1. Twelve years ago, your grandma put money into a savings account for you that earns 7.5% interest annually and is
continuously compounded. How much money is currently in your account if she initially deposited $10,000 and you
have not taken any money out?

Answer:

( x - y ) ( a - b ) = -1

Step-by-step explanation:

ax + by = c  and  bx + ay = 1 + c

ax + by = c  and  bx + ay - 1 = c

And now we set c equivalent

ax + by = bx + ay - 1

ax - bx + by - ay = -1

x (a - b) + -y (a - b) = -1

(x - y) ( a - b) = -1

So we can leave it like that, or we can solve for one of the variables.

If we solve for y:

(x - y) ( a - b) = -1

(x - y) = -1 / (a - b)

-y = (-1 / (a - b)) - x

y = (1 / (a-b)) + x

Cheers.

Answer:

Step-by-step explanation:

Given the set of datas 3, 7 and 2, we are to evaluate the folowing;

Σ2X – 2 and Σ(X – 1)² =where X are the individual datas.

We will substitute each of the data as value of X and ten take the sum as shown;

For Σ2X – 2

Σ2X – 2 = [2(3)-2]+[2(7)-2]+[2(2)-2]

Σ2X – 2 = (6-2)+(14-2)+(4-2)

Σ2X – 2 = 4+12+2

Σ2X – 2 = 18

For Σ(X – 1)² where x values are also 3, 7 and 2 we will have;

Σ(X – 1)² = (3 – 1)²+(7 – 1)²+(2 – 1)²

Σ(X – 1)² = 2²+6²+1²

Σ(X – 1)² = 4+36+1

Σ(X – 1)² = 41

Answer:

Q (3.4)

Step-by-step explanation:

Midpoint for point (x1,y1) and (x2,y2) is given by

(x1+x2)/2, (y1+y2)/2.

__________________________________________________________

Given

one endpoint ( R(1, -1)

midpoint is M(2,1.5)

we have to find coordinates of endpoint Q

let Q(x,y)

Thus, for x coordinate of  midpoint

2 = (1+x)/2

=> 2*2 = 1+x

=> 4 = 1+x

=> x = 4-1 = 3

x coordinate of midpoint m is 3

________________________

for y coordinate of  midpoint

1.5 = (-1+y)/2

=> 2*1.5 = -1+y

=> 3 = -1+ y

=> y = 3 + 1 = 4

y coordinate of midpoint m is 4

Thus,  the coordinates of endpoint Q (3.4)

Answer:

ADD 4

Step-by-step explanation:

you want to get 2x by itself so you want to do opposite of -4 so you would do +4 and they cancel out, and what you do to one side you do to the other so

2x = 12 +4

2x = 16

and then you would divide the 2 on both sides so

x = 8 ... just in case you later need to know what x is :)

Answer:

Hey!

Your answer is 15,360!

Step-by-step explanation:

4% of 16,000 is 640

SO...

To find out the last year's amount of voters we have to minus 640 from 16,000...

16,000 - 640 = 15,360

HOPE THIS HELPED!!

Answer:

Step-by-step explanation:

What is the probability that a randomly selected person with adequate lung capacity is a non-exerciser?

This depends on statistics given in the prior part of the question.

From this question, i can pick that there is an assumption or statement (in the full question) that exercisers have adequate lung capacity, in a population of both exercisers and non-exercisers.

Data that will help solve this include:

- Population Count or Total number of subjects in the population

- Number of exercisers

- Number of non-exercisers

- Number of subjects with adequate lung capacity

- Number of subjects with inadequate lung capacity

The formula to get the desired answer would be:

Number of non-exercisers

Number of persons with adequate lung capacity

The figure you get from this computation is the answer you seek!

Since it is a probability figure, it must lie between the values of 0 and 1.

Answer:

4/6=t/(t+1)

Step-by-step explanation:

4/6=t/(t+1)

Answer:

Your friends data

Step-by-step explanation:

The rule of statistics is: the more exact the data, the better.

It looks like you just rounded your data to the nearest tenth. This is good, but not nearly as good as rounding it to the nearest hundredth.

This is because when you have data that is more exact, you get a better estimation for mean, median, etc. This can help make patterns in your data.

This means that your friend had better data than you.

Hope this helped!

Answer:

The GCF of 30 and 45 is

15.

Hope it helps.

Answer:

C=0,10E+5

Step-by-step explanation:

La respuesta es que la expresión que indica el costo mensual "C" en función de la energía "E" consumida es:

C=0,10E+5

Esto teniendo en cuenta que se indica que hay una tarifa fija de $5 por mes y que a esto se debe sumar el resultado de multiplicar la energía consumida por el valor del kilowatt-hora.

Answer:

  x ≤ -7

Step-by-step explanation:

Eliminate parentheses using the distributive property.

  -8 -2x ≥ 40 +6x +8

  -8 ≥ 48 +8x . . . . . . . . . add 2x

  -56 ≥ 8x . . . . . . . . . . . subtract 48

  -7 ≥ x . . . . . . . . . . . . . . divide by 8

The solution is x ≤ -7.

Answer:

A) [tex]y=-5x-4[/tex]

B) [tex]y=-5x+4[/tex]

C) [tex]y=\frac{x-4}{5}[/tex]

Step-by-step explanation:

So we have the equation:

[tex]y=5x+4[/tex]

Let's write this in function notation. Thus:

[tex]y=f(x)=5x+4[/tex]

A)

To flip a function over the x-axis, multiply the function by -1. Thus:

[tex]f(x)=5x+4\\-(f(x))=-(5x+4)[/tex]

Simplify:

[tex]-f(x)=-5x-4[/tex]

B) To flip a function over the y-axis, change the variable x to -x. Thus:

[tex]f(x)=5x+4\\f(-x)=5(-x)+4[/tex]

Simplify:

[tex]f(-x)=-5x+4[/tex]

C) A reflection over the line y=x is synonymous with finding the inverse of the function.

To find the inverse, switch x and f(x) and solve for f(x):

[tex]f(x)=5x+4[/tex]

Switch:

[tex]x=5f^{-1}(x)+4[/tex]

Subtract 4 from both sides:

[tex]x-4=5f^{-1}(x)[/tex]

Divide both sides by 5:

[tex]f^{-1}(x)=\frac{x-4}{5}[/tex]

And we're done :)

Answer:

$133.4

Step-by-step explanation:

1. Find the increased pay:

29 * 1.15 = 33.35

2. Find how much she makes in 4 hrs

33.35 * 4 = 133.4

Answer:

b) yes

The manufacturer has the right to state that the light bulbs last on average 400 hours

Step-by-step explanation:

Explanation:-

Given sample size 'n' = 64

Given standard deviation of the Population (σ)=100

Mean of the sample (x⁻) = 350 hours

95% of confidence interval is determined by

[tex](x^{-} -Z_{0.95} \frac{S.D}{\sqrt{n} } , x^{-} +Z_{0.95} \frac{S.D}{\sqrt{n} } )[/tex]

([tex](350 -1.96 \frac{100}{\sqrt{64} } , 350+1.96\frac{100}{\sqrt{64} } )[/tex]

(350-24.5 , 350+24.5)

(325.5 , 374.5)

Conclusion:-

Yes

The manufacturer has the right to state that the light bulbs last on average 400 hours

Answer:

y = 12

Step-by-step explanation:

Use the equation y = kx

Plug in x and y to find k:

2 = k(16)

1/8 = k

Then, plug in 1/8 as k and 96 as x to find y:

y = 1/8(96)

y = 12

Answer:

35^8

Step-by-step explanation:

5^8 x 7^8

(5 x 7)^8

=35^8

Answer:

y=3x+25

Step-by-step explanation:

So to find the slope-intercept we need to find the slope and the y intercept. we already know the slope so to find the y intercept you subtract 2 from the x coordinate and 6 from the y, because the slope is 3. So the answer is y=3x+23

Answer:

y=3x+25

Step-by-step explanation:

We are given a point and the slope, so let's use the slope-intercept equation.

[tex]y-y_{1}=m(x-x_{1})[/tex]

where m is the slope and (x₁, y₁) is the point given. The slope is 3 and the point is (2,31). Therefore,

[tex]m= 3 \\x_{1}=2\\y_{1}=31[/tex]

Substitute the values into the equation.

[tex]y-31=3(x-2)[/tex]

We want the equation in slope intercept form: y=mx+b. We must isolate y on the left side of the equation.

First, distribute the 3. Multiply each term inside the parentheses by 3.

[tex]y-31= (3*x)+(3*-2)[/tex]

[tex]y-31=(3x)+(-6)[/tex]

[tex]y-31=3x-6[/tex]

Next, add 31 to both sides of the equation.

[tex]y-31+31=3x-6+31[/tex]

[tex]y=3x-6+31[/tex]

[tex]y=3x+25[/tex]

This equation is in slope intercept form, so our final answer is:

y= 3x+25 (slope⇒3 , y-intercept ⇒25)

Answer: The area  is 13[tex]\pi[/tex]ft^2 or  40.84 ft^2

Step-by-step explanation:

First find the area of the square and subtract it from the area of the circle.

The area of a square is  one of the side length squared.

A= 6^2

A = 36  

Now find the area of the whole circle.As it indicates that the diameter is 14ft and to find the area of a circle,we need square the radius and multiply it by pi.

Since the diameter is 14 divide it by 2 to find the radius.  14/2 = 7  

A= 7^2*[tex]\pi[/tex]  

A = 49[tex]\pi[/tex]   We will leave the area in terms of pi.

49[tex]\pi[/tex] - 36 = 13[tex]\pi[/tex]

Answer:

i need the number line first lol

Step-by-step explanation:

mark brainliest

Answer: if your on apeand your options were

79,72,63,83 the answer is 72

Answer:

⅓y

Step-by-step explanation:

[tex] \frac{1}{3} \times y \\ = \frac{1}{3} y[/tex]

Answer:

35000

Step-by-step explanation:

Answer:

For F=GMm/r^2

[tex]F = \frac{GMm}{r^{2} }[/tex]

a. [tex]M = \frac{Fr^{2} }{Gm}[/tex]

b. [tex]r = \sqrt{\frac{GMm}{F}}[/tex]

M=kxa^3/p^2

[tex]M = \frac{kxa^{3} }{p^{2} }[/tex]

a. [tex]p = \sqrt{\frac{kxa^{3} }{M}}[/tex]

b. [tex]a = \sqrt[3]{\frac{Mp^{2} }{kx}}[/tex]

Step-by-step explanation:

To solve for the unknown quantity, we will make the unknown quantity the subject of the given equation.

For F=GMm/r^2

a. M =

F=GMm/r^2

[tex]F = \frac{GMm}{r^{2} }[/tex]

The first thing to do is cross multiply, so that the equation gives

[tex]Fr^{2} = GMm[/tex]

Now, divide both sides of the equation by [tex]Gm[/tex], we then get

[tex]\frac{Fr^{2} }{Gm} = \frac{GMm}{Gm}[/tex]

Then, [tex]\frac{Fr^{2} }{Gm} = M[/tex]

Hence,

[tex]M = \frac{Fr^{2} }{Gm}[/tex]

b. r =

F=GMm/r^2

[tex]F = \frac{GMm}{r^{2} }[/tex]

Likewise, we will first cross multiply, we then get

[tex]Fr^{2} = GMm[/tex]

Now, divide both sides by [tex]F[/tex], so that the equation becomes

[tex]\frac{Fr^{2} }{F} = \frac{GMm}{F} \\[/tex]

∴ [tex]r^{2} = \frac{GMm}{F} \\[/tex]

Then,

[tex]r = \sqrt{\frac{GMm}{F}}[/tex]

For M=kxa^3/p^2

a. P =

M=kxa^3/p^2

[tex]M = \frac{kxa^{3} }{p^{2} }[/tex]

The first thing to do is cross multiply, so that the equation becomes

[tex]Mp^{2} = kxa^{3} \\[/tex]

Now, divide both sides by M, we then get

[tex]\frac{Mp^{2} }{M} = \frac{kxa^{3} }{M}[/tex]

∴ [tex]p^{2} = \frac{kxa^{3} }{M}[/tex]

Then,

[tex]p = \sqrt{\frac{kxa^{3} }{M}}[/tex]

b. a =

M=kxa^3/p^2

[tex]M = \frac{kxa^{3} }{p^{2} }[/tex]

Also, we will first cross multiply to get

[tex]Mp^{2} = kxa^{3} \\[/tex]

Then, divide both sides of the equation by [tex]kx[/tex] to get

[tex]\frac{Mp^{2} }{kx}= \frac{kxa^{3} }{kx}\\[/tex]

[tex]\frac{Mp^{2} }{kx}= a^{3}[/tex]

∴ [tex]a^{3} = \frac{Mp^{2} }{kx}[/tex]

Then,

[tex]a = \sqrt[3]{\frac{Mp^{2} }{kx}}[/tex]

Answer:

The positive value of k that the function y = sin(kt) satisfies the differential equation y'' + 144y = 0 is +12

Step-by-step explanation:

To determine the positive values of k that the function y = sin(kt) satisfy the differential equation y''+144y=0.

First, we will determine y''.

From y = sin(kt)

y' = [tex]\frac{d}{dt}(y)[/tex]

y' = [tex]\frac{d}{dt}(sin(kt))\\[/tex]

y' = kcos(kt)

Now for y''

y'' = [tex]\frac{d}{dt}(y')[/tex]

y'' = [tex]\frac{d}{dt}(kcos(kt))[/tex]

y'' = [tex]-k^{2}sin(kt)[/tex]

Hence, the equation y'' + 144y = becomes

[tex]-k^{2}sin(kt)[/tex] + [tex]144(sin(kt))[/tex] [tex]= 0[/tex]

[tex](144 - k^{2})(sin(kt)) = 0[/tex]

[tex](144 - k^{2})= 0[/tex]

∴ [tex]k^{2} = 144\\[/tex]

[tex]k =[/tex] ±[tex]\sqrt{144}\\[/tex]

[tex]k =[/tex] ± [tex]12[/tex]

∴ [tex]k = +12[/tex] or [tex]-12[/tex]

Hence, the positive value of k that the function y = sin(kt) satisfies the differential equation y'' + 144y = 0 is +12

The positive value of k that satisfies the differential equation is k = 12.

To find the value of k that satisfies the equation, we differentiate the function y = sin(kt) twice to obtain y" and we insert it into the differential equation y" + 144y = 0.

So, y' = dy/dt

= dsin(kt)/dt

= kcos(kt)

y" = dy'/dt

y" = dkcos(kt)/dt

y" = -k²sin(kt)

So, substituting y and y" into the differential equation, we have

y" + 144y = 0

-k²sin(kt) + 144sin(kt) = 0

-k²sin(kt) = -144sin(kt)

k² = 144

k = ±√144

k = ±12

Since we require a positive value, k = 12

So, the positive value of k that satisfies the differential equation is k = 12.

Learn more about differential equations here:

https://brainly.com/question/18760518

Answer:

D. 6 feet.

Step-by-step explanation:

The third longest side of ABCD is 12 feet long and the third longest side of EFGH is 18 feet long.

As they are similar the corresponding sides are in the same ratio so

12/18 =  x/9 where x is the 4th side of ABCD.

2/3 = x/9

3x = 18

x = 6 feet.

Answer:

Y varies directly as X.

y=kx.

6=K72.

x=6/72.

x=0.08.

Y=0.08x.

when y=?, x=8.

y=0.08×8=0.64.

Answer:

4

just go with it the explaining  would take to long

Step-by-step explanation:

Answer:

1/4 is greater than 1/10, 2/10, and 1/5 but not 4/5, and 2/4

Step-by-step explanation:

1/4 = 25%

4/5 = 80%

2/4 = 50%

1/10 = 10%

2/10 = 20%

1/5 = 20%

Answer:

1-70: Purple- 9/10= 0.18= 2 marbles

        Orange- 16/50= 0.32= 3 marbles

        Yellow- 6/50= 0.12= 1 marble

        Green- 19/50= 0.38= 4 marbles

1-71: Part A. 3/6= 1/2

       Part B. 4/6= 2/3

Answer:

Step-by-step explanation:

4x12-5x6-14=0, the highest power of the variable in this equation is 12 so to make it a quadratic equation we should replace x12 by y2. Hence to rewrite the given equation as quadratic just substitute x6=y.