Answers
Related Questions
Find the dimensions of the rectangular box with largest volume if the total surface area is given as 64cm^2
Answers
The volume of the box is equal to V = xyz
Subject to the surface area
S = 2xy + 2xz + 2yz = 64
= 2(xy + xz + yz)
= 2[xy + x(64/xy) + y(64/xy)]
S(x,y)= 2(xy + 64/y + 64/x)
Then
Mx(x, y) = y = 64/x^2
My(x, y) = x = 64/y^2
y^2 = 64/x
(64/x^2)^2 = 64
4096/x^4 = 64/x
x^3 = 4096/64
x^3 = 64
x = 4
y = 64/x^2
y = 4
z= 64/yx
z= 64/16
z = 4
Therefor the dimensions are cube 4.
Tony plans to deposit $1,000 at the end of each of the next three years. if his funds earn 5% compounded annually, how much will he have at the end of three years?
Answers
Final answer:
Tony will have a total of $3,152.50 after depositing $1,000 annually for three years in an account with 5% interest compounded annually, by calculating the future value of each deposit and summing them up.
Explanation:
When Tony deposits $1,000 at the end of each year into an account that earns 5% interest compounded annually for three years, we need to calculate the future value of an annuity. Each deposit will earn interest for a different amount of time based on when it was deposited.
The first $1,000 will earn interest for two years.
The second $1,000 will earn interest for one year.
The third $1,000 will not earn interest, as it is deposited at the end of the third year.
The formula to calculate the future value of each deposit is:
Future Value = Principal × [tex](1 + Interest rate)^{number of years}[/tex]
Calculating each separately:
First deposit: $1,000 × [tex](1 + 0.05)^2[/tex] = $1,102.50
Second deposit: $1,000 × [tex](1 + 0.05)^1[/tex] = $1,050.00
Third deposit: $1,000 × [tex](1 + 0.05)^0[/tex] = $1,000 (as it earns no interest)
Adding them together gives us the total amount Tony will have at the end of three years:
Total amount = $1,102.50 + $1,050.00 + $1,000 = $3,152.50.
Therefore, at the end of three years, Tony will have $3,152.50 in his account.
How much times does 7 go into 48??
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7 * 6 = 42.
If you did 7 * 7 it equals 49 which goes over 48, so it would not work. Therefor your answer is 6.
Tom predicted that the Giants would score three 3-point field goals, score two 6-point touchdowns, and score 1 extra point. If Tom were correct, what would the Giants' score be at the end of the game?
Answers
3x3 = 9
2x6 = 12
12+9 = 21+1 =22
score would be 22 points
Answer:
The Giants' score will be 22 points.
Step-by-step explanation:
Consider the provided information.
It is given that tom predicted that the Giants would score three 3-point field goals. Which can be written as:
3 × 3 = 9
Total score by field goals is 9 points.
If he score two 6-point touchdowns, this can be written as:
2 × 6 = 12
Total score by touchdown is 6 points.
And 1 extra point.
Now add all the points as shown below:
Total score is: 9 + 12 + 1 = 22 points
Hence, the Giants' score will be 22 points.
After 5 years of earning interest at an annual rate of 3% an investment has earned $950 in interest. To the nearest whole dollar, determine the amount of the initial investment
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solve for P.
Find the Taylor series for
f(x), centered at the given value of a.
f(x) = sin(x), a = π
Written as a summation?
Radius of convergence?
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The Taylor series for [tex]\( \sin(x) \)[/tex] centered at [tex]\( a = \pi \)[/tex] is:[tex]\[ \sin(x) = \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n + 1)!}(x - \pi)^{2n + 1} \][/tex]
The radius of convergence of this Taylor series is infinite, meaning it converges for all values of ( x ).
To find the Taylor series for [tex]\( f(x) = \sin(x) \)[/tex] centered at [tex]\( a = \pi \),[/tex] we first need to find the derivatives of \( \sin(x) \) and evaluate them at \( x = \pi \). Then, we'll write out the Taylor series using the formula:
[tex]\[ f(x) = f(a) + f'(a)(x - a) + \frac{f''(a)}{2!}(x - a)^2 + \frac{f'''(a)}{3!}(x - a)^3 + \cdots \][/tex]
Let's find the derivatives of [tex]\( \sin(x) \)[/tex] and evaluate them at [tex]\( x = \pi \):[/tex]
1. [tex]\( f(x) = \sin(x) \)[/tex]
2. [tex]\( f' (x) = \cos(x) \)[/tex]
3.[tex]\( f''(x) = -\sin(x) \)[/tex]
4.[tex]\( f'''(x) = -\cos(x) \)[/tex]
Now, evaluate these derivatives at \( x = \pi \):
1. [tex]\( f(\pi) = \sin(\pi) = 0 \)[/tex]
2. [tex]\( f'(\pi) = \cos(\pi) = -1 \)[/tex]
3.[tex]\( f''(\pi) = -\sin(\pi) = 0 \)[/tex]
4. [tex]\( f'''(\pi) = -\cos(\pi) = 1 \)[/tex]
Now, plug these values into the Taylor series formula:
[tex]\[ \sin(x) = 0 - 1(x - \pi) + \frac{0}{2!}(x - \pi)^2 + \frac{1}{3!}(x - \pi)^3 + \cdots \][/tex]
Simplify:
[tex]\[ \sin(x) = -\sum_{n=0}^{\infty} \frac{(-1)^n}{(2n + 1)!}(x - \pi)^{2n + 1} \][/tex]
So, the Taylor series for [tex]\( \sin(x) \)[/tex] centered at [tex]\( a = \pi \)[/tex] is:
[tex]\[ \sin(x) = \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n + 1)!}(x - \pi)^{2n + 1} \][/tex]
The radius of convergence of this Taylor series is infinite, meaning it converges for all values of ( x ).
The average national basketball association player is over 6 feet tall. the average horse jockey is shorter than 5 1/2 feet tall. this is because height provides nba players with:
Answers
Final answer:
Height is crucial for NBA players due to its impact on their performance. Z-scores help compare player heights to the average. Taller stature offers basketball players notable advantages.
Explanation:
Height is a critical factor for NBA players as it can significantly impact their performance, especially in areas like rebounding, shot-blocking, and scoring.
Z-score calculations help determine how a player's height compares to the average, with values above the mean indicating taller heights, which are advantageous in basketball.
Being taller provides NBA players with advantages in terms of reaching high for shots, blocking opponents, and having a better field of vision on the court.
tan 2θ; cos θ = 8 17 , θ in Quadrant I
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We first found sin θ using the Pythagorean identity, then found tan θ, and finally used the double-angle formula for tan to find tan 2θ.
Explanation:To find the value of tan 2θ when cos θ = 8/17 and θ is in Quadrant I, you need first to find the value of sin θ. Since we are in Quadrant I, both cos and sin are positive. You can use the Pythagorean Identity for sin, cos, and tan, which states sin² θ + cos² θ = 1, to find sin θ. Substituting the given value of cos θ in this identity, we can find that sin θ = sqrt(1 - (8/17)²) = 15/17.
With sin and cos known, we can now find tan θ using the formula tan θ = sin θ/cos θ which gives tan θ = (15/17)/(8/17) = 15/8.
Finally, to find tan 2θ, use the Double-Angle formula for the tangent, which states tan 2θ = 2 tan θ / (1 - tan² θ). Substituting tan θ = 15/8 into this formula, we get tan 2θ = 2 * (15/8) / (1 - (15/8)²).
Learn more about Trigonometric values here:https://brainly.com/question/29069676
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To find tan 2θ, given cos θ is 8/17 and θ is in the first quadrant, first find sin θ using the Pythagorean identity, then use the double-angle formula where tan 2θ equals 2 tan θ divided by 1 minus tan squared θ, yielding -2.
To find tan 2θ given that cos θ is 8/17 and θ is in the first quadrant, we first need to find the value of sin θ. Since θ is in the first quadrant, all trigonometric functions are positive. Using the Pythagorean identity, we have:
sin θ = √(1 - cos² θ)
Substituting cos θ = 8/17:
sin θ = √(1 - (8/17)²) = √(1 - 64/289) = √(225/289) = 15/17.
Next, we use the double-angle formula for tangent:
tan 2θ = (2 tan θ) / (1 - tan² θ)
To find tan θ, we use:
tan θ = sin θ / cos θ = (15/17) / (8/17) = 15/8
Now, substitute tan θ into the double-angle formula:
tan 2θ = (2 × 15/8) / (1 - (15/8)²)
= (30/8) / (1 - 225/64)
= (30/8) / (-161/64) = -1920/1288 = -15/7.5 = -2
The complete question is :
Given that [tex]\(\cos \theta = \frac{8}{17}\)[/tex] with [tex]\(\theta\)[/tex] in the first quadrant, determine [tex]\(\tan 2\theta\).[/tex]
The total cost to rent a row boat is $14 times the number of hours the boat is used. Write an equation to model this situation if c = total cost and h = number of hours.
Answers
c = 14h
this would give you the total cost by multiplying 14 by the number of hours
The vertex angle of an isosceles triangle measures 40°. What is the measure of a base angle?
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In an isosceles triangle, the base angles are the same and the vertex angle is different from the rest.
b= (180-40)/2
b= 140/2
b=70
Final answer: 70 degrees
A drawer contains 12 identical white socks, 18 identical black socks and 14 identical brown socks. What is the least number of socks you must choose, without looking, to be certain that you have chosen two brown socks?
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The only time you can be so certain that you have picked 2 brown socks is when there are no more white socks and black socks. This means that to be 100% sure that you have picked 2 brown socks, you must pick all 12 white socks and all 18 black socks and only then you can pick 2 brown socks without looking. Therefore the total number of socks that should be picked is:
Total number of socks = 12 white socks + 18 black socks + 2 brown socks
Total number of socks = 32 socks
A total picking of 32 socks is required to be certain without looking that 2 brown have already been chosen.
Four students did a survey to find the soda flavor sixth-grade students perefer. The table below shows the method each student used to conduct the survey:
Student. Method
Trey- asked 100 students at random from his seventh- grade class what their favorite soda flavor is
Jesse- asked 100 sixth-grade students at random what their favorite soda flavor is
Nita-asked 100 eighth-grade students at random what their favorite soda flavor is
Ruben- asked 100 third- grade students at random what their favorite soda flavor is
Which students survey is most likely not biased?
Trey
Jesse
Nita
Ruben
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Triangle xyz has sidesxy equals 3 yz equals 4 and xz equals 5.if angle y is a right angle and yz is opposite angle x what is the tan of angle x
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The tangent of an angle in a right triangle, is the ratio of the opposite side, to the adjacent side of that angle.
That is tanx=|ZY|/|YX|=4/3=1.333
Answer: 4/3=1.333
What is 40 kilometers per hour in meters per hour
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1000*40
=40000 meters
Hope this helps!
-Benjamin
91284 the nearest ten thousand
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Its more closer to 91,000 then 92,000
The sum of two #'s is 29. The sum of the smaller and 2 times the larger is 45. Find the #'s.
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y=16
Work:
x+y=29
x=29-y
x+2y=45
29-y+2y=45
y=45-29
y=16
x=29-16
x=13
x+y=29
y=29-x
x+2y=45
x+2(29-x)=45
x+58-2x=45
-1x=-13
x=13
y=29-13=16
x+y = 13+16 = 29
x+2y= 13 + 2(16) = 13+32 = 45
so the numbers are 13 & 16
If you have 18 out of 20 homework sections completed what percentage do you have
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In the question, we have 20 homework sections. 20 can be thought as the 100%. We word 'per' in 'percent' can be sought of as a division operator or the fraction line that separates the numerator and denominator.
So, we can think 18 out of 20 as [tex]\frac{18}{20}[/tex]
First simplify the fraction.
[tex]\frac{18}{20} = \frac{9}{10}[/tex]
Convert the fraction into a decimal.
We can convert a fraction into a decimal by dividing the numerator by the denominator.
9 / 10 = 0.9
Now convert the decimal into a percent by moving the decimal point two places to the right and making the decimal point into a % sign.
0.9 = 90%
So, 90% is the answer.
In an inductive generalization, in order to achieve an error margin of plus or minus 3 percentage points at a confidence level of about 95 percent, whats the smallest random sample we can get away with, regardless of the size of the target population
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Assume that the population standard deviation is known as σ.
Let m = sample mean.
At the 95% confidence level, the expected range is
(m - k(σ/√n), m + k(σ/√n))
where k = 1.96.
Therefore the error margin is 1.96(σ/√n).
Because the error margin is specified as 3% or 0.03, therefore
(1.96σ)/√n = 0.03
√n = (1.96σ)/0.03
n = 128.05σ²
This means that the sample size is about 128 times the population variance.
Answer:
Smallest sample size = 128.05σ², where σ = population standard deviation.
Erika worked 14 hours last week and 20 hours this week. If she earns $9 per hour, how much did she earn during these two weeks? 4 of 60
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we know that
Erika earns [tex]\$9[/tex] per hour
so
By proportion
Find how much she earn during the total hours of two weeks
The total hours of two weeks is equal to
[tex]14+20=34\ hours[/tex]
[tex]\frac{9}{1} \frac{\$}{hour} =\frac{x}{34} \frac{\$}{hours} \\ \\x=34*9 \\ \\x=\$306[/tex]
therefore
the answer is
[tex]\$306[/tex]
Hiroto’s texting plan costs $20 per month, plus $0.05 per text message that is sent or received. Emilia’s plan costs $10 per month and $0.25 per text. Using the graph below, which statement is true? Hiroto’s plan costs more than Emilia’s plan when more than 50 texts are sent. Both plans cost the same when 22 texts are sent. Emilia’s plan costs more than Hiroto’s plan when more than 22 texts are sent. Both plans cost the same when 50 texts are sent
Answers
[tex] \left \{ {{y=0.05x+20} \atop {y=0.25x+10}} \right. [/tex]
Set the equations equal to each other and solve:
[tex]$0.05x+20=0.25x+10$[/tex]
[tex]$0.2x=10$[/tex]
[tex]$x=50$[/tex]
We then plug in to get [tex]$y$[/tex]:
[tex]$0.25(50)+10=22.5$[/tex]
The solution to the system is [tex] \left \{ {{x=50} \atop {y=22.5}} \right. [/tex].
Now, let's turn our attention to the statements.
The first one is false: Emilia's rate is higher, and the two plans cost the same at 50 texts, after which point Hiroto's plan becomes cheaper!
The second one is also false: we already figured out that the lines intersect at [tex]$x=50$[/tex].
The third statement is also false: as above, the lines intersect at [tex]$x=50$[/tex].
The fourth statement is true: the lines intersect at [tex]$x=50$[/tex].
In conclusion, the fourth statement - "Both plans cost the same when 50 texts are sent" - is true.
Answer:
d
Step-by-step explanation:
took the test yahoot
If the following system of equations was written as a matrix equation in the form AX = C, and matrix A was expressed in the form: A= {A C} {B D}, find the value of a-b +c+d. 2x+8y=7 4x-2y=9 Please help, i dont know which number would be which letters
Answers
Answer: a-b+c+d =4
Step-by-step explanation:
The given system of equation is
[tex]2x+8y=7\\4x-2y=9[/tex]
from this we have the following matrices
[tex]A_1 =\begin{bmatrix}\\2 &8 \\ \\4&2 \\\end{bmatrix}\ ,X=\begin{bmatrix}\\x\\ \\y\\\end{bmatrix}\text{and}\ C=\begin{bmatrix}\\7\\ \\9\\\end{bmatrix}[/tex]
the given matrix A =[tex]\begin{bmatrix}\\a &c \\ \\b &d \\\end{bmatrix}[/tex]
On comparing Matrix [tex]A_1[/tex] with Matrix A
[tex]\begin{bmatrix}\\a &c \\ \\b &d \\\end{bmatrix}=\begin{bmatrix}\\2&8 \\ \\4 &-2 \\\end{bmatrix}[/tex]
we have the following values
a=2 ,b=4,c=8,d=-2
Thus a-b+c+d =2-4+8+(-2)=4
p=m/1+rt solve for t
Answers
P=m/(1+rt) multiply both sides by (1+rt)
P(1+rt)=m perform indicated multiplication on left side
P+Prt=m subtract P from both sides
Prt=m-P divide both sides by Pr
t=(m-P)/(Pr)
(1) First, let's take a look at what we're dealing with.
We have an equation;
P = m/1 + rt, solve for t.
(2) Understand the problem, and know how to handle it.
Since we're solving for t, we need to isolate t by performing the opposite order of operations on the side that t is on.
(3) Take action once procedures (1) and (2) are understood/done.
P = m/1 + rt
We can get rid of the "1" in the equation, as multiplying anything by 1 does nothing.
Now we have:
P = m + rt
Now, we need to subtract m from both sides to isolate rt.
P - m = rt
Now to solve for t and the problem overall, we need to divide both sides by r.
[tex] \frac{P - m}{r} [/tex] = t
Your final solution for t is:
t = [tex] \frac{P - m}{r} [/tex]
Remember your 3 steps:
(1) Examine what you're dealing with.
(2) Understand the problem that's been given to you, and how to handle it.
(3) Apply the proper steps to come to your solution.
I hope this helps!
a full-time employee who works 40 hours per week earns 29.85 per hour estimate the person's annual income
Answers
40h x $29.85 = $1,194 per week
then take $1,194 x 52 (because there are 52 weeks in a year) = $62,088 annual income
If you know out of 140 pounds, 60 pounds is muscle weight, what is the muscle weight of a 200 pound male?
Answers
140 / 60 = 200 / x
140x = 12000
x= 85.7142857143
x= 85.7
What is 46 2/3% of 28
Answers
so 46 2/3 will be the same as 46.666 multiply by 28 divided by 100
answer=13.06
Answer:
46 2/3% of 28 is 13.06
Step-by-step explanation:
Hello,
thank you very much for asking this here in brainly, I think I can help you with this one
Let's remember
[tex]a\frac{b}{c} =\frac{(a*c)+b}{c}\\[/tex]
Step 1
[tex]46\frac{2}{3} =\frac{(46*3)+2}{3} =\frac{140}{3} =46.67[/tex]
so 46 2/3% =46.67%
Step 2
using a rule of three
define the relationships
if
28⇒ 100%
x? ⇒46.67%
[tex]\frac{28}{100}=\frac{x}{46.67} \\[/tex]
isolating x
[tex]\frac{28}{100}=\frac{x}{46.67} \\x=\frac{28*46.67}{100}\\x=\frac{1306.67}{100} \\x=13.06[/tex]
46 2/3% of 28 is 13.06
I hope it helps, have a great day
Ethel is arranging rides so that 27 members go bowling. Some people can ride in a van that belonges to the center where they meet the rest must ride in cars if 12 can go in the van and 5 can go in each car how many cars will they need?
Answers
This is because the only possible combination of cars and vans that add up to the total seating of 27 people is one van (12 seats) and three cars (15 seats).
12+15=27 seats total.
Answer:
Number of cars needed=3
Step-by-step explanation:
Ethel is arranging rides for 27 members.
If 12 can go in the van and 5 can go in each car.
Let c cars are needed
Then, 12+5c=27
5c=27-12
5c= 15
c= 15/5
c=3
Hence, number of cars needed equals:
3
9.8 is 2% of what number
Answers
Work:
9.8 / .02
= 490
Consider the equation ay'' + by' + cy = d, where a, b, c, and d are constants. (a) find all equilibrium, or constant, solutions of this differential equation. (enter your answers as a comma-separated list of equations.)
Answers
The constant solutions are given by [tex]\(y'' = 0\) and \(y' = 0\)[/tex].
The equilibrium solutions of the given differential equation [tex]\(ay'' + by' + cy = d\)[/tex] are found by setting the derivatives equal to zero.
1. Setting [tex]\(y'' = 0\)[/tex]: When [tex]\(y'' = 0\)[/tex], the equation becomes [tex]\(a \cdot 0 + b \cdot 0 + c \cdot y = d\)[/tex]. Solving for y, we get [tex]\(cy = d\)[/tex], and therefore, [tex]\(y = \frac{d}{c}\)[/tex].
2. Setting [tex]\(y' = 0\)[/tex]: When [tex]\(y' = 0\)[/tex], the equation becomes [tex]\(a \cdot 0 + b \cdot 0 + c \cdot y = d\)[/tex]. Again, solving for y, we obtain [tex]\(cy = d\)[/tex], and hence, [tex]\(y = \frac{d}{c}\)[/tex].
So, the constant solutions are [tex]\(y = \frac{d}{c}\)[/tex], and this is the equilibrium solution for the given differential equation.
Therefore, the constant solutions are given by [tex]\(y'' = 0\) and \(y' = 0\)[/tex].
Jonathan's Antiques purchased an old wooden sled at an auction for $210. Jonathan wants to mark up the sled 60% of the selling price. What would be the selling price of the sled?
Answers
[tex]\bf \begin{array}{ccllll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 210&100\\ x&160 \end{array}\implies \cfrac{210}{x}=\cfrac{100}{160}[/tex]
solve for "x".
A trucker had a load of grain containing 2 tons. She unloaded 1 ton 1,200 pounds at the warehouse. How much grain does she still have left on the truck?