George invests a sum of money into a savings account with a fixed annual interest rate of 5.5% and compounded 6 times a year. After 7 years the account has a balance of $3,820. What is the initial investment?
Group of answer choices

a. $1506.30
b. $2603.88
c. $7082.77
d. $5604.10

The 99.5% confidence interval for a sample of size 353 with a mean of 75.7 and a standard deviation of 6.8 is: (74.94, 76.46)

To calculate the confidence interval, we can use the following formula:

CI = x ± tα/2 * s / √n

In this case, the critical value of the t-distribution for a confidence level of 99.5% is 2.776. Plugging in the other values, we get the following confidence interval:

CI = 75.7 ± 2.776 * 6.8 / √353

CI = (74.94, 76.46)

Leaned more about confidence interval on

https://brainly.com/question/15712887

#SPJ1

The value of the resistor needed in this scenario is approximately 1.2 ohms.

To find the value of the resistor in the given scenario, we can apply Ohm's Law, which states that the current (I) flowing through a resistor is directly proportional to the voltage (V) across it, and inversely proportional to the resistance (R) of the resistor.

Using Ohm's Law, we have the formula:

V = I * R

Where:

V is the voltage across the resistor (12 volts in this case),

I is the current flowing through the resistor (5 amps for each light, so a total of 10 amps),

R is the resistance of the resistor (which we need to find).

Rearranging the formula, we have:

R = V / I

Plugging in the values:

R = 12 volts / 10 amps

R = 1.2 ohms

Therefore, the value of the resistor needed in this scenario is approximately 1.2 ohms.

It's worth noting that this calculation assumes the lights are connected in parallel, as the current remains the same for each light. If the lights were connected in series, the total resistance would be the sum of the individual resistances, and the calculation would be different.

For more such question on resistor visit:

https://brainly.com/question/4703820

#SPJ8

Answer:

Not enough information !!

Step-by-step explanation:

Option D : The polygon in the image has 12 sides. Therefore, the term describes this polygon is 12-gon.

A polygon is a closed two-dimensional shape with straight sides. The number of sides a polygon has is called its order or number of sides, and is often used to name the polygon. In the case of the polygon shown in the image, it has 12 sides, which means it is a 12-gon.

The prefixes used to name polygons based on their number of sides are derived from Greek and Latin numerical prefixes. For example, the prefix "hepta-" means seven, so a polygon with seven sides is called a heptagon. Similarly, the prefix "dodeca-" means twelve, so a polygon with twelve sides is called a dodecagon.

In conclusion, a polygon is a closed two-dimensional shape with straight sides, and its order or number of sides is used to name it. The polygon in the image has 12 sides, so it is called a 12-gon, with the prefix "dodeca-" meaning twelve.

Therefore, the polygon has 12 sides, so the correct term to describe it is a 12-gon.

To learn more about polygon please click on below link        

https://brainly.com/question/10441863

#SPJ1

A=5 and 0=5A is there answer

Answer:

10,000 is the answer

Step-by-step explanation:

14 465

round up the 4 which is 0 then your answer would be 10000

Answer:

600/7% OR 85.71%

Step-by-step explanation:

increase in speed =v-u

I=115-85

I=30km/h

percentage increase =(I/u) ×100

30/85 ×100

6/17×100

600/7%

The surface area of the pyramid is 113 cm².

A rectangular pyramid is a type of pyramid where the base is a rectangle and the triangular faces meet at a single point called the apex or vertex. It has five faces, including a rectangular base and four triangular faces, and it is a polyhedron with five vertices and eight edges.

The rectangular pyramid has a base of dimensions 7 cm by 5 cm, and the two large triangular faces have a height of 7.6 cm, while the two small triangular faces have a height of 8 cm.

To find the surface area of the pyramid, we need to find the area of each face and then add them up.

Area of the base:

The base of the pyramid is a rectangle with dimensions 7 cm by 5 cm, so its area is:

Area of base = length × width = 7 cm × 5 cm = 35 cm²

Area of the four triangular faces:

Each of the four triangular faces has a base of 5 cm (the width of the rectangle) and a height of either 7.6 cm or 8 cm. Using the formula for the area of a triangle, we can find the area of each face:

Area of each large triangular face = 1/2 × base × height = 1/2 × 5 cm × 7.6 cm = 19 cm²

Area of each small triangular face = 1/2 × base × height = 1/2 × 5 cm × 8 cm = 20 cm²

There are two large triangular faces and two small triangular faces, so the total area of the four triangular faces is:

Total area of four triangular faces = 2 × area of large triangular face + 2 × area of small triangular face

= 2 × 19 cm² + 2 × 20 cm²

= 78 cm²

Total surface area:

Finally, we can find the total surface area of the pyramid by adding the area of the base to the total area of the four triangular faces:

Total surface area = area of base + total area of four triangular faces

= 35 cm² + 78 cm²

= 113 cm²

Therefore, the surface area of the pyramid is 113 cm²

.

To know more about rectangular pyramid visit:

https://brainly.com/question/31272240

#SPJ1

Answer:

D

Step-by-step explanation:

by looking at the point you can see what has a slope.

it is also a decreasing slope

Answer:

ANSWER

Step-by-step explanation:

Without knowing the specific function w(x), it is impossible to determine the domain of the inverse function w^-1(x). However, in general, the domain of an inverse function is the range of the original function, and vice versa.

If we assume that w(x) is a one-to-one function (which is necessary for it to have an inverse function), we can determine the range of w(x) and use it to find the domain of w^-1(x).

For example, if we know that w(x) is a function that takes all real numbers except x=2, then the range of w(x) is (-∞,2) U (2,∞). The domain of w^-1(x) is then the same as the range of w(x), which is (-∞,2) U (2,∞). Therefore, the domain of w^-1(x) is x ≠ 2.

Without more information about w(x), we cannot determine the domain of w^-1(x) more precisely.

Answer:

The probability that the selected number is an odd number or a multiple of 3 is 6/9, or 2/3. This is because there are 6 numbers that meet the criteria out of the 9 numbers in the set: 1, 3, 5, 7, 9, and 3.

Answer: $1159.42

Step-by-step explanation:

A simple rule to remember
Specific Currency to Dollars ----> Divide
Dollars to Specific Currency ----> Multiply
R20,000/17.25

=$1159.42

Ryan will get 1160 dollars if he exchanges 20,000 into dollars.

The study and use of numbers, their relationships, and mathematical observations are topics covered by the area of mathematics known as arithmetic. The term "arithmetic" (which originates from the Greek word "arithmos," "number") often refers to the fundamental principles in number theory, measurement, and calculation (that is, the processes of addition, subtraction, multiplication, division, raising to powers, and extraction of roots).

As per the given data:

We are given the amount of money that Ryan had saved for a holiday in America.

We have to find out how much money in dollars Ryan will have after converting his money into dollars.

Money Ryan saved for the holiday (M) = 20,000

Conversion rate to dollar = 17.25 per dollar

Money Ryan have after converting into dollars:

= M / 17.25 dollars

= 20,000 / 17.25

= 1160 dollars

Ryan will get 1160 dollars if he exchanges 20,000 into dollars.

Hence, Ryan will get 1160 dollars if he exchanges 20,000 into dollars.

To learn more about arithmetic, click:

brainly.com/question/23848329

#SPJ2

\(x^2 -8x-2=0\\\\x^2 -8x=2\\\\x^2 -8x+16=18\\\\(x-4)^2 =18\\\\x-4=\pm \sqrt{18}\\\\\boxed{x=4 \pm \sqrt{18}}\)

Answer:

b.

Step-by-step explanation: its 50 shares the to straiges you should use is multiplying or adding i used both bt its b.

Answer:

33%

Step-by-step explanation:

6/9 = .66 which is the amount that do have it

1 - .66 = .33 which is the amount that dont.

.33 x 100 = 33%

it's 26 because u count the squares in the poygon

On observing the provided question, we can say that the the provided equation f(x) =  is the basic cubic function.f(x) = 8100

An statement, rule, or law in mathematics that specifies the connection between an independent variable and a dependent variable (the dependent variable). A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. Y=X2 is an illustration of this. You only receive one output for y if you enter anything for x. The fact that x is the input value leads us to argue that y is a function of x.

basic cubic function is =  f(x) = x^2

x =  90

f(x) = 8100

To know more about functions visit:

brainly.com/question/28193995

#SPJ1

On solving the provided question, we can say that It is possible to construct a parking lot since the angle J's measurement is 180 - (50 + 90) = 40. More than 38 degrees, 40 degrees.

An angle is a form in Euclidean geometry made composed of two rays, called the angle's sides, that meet at a point in the middle known as the angle's vertex. In the plane where the rays are placed, two rays can produce an angle. An angle is also produced when two planes intersect. They're known as dihedral angles. In plane geometry, an angle is the form that two rays or lines with a common termination might take. The Latin word "angulus," which means "horn," is where the English word "angle" comes from. The two rays, also known as the sides of the angle, have a common termination known as the vertex.

It is possible to construct a parking lot since the angle J's measurement is 180 - (50 + 90) = 40. More than 38 degrees, 40 degrees.

To know more about angles visit:

https://brainly.com/question/14569348

#SPJ1

9514 1404 393

Answer:

  cos(210°) = -(√3)/2

Step-by-step explanation:

The terminal ray of a 210° angle is in the third quadrant. The angle it makes with the -x axis is (210° -110°) = 30°. This is the "reference angle". In the 3rd quadrant, the x-coordinate of the terminal ray's intersection with the unit circle has a negative sign. This will be the sign of the cosine of the angle.

__

The reference angle of 30° tells you that the trig functions of the angle can be found from the side ratios of the "special right triangle" with angles of 30°, 60°, and 90°. The side ratios, shortest to longest, in that triangle are 1 : √3 : 2.

The cosine of the angle is the ratio ...

  Cos = Adjacent/Hypotenuse

In the above special triangle, the side adjacent to the 30° angle is the one that is √3 ratio unis. The hypotenuse is 2 ratio units. So, the cosine of 30° is ...

  cos(30°) = (√3)/2

As we said above, the sign of the adjacent side of the reference angle for 210° has a negative value. (The hypotenuse is always considered to be positive.) Then the desired cosine is ...

  cos(210°) = -cos(30°)

  cos(210°) = -(√3)/2

Sphenathi and the other matriculants must travel at an average speed of approximately 107 km/h to reach Uptington by 09:45.

To determine the average speed at which Sphenathi and the other matriculants must travel to reach Uptington by 09:45, we need to calculate the time available for the journey and the distance between the two locations.

The time available is from 07:25 to 09:45, which is a total of 2 hours and 20 minutes. We need to convert this time to hours by dividing by 60:

2 hours + 20 minutes / 60 = 2.33 hours

Now, let's calculate the distance between Bloemfontein and Uptington. Suppose the distance is 'd' kilometers.

We can use the formula for average speed: average speed = distance / time

In this case, the average speed should be such that the distance divided by the time is equal to the average speed.

d / 2.33 = average speed

Now, let's assume that Sphenathi and the other matriculants must travel a distance of 250 kilometers to reach Uptington. We'll substitute this value into the equation:

250 / 2.33 = average speed

To find the average speed to the nearest km/h, we'll calculate the result:

average speed ≈ 107.3 km/h

Therefore, Sphenathi and the other matriculants must travel at an average speed of approximately 107 km/h to reach Uptington by 09:45.

For more questions on average speed

https://brainly.com/question/553636

#SPJ8

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

Read more about tangent lines at

https://brainly.com/question/21595470

#SPJ1

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

Work Shown:

Consecutive numbers follow right after another (eg: 7,8,9,10,...)

x = first number

x+1 = second number

x+2 = third number

x+3 = fourth number

Add up the expressions and set this equal to 126

(x) + (x+1) + (x+2) + (x+3) = 126

x+x+1+x+2+x+3 = 126

(x+x+x+x) + (1+2+3) = 126

4x+6 = 126

4x = 126-6

4x = 120

x = 120/4

x = 30 = first number

x+1 = 30+1 = 31 = second number

x+2 = 30+2 = 32 = third number

x+3 = 30+3 = 33 = fourth number

Check:

30+31+32+33 = 126

Answer is confirmed.

Answer:

D)6x^4+3x^3y

Step-by-step explanation:I hope this helps,good luck with everything,have a nice day.

Answer:

6,100

Step-by-step explanation:

7.83n= 47,763

Now, we can solve for n by dividing both sides by 7.83 and simplifying.

n=6100

Answer:

Determine the measure, in degrees, ... Score 2: The student had a complete and correct response. ... a conceptual error and did not find the measure of the smallest angle. ... y x is ΔA B C . State and label the coordinates of ΔA B C . [The use of ... Score 1: The student stated and labeled two points correctly.

Step-by-step explanation:

Answer: x<5

Step-by-step explanation: Subtract 10 from both sides. Simplify  -15-10 to  -25. Divide both sides by -5. Two negatives make a positive. Simplify 25/5 to 5.

Answer:

63.3232

Step-by-step explanation:

Answer:

she needs to deposit $40.20

Step-by-step explanation:

B . (3,2)

Step-by-step explanation:

I'm unsure of how to explain it but it is B :) have a good day !

Hence Proved N to N is uncountable set by using a diagonalization argument

What is Diagonalization Argument?

Georg Cantor published the Cantor's diagonal argument in 1891 as a mathematical demonstration that there are infinite sets that cannot be put into one-to-one correspondence with the infinite set of natural numbers. It is also known as the diagonalization argument, the diagonal slash argument, the anti-diagonal argument, the diagonal method, and Cantor's diagonalization proof.

Proof:

We write f as the sequence of value it generates

that is, say f:N-N is defined as f(x) =x then

we write f as : 1,2,3,4........

similarly if f:N-N were f(x) = 2x then we write it as :2,4,6,8.......

now assume on the contrary that the set of functions from N to N is countable

then,

\(f_{1}\)   :     \(f_{11}\)        \(f_{12}\)       \(f_{13}\) , ...........

\(f_{2}\)   :     \(f_{21}\)        \(f_{22}\)       \(f_{23}\) , ...........

\(f_{3}\)   :     \(f_{31}\)        \(f_{32}\)       \(f_{33}\) , ........... and so on

Here \(f_{ij}\) =\(f_{i}(j)\)

consider the function f as :

f : (\({f11}\) +1 ) , (\({f22}\) +1) , (\({f33}\) +1),.........

Then f wouldn't appear in the list of the function we had above since any \(f_{i}\) would disagree with f at the i th place

Therefore the set of the function from N to N is an uncountable set

To learn more about diagonalization argument visit:

brainly.com/question/16991671

#SPJ4

Answer:

551.8

Step-by-step explanation:

5.2\times 104 is 540.8

1.3\times 10-2 is 11

540.8 + 11 =551.8

Answer:

The answer is 676.

Step-by-step explanation:

I think you mean 5.2 multiplied by \(10^{4}\), and 1.3 multiplied by \(10^{-2}\).

Or do you mean 5.2 multiplied by 104 and 1.3 multiplied by 10 then subtract 2? Not really clear, but I'm going to go with the first option.

5.2 * \(10^{4}\) = 52,000

1.3 * \(10^{-2}\) = 0.013

52,000 * 0.013 = 676

The answer is 676.

The expression representing the perimeter of the polygon is given as follows:

7mn³/3 + 4m² + 3mn².

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

Hence the perimeter for the polygon in this problem is given as follows:

mn³(1/3 + 2) + m²(1 + 3) + mn²(1 + 2) = 7mn³/3 + 4m² + 3mn².

More can be learned about the perimeter of a polygon at https://brainly.com/question/3310006

#SPJ1