An investment of $7,650 at the rate of 5% and is compounded quarterly. What is the investment at the end of 9 years?

6. 4x + 2y = 16<br> | 5x - 2y = 38

Zolol [24]

Answer:

1. Slope = -4.000/2.000 = -2.000

x-intercept = 8/2 = 4

y-intercept = 8/1 = 8.00000

2. Slope = 5.000/2.000 = 2.500

x-intercept = 38/5 = 7.60000

y-intercept = 38/-2 = 19/-1 = -19.00000

Step-by-step explanation:

1.

Step 1 :

Pulling out like terms :

1.1 Pull out like factors :

4x + 2y - 16 = 2 • (2x + y - 8)

Equation at the end of step 1 :

Step 2 :

Equations which are never true :

2.1 Solve : 2 = 0

This equation has no solution.

A a non-zero constant never equals zero.

Equation of a Straight Line

2.2 Solve 2x+y-8 = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 2x+y-8 = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 8/1 so this line "cuts" the y axis at y= 8.00000

y-intercept = 8/1 = 8.00000

Calculate the X-Intercept :

When y = 0 the value of x is 4/1 Our line therefore "cuts" the x axis at x= 4.00000

x-intercept = 8/2 = 4

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 8.000 and for x=2.000, the value of y is 4.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 4.000 - 8.000 = -4.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = -4.000/2.000 = -2.000

Geometric figure: Straight Line

Slope = -4.000/2.000 = -2.000

x-intercept = 8/2 = 4

y-intercept = 8/1 = 8.00000

Processing ends successfully

2.

Step 1 :

Equation of a Straight Line

1.1 Solve 5x-2y-38 = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 5x-2y-38 = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 19/-1 so this line "cuts" the y axis at y=-19.00000

y-intercept = 38/-2 = 19/-1 = -19.00000

Calculate the X-Intercept :

When y = 0 the value of x is 38/5 Our line therefore "cuts" the x axis at x= 7.60000

x-intercept = 38/5 = 7.60000

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -19.000 and for x=2.000, the value of y is -14.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -14.000 - (-19.000) = 5.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = 5.000/2.000 = 2.500

Geometric figure: Straight Line

Slope = 5.000/2.000 = 2.500

x-intercept = 38/5 = 7.60000

y-intercept = 38/-2 = 19/-1 = -19.00000

Processing ends successfully

plz mark me as brainliest :)

4 0

3 years ago

Anyone who answers correctly gets brainlist!

Alex787 [66]

Answer:

B

Step-by-step explanation:

easy

3 0

2 years ago

Read 2 more answers

PLZZZZZ NEED HELP!!!!!!!

ruslelena [56]

Answer:

1.90

Step-by-step explanation:

7 0

3 years ago

Question Help Suppose that the lifetimes of light bulbs are approximately normally distributed, with a mean of 5656 hours and a

koban [17]

Answer:

a)3.438% of the light bulbs will last more than 6262 hours.

b)11.31% of the light bulbs will last 5252 hours or less.

c) 23.655% of the light bulbs are going to last between 5858 and 6262 hours.

d) 0.12% of the light bulbs will last 4646 hours or less.

Step-by-step explanation:

Normally distributed problems can be solved by the z-score formula:

On a normaly distributed set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a value X is given by:

$Z = \frac{X - \mu}{\sigma}$

After we find the value of Z, we look into the z-score table and find the equivalent p-value of this score. This is the probability that a score will be LOWER than the value of X.

In this problem, we have that:

The lifetimes of light bulbs are approximately normally distributed, with a mean of 5656 hours and a standard deviation of 333.3 hours.

So $\mu = 5656, \sigma = 333.3$

(a) What proportion of light bulbs will last more than 6262 hours?

The pvalue of the z-score of $X = 6262$ is the proportion of light bulbs that will last less than 6262. Subtracting 100% by this value, we find the proportion of light bulbs that will last more than 6262 hours.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{6262 - 5656}{333.3}$

$Z = 1.82$

$Z = 1.81$ has a pvalue of .96562. This means that 96.562% of the light bulbs are going to last less than 6262 hours. So

$P = 100% - 96.562% = 3.438%$ of the light bulbs will last more than 6262 hours.

(b) What proportion of light bulbs will last 5252 hours or less?

This is the pvalue of the zscore of $X = 5252$

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{5252- 5656}{333.3}$

$Z = -1.21$

$Z = -1.21$ has a pvalue of .1131. This means that 11.31% of the light bulbs will last 5252 hours or less.

(c) What proportion of light bulbs will last between 5858 and 6262 hours?

This is the pvalue of the zscore of $X = 6262$ subtracted by the pvalue of the zscore $X = 5858$

For $X = 6262$ , we have that $Z = 1.81$ with a pvalue of .96562.

For X = 5858

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{5858- 5656}{333.3}$

$Z = 0.61$

$Z = 0.61$ has a pvalue of .72907.

So, the proportion of light bulbs that will last between 5858 and 6262 hours is

$P = .96562 - .72907 = .23655$

23.655% of the light bulbs are going to last between 5858 and 6262 hours.

(d) What is the probability that a randomly selected light bulb lasts less than 4646 hours?

This is the pvalue of the zscore of $X = 4646$

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{4646- 5656}{333.3}$

$Z = -3.03$

$Z = -3.03$ has a pvalue of .0012. This means that 0.12% of the light bulbs will last 4646 hours or less.

5 0

3 years ago

Wally is rebuilding his fence. Each section of the fence will have 12 vertical boards that are each eight inches wide. He’s goin

Leokris [45]

Answer:

Part A)

Each diagonal is about 9.43 feet.

Part B)

In total, Wally needs about 736.02 feet of wood.

Step-by-step explanation:

Part A)

Since each vertical board has a width of 8 inches, for one section with 12 vertical boards, the total width will be 8(12) = 96 inches.

96 inches is the same as 96/12 = 8 feet.

We are also given that the horizontal pieces will be 5 feet apart.

To find the diagonal, we can use the Pythagorean Theorem. The 8 is the base and 5 is the height. Therefore:

$\displaystyle d^2=8^2+5^2$

Compute:

$d^2=89$

Taking the square root, we acquire:

$\displaystyle d=\sqrt{89}\approx9.43 \text{ feet}$

So, each diagonal is about 9.43 feet.

Part B)

For each section, we have two horizontal pieces (each 8 feet) and one diagonal piece (each √89 feet).

Therefore, for one section, we will need a total of:

$\displaystyle L=8+8+\sqrt{89}=16+\sqrt{89}$

Then for 30 sections, we will need:

$T=30(16+\sqrt{89})$

Approximate:

$T\approx 763. 02$

Wally will need about 736.02 feet of wood in total.

3 0

3 years ago