Answer:
FV= $38,735.32
Step-by-step explanation:
Giving the following information:
Monthly deposit= $100
Number of periods= 18*12= 216 months
The interest rate is confusing. I will assume an interest rate of 6%. If it is not correct, just change it in the formula.
Monthly interest rate= 0.06/12= 0.005
To calculate the future value, we need to use the following formula:
FV= {A*[(1+i)^n-1]}/i
A= monthly deposit
FV= {100*[(1.005^216) - 1]} / 0.005
FV= $38,735.32
Lisa paid 45.30 for 15.9 gallons of gasoline.what was the cost per gallon, rounded to the nearest hundreath
Answer:
About $2.85 per gallon
Step-by-step explanation:
We can set up a proportion [tex]\frac{45.3}{15.9}[/tex]=[tex]\frac{x}{1}[/tex] we can then cross multiply, getting 15.9x=45.3. When you divide you get about $2.85
Solve this equation, and show work. worth 40 points.
Recall the following property of exponents:
[tex]a^b\cdot a^c=a^{b+c}[/tex]
[tex]\implies 216^{-3k}\cdot 216^{-2k}=216^{-3k-2k}=216^{-5k}[/tex]
Now, notice that 6² = 36 and 6³ = 216, which means that
[tex]216^{-5k}=36^{2k-1} \iff (6^3)^{-5k}=(6^2)^{2k-1}[/tex]
Recall another property of (real) exponents:
[tex](a^b)^c=a^{bc}[/tex]
[tex]\implies(6^3)^{-5k}=6^{3(-5k)}=6^{-15k}\text{ and }(6^2)^{2k-1}=6^{2(2k-1)}=6^{4k-2}[/tex]
So we have
[tex]216^{-5k}=36^{2k-1} \iff 6^{-15k}=6^{4k-2}[/tex]
Since both sides are equal powers of 6, that must mean that the exponents must be equal, so
[tex]-15k=4k-2[/tex]
Solve for k :
[tex]-15k-4k=(4k-4k)-2[/tex]
[tex]-19k=-2[/tex]
[tex]k=\dfrac{-2}{-19}=\boxed{\dfrac2{19}}[/tex]
Water freezes at 0 celcius and 32 fahrenheit
Answer:
true
Step-by-step explanation:
Can you help me fill the graph please?
Answer:
8=6 2/5
50=40
100=80
Step-by-step explanation:
8x4/5=6 2/5
4x10=40 so 5x10=50 (I got this from the second row)
5x20=100 so 4x20=80 (also from second row)
Graph the line y=−3x+b if it is known that the graph goes through point:
b
B(5, 2)
Answer: y=-3x+17
b = 17
Simplify the question 8(x+9)
Step-by-step explanation:
8(x + 9)
8x + 72 = 0
8x = -72
x = -72/8
x = -9
Answer:
Given : 8(x + 9)
Solution :
[tex]8(x + 9) = 0\\ [/tex]
Multiply 8 to both x and 9
[tex]8x + 72 = 0 \\ [/tex]
Now, Move 72 to RHS from LHS
[tex]8x = - 72 \\ [/tex]
[tex]x = \dfrac{ - 72}{8} \\ [/tex]
And the final ans we get is :
[tex]\boxed{x = - 9}[/tex]
Which expression can be used to find 80% of 120?
Answer: the expression (120/100)*80 results in 80% of 120
Step-by-step explanation:
Find an equation of the circle that has center (-6, 4) and passes through (4, -5).
Answer:
waala kang jowa sabi ko
Write an equation for the description.
Tanmayi wants to raise $150 for a school fundraiser. She has raised $120 so far. How much more does she
need to reach her goal? Let m be how much more is needed.
Plzzzz hellpppp
Tanmayi will need $30 more to reach her goal.
$120 + n = $150
$150 - $120 = 30
n = 30
Kendra is participating in a fundraiser walk-a-thon she walks 4 miles in 60 minutes how many minutes will it take to walk 7 miles
Answer:
105 min
Step-by-step explanation:
60 minutes ÷ 4 miles= 15 minutes per mile
15min per mile x 7 miles = 105 minutes
HELPPPP!!!! PLEASEEE!!!
Which statement below is true?
A. If p → q is true, then q → p is true.
B. If p → q is true and p is true, then q is true.
C. If p → q and q → r are true, then q → p is true.
D. If p → q and q → r are true, then r → p is true.
Answer: i believe the answer is B
Step-by-step explanation: because if p to q is true, then that means p and q are both true!
Marco spent $85.43 on a new pair of
shoes, $21 on a t-shirt, and $7.84 on a
pair of socks. If he gave the sales clerk
$120, how much change should he
receive?
Answer:
5.73
Step-by-step explanation:
Answer:
He should have $5.73 as change
Step-by-step explanation:
First add 85.43 with 21 and 7.84 and then do 120 - 114.27.
What's the number of people left to play at 10 of
15 have played
Answer:
5 people will be left to play
Answer: Out of 10 to 15 people played, 5 people are left to play
Let f(x) = 2x – 3 and g(x) = 3x – 2. Find the value.
(fog)(-2)
(fog)(-2) =
PLEASE HELP!!!
Answer:
Ok:
Step-by-step explanation:
So f°g . means f(g(x)). (The ° should be more center and bigger but I don't know to do that on a keyboard). f(g(x)) means that you replace the x in f(x) with the g(x) function. i.e:
if f(x) = 2x+2
and g(x) = [tex]x^2[/tex]
f(g(x)) = [tex]2x^2+2[/tex].
Similarly, in this case, we get f(x) = 2x-3 and g(x) = 3x-2.
Then, f(g(x)) or f°g(x) is 2(3x-2) - 3.
And we plug in -2 to solve:
2(3(-2)-2)-3.
and get -19.
Check if I am wrong because everyone makes mistakes but that is the way to solve this.
HELPPP!!!! It’s due tmmr
Answer:
total of 482
Step-by-step explanation:
He sold 1940
20% on first 500
500 *.20 = 100 commission
Then 25% on the next 1000
1940 -500 = 1440 left
He has 1000
1000 * 25%
1000*.25 = 250 commission
1440-1000 = 440 left
440 at 30%
440*.30 =132 commission
Add together
100+250+132 = 482
Use the geometric probability distribution to solve the following problem. On the leeward side of the island of Oahu, in a small village, about 74% of the residents are of Hawaiian ancestry. Let n = 1, 2, 3, … represent the number of people you must meet until you encounter the first person of Hawaiian ancestry in the village. (a) Write out a formula for the probability distribution of the random variable n. (Enter a mathematical expression.) P(n) = p(1 - p)n-1 (b) Compute the probabilities that n = 1, n = 2, and n = 3. (For each answer, enter a number. Round your answers to three decimal places.) P(1) = 0.740 P(2) = 0.192 P(3) = 0.050 (c) Compute the probability that n ≥ 4. Hint: P(n ≥ 4) = 1 − P(n = 1) − P(n = 2) − P(n = 3). (Enter a number. Round your answer to three decimal places.) 0.018 (d) What is the expected number of residents in the village you must meet before you encounter the first person of Hawaiian ancestry? Hint: Use μ for the geometric distribution and round. (Enter a number. Round your answer to the nearest whole number.) residents
Answer:
(a) [tex]\text{P(n)} = \text{p} \times \text{(1 - p)}^{n-1} ; \text{ n} = 1, 2, 3,....[/tex]
(b) P(1) = 0.740, P(2) = 0.192, and P(3) = 0.050.
(c) The probability that n ≥ 4 is 0.018.
(d) The expected number of residents in the village you must meet before you encounter the first person of Hawaiian ancestry is 3.
Step-by-step explanation:
We are given that on the leeward side of the island of Oahu, in a small village, about 74% of the residents are of Hawaiian ancestry.
Let n = 1, 2, 3, … represent the number of people you must meet until you encounter the first person of Hawaiian ancestry in the village.
(a) We can observe that the above situation can be represented through the geometric distribution because the geometric distribution states that we will keep on going with the trials until we achieve our first success,
Here also, n represent the number of people you must meet until you encounter the first person of Hawaiian ancestry in the village.
So, the probability distribution of the geometric distribution is given by;
[tex]\text{P(n)} = \text{p} \times \text{(1 - p)}^{n-1} ; \text{ n} = 1, 2, 3,....[/tex]
where, p = probability that the residents are of Hawaiian ancestry = 74%
(b) The probabilities that n = 1, n = 2, and n = 3 is given by;
[tex]\text{P(n)} = \text{p} \times \text{(1 - p)}^{n-1}[/tex]
P(1) = [tex]\text{0.74} \times \text{(1 - 0.74)}^{1-1}[/tex] = 0.74
P(2) = [tex]\text{0.74} \times \text{(1 - 0.74)}^{2-1}[/tex] = 0.192
P(3) = [tex]\text{0.74} \times \text{(1 - 0.74)}^{3-1}[/tex] = 0.050
(c) The probability that n ≥ 4 is given by = P(n ≥ 4)
P(n ≥ 4) = 1 - P(n = 1) - P(n = 2) - P(n = 3)
= 1 - 0.74 - 0.192 - 0.050
= 0.018
(d) The expected number of residents in the village you must meet before you encounter the first person of Hawaiian ancestry is given by = E(n)
We know that the mean of the geometric distribution is given by;
Mean = [tex]\dfrac{p}{1-p}[/tex] = [tex]\dfrac{0.74}{1-0.74}[/tex]
= [tex]\dfrac{0.74}{0.26}[/tex] = 2.85 or 3 (approx).
50 apples cost $25.how much would 75 apples cost
Answer:
150
Step-by-step explanation: one apple cost $0.50, so 75/ $0.50= 150
The perimeter of a rectangular room is 60 feet. Let x be the width of the room (in feet) and let y be the length of the room (in feet). Select all of the equations below that could model this situation.
2(x+y)=60
2x+2y=60
x+2y=60
2x+y=60
x+y=60
Answer:
Step-by-step explanation:
2(x+y)=60
2x+2y=60
The second is the same as the 1st but with the distribution
perimeter formula: P=2(W+L)
We can distribute .Then P = 2W+2L
Evaluate 12y when y = 4.
Answer:
48
Step-by-step explanation:
12*4=48
substitute y for the given value
Answer:
48
Step-by-step explanation:
12y
Let y=4
12*4 = 48
Please hurry it’s urgent Thank you
Answer:
D
Step-by-step explanation:
the answer is the graph on the bottom right corner, 400 pages on the y axis and 16 days on the x axis. 25 pages a day.
hope this helped!
Mark's grade went from 65% to 90%. What was his percent increase?
А
25%
B
28%
С
38%
D
90%
Answer:
A
Step-by-step explanation:
Why is near impossible to draw a rhombus on Geoboard and easy to draw a square?
Thank you in advance :)
Answer: Think about diagonal sides and horizontal bases.
Step-by-step explanation: "Think outside of the box." as they say.
See the screenshot attached.
A farmer notes that in a field full of horses and chickens there are 35 heads and 98 feet. How many of each animal are there?
Answer:
There are 14 horses and 21 chickens.
Step-by-step explanation:
First, you have to make expression for horse and chicken. So we can let x be the number of horses and y will be the number of chickens. Next, given that the total number of feet for both animals is 98 so you have to make simultaneous equation :
[tex]4x + 2y = 98[/tex]
( horse has 4 feet and chicken has 2 feet )
There are a total of 35 heads so the other equation will be :
[tex]x + y = 35[/tex]
Lastly, you have to solve it :
[tex]4x + 2y = 98[/tex]
[tex]2(2x + y) = 98[/tex]
[tex]2x + y = 49 - - - (1)[/tex]
[tex]x + y = 35 - - - (2)[/tex]
[tex](1) - (2)[/tex]
[tex]2x + y - x - y = 49 - 35[/tex]
[tex]x = 14[/tex]
[tex]substitute \: x = 14 \: into \: (2)[/tex]
[tex]14 + y = 35[/tex]
[tex]y = 35 - 14[/tex]
[tex]y = 21[/tex]
what the biggest 7/2 or 3 1/4?
Answer:
7/2
Step-by-step explanation:
help please (: picture is included
Find the equation of this line.
Simplify the fractional part.
(Picture)
Answer:
y = 1/3x + 2
Step-by-step explanation:
Rise over run + y intercept
URGENT!!!!!! Find the value of q in the following system so that the solution to the system is——
====================================================
Explanation:
The left hand side of the first equation is x-3y
The left hand side of the second equation is 2x-6y = 2(x-3y). Note how it's simply double of the first expression x-3y
If we multiply both sides of the first equation by 2, we get
x-3y = 4
2(x-3y) = 2*4
2x-6y = 8
Meaning that 2x-6y = 8 is equivalent to x-3y = 4. Both produce the same line leading to infinitely many solutions. Each solution will lay along the line x-3y = 4.
We can say each solution is in the set {(x,y): x-3y = 4}
Which is the same as saying each solution is of the form (3y+4,y)
68,347 rounded tp the nearest hundred
Ling spent $23.96 on cooking fuel for an upcoming camping trip. If she bought 4 cans of fuel, how much did she pay for each can?
Answer:
The answer is $5.99
Step-by-step explanation:
$23.96 divided by 4 is $5.99
Answer:
The answer is $5.99
Step-by-step explanation:
I just did the quiz.
the average weight of 6 people is 173, a 7th person gets on and now the average weight is 165, how much did the 7th person weigh
Answer:
117
Step-by-step explanation:
The average of all 7 people is the total weight of the original 6 people, plus the weight of the 7th person, all divided by 7.
For problems like this involving an average of numbers that are "close" together, here is a different strategy for solving the problem that you might like to try.
The original 6 people have an average weight of 173, which is 8 pounds more than the average of all 7 people. So all together, the weight of those 6 people is 6*8=48 pounds over the 165 average. That means the 7th person's weight must be 48 pounds below the 165 average.
So the weight of the 7th person is 165-48 = 117 pounds.
Answer:
The 7th person weighted 117
Step-by-step explanation:
Average Value
The mean or average of a number n of measurements is defined as the sum of all values divided by n.
[tex]\displaystyle \bar x=\frac{\sum x_i}{n}\\[/tex]
The question gives us some input data. The average weight of n=6 people is [tex]\bar x=173[/tex]. With this information, we can set this relationship:
[tex]\displaystyle 173=\frac{\sum x_i}{6}[/tex]
From the above equation, we know the sum of the first 6 persons:
[tex]\sum x_i=6*173=1,038[/tex]
When a 7th person gets on, the new average gets down to 165 and n=7. The equation for the new average is:
[tex]\displaystyle 165=\frac{\sum x_i+X}{7}[/tex]
Note we have a new summand to the numerator. It's the weight of the 7th person. Let's solve for X:
[tex]\displaystyle 165=\frac{1,038+X}{7}[/tex]
Multiply by 7:
[tex]7*165=1,038+X[/tex]
Operate and swap sides:
[tex]1,038 +X=1,155[/tex]
[tex]X=1,155-1,038=117[/tex]
The 7th person weighted 117
