The simpliest way to answer the question is by iteration, substituting n with the numbers 1, 2, 3, 4 to find the first 4 numbers. So we have the formula;
[tex]A_n=3(2)^{n-1}[/tex]When n = 1,
[tex]\begin{gathered} A_n=3(2)^{n-1} \\ A_1=3(2)^{1-1} \\ A_1=3(2)^0 \\ A_1=3 \end{gathered}[/tex]When n = 2,
[tex]\begin{gathered} A_n=3(2)^{n-1} \\ A_2=3(2)^{2-1} \\ A_2=3(2)^1 \\ A_2=6^{} \end{gathered}[/tex]When n = 3,
[tex]\begin{gathered} A_n=3(2)^{n-1} \\ A_3=3(2)^{3-1} \\ A_3=3(2)^2 \\ A_3=12 \end{gathered}[/tex]When n = 4,
[tex]\begin{gathered} A_n=3(2)^{n-1} \\ A_4=3(2)^{4-1} \\ A_4=3(2)^3 \\ A_4=24 \end{gathered}[/tex]Therefore when n = {1, 2, 3, 4}, An = {3, 6, 12, 24}, making 3, 6, 12, 24 the first 4 numbers of our formula.
Therefore the answer is LETTER C.
Andrea, Ben, Christine, and Doug all live on the same street as their school. The street runs from east to west.Andrea lives 5 1/2 blocks to the west of school.Ben lives 4 blocks to the east of school.Christine lives 2 blocks to the west of school.Doug lives 6 1/2 blocks to the east of school.Use this information to complete the following.Part ARepresent the relative position of the houses on a number line with the school at zero, points to the west represented by negative numbers, and points to the east represented by positive numbers.Part BHow far does Ben live from Andrea? Show how you arrived at your answer using sums or differences.
From the statement of the problem, we know that.
• Andrea lives 5 1/2 blocks to the west of school → x = -5.5,
,• Ben lives 4 blocks to the east of school → x = +4,
,• Christine lives 2 blocks to the west of school → x = -2,
,• Doug lives 6 1/2 blocks to the east of school → x = +6.5.
A) Using the data above, we have:
B) The x coordinate of:
• Andrea is x_A = -5.5,
,• Ben is x_B = +4.
The distance between Ben and Andrea is equal to the difference between its coordinates:
[tex]d=x_B-x_A=4-(-5.5)=4+5.5=9.5.[/tex]We find that Ben lives 9.5 blocks from Andrea.
Diane opened a savings account 3 years ago the account earns 9% interest compounded monthly if the current balance is 100.00 how much did she despoit initially
Answer:
The amount she deposited initially is $76.41.
[tex]\text{ \$76.41}[/tex]Explanation:
We want to find the amount of Principal she deposited initially.
Recall that the formula for calculating the Principal of a compound interest is;
[tex]P=\frac{A}{(1+\frac{r}{n})^{nt}}[/tex]Where;
P = Principal / initial amount
A = Future/ final amount
r = Interest rate (decimal)
n = number of times the interest is compounded per year.
t = Time in years
From the question, we were given the following;
A = $100.00
r = 9% = 0.09
n = monthly (12 months in a year) = 12 times
t = 3 years
Substituting the given values into the formula, we have;
[tex]\begin{gathered} P=\frac{100.00}{(1+\frac{0.09}{12})^{12(3)}} \\ P=\frac{100.00}{(1+0.0075)^{36}} \\ P=\frac{100.00}{(1.0075)^{36}} \\ P=76.41 \\ P=\text{ \$76.41} \end{gathered}[/tex]Therefore, the amount she deposited initially is $76.41.
[tex]\text{ \$76.41}[/tex]In Exercises 1-3, the perpendicular blsectors of ABC Intersect at point G, or the anglebisectors of AXYZ intersect at point P. Find the Indicated measure. Tell which theoremyou used.
We have a line:
And we draw its perpendicular bisector:
Then, any point on the bisector is equidistant to the endpoints of the line:
This is called: the perpendicular bisector theorem.
1In this case we have that:
Since the line is the black one, the bisector is the purple one, then both red segments measure the same : 9.
Answer: BG = 9 (bisector theorem)
2In this case, as we can observe in the image, the red lines are equidistant then CG = 10
Answer: CG = 10 (bisector theorem)
Unit 4 What is the rate of return when 20 shares of Stock A, purchased for $20/share, are sold for $490? The commission on the sale is $6. Rate of Return = [?] % Give your answer as a percent rounded to the nearest tenth.
Answer:
21%
Step-by-step explanation:
You want the rate of return on 20 shares of stock bought for $20 per share and sold for $490 with a commission on the sale of $6.
Rate of returnThe rate of return is the percentage change between the sale proceeds and the cost of the stock.
rate of return = (proceeds/cost -1) × 100%
= ((490 -6)/(20·20) -1) × 100% = 21%
The rate of return is 21%.
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Use graph to find the slope and y-intercept of the line. Compare the values to the equation y= -x+5
As given by the question
There are given that the graph of the line.
Now,
To find the slope and y-intercept of the line, first select two intersect point from the graph.
Then,
The points are:
[tex](0,\text{ 5) and (5, 0)}[/tex]Then,
First find the slope,
So,
From the formula of slope,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where,
[tex]x_1=0,y_1=5,x_2=5,y_2=0[/tex]Then,
Put all the value into the given formula.
So,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{0_{}-5_{}}{5_{}-0_{}} \\ m=-\frac{5}{5} \\ m=-1 \end{gathered}[/tex]Now,
From the standard form of the line,
[tex]y=mx+b[/tex]Then,
Put y is 5, x is 0 and m is -5 into the above equation to find the y-intercept
So,
[tex]\begin{gathered} y=mx+b \\ 5=-1(0)+b \\ b=5 \end{gathered}[/tex]Hence, the value of the y-intercept is 5.
Now,
The line equation is shown below:
[tex]\begin{gathered} y=mx+b \\ y=-1x+b \\ y=-x+5 \end{gathered}[/tex]Hence, the slope of the line is -1, y-intercept of the line is 5 and the equation of line is y = -x + 5.
9. Leyla has 18 50-cent and 20-cent coins altogether. She has a total of $6.90. How many 20-cent coins does she have?
According to the information given in the exercise:
- Leyla has 18 coins of 50 cents and 20 cents.
. She has a total of $6.90.
Let be "f" the number 50-cent coins and "t" the number 20-cent coins.
Since 1 dollar is equal to 100 cents, you know that:
[tex]6.90dollars=690cents[/tex]Then, knowing the above, you can set up the following System of Equations:
[tex]\begin{cases}f+t=18 \\ \\ 50f+20t=690\end{cases}[/tex]To find the value of "t", you can apply the Substitution Method:
1. Take the first equation and solve for "f":
[tex]f=18-t[/tex]2. Substitute this equation into the second equation and solve for "t":
[tex]\begin{gathered} 50f+20t=690 \\ \\ 50(18-t)+20t=690 \end{gathered}[/tex][tex]\begin{gathered} 50(18-t)+20t=690 \\ \\ 900-50t+20t=690 \end{gathered}[/tex][tex]\begin{gathered} 900-30t=690 \\ \\ -30t=690-900 \\ \\ -30t=-210 \end{gathered}[/tex][tex]\begin{gathered} t=\frac{-210}{-30} \\ \\ t=7 \end{gathered}[/tex]Therefore, the answer is: She has 7 coins of 20 cents.
a 180 ounce bag weighs more than an 11 lb bag true or false
Let's make a conversion:
[tex]180oz\times\frac{1lb}{16oz}=11.25lb[/tex]Since:
[tex]11.25lb>11lb[/tex]It's true
Which of these frequency counts would be represented by the largest number of dots in a dot plot?
A. 25
B.23
C.24
D.22
The frequency count that a dot plot's greatest number of dots would depict is 25 (option A).
Given that,
The Option a is 25, b is 23, c is 24 and d is 22.
What is a dot plot?A dot plot is a graph that shows the frequency of a set of data and is comparable to a histogram. The frequency of the data is represented by the dots in the dot plot. The number of dots increases as the frequency of a data increases.
According to the information in this question, 25 would have the most dots, whilst 22 would have the fewest. A dot plot is a useful tool for displaying frequencies. Additionally, it works well with small data sets.
Therefore, The frequency count that a Gain on equipment sale equals selling price minus book value of equipment dot plot's greatest number of dots would depict is 25 (option A).
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Solve the following equation for x. Please show all your solution steps. 2x - 5 + 3x = x - 41
Three girls play three rounds of a game. On each round there are two winners and one loser. The girl who loses on a round has to double the number of chips that each of the other girls has by giving up some of her own chips. Each girl loses one round. At the end of three rounds, each girl has 24 chips. How many chips did each girl have at the beginning of the game?
The Solution:
Let the 3 girls be represented with A, B, and C.
At round 1:
Let C be the loser while A and B are winners.
A has 12 chips
B has 21 chips
C has 39 chips
At round 2:
Let B be the loser while A and C are winners.
A has 24 chips
B has 42 chips
C has 6 chips
At round 3:
Let A be the loser while A and C are winners.
A has 24 chips.
B has 24 chips.
C has 24 chips.
Therefore, the girl A has 12 chips, girl B has 21 chips and girl C has 39 chips at the beginning of the game.
2. Find the radian measure of an angle of 320°. (Leave in terms of rr.) A. 9 16 0 B. 16 9t 0 90 ID 10
SOLUTION
Find the radian measure of an angle of 320°. (Leave in terms of rr.)
We have that 360° × π/180 = 6.283rad
Do you
320° x π / 180 =
The table below shows the number of months and the amount spent on internet service. Which equation represents the total cost (t) based on the number of months (m) of service?1. t=45m 2. t=2m 3. t=90m4. t=4me
Given:
Number of months and the amount spent on internet service is tabulated.
Let the total cost (t) and the number of months (m)
Therefore equation is
[tex]t=45m[/tex]
The Panthers and the Vikings are competing for the state basketball championship. The data shows the height in inches of the starting lineup for
each team.
Panthers: 72, 74, 71, 73, 75
Vikings: 71, 77, 76, 74, 74
Which statement is true about the data?
The average height of the Viking's starting lineup is 1.4 inches greater than the average height of the Panther's starting lineup.
The Panthers and the Vikings are competing for the state basketball championship. The data shows the height in inches of the starting lineup for each team.
The heights of the players on the Panther's team are 72, 74, 71, 73, and 75. The heights of the players on the Viking's team are 71, 77, 76, 74, and 74.
Let the average height of the Panther's starting lineup be denoted by the variable "A1".
A1 = (72 + 74 + 71 + 73 + 75)/5
A1 = 365/5
A1 = 73
So, the average height of the Panther's starting lineup is 73 inches.
Let the average height of the Viking's starting lineup be denoted by the variable "A2".
A2 = (71 + 77 + 76 + 74 + 74)/5
A2 = 372/5
A2 = 74.4
So, the average height of the Viking's starting lineup is 74.4 inches.
The difference in the average height is calculated below.
d = A2 - A1
d = 74.4 - 73
d = 1.4
Hence, the average height of the Viking's starting lineup is 1.4 inches greater than the average height of the Panther's starting lineup.
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An uber charges a flat fee of $1.50, plus an additional $0.75 per mile. If Max only
has up to $12 to spend?
Answer:
14 miles
Step-by-step explanation:
If you have $12 to spend and there's a flat fee $1.50
You subtract your $1.50 from $12
12-1.50=10.50
Then you divide 10.50 by .75
10.50÷.75=14
So you get 14 miles with $12
Which is less: (-25) + 12 or 40 + (-63)? Show your work.
The first expression
(-25) + 12
open the parentheses
-25 +12
= - 13
for the second expression
40 + (-63)
in mathematics
- x + = -
40 - 63
= -23
from the two results
-13 and -23
-13 is greater than -23, therefore -23 is less or 40 + (-63)
answer: 40 + (-63) is less
graph the function f(x)=3-(x)
The given function is
[tex]f(x)=3-x[/tex]To graph this linear function we have to complete a table of values. We replace each x-value in the function to get each y-values to form coordinated pairs.
x f(x)
-2 5
-1 4
0 3
1 2
Let's do the calculations for each f(x) value.
[tex]\begin{gathered} f(-2)=3-(-2)=3+2=5 \\ f(-1)=3-(-1)=3+1=4 \\ f(0)=3-0=3 \\ f(1)=3-1=2 \end{gathered}[/tex]At last, we have to graph each point and draw a straight line. The graph below shows the graph for the function.
Sam paid $4.50 to have two shirts cleaned. If the dry cleaning service charges the same amount for any shirt, which equation can be used to represent the total cost, c, of having n shirts cleaned? A c = 4.5n B. c = 2.25n C. c = 4.5 +n D. c = 2.25 + n
Sam paid $4.50 to have two shirts cleaned.
If the dry cleaning service charges the same amount for any shirt then it means that for each shirt the rate is
[tex]\frac{\$4.50}{2}=\$2.25[/tex]If there are n shirts then the total cost (c) of the shirts can be represented by the following equation.
[tex]c=2.25n[/tex]If you substitute n = 2 shirts into the above equation then the total cost will be $4.50 which satisfies the given information.
Therefore, the correct answer is option B
An employee at a state park has 84 photos of animals found at the park. She wants to arrange the photos in rows so that every row except the bottom row has the same number of photos. She also wants there to be at least 8 rows. Complete the description of two different ways she can arrange the photos.
Reverse the rows and photos in each row (ex 5 rows 10 photos=10 rows 5 photos) to get another 3 sets.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.5 rows of 10 photos and last row with 3 photos,
6 rows of 8 photos and last row with 5 photos,
7 rows of 7 photos and last row with 4 photos,
Hence, reverse the rows and photos in each row (ex 5 rows 10 photos=10 rows 5 photos) to get another 3 sets.
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expand and simplify(p+4)(P+3)P-1)
In linear equation, p³ - 6p² + 5p - 12 is simplify od equation .
What is a linear equation example?
Ax+By=C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5.Finding both intercepts of an equation in this format is rather simple (x and y).(p+4)(P+3)(P-1)
= p² + 3p + 4p + 12
= ( p - 1 ) ( p² + 3p + 4p + 12 )
= p³ + 7p² + 12p - p² - 7p - 12
= p³ - 6p² + 5p - 12
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The following histogram represents the points earned by students on a vocabulary pre-test.
Explanation
By observation, the number of student scores represented on the histogram can be gotten by adding up the frequency. This can be seen below.
[tex]3+2+7+8+4=24[/tex]Answer: 24(option 1)
-0.15 decimal as a fraction or mixed number in simplified
Answer:
-3/20
Explanation:
Given the decimal number: -0.15
There are 2 digits after the decimal point, therefore in fraction form, we have:
[tex]-0.15=-\frac{15}{100}[/tex]Next, the fraction is reduced to its simplest form.
[tex]-\frac{15}{100}=-\frac{5\times3}{5\times20}=-\frac{3}{20}[/tex]The simplified form is -3/20.
what is the acceleration of a car that goes from 10 mph to the speed of 50 mph in four seconds
The acceleration is given by the variation of the speed divided by the time.
So:
[tex]\begin{gathered} a=\frac{v-v0}{t} \\ a=\frac{50-10}{4} \\ a=40/4 \\ a=10m/s^{2} \end{gathered}[/tex]Answer: 10m/s²
2 (3s' + 9s + 3) - (6s + 1) Submitadd and subtract polynomialswe're doing subtract for this one
SOLUTION
[tex]undefined[/tex]9. If two lines are cut by a transversal so that (alternate interior, alternate exterior, corresponding, consecutive interior) angles are congruent, then the lines are parallel.
Answer:
If two lines are cut by a transversal so that (alternate interior, alternate exterior, corresponding, consecutive interior) angles are congruent, then the lines are parallel
Explanation:
When two lines are cut by a transversal so that alternate interiors, alternate exterior or corresponding, are congruent, then the line must be parallel
If;
[tex]\begin{gathered} \measuredangle a=\measuredangle b\text{ (alternate interior)} \\ \measuredangle x=\measuredangle y\text{ (alternate exterior)} \\ \measuredangle x=\measuredangle b\text{ (corresponding angles)} \end{gathered}[/tex]then the lines are parallel.
Trey made $2000 in taxable income last year. suppose the income tax rate is 10% for the first $9500 plus 14% for the amount over $9500. How much must trey pay in income tax for last year?
SInce he made $2000 , and this is less than the limit for the first bracket, Trey will need to pay just 10% on his gain:
10% of $2000 = 0.1 * 2000 = $200.
His tax is $200.
[tex] \frac{1}{5} [/tex]convert into a prercentage
Answer:
20%
Explanation:
To convert a fraction into a percentage, multiply the fraction by 100.
Thus, the fraction 1/5 as a percentage is:
[tex]\begin{gathered} =\frac{1}{5}\times100 \\ =\frac{100}{5} \\ =20\% \end{gathered}[/tex]The percentage equivalent of 1/5 is 20%.
The product of two consecutive odd numbers is 323. Find the numbers.
Let the two consecutive numbers be x and (x+2).
According to the given condition,
to rent a booth at a County Fair cost $42 per day plus a one-time equipment fee of $85 find the number of days mr. Jones rented a booth if he paid a total of $337
Consider the following quadratic equation - x ^ 2 + 3x - 7 = 0 Step 1 of 2 Find the values of a , b, and that should be used in the quadratic formula to determine the solution of the quadratic equation
Recall that the quadratic formula states that the solution to the quadratic equation:
[tex]ax^2+bx+c=0[/tex]are:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}.[/tex]Notice that a is the coefficient of the quadratic part, b is the coefficient of the linear part and c is a constant.
We can rewrite the given equation as follows:
[tex](-1)x^2+3x+(-7)=0.[/tex]Therefore, the values a, b, and c that should be used in the quadratic formula to compute the solutions to the quadratic equation:
[tex]-x^2+3x-7=0[/tex]are:
[tex]\begin{gathered} a=-1, \\ b=3, \\ c=-7. \end{gathered}[/tex]Answer:
[tex]\begin{gathered} a=-1, \\ b=3, \\ c=-7. \end{gathered}[/tex]without graphing, identify the equation of the axis of symmetry for f(x)=-3|x-2|-7
Solution:
Given:
[tex]f(x)=-3|x-2|-7[/tex]From the absolute function, the axis of symmetry is;
[tex]\begin{gathered} y=|x-a| \\ where: \\ a\text{ is the axis of symmetry} \end{gathered}[/tex]Hence, comparing it to the equation given;
[tex]\begin{gathered} f(x)=-3|x-2|-7 \\ y=|x-a| \\ \\ a=2 \\ Hence,\text{ the axis of symmetry is at x = 2} \end{gathered}[/tex]Therefore, OPTION C is correct.
Answer: other guy is wrong it’s x= -2
Step-by-step explanation: