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3 years ago

Which of the following options is an equivalent function to f(x) = 3(2)3x?

Mathematics

2 answers:

Nataly_w [17]3 years ago

7 0

Answer:

F(x)=3(8)^x

Step-by-step explanation:

belka [17]3 years ago

5 0

So based on the given function above, the one that is equivalent to it would be the first option. So as you see, there might be a slight difference because the actual function should be written like this: f(x) = 3(2)^3x. Therefore, basing on this, the answer would be the first option: f(x) = 3(8)^x. Hope this answer helps.

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Find the missing side length ED Round answe to the nearest tenth please.

GarryVolchara [31]

Answer:

Step-by-step explanation:

Considering the given triangle EDI, to determine ED, we would apply the sine rule. It is expressed as

a/SinA = b/SinB = c/SinC

Where a, b and c are the length of each side of the triangle and angle A, Angle B and angle C are the corresponding angles of the triangle. Likening it to the given triangle, the expression becomes

ED/SinI = DI/SinE = EI/SinD

Therefore

Recall, the sum of the angles in a triangle is 180°. Therefore,

I° = 180 - (36 + 87) = 57°

Therefore,

ED/Sin 57 = 26/Sin 36

Cross multiplying, it becomes

EDSin36 = 26Sin57

0.588ED = 26 × 0.839

0.588ED = 21.814

ED = 21.814/0.588

ED = 37.1 m

8 0

3 years ago

Lie detectors have a 15% chance of concluding that a person is lying even when they are telling the truth. a bank conducts inter

Otrada [13]

Part A:

Given that lie detectors have a 15% chance of concluding that a person is lying even when they are telling the truth. Thus, lie detectors have a 85% chance of concluding that a person is telling the truth when they are indeed telling the truth.

The case that the lie detector correctly determined that a selected person is saying the truth has a probability of 0.85
Thus p = 0.85

Thus, the probability that the lie detector will conclude that all 15 are telling the truth if all 15 applicants tell the truth is given by:

 $P(X)={ ^nC_xp^xq^{n-x}} \\ \\ \Rightarrow P(15)={ ^{15}C_{15}(0.85)^{15}(0.15)^0} \\ \\ =1\times0.0874\times1=0.0874$


Part B:

Given that lie detectors have a 15% chance of concluding that a person is lying even when they are telling the truth. Thus, lie detectors have a 85% chance of concluding that a person is telling the truth when they are indeed telling the truth.

The case that the lie detector wrongly determined that a selected person is lying when the person is actually saying the truth has a probability of 0.25
Thus p = 0.15

Thus, the probability that the lie detector will conclude that at least 1 is lying if all 15 applicants tell the truth is given by:

$P(X)={ ^nC_xp^xq^{n-x}} \\ \\ \Rightarrow P(X\geq1)=1-P(0) \\ \\ =1-{ ^{15}C_0(0.15)^0(0.85)^{15}} \\ \\ =1-1\times1\times0.0874=1-0.0874 \\ \\ =0.9126$

Part C:

Given that lie detectors have a 15% chance of concluding that a person is lying even when they are telling the truth. Thus, lie detectors have a 85% chance of concluding that a person is telling the truth when they are indeed telling the truth.

The case that the lie detector wrongly determined that a selected person is lying when the person is actually saying the truth has a probability of 0.15
Thus p = 0.15

The mean is given by:

$\mu=npq \\ \\ =15\times0.15\times0.85 \\ \\ =1.9125$

Part D:

Given that lie detectors have a 15% chance of concluding that a person is lying even when they are telling the truth. Thus, lie detectors have a 85% chance of concluding that a person is telling the truth when they are indeed telling the truth.

The case that the lie detector wrongly determined that a selected person is lying when the person is actually saying the truth has a probability of 0.15
Thus p = 0.15

The probability that the number of truthful applicants classified as liars is greater than the mean is given by:

 $P(X\ \textgreater \ \mu)=P(X\ \textgreater \ 1.9125) \\ \\ 1-[P(0)+P(1)]$

 $P(1)={ ^{15}C_1(0.15)^1(0.85)^{14}} \\ \\ =15\times0.15\times0.1028=0.2312$

8 0

4 years ago

A drinking straw has a circumference of 30 mm and a height of 210 mm.

dexar [7]

I think the straw can hold about 15000 mm^3.

3 0

4 years ago

Help please its geometry

Anna11 [10]

Answer:

Step-by-step explanation:

Opposite angles are equal in a parallelogram. Therefore 2 angles are 112°. Angles in a parallelogram or any quadrilateral are equal to 360°. To find the remaining sides: 360-(112×2) and divide your answer by 2.

4 0

3 years ago

You wonder if weather (rain, cloudy or sunny) makes a difference on mood (happy or not). To determine this, you sample the moods

gizmo_the_mogwai [7]

Answer:

Step-by-step explanation:

Drawing a table to show the different weather and mood options :

The degree of freedom :

________ WEATHER ________

__________Rain ____ sunny _____ cloudy

Happy

Not happy

Here, we have a contingency table formatted in rows and columns

The columns = 3

The rows = 2

Degree of freedom :

(rows - 1) * ( columns - 1)

(2 - 1) * (3 - 1)

1 * 2

= 2

The degree of freedom = 2

6 0

3 years ago