MATHEMATICS HIGH SCHOOL

Brian invests £600 into his bank account. He receives 3.2% per year compound interest. How much will Brian have after 6 years? Give your answer to the nearest penny where appropriate.

Answers

Answer 1

Answer:

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P(1 + r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = £600

r = 3.2% = 3.2/100 = 0.32

n = 1 because it was compounded once in a year.

t = 6 years

Therefore,.

A = 600(1 + 0.032/1)^1 × 6

A = 600(1.032)^6

A = £724.82

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Answers

Answer:

The solutions to the system of the equations are:

$y=1,\:x=3$

Step-by-step explanation:

Given the equations

$y=(2)/(3)x-1;\:y=-x+4$

solving the system of equation

$\begin{bmatrix}y=(2)/(3)x-1\n y=-x+4\end{bmatrix}$

Arrange equation variables for elimination

$\begin{bmatrix}y-(2)/(3)x=-1\n y+x=4\end{bmatrix}$

$y+x=4$

$-$

$\underline{y-(2)/(3)x=-1}$

$(5)/(3)x=5$

$\begin{bmatrix}y-(2)/(3)x=-1\n (5)/(3)x=5\end{bmatrix}$

solving for x

$(5)/(3)x=5$

$5x=15$

Divide both sides by 15

$(5x)/(5)=(15)/(5)$

$x=3$

$\mathrm{For\:}y-(2)/(3)x=-1\mathrm{\:plug\:in\:}x=3$

$y-(2)/(3)\cdot \:3=-1$

$y-2=-1$

Add 2 to both sides

$y-2+2=-1+2$

$y=1$

Therefore, the solutions to the system of the equations are:

$y=1,\:x=3$

A system of linear equations in two variables can have _____ solutions

Answers

If the lines are parallel (have the same slope but different intercepts) . . .
   no solution, because they never cross.

If the lines have different slopes . . .
   one solution, because they have exactly one common point.

If the lines have the same slope and the same intercept . . .
   infinitely many solutions, because every point on one line is also a point on
   the other line, one lays right on top of the other, and when you look at them on
   the graph, it looks like only one line.

one solution
or no solution
or an infinite number of solutions

8. What is the solution to the system? y = 1/2x, 2x + 3y = 28A) (2, 3)
B) (8, 4)
C) (7, 3.5)
D) (2, 14)

Answers

$y=(1)/(2)x \n2x+3y=28 \n \n\hbox{substitute } (1)/(2)x \hbox{ for y in the second equation:} \n2x+3 ((1)/(2)x)=28 \n2x+(3)/(2)x=28 \ \ \ \ \ |* 2 \n4x+3x=56 \n7x=56 \ \ \ \ \ \ \ \ \ \ \ \ |/ 7 \nx=8 \n \ny=(1)/(2)x=(1)/(2) * 8=4 \n \n\boxed{(x,y)=(8,4)} \Leftarrow \hbox{answer B}$

The mean and standard deviation of a population being sampled are 64 and 6, respectively. If the sample size is 50, what is the standard error of the mean? how do I find the standard error?

Answers

SEM - Standard error of the mean;
You can find the standard error with a formula:
SEM = s / √n, where s is the standard deviation and n is the sample size;
SEM = 6 / √50 = 6 / 7.071
Answer:
SEM = 0.8485

Final answer:

The standard error is calculated as the standard deviation divided by the square root of the sample size. For a population with a standard deviation of 6 and a sample size of 50, the standard error is 6 / sqrt(50).

Explanation:

The standard error can be defined as the standard deviation divided by the square root of the number of samples. It helps to estimate the variability in the population. In this case, the mean is 64, the standard deviation is 6, and the sample size is 50. The equation to calculate the standard error is:

$Standard Error = Standard Deviation / \sqrt(Sample Size).$

Plugging in the values given in the question, we get:

$Standard Error = 6 / \sqrt(50)$

. After performing the division, you will get the standard error of the mean which tells you how far your sample mean could be from the true population mean.

Learn more about Standard Error here:

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In a circle, the circumference and diameter vary directly. Which of the following equations would allow you to find the diameter of a circle with a circumference of 154 if you know that in a second circle the diameter is 14 when the circumference is 44?