The number of people playing a new phone app game triples every month. When the app first launched, 800 people started playing the game right away. There are currently 194,400 people playing the game. Write an equation to represent this situation, and determine the number of months, t, that have passed since the app launched.

Answers

Answer 1

Answer:

[tex]a_t=ar^{t-1}[/tex]

t=6 months

Step-by-step explanation:

We are given that the number of people playing a new phone app game triples every month

When the app first launch , the number of people started playing the  game  right away=800

According to question

The number of peoples are currently playing the game=194,400

We solve by using the formula of  geometric series because we get a geometric series pattern

The number of people playing the game when app game launch=800

The number of people playing game after one month=2400

800,2400,7200,........,194,400

[tex]a_1=800,a_2=2400,a_3=7200,a_t=194,400[/tex]

We are finding common ratio

[tex]\frac{a_2}{a_1}=\frac{2400}{800}=3[/tex]

[tex]\frac{a_3}{a_2}=\frac{7200}{2400}=3[/tex]

Hence, the common ratio is 3 therefor nth term of  G.P

[tex]a_t=ar^{t-1}[/tex]

a=800,r=3,[tex]a_t=194,400[/tex]

Substitute the values then we get

[tex]194,400=800(3)^{t-1}[/tex]

[tex]\frac[194400}{800}=(3)^{t-1}[/tex]

[tex]243=3^{t-1}[/tex]

[tex]3^5=3^{t-1}[/tex]

When base are same on both side then the power are equals

Therefore, t-1=5

t=5+1=6

Hence, when there are 194,400 people currently playing the game then

the number of months ,t=6 that have passed since the app launched.

Answer 2

Answer:

800(3)^t = 194,400; t = 5 months

Step-by-step explanation:


Related Questions

Evaluate: −4 + 12 ÷(−3)/10 + 3(−2)

Answers

Answer:

Step-by-step explanation:

First we calculate (-3)÷10 = -0.3

Then 12÷(-0.3) = -40

After that -4 + (-40) = -44

3(-2) = -6

Finally -44 + (-6) = -50

For this case we have that the order of algebraic operations is determined by PEMDAS:

P: Perform any calculation inside the parentheses, making the most internal ones first.

E: Simplify any exponential expressions.

MD: Do all the multiplications and divisions, from left to right, as they appear.

AS: Do all the addition and subtraction, from left to right, as they appear.

Then, we have the following expression:

-4 + 12 ÷ (-3) ÷ 10 + 3 (-2) =

-4-4 ÷ 10 + 3 (-2) =

-4-0.4 + 3 (-2) =

-4-0.4-6 =

-4.4-6 =

-10.4

Answer:

-10.4

Find the range. 4.7 6.3 5.4 3.2 4.9 3.1 –3.1 9.5 –9.5

Answers

Answer:

The range is 19

Step-by-step explanation:

First, you have to order the numbers from least to greatest:

-9.5, -3.1, 3.1, 3.2, 4.7, 4.9, 5.4, 6.3, 9.5

Then, you have to find the difference between the largest number and and smallest number. You do this by subtracting them:

9.5 - (-9.5)= 19

So, the range is 19

Need Help!!! ASAP

A probability model includes P(red) = 2/7 and P(blue) = 3/14 which of the following probabilities could complete the model? Select all that apply.

P(green) = 2/7 P(yellow) = 2/7
P(green) = 3/8 P(yellow) = 1/8
P(green) = 1/4 P(yellow) = 1/4
P(green) = 5/21 P(yellow) = 11/21
P(green) = 3/7 P(yellow) = 1/14

Answers

Answer:

[tex]P(green)+P(yellow)=\frac{3}{8}+\frac{1}{8}[/tex]

[tex]P(green)+P(yellow)=\frac{1}{4}+\frac{1}{4}[/tex]

[tex]P(green)+P(yellow)=\frac{3}{7}+\frac{1}{14}[/tex]

Step-by-step explanation:

The given probabilities are:

[tex]P(red)=\frac{2}{7}[/tex]

[tex]P(blue)=\frac{3}{14}[/tex]

Their sum is [tex]P(red)+P(blue)=\frac{2}{7}+\frac{3}{14}[/tex]

The probabilities that will complete the model should add up to [tex]\frac{1}{2}[/tex] so that the sum of all probabilities is 1.

[tex]P(green)+P(yellow)=\frac{2}{7}+\frac{2}{7}\ne\frac{1}{2}[/tex]

[tex]P(green)+P(yellow)=\frac{3}{8}+\frac{1}{8}=\frac{1}{2}[/tex]

[tex]P(green)+P(yellow)=\frac{1}{4}+\frac{1}{4}=\frac{1}{2}[/tex]

[tex]P(green)+P(yellow)=\frac{5}{21}+\frac{11}{21}\ne\frac{1}{2}[/tex]

[tex]P(green)+P(yellow)=\frac{3}{7}+\frac{1}{14}=\frac{1}{2}[/tex]

Answer:

According to the information you provided, a probability model includes P(red) = 2/7 and P(blue) = 3/14. The probabilities that could complete the model are P(green) = 5/21 and P(yellow) = 11/21. This is because the sum of all probabilities in a probability model must equal 1. In this case, 2/7 + 3/14 + 5/21 + 11/21 = 1.

Divide.
(x2 +11x+24) =(x+4)
Your answer should give the quotient and the remainder.
Quotient:
Remainder:

Answers

For this case we must find the quotient of [tex]x ^ 2 + 11x + 24[/tex] between [tex]x + 4[/tex]

As you can see in the figure, we must build a quotient in such a way that when multiplied by the divisor, we eliminate the terms of the dividend until we reach the remainder.

Answer:

Quotient: x + 7

Remainder: -4

See attached image

Please Help Quickly!!!

If lim x--> 4 f(x) = 5

Answers

Answer:

D

Step-by-step explanation:

Value of the function [tex]\lim_{x \to 4} \dfrac {g}{h}(x)[/tex] is zero.

Correct option is b.

What is limit?

Limits are defined as values ​​to which the function approximates the output for given input values. The limit is the unique real numbers. Given a real-valued function "f" and a real number "c", the limit is usually defined as [tex]\lim_{x \to c} f(x) = L[/tex]. We read that "the limit of f of x is equal to L as x approaches c". "lim" represents the limit, and the right arrow indicates that the function f(x) approaches the limit L as x approaches c.

Given functions,

[tex]\lim_{x \to 4} f(x) = 5 , \lim_{x \to 4} g(x) = 0, \lim_{x \to 4} h(x) = -2[/tex]

[tex]=\lim_{x \to 4} \dfrac {g}{h}(x)[/tex]

[tex]=\lim_{x \to 4} \dfrac {g(x)}{h(x)}[/tex]

[tex]=\dfrac{\lim_{x \to 4} g(x)} {\lim_{x \to 4} h(x)}[/tex]

= 0/-2

= 0

Hence, 0 is the value of function [tex]\lim_{x \to 4} \dfrac {g}{h}(x)[/tex] .

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Name the constansin the expression
7x + 9y + 3.

Answers

Your constant is 3 because it’s alone

Answer:3

Step-by-step explanation:

A tank with a volume of 61.25 cubic meters is filled with pull. The oil has a density of 865 kilograms per cubic meter that is the mass in kilometers of the oil?

Answers

Answer:

Step-by-step explanation:

Density is mass divided by volume:

ρ = M / V

So mass is density times volume:

M = ρV

If the density is 865 kg/m³ and the volume is 61.25 m³:

M = (865 kg/m³) (61.25 m³)

M = 52981.25 kg

Final answer:

To find the mass of oil in a tank, multiply the tank's volume (61.25 cubic meters) by the oil's density (865 kg/m³), resulting in 52,981.25 kilograms. The mass is not measured in kilometers, which suggests a typo in the original question.

Explanation:

The question concerns the calculation of the mass of oil if its density and the volume of the tank it fills are known. To find the mass, you would multiply the volume of the oil by its density:

Step-by-Step Calculation:

Determine the volume of the oil. In this case, the volume is already given as 61.25 cubic meters.

Identify the density of the oil. According to the question, it is 865 kilograms per cubic meter.

Multiply the volume by the density to get the mass. That is:

61.25 m³ × 865 kg/m³ = 52,981.25 kilograms.

In terms of mass in kilometers, there appears to be a typo, as mass is not measured in distances like kilometers. The correct unit should likely be kilograms.

Annual sales for a fast food restaurant are $650,000 and are increasing at a rate of 4℅ per year. what are the annual sales after 7 years?​

Answers

Answer:

$855355.656503296, but we round to $855355.66

Step-by-step explanation:

Set up an equation where f(x)=650000(1.04)^n. The 1.04 represents the growth because if it were just .04 we wouldn't be including the initial value and it would decay. The 650000 is the initial value, and we put 1.04 to the nth power because it represents the amount of years. To plug in seven years, simply do 650000(1.04)^7 in your calculator.

A bag contains 10 marbles. Four of the marbles are purple. What is the probability you will choose a purple marble from the bag

1/2
3/10
2/5
1/5

Answers

Answer:

2/5

Step-by-step explanation:

There are 10 marbles and 4 of them are purple. That would give you the fraction 4/10. 4/10 can be simplified to 2/5. So, you have a 2/5ths chance of choosing a purple marble.

The probability of selecting a purple marble from a bag containing 10 marbles, 4 of which are purple, is 2/5.

The question asks: "A bag contains 10 marbles. Four of the marbles are purple. What is the probability you will choose a purple marble from the bag?" To find the probability, you divide the number of favorable outcomes (choosing a purple marble) by the total number of outcomes (all the marbles in the bag). Here, there are 4 purple marbles and 10 marbles in total.

The probability is therefore 4/10, which can be simplified to 2/5. So, the probability of choosing a purple marble from the bag is 2/5.

I need help solving this step by step please.

Answers

Answer:

Yes, i believe that the generalization about the measure of a point angle of a star polygon is true.

First we find sum of interior angle of an n-sided star polygon.

number of triangle in a polygon = n - 2

sum of interior angle of a triangle = 180°

sum of interior angle of an n-sided star polygon = ( n - 2 ) × 180°

To find measure of a point angle, we use:

[tex]\frac{|n-2(d)|}{n}[/tex] × 180°                                                            

To find a point angle we eliminate density by multiplying d by 2  in the formula for finding number of triangle, divide the whole by total number of sides and then multiply by the sum of interior angle of triangle(180°).  

Since all the angle of a regular star polygon are equal, we can calculate each pointy interior angle of a regular star polygon using the formula given below:

[tex]\frac{|n-2(d)|}{n}[/tex] × 180°    

Which stamens is true about f(x)=-6|x+5|-2?
A.) The graph of f(x) is horizontally compressed.
B.) The graph of f(x) is horizontally stretched.
C.) The graph of f(x) opens upward.
D.) The graph of f(x) opens to the right.

Answers

ANSWER

A.) The graph of f(x) is horizontally compressed.

EXPLANATION

The given absolute value function is

[tex]f(x) = - 6 |x + 5| - 2[/tex]

The parent function is

[tex]y = |x| [/tex]

Since the factor -6 has an absolute value greater than 1, the graph of the given function will be narrower than the graph of the base function.

Hence the graph is horizontally stretched by a factor of 6.

The graph opens downwards because of the negative sign.

It has vertex at (-5,-2)

A rectangular prism has a volume of 144 cubic inches. If the length is 2 times the width and the width is 4, find the height of the prism.

Show your work.

Answers

V = Bh

144 = (8 x 4)h

144 = 32h

4.5 = h

Final answer:

To calculate the height of the rectangular prism, we use the formula for volume and the given values to solve for height, resulting in a height of 4.5 inches.

Explanation:

To find the height of a rectangular prism with a given volume where the length is two times the width and the width is known, we use the formula for the volume of a rectangular prism: volume = length × width × height.

Given that the volume is 144 cubic inches, the width is 4 inches, and the length is two times the width, which is 2 × 4 inches = 8 inches, we can substitute these values into the formula:

144 in³ = 8 in × 4 in × height

Next, we need to isolate 'height' by dividing both sides of the equation by the length times the width of the prism:

144 in³ / (8 in × 4 in) = height

144 in³ / 32 in² = height

4.5 in = height

Therefore, the height of the rectangular prism is 4.5 inches.

If AB = 11, BC = 16, and CA = 14, list the angles of ABC in order from smallest to largest.

Answers

Answer:

AB, CA, BC is my answer

It goes AB,CA,BC hopefully this helped

f(x)=x^2+x-30

complete the square

Answers

f(x)= x[tex]x^2+x-30[/tex

    = [tex](x)^2+2*x*\frac{1}{2} +(\frac{1}{2} )^2-(\frac{1}{2} )^2-30[/tex]

    = [tex](x+\frac{1}{2} )^2-\frac{1}{4} -30[/tex]

    = [tex](x+\frac{1}{2} )^2-\frac{121}{4}[/tex]

    =[tex](x+\frac{1}{2} )^2-30\frac{1}{4}[/tex] (Answer)



x y
0 3
1 1
2 -1
Which set of values in the RANGE corresponds to the set {0,2} in the DOMAIN?

Answers

2, -1. I think, possibly.

Answer:

3, -1

Step-by-step explanation:

Which of the following figures does not have line symmetry?

Answers

Answer:

The parallelogram.

Step-by-step explanation:

Line symmetry means that if you folded the shape in half, then both halves would be equal. There is no way to fold a parallelogram in half and have both halves be equal.

B. does not have the line symmetry

What does it mean by exactly one line of symmetry?

The line of symmetry is the line that cuts the shape exactly in half. it means that if you were to fold the shape along a line, both halves will match exactly. Equally, if you were to place the mirror along the line, the shape will remain unchanged. the square has four lines of symmetry.

How many lines of symmetry does a line have?

A line of symmetry is a imaginary axis passing through the center of the object or divides into 2 equal halves. Since the diamond has all 4 sides equal, it has 2 lines of symmetry. the shape could have more than 1 line of symmetry.

Learn more about lines of symmetry here https://brainly.com/question/1597409

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Finish this simile. Use your imagination to complete the description.

Writing similes is like . . .

Answers

Flying a plane through your own imagination. This implies how dominoes make you think and create, using your mind to make comparisons. The other option is like banging my head against the wall. It’s pointless and painful.

Answer:

writing answers to math questions

Step-by-step explanation:

writing a sentance

writing an add

writing a book

How do you write 900.5 and expanded form and word form?

Answers

(9 x 100) + (5 x 0.1)

OR

900 + .5

Nine hundred and five tenths

Hope this helped!

Hello!

-EXPANDED FORM- To make the number 900.5 in expanded form, We use 900 and then add 0.5 which is also 1/2.

-WORD FORM- To make the number 900.5 in word form, the answer would be nine hundred and five tenths

A car travels 102 miles on 3gallons of gas. How far can it travel on 11 Gallons of gas

Answers

Answer:

374 miles

Step-by-step explanation:

To see how many miles each gallon gets, divide 102/3 which is 34 meaning there are 34 miles per gallon so if you multiply 34 x 11 gallons it equals 374 miles.

Hope this helps!

To solve this problem, we will use the concept of a unit rate, which in this scenario is the car's miles per gallon (mpg). A unit rate compares a quantity to one unit of another quantity. Here's how to do it step by step:
1. **Find the unit rate (mpg).**
  The car travels 102 miles on 3 gallons of gas. To find out how many miles it travels per gallon, we'd divide the total number of miles by the number of gallons of gas used:
  \[ \text{mpg} = \frac{\text{miles traveled}}{\text{gallons used}} \]
  \[ \text{mpg} = \frac{102 \text{ miles}}{3 \text{ gallons}} \]
  \[ \text{mpg} = 34 \text{ miles per gallon} \]
  So the car travels 34 miles per gallon of gas.
2. **Calculate the distance the car can travel on 11 gallons of gas.**
  Now that we know the car travels 34 miles on one gallon of gas, we can find out how far it travels on 11 gallons by multiplying the mpg by the number of gallons:
  \[ \text{distance} = \text{mpg} \times \text{gallons available} \]
  \[ \text{distance} = 34 \text{ miles/gallon} \times 11 \text{ gallons} \]
  \[ \text{distance} = 374 \text{ miles} \]
So, the car can travel 374 miles on 11 gallons of gas.

What is 4 groups of 2/7?

Answers

Is 2/7 four time

so is 2•4/7=8/7 =1 1/7

the answer is 1 and 1/7

please help i am timed

Answers

Answer:

Step-by-step explanation:

2x-10 is your answer

Answer:

D. 2x+5

Step-by-step explanation

All you have to do is put them all together and there you have it your answer of D 2x+5

Please help will give brainliest

Answers

Answer:

No, two ordered pairs in this list have a repeated of the domain element.

Step-by-step explanation:

We know that the definition of functions tells us that a function [tex]f[/tex] from a set [tex]A[/tex] to a set [tex]B[/tex] is a relation that assigns to each element [tex]x[/tex] in the set [tex]A[/tex] exactly one element [tex]y[/tex] in the set [tex]B[/tex]. The set [tex]A[/tex] is the domain (also called the set of inputs) of the function and the set [tex]B[/tex] contains the range (also called the set of outputs).

So here is important to know the term exactly one element, Why? because if you don't have this, you don't have a function. From the figure, two ordered pairs in this list have a repeated of the domain element. This can be proven by plotting these three points as indicated below. As you can see, the element 4 in the domain matches both 2 and -2 in the range. In conclusion, this relation is not a function.

Determine the slope of a line parallel to a line whose slope is -5

Answers

Answer:

-5

Step-by-step explanation:

A line that is parallel to another line must have the same slope.

Answer:

-5

Step-by-step explanation:

Parallel lines all have the same slope (as each other). Both of the parallel lines you are describing have a slope of -5.

Sofia bought a motorcycle with a sticker price of $5300. If she paid $310 a
month for 24 months, how much interest did she pay?

A. $7440
B. $3720
c. $2140
D. $5300

Answers

Answer:

2140

Step-by-step explanation:

Sofia paid a total of $7,440 over 24 months for a motorcycle with a sticker price of $5,300. The interest she paid can be found by subtracting the sticker price from the total amount paid, which comes to $2,140. Hence correct option C.

Sofia bought a motorcycle with a sticker price of $5300. If she paid $310 a month for 24 months, first we need to find out the total amount she paid over the 24 months. To do this, we multiply the monthly payment amount by the number of months:

$310 × 24 = $7,440

Now, to find the amount of interest paid, we subtract the original sticker price from the total amount paid:

$7,440 - $5,300 = $2,140

Therefore, Sofia paid $2,140 in interest.

Daniel is choosing between two cellphone plans. "Plan A" charges $80 per month, which includes unlimited text messaging. "Plan B" costs $20 per month plus $0.15 per text message.
What is the system of equation that represents the fees of both "Plan A" and "Plan B"? Identify what your variables represent.

Answers

Answer:

Plan A:

C = $80

C = cost

Plan B:

C = 0.15t + 20

C = cost; t = amount of text messages

Step-by-step explanation:

Let C = cost.

Let t = amount of text messages.

Plan A:

C = $80

Plan B:

C = 0.15t + 20

If the next question asks for you to solve when Plan B will be equal to Plan A, set the two equations equal to each other.

80 = 0.15t + 20

Isolate the variable, t. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

First, subtract 20 from both sides.

80 (-20) = 0.15t + 20 (-20)

80 - 20 = 0.15t

60 = 0.15t

Divide 0.15 from both sides.

(60)/0.15 = (0.15t)/0.15

60/0.15 = t

t = 400

Those who use Plan B must send at least 400 text message to have the same price as Plan A.

~

How many choices are possible with 1 topping

Answers

The answer is 45, I believe so

Graph the linear equation. Find the three points that solve the equation then plot on the graph. -y=x+0

Answers

Answer:

Step-by-step explanation:

We can first make y the subject of the formula by multiplying both sides of the equation by -1 ;

y = -x + 0

This is the equation of a line with a slope of -1, the coefficient of x, and passing through the origin.

In order to find three points that solve the equation, we can let x be;

0, 1, 2

then determine the corresponding values of y.

When x = 0, y = -(0) + 0 = 0

When x = 1, y = -(1) + 0 = -1

When x = 2, y = -2 + 0 = -2

Therefore, we have the following three sets of points that can be used to graph the linear equation;

(0,0)

(1,-1)

(2,-2)

Find the attached for the graph of the equation;

Answer: (-1,1) (0,0) (2,-2)

Step-by-step explanation:

F(x)=x^2+3x+2 is shifted 2 units right the reuslt is g(x) what is g(x)

Answers

Answer:

[tex]g(x)=x^2-x[/tex]

Step-by-step explanation:

Given function is [tex]F\left(x\right)=x^2+3x+2[/tex].

Function [tex]F\left(x\right)=x^2+3x+2[/tex] is shifted 2 units right and gives result to a new function g(x).

Now we need to find about what is the equation of g(x).

We know that f(x-h) indicates right shift by "h" units.

So to get 2 units shift, replace x by (x-2) into given function

[tex]g(x)=F\left(x-2\right)[/tex]

[tex]g(x)=(x-2)^2+3(x-2)+2[/tex]

[tex]g(x)=x^2-4x+4+3x-6+2[/tex]

[tex]g(x)=x^2-x[/tex]

Hence final answer is [tex]g(x)=x^2-x[/tex].

Which is the graph of y = cos(x) + 3? HURRYY!!

Answers

Answer:

See attachment

Step-by-step explanation:

The given function is [tex]y=\cos x +3[/tex]

The base function is [tex]y=\cos x[/tex]

The single transformation applied to this function is a vertical upward shift by 3 units.

Therefore the graph of  [tex]y=\cos x +3[/tex] is graph of  [tex]y=\cos x [/tex] shifted up 3 units.

See attachment

Answer: B

Step-by-step explanation:

Just did the test on edge

If the endpoints of have the coordinates A(9, 8) and B(-1, -2), what is the midpoint of ?

A.
(5, 3)

B.
(4, 5)

C.
(5, 5)

D.
(4, 3)

Answers

Your answer is D. (4,3)

ANSWER

D(4,3)

EXPLANATION

The endpoints of AB have the coordinates A(9, 8) and B(-1, -2).

To calculate the coordinates of the midpoint of AB, we use the midpoint formula,

[tex]( \frac{x_1+x_2}{2},\frac{y_1+y_2}{2} )[/tex]

We substitute the coordinates of the endpoints into the formula to get,

[tex]( \frac{9+ - 1}{2},\frac{8+ - 2}{2} )[/tex]

[tex]( \frac{8}{2},\frac{6}{2} )[/tex]

We simplify further to obtain,

[tex]( 4,3)[/tex]

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Ribosome on which enzyme X is made 2. Ability of the DNA to replicate 3. Amino acid sequence of RNA 4. Gene that codes for enzyme X label the nervous system For biology, what is considered to be beautiful. How do people comprehend in there mind that certain people are and arent beautiful? What is the standard of beauty? Question 9(Multiple Choice Worth 4 points)(08.01 LC) What happens to water when it warms above 4 C? It contracts. It forms ice. Its density decreases. Its composition changes. CAN SOMEONE REWRITE/SHORTEN THIS FOR ME PLEASE? I'LL GIVE BRAINLIESTGenetically modified organisms/ GMOs can be defined as organisms in which the genetic material (DNA) has been altered in a way that does not occur naturally by mating and/or natural recombination. The technology is often called modern biotechnology or gene technology, sometimes also recombinant DNA technology or genetic engineering. It allows selected individual genes to be transferred from one organism into another, also between nonrelated species. Foods produced from or using GM organisms are often referred to as GM foods.GM foods are developed and marketed because there is some advantage either to the producer or consumer of these GM foods. This is meant to translate into a product with a lower price, greater benefit ,or both. GM seed developers wanted their products to be accepted by producers and have concentrated on innovations that bring direct benefit to farmers and generally the food industry.One objective for developing plants based on GM organisms is to improve crop protection. The GM crops currently on the market are mainly aimed at an increased level of crop protection through the introduction of resistance against plant diseases caused by insects or viruses or through increased tolerance towards herbicides.Resistance against insects is achieved by incorporating into the food plant the gene for toxin production from the bacterium Bacillus thuringiensis. This toxin is currently used as a conventional insecticide in agriculture and is safe for human consumption. GM crops that inherently produce this toxin have been shown to require lower quantities of insecticides in specific situations, where pest pressure is high. Virus resistance is achieved through the introduction of a gene from certain viruses which cause diseases in plants. Virus resistance makes plants less susceptible to diseases caused by such viruses, resulting in higher crop yields. How are the details about Twain's failures in his odd jobs important to our understanding of the character? A They reinforce the notion that the character is lazy, does not want to work, and is not capable of working hard. B They detail how prospects in the American West were much dimmer than advertised, making for a harder life for those who sought fame and fortune in the new frontier. C They mark his development from an inexperienced Easterner trying to make-it-rich to an experienced, yet cynical, Western writer. D They show that he is eager to work but has few useful skills, making him a loveable but pathetic Please help with the first portion, Ive already figured out the bottom and so one just that part. How many countries have spanish as their official language? Miguel and Grace started collecting rare coins at the same time. Back then, they had the same number of rare coins. Miguel has been collecting 5 coins each week and he now has 38 coins. Grace has been collecting 3 coins each week and she now has 24 coins. How many rare coins did they have altogether when they started collecting?A)3B)6C)7D)14 Match the following vocabulary words with their definitions. 1 a title or key accompanying an illustration or map abstract 2.facts from which conclusions can be drawn legend 3.thought of apart from material objects; the opposite of concrete data Steam Workshop Downloader