Find the solution of the system of equations.
6x – 3y = -30
3x – 6y = 12

1) The interest if it is compounded using simple interest is $240

2) The interest if it is compounded annually is $249.73

3) The interest if it is compounded semiannually is $252.325

4) The interest if it is compounded quarterly is $253.650

5) The interest if it is compounded monthly is $254.543

6) The interest if it is compounded daily is $254.978

7) The interest if it is compounded hourly is $254.993

8) The interest if it is compounded every minute is $254.993

9) The interest if it is compounded continuously is $254.993

10) The difference in interest between simple interest and interest compounded continuously is $14.993

Compound interest is the addition of interest to the principal sum of a loan or deposit, or interest on interest plus interest.

Given, P=2000

r=4%

r=4/100

r=0.04

t=3 years

1) Simple interest⇒ A=P(1+rt)

=2000(1+3(0.04)

=2000(1+0.12)

=2240

S.I= 2240-2000

S.I=$240

2) Compound interest(yearly)

1st year= 2000(4/100)=80

2nd year=2080(4/100)=83.2

3rd year=(2080+83.2)(4/100)=86.528

P=2163.2+86.528

P=2249.728

C.I=2249.728-2000

C.I=249.728≈$249.73

3) Compounded semiannually

A= P(1+(R/200))²ⁿ

A=2000(1+(4/200))⁶

A=2000(1.12616)

A=2252.325

C.I= 2252.325-2000

C.I=$252.325

4) Compounded quarterly

A=P(1+(R/400))⁴ⁿ

A=2000(1+(4/400))¹²

A=2253.650

C.I=2253.650-2000

C.I=$253.650

5) Compounded monthly

A=P(1+(R/1200))³⁶

A=2000(1+(4/1200))³⁶

A=2254.543

C.I= 2254.543-2000

C.I=$254.543

6) Compounded daily

A=P(1+(R/36500))³⁶⁵ⁿ

A=2000(1+(4/36500))¹⁰⁹⁵

A=2254.978

C.I=2254.978-2000

C.I=$254.978

7) Compounded hourly

A=P(1+(R/876000))²⁶²⁸⁰

A=P(1+(4/876000))²⁶²⁸⁰

A=2254.993

C.I=2254.993-2000

C.I=$254.993

8) Compounded every minute

A=P(1+(R/52560000))¹⁵⁷⁶⁸⁰⁰

A=P(1+(4/52560000))¹⁵⁷⁶⁸⁰⁰

A=2254.993

C.I=2254.993-2000

C.I=$254.993

9) Compounded continuously

A= \(Pe^{rt}\)

A=2000(\(e^{0.04*3}\))

A=2254.993

C.I=2254.993-2000

C.I=$254.993

10) The difference in interest between simple interest and interest compounded continuously is

254.993-$240=$14.993

To know more about compound interest, visit:

https://brainly.com/question/14295570?referrer=searchResults

#SPJ13

the correct answer is No

Step-by-step explanation:

it's not equal

Answer:

\(\frac{1}{3}\neq\frac{3}{3}\)

Step-by-step explanation:

The two numbers are different

Answer:

The mean is: 52.67

Step-by-step explanation:

Given the group of data items

\(37, 37, 63, 55, 87, 37\)

Since we have 6 points.

so

The sum of the values is:

\(37+37+63+55+87+37=316\)

Therefore, the mean is:

Sum of values ÷ n

=316 ÷ 6

=52.67

Thus, the mean is: 52.67

The solution in interval notation is; (-∞,  49/2).

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

To solve the equation 5/16x - 7/4 < 3/4x + 21/2, we can simplify both sides:

5/16x - 7/4 < 3/4x + 21/2

Combining like terms:

5/16x  -3/4x  < 21/2 + 7/4

8/16x < 49/4

1/2x < 49/4

Simplifying the fraction;

x < 49/2

Therefore, the solution in interval notation is (-∞,  49/2).

Learn more about Inequality here:

brainly.com/question/20383699

#SPJ1

Answer:The answer is B.  I hope I've helped you

Step-by-step explanation:

Answer: its D

Step-by-step explanation:

that's the answer

Answer:21,35.21,45

Step-by-step explanation:

Find the error interval: :21,35.21,45

Answer:21,35.21,45

Answer:

486 square inches

Step-by-step explanation:

ANSWER

angle A, CAB, BAC

The fraction computed indicates that the amount donated will be $2000000.

Your information is incomplete. Therefore, an overview will be given.

In this case, let's assume that the profit is 3,000,000. Therefore, the amount that is donated will be:

= 2/3 × $3000000

= $2000000

Learn more about fractions on:

https://brainly.com/question/786722

Applying the knowledge of fractions, the number of t-shirts that can be made is: 30 t-shirts.

In the problem given, we have the following information:

Material needed for one t-shirt = 1 3/8 yards

We want to find how many 1 3/4 we would find in 41 1/4.

Applying the knowledge of fraction, we are to divide 41 1/4 by 1 3/8. Convert both mixed fractions to improper fractions then divide:

41 1/4 ÷ 1 3/8

165/4 ÷ 11/8

165/4 × 8/11

165/4 × 8/11

15/1 × 2/1

= (15 × 2)/(1 × 1)

= 30/1

= 30.

Therefore, applying the knowledge of fractions, the number of t-shirts that can be made is: 30 t-shirts.

Learn more about fractions on:

https://brainly.com/question/17220365

#SPJ1

Answer:

D) 32

Step-by-step explanation:

Given;

series: 56, 54, 50, 38, 34, ....

find the difference between successive numbers;

56         54        50             38            34             x

     2            4             12              4             2            

The highest difference between the numbers is  12, after which it decreases to 4 and finally back 2.

The next number "x" is calculated as;

34 - 2  = x

34 - 2 = x

32 = x

Therefore, the next number should be 32.

The next number that should come next in the series is 32.

Sequence is an arrangement of two or more things in a successive order.  Series is the cumulative sum of a given sequence of terms.

Given the numbers in the series: 56, 54, 50, 38, 34, . . ..

The difference is 2, 4, 12, 4, 2

The highest difference between the numbers is  12, after which it decreases to 4 and finally back 2. Hence:

The next number = 34 - 2 = 32

The next number that should come next in the series is 32.

Find out more on series at: https://brainly.com/question/13171394

The interest is 16% compounded semi-annually, is Rs. 121,179.10.

To determine how much money needs to be deposited now to provide a payment of Rs. 15,000 at the end of each half year for 10 years, we will use the formula for the present value of an annuity.

Present value of an annuity = (Payment amount x (1 - (1 + r)^-n))/rWhere:r = interest rate per compounding periodn = number of compounding periodsPayment amount = Rs. 15,000n = 10 x 2 = 20 (since there are 2 half years in a year and the payments are made for 10 years)

So, we have:r = 16%/2 = 8% (since the interest is compounded semi-annually)Payment amount = Rs. 15,000Using the above formula, we can calculate the present value of the annuity as follows:

Present value of annuity = (15000 x (1 - (1 + 0.08)^-20))/0.08 = Rs. 121,179.10Therefore, the amount that needs to be deposited now to provide payment of Rs. 15,000 at the end of each half year for 10 years, if the interest is 16% compounded semi-annually, is Rs. 121,179.10.

For more such questions on semi-annually

https://brainly.com/question/30573341

#SPJ8

Answer:

x = 91°

Step-by-step explanation:

According to the angle sum property of Pentagons, all interior angles in a pentagon add up to 540°

So we can find x as follows

109 + 126 + 98 + 116 + x = 540

x = 540 - 449

x = 91°

Answer:

32.5x

Step-by-step explanation:

She earns 32.5 dollars every hour, so if she worked 14 hours she would earn 455 dollars.

Answer:

32.5x

Step-by-step explanation:

She earns 32.5 dollars every hour, so if she worked 14 hours she would earn 455 dollars.

Answer:

27.5

Step-by-step explanation:

Answer: I got 27.5

Step-by-step explanation:

This is a fraction equal to

220 miles ÷ 8 hours

We want a unit rate where

1 is in the denominator,

so we divide top and bottom by 8

220 miles ÷ 8

8 hours ÷ 8

=

27.5 miles

1 hour

=

27.5 miles

hour

= 27.5 miles per hour

The margin of error for a 90% confidence interval in this scenario is 0.0068.

The sample consists of 250 individuals with a mean BAC of 145.

Based on past data, the researcher assumes a population standard deviation of 0.065.

We have to determine the margin of error for a 90% confidence interval in this scenario.

The z critical value at 90% confidence interval is 1.645 from the standard normal table.

The margin of error = Z × (standard deviation/√sample size)

The margin of error = 1.645 × (0.065/√250)

The margin of error = 1.645 × (0.065/15.81)

The margin of error = 1.645 × 0.0041

The margin of error = 0.0068

To learn more about margin of error link is here

brainly.com/question/10501147

#SPJ4

The set of side measurement could be used to form a triangle is option(4) 7, 12 and 18

If the sides of the triangles are a, b and c. There will be three condition

a + b > c

b + c > a

c + a > b

We have to check these condition

Part 1

The sides are 3, 5 and 7

3 + 5 > 11

8 < 11

It does not form a triangle

Part 2

The sides are 4, 18 and 23

4+18 >23

22 < 23

It does not form a triangle

Part 3

The sides are 5, 9 and 14

5+9 > 14

14 = 14

It does not form a triangle

Part 4

The sides are 7, 12 and 18

7+12 > 18

19 > 18

12 + 18 > 7

30 > 7

7+18 > 12

25 > 12

It forms a triangle

Hence, the set of side measurement could be used to form a triangle is option(4) 7, 12 and 18

Learn more about triangle here

brainly.com/question/2773823

#SPJ1

Answer:

V = 460.68

Step-by-step explanation:

V=(lwh)/3

Answer:

  B.  A point

Step-by-step explanation:

You want a description of the intersection between a plane and a cone given that the plane is parallel to the base and passes through the vertex of the cone.

The vertex of a cone is a single point. If a plane passes through that, but does not intersect the base of the cone, it will not intersect anywhere else.

The intersection is one point.

__

Additional comment

Figure f in the attachment illustrates this case.

The decimal representation of the given sequence is 4,063.21.

The given sequence can be interpreted as follows: "63 ones, 21 hundredths, 4 thousand." To convert this sequence into decimal form, we need to understand the place value of each digit.

Starting from the left, we have "63 ones." This means we have 63 units, which can be represented as 63.

Next, we have "21 hundredths." Since there are two digits after the decimal point, the number becomes 0.21.

Finally, we have "4 thousand." Considering the place value, 4 thousand would be written as 4,000.

Putting it all together, we have 63 + 0.21 + 4,000, which equals 4,063.21. Therefore, the decimal representation of the given sequence is 4,063.21.

For more such questions on decimal

https://brainly.com/question/28393353

#SPJ8

From the options given, Dustin's hopscotch path was the longest in comparison to the other two friends.

Based on this, let's make sure all distances are in feet.

Based on this, the person with the longest path is Dustin.

Learn more about distances in: https://brainly.com/question/15172156

#SPJ1

Answer:

A. 6

Step-by-step explanation:

Using the Pythagorean theorem which states that: Hypotenus² = Opposite² + Adjacent²

Where: hypotenus = 10, opposite = x, adjacent = 8

So:

\( {10}^{2} = {x}^{2} + {8}^{2} \)

Solving for x

\(100 = {x}^{2} + 64\)

Collect like terms to make x the subject of formula

\(100 - 64 = {x}^{2} →36 = {x}^{2} \)

\(36 = {x}^{2} ⟹ {x}^{2} = 36\)

square root both sides of the equation to find the value of x

\( \sqrt{ {x}^{2} } = \sqrt{36} →x = 6\)

Therefore: Option A is correct

Answer:

x = 15

Step-by-step explanation:

Step 1: Write out equation

1/4x - 7/4 = 2

Step 2: Add 7/4 to both sides

1/4x = 15/4

Step 3: Divide both sides by 1/4

x = 15

Answer:

the intersection point is ( -5/4, -5/4, -9/8)

Step-by-step explanation:

F(x,y,z) = x² +y² -z= 0

Then find differential of each terms then we have

∀f(x)=2x

∀f(y)=2y

∀f(z)=-1

The partial differential which is the director vector is at F(x,y,z)= (1,1,2)

Vf(1,1,2) = (2,2,-1)

But the given point is ( 1.1,2)

Then the parametric equation of normal line will be

x= 1+2t

y= 1+2t

z= 2 -t

The parametric equation can be formed as

(1+2t)² + (1+2t)² - (2-t)= 0

If we expand the expression above we have,

2(1+4t+4t²) - 2+t= 0

0= 8t² + 9t

t= 0 or t= -9/8

Substitute the value of t into the parametric equation above

At t=0

x= 1+2t; x= 1+2(0)=1

y= 1+2t; y= 1+2(0)=1

z=2 -t ; z= 2-(0)= 2

At =0 , we have (1,1,2)

At t= -9/8

x= 1+2t; x= 1+2(-9/8)=-5/4

y= 1+2t; y= 1+2(-9/8)=-5/4

z=2 -t ; z= 2-(-9/8)= -9/8

Therefore, the intersection point is ( -5/4, -5/4, -9/8)

The normal intersects the paraboloid at \((-\frac{5}{4},-\frac{5}{4},\frac{25}{8} )\)

A surface all of whose intersections by planes are either parabolas and ellipses or parabolas and hyperbolas.

Given function is,

\(z = x^2 + y^2\)

We can write the given function as,

\(F(x,y,z)=x^2+y^2-z\)

Compute the gradient  \(F\) by using the formula,

\(\nabla F(x,y,z)=\left\langle 2x,2y,-1\right\rangle\)

At (1,1,2) we get,

\(\nabla F(x,y,z)=\left\langle 2,2,-1\right\rangle\)

The equation of the tangent plane at (1,1,2) is,

\(2(x-1)+2(y-1)-(z-2)=0\\2x+2y-z-2=0\\\frac{x-1}{2}=\frac{y-1}{2}=\frac{z-2}{-1}=t\\ x=2t+1,y=2t+1,z=-t+2\)

Replace the values of \(x,y,z\) in \(z = x^2 + y^2\) and then solve for \(t\) then,

\(-t+2=(2t+1)^2+(2t+1)^2\\8t^2+9t=0\\t=0,-\frac{9}{8}\)

Substituting the value into the parametric equations,

\(x=2(-\frac{9}{8} )+1,y=2(-\frac{9}{8} )+1,\ and \ z=-(-\frac{9}{8} )+2\\x=-\frac{5}{4}, \ y= -\frac{5}{4} ,z=\frac{25}{8}\)

Therefore, the normal intersects the paraboloid at \((-\frac{5}{4},-\frac{5}{4},\frac{25}{8} )\)

Learn more about the topics paraboloid:

https://brainly.com/question/17593461

Solution for the given System of linear equation is:

Simultaneous equations, system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

There are four methods to solving systems of equations: graphing, substitution, elimination and matrices.

Given,  the system of linear equations on the left with its solution type on the right

For  Y=2x-1 and Y=2x+1

Adding both equation,  we will get y = 4x

Thus, these equations have infinite number of solution

For 2x - y = 7 and 3x + y = 3

Adding these equations

5x = 10

x= 2

Substitute the value in equation 1

y = -3

Thus, solution is (2, - 3)

therefore, the Solution for the given System of linear equation is:

Learn more about System of equation here:

https://brainly.com/question/12628931

#SPJ1

Complete question: