$3,717.14
Step-by-step explanation:Compound interest is the interest on the principal funding as well as the interest itself.
Compound Interest Formula
Compound interest can be solved by plugging known values into a formula.
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]In this formula, the variables stand for different values.
A = total amountP = principal amountr = rate as a decimaln = times compounded per time periodt = timeSo, for this question, we can plug in the values we are given and solve for P.
Identifying Known Values
First, let's find the exact numbers we are going to plug in.
6000 is the final amount we want, so A = 6000.6%, the rate, is 0.06 as a decimal, so r = 0.06.Since interest is compounded each month per year, n = 12.The total time is 8 years, so t = 8.Solving For P
Now we can plug all of these values in.
[tex]6000=P(1+\frac{0.06}{12})^{12*8}[/tex]First, simplify the values within the parentheses and in the exponent through arithmetic.
[tex]6000 = P(1.005)^{96}[/tex]Next, divide both sides by [tex]1.005^{96}[/tex]
3717.14 ≈ P*Note that the answer has been rounded to the nearest hundredth.
This means that you would need to deposit $3,717.14 into the account to have $6,000 in 8 years.
A tower that is 114 feet tall casts a shadow 121 feet long. Find the angle of elevation of the sun to the
nearest degree
Answer:
43 degrees
Step-by-step explanation:
First, notice that we can draw a right triangle to represent this situation. The vertical leg of the triangle corresponds to the tower, and the horizontal leg corresponds to the shadow. The height of the tower, 114, is OPPOSITE, and the length of the shadow, 121, is ADJACENT to the angle of elevation to the top of the tower. Remember SOH CAH TOA, we can use TAN to find the angle since we know the values of O and A.
TAN(x) = O/A
TAN(x) = 114/121
x = ARCTAN(114/121)
x = 43
– 30% OF THE CELL PHONE USERS TODAY USE A MOTOROLA
PHONE. DETERMINE THE PROBABILITY THAT IF SIX CELL PHONE USERS
ARE SELECTED AT RANDOM, EXACTLY FOUR OF THEM USE A MOTOROLA CELL
PHONE.
Using the binomial distribution, there is a 0.0595 = 5.95% probability that exactly four of them use a Motorola cell phone.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.For this problem, the values of the parameters are given by:
p = 0.3, n = 6.
The probability that exactly four of them use a Motorola cell phone is given by P(X = 4), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
P(X = 4) = C(6,4) x (0.3)^4 x (0.7)² = 0.0595
0.0595 = 5.95% probability that exactly four of them use a Motorola cell phone.
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5. Based on your data, what is the experimental probability that the family has two dogs or
two cats?
Answer:
2 dogs
Step-by-step explanation:
In a student club, the probability that a randomly selected member volunteered for a recent activity was 24/43. What is the probability that a randomly selected member did not volunteer for the recent activity?
The probability that a randomly selected member did not volunteer for the recent activity is 19/43.
What is the probability?Probability determines the odds that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0. The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.
The probability that a randomly selected member did not volunteer for the recent activity = 1 - ratio of randomly selected members that volunteered
1 - 24/43
(43/43) - (24/43) = 19/43
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8v(v+3)(v+3) rewrite the expression factoring out (v+3)
If we rewrite the expression 8v(v+3)(v+3) then we will get [tex]v^{3}+6v^{2} +9v[/tex]
Given an expression 8v(v+3)(v+3).
We are required to rewrite the given expression.
Expression is a combination of numbers, symbols, fraction , determinants,indeterminants, coefficients. They are not mostly found in equal to form. It expresses a relationship of a line or something else.
The expression is 8v(v+3)(v+3). There are three terms in which variable is v.
To rewrite the expression we have to multiply all the three terms with each other which can be done as under:
=8v(v+3)(v+3)
=[tex](8v^{2}+24v)(v+3)[/tex]
=[tex]8v^{3}+24v^{2}+24v^{2}+72v[/tex]
=[tex]8v^{3}+48v^{2} +72v[/tex]
Now divide it by 8.
=[tex]v^{3}+6v^{2} +9v[/tex]
Hence if we rewrite the expression 8v(v+3)(v+3) then we will get [tex]v^{3}+6v^{2} +9v[/tex] .
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Name plane K using three noncollinear points.
Answer:
plane HNA, HMB, ANG ...
Step-by-step explanation:
Any combination of three points on plane K will work unless all three are on the same line.
The cheetah area at a zoo is designed in a triangular fashion, surrounded on all three sides by sidewalks. The property has 67 feet of frontage on one sidewalk, and 48 feet of frontage on another; these two sidewalks intersect at a 72° angle. What is the square footage of the cheetahs' habitat? Round to the nearest hundredth.
1529.3 square unit is the area of the cheetah area at a zoo is designed in a triangular fashion, surrounded on all three sides by sidewalks, given that the property has 67 feet of frontage on one sidewalk, and 48 feet of frontage on another; these two sidewalks intersect at a 72° angle. This can obtained by using the formula of Area of a Triangle with 2 Sides and Included Angle.
Find the area of the cheetah area at the zoo:Area of a triangle is obtained using the formula of Area of a Triangle with 2 Sides and Included Angle.
If in a triangle ΔABC,
1/2 × bc × sin(A), if b and c are two sides of a triangle and angle A is the included angle1/2 × ac × sin(B), if a and c are two sides of a triangle and angle B is the included angle1/2 × ab × sin(C), if a and b are two sides of a triangle and angle C is the included angleHere it is given that,
67 feet and 48 feet are the sides of the triangular space and angle 72° is the included angle.
By using the formula of Area of a Triangle with 2 Sides and Included Angle,
Area of the cheetah area = 1/2 × bc × sin(A)
Area of the cheetah area = 1/2 × (67)(48) × sin(72°)
sin(72°) = 0.951056516
Area of the cheetah area = 1608 × 0.951056516
Area of the cheetah area = 1529.29888 ≈ 1529.3 square unit
Hence 1529.3 square unit is the area of the cheetah area at a zoo is designed in a triangular fashion, surrounded on all three sides by sidewalks, given that the property has 67 feet of frontage on one sidewalk, and 48 feet of frontage on another; these two sidewalks intersect at a 72° angle.
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Calculus HW , will someone please teach me how to do this problem. I'm struggling, thanks! 10 Points
Compute the first two derivative.
[tex]f(x) = x \sqrt{16 - x^2} = x (16 - x^2)^{1/2}[/tex]
[tex]f'(x) = x \dfrac{d}{dx} (16 - x^2)^{1/2} + (16 - x^2)^{1/2} \dfrac{d}{dx} x \\\\ ~~~~ = \dfrac x2 (16 - x^2)^{-1/2} \dfrac{d}{dx} (16-x^2) + (16 - x^2)^{1/2} \\\\ ~~~~ = \dfrac x2 (16 - x^2)^{-1/2} (-2x) + (16 - x^2)^{1/2} \\\\ ~~~~ = (16-x^2)^{-1/2} \left(-x^2 + (16 - x^2)\right) \\\\ ~~~~ = \dfrac{16 - 2x^2}{(16 - x^2)^{1/2}}[/tex]
[tex]f''(x) = \dfrac{(16-x^2)^{1/2} \frac d{dx} (16-2x^2) - (16-2x^2) \frac{d}{dx} (16-x^2)^{1/2}}{\left((16-x^2)^{1/2}\right)^2} \\\\ ~~~~ = \dfrac{(16-x^2)^{1/2} (-4x) - (8-x^2) (16 - x^2)^{-1/2} \frac{d}{dx} (16-x^2)}{16 - x^2} \\\\ ~~~~ = \dfrac{-4x (16-x^2) - (8-x^2) (-2x)}{(16 - x^2)^{3/2}} \\\\ ~~~~ = \dfrac{2x^3-48x}{(16 - x^2)^{3/2}}[/tex]
Take note of the domain of [tex]f(x)[/tex]. We must have [tex]16-x^2\ge0[/tex] for the square root to be defined, so
[tex]16 - x^2 \ge 0 \implies x^2 \le 16 \implies |x| \le 4[/tex]
and [tex]f(x)[/tex] exists only for [tex]-4 \le x \le 4[/tex].
Intercepts
Set [tex]x=0[/tex] to find the [tex]y[/tex]-intercepts. The only one is (0, 0), since
[tex]f(0) = 0 \sqrt{16-0^2} = 0[/tex]
The first intercept you listed is not a valid intercept. One or both coordinates must be 0.
Set [tex]f(x)=0[/tex] and solve for [tex]x[/tex] to find [tex]x[/tex]-intercepts. We already found (0, 0); there are two others at (-4, 0) and (4, 0).
[tex]f(x) = x \sqrt{16 - x^2} = 0 \\\\ x = 0 \text{ or } \sqrt{16 - x^2} = 0 \\\\ x = 0 \text{ or } 16 - x^2 = 0 \\\\ x = 0 \text{ or } x^2 = 16 \\\\ x = 0 \text{ or } x = \pm4[/tex]
The instructions say to list these in order from smallest to largest by [tex]x[/tex]-coordinate first, then by [tex]y[/tex]-coordinate. So the proper order of the intercepts would be (-4, 0), (0, 0), and (4, 0).
Relative minima/maxima
Find the critical points. We have [tex]f'(x) = 0[/tex] when
[tex]f'(x) = \dfrac{16 - 2x^2}{(16 - x^2)^{1/2}} = 0 \\\\ 16 - 2x^2 = 0 \\\\ x^2 = 8 \\\\ x = \pm2\sqrt2 \approx \pm 2.83[/tex]
and [tex]f'(x)[/tex] is undefined when
[tex](16 - x^2)^{1/2} = 0 \\\\ 16 - x^2 = 0 \\\\ x^2 = 16 \\\\ x = \pm4[/tex]
Check the sign of the second derivative at the first two critical points.
[tex]f''(-2\sqrt2) = 4 > 0 \implies \text{rel. min. at } f(-2\sqrt2) = -8[/tex]
[tex]f''(2\sqrt2) = -4 < 0 \implies \text{rel. max. at } f(2\sqrt2) = 8[/tex]
For posterity, we should also check the value of [tex]f(x)[/tex] at the endpoints of the domain.
[tex]f(-4) = f(4) = 0[/tex]
So [tex]f(x)[/tex] has a relative minimum at (-2.83, -8) and a relative maximum at (2.83, 8).
Inflection points
We have [tex]f''(x) = 0[/tex] for
[tex]f''(x) = \dfrac{2x^3-48x}{(16 - x^2)^{3/2}} = 0 \\\\ 2x^3 - 48x = 0 \\\\ 2x (x^2 - 24) = 0 \\\\ 2x = 0 \text{ or } x^2 - 24 = 0 \\\\ x = 0 \text{ or } x = \pm2\sqrt6\approx\pm4.90[/tex]
The two non-zero solutions fall outside the domain, so the only inflection point is (0, 0).
Can you tell which 3-D shape this would make?
The three dimensional shape formed by the net shown below is a cube.
What is a three dimensional shape?A three dimensional shape is a shape that has length, width and height. Examples of three dimensional shapes are cone, cylinder, prism and pyramid.
A two dimensional shape is a shape that have both length and width. Examples of two dimensional shape are circle, rectangle, square.
The cube is a a three-dimensional solid object bounded by six square faces.
The three dimensional shape formed by the net shown below is a cube.
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If you borrow $100 for 5 years at an annual interest rate of 8%, how much will you pay all together
Answer:
$140
Step-by-step explanation:
interest = 8x5 = 40
total = time + interest
total = 100 + 40 = $140
Find d²y/dx² for implicitly in terms of x and y
xy-1=2x+y²
The second derivative of the implicit function x · y - 1 = 2 · x + y² is equal to y'' = [2 / (2 · y - x)] · [(2 - y) / (x - 2 · y)] · [1 - [(2 - y) / (x - 2 · y)]].
What is the second derivative of an implicit equation?
In this problem we have a function in implicit form, that is, an expression of the form: f(x, y, c) = 0, where c is a constant. Then, we should apply implicit differentiation twice to determine the second derivative of the function:
Original expression
x · y - 1 = 2 · x + y²
First derivative
y + x · y' = 2 + 2 · y · y'
(x - 2 · y) · y' = 2 - y
y' = (2 - y) / (x - 2 · y)
Second derivative
y' + y' + x · y'' = 2 · (y')² + 2 · y · y''
2 · y' - 2 · (y')² = (2 · y - x) · y''
y'' = 2 · [y' - (y')²] / (2 · y - x)
y'' = [2 / (2 · y - x)] · [(2 - y) / (x - 2 · y)] · [1 - [(2 - y) / (x - 2 · y)]]
The second derivative of the implicit function x · y - 1 = 2 · x + y² is equal to y'' = [2 / (2 · y - x)] · [(2 - y) / (x - 2 · y)] · [1 - [(2 - y) / (x - 2 · y)]].
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need heeeelp please
Answer:
x = 1.086
Step-by-step explanation:
Formula
6^x = 7 Take the log of both sides.
Solution
log 6^x = log 7 Bring the power down You are now dealing with log 6
x * log 6 = log 7 Divide by log 6
x = log 7/log 6
x = .8451 / .7782 Divide
Answer
x = 1.086
The world price of umbrellas is $20 each. The pre-trade price of baskets in England is S15 each. What would happen if England allows trade in baskets?
Answer: Ans. Option c As the price of basket in England is $15, which is less than the world
integer for 1,440 feet below sea level
the size of the second application is 3.45 MB less than he first application. What is the size of the second application
The size of the second application given the size of the first application and the expression ( x - 3.45 mb) for the size of the second application is 293.55 MB.
EquationLet
Size of the first application = xSize of the second application= x - 3.45 mbFor instance,
if the size of the first application is 297 MB
Size of the second application= x - 3.45 mb
= 297 MB - 3.45 MB
= 293.55 MB
Therefore, the size of the second application given the size of the first application and the expression for the size of the second application is 293.55 MB
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Solve for y. Simplify your answer as much as possible. 9/12=y/8
Answer:
6
Step-by-step explanation:
Solve for y:
[tex]y/8=9/12[/tex]
Multiply both sides by 8:
[tex]y=72/12[/tex]
Solve fraction
[tex]y=6[/tex]
A total of 646 tickets were sold. They were either adult ticket or student tickets. There were 54 fewer student tickets sold than adult tickets. How many adult tickets were sold?
Answer:
350
Step-by-step explanation:
Let the number of adult tickets be x, then the number of student tickets sold would be (x–54).
We now have
x+(x–54)=646
2x=700
x=350
Therefore, 350 adult tickets were sold.
You plan to make a new fenced area in your back yard for your dog. The length of each side of the new dog area is
shown in meters in the diagram below. What is the perimeter of the new dog area?
20 meters
23 meters
29 meters
26 meter
Solve for exponential the value of X
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
The two triangles are right angled Triangles and they have one common angle. so the two triangles are similar to each other.
By using similarity, ratio of their corresponding sides must be equal as well~
[tex]\qquad \sf \dashrightarrow \: \cfrac{1}{2 + 1} = \cfrac{3}{x} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{1}{3} = \cfrac{3}{x} [/tex]
[tex]\qquad \sf \dashrightarrow \: x = 3 \times 3[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 9 \: \: units[/tex]
Hi, please help me me by demonstrating how to solve these 2 questions step by step :)
The given height of the shape is calculated to be 1,895.04 inches.
How to solve for the heightWe have the following details required to solve this problem
The distance b1 = 800 m
The angle of elevation β1 = 50°
distance b2 = 1450 m
- The new angle of elevation α = 33°
We first have to find the height of h1
800 x tan 50 degrees
= 953.40
The height of h2
1450 x tan 33
= 941.641
The height of the shape is the sum of the heights of h1 and h2
953.40 + 941.641
= 1,895.04
Hence the height of the shape is given as 1,895.04 inches.
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Which pair of words describe this system of equations
3y=9x-6
2y-6x=4
The pair of words that describe the given system of equations is: consistent and dependent.
A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.
It demonstrates the equality of the relationship between the expressions written on the left and the right.
Given equations:
3y=9x-6
2y-6x=4
The first equation can be simplified and written as: y=3x-2
Similarly, the second equation can be written as: y-3x=2
It can be seen that the two equations are the same. Thus, the given system of equations is consistent and dependent.
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-7πh = 98π
solve for h
Answer:
h = -14
Step-by-step explanation:
-7πh = 98π
⇔ -7h = 98 (Just Divide both sides by π)
⇔ h = 98 ÷ (-7) = -14
Hi :)
We should find h. All it takes is some algebra skills ^•^
————————First off, you can see than we have π on both sides. So, why not divide both sides by π and get it out of the way?
We end up with
[tex]\boldsymbol{-7h=98}[/tex]
Super! Now all we have to do is divide both sides by -7
We end up with
[tex]\boldsymbol{h=-14}[/tex]
[tex]\tt{Learn~More;Work~Harder}[/tex]
:)
If f ( x ) = 3x 2 - 6x + 2 and g ( x ) = 2x 2 + 2x - 11,
then find f ( x ) + g ( x ).
Answer:
[tex]5x^{2} -4x-9[/tex]
Step-by-step explanation:
f(x)+g(x)
[tex](3x^{2} -6x+2) + (2x^{2} +2x-11)\\3x^{2} -6x+2 + 2x^{2} +2x-11\\[/tex]
combine like terms --
[tex]5x^{2} -4x-9[/tex]
The sum of the given two functions f(x) = 3x² -6x + 2 and g(x) = 2x²+ 2x -1 is: f(x) + g(x) = 5x² - 4x - 9
Given that:
Functions, f ( x ) = 3x² - 6x + 2
And g ( x ) = 2x² + 2x - 11.
Then find f ( x ) + g ( x ).
To find the sum of two functions, f(x) + g(x), simply add the corresponding terms together.
To find f(x) + g(x), add the coefficients of the corresponding terms:
f(x) + g(x) = (3x² + 2x²) + (-6x + 2x) + (2 - 11)
Now, combine like terms:
f(x) + g(x) = 5x² - 4x - 9
So, the sum of the two functions is:
f(x) + g(x) = 5x² - 4x - 9
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If Usman buys 8 books that cost Rs. 120/- each, he will be left Rs. 140/-. If he buys 25 copies, how much he will be left with?
He will be left no money after buying 25 copies because he has 1900 rupees less.
Given that Usman buys 8 books that cost Rs. 120/ each, he will be left Rs. 140.
The cost of 1 books is Rs 120.
The cost of 8 book is 120×8=960.
The cost of 25 books is 120×25=3000
To find the money usman will left with him is the difference between the total money and the cost of 25 books.
Total money=960+140=1100
money left=Total money -cost of 25 books
money left=1100-3000
Usman have less money to buy 25 books. He has 1900 rupees less to buy 25 books.
Hence, Usman does leave any money with even he has less money to buy 25 books
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How many three-digit positive integers have three different digits and at least one prime digit?
The number of three-digit positive integers that have three different digits and at least one prime digit are 7960.
The only two components in prime numbers are 1 and the number itself.
Any whole number greater than one is a prime number.
It has exactly two factors—1 and the actual number.
There is just one 2-digit even prime number.
Every pair of prime numbers is always a co-prime.
The product of prime numbers can be used to represent any number.
Three-digit positive integers that have three different digits and at least one prime digit = 3!*4!*10*9 = 7960
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12.Find the range, the standard deviation, and the variance for the given samples.
13. A data set has a mean of x=3905 and a standard deviation of 110.Find the z-score for each of the following
Answer:
12. standard deviation =6.22972...
. variance = 38.80952...
solve for x in the diagram
sorry its a little messy!! not good at drawing with a finger haha. all you need to do is follow pedmas and isolate, knowing that a right angle=90°. hope this helps!<3<3
Answer: [tex]\Large\boxed{x=12}[/tex]
Step-by-step explanation:
Given information
∠1 = x + 42°
∠2 = 3x°
Total Angle = 90° (Right Angle)
Derived formula from the given information
∠1 + ∠2 = Total Angle
Substitute values into the given formula
(x + 42) + (3x) = (90)
Combine like terms
x + 3x + 42 = 90
4x + 42 = 90
Subtract 42 on both sides
4x + 42 - 42 = 90 - 42
4x = 48
Divide 4 on both sides
4x / 4 = 48 / 4
[tex]\Large\boxed{x=12}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Useing graph paper draw a array for 237×43
The attached figure represents the array for 237 x 43
How to draw the array?The array is given as:
237 x 43
An array is represented as:
Row x Column
This means that:
Row = 237
Column = 43
i.e. the array has 237 rows and 43 columns
The numbers are large, so the cells would be small when the arrays are drawn
See attachment for the array
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Need help please...
Step-by-step explanation:
Here! ●□●□●□●□● THIS IS THE ANSWER BRO
Circle A has center of (6, 7) and a radius of 4, and circle B has a center of (2, 4) and a radius of 16. What steps will help show that circle A is similar to circle B? (5 points)
Circle A has center of (6, 7) and a radius of 4, and circle B has a center of (2, 4) and a radius of 16. Now, in order to show that circle A is similar to circle B, we will have to dilate circle A by a scale factor of 4. We can use transformations like dilation and translation to make two circles similar.
Given Information:
For circle A,
Center, C1(x, y) = (6, 7)
Radius, r1 = 4
For circle B,
Center, C2(x, y) = (2, 4)
Radius, r2 = 16
Showing the Two Circles Similar
Now, to make circles A and B similar, we will have to make their centers coincide. It can be done by following the steps listed below:
First, translate circle A using the rule (x + 4, y + 3).Then, rotate circle A by 45° about the center.In the third step, dilate circle A by a scale factor of 4 (r2/r1).Finally, Reflect circle A about the origin to make it similar to circle BHence, we can now see that circle A is similar to circle B.
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