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2 years ago

PLEASE HELP: Choose the function whose graph is given by:

Mathematics

1 answer:

DIA [1.3K]2 years ago

4 0

Answer:

The function of the graph is y = 3 cos (4x) ⇒ answer A

Step-by-step explanation:

- If the equation is y = A cos (B x)

* A is the amplitude

- The amplitude is the height from highest to lowest points and

divide the answer by 2

* The period is 2π/B

- The period is the distance from one peak to the next peak

* Lets look to the graph

- The maximum value is 3 and the minimum value is -3

∵ The height from the maximum point to the minimum point is

3 - (-3) = 3 + 3 = 6

∴ The amplitude is 6/2 = 3

∵ A is the amplitude

∴ A = 3

- The distance between two consecutive peaks is π/2

∵ The period is the distance from one peak to the next peak

∴ The period = π/2

∵ The period = 2π/B

∴ 2π/B = π/2 ⇒ divide both sides by π

∴ 2/B = 1/2 ⇒ by using cross multiplication

∴ B = 4

- Lets write the form of the function

∵ y = A cos (Bx)

∵ A = 3 and B = 4

∴ y = 3 cos (4x)

* The function of the graph is y = 3 cos (4x)

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A log is 16m long, correct to the nearest metre. It has to be cut into fence posts which must be 70cm long, correct to the neare

dmitriy555 [2]

Answer:

25 posts

Step-by-step explanation:

So the number of fence post would be the total length of the log divided by the length of each post. As the log is 16m and is corrected to the nearest metre, it could possibly be 16.499m. As for the post that is 70 cm long and corrected to the nearest 10cm, it may as well be 65 cm (or 0.65m) each post

So the max number of fence point once can possibly cut from the log would be

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2 years ago

2. A statistics student plans to use a TI-84 Plus calculator on her final exam. From past experience, she estimates that there i

Anarel [89]

Answer:

P(≥1 working) = 0.9936
She raises her odds of completing the exam without failure by a factor of 13.5, from 11.5 : 1 to 155.25 : 1.

Step-by-step explanation:

1. Assuming the failure is in the calculator, not the operator, and the failures are independent, the probability of finishing with at least one working calculator is the complement of the probability that both will fail. That is ...

... P(≥1 working) = 1 - P(both fail) = 1 - P(fail)² = 1 - (1 - 0.92)² = 0.9936

2. The odds in favor of finishing an exam starting with only one calculator are 0.92 : 0.08 = 11.5 : 1.

If two calculators are brought to the exam, the odds in favor of at least one working calculator are 0.9936 : 0.0064 = 155.25 : 1.

This odds ratio is 155.25/11.5 = 13.5 times as good as the odds with only one calculator.

_____

My assessment is that there is significant gain from bringing a backup. (Personally, I might investigate why the probability of failure is so high. I have not had such bad luck with calculators, which makes me wonder if operator error is involved.)

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2 years ago

A washer contains a drum that spins at 750 revolutions per minute. To the nearest hundredth, the angular velocity of the drum is

LenaWriter [7]

For this case, the first thing we must do is to take into account the following transformation of units:
1 revolution = 2pi radians
1 minute = 60 seconds
Applying the transformation of units we have:
$(750) * (1/60) * (2 * pi) = 78.54 rad / sec
$
Answer:
To the nearest hundredth, the angular velocity of the drum is 78.54 radians per second.

8 0

2 years ago

A toddler is allowed to dress himself on Mondays, Wednesdays, and Fridays. For each of his shirt, pants, and shoes, he is equall

avanturin [10]

Answer:

0.0286 = 2.86% probability that today is Monday.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Dressed correctly

Event B: Monday

Probability of being dressed correctly:

100% = 1 out of 4/7(mom dresses).

(0.5)^3 = 0.125 out of 3/7(toddler dresses himself). So

$P(A) = 0.125\frac{3}{7} + \frac{4}{7} = \frac{0.125*3 + 4}{7} = \frac{4.375}{7} = 0.625$

Probability of being dressed correctly and being Monday:

The toddler dresses himself on Monday, so (0.5)^3 = 0.125 probability of him being dressed correctly, 1/7 probability of being Monday, so:

$P(A \cap B) = 0.125\frac{1}{7} = 0.0179$

What is the probability that today is Monday?

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.0179}{0.625} = 0.0286$

0.0286 = 2.86% probability that today is Monday.

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2 years ago

What is the measure (in degrees) of the smallest interior angle of a triangle in which the exterior angle measures have the rati

steposvetlana [31]

Let

3x----> angle exterior 1

4x----> angle exterior 2

5x----> angle exterior 3

we know that

The exterior angles of any polygon add up to 360 degrees

3x+4x+5x=360-------> 12x=360----------> x=30°

The largest of exterior angles is equal to the smallest of interior angles

the largest of exterior angles is 5x------> 5*30=150°

the smallest of interior angles is 180°-150°=30°

therefore

the answer is

the smallest of interior angle measure 30 degrees

8 0

1 year ago

Read 2 more answers