Jace invested $65,000 in an account paying an interest rate of 2.5% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $93,400?

Answer:

Step-by-step explanation:

h

Answer:

She has completed 4 problems

Step-by-step explanation:

Take the total number of problems and multiply by the percent completed

20 * 20%

20 * .20

4

She has completed 4 problems

Answer:

4

Step-by-step explanation:

Answer:

216

Step-by-step explanation:

(6 to the -4th) * (6 to the 7th)

Answer:

[tex]Length = Width = 6\ units[/tex]

Step-by-step explanation:

Given

[tex]Area=36[/tex]

Required

The least possible material

Sandboxes usually, are rectangles or squares.

Using the above assumption, the area is calculated as:

[tex]Area= Length * Width[/tex]

[tex]Area= L* W[/tex]

[tex]L * W = 36[/tex]

Make L the subject

[tex]L = \frac{36}{W}[/tex]

The material of the outer edge is calculated by the perimeter.

[tex]Perimeter = 2 * (L +W)[/tex]

[tex]P = 2 * (L + W)[/tex]

Substitute [tex]L = \frac{36}{W}[/tex]

[tex]P = 2 * (\frac{36}{W} + W)[/tex]

Open bracket

[tex]P = \frac{72}{W} + 2W[/tex]

[tex]P = 72W^{-1} +2W[/tex]

To get the minimum material needed, we differentiate P

[tex]P' = -72W^{-2} + 2[/tex]

Set: [tex]P' = 0[/tex]

[tex]-72W^{-2} + 2 = 0[/tex]

Collect like terms

[tex]72W^{-2} = 2[/tex]

Divide both sides by 72

[tex]W^{-2} = \frac{2}{72}[/tex]

[tex]W^{-2} = \frac{1}{36}[/tex]

Rewrite as:

[tex]\frac{1}{W^2} = \frac{1}{36}[/tex]

Take positive square roots of both sides

[tex]\frac{1}{W} = \frac{1}{6}[/tex]

Cross multiply

[tex]W = 6[/tex]

Recall that: [tex]L = \frac{36}{W}[/tex]

So, we have:

[tex]L =\frac{36}{6}[/tex]

[tex]L = 6[/tex]

Hence, the dimension with the littlest material as possible is:

[tex]Length = Width = 6\ units[/tex]

Answer:

For a function f(x), a reflection across the y-axis is written as:

g(x) = f(-x)

While a reflection across the x-axis is written as:

g(x) = -f(x)

So, if the negative sign is outside the transformation, like in:

g(x) = -f(x + 2) - 8

We can conclude that this is a reflection over the x-axis.

While if the "x" inside the function has a negative sign, like in:

g(x) = 5*f(-x + 4) - 3

The reflection is over the y-axis.

Tn = a + (n-1) d

= 3 + (n-1) (-4)

= 3 -4n +4

= 7-4n

hope it helped you dear

Answer:

[tex]m=-\frac{1}{2}[/tex]

Step-by-step explanation:

[tex]\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{9-10}{6-4}[/tex]

Answer:

-2

Step-by-step explanation:

Given equation

x - 2y = 4

2y = x - 4

y = ( x - 4 ) / 2

y = x/2 - 4 /2

y = x/2 - 2

Comparing with y = mx + b

y-intercept (b) = - 2

Hope it will help :)❤

Answer:

B

Step-by-step explanation:

Use the definition of a logarithm,  log b ( x ) = y  ⟹  b y = x , to convert from the logarithmic form to the exponential form. 10^ 4 = x

The exponential equation out of the specified options that is equivalent to this logarithmic equation log x = 4 is given by: Option B: 10^4 = x

When you raise a number with an exponent, there comes a result.

Lets say you get [tex]a^b = c[/tex]

Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows

[tex]b = \log_a(c)[/tex]

'a' is called base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'

Log with base e = 2.71828... is written as [tex]\ln(x)[/tex] simply.

Log with base 10 is written as [tex]\log(x)[/tex] simply.

The given logarithmic equation is;

[tex]\log x = 4[/tex]

Since, log with base 10 is written as [tex]\log(x)[/tex] simply, therefore, we have:

[tex]\log_{10} x = 4[/tex]

Using the definition of logarithm, we get;

[tex]x = 10^4[/tex]

Equivalently, [tex]10^4 = x[/tex] (option B).

Thus, the exponential equation out of the specified options that is equivalent to this logarithmic equation log x = 4 is given by: Option B: 10^4 = x

Learn more about logarithm here:

https://brainly.com/question/20835449

Answer:

B. 44°

Step-by-step explanation:

Central angle = 3x + 10°

Inscribed angle = 2x - 17°

Now

Central angle = 2 * inscribed angle

( Central angle is double of the inscribed angle standing on same arc)

3x + 10° = 2 ( 2x - 17°)

3x + 10° = 4x - 34°

4x - 3x = 34 ° + 10°

x = 44°

Hope it will help :)❤

Answer:

The projectile will hit the ground after 38.8 seconds.

Step-by-step explanation:

You know that the height s (t) in feet of the projectile after t seconds is given by the function

s(t) = - 16t² + 600t + 800.

To know the time at which the projectile will hit the ground, you must replace s(t) by height 0:

0=- 16t² + 600t + 800

This is a quadratic function of the form ax2 + bx + c, where a= -16, b=600 and c=800.

To solve a quadratic function, you must apply the expression:

[tex]x1,x2=\frac{-b+-\sqrt{b^{2}-4*a*c } }{2*a}[/tex]

In this case:

[tex]x1,x2=\frac{-600+-\sqrt{600^{2}-4*(-16)*800 } }{2*(-16)}[/tex]

Solving:

[tex]x1,x2=\frac{-600+-\sqrt{360000+51200 } }{-32}[/tex]

[tex]x1,x2=\frac{-600+-\sqrt{411200 } }{-32}[/tex]

[tex]x1,x2=\frac{-600+-641.25 }{-32}[/tex]

So:

[tex]x1=\frac{-600+641.25 }{-32}[/tex]

[tex]x1=\frac{41.25 }{-32}[/tex]

x1= -1.289 seconds

and

[tex]x2=\frac{-600-641.25 }{-32}[/tex]

[tex]x2=\frac{-1241.25 }{-32}[/tex]

x2= 38.789 ≅ 38.8 seconds

Time cannot be negative. So, the projectile will hit the ground after 38.8 seconds.

Answer:

A

Step-by-step explanation:

I am to determine the future value of Thomas' deposit with annual compounding

The formula for calculating future value:

FV = P (1 + r)^n

FV = Future value  

P = Present value  

R = interest rate  

N = number of years  

840 x (1.075)^5 = 1205.93

I am to determine the future value of Sherill's deposit in 5 years using simple interest

The amount that would be in the account = amount deposited + interest earned on deposit

interest earned on deposit can be determined by determining the simple interest

Simple interest = amount deposited x time x interest rate

1250 x 0.069 x 5 = 431.25

Amount that would be in her account after 5 years = 1250 +  431.25 =  1681.25

Sheril's money is higher by - 1681.25 -  1205.93 = 475.32

Answer:

the answer is D :)

Step-by-step explanation:

Answer:

5 / 8

Step-by-step explanation:

Total possible outcomes = (1, 2, 3, 4, 5, 6, 7, 8)

Odd outcomes = (1, 3, 5, 7)

Outcomes > 7 = 8

Required outcomes = (1, 3, 5, 7, 8)

Number of required outcomes = 5

P(pointer stops on odd or number > 7) = required outcome / Total possible outcomes

P(pointer stops on odd or number > 7) :

= 5 / 8

Answer:

C. 70%

Step-by-step explanation:

35 / 50 = 70/100 = 70%

So she will be 70% accurate in the next shot.

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

[tex]x^2+y^2=9[/tex]

Step-by-step explanation:

Equation of a circle (when centred at the origin):

[tex]x^2+y^2=r^2[/tex] where r is the radius of the circle

Plug in the point (0,3) to solve for the radius squared

[tex]0^2+3^2=r^2\\9=r^2[/tex]

Plug r² back into the original equation

[tex]x^2+y^2=9[/tex]

I hope this helps!

Answer:

£1500

Step-by-step explanation:

If Dan starts out with £1200 and he gets 5% per year compound interest you would multiply 1200×0.05 and get 60, this is the amount of money that was collected with interest every year. Now you need to multiply 60×5 and get 300. With the total interest over 5 years we need to add the interest and the original amount which would be 1200+300=1500.

Complete Question

Tyrone is making 52 cookies for a party. Some will be a pecan cookies and some will be honey ginger. The ratio of pecans to a honey ginger is 7:6. How many of each kind of cookie will he make

Answer:

28 pecan cookies and 24 Honey ginger cookies

Step-by-step explanation:

From the above question

Pecans : Honey ginger = 7:6

Sum of Proportion = 7 + 16 = 13

Total number of cookies = 52

Number of pecans

= 7/13 × 52 = 28 pecans cookies

Number of Honey ginger

= 6/13 × 52 = 24 Honey ginger cookies

Therefore, we have:

28 pecan cookies and 24 Honey ginger cookies

Answer:

A = 11²/{4π}

Step-by-step explanation:

The circumference equation is C = 2πr.  Thus, r = C / (2π), and:

         C²                                                   (22π)²          2²11²π²             11²  

r² = ----------     so, if C = 22π units, r² = -------------- = ---------------- = -------------

       (2π)²                                                    (2π)^4        (2π)²(2π)²       (2π)²

             11²π²

or  r² = ---------------

The area equation for a circle is A = πr² which here is π·11²/(2π)²

This reduces to 11²/{4π}

Answer:

A

Step-by-step explanation:

I believe it is A If I remember correctly

Answer:

Area of a rectangle that is 9 units² + Area of a rectangle that is 4 units²

Step-by-step explanation:

Line PQ is 1 unit because 3 units - 2 units = 1 unit

Line PO is 4 units because 7 units - 3 units = 4 units

1 unit × 4 units = 4 units²

4 units² + 9 units² = 13 units²

Answer:

adding an answer so the other guy can get brainlist!

Step-by-step explanation:

Answer:

hello your question has a missing diagram attached below is the missing diagram

answer :  

Mark the point of intersection S of circles R and P, and construct line QS ( option 2 )

Step-by-step explanation:

when constructing a tangent line from one point ( lets say Q as seen in the question ) to a circle P. The next step should be to mark a point of intersection between  the given circles and then construct a line through it

Answer:

Mark the point of intersection S of circles R and P, and construct line QS.

Step-by-step explanation:

This is correct because after you create circle R that intersects circle p, you're supposed to mark the intersection points.  If your in FLVS, it would be in lesson 7.04.  I also got this right on my test.  Good luck!

Answer:

[tex]X=85.123m[/tex]

[tex]Y=184.88m[/tex]

Step-by-step explanation:

From the question we are told that:

Campfire Bearing from Colonel[tex]x=N 71 \textdegree E[/tex]

Distance b/w Colonel and Sarge [tex]Z=235feet[/tex]

Campfire Bearing from Sarge [tex]y=N 45 \textdegree E[/tex]  

Generally the angles x' and y' are solved

[tex]x'=90 \textdegree-71 \textdegree[/tex]

[tex]x'=19 \textdegree[/tex]

[tex]y'=90 \textdegree-45 \textdegree[/tex]

[tex]y'=45 \textdegree[/tex]

Generally the angle z' is  solved

Sum of angles of a triangle is 180

Therefore

[tex]z'=180 \textdegree-(19+45) \textdegree[/tex]

[tex]z'=116 \textdegree[/tex]

Generally the sine rule equation for for all distances is mathematically given by

[tex]\frac{Z}{sinz'}=\frac{X}{sinx'}=\frac{Y}{siny}[/tex]

Generally the the distance b/w the Colonel and the campfire X is mathematically given as

[tex]\frac{235}{sin116}=\frac{X}{sinx'}[/tex]

[tex]\frac{235}{sin116}=\frac{X}{sin19}[/tex]

[tex]X=85.123m[/tex]

Generally the the distance b/w Sarge and the campfire X is mathematically given as

[tex]\frac{235}{sin116}=\frac{Y}{siny}[/tex]

[tex]\frac{235}{sin116}=\frac{Y}{sin45}[/tex]

[tex]Y=184.88m[/tex]

Answer:

a. x = 180 - (j + k)

b.

j + k = (5x - 2) + (2x - 2) = 7x - 4

l = x

x = 180 - (7x - 4)

x = 180 - 7x + 4

8x = 184

x = 184/8

x = 23

l = 23°

j = 5x - 2

j = 5 × 23 - 2

j = 115 - 2

j = 113°

k = 2x - 2

k = 2 × 23 - 2

k = 46 - 2

k = 44°

or k = 180 - (23 + 113) = 180 - 136 = 44°