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2 years ago

25 points

Mathematics

1 answer:

ohaa [14]2 years ago

8 0

Answer:

y ≈ 12.6

Step-by-step explanation:

the angle between a tangent and the radius of the circle at the point of contact is 90°

then the triangle with y as a leg is right.

using Pythagoras' identity in the right triangle.

y² + 39² = 41²

y² + 1521 = 1681 ( subtract 1521 from both sides )

y² = 160 ( take square root of both sides )

y = $\sqrt{160}$ ≈ 12.6 ( to the nearest tenth )

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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

We are told that the price of basket of fries is drawn from a normal distribution with mean 6 and standard deviation of 2. You w

Masja [62]

Answer:

32.64% probability that you would have enough money to pay for all five baskets of fries

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sample means with size n can be approximated to a normal distribution with mean

In this problem, we have that:

$\mu = 6, \sigma = 2, n = 5, s = \frac{2}{\sqrt{5}} = 0.8944$

You want to get 5 baskets of fries but you only have $28 in your pocket. What is the probability that you would have enough money to pay for all five baskets of fries?

28/5 = 5.6

So this is the pvalue of Z when X = 5.6.

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

By the Central Limit Theorem

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

$Z = \frac{5.6 - 6}{0.8944}$

$Z = -0.45$

$Z = -0.45$ has a pvalue of 0.3264

32.64% probability that you would have enough money to pay for all five baskets of fries

5 0

3 years ago

Please i need help :/

lozanna [386]

Answer:

Step-by-step explanation:

3 0

3 years ago

F(x) = –2x2 + 4x and g(x) = x2 + 18x + 77.<br> What is (f•g)(x) in standard form?

Vikki [24]

Step-by-step explanation:

I take it this is meant to be a multiplication, right ?

not a "function of function", which would be symbolized by a little empty circle.

to multiply 2 function means basically the same as to add, subtract or divide 2 functions : to apply the arithmetic operation in both expressions.

(f×g)(x) = (-2x² + 4x)(x² + 18x + 77) =

= -2x⁴ - 36x³ - 154x² + 4x³ + 72x² + 308x =

= -2x⁴ - 32x³ - 82x² + 308x

7 0

3 years ago

I need help i will give 19 po.ints

Musya8 [376]

-5 7/10

How?

13 4/5

8 1/10

you need similar denominators.

13 4/5 x 2 = 13 8/10

13 8/10 + ? = 8 1/10

8 1/10 + 5 7/10 = 13 4/5

(5 7/10 turned negative bc its below sea level and your technically adding.)

MAY BE INCORRECT!

5 0

3 years ago

Read 2 more answers