How many fourthsare there in 1 7/16

Using the chart "Amount of $1 at Compound Interest" from previous reading section "More Compound Interest", find the total amoun

tatyana61 [14]

Annually: Total Amount= $1,611.76 Interest Amount= $711.76

Semiannually: Total Amount= $1,625.50 Interest Amount= $725.50

Quarterly: Total Amount= $1,632.62 Interest Amount= $732.62

7 0

3 years ago

Read 2 more answers

Item 11

marysya [2.9K]

Answer:

4 ft higher

Step-by-step explanation:

Since the ladder is 10 ft long and its top is 6 feet high(above the ground), we find the distance of its base from the wall since these three (the ladder, wall and ground) form a right angled triangle. Let d be the distance from the wall to the ladder.

So, by Pythagoras' theorem,

10² = 6² + d² (the length of the ladder is the hypotenuse side)

d² = 10² - 6²

d² = 100 - 36

d² = 64

d = √64

d = 8 ft

Since the ladder is moved so that the base of the ladder travels toward the wall twice the distance that the top of the ladder moves up.

Now, let x be the distance the top of the ladder is moved, the new height of top of the ladder is 6 + x. Since the base moves twice the distance the top of the ladder moves up, the new distance for our base is 8 - 2x(It reduces since it gets closer to the wall).

Now, applying Pythagoras' theorem to the ladder with these new lengths, we have

10² = (6 + x)² + (8 - 2x)²

Expanding the brackets, we have

100 = 36 + 12x + x² + 64 - 32x + 4x²

collecting like terms, we have

100 = 4x² + x² + 12x - 32x + 64 + 36

100 = 5x² - 20x + 100

Subtracting 100 from both sides, we have

100 - 100 = 5x² - 20x + 100 - 100

5x² - 20x = 0

Factorizing, we have

5x(x - 4) = 0

5x = 0 or x - 4 = 0

x = 0 or x = 4

The top of the ladder is thus 4 ft higher

7 0

3 years ago

The lengths of a particular snake are approximately normally distributed with a given mean mu = 15 in. and standard deviation si

Helga [31]

The percentage of the snakes is longer than 16.6 in. with a mean of 15 in. and a standard deviation of 0.8 in. is 2.275%.

<h3>What is a normal distribution?</h3>

It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.

The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.

The lengths of a particular snake are approximately normally distributed with a given mean = 15 in. and standard deviation = 0.8 in.

Then the percentage of the snakes is longer than 16.6 in. will be

$z = \dfrac{ x - \mu }{ \sigma }\\\\z = \dfrac{16.6-15}{0.8}\\\\z = 2$