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3 years ago

A ramp has an angle of inclination of 20 degrees. it has a vertical height of 1.8 m. what is the length, l metres, of the ramp?

Mathematics

1 answer:

Vinvika [58]3 years ago

5 0

Sin 20 = 1.8/hypotenuse
hypotenuse = 1.8 / sin 30 = 2.34 m
answer: 2.34m

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Which expression is equivalent to 15 (n+3/n) ?<br> £ <br> N=10

Alika [10]

Answer:

$\sum_{n=10}^{15}(n+\frac{3}{n})=\sum_{n=10}^{15} n + \sum_{n=10}^{15} \frac{3}{n}$

Step-by-step explanation:

Given expression : $\sum_{n=10}^{15}(n+\frac{3}{n})$

Solving further:

$\sum_{n=10}^{15}(n+\frac{3}{n})$

$\Rightarrow \sum_{n=10}^{15} n + \sum_{n=10}^{15} \frac{3}{n}$

So, $\sum_{n=10}^{15}(n+\frac{3}{n})=\sum_{n=10}^{15} n + \sum_{n=10}^{15} \frac{3}{n}$

So, Option A is true

Hence the given expression is equivalent to Option A

6 0

3 years ago

The heights in inches of orangutans Are normally distributed with a population standard deviation of 3" and an unknown populatio

CaHeK987 [17]

Answer: The 95% confidence interval is approximately (55.57, 58.43)

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

Explanation:

At 95% confidence, the z critical value is about z = 1.960 which you find using a table or a calculator.

The sample size is n = 17

The sample mean is xbar = 57

The population standard deviation is sigma = 3

The lower bound of the confidence interval is

L = xbar - z*sigma/sqrt(n)

L = 57 - 1.960*3/sqrt(17)

L = 55.5738905247863

L = 55.57

The upper bound is

U = xbar + z*sigma/sqrt(n)

U = 57 + 1.960*3/sqrt(17)

U = 58.4261094752137

U = 58.43

Therefore the confidence interval (L, U) turns into (55.57, 58.43) which is approximate.

7 0

3 years ago

On a certain river, a paddleboat travels 12 miles upstream (against the current) in the same amount of time it travels 20 mil

marin [14]

Given :

a paddle boat travels upstream = 12 miles

a paddle boat travels downstream = 20 miles

speed of the current = 2 miles per hour

Let the speed of the boat =x

Let the time taken = t

We know the distance for upstream D= (boat speed - current speed) * time

the distance for downstream D= (boat speed + current speed) * time

Plug in all the values and variables in the distance

For upstream 12 = (x-2)t, then $t = \frac{12}{x-2}$

For downstream 20 = (x+2)t then $t = \frac{20}{x+2}$

we got two equations for t, equate it and solve for x

$\frac{12}{x-2} = \frac{20}{x+2}$

Cross multiply it

12(x+2) = 20(x-2)

12x + 24 = 20x - 40 (subtract 12x and add 40 on both sides)

64 = 8x

x= 8

the speed of the boat in still water = 8 miles per hour

3 0

3 years ago

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An icicle drips at a rate that can be represented by the function f(x) = −x2 + 11x − 18, where 0 ≤ x ≤ 10 and x is the number of

FrozenT [24]

Calculate f(x) for all numbers between 0 and 10:

f(0) = −0^2 + 11(0) − 18 = -18

f(1) = −1^2 + 11(1) − 18 = -8

f(2) = −2^2 + 11(2) − 18 = 0

f(3) = −3^2 + 11(3) − 18 = 6

f(4) = −4^2 + 11(4) − 18 = 10

f(5) = −5^2 + 11(5) − 18 = 12

f(6) = −6^2 + 11(6) − 18 = 12

f(7) = −7^2 + 11(7) − 18 = 10

f(8) = −8^2 + 11(8) − 18 = 6

f(9) = −9^2 + 11(9) − 18 = 0

f(10) = −10^2 + 11(10) − 18 = -8

When the value is negative it doesn't drip, so it starts and stops dripping when the values = 0

Which is f(2) and f(9), the values are 2 and 9.

4 0

3 years ago

Stewart spent $56.29 at the science supply store. The taxes are 14%. How much did he spend in all?

dalvyx [7]

Answer:

64.17

Step-by-step explanation:

multiply the 56.29 by 0.14 and add the product to the total.

7 0

3 years ago

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