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Gnom [1K]
2 years ago
5

A surveyor, Toby, measures the distance between two landmarks and the point where he stands. He also measured the angles between

the landmarks in degrees.
What is the distance, x, between the two landmarks? Round the answer to the nearest tenth.

A. 32.5 m
B. 42.1 m
C. 85.1 m
D. 98.5 m

Mathematics
2 answers:
LenKa [72]2 years ago
8 0

Answer:

The correct answer is 98.5 m, or D.

I just took the test and got it correct.

KonstantinChe [14]2 years ago
4 0
X² = Side1² + Side2² - 2[(Side1)(Side2)] cos(Toby's Angle)x² = 55² + 65² - 2[(55)(65)] cos(110°)x² = 3025 + 4225 -7150[cos(110°)]x² = 7250 - 2445.44x = √4804.56x = 69.31m
∴The distance, x, between two landmarks is 69.31m

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Which of the following exponential functions represents the graph below?
mario62 [17]

Answer:

the graph corresponds to function "D"  f(x)=3\,(\frac{1}{5} )^x

Step-by-step explanation:

Since the graph shown corresponds to an exponential "decay" (the function decreases as we move from left to right), the base of the exponent has to be a number smaller than 1 (one). So we examine the only two options that give such (options C and D which have fractions as the base - 1/3 and 1/5 respectively)

From there, we analyze which of the two functions satisfies the crossing of the y-axis at (0,3) which is clearly shown in the graph:

We study both:

function C at x = 0 gives:

f(x)= 5\,(\frac{1}{3})^x\\f(0)=5\,(\frac{1}{3})^0 \\f(0)=5\,(1)\\f(0)=5

while function D at x = 0 gives:

f(x)= 3\,(\frac{1}{5})^x\\f(0)=3\,(\frac{1}{5})^0 \\f(0)=3\,(1)\\f(0)=3

Therefore, the graph corresponds to function "D"

3 0
2 years ago
At a certain airport, 75% of the flights arrive on time. A sample of 10 flights is studied. Assume each flight is independent of
mars1129 [50]

Answer:

52.56% probability that eight or more of the flights will arrive on time.

Step-by-step explanation:

For each flight, there are only two possible outcomes. Either it is on time, or it is not. The probability of a flight being on time is independent from other flights. So we use the binomial probability distribution to solve this question.]

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

At a certain airport, 75% of the flights arrive on time.

This means that p = 0.75

A sample of 10 flights is studied.

This means that n = 10

Find the probability that eight or more of the flights will arrive on time.

P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)

In which

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 8) = C_{10,8}.(0.75)^{8}.(0.25)^{2} = 0.2816

P(X = 9) = C_{10,9}.(0.75)^{9}.(0.25)^{1} = 0.1877

P(X = 10) = C_{10,10}.(0.75)^{10}.(0.25)^{0} = 0.0563

P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) = 0.2816 + 0.1877 + 0.0563 = 0.5256

52.56% probability that eight or more of the flights will arrive on time.

4 0
2 years ago
Read 2 more answers
a phone company offers a monthly data plan at for $10 a month . the plan includes two megabytes of data and charges $0.10 per me
tatuchka [14]

Answer:

\ m(x) = \{ {{10, if x\leq 2} \atop {0.1x + 9.8, if x>2}} \right.

Step-by-step explanation:

  • One off charge = $10
  • Charge for data over 2 Mb is =  $0.10 per MB

<u>The monthly charge for x MB data is:</u>

1 . Data ta used up to 2 Mb

  • $10  

2 . Data used more than 2 Mb

  • m(x) = 10 + 0.1(x - 2) = 10 + 0.1x - 0.2 = 0.1x + 9.8
  • m(x) = 0.1x + 9.8

So the function is:

  • \ m(x) = \{ {{10, if x\leq 2} \atop {0.1x + 9.8, if x>2}} \right.
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2 years ago
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Eddi Din [679]
The most accurate would be the second statement: <span>The graph is misleading because it uses 3-dimensional bars.

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4 0
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solve for P
5 0
2 years ago
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