Stephen invests in an account that pays 3% compound interest annually. He invests $5,500. He uses the expression P(1+r)t to find the total value of the account. What will be the total value of the account after 6 years?

Answer:

The vertices are:

A' = (-3, -3)

B' = (3, -3)

C' = (3, 3)

D' = (-3, 3)

Step-by-step explanation:

Given:

A 2 x 2 square is centered at the origin.

So, the center of the square is (0, 0)

Since it is 2 x 2 square, the side of the square is 2 units.

So, the vertices of the 2 x 2 square are A (-1, -1),  B(1, -1), C(1. 1), D(-1, 1)

The above square is dilated by a factor of 3.

Let's name the dilated square A'B'C'D'

To find the coordinates of the vertices of dilated square, we need to multiply each vertices of ABCD by 3.

A(-1, -1) = 3(-1, -1) = A'(-3, -3)

B(1, -1) = 3(1, -1) = B'(3, -3)

C(1, 1) = 3(1, 1) = C'(3, 3)

D(-1, 1) = 3(-1, 1) = D'(-3, 3)

Answer:

[tex]x=475[/tex] units

Step-by-step explanation:

Method 1

The given revenue function is [tex]R(x)=95x-0.1x^2[/tex].

We rewrite this function in the vertex form by completing the square.

[tex]\Rightarrow R(x)=-0.1x^2+95x[/tex].

[tex]\Rightarrow R(x)=-0.1(x^2-950x)+0[/tex].

We add and subtract half the coefficient of [tex]x[/tex] multiplied by a factor of [tex]-0.1[/tex], which is [tex]-0.1(-\frac{950}{2})^2=-0.1( -475)^2[/tex] to get,

[tex]R(x)=-0.1(x^2-950x)+-0.1(-475)^2--0.1(-475)^2 +0[/tex].

We factor [tex]-0.1[/tex] out of the first two expressions again to get,

[tex]R(x)=-0.1(x^2-950x+(-475)^2)--0.1(-475)^2 +0[/tex].

We now got a perfect square.

[tex]\Rightarrow R(x)=-0.1(x-475)^2+22562.5[/tex].

Therefore the maximum revenue occurs when [tex]x=475[/tex] units were sold.

Method 2

Use derivatives to find the x-value of the maximum point.

[tex]R(x)=-0.1x^2+95x[/tex]

[tex]R'(x)=-0.2x+95[/tex]

At maximum point,

[tex]R'(x)=0[/tex]

[tex]\Rightarrow -0.2x+95=0[/tex].

[tex]\Rightarrow -0.2x=-95[/tex].

[tex]\Rightarrow x=\frac{-95}{-0.2}[/tex].

[tex]\Rightarrow x=475[/tex].

The maximum revenue is achieved when 475 units are sold in the given function R = 95x - 0.1x^2, which was determined by taking the first and second derivatives of the revenue function.

In order to find the number of units that produce maximum revenue in the equation R = 95x - 0.1x^2, you have to differentiate the revenue function R with respect to x and set the derivative (first derivative) equal to 0 to find the critical points.

The derivative of the function R with respect to x is R' = 95 - 0.2x. Setting this equal to zero gives: 95 - 0.2x = 0. Solving for x provides x = 95/0.2 = 475. Hence, 475 units sold will maximize revenue according to the provided revenue function.

To confirm this is a maximum, you can use the second derivative test. The second derivative of R, R'' = -0.2. Since this value is negative, x = 475 indeed corresponds to a maximum point on the graph of R(x). Hence, maximum revenue is achieved when 475 units are sold.

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Answer: The area is 572.5566

Step-by-step explanation:

27÷2=r=13.5

A=πr²

A=3.1416(π) · 13.5²(r)

A=572.5566

Answer:

Given:

Diameter= 27 inches

radius= d/2

        =27/2

        =13.5

Answer:

Groceries is 625 a month

Step-by-step explanation:

25 percent of 2500 is 625. To get this answer take the percent and go back 2 decimal places this will turn 25% into 0.25 then multiply 2500 by 0.25 and the answer is 625. This also is the same with the other values. 0.30 0.15 etc.

Answer:

Groceries is 625 a month.(A lot of food for a single)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Rounding, we get 11.5 percent

Step-by-step explanation:

To find the percent of discount, we take the original price, subtract the new price, and divide by the original price.  Then multiply by 100 for the percent.

percent discount = (original - new)/ original * 100

percent discount = (36.30-32.12) /36.30 * 100

percent discount = (4.18) /36.30 * 100

percent discount = .115151515 * 100

percent discount = 11.51515 percent

Rounding, we get 11.5 percent

Answer:

Hello from MrBillDoesMath!

Answer:

Choice A.   (1/25 )

Discussion:

The caret symbol, "^", denotes "exponentiation".  So

5 ^-2  = (1/5)^2 = (1/5)* (1/5) = 1/25

Regards,  

MrB

The proportional relationship between x and y is;

x 7 14 28 35

y 1 2 4 5

The correct option is D.

Proportional relationships between x and y satisfy the following equation;

[tex]\rm y=kx[/tex]

Where k is some constant.

Rearranging the equation;

[tex]\rm y=kx\\\\k=\dfrac{y}{x}[/tex]

Then,

The proportional relationship between x and y is;

[tex]\rm k = \dfrac{y}{x}\\\\\rm When \ x= 7 \ and \ y= 1\\\\K=\dfrac{1}{7}\\\\\rm When \ x= 14 \ and \ y= 2\\\\K=\dfrac{2}{14}=\dfrac{1}{7}\\\\\rm When \ x= 28 \ and \ y= 4\\\\K=\dfrac{4}{28}=\dfrac{1}{7}\\\\\rm When \ x= 35 \ and \ y= 5\\\\K=\dfrac{5}{35}=\dfrac{1}{7}[/tex]

Hence, the proportional relationship between x and y is the correct option is D.

To know more about proportional relationships click the link given below.

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f  ( x ) =  3 x −  1

Hope that helps

$960

720÷30=24

24×40=960

The equation of the line through (5,6) has a slope of 2 will be y=2x-4.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

It is given that, the line passes through (-10,-7)and (-5,-9).

We have to find the equation of the line through given points,

The slope of the line is,

m= 2

The equation of the line is obtained as,

y-y₁=m(x-x₁)

y-(6)=-2(x-(5)

y-6=2x-10

y=2x-10+6

y=2x-4

Thus, the equation of the line through (5,6) has a slope of 2 will be y=2x-4.

Learn more about the straight line here:

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Final answer:

To find the equation of the line with a slope of 2 passing through the point (5,6), we use the point-slope formula and obtain y = 2x - 4.

Explanation:

To write an equation of a line that passes through a given point, such as (5,6), with a given slope of 2, we can use the point-slope form of a linear equation, which is: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Substituting the given point and slope into this formula, we have:

y - 6 = 2(x - 5)

Expanding this equation and solving for y, we get:

y - 6 = 2x - 10

Add 6 to both sides to find the y-intercept:

y = 2x - 4

This equation represents the line with a slope of 2 that passes through the point (5,6).

Answer:

It is a sequence of integers cubed.

1^3 = 1

2^3 =8

3^3 = 27

4^3 =64

5^3 = 125

6^3 = 216

Step-by-step explanation:

Answer:

You must have all A's for Honor roll.

Step-by-step explanation:

My sister is in it and she has all A's

A 3.4 unweighted GPA is generally considered good and may qualify for the honor roll, depending on your school's criteria.

Based on your grades, you have a 3.4 unweighted GPA.

To determine if this qualifies you for the honor roll, it would be best to check your school's specific requirements, as they can vary.

Typically, a 3.4 GPA is considered solid and may be sufficient for honor roll status in many high schools.

Here is a breakdown of your grades:

While you have mostly As and Bs, the C in Spanish 2 may affect your honor roll eligibility depending on your school's criteria.

Answer:

Speed = 10.42 m/secs

Step-by-step explanation:

We have been given with:-

Distance = 100m

Time taken = 9[tex]\frac{3}{5}[/tex] secs

1) First, we need to convert the mixed number 9[tex]\frac{3}{5}[/tex] to an improper fraction.

Method to convert a mixed number to an improper fraction

[tex]a\frac{b}{c} = \frac{c*a+b}{c}[/tex]

Applying the above formula, we get

9[tex]\frac{3}{5}[/tex] = [tex]\frac{5*9+3}{5}[/tex]

= [tex]\frac{45+3}{5}[/tex]

= [tex]\frac{48}{5}[/tex]

2) Now we need to convert [tex]\frac{48}{5}[/tex] into a decimal by dividing 48 by 5.

We get time taken as 9.6 secs

3) We need to find the speed using the below formula:-

Speed = [tex]\frac{Distance}{Time taken}[/tex]

Plugging the values of Distance and Time taken into the formula, we get

Speed = [tex]\frac{100}{9.6}[/tex]

= 10.416 m/secs

4) Upon rounding it to the nearest hundredth, we get

Speed = 10.42 m/secs

Heya!

Your question states: Solve for x in simplest form 15 = 1/3(x+9)

Answer: X = 36

Numerical Explanation:

1. Step by step

   I. 15 = 1/3(x+9)

2. Simplify both sides of the equation:

    II. 15 = 1/3x + 3

3. Flip the equation:

      III. 1/3x + 3 = 15

4. Subtract 3 from both sides:

          IV. 1/3 x +3 = 15

                          -3    -3

5.  Multiply both sides by 3:

              V.  3 * (1/3 x) = (3) * (12)

6. Final answer:

                  VI. x = 36

I Hoped I Helped!

~KINGJUPITER

Answer:

x = 36

Step-by-step explanation:

Note the equal sign, what you do to one side, you do to the other. Isolate the variable, x. Do the opposite of PEMDAS:

Remember to follow PEMDAS and the left -> right rule.

PEMDAS:

Parenthesis

Exponent (& roots)

Multiplication

Division

Addition

Subtraction

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

15 = 1/3(x + 9)

First, multiply 3 to both sides of the equation

(15)(3) = (1/3(x + 9))(3)

(15)(3) = x + 9

45 = x + 9

Next, to isolate the x, subtract 9 from both sides

45 (-9) = x + 9 (-9)

45 - 9 = x

36 = x

-----------

36 is your answer for x.

~

Answer:

The value of x is -0.5.

Step-by-step explanation:

The given equation is

[tex]-2(5x-6)+6x=4(x+4)[/tex]

Use distributive property to solve the above equation.

[tex]-2(5x)-2(-6)+6x=4(x)+4(4)[/tex]

[tex]-10x+12+6x=4x+16[/tex]

[tex]-4x+12=4x+16[/tex]

Add 4x both sides.

[tex]12=8x+16[/tex]

Subtract 16 from both sides.

[tex]-4=8x[/tex]

Divide both sides by 8.

[tex]\frac{-4}{8}=\frac{8x}{8}[/tex]

[tex]-0.5=x[/tex]

Therefore value of x is -0.5.

Answer:

B

Step-by-step explanation:

Answer:

Option A is the correct choice.

Step-by-step explanation:  

We have been given the system of linear equations written by Draco. We are asked to find Draco's error.

Let us form a system of equations using our given information.

Let m represent the price of one muffin and b represent the cost of one bagel.

We are told that in one hour a bakery sold five muffins and nine bagels for a total of $25.50. We can represent this information in an equation as:

[tex]5m+9b=25.50...(1)[/tex]

The next hour the bakery sold three muffins and 12 bagels for a total of $28.50. We can represent this information in an equation as:

[tex]3m+12b=28.50...(2)[/tex]

Now let us see system of equations written by Draco.

[tex]5m+9b=28.50[/tex]

[tex]3m+12b=25.50[/tex]

We can see that Draco has set the price of 5 muffins and 9 bagels equal to $28.50, which is the price of 3 muffins and 12 bagels.

Therefore, Draco should have set the first equation equal to 25.50 and the second equation equal to 28.50. The correct choice is option A.

Answer:

9[tex]\sqrt{85}[/tex]

Step-by-step explanation:

9v = 9(2i + 9j) = 18i + 81j

|9v | = [tex]\sqrt{18^2+81^2}[/tex] = [tex]\sqrt{x6885}[/tex] = 9[tex]\sqrt{85}[/tex]

Answer:

time upstream=24/8=3 hours

time downstream=24/12=2 hours

Step-by-step explanation:

If R*T=D, and R is speed + or - current, how can you find the rate without the time, and how can you find the time without the rate?

THE KEY WAS WHEN WE WERE TOLD THAT IT TAKES ONE HOUR LONGER TO GO UPSTREAM THAN DOWNSTREAM BECAUSE T=D/R AND WE ARE TOLD THAT:

D/R(Upstream) minus 1 equals D/R (DOWNSTREAM)

Let x=rate of current

distance(d)=rate(r) times time(t) or d=rt or t=d/r

distance upstream=distance downstream=24 mi

rate upstream=10-x

rate downstream=10+x

time upstream=(distance upstream)/(rate upstream)=24/(10-x)

time downstream=(distance downstream)/(rate downstream)=24/(10+x)

Now, we are told that time upstream minus one hour equals time downstream. So our equation to solve is:

24/(10-x)-1=24/(10+x) Multiply both sides by (10-x)(10+x)

24(10+x)(10-x)/(10-x)-1(10-x)(10+x)=24(10-x)/(10+x)/(10+x) clear fractions

24(10+x)-(10-x)(10+x)=24(10-x) clear parens

240+24x-100-10x+10x+x^2=240-24x subtract 240 from and add 24x to both sides

240-240+24x+24x-100+x^2=240-240-24x+24x collect like terms

x^2+48x-100=0 ----------------quadratic equation in standard form

This equation can be factored:

(x+50)(x-2)=0

x=-50 mph----------------discount the negative value for speed

and

x=2 mph----------------------speed of the current

CK

10-x=10-2= 8 mph -----------------------speed upstream

10+x=10+2=12 mph--------------------------speed downstream

time upstream=24/8=3 hours

time downstream=24/12=2 hours

so 3-2=1----takes 1 hour longer upstream

Answer:

Distance = 70 + 55 = 125 kilometers

Time = 4 + 3 = 7 hours

Rate = Distance / Time

Rate = 125 / 7 = 17.8571428571 kilometers per hour

Step-by-step explanation:

The average speed:

[tex]v=\dfrac{total\ distance}{total time}[/tex]

We have

total distance = 70 km + 55 km = 125 km

total time = 4 h + 3 h = 7 h

The average speed:

[tex]v=\dfrac{125\ km}{7\ km}\approx18\ \dfrac{km}{h}[/tex]

Answer:

4:!

Step-by-step explanation:

4:1 because their are 4 boys for every 1 girl

Let's read this in a more proper way.

The number of boys in Mr. Watson's class is 2/3 the number of girls. So:

[tex]18 * \frac{2}{3} = 12\\18 + 12 = 30[/tex]

There are 30 students in Mr. Watson's class.

For this ratio to be in true in the second problem (306 boys, 459 girls), 306 must be 2/3 of 459.

[tex]459 * \frac{2}{3} = 306[/tex]

The ratio holds true for the second problem.

30 students,

Yes it is possible, because 306 is 2/3 of 459.

Answer:

AB = JK = 49

Step-by-step explanation:

Since ABC = JKL

We know the length of AB has to equal the length of JK.

AB = JK

14x+7 = 5x+34

Subtract 5x from each side.

14x-5x +7 = 5x-5x+34

9x+7 = 34

Subtract 7 from each side

9x+7-7 = 34 -7

9x = 27

Divide each side by 9.

9x/9 = 27/9

x =3

AB = 14x+7

Substitute x=3

      14(3) +7

      42+7

AB =    49

Answer:

The Han dynasty last was, 215 years

Step-by-step explanation:

Given statement: The Han dynasty lasted from 206 B.C. to 9 A.D.

To find how many years did the dynasty last.

B.C. represents Before Christ

A.D. represents After Death

To find the difference between two dates,

You can see that the endings in the given 206 B.C. and 9 A.D. are B.C. and A.D. are different.

Just add these 206 and 9 we get;

[tex]206 + 9 = 215[/tex] years

Therefore, 215 years did the Han dynasty last.

Answer:

thousands place?

Step-by-step explanation:

169.866666667

9 in tenths place

6 in hundredths place

1 is in the thousands place

Answer:

Your y-intercept is 1 and your slope is 2

Step-by-step explanation:

How to find Slope

To find your slope you have to do the change of y over the change of x. So if you go to your table find how much each value of numbers is changing by. Your y-values are changing differently, but it is fine so to get to 5 from 3 you add 2 and to get to 9 from 5 you add 4. You do the same thing for the x-values are changing differently, but it is fine, so to get to -1 from -2 you add 1 and to get  to 1 from -1 you add 2. Next you will take the two values that you get on the y side which are 2 and 4 and the x side which are 1 and 2 and put them in change of y over change of x. So 4/2 with equal 2 and 2/1 equal 2. So the slope is changing by 2.

Answer:

Step-by-step explanation:You can first divide 15 by 5, which equals 3.Then multiply that by 10.8.which gives 32.4. Then divide by 5 which would give you 2.16. Hopefully it helps?!

Also if it is right,Please make me brainliest!!!!!!!!!!!!!!!!!!!

Answer:

43.2 minutes  PLEASE GIVE BRAINLIEST

Step-by-step explanation:

10.8 ÷ 15 = .72  (72%)

Now find what 72% of an hour is:

60 x .72 = 43.2

43.2 minutes

Answer:   88 Feet Per Second

Step-by-step explanation:  

Firstly you need to know 3 things:  

> 60 mph = 60 Miles Per Hour  

> 1 Hour = 60 mins = 60*60 = 3600 seconds  

> 1 Mile = 5280 feet  

Next you can change the miles to feet and hours to seconds.  

60 mi/ 1 hour = 60*5280/ 3600 = 316800ft/ 3600sec  

Now time to reduce that big fraction! (Or in this case just divide by 3600 sec)  

316800ft/ 3600sec  

= 88ft/1sec  

= 88 Feet Per Second  

Hope that helps!