Out of a group of 20 volunteers, 14 people are chosen to participate in a survey about the

if a 20 foot ladder makes a 50 degree angle with the ground, how many feet up a wall will it reach. Round to the nearest tenth.

GalinKa [24]

Answer: The ladder would reach 15.3 ft up the wall

Step-by-step explanation: Please refer to the attached diagram.

If the ladder (represented by line AC) rests on the wall (represented by line AB), it forms an angle of 50 with the ground (at point C). The ground is represented by line BC.

We need to remember that we have one side and one angle given in this question. The given side is the hypotenuse (the side facing the right angle, B in this case) and the given angle is the reference angle. The unknown side which is x, is the opposite as it is facing the reference angle.

Having the opposite and the hypotenuse, we can use the Sine ratio which is,

Sine C = opposite/hypotenuse

Sine 50 = x/20

Checking our table of values or by use of our calculator, sin 50 is 0.766

Sin 50 = x/20

0.766 = x/20

By cross multiplication, we now have our equation rewritten as;

0.766 (20) = x

15.32 = x

Rounded to the nearest tenth,

x = 15.3 ft

3 0

4 years ago

ANSWER QUICKLY PLEASE 2. Molecules in the air are moving with speeds based on the normal model.

raketka [301]

Answer:

(a). The mean speed is 760 m/s.

(b). The standard deviation for our normal model is 142.1 m/s.

(c). The unusual speed is 1127 m/s.

(d). The average molecule speed is 929.48 m/s.

Step-by-step explanation:

Given that,

Molecules in the air are moving with speeds based on the normal model.

Let x be the speed of the molecules.

(a). If half of the air molecules are moving faster than 760 m/s.

We can say speed of a molecules is normally distributed.

So, the mean, median and mode of this distribution is at least greater than 760 m/s.

(b). If exactly 95% of the molecules are moving with speeds between 475.8 m/s and 1044.2 m/s,

If the standard deviation is σ and the mean is μ,

We need to calculate the standard deviation for our normal model

Using empirical rule

$\mu-2\sigma=475.8$ ...(I)

$\mu+2\sigma=1044.2$ ....(II)

Put the value of μ in equation (I)

$760-2\sigma=475.8$

$-\sigma=\dfrac{475.8-760}{2}$

$\sigma=142.1\ m/s$

(c). One molecule is found to be moving with a speed of 1127 m/s.

We know that,

1127 is the between 1126 and 1128.

Since, it is a continuous distribution,

We need to find the probability that speed is between this

Using excel function

$P(1126$

We know that,

Any probability less than 0.05 is considered as unusual

So, 0.0002<0.05

So, 1127 will be considered as the unusual speed.

(d). If the temperature increase caused the z-score of a particle moving at 1100 m/s particle to drop to 1.2 after the temperature increase.

We need to calculate the average molecule speed

Using formula of average molecule speed

$z=\dfrac{x-\mu'}{\sigma}$

$-\mu'=z\sigma-x$

Put the value in to the formula

$-\mu'=1.2\times142.1-1100$

$\mu'=929.48\ m/s$

Hence, (a). The mean speed is 760 m/s.

(b). The standard deviation for our normal model is 142.1 m/s.

(c). The unusual speed is 1127 m/s.

(d). The average molecule speed is 929.48 m/s.

8 0

3 years ago

A record store is having a sale. CDs that were regularly priced at $14 are on sale for $10.50. What is the percentage of decreas

alisha [4.7K]

25% off would be the answer.

3 0

4 years ago

Use the discriminant to determine the nature of the solutions.

frosja888 [35]

B

Step-by-step explanation:

2x2 - 6x + 7 = 0. A) Two rational Solutions B) Two irrational Conjugate Solutions C) One Rational Solutions D) Two Complex/Imaginary ...

4 0

3 years ago

2 2/5 divided by (-1/4) ?

andrew11 [14]

Answer:

-9.6

Step-by-step explanation:

mark as brainliest

5 0

3 years ago

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