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2 years ago

A dog walks due east 180 ft to a corner.

Mathematics

1 answer:

slega [8]2 years ago

5 0

Answer:

Area = 29284.87 ft²

Step-by-step explanation:

I've drawn a triangle to depict the movement of the dog with the angle and dimensions.

From the attached triangle, we see that the starting point is C, the first point is A and the second point is B.

Let's find the third side from the image using law of cosine.

Thus;

b² = a² + c² - 2ac cos B

Thus;

b² = 180² + 329² - 2(180 × 329)cos 81.5

b² = 32400 + 108241 - 17506.55

b² = 123134.45

b = √123134.45

b = 350.91 ft

We calculate the area of the triangle using heron's formula.

Area = √(p(p − a)(p − b)(p − c))

Where p = (a + b + c)/2 = (180 + 350.91 + 329)/2 = 429.955 ft

Area = √(429.955(429.955 - 180)(429.955 - 350.91)(429.955 - 329)

Area = 29284.886 ft²

To the nearest Hundredth gives;

Area = 29284.87 ft²

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How to write 6/10 in a simple form

s2008m [1.1K]

It is 3/5

Hope this helps:)

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3 years ago

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Suppose that the probabilities are 0.4, 0.3, 0.2, and 0.1, respectively, that 0, 1, 2, or 3 power failures will strike a certain

defon

Answer:

mean = 1 power failure

variance = 1 (power failure)²

Step-by-step explanation:

Since the mean is computed as

mean = E(x) = ∑ x * p(x) for all x

then for the random variable x=power failures , we have

mean = ∑ x * p(x) = 0 * 0.4 + 1* 0.3 + 2*0.2 + 3* 0.1 = 1 power failure

since the variance can be calculated through

variance = ∑[x-E(x)]² * p(x) for all x

but easily in this way

variance = E(x²) - [E(x)]² , then

E(x²) = ∑ x² * p(x) = 0² * 0.4 + 1²* 0.3 + 2²*0.2 + 3²* 0.1 = 2 power failure²

then

variance = 2 power failure² - (1 power failure)² = 1 power failure²

therefore

mean = 1 power failure

variance = 1 power failure²

7 0

2 years ago

Valentino sells ice cream cones and ice cream tubs.

adoni [48]

Answer:

11/60 so around 18.33%

Step-by-step explanation:

hello

in total there are 120 ppl

22 are vanilla cones

so the probability that this person bought a vanilla a ice cream cone is 22/120=11/60

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3 years ago

*15 POINTS*

Naddik [55]

I think the answer is C, but I'm not sure.

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3 years ago

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A random sample of 64 bags of white cheddar popcorn weighed, on average, 5.23 ounces with a standard deviation of 0.24 ounce.

emmasim [6.3K]

Answer:

We conclude that cheddar popcorn weighed less than 5.5 ounces.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ =5.5 ounces

Sample mean, $\bar{x}$ = 5.23 ounces

Sample size, n = 64

Alpha, α = 0.05

Sample standard deviation, σ = 0.24 ounce.

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 5.5\text{ ounces}\\H_A: \mu < 5.5\text{ ounces}$

We use One-tailed z test to perform this hypothesis.

Formula:

$z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

Putting all the values, we have

$z_{stat} = \displaystyle\frac{5.23 - 5.5}{\frac{0.24}{\sqrt{64}} } = -9$

Now, $z_{critical} \text{ at 0.05 level of significance } =-1.645$

Since,

$z_{stat} < z_{critical}$

We reject the null hypothesis and accept the alternate hypothesis. Thus, we conclude that cheddar popcorn weighed less than 5.5 ounces.

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3 years ago