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3 years ago

What is t in 197sin(12t)=141

Mathematics

1 answer:

spayn [35]3 years ago

6 0

Answer:

t ≈ 0.0664731

Step-by-step explanation:

Use the inverse sine function.

sin(12t) = 141/197

12t = arcsin(141/197)

t = arcsin(141/197)/12

t ≈ 0.0664731 . . . . . . . radians

This is the principal value. There are other solutions at values of t that have integer multiples of π/6 added to this. There are also solutions where any of those values is subtracted from π.

_____

In general, angles in math are assumed to be in radians, unless specified otherwise. This angle corresponds to about 3.81°. (In geometry, the usual assumption is that angles are measured in degrees.)

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Three good friends are in the same algebra class. Their scores on a recent test are three consecutive integers whose sum is 219?

Nookie1986 [14]

Answer:

Their scores are 72, 73, and 74.

Step-by-step explanation:

(x-1) + x + (x+1) = 219

3x = 219

x = 73

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3 years ago

Solve for x hhhhhhhhhhhhhhhhhhhhhhhhhh

MAVERICK [17]

9514 1404 393

Answer:

x = 5

Step-by-step explanation:

In order to obtain a solution, we must assume that the figure is a parallelogram.

Angle BED will be congruent to angle BCD. The sum of angles in triangle BED is 180°, so we have ...

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3 years ago

Pilar used five reusable shopping bags on a recent purchase she made at a grocery store. Each bag decreased the amount she spent

almond37 [142]

Answer:

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Step-by-step explanation:

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7 0

3 years ago

Find set A={1, 2, 6, 10} B={3, 6, 9, 10, 11} C = {1, 2, 4, 7, 11}

PilotLPTM [1.2K]

If U = {1, 2, 3, …, 12} is the universal set, and

A = {1, 2, 6, 10}

B = {3, 6, 9, 10, 11}

C = {1, 2, 4, 7, 11}

then

(1) A U B is the set containing all elements from A and B,

A U B = {1, 2, 3, 6, 9, 10, 11}

(2) A ∩ B is the set of elements that are contained in both A and B,

A ∩ B = {6, 10}

(3) Unfortunately, A ∩ B U C is somewhat ambiguous. It could mean (A ∩ B) U C or A ∩ (B U C ). Then either

(A ∩ B) U C = {6, 10} U {1, 2, 4, 7, 11} = {1, 2, 4, 6, 7, 10, 11}

A ∩ (B U C ) = {1, 2, 6, 10} ∩ {1, 2, 3, 4, 6, 7, 9, 10, 11} = {1, 2, 6, 10}

The first interpretation is probably the intended one, since that essentially reads the set operations from left to right.

(4) A' U B is the union of A' and B, where A' is the complement of A, or all elements in U that are not in A. We have

A' = U - A = {3, 4, 5, 7, 8, 9, 11, 12}

and so

A' U B = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

(5) We have

A U C = {1, 2, 4, 6, 7, 10, 11}

so that

(A U C )' = U - (A U C ) = {3, 5, 8, 9, 12}

(6) We have

B' = U - B = {1, 2, 4, 5, 7, 8, 12}

and so

A ∩ B' = {1, 2}

(7) Using the complements found in (4) and (6), we have

A' U B' = {1, 2, 3, 4, 5, 7, 8, 9, 11, 12}

Alternatively, we can use the fact that

A' U B' = (A ∩ B)'

and since we know from (2) that A ∩ B = {6, 10}, we end up with the same result,

(A ∩ B)' = U - (A ∩ B) = {1, 2, 3, 4, 5, 7, 8, 9, 11, 12}

(8) We have

A U B U C = {1, 2, 3, 4, 6, 7, 9, 10, 11}

so that

(A U B U C )' = {5, 8, 12}

6 0

3 years ago

Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and th

blondinia [14]

Answer:

0.7823 = 78.23% probability that the response time is between 3 and 9 minutes.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Normal distribution with a mean of 7.2 minutes and a standard deviation of 2.1 minutes.

This means that $\mu = 7.2, \sigma = 2.1$