.1) to (2.1) as you go from point A to point B. (4,2).

Consequently, the change in x-coordinate is what determines the point's horizontal displacement and will be,

4 2 2

Therefore, the horizontal displacement is two units.

The vertical displacement is also one unit.

Now, the graph's rate of change may be calculated by looking at the graph's line's slope.

The rate of change will thus be,

m = y2- y1 / x2 - x1

m =2-1 / 4-2

m = 1/2

Consequently, the rate of change = 0.5

horizontal displacement = 2 units.

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Complete question -

What is the vertical change from Point A to Point B?

1

What is the horizontal change from Point A to Point B?

What is the rate of change shown on the graph? Give the answer as a decimal rounded to the nearest tenth, if necessary

ASAP pls..............

Answers

Answer: t = 6/11

Step-by-step explanation:

3t - 2 + t = 4 - 7t

4t - 2 = 4 - 7t

4t + 7t = 4 + 2

11t = 4 + 2

11t = 6

Divide both by 11

Answer : t = 6/11

Answer:

t = 6/11

Step-by-step explanation:

Hello!

Solve the equation for t by isolating the variable.

Solve for t3t - 2 + t = 4 - 7t        Add like Terms4t - 2 = 4 - 7t             Collect Like terms 11t - 2 = 4                   Isolate the Variable11t = 6                        Isolate the Variablet = 6/11

The value for t is 6/11.

y = -3x - 10


I have to graph points. The first point is at (0, -10) because of the y-intercept. How should I graph the next point using the slope? The graph they gave me cuts off at 0, -10 so I can't go any lower for y. Help.

Answers

The next point to be graphed after graphing the y-intercept since the slope is negative and the graph cuts of at; (0, -10) is; (-5, 5).

What is the next point to be graphed apart from the y-intercept since the graph cuts off at (0, -10)?

According to the task content; it follows that the next point to be graphed apart from the given y-intercept is to be determined.

It follows from comparison with the slope-intercept form of a linear equation;

y = mx+c that the slope of the given equation is; -3.

Hence, considering the point, x = -5, the value of y is;

y = -3(-5) -10

y = 15 - 10

y = 5.

Therefore, the required coordinate to be graphed is; (-5, 5).

Ultimately, the next point to be graphed after graphing the y-intercept since the slope is negative and the graph cuts of at; (0, -10) is;

(-5, 5).

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i need help again yall..............................

Answers

Answer:

the answer is c !!!!!!!!!!!!!!!!!!

What is the value of the expression below when x=5x=5?
8x+9

Answers

The value of the expression below when x=5x=5?

8x+9 is equal to [tex]7^{2}[/tex] (or) 49.

Substitute [tex]\left \{ {{x=5x} \atop {5x=5}} \right. into (8x+9)[/tex]

The expression,

y = 8x + 9

If the domain of the function is x = 5, hence the range of the function is gotten by substituting x = 5 into the given function as shown:

So, we can substitute x = 5,

Then, y = 8 * 5 + 9

Calculate the product or quotient,

y = 40 + 9

Calculate the sum or difference,

y = 49

We can write alternative form,

y = [tex]7^{2}[/tex]

Therefore,

Hence the value of the expressions if x = 5 is [tex]7^{2}[/tex] (or) 49.

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Write an example from daily life that uses each type of real number.
whole numbers

Answers

Whole numbers are defined as a set of natural numbers plus the integer zero. There exists no fractions, decimals, or negative integers in whole numbers, which are actual numbers.

What are whole numbers?

Whole numbers are defined as a set of natural numbers plus the integer zero. In mathematics, the set of whole numbers is denoted by the letter W and is given as 0, 1, 2, 3, etc.

Examples:

1. Learning geometry and trigonometry can help people who desire to get better at sports.

2. The ability to compute an area is useful since it will be useful when we renovate our homes and rental properties.

3. When making many purchases, we must decide which retailer gives the best price or financing.

4.People use ratios or proportions to calculate the right amount of each item when they cook.

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What is the key phrase?

Answers

A phrase used in encryption in the style of a keyword.

As a race is finished the amount of elapsed time for the racer is recorded. what measurement scale is this?

Answers

The answer is Numeric.

What is a measuring scale?Items are weighed on a scale to determine their weight. In order to ensure that the components are utilized exactly as specified in the recipe, they are frequently used in cooking.The four common scales of measurement—nominal, ordinal, interval, and ratio—were created by psychologist Stanley Stevens.The type of measurement scale to be used for statistical measurement depends on the type of data being collected. There are various types of measurement scales. The nominal, ordinal, interval, and ratio scales are the four measurement scales that make up this set.

What measurement scale is this?

There are mainly two types of variables

Numerical(quantitative): observations that can be measured in numerical form

Agin two types: ratio scale and interval scale

Categorical(qualitative ): named categories

Again two types: Ordinal or nominal

Her in the given an example,

Measured time of race have  numerical observations

The measurement scale is Numeric.

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please answer i will give 100 extra points if correct

Answers

The answer is 4 brotha

Answer:

-6, -5, -5.9, -1, 0, 1, 5, 5.9, 6, 6.1, 7, 11

Step-by-step explanation:

Its basically saying that all values of x must be greater than or equal to -6. So, we can substitute -6, -5, -5.9, -1, 0, 1, 5, 5.9, 6, 6.1, 7, 11

-6.1, -7, and -11, is wrong because it is less than -6,

hope this helped


Express each fraction as a decimal to the nearest hundredth. 17/54

Answers

The fraction 17/54 as a decimal to the nearest hundredth is 0.32

Given fraction is 17/54

In decimal form it is 0.3148.

To round it to the nearest hundredth, we have to make round it to two decimal places.

So 17/54 = 0.3148 = 0.32

0.32 is the decimal form of 17/54 to the nearest hundredth.

We can verify this by multiplying and dividing 100 to 0.32,

That is 0.32 = 32/100.

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A rectangular prism has a base with side lengths x and x+3 and height 2 x . Find the surface area and volume of the prism.

Answers

The surface area is 10x²+18x sq. units and volume of the rectangular prism is 2x³ + 6x² cubic units.

As given,

In rectangular prism

Base side lengths x and x+3

Height = 2 x

Volume of a rectangular prism V = l w h

V = volume , l =length, w= width  h =height.

For rectangular prism,

V = (x). (x +3). (2x)

  = (x² +3x)2x

  =2x³ +6x²cubic units

Surface Area of Rectangular Prism:

=2(x*2x)+2(x(x+3))+2(2x(x+3))

=4x²+2x²+6x+4x²+12x

=10x²+18x sq. units

Hence, the surface area is 10x²+18x sq. units and volume of the rectangular prism is 2x³ + 6x² units

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Message instructor about this question
Which of the following are arithmetic sequences? Select all that apply.
115, 105, 95, 85, ...
-12, -8, -4, 0, ..., 152
5, 10, 20, 40, ...
18, 25, 32, 39, ..., 214
1, -7, 49, -343, ..., 5764801
18, -22, 26, -30, ...

Answers

The arithmetic sequences are given as follows:

115, 105, 95, 85, ...-12, -8, -4, 0, ..., 15218, 25, 32, 39, ..., 214

What is an arithmetic sequence?

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The nth term of an arithmetic sequence is given by:

[tex]a_n = a_1 + (n - 1)d[/tex]

Hence, the arithmetic sequences are given as follows:

115, 105, 95, 85, ... d = -10.-12, -8, -4, 0, ..., 152. d = 4.18, 25, 32, 39, ..., 214. d = 7.

For the other sequences, there are different differences between consecutive terms, hence the sequence is not arithmetic, for example:

10 - 5 = 5, 20 - 10 = 10.

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Solve the System of Equations:


y = [tex]\frac{1}{6}[/tex]x + 6

y = [tex]\frac{1}{3}[/tex]x + 2

Answers

Answer:

(x;y)=(24;10)

y = 1/6 * x + 6; y = 1/3 * x + 2

Substitute the given value of y into the equation y = 1/3 * x + 2

1/6 * x + 6 = 1/3 * x + 2

Solve the equation for x

x = 24

Substitute the given value of x into the equation y = 1/3 * x + 2

y = 1/3 * 24 + 2

Solve the equation for y

y = 10

2-inch candle burns down in 8 hours. At what rate does the candle burn, in inches per hour?

Answers

Answer:

1/4 inches/hour

Step-by-step explanation:

We need inches per hour, which means inches divided by hours, so we divide the number of inches by the number of hours.

2 inches / 8 hours = 2/8 inches/hour = 1/4 inches/hour

Important need help fast!

Answers

The function of correct growth or decay factors are,

[tex]y = (0.3) (0.5)^{x}[/tex] is an exponential decay factor of 50%.

[tex]y = 2000(\frac{4}{5} )^{x}[/tex] is an exponential decay factor of 15%.

[tex]y = 800 (1.15)^{x}[/tex] is an not exponential decay factor related to growth factor 15%.

[tex]y = 1200 (1.05)^{x}[/tex] is an not exponential decay factor related to growth factor 5%.

[tex]y = 3(0.85)^{x}[/tex] is an exponential decay factor of 85%, then the related to  20%.

We know that,

Exponential Decaying factor is [tex]y = ab^{x}[/tex]

Where, 0<b<1

The decay rate is expressed as a percentage. We convert it to a decimal by simply reducing the percent and dividing it by 100.

Growth factor is the factor by which a quantity multiplies itself over time. Growth rate is the addend by which a quantity increases (or decreases) over time.

Here,

Option(1) : [tex]y = (0.3)(0.5)^{x}[/tex]

Then,  0.5 < 1        (0.5 means 50%)

So, [tex]y = (0.3) (0.5)^{x}[/tex] is an exponential decay factor .

Hence,  [tex]y = (0.3) (0.5)^{x}[/tex] is an exponential decay factor of 50%.

Option(2) : [tex]y = 2000(\frac{4}{5}) ^{x}[/tex]

Then,  4/5 < 1

⇒ 0.8 < 1

So, [tex]y = 2000(\frac{4}{5} )^{x}[/tex] is an exponential decay factor.

Hence, [tex]y = 2000(\frac{4}{5} )^{x}[/tex] is an exponential decay factor of 15%.

Option(3) : [tex]y = 800 (1.15)^{x}[/tex]

Then,  1.15 > 1

So, [tex]y = 800 (1.15)^{x}[/tex] is an not exponential decay factor.

Hence, [tex]y = 800 (1.15)^{x}[/tex] is an not exponential decay factor of 115%, so it is not decay factor, then the related to growth factor 15%.

Option(4) : [tex]y = 1200 (1.05)^{x}[/tex]

Then,  1.05 > 1

So, [tex]y = 1200 (1.05)^{x}[/tex] is an not exponential decay factor.

Hence, [tex]y = 1200 (1.05)^{x}[/tex] is an not exponential decay factor of 105%, so it is not decay factor, then the related to growth factor 5%.

Option(5) : [tex]y = 3(0.85)^{x}[/tex]

Then,  0.85 < 1

So, [tex]y = 3(0.85)^{x}[/tex] is an exponential decay factor.

Hence, [tex]y = 3(0.85)^{x}[/tex] is an exponential decay factor of 85%, then the related to  20%.

Therefore,

[tex]y = (0.3) (0.5)^{x}[/tex] is an exponential decay factor of 50%.

[tex]y = 2000(\frac{4}{5} )^{x}[/tex] is an exponential decay factor of 15%.

[tex]y = 800 (1.15)^{x}[/tex] is an not exponential decay factor related to growth factor 15%.

[tex]y = 1200 (1.05)^{x}[/tex] is an not exponential decay factor related to growth factor 5%.

[tex]y = 3(0.85)^{x}[/tex] is an exponential decay factor of 85%, then the related to  20%.

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PLEASE HELP ME RUNNING OUT OF TIME Determine if the point (3, 1) is a solution to the system of inequalities shown below and use the characteristics of inequality graphs to justify your answer

Answers

Answer:

nope

Step-by-step explanation:

aight so basically . you see how the line , that the point is , on is dotted ? that means that nothing on the line is included aka ">" or "<" . and the line that solid , that means if a point is on that line , you can include it . aka "[tex]\leq[/tex]" or "[tex]\geq[/tex]" cause that means or equal to or whatever . so overall if we were only looking at the lil triangle that both of the colors intersect on , ( 3 , 1 ) wouldnt work . sorry if my explaination sucks :)

can someone help me with this? Thank you!

Answers

Answer:

4 5/6

Step-by-step explanation:

1/2 -> 3/6

2/3 -> 4/6

? 3/6 - ? 4/6 = ? 5/6

10 - 5 ( Take away one because you needed to do 3/6-4/6 which results in a negative number )

4 5/6

Answer:
4 5/6
Step-by-step explanation:
1/2 -> 3/6
213 -> 416
? 316-?4/6=? 516

I have a crush on a Virgo dude and I’m a Libra . Should I ask if I can kiss him or just do it , or just wait . I’m in love with this guy and he says im pretty too

Answers

What does astrology signs have to do with anything?

2x² - y
if x = 3 and y = 8

Answers

Answer:

10

Step-by-step explanation:

2(9)-8

10

Hey there!

2x^2 - y

= 2(3)^2 - 8

= 2(3^2) - 8

= 2(3 * 3) - 8

= 2(9) - 8
= 18 - 8

= 10


Therefore, your answer should be:

10


Good luck on your assignment & enjoy your day!


~Amphitrite1040:)



b. Do transformations of the form y=|x|+k affect the axis of symmetry? Explain.

Answers

A line that bisects or cuts an objects into two equals parts is called the axis of symmetry for that object. The axis of symmetry creates a mirror-like reflection of each side of the object.

The function f(x) = |x| is called an absolute value function. The highest or lowest point on the graph of the absolute value function is called the vertex. The absolute value graph has an axis of symmetry through the vertices.

The axis of symmetry (x=0 or y-axis) is the line that divides the graph into two congruent halves. Translate is a transformation that moves the graph horizontally or vertically, but does not change its overall shape or orientation.

So, it does not affect the axis of symmetrical. Is symmetrical about the Y axis (axis of symmetry).

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Compare the two numbers. Use > or < .
-√3,-√5

Answers

As the value of Square root -√5 is equal to -2.23, and the value of Square root -√3 is -1.73, which is larger.

A square root is what?The square root of a number x is the number y whose square (the result of multiplying the number by itself, or y y), equals x in mathematics.

The term "radicand" refers to the word (or number) whose square root is being considered.

The term or number under the radical sign in this instance is known as the radicand, and it is 9.

One can discuss square roots of negative values while discussing complex numbers.

Any time the idea of an object's "square" is mentioned, square roots can be more extensively considered.

These include square matrices and function spaces, among other mathematical structures.

The value of Square root -√5 = -2.23, and the value of Square root

-√3 = -1.73, which is larger.

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Evaluate each expression for the given value of the variable. 3(2 a+5)+2(3-a) ; a=4

Answers

The value of the expression 3(2 a+5)+2(3-a) at a=4 is 37 .

An Algebraic expression is defined as an expression that consists of variables and constants linked with mathematical operators (+,-,x,÷).

According to the question

=3(2 a+5)+2(3-a)

Substituting the value a=4 in the above expression.

We get,

=3(2(4)+5)+2(3-4)

=3(8+5)+2(3-4)

Solving terms in bracket first ,

=3(13)+2(-1)

=39-2

=37

Therefore , The value of the expression 3(2 a+5)+2(3-a) at a=4 is 37 .

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Find the slope of the line through (3,5) , parallel to y=5 x-1

Answers

Find the slope of the line through (3,5) , parallel to y=5 x-1

Slope=5

How to find slope?

Given:

y=5x-1 ( where, slope=5)

Any line parallel to y=5x-1  also has slope 5

What is the line?

y=5x+b

We can find b ,using the given points  (3,5)

5=15+b

b=-10

The line is, y=5x-10

What is a slope?

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.The letter m is frequently used to represent slope; the reason for this usage is unclear, but it can be found in O'Brien's and Todhunter's versions of the equation for a straight line, respectively, where they are written as y = mx + b and y = mx + c.

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For each equation, find the center and radius of the circle.
(x+2)²+(y-10)²=4

Answers

The equation of the circle (x + 2)^2 + (y - 10)^2 = 4 has a radius of 2 and a center located at (-2 , 10).

The standard form of the equation of  circle is given by

(x - h)^2 + (y - k)^2 = r^2

where (h , k) is the location of the center and r is the radius of the circle.

On the other hand, the general form of the equation of  circle is given by

x^2 + y^2 + Dx + Ey + F = 0

where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.

If the equation of the circle, (x + 2)^2 + (y - 10)^2 = 4, is in standard form, then

h = -2

k = 10

r = 2

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what is the probability of drawing a club from a deck of cards

Answers

The probability of drawing a club from a deck of cards is 1/4

How to determine the probability of drawing a club from a deck of cards?

In a standard deck of cards, we have the following parameters

Club = 13

Cards = 52

The probability of drawing a club from a deck of cards is calculated as

P = Club/Cards

This gives

P = 13/52

Simplify the fraction

P = 1/4

Hence, the probability of drawing a club from a deck of cards is 1/4

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John was explaining about an attack that accepts user input without validating it and uses that input in a response. what type of attack was he describing? what makes povery point different from most hunter gathers societies? I need to sketch force diagram This problem is already solved Newton's third law explains that for every action force there is an equal and opposite reaction force. In the image below, the arrow represents the force of Earth pulling down on the book. This is also called the force of gravity.Based on Newton's third law and the force represented by the arrow, what is the reaction force in this scenario? A. The force of the book pulling down on the table. B. The force of the table pushing up on the book. C. The force of the table pushing down on Earth. D. The force of the book pulling up on Earth. Two similar hexagonal prisms have volumes of 250 cubic feet and 2 cubic feet. What is the ratio of the height of the large cylinder to the height of the small cylinder? If a researcher only wanted to examine the relationship between exercise and grade point average, _________ would be used to test the variables. a. correlation analysis b. regression c. hypothesis d. central tendency measures please select the best answer from the choices provided a b c d The sum of the squares of three consecutive positive integers is 2030. What is the middle integers? On a highway with two-way traffic, after passing a vehicle, you must get back to the right-hand side of the road before coming within _____ feet of any vehicle approaching from the opposite direction. I need help with number 42 please Make a conjecture about the distances from the center of rotation P to each corresponding vertex of ABCD and A' B' C' D' . Lisa wants to buy some new shirts at her favorite store. Each shirt costs $15 and she wants to buy a pair of shoes that are $35. Lisa only has $137 to spend.Let S represent the number of shirts that Lisa buys.Which inequality describes this scenario?(A) 137> 15s +35(B) 137< 15s +35(C) 137 15s +35(D) 137 15s +35 The Equation a = 1/2(8)h Represents the area a of a triangle with base of 8cm and a height of h cm. Make a table to find the areas of triangles with heights of 6 cm, 7cm, 8 cm, and 9 cm. Which former president founded the Secret Service?Question 3 options:President William McKinleyPresident John F. KennedyPresident Abraham LincolnPresident Warren G. Harding What changes in behaviour can be seen in a drug addiction? Determine whether each sequence is arithmetic. If so, identify the common difference and find the 32 nd term of the sequence. 7,10,13,16, . . . . . why was god seperated from men? how were heaven and earth connected in Africa religous mythology I Need help on starting this essay. Im not a really good writer. =cRespond to the following topic by writing an essay that is controlled by a central idea and is specifically developed.In his essay (note to selfe), John Dickerson explains why he believes we dont need to put down our cell phones in order to fully engage in the world.What does he say about the way we use cell phones?How do his ideas apply to your own use of a cell phone?To develop your essay, be sure to discuss examples from your own experience, your observation of others (or interviews), or any of your reading, including Dickerson. Which three statements describe accomplishments of the 2017 women's rights protests? Ryan downloaded a video game to his computer. The size of the file was 3.1 times 10E4 kilobytes. After the game, Ryan installed a patch that is 40000 kilobytes. What is the size of the game file written in standard form? 1. Scientists often work together in teamsto solve problems. In 2009, an influenzavirus emerged from pigs that went on toinfect an estimated 24 percent of the worldhuman population. How could biologistsfrom a variety of fields contribute tostudying this widespread disease anddeveloping a treatment, prevention, orcure?