Avery and Caden have saved $27,000 towards a down payment on a house. They want to keep some of the money in a bank account that pays 2.4% annual interest and the rest in a stock fund that pays 7.2% annual interest. How much should they put into each account so that they earn 6% interest per year?

Answer:

  A:  -2

Step-by-step explanation:

You want some factor k such that k(5x) +(10x) = 0. That is, 5k+10 = 0. The solution to this is k=-2, corresponding to selection A.

k = -2 for sure

I normally multiply 5x+10y=15 by -2 to cancel out the x's.

This is because you can only solve the problem if one of your variables is canceled out and then you solve!

From the information below the games is over in 3 sets. For Gina to win the match there are 3 possibilities.

1) Gina wins the first 2 sets with probability

2)Gina wins the first set. Looses the next set. Wins the third set.

3)Gina looses the first set. Wins the next 2 sets.

The required probability that Gina wins is the sum of the above 3 probabilities . That is the probability that Gina wins the match is

Answer:[tex] P=\frac{9+4}{25}=\frac{13}{25}[/tex]

Step-by-step explanation:

Given

Fred has a chance of 3/5 to win

and Gina has a chance of 2/5 to win

Probability(P) that the match is decided in only two sets is when

Either Fred or Gina win both matches continuously

P=P(Fred win both match)+P(Gina win both match)

[tex]P=\frac{3\times 3}{5\times 5}+\frac{2\times 2}{5\times 5}[/tex]

[tex] P=\frac{9+4}{25}=\frac{13}{25}[/tex]

Step-by-step explanation:

[tex] f(x) = \log_a x [/tex]

[tex] \dfrac{f(x + h) - f(x)}{h} = [/tex]

[tex] = \dfrac{log_a(x + h) - \log_a x}{h} [/tex]

[tex] = \dfrac{log_a \dfrac{x + h}{x}}{h} [/tex]

[tex] = \dfrac{1}{h}log_a ( 1 + \dfrac{h}{x} ) [/tex]

[tex] = log_a ( 1 + \dfrac{h}{x} )^{\frac{1}{h}} [/tex]

Answer:

the balance of Osborn’s Equity Investment (Shea) account be at the end of 2017 is $233,500

Step-by-step explanation:

Given data

Acquistion price = $220000

purchased = 30%

net income = $75,000

cash dividends = $30,000

to find out

the balance of Osborn’s Equity Investment (Shea) account be at the end of 2017

solution

we will find out balance of investment i.e. given by formula

balance of investment = Acquistion price + share of income - share of dividend   .................1

so here

share of income = 30% of net income

share of income =30% × 75,000 = $22500    ..............2

and

share of dividend = 30% of cash dividends

share of dividend = 30% × 30000 = $9000  ...............3

put equation 2 and 3 in equation 1 and we get

balance of investment = Acquistion price + share of income - share of dividend

balance of investment = 220000 + 22500 - 9000

balance of investment = $233,500

Answer:

The solution of the equation is [tex]x=\frac{(ln4)-5}{2}[/tex] ⇒ 3rd answer

Step-by-step explanation:

* Lets explain how to solve this problem

- The function f(x) = e^x is called the (natural) exponential function

- The natural logarithm (㏑), or logarithm to base e, is the inverse

 function to the natural exponential function

∵ [tex]e^{2x+5}=4[/tex] is an exponential function

∴ We can solve it by using the inverse of e (㏑)

- Remember:

# [tex]ln(e)=1[/tex]

# [tex]ln(e^{m})=m(ln(e))=m[/tex]

- Insert ln in both sides

∴ [tex]ln(e^{2x+5})=ln(4)[/tex]

∵ [tex]ln(e^{2x+5})=(2x+5)ln(e)=2x+5[/tex]

∴ 2x + 5 = ㏑(4)

- Subtract 5 from both sides

∴ 2x = ㏑(4) - 5

- Divide both sides by 2 to find x

∴ [tex]x=\frac{ln(4)-5}{2}[/tex]

* The solution of the equation is [tex]x=\frac{(ln4)-5}{2}[/tex]

Answer:

Answer is C on edge

Step-by-step explanation:

x= (ln 4)- 5/2

The best predicted value of y for x = 5 is 27.

A regression equation is a mathematical model that represents the relationship between a dependent variable and one or more independent variables. It expresses the linear or nonlinear association between these variables and is derived from statistical methods like linear regression analysis.

To predict the value of y for x = 5 using the regression equation, you can substitute x = 5 into the equation y = 5x + 2:

y = 5(5) + 2 = 27

Therefore, the predicted value of y for x = 5 is 27.

The best predicted value of [tex]\( y \) for \( x = 5 \) is \( y = 27 \).[/tex]

To find the best predicted value of [tex]\( y \) for \( x = 5 \),[/tex]we substitute [tex]\( x = 5 \)[/tex] into the regression equation:

[tex]\[ y = 5x + 2 \] \[ y = 5(5) + 2 \] \[ y = 25 + 2 \] \[ y = 27 \][/tex]

To reconcile this discrepancy, if we assume that the provided value of [tex]\( y = 18.3 \)[/tex] corresponds to [tex]\( x = 5 \),[/tex] then we would set the regression equation equal to 18.3 and solve for \( x \):

[tex]\[ 18.3 = 5x + 2 \] \[ 16.3 = 5x \] \[ x = \frac{16.3}{5} \] \[ x = 3.26 \][/tex]

Answer:

the music is both dubstep and trance

Answer:

The radius of a sphere is 2 millimeters

The surface area of a sphere is 50.24 square millimeters.

The circumference of the great circle of a sphere is 12.56  millimeters.

Step-by-step explanation:

Verify each statement

case A) The radius of a sphere is 8 millimeters

The statement is false

we know that

The volume of the sphere is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

we have

[tex]V=100.48/3\ mm^{3}[/tex]

[tex]\pi =3.14[/tex]

substitute and solve for r

[tex]100.48/3=\frac{4}{3}(3.14)r^{3}[/tex]

[tex]r^{3}=(100.48)/(4*3.14)[/tex]

[tex]r=2\ mm[/tex]    

case B) The radius of a sphere is 2 millimeters

The statement is True

(see the case A)

case C) The circumference of the great circle of a sphere is 9.42 square millimeters  

The statement is false

The units of the circumference is millimeters not square millimeters

The circumference is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=2\ mm[/tex]  

[tex]\pi =3.14[/tex]

substitute

[tex]C=2(3.14)(2)[/tex]

[tex]C=12.56\ mm[/tex]

case D) The surface area of a sphere is 50.24 square millimeters.

The statement is True

Because

The surface area of the sphere is equal to

[tex]SA=4\pi r^{2}[/tex]

we have

[tex]r=2\ mm[/tex]  

[tex]\pi =3.14[/tex]

substitute

[tex]SA=4(3.14)(2)^{2}[/tex]

[tex]SA=50.24\ mm^{2}[/tex]

case E)  The circumference of the great circle of a sphere is 12.56  millimeters.  

The statement is true

see the case C

case F) The surface area of a sphere is 25.12 square millimeters

The statement is false

because the surface area of the sphere is [tex]SA=50.24\ mm^{2}[/tex]

see the case D

Answer:

B, D,E

Step-by-step explanation:

Answer:

  see below

Step-by-step explanation:

The formula for the sum of an infinite geometric series with first term a1 and common ratio r (where |r| < 1) is ...

  sum = a1/(1 -r)

Applying this to the given series, we get ...

a. sum = 5/(1 -3/4) = 5/(1/4) = 20

b. sum = d/(1 -1/t) = d/((t-1)/t) = dt/(t-1)

_____

The derivation of the above formula is in most texts on sequences and series. In general, you write an expression for the difference of the sum (S) and the product r·S. You find all terms of the series cancel except the first and last, and the last goes to zero in the limit, because r^∞ → 0 for |r| < 1. Hence you get ...

  S -rS = a1

  S = a1/(1 -r)

Answer:

0.60b + 0.30w = 150; 60 + 0.30w = 150

Step-by-step explanation:

Answer:

C. 0.60b + 0.30w = 150; 60 + 0.30w = 150

Step-by-step explanation:

Answer:

B and D.

Step-by-step explanation:

B  This is a fair method. There is an equal chance  for all 3 people because picking one of the three is random.

D. I can't see all of it  but it looks like it will be  ' if the number is 5 or 6 Elena will bathe the dog. This is fair because the probabilities are all 1/3.

Method D is a fair method because the probability of each is equal.

Determining the proper option, acquiring evidence, and exploring various options are all steps in the decision-making process.

Ana, Mateo, and Elena are arguing about who has to give the dog a bath.

Then a fair decision will be

A. Roll a number cube. If the number rolled is 2 or 4, Ana bathes the dog. If the number is odd, Elena bathes the dog. If it lands on any other number, Mateo bathes the dog.

This is not a fair method because the probability of each is not equal.

B. Put each person's name on a separate piece of paper in a bag Randomly draw a name. The person whose name is chosen bathes the dog.

This is not a fair method because the number of pieces of paper is not given.

C. Flip a coin twice. If both tosses are heads, Ana bathes the dog. If one is headed and one is tail, Mateo bathes the dog. If both are tails, Elena bathes the dog.

This is not a fair method because the probability of each is not equal.

D. Roll a number cube. If the number rolled is 1 or 2, Ana bathes the dog. If the number is 3 or 4, Mateo bathes the dog. If the number​ rolled is 5 or 6, Elena bathes the dog.

This is a fair method because the probability of each is equal.

Then the correct option is D.

More about the decision-making link is given below.

https://brainly.com/question/3369578

#SPJ2

Answer:

[tex]PQ=9.6\ units[/tex]

Step-by-step explanation:

In this problem

If AB=31.8 units

then

ZY=31.8 units

ZP=PY=31.8/2=15.9 units

In the right triangle MZP

we have

[tex]ZP=15.9\ units[/tex]

[tex]MZ=18\ units[/tex] ----> the radius of the circle

Applying Pythagoras Theorem Find MP

[tex]MP^{2}=MZ^{2}-ZP^{2}[/tex]

substitute

[tex]MP^{2}=18^{2}-15.9^{2}[/tex]

[tex]MP^{2}=71.19[/tex]

[tex]MP=8.4\ units[/tex]

Find the value of PQ

we know that

[tex]MQ=MP+PQ\\ PQ=MQ-MP[/tex]

we have

[tex]MQ=18\ units[/tex]

[tex]MP=8.4\ units[/tex]

substitute

[tex]PQ=18-8.4=9.6\ units[/tex]

Answer:

Step-by-step explanation:

A man steps out of a plane at 4,000m of height above the ground.The point at which he jumps out of the plane would make a good reference point. However, if his acceleration is going to change as a result of him opening his parachute 2000m above the ground, a good reference point would be there. Keep in mind though, that his velocity at that instant would need to be known for it to be useful- otherwise the airplane reference point would be just as good with appropriate modeling....

Answer:4000m easy !!

Answer:

[tex]r=\sqrt[3]{\dfrac{T^2GM}{4\pi^2}}[/tex]

Step-by-step explanation:

Divide by the coefficient of the r factor, then take the cube root.

[tex]T^2=\dfrac{4\pi^2}{GM}r^3 \qquad\text{given formula}\\\\\dfrac{T^2GM}{4\pi^2}=r^3 \qquad\text{divide by the coefficient of the r factor}\\\\r=\sqrt[3]{\dfrac{T^2GM}{4\pi^2}} \qquad\text{cube root}[/tex]

Answer:

The formula to solve r is [tex]r=\sqrt[3]{\frac{GMT^{2}}{4\pi^{2}}}[/tex].

Step-by-step explanation:

Consider the provided formula:

[tex]T^{2}=\frac{4\pi^{2}r^{3}}{GM}[/tex]

Where r is the orbit’s mean radius, M is the mass of the planet, and G is the universal gravitational constant.

Multiply both side by GM.

[tex]T^{2}GM=4\pi^{2}r^{3}[/tex]

Further solve the above equation.

[tex]\frac{T^{2}GM}{4\pi^{2}}=r^{3}[/tex]

[tex]\sqrt[3]{\frac{GMT^{2}}{4\pi^{2}}}=r[/tex]

Hence, the formula to solve r is [tex]r=\sqrt[3]{\frac{GMT^{2}}{4\pi^{2}}}[/tex].

Answer:

  D)  33

Step-by-step explanation:

The sum of the lengths of the segments is equal to the overall length:

  (3x -5) + 8 = 4x -7

  10 = x . . . . . . . . . . . . add 7-3x to both sides

Then the overall length is ...

  MO = 4·10 -7 = 33

Answer:

Step-by-step explanation:

(3x -5) + 8 = 4x -7

10 = x what you wnat to do is  add 7-3x to both sides

= 4·10 -7 = 33

and that should be your answer 33

Step-by-step explanation:

10.

First, convert 1+i from Cartesian to polar.

r = √(1² + 1²)

r = √2

θ = atan(1/1), θ in first quadrant

θ = 45°

Therefore:

(1+i)²⁰ = (√2 (cos 45° + i sin 45°))²⁰

(1+i)²⁰ = 1024 (cos 45° + i sin 45°)²⁰

Now applying the De Moivre theorem:

1024 (cos (20×45°) + i sin (20×45°))

1024 (cos (900°) + i sin (900°))

1024 (-1 + 0)

-1024

11.

Repeat the same steps from Question 10.  First, convert to polar:

r = √(1² + (-1)²)

r = √2

θ = atan(-1/1), θ in fourth quadrant

θ = 315°

Therefore:

(1−i)¹⁰ = (√2 (cos 315° + i sin 315°))¹⁰

(1−i)¹⁰ = 32 (cos 315° + i sin 315°)¹⁰

Now applying the De Moivre theorem:

32 (cos (10×315°) + i sin (10×315°))

32 (cos (3150°) + i sin (3150°))

32 (0 − i)

-32i

Answer:

  4/9

Step-by-step explanation:

The easiest segment to work with is BC, since the y-values are the same for coordinates B and C and for B' and C'.

The length of BC = 9 -(-9) = 18.

The length of B'C' = 7 -(-1) = 8.

The scale factor is B'C'/BC = 8/18 = 4/9.

Answer:

The answer is

D.

GD/MJ = DE/JK

Answer:

GD/MJ = DE/JK

Step-by-step explanation:

This answer is correct because GD and MJ are similar sides and DE and JK are similar sides as well

Answer:

  y = -2.5

Step-by-step explanation:

For such a problem as this, you can replace all sine or cosine functions with their midline value of 0. Then you have ...

  f(x) = 0 -2.5

which simplifies to ...

  f(x) = -2.5

You can leave the equation like this, or write it as ...

  y = -2.5

_____

Perhaps you can see that the midline is the value of any constant added to a sine or cosine function.

Answer: y=-2.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

Horizontal lines have the form " y = " where vertical lines have the form " x = ".

Horizontal lines run parallel to the y = 0 line, the x-axis, so horizontal lines are found in the y coordinate of the point.  Therefore, the horizontal line at that point is y = 7.

The vertical lines run parallel to the y-axis, which is the line x = 0.  The vertical lines are found then in the x coordinate of the point.  Therefore, the vertical line at that point is x = -10

Answer:

[tex]8\frac{2}{8}[/tex]

Step-by-step explanation:

x = number of granola bars

[tex]\frac{3}{4} + 7\frac{1}{2} = \frac{6}{8} + 7\frac{4}{8} = 7\frac{10}{8} = 8\frac{2}{8}[/tex] = x[/tex]

Solve the equation

Answer: The answer would be choice C because there is a constant rate of change of 3 :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

If x and y are proportional then the ratio y/x is constant.

[tex]A.\\\\\dfrac{4}{2}=2,\ \dfrac{6}{3}=2,\ \dfrac{9}{4}\neq2\\\\B.\\\\\dfrac{4}{3},\ \dfrac{16}{9}\neq\dfrac{4}{3}\\\\C.\\\\\dfrac{12}{4}=3,\ \dfrac{15}{5}=3,\ \dfrac{18}{6}=3\ \qquad\bold{CORRECT}\\\\D.\\\\\dfrac{4}{1}=4,\ \dfrac{8}{2}=4,\ \dfrac{15}{3}=5\neq4[/tex]

Answer:

(x^12y)

Step-by-step explanation:

= (x^4y)^3

= (x^12y)

Answer:

The simplified form of given expression is  x¹²y³

Step-by-step explanation:

Points to remember

Identities

(xᵃ)ᵇ = xᵃᵇ

xᵃ * xᵇ = x⁽ᵃ ⁺ ᵇ⁾

To find the simplified form

It is given that, (x⁴y)³

By using the above identities we can write (x⁴y)³ as,

(x⁴y)³ =  (x⁽⁴ * ³ ⁾ * y³

 = x¹² * y³

 = x¹²y³

Therefore the  simplified form of given expression is  x¹²y³

[tex]|\Omega|=16\cdot15=240\\|A|=6\cdot10=60\\\\P(A)=\dfrac{60}{240}=\dfrac{1}{4}[/tex]

He's wrong.

Answer:

The total momentum of the system remains the same.Momentum before collision is equal to momentum after collision

Step-by-step explanation:

Momentum is defined as the product of mass and velocity of the bodies.According to the law of conservation of momentum, a collision that occurs in an isolated system, the momentum before collision equals that after collision.After collision, the bodies can move in the same direction thus their momentum is combined.

Answer:

According to the law of conservation of momentum, in a system where particles collide, the momentum loss on one particles is gained by the other one. This is what create an reaction during the collision, for example, if two bodies collide, one will decrease its speed while the other will increase its speed, that's why the momentum is conserved.

So, basically, after the train cars collide, the momentum must be conserved, remaining the same.

Answer:3 minute

Step-by-step explanation:

Sakura speaks hungarian =150 words per minute

Sakura speaks polish =190 words per minute

and it is given she speaks 270 more words in polish than in hungarian

She speaks for a total of 5 minutes

let she speaks hungarian for t mins

therefore [tex]150\times t+270=190\left ( 5-t\right )[/tex]

t=2 mins

therefore sakura speaks hungarian for 2 mins and polish for 3 mins

Sakura speaks hungarian for 2 mins and polish for 3 mins

The zeros of the polynomial function f(x) = x^3 + x^2 + 20x are 0, -5, -4.

The zeros of a polynomial function are the values of x that make the function equal to zero.

We are given that one zero of the polynomial function f(x) = x^3 + x^2 + 20x is x = 0.

To find the other zeros, we can use polynomial long division or synthetic division to factor out x = 0 and find the remaining quadratic equation.

Factoring the quadratic equation, we find that the zeros are x = -5 and x = -4.

Therefore, the correct answer is 0, -5, -4.

Final answer:

The zeros of the polynomial function f(x) = x^3 + x^2 + 20x are 0, -5, and -4.

Explanation:

The zeros of a polynomial function are the values of x that make the function equal to zero. Given that one zero of the polynomial function f(x) = x^3 + x^2 + 20x is x = 0, we need to find the other zeros. To do this, we factor the polynomial using synthetic division or long division. In this case, the factored form of the polynomial is f(x) = (x)(x + 5)(x + 4). Therefore, the zeros of the polynomial function are 0, -5, and -4.

Answer:

0.000052

1 nanometer = .000000001 meters

.000000001 x 52000 = 0.000052

To convert 52,000 nanometers to meters, divide by the conversion factor of 1,000,000,000 nanometers per meter, resulting in a thickness of 5.2 x 10-8 meters in standard form.

To convert the thickness of a piece of thread from nanometers to meters, we need to use the conversion factor that 1 meter equals 1,000,000,000 nanometers, or 1 m = 109 nm.

Using this conversion factor, we can set up the following calculation:

Thickness in meters = Thickness in nanometers \/ Conversion factor

Thickness in meters = 52,000 nm \/ (109 nm/m)

Thickness in meters = 52,000 nm \/ 1,000,000,000 nm/m

Thickness in meters = 0.000000052 m or 5.2 x 10-8 meters when expressed in standard form.

Answer:

$30,000.

Step-by-step explanation:

Wave Corporation began the current year with a retained earnings balance of $25,000.

Depreciation expense was of $5000

During the current year, the company earned net income of $15,000

Also gave cash dividends of $5,000.

So, year end retained earnings will be :

Year end retained balance = total net income minus net losses and dividends.

[tex]25000-5000+15000-5000=30000[/tex] dollars

The answer is $30,000.