Roxanne invests $4.000 into an account that pays 4% simple interest. Roger invests the same amount of money with the same rate, but the
Interest is compounded annually. What will be the difference in Roxanne's and Roger's accounts after five years if no additional amounts are
deposited? Round to the nearest cent.

Answer:

(1) = (e) 7x. (2) = (b) 7+x. (3) = (d) x-7. (4) = (c) 2x+7

Answer:

A

Step-by-step explanation:

Answer:

Exact Distance = [tex]\frac{4\sqrt{10}}{5}[/tex]

Approximate Distance = 2.529822

============================================

Explanation:

This process is quite involved if you don't know the shortcut formula. I'll go over the long method first, and then show the shortcut in the next section.

First we'll need the equation of the line through points O and M. Use of the slope formula will show line OM has slope -1/3, which you are correct in stating.

Then use point slope form to determine the equation of line OM is y = (-1/3)x+11/3. This converts to the standard form x+3y = 11.

For anything in the form Ax+By = C, the equation perpendicular to this is of the form Bx-Ay = D. The A,B coefficients swap, and one item is negated. This helps form the negative reciprocal slope needed for the perpendicular line.

Compare x+3y = 11 to Ax+By = C. We see that A = 1 and B = 3.

So Bx-Ay = D turns into 3x-y = D. Then plug in the coordinates of H(-3,2) and compute to get

3x-y = 3(-3)-2 = -9-2 = -11. So D = -11

The equation 3x-y = D turns into 3x-y = -11 which is the equation of the line through point H and this line is perpendicular to line OM.

At this point, we have this system of equations

x+3y = 11

3x-y = -11

Solve that system however you wish. Substitution may be the best choice. Doing so leads to the intersection point (-2.2, 4.4)

The last step is to apply the distance formula between the points H(-3,2) and the intersection point (-2.2, 4.4)

The distance you should get is [tex]\frac{4\sqrt{10}}{5} \approx 2.529822[/tex]

I'm skipping steps because listing everything out would take up way too much space in my opinion.

--------------------------------------------------------

The first section goes over a fairly lengthy process of finding the perpendicular distance. Luckily, there's a shortcut.

Consider an equation of the form Ax+By=C, aka standard form. Now consider a point P located at (m,n) that is not on the line Ax+By = C. We can find the distance from P to the line using this formula below

[tex]d = \frac{|Am+Bn-C|}{\sqrt{A^2+B^2}}[/tex]

In this case, A = 1, B = 3 and C = 11 found back in the previous section. So you'll still need to calculate the equation of line OM.

Also, we'll use (m,n) = (-3,2) which are the coordinates of point H

From here it's a fairly straightforward computation

[tex]d = \frac{|Am+Bn-C|}{\sqrt{A^2+B^2}}\\\\d = \frac{|1*(-3)+3*2-11|}{\sqrt{(1)^2+(3)^2}}\\\\d = \frac{|-8|}{\sqrt{1+9}}\\\\d = \frac{8}{\sqrt{10}}\\\\[/tex]

Optionally we can rationalize the denominator like so

[tex]d = \frac{8}{\sqrt{10}}\\\\d = \frac{8\sqrt{10}}{\sqrt{10}\sqrt{10}}\\\\d = \frac{8\sqrt{10}}{\sqrt{10*10}}\\\\d = \frac{8\sqrt{10}}{\sqrt{100}}\\\\d = \frac{8\sqrt{10}}{10}\\\\d = \frac{2*4\sqrt{10}}{2*5}\\\\d = \frac{4\sqrt{10}}{5}\\\\d \approx 2.529822\\\\[/tex]

There are different ways to write down the answer, but they all represent the same number.

Answers:

Probability of landing all three coins on head: [tex]\frac{1}{8}[/tex]

Probability of landing all three coins on tail: [tex]\frac{1}{8}[/tex]

Probability of landing two coins on head and one on tail: [tex]\frac{3}{8}[/tex]

Probability of landing two coins on tails and one on head: [tex]\frac{3}{8}[/tex]

Step-by-step explanation (Read Carefully):

-How to calculate this is that there are three possible outcomes when tossing the three coins. So, if you group all the possible outcomes of heads and tails when tossing the three coins in one event, you’ll get eight events. Let’s take a look at it:

-A way to organize this is to have:

H = heads

T = tails

-Total of eight events, where each event is the probability of the three coins being tossed (possible events with equal probability, and order matters):

HHH

HHT

HTH

HTT

THH

THT

TTH

TTT

Now, let’s apply some questions:

⇒ Probability of landing all three coins on heads: [tex]\frac{1}{8}[/tex]

Explanation: Look at the events above. How many times (out of the eight events) that all three coins land on heads? Well, you can see that there is only one possible event that has HHH. So, the probability of landing all three coins on heads (out of the eight events) is [tex]\frac{1}{8}[/tex].

⇒ Probability of landing all three coins on tails: [tex]\frac{1}{8}[/tex]

Explanation: Look at the events above. How many times (out of the eight events) that all three coins land on tails? Well, you can see that there is only one possible event that has TTT. So, the probability of landing all three coins on tails (out of the eight events) is [tex]\frac{1}{8}[/tex].

⇒ Probability of landing two coins on heads and one on tails: [tex]\frac{3}{8}[/tex]

Explanation: Look at the events above. How many times (out of the eight events) where two coins land on heads and one on tails? Well, you can see that there are three possible events that include HHT, HTH, THH. So, the probability of landing two coins on heads and one on tails (out of the eight events) is [tex]\frac{3}{8}[/tex].

⇒ Probability of landing two coins on tails and one on heads: [tex]\frac{3}{8}[/tex]

Explanation: Look at the events above. How many times (out of the eight events) where two coins land on tails the one on heads? Well, you can see that there are three possible events that include HTT, THT, TTH. So, the probability of landing two coins on tails and one on heads (out of the eight events) is [tex]\frac{3}{8}[/tex].

I hope you understand and that this helps with your question! :)

Answer:

$36.75

Step-by-step explanation:

You do 5% of 35 which equals 1.75 that’s your sales tax.

then add 1.75+35.00= 36.75

9514 1404 393

Answer:

  17. True

  18. False

Step-by-step explanation:

A dilation will be an enlargement when the magnitude of the scale factor is greater than 1.

__

17. The magnitude of the scale factor is 1 2/3, a value greater than 1. The dilation is an enlargement (True).

__

18. The magnitude of the scale factor is 1/2, a value less than 1. The dilation is not an enlargement. The statement is False.

Answer:

6/0, 5/0, 6/5-5

Step-by-step explanation:

You cannot divide a number by 0:

Answer:

x=102

Step-by-step explanation:

Answer:

Rate Of Change= 7

Step-by-step explanation:

all you have to do is see the difference, imma make a table here first

x       y

1       10

3      24

6      45

11      80

15    108

from 10 to 24 you add 14

from 1 to 3 you add 2

so y/x

14/ 2 = 7

check:

from 24 to 45 you add 21

from 3 to 6 you add 3

so y/x

21/3 = 7

From y/x your final answer will always be 7.

So the rate of change will be 7.

Hope this helped a little!

Answer:

Step-by-step explanation:

Given the angle ∠AOB

It is stated that CO is the angle bisector of ∠AOB.

Given that ∠AOB = 30°

As we know that the angle bisector bisects the angle into two equal angles.

Thus, the angle bisector CO bisects the angle ∠AOB into two equal angles, which are:

as

∠AOB = 30°

Thus, the two formed angles i.e m∠AOC and m∠BOC by the angle bisector would be half of the angle bisector as the angle bisector bisects the angle ∠AOB into two equal angles.

Therefore,

Answer:

46800

Step-by-step explanation:

10x15x24x13=46800

Answer:

x=3.91

Step-by-step explanation:

29.46=13.82+4x

13.82+4x=29.46

subtract 13.82 from both sides

4x=15.64

divide by 4

x=3.91

Answer:

Your correct answer is 14t - 40

Step-by-step explanation:

Combine like terms:

10t + 3t + t = 14t

Since there are no other integers, just tag on the -40:

14t - 40

**please mark brainliest!!

Answer:

Gabe worked for 6 2/3 hours and Paula worked for 4 hours.

Step-by-step explanation:

It is given that,

Diana worked on her science project for 5 1/3 hours.

Gabe worked on his science project 1 1/4 times as long as Diana.

Paula worked on her science project 3/4 as long as Diana.

Solution,

ATQ,

Gabe worked for :

[tex]5\dfrac{1}{3}\times 1\dfrac{1}{4}\\\\=\dfrac{16}{3}\times \dfrac{5}{4}\\\\=\dfrac{20}{3}\ h\\\\=6\dfrac{2}{3}\ h[/tex]

Pauls worked for :

[tex]\dfrac{3}{4}\times 5\dfrac{1}{3}\\\\=\dfrac{3}{4}\times \dfrac{16}{3}\\\\=4\ h[/tex]

Hence, Gabe worked for 6 2/3 hours and Paula worked for 4 hours.

Answer:

g = 2d - 8

g + d = 46

Answer:

Square root2 /3

Step-by-step explanation:

1. Multiply both numerator and denominator by square root of 2.

2. Square root 2 times itself is just 2 that so denominator is 5-2

3. 1 times Square root 2 is just Square root 2. So numerator is Square root 2

4. 5-2=3 so final answer is Square root 2 over 3

Answer:

A

Step-by-step explanation:

not sure gusto ko lang tumulong

Answer:

71

Step-by-step explanation:

There are 12 inches in a foot:

12 inches x 5 feet = 60

60 + 11 inches = 71 inches total

Answer:

71 inches

Step-by-step explanation:

12 inches in a foot

12*5

60+11

71 inches

Hope this hopes. Have a great day. May it be filled with joy and happiness.

Answer:

9:00

Step-by-step explanation:

Answer:

Step-by-step explanation:

if you look at the graph 0-3 is positive

so that gives us 3+

3-2(you count 3 to -2 is negative since it goes left

so that gives us 3+(-5)

thks

Answer:

you might’ve already answered this but it’s 65

Step-by-step explanation:

the two sides in a triangle have to be congruent so if one angle is 65, the other has to be 65 too :)

Answer:

65

Step-by-step explanation:

the given triangle is an isoceles triangle and opposite angles of opposite equal sides of isosceles triangle are equal

3 out of 12

1 out of 4

yea hopefully correct

Answer:

Step-by-step explanation:

As per graph, using the points (-6, 0) and (0, 3) we determine that:

So the equation is:

Answer:

Step-by-step explanation:

63

1/7x-5=4

1/7x=9

X=63

Answer:

The average rate of change on the given interval is 9/70

Step-by-step explanation:

Here, we are to find the average rate of change of the function on the given interval

We proceed as follows;

on an interval [a,b] , we can find the average rate of change using the formula;

f(b) - f(a)/b-a

From the question;

a = 0

b = 3

f(0) = -3/5

f(3) = -3/14

Substituting the values, we have;

-3/14-(-3/5)/3-0

= 3/5-3/14/3

= (42-15)/70/3

= 27/70/3

= 27/70 * 1/3 = 9/70

Answer:

The answer is 0.5 and the Mixed Fraction is 1/2

Step-by-step explanation:

Answer:

3 1/8

Step-by-step explanation:

im only answering this late incase if someone else is looking for the right answer