Answer:
$2774.47
Step-by-step explanation:
To find how much Antuan's ending balance will be, we can use the formula for compound interest.
[tex]A=P(1+\dfrac{r}{n})^{nt}[/tex]
The values that we currently have are:
P = 2590
t = 3
n = 4 quarterly
r = 2.3% or 0.023
Now we can plug these values into our formula.
[tex]A=P(1+\dfrac{r}{n})^{nt}[/tex]
[tex]A=2590(1+\dfrac{0.023}{4})^{4(3)}[/tex]
[tex]A=2590(1+0.00575)^{12}[/tex]
[tex]A=2590(1.00575)^{12}[/tex]
[tex]A=2774.47[/tex]
So Antuan's ending balance will be $2774.47.
What is the answer for #7?
Answer:
radius: 1.84 inheight: 3.68 inStep-by-step explanation:
After you've worked a couple of "optimum cylinder" problems, you find that the cylinder with the least surface area for a given volume has a height that is equal to its diameter. So, the volume equation becomes ...
V = πr²·h = 2πr³ = 39 in³
Then the radius is ...
r = ∛(39/(2π)) in ≈ 1.83779 in ≈ 1.84 in
h = 2r = 3.67557 in ≈ 3.68 in
_____
The total surface area of a cylinder is ...
S = 2πr² + 2πrh
For a given volume, V, this becomes ...
S = 2π(r² +r·(V/(πr²))) = 2πr² +2V/r
The derivative of this with respect to r is ...
S' = 4πr -2V/r²
Setting this to zero and multiplying by r²/2 gives ...
0 = 2πr³ -V
r = ∛(V/(2π)) . . . . . . . . looks a lot like the expression above for r
__
If we substitute the equation for V into the equation just above this last one, we have ...
0 = 2πr³ - πr²·h
Dividing by πr² gives ...
0 = 2r - h
h = 2r . . . . . generic solution for cylinder optimization problems
Need help. Also what graphing utility could I use?
sadly i haven’t learned this so i can’t help you with the answers themselves but a graphing utility you could use is a graphing calculator or a graphing calculator online i know one called desmos.com just not sure if it has the intersect feature so i recommend graphing calculator
What is this quadratic function in standard form? y=(x+7) (x−5) Enter your answer in the box.
Answer:
y = x^2 +2x -35
Step-by-step explanation:
Multiply the binomials. The distributive property is helpful.
y = x(x -5) +7(x -5) . . . . the terms of the first binomial multiplied by the second
= x^2 -5x +7x -35 . . . . eliminate parenthses
y = x^2 +2x -35 . . . . . . collect terms
Find the quotient 3/4 divided by 1/3 =
Answer:
1/4
Step-by-step explanation:
3 x 1 = 3
4 x 3 = 12
3/12 simplified is 1/4
The quotient of the numbers 3/4 and 1/3 will be 9/4.
What is division?Division means the separation of something into different parts, sharing of something among different people, places, etc.
Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
The numbers are given below.
3/4 and 1/3
The quotient of the numbers 3/4 and 1/3 is given by the number 3/4 divided by 1/3. Then we have
⇒ (3/4) / (1/3)
Simplify the expression, then we have
⇒ (3/4) x (3/1)
⇒ 9 / 4
The quotient of the numbers 3/4 and 1/3 will be 9/4.
More about the division link is given below.
https://brainly.com/question/369266
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Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a radius of 13 feet and a height of 13 feet. Container B has a radius of 9 feet and a height of 14 feet. Container A is full of water and the water is pumped into Container B until Conainter B is completely full.
To the nearest tenth, what is the percent of Container A that is full after the pumping is complete?
The percent that Container A is full after pumping its water into Container B until it is full is that Container A is 49.1% full after pumping water to Container B.
The problem asks us to determine what percent of Container A is full after Container B is full when water is transferred from Container A to Container B. We start by calculating the volume of both cylinders. The volume of a cylinder is given by the formula V = π r² h where V is volume, r is radius, and h is height.
Container A has a radius of 13 feet and a height of 13 feet, so:
π r² h ≈ 6985.3 cubic feet
Container B has a radius of 9 feet and a height of 14 feet, so:
π r² h≈ 3553.0 cubic feet
After filling Container B completely, the volume of water left in Container A is the original volume of Container A minus the volume of Container B. Therefore, the remaining volume in Container A is (6985.3 - 3553.0) cubic feet ≈ 3432.3 cubic feet.
To find the percentage full, we divide this remaining volume by the total volume of Container A and multiply by 100:
Percentage = (3432.3 / 6985.3) * 100 ≈ 49.1%.
After the pumping is complete, Container A is 48.4% full.
Calculate the volume of each container
The volume of a cylinder is given by the formula:
[tex]\[V = \pi r^2 h\][/tex]
Volume of Container A
- Radius [tex]\( r_A = 13 \)[/tex]feet
- Height [tex]\( h_A = 13 \)[/tex] feet
[tex]\[V_A = \pi (13)^2 (13) = \pi (169)(13) = 2197\pi \text{ cubic feet}\][/tex]
Volume of Container B
- Radius [tex]\( r_B = 9 \)[/tex]feet
- Height [tex]\( h_B = 14 \)[/tex] feet
[tex]\[V_B = \pi (9)^2 (14) = \pi (81)(14) = 1134\pi \text{ cubic feet}\][/tex]
Calculate the remaining volume of water in Container A
Since Container A is initially full and the water is pumped into Container B until Container B is full, the remaining volume of water in Container A is:
[tex]\[V_{\text{remaining}} = V_A - V_B = 2197\pi - 1134\pi = (2197 - 1134)\pi = 1063\pi \text{ cubic feet}\][/tex]
Calculate the percent of Container A that is still full
The percent of Container A that is full is given by:
[tex]\[\text{Percent full} = \left( \frac{V_{\text{remaining}}}{V_A} \right) \times 100\%\][/tex]
Substituting the volumes we calculated:
[tex]\[\text{Percent full} = \left( \frac{1063\pi}{2197\pi} \right) \times 100\% = \left( \frac{1063}{2197} \right) \times 100\%\][/tex]
Simplifying the fraction:
[tex]\[\text{Percent full} = 0.484 \times 100\% = 48.4\%\][/tex]
Given that a^b = x, evaluate the following: a^2b
[tex]\bf a^{2b}\implies a^{2\cdot b}\implies (a^2)^b\implies (a^b)^2\qquad \boxed{a^b=x}\qquad (x)^2\implies x^2[/tex]
All rectangles are parallelogram. Are all parallelogram rectangles? Explain
Answer:
No
Step-by-step explanation:
A parallelogram may have a right angle (making it a rectangle), but may not.
Which point is closest to the y-axis?
(10, 15)
(5, –12)
(–9, 11)
(–4, 14)
(-9,11) This one is eleven units from the y-axis
(10,15) is fifteen units away
(5,-12) is 12 units away
(-4,14) is 14 units away
so the one closest to the y-axis is (-9,11)
Please mark me as brainliest
The above answer is wrong. Once graphing the lines you will see the -4 and 14 is the closet to the y axis
Enter the ratio as a fraction in lowest terms
3 ft to 48 in.
Answer:
The correct answer is 3/4
Step-by-step explanation:
This is because if we first change them to using the same unit of measure we get the following.
3 ft/48 in
36 in/48 in
Now we can simplify by dividing both by 12
3/4
Find the area of the Figure.
would love some help, please, and thank you
Answer:
430
Step-by-step explanation:
All you have to do is add up all the sides So 80+80+250+20=430 And there you have it!
Ryan the trainer has two solo workout plans that he offers his clients: Plan A and Plan B. Each client does either one or the other (not both). On Wednesday there were 5
clients who did Plan A and 3 who did Plan B. On Thursday there were 2 clients who did Plan A and 6 who did Plan B. Ryan trained his Wednesday clients for a total of 10
hours and his Thursday clients for a total of 10 hours. How long does each of the workout plans last?
Answer:
Both plans last for 1.25 hours (1 hour 15 minutes)
Step-by-step explanation:
Let x hours be the time needed for plan A and y hours be the time needed for plan B.
On Wednesday there were 5 clients who did Plan A and 3 who did Plan B. Thus, 5x+3y=10.
On Thursday there were 2 clients who did Plan A and 6 who did Plan B. Thus, 2x+6y=10.
Solve the sytem of two equation. Multiply the first equation by 2, the second by 5 and subtract them:
[tex]10x+6y-10x-30y=20-50,\\ \\-24y=-30,\\ \\y=\dfrac{30}{24}=\dfrac{5}{4}=1.25\ hours.[/tex]
Therefore,
[tex]5x+3\cdot 1.25=10,\\ \\5x=10-3.75=6.25,\\ \\x=1.25\ hours.[/tex]
Hi if someone could explain the right answer that would be great i’m totally lost!!
Answer:
A. lim [x ⇒ -∞] g(x) = -5 . . . . . . written in text form, not typeset
Step-by-step explanation:
A horizontal asymptote is a line that the function approaches but never reaches. It represents the limiting value that the function can have. (The function can come as close to that value as you like for some value of x, but can never actually reach that value.)
Here, you're told the asymptote for negative x values is -5. That means g(x) gets closer and closer to -5 for values of x that are more and more negative. That is, as x approaches infinity, g(x) approaches -5. We say -5 is the limit of g(x) as x approaches negative infinity.
___
The attached graph shows a function that has characteristics like those of g(x).
___
This question is about vocabulary: what is the meaning of "asymptote" and "limit", and how do you read a description of a limit written using math language.
What is the first step when dividing 3x^2+3x+1 by x-2 using long division?
Answer:
You need to find the number of times x goes into 3x^2 which is 3x, so you write 3x as the beginning of the quotient to start the division.
Answer:
3x^2 / x.
Step-by-step explanation:
The first step is to divide 3x^2 by the first term of x - 2 ( that is x).
A plumber charges a rate of $65 per hour for his time but gives a discount of $7 per hour to senior citizens. Write an expression which represents a senior citizen’s total cost for the plumber in 2 different ways.
Answer:
t = 58x or t + 7x = 65x
The expression that represents a senior citizen's total cost for the plumber in 2 different ways can be written as: Method 1: Total Cost = $65 - $7 per hour. Method 2: Total Cost = $65 - ($7 per hour x Number of hours)
Explanation:The expression that represents a senior citizen's total cost for the plumber in 2 different ways can be written as:
Method 1: Total Cost = $65 - $7 per hourMethod 2: Total Cost = $65 - ($7 per hour x Number of hours)Method 1 calculates the total cost by applying the discount of $7 per hour directly to the base rate of $65. Method 2 calculates the total cost by multiplying the discount per hour ($7) by the number of hours and subtracting it from the base rate of $65.
Learn more about Plumber here:https://brainly.com/question/3200361
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Three people share half a pizza evenly. What fractional part of the original pizza does each one get?
Answer:
The fractional part of the original pizza is [tex]\frac{1}{6}[/tex]
Step-by-step explanation:
Let
x-----> the original pizza (complete pizza)
we know that
Half a pizza represent ------> [tex]\frac{x}{2}[/tex]
Divide half a pizza by three people
[tex](\frac{x}{2})/3=\frac{x}{6}[/tex]
therefore
The fractional part of the original pizza is [tex]\frac{1}{6}[/tex]
HELP
Nevin started a geometric sequence. The first four terms of his sequence are show below.
162,54,18,6, . . .
3.) What is the sixth therm of Nevin sequence? Show or explain how you got the answer.
4.) Write an expression that represents the ᵗʰ term of Nevin sequence.
Answer:
3) 2/3
4) an = 162·(1/3)^(n-1)
Step-by-step explanation:
3) A geometric sequence has a common ratio between adjacent terms. Here, that ratio is ...
r = 54/162 = 18/54 = 6/18 = 1/3
Then the next two terms can be found by multiplying by the common ratio:
6 · 1/3 = 2
2 · 1/3 = 2/3 . . . . . the sixth term
____
4) The generic expression for the n-th term of a geometric sequence with first term a1 and common ratio r is ...
an = a1·r^(n-1)
We can put in the numbers for a1 and r, and we have ...
an = 162·(1/3)^(n-1)
A restaurant offers a lunch special for $15 plus a $3 tip for the server. Write an expression that represents the total cost for the special in 2 different ways.
Answer:
s= 15x+3x and s=18x
Step-by-step explanation:
Answer:
The total cost for the special would be $15.45
Step-by-step explanation:
One equation would be 15 x 1.03 = 15.45
Second equation would be (15 x .03) + 15 = $15.45
Practice zscore question help??
The height of a sunflower is normally distributed with a mean of 14.2 feet and a standard deviation of 2.15
what is the probability of picking a sunflower that has a height greater than 16.4 feet?
Please show all work (how you found z score and final answer)
The [tex]z[/tex]-score for a height of 16.4 feet is
[tex]z=\dfrac{16.4-14.2}{2.15}\approx1.023[/tex]
So
[tex]P(\text{height}>16.4\,\mathrm{ft})=P(Z>1.023)=1-F_Z(1.023)\approx0.153[/tex]
where [tex]F_Z(z)=P(Z\le z)[/tex] is the cumulative distribution function for the standard normal distribution.
HELP BRAINIEST AND LOTS OF POINTS Two twins, Mason and Jason, play a game in which they have a pile of 99 marbles. They can take anywhere from 1 to 10 marbles each turn. Whoever takes the last marble loses. Mason starts. Both play optimally. Who wins, and how many turns will Mason and Jason take combined? NEED NOW
Answer:
Mason wins after 18 total moves
Step-by-step explanation:
Mason's optimal strategy is to keep the total number of marbles at 11n+1, so he will take 10 marbles to start. For each move Jason makes, Mason will take a number of marbles that makes the sum from the two turns be 11.
After each of Mason's 9 turns, the number of remaining marbles will be ...
89, 78, 67, 56, 45, 34, 23, 12, 1
It doesn't matter how many marbles Jason takes. He will lose on his 9th turn.
Mason's best strategy is to stay the overall variety of marbles at 11n+1, thus he can take ten marbles to begin. for every move Jason makes, Mason can take variety of marbles that creates the add from the 2 turns be eleven.
After every of Mason's nine turns, the amount of remaining marbles are
89, 78, 67, 56, 45, 34, 23, 12, 1
It doesn't matter what number marbles Jason takes. He can lose on his ninth flip.
mason will win after 18 moves
The school yearbook committee surveyed the student body for an article about colleges in which they are pursuing enrollment. The table below shows the number of students in each grade level who are pursuing one or more college.
If there are 170 students in 12th grade, what percentage of the twelfth grade students have more than one college in mind? Round your answer to the nearest percent.
Out of 170 students in 12th grade, 27+23 = 50 students have more than 1 college in mind.
So 50/170, or 29% is your answer.
Answer:
29%
Step-by-step explanation:
You have $2000 to deposit for 7 years and two account options. The first earns you simple interest at a rate of 4% and the second earns you compound interest (compounded annually) at a rate of 2%. Which account earns you more money?
First account (simple interest)
Second account (compound interest)
They earn you the same
Not enough information to say
Answer:
First account (simple interest)
Step-by-step explanation:
The amount of interest earned by the first account is ...
I = Prt = $2000·0.04·7 = $2000·0.28 = $560
The amount in the second account at the end of 7 year is ...
FV = P·(1+r)^t = $2000·1.02^7 = $2297.37
so you have earned $297.37 in interest on the second account.
$560 is more than $297, so the First Account (simple interest) earns more money.
Which of the following is a geometric sequence?
Answer:
B. -1, 2, -4, 8
Step-by-step explanation:
The characteristic of a geometric sequence is that adjacent terms have a common ratio. Sequence B is the only one.
2/-1 = -4/2 = 8/-4 = the common ratio: -2
___
Ratios of adjacent terms are different for the other sequences.
Need help multiplying -300 to N+M&M=10 for equation (1)
Answer:
3.5 pounds of nuts; 6.5 pounds of M&Ms
Step-by-step explanation:
Let m represent the number of pounds of M&Ms to use. Then 10-m is the number of pounds of nuts, and the cost of the mix is ...
6·m + 3·(10-m) = 4.95·10 . . . . . cost = cost per pound times pounds
3m +30 = 49.5 . . . . . . simplify
3m = 19.5 . . . . . . . . . . . subtract 30
m = 6.5 . . . . . . . . . . . . . divide by 3
Then 10-m = 10-6.5 = 3.5.
The manager should use 3.5 pounds of nuts and 6.5 pounds of M&Ms in the mix.
9 out of 10 people at a game are rooting for the home team. What is the probability that exactly 6 of 8 people sitting together are rooting for the home team?
A random supporter roots the home team with probability 0.9, and the away team with probability 0.1.
Choosing 6 out of 8 supporters who root for the home team has probability
[tex]\displaystyle\binom{8}{6}\cdot 0.9^6\cdot 0.1^2 = 28\cdot0.531441\cdot 0.01=0.14[/tex]
A rectangle’s width is one-fourth of its length. Its area is 9 square units. The equation l(1/4l) = 9 can be used to find l, the length of the rectangle.
I see no actual question, but I'm assuming that you want to find the dimensions of the rectangle.
In general, the area of a rectangle with width [tex]w[/tex] and length[tex]l[/tex] is
[tex] A = wl [/tex]
In this case, we know that the width is one-fourth of its length, which means [tex] w = \frac{1}{4}l[/tex]
If we plug this expression for w in the formula for the area, we get
[tex] A = wl = \dfrac{1}{4}l\cdot l = \dfrac{1}{4}l^2 [/tex]
We also know that the area is 9 squared units, so we have
[tex] 9 = \dfrac{1}{4}l^2 [/tex]
If we multiply both sides by 4, we get
[tex] l^2 = 36 [/tex]
Consider the square root of both sides (we only accept the positive solution, since a negative length would make no sense:
[tex] l = \sqrt{36} = 6 [/tex]
So, the length is 6, and the width is one-fourth of 6, i.e.
[tex]\dfrac{1}{4} \cdot 6 = \dfrac{6}{4} = \dfrac{3}{2} = 1.5[/tex]
Answer:
1.5
Step-by-step explanation:
Which is the rate of change for the interval between 3 and 6 on the x-axis?
–3
–2
2
3
Answer:
The correct answer is 2.
Step-by-step explanation:
To find this, first identify the ordered pairs at those two points. They would be (3, -2) and (6, 4). Then use the slope formula with those two points to find the rate of change.
m(slope) = (y2 - y1)/(x2 - x1)
m = (4 - - 2)/(6 - 3)
m = 6/3
m = 2
Answer:
2
Step-by-step explanation:
Rate of change on the given interval a to b is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
a=3 and b=6
f(a) and f(b) are the y values on the graph at x=3 and x=6
f(3)= -3 and f(6) is 4
Now plug in the values in the formula
[tex]rate of change =\frac{4-(-2)}{6-3} =\frac{6}{3} =2[/tex]
answer is 2
solve
y^2 + 3y = -1
-PlushDNA
Answer:
[tex]y=-\frac{3+\sqrt{5}}{2}[/tex] AND [tex]y=-\frac{3-\sqrt{5}}{2}[/tex]
Step-by-step explanation:
Given: [tex]y^2+3y=-1[/tex]
To solve for [tex]y[/tex], we need to get everything on one side of the equal sign and set it to zero. We can do this by adding 1 to both sides. We then get:
[tex]y^2+3y+1=0[/tex]
We can solve for [tex]y[/tex] by using the quadratic formula:
[tex]y=\frac{-b+\sqrt{(b)^2-4(a)(c)}}{2a}[/tex] AND [tex]y=\frac{-b-\sqrt{(b)^2-4(a)(c)}}{2a}[/tex]
Let's identify our values:
[tex]a: 1\\b: 3\\c: 1[/tex]
Plug in the values and simplify.
[tex]y=\frac{-3+\sqrt{(3)^2-4(1)(1)}}{2(1)}\\y=\frac{-3+\sqrt{5}}{2}\\-------------------------\\y=\frac{-3-\sqrt{(3)^2-4(1)(1)}}{2(1)}\\\\y=\frac{-3-\sqrt{5}}{2}\\[/tex]
Your final answers are:
[tex]y=-\frac{3+\sqrt{5}}{2}[/tex] AND [tex]y=-\frac{3-\sqrt{5}}{2}[/tex]
Which of the following expressions represents the sum of a number and three is divided by two? A. 2 ÷ x + 3
B. 2 ÷ (x + 3)
C. (x + 3) ÷ 2
D. x + 3 ÷ 2
PLS ANSWER ASAP!
answer should be C
let me know if that’s right
Answer:
answer should be C
Step-by-step explanation:
A party rental company has chairs and tables for rent. The total cost to rent 3
chairs and 8 tables is $55. The total cost to rent 5 chairs and 2 tables is $18. What is the cost to rent each chair and each table
Answer:
chair: $1.00table: $6.50Step-by-step explanation:
When you have a non-trivial number of sets of equations to solve, it can be useful to let a machine solve them for you. Here, suitable equations for chair cost (c) and table cost (t) can be written as ...
3c+8t = 555c+2t = 18___
I find a graphing calculator easy to use for solving such equations.
___
A spreadsheet programmed with Cramer's Rule can do it, too. The second attachment shows the spreadsheet formulas used to solve the standard-form linear equations of the kind that can be written for this problem. The third attachment shows the solution(s).
Which of the following relations has a domain of {-6, 10}? Choose all that apply.
(A) {(-6, 7), (-6, 10)}
(B) {(-6, 6), (-6, 7), (10, 12)}
(C) {(4, -6), (5, 10)}
(D) {(-6, 4), (10, 5)}
Answer:
The correct answer options are (B) {(-6, 6), (-6, 7), (10, 12)} and (D) {(-6, 4), (10, 5)}.
Step-by-step explanation:
Here, we are given the domain {-6, 10} and we are to determine which of given relations in the options has this domain.
Domain is the set made up of the first elements of each ordered pair (x, y).
For {-6, 10} to be the domain, we will check which of the options have ordered pairs that start with -6 and 10.
If we look at option (B) {(-6, 6), (-6, 7), (10, 12)} and D. {(-6, 4), (10, 5)}, the first (two) ordered pair(s) start with -6 while the last ordered pair starts with 10.
Therefore, B and D are the correct answer option.