Calculate the average ratw of change of a function, f(x)=x^2 as x changes from 5 to 15

Chee is flying a kite, holding her hands a distance of 3.25 feet above the ground and

Mademuasel [1]

The height of the kite above the ground is 58.68 ft

Let x be the height of the kite above Chee's hand.

The height of the kite above Chee's hand, the string and the horizontal distance between Chee and the kite form a right angled triangle with hypotenuse side, the length of the string and opposite side the height of the kite above Chee's hand.

Since we have the angle of elevation from her hand to the kite is 29°, and the length of the string is 100 ft.

From trigonometric ratios, we have

tan29° = x/100

So, x = 100tan29°

x = 100 × 0.5543

x = 55.43 ft.

Since Chee's hand is y = 3.25 ft above the ground, the height of the kite above the ground, L = x + y

= 55.43 ft + 3.25 ft

= 58.68 ft to the nearest hundredth of a foot

So, the height of the kite above the ground is 58.68 ft

Learn more about height of kite above the ground here:

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6 0

3 years ago

g A sample of 3 items is chosen at random from a box containing 20 items, out of which 4 are defective. Let X be the number of d

professor190 [17]

Answer:

The variance and standard deviation of X are 0.48 and 0.693 respectively.

The variance and standard deviation of (20 - X) are 0.48 and 0.693 respectively.

Step-by-step explanation:

The variable X is defined as, X = number of defective items in the sample.

In a sample of 20 items there are 4 defective items.

The probability of selecting a defective item is:

$P (X)=\frac{4}{20}=0.20$

A random sample of n = 3 items are selected at random.

The random variable X follows a Binomial distribution with parameters n = 3 and p = 0.20.

The variance of a Binomial distribution is:

$V(X)=np(1-p)$

Compute the variance of X as follows:

$V(X)=np(1-p)=3\times0.20\times(1-0.20)=0.48$

Compute the standard deviation (σ (X)) as follows:

$\sigma (X)=\sqrt{V(X)}=\sqrt{0.48}=0.693$

Thus, the variance and standard deviation of X are 0.48 and 0.693 respectively.

Now compute the variance of (20 - X) as follows:

$V(20-X)=V(20)+V(X)-2Cov(20,X)=0+0.48-0=0.48$

Compute the standard deviation of (20 - X) as follows:

$\sigma (20-X)=\sqrt{V(20-X)} =\sqrt{0.48}0.693$

Thus, the variance and standard deviation of (20 - X) are 0.48 and 0.693 respectively.

3 0

3 years ago

Naomi has 45 minutes to get ready for school she spends x minutes getting dressed write an expression that respetents the number

andriy [413]

ANSWER

$(45 - x) \: minutes$

EXPLANATION

Total minutes Naomi has at her disposal is 45 minutes.

The number of minutes she spends getting dressed is

$x$

To find the number of minutes she still has to get ready, we subtract the minutes spent from the total minutes.

The number of minutes she still have to get ready is

$(45 - x) \: minutes$

5 0

3 years ago

Lenox ironed 1/4 of the shirts over the weekend. She plans to split the remainder of the work equally over the next 5 evenings.

MrMuchimi

3/20, or 0.15 of the shirts each evening

1 - 1/4 = 3/4

(3/4) / 5 = (3/4) / (5/1) = (3/4) x (1/5) = 3/20 = 0.15

4 0

3 years ago

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Marissa bought 60 horns for her New Year’s Eve party for $83.40. She needs to purchase an additional 18 horns for the party at t

Degger [83]