A bank offers a CD that pays a simple interest rate of 11.5% how much how must you put in this CD now in order to have 3500 for a home-entertainment center in 5 years ( round up to the nearest cent) .

Answer:

Step-by-step explanation:

Formula for calculating interest is expressed as;

I = PRT/100

P is principal

R is the rate

T is the time

For first account

I = P(1)(6)/100

I1 = 0.06P1

For the second bank!

I2 =>P2(1)(4)/100

I2 = 0.04P2

If the total interest is $3520, then

I1+I2 = 3520

0.06P1+0.04P2 = 3520.... 1

If the Amount invested = $65000

P1+P2 =65000..... 2

Solve. 1 and 2 simultaneously

Eqn 2 × 0.06

0.06P1+0.06P2 = 3900.... 3

Subtract 1 from 3;

0.04P2-0.06P2 = 3520-3900

-0.02P2 = -380

P2 = 380/0.02

P2 = $19000

Get p1;

P1 = 65000-P2

P1 = 65000-19000

P1 = $46000

Hence $46000 was invested in the first account and $19000 in the second

Answer:

Should be 50

Step-by-step explanation:

Answer: The distance between the complex numbers is approximately \(\(14.8661\)\) or \(\sqrt{221}\)

Step-by-step explanation:

The distance between two complex numbers \(\(a + bi\) and \(c + di\)\) is given by the formula:

\($$\sqrt{(c - a)^2 + (d - b)^2}$$\)

This formula is similar to the Euclidean distance formula in two dimensions, where \(\(a\)\) and \(\(b\)\) represent the x and y coordinates of the first point, and \(\(c\)\) and \(\(d\)\) represent the x and y coordinates of the second point.

In this case, the two complex numbers are \(\(2 + 3i\)\) and \(\(-8 + 14i\)\). So, \(\(a = 2\), \(b = 3\), \(c = -8\), and \(d = 14\)\).

Substituting these values into the formula, we get:

\($$\sqrt{(-8 - 2)^2 + (14 - 3)^2} = \sqrt{(-10)^2 + (11)^2} = \sqrt{100 + 121} = \sqrt{221}$$\)

So, the distance between \(\(2 + 3i\)\) and \(\(-8 + 14i\)\) is \(\(\sqrt{221}\)\), which is approximately \(\(14.8661\)\) or \(\sqrt{221}\)

To find the equation of a line parallel or perpendicular to a given line through a point, determine the slope and substitute the point's coordinates into the slope-intercept form.



To find the equation of a line parallel or perpendicular to a given line through a specific point, follow these steps:

1. Determine the slope of the given line. If the given line is in the form y = mx + b, the slope (m) will be the coefficient of x.

2. Parallel Line: A parallel line will have the same slope as the given line. Using the slope-intercept form (y = mx + b), substitute the slope and the coordinates of the given point into the equation to find the new y-intercept (b). This will give you the equation of the parallel line.

3. Perpendicular Line: A perpendicular line will have a slope that is the negative reciprocal of the given line's slope. Calculate the negative reciprocal of the given slope, and again use the slope-intercept form to substitute the new slope and the coordinates of the given point. Solve for the new y-intercept (b) to obtain the equation of the perpendicular line.

Remember that the final equations will be in the form y = mx + b, where m is the slope and b is the y-intercept.Therefore, To find the equation of a line parallel or perpendicular to a given line through a point, determine the slope and substitute the point's coordinates into the slope-intercept form.

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Answer:

AB = ½XZ. XZ = 5*2=10. (The middle line of the triangle)

AC = ½YZ. YZ = 7*2=14. The middle line of the triangle)

XY+YZ+XZ=P. P=110+14+24.P=48

Step-by-step explanation:

The SSS(Side-Side-Side) Triangle congruency is proven by following rule.

In SSS (Side-Side-Side) condition the two triangles are said to be congruent if the three sides of one triangle are equivalent to the corresponding three sides of the second triangle.

In mathematics, the term "congruent" refers to figures and shapes that can be flipped or rearranged to match up with other ones. These forms can be mirrored to produce related shapes. A triangle is a closed polygon with three line segments that intersect at each of its three angles.

Two shapes are congruent if their sizes and forms are comparable. Additionally, if two shapes are congruent, then their mirror images are likewise congruent.

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Answer: the first term in the sequence is 9.

Step-by-step explanation:

Let the primary term be x.

At that point the moment term is 2x + 4.

And the third term is 2(2x + 4) + 4 = 4x + 12.

Since the third term is given as 48, we will set up an condition and unravel for x:

4x + 12 = 48

4x = 36

x = 9

Answer:

every other student who enters the school

Step-by-step explanation:

It is given that the middle school students have an average height of 5.25 feet. The students belongs to Seton Grove School.

It means that every student who comes to this school or enters the school has a height that is around 5 feet or more.

Thus we can say that every other student who enters the school has a average height of 5.25 feet.

This sample makes the generalization about the heights of the school students valid.

Answer:

c

Step-by-step explanation:

correct on edmentum / plato

The measure of angle b is 108 degree.

An equilateral triangle is a plane figure with at least three straight sides and angles, and usually five or more. A polygon is a two-dimensional, closed shape that is flat or plane and is bounded by straight sides. Its sides are not curved. A polygon's edges are another name for its sides. The vertices (or corners) of a polygon are the places where two sides converge.

The total interior angles will equal to 180 * (6 - 2) = 720°.

∠B = 720 - 170 - 133 - 102 - 117 - 90 = 108°.

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6 feet 7 inches

1 feet = 12 inches

6 feet = 6(12) = 72 inches

6 feet 7 inches = 72 + 7 = 79 inches

Answer:

79 inches

Answer:

to square a number you multiply the number by itself.

a positive number times a positive number is a positive number.

a negative number times a negative number is a negative number.

and if you are multiplying 2 numbers with the same sign they will always be a positive number.

The balance in a saving account after 4 years is $1440.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

Simple interest is calculated with the following formula: S.I. = (P × R × T)/100, where P = Principal, R = Rate of Interest in % per annum, and T = Time.

Given that, principal = $1200, rate of interest =5% and time period = 4 years.

Now, simple interest = (1200×5×4)/100

= $240

We know that, Amount=Principal+Simple Ineterst

= 1200+240

=$1440

Therefore, the balance after 4 years is $1440.

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Answer:Samsung Galaxy Z Fold3 5G 256GB Phantom Black Smartphone

USD 1343

a) All the plans have a base service charge of $23 per month plus the cost of the phone. Write an expression to represent the service charge.

1343 + 23m

b) There are three unlimited plans, and each plan incorporates the service charge. Translate each plan into an algebraic expression using the service charge expression from the above question.

Plan 1: $8 less than twice the amount of the service charge.

(service charge is 23 per month so)

1343 + 2(23m– 8)

Plan 2: The quotient of the service charge and 2 increased by a fee of $50 per month.

1343 + (23m/2 + 50m)

Plan 3: The sum of half the number of months cubed and a third of the service charge.

1343 + (1/2m3 + 1/3(23m))

c) Which plan would be most cost effective for a 2-year contract? Show all calculations that led to your results. Explain your results comparing the 3 plans.

Plan 1: 1343 + (24(23 – 8) = 1703

Plan 2: 1343+ (24x61.5) = 2819

Plan 3: 1343 + (1728 + 552) = 3623

Plan 1 is the most cost effective because it is the cheapest

d) Sharaf Digital is having a special promotion by challenging customers to create their own plan. Customers must write a verbal expression that must include the service charge and at least two operations. The operations to choose from are listed below.

If the plan is within $15 per month of one of the original 3 plans then the customer could choose that plan.

Create a 4th plan and show all calculations that led to your results.

Operations: product, more than, less than, double, sum, divided by, square

The product of 3.5 and the total cost divided by 4

3.5(1343 + (24(23 – 8))/4 = 1490.13

Plan 4 = 1490.13/24 = 62.09

Plan 1: 1703/24

70.95

Step-by-step explanation:

The volume of the solid with the semicircular base is equal to 2250π units³

In general term integral value means the value obtained after integrating or adding the terms of a function which is divided into an infinite number of terms .

Given here: A solid with a semi circular base with radius = 15 units

We know the the equation of the circle with its center at the origin is given by

x²+y²=15²

\(y=\sqrt{15^2-x^2}\)

Thus constructing the integral we get

 \(\int\limits^{15}_{-15} \ \pi .\frac{1}{2}.( {15^2-x^2}} )\, dx\)

=-πx.(x²-675) /6 +C |¹⁵₋ ₁₅

=2250π

Hence, The volume of the solid with the semicircular base is equal to 2250π units³

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Answer:

14 weeks till he has $480

Step-by-step explanation:

He needs $480

He has $60

He has to earn the rest over the span of the next few weeks, which is $30 for an unknown number of weeks.

Let the unknown number be x in our equation

What he needs to buy the TV and Stereo system is $480 which is our total

The $60 dollars he received is a complete variable

hence we can say, 30x+60=480

This is our equation but it isn't simplified.

first, divide everything by 10(it is a common divisor)

3x+6=48

subtract 6 which is complete from the total

3x=42

Make x the subject and divide both sides by 3

x=14

so the unknown number of weeks is 14.

If a rocket is launched from the surface of the Earth, it needs to reach a speed of at least 7.9 kilometers per second (4.9 miles per second) in order to reach space. This speed of 7.9 kilometers per second is known as the orbital velocity, it corresponds to more than 20 times the speed of sound.

If the selling price is $90 and the rate of sales tax is 3%, then the total price is $92.7

The selling price = $90

The rate of sales tax = 3%

The amount of sale tax = The selling price × The rate of sales tax

Substitute the values in the equation

The amount of sale tax = 90 × (3/100)

= 90 × 0.03

= $2.7

The total price = The selling price + The amount of sale tax

Substitute the values in the equation

The selling price  = 90 + 2.7

= $92.7

Hence, if the selling price is $90 and the rate of sales tax is 3%, then the total price is $92.7

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An off-by-one error is a common type of error that occurs when programming or solving mathematical problems.

It refers to a situation where a programmer or mathematician makes an error by including or excluding an element that they should have not. This can lead to unexpected results and bugs in the code or calculation. The error is typically caused by a misunderstanding of the boundaries of an array, list or any other data structure. These types of errors can be difficult to spot and can cause serious problems, especially in situations where precision is important.

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If the length of the rectangle is represented by "x," then the width is (x - 58), and the area can be calculated as x² - 58x.

Let's go through the problem step by step to find the area of the rectangle.

Let's assume that the length of the rectangle is represented by the variable "x" (as stated in the question). According to the given information, the width of the rectangle is 58 units less than its length.

If the width is 58 units less than the length, we can represent the width as (x - 58). This means that the length minus 58 gives us the width.

Now, to find the area of the rectangle, we use the formula:

Area = Length × Width

Substituting the values we have:

Area = x × (x - 58)

Expanding the equation:

Area = x² - 58x

So, the area of the rectangle is given by the expression x² - 58x.

To summarize, if the length of the rectangle is represented by "x," then the width is (x - 58), and the area can be calculated as x² - 58x.

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Answer:

30%

Step-by-step explanation:

Answer:

65-50=15/50 x 100= 30%

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

Use PEMDAS:

Parenthesis:

(27-19)=(8)

Then multiplication:

6+(2*3)+4+(8)

6+(6)+4+(8)

Then add everything:

24

Answer:

\(A_w=238x-2176\)

Step-by-step explanation:

From the question we are told that:

Length of pool \(L=34ft\)

Width of Pool \(W=x\).

Brick walkway Width \(W_b=4\)

Generally the expression for a Area of pool is mathematically given by

 \(A=L*W\)

 \(A=34*x\)

 \(A=34x\)

Generally the expression for a Area of pool + Walkway is mathematically given by

 \(A'=L'*B'\)

where

 \(L' =L+2(W_b)\)

 \(L' =34+2(4)\)

 \(L'=34+8\)

 \(L'=272\)

And

 \(W'=W+2(W_b)\)

 \(W' =x+2(4)\)

 \(W' =x+8\)

Therefore

 \(A'=L'*B'\)

 \(A'=(272)*(x+8)\)

 \(A'=272x+2176\)

Generally the expression for a Area of Walkway is mathematically given by

 \(A_w=Area\ of\ Pool+Walkway-Area\ of\ Pool\)

 \(A_w=A'-A\)

 \(A_w=272x+2176-34x\)

 \(A_w=238x-2176\)

Answer:

No

Step-by-step explanation:

Answer:

Yes or No = No

Simalarity Statement "TNS"

Step-by-step explanation:

Answer:

5 2/3 pound of 1 cake

Step-by-step explanation:

34 / 6 =

(30 / 6) + (4 / 6) =

5 + 2/3 =

5 2/3

This is based on a survey conducted by the American Customer Satisfaction Index (ACSI) in 2020 that surveyed 1,097 passengers who had flown on U.S. airlines in the past 12 months.

A survey is a research method used to collect quantitative and qualitative data from a specific population. Surveys are often used to assess attitudes, opinions, and behaviors of a given group of people. They are typically administered in the form of a questionnaire, which can be administered in person, over the phone, or online. Surveys are often used in market research, political polling, social science research, and other types of research.

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Answer:

Combine like terms by subtracting

Step-by-step explanation:

Answer:

1.5

Step-by-step explanation: half an hour is 28 dollars. if he worked for 1 hour, it would be 186 +28 which was the left over amount of money to add up to 214, simply put, 1 hour and 30 minutes or 1.5 hours

Answer:

its 1.4

Step-by-step explanation:

Answer:

1.4

Step-by-step explanation: