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3 years ago

Juan Carlos graphs the functions f(x) = 8x - 2 and g(x) = -8x + 2

Mathematics

1 answer:

Mamont248 [21]3 years ago

8 0

Answer:

$x = 0.25$

Step-by-step explanation:

Given

$f(x) = 8x - 2\\ g(x) = -8x + 2$

Required

Determine their point of intersection

To do this, we simply do:

$f(x) = g(x)$

This gives:

$8x - 2 = -8x + 2$

Collect Like Terms

$8x + 8x = 2 + 2$

$16x = 4$

Solve for x

$x = 4/16$

$x = 0.25$

Hence:

Their point of intersection is at $x = 0.25$

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The number of texts per day by students in a class is normally distributed with a

kobusy [5.1K]

Answer:

1, 2, 6

Step-by-step explanation:

The z score shows by how many standard deviations the raw score is above or below the mean. The z score is given by:

$z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score,\mu=mean, \ \sigma=standard\ deviation$

Given that mean (μ) = 130 texts, standard deviation (σ) = 20 texts

1) For x < 90:

$z=\frac{x-\mu}{\sigma} \\\\z=\frac{90-130}{20} =-2$

From the normal distribution table, P(x < 90) = P(z < -2) = 0.0228 = 2.28%

Option 1 is correct

2) For x > 130:

$z=\frac{x-\mu}{\sigma} \\\\z=\frac{130-130}{20} =0$

From the normal distribution table, P(x > 130) = P(z > 0) = 1 - P(z < 0) = 1 - 0.5 = 50%

Option 2 is correct

3) For x > 190:

$z=\frac{x-\mu}{\sigma} \\\\z=\frac{190-130}{20} =3$

From the normal distribution table, P(x > 3) = P(z > 3) = 1 - P(z < 3) = 1 - 0.9987 = 0.0013 = 0.13%

Option 3 is incorrect

4) For x < 130:

$z=\frac{x-\mu}{\sigma} \\\\z=\frac{130-130}{20} =0$

For x > 100:

$z=\frac{x-\mu}{\sigma} \\\\z=\frac{100-130}{20} =-1.5$

From the normal table, P(100 < x < 130) = P(-1.5 < z < 0) = P(z < 0) - P(z < 1.5) = 0.5 - 0.0668 = 0.9332 = 93.32%

Option 4 is incorrect

5) For x = 130:

$z=\frac{x-\mu}{\sigma} \\\\z=\frac{130-130}{20} =0$

Option 5 is incorrect

6) For x = 130:

$z=\frac{x-\mu}{\sigma} \\\\z=\frac{160-130}{20} =1.5$

Since 1.5 is between 1 and 2, option 6 is correct

5 0

3 years ago

A special deck of cards has ten cards. Four are green (G), four are blue (B), and two are red (R). When a card is picked, the co

a_sh-v [17]

Answer:

{GT, GH, BT, BH, RT, RH};

1 /5;

Mutually exclusive ;

Not mutually exclusive.

Step-by-step explanation:

Given :

Green cards, G = 4

Blue cards, B = 4

Red cards, R = 2

For a coin toss :

{H, T}

A card is picked, then a coin is tossed :

Sample space :

{GT, GH, BT, BH, RT, RH}

2.) probability of picking a green card, then probability of landing a head on a coin toss

P(A) = number of required outcome / Total possible outcomes

P(A) = P(green card) * P(Head)

P(A) = (4 / 10) * (1/2)

P(A) = 4 /20

P(A) = 1/5

C.)

Both A and B are mutually exclusive, since both event A and event B cannot occur together, since both red and green cannot be picked during a single pick, this either a red is picked or green is picked, then they are A and B are mutually exclusive.

D.) Event A and C are not mutually exclusive, picking a green card, event A and picking a red or blue card, event B. Both event can happen simultaneously, hence, event A and B are not mutually exclusive.

6 0

3 years ago

Write the polar form of a complex number in standard form for <img src="https://tex.z-dn.net/?f=8%5Bcos%28%5Cfrac%7B%5Cpi%7D%7B2

laila [671]

Answer:

Solution : 8i

Step-by-step explanation:

We can use the trivial identities cos(π / 2) = 0, and sin(π / 2) = 1 to solve this problem. Let's substitute,

$8\left[cos\left(\frac{\pi }{2}\right)+isin\left(\frac{\pi \:}{2}\right)\right]$ = $8\left(0+1i\right)$

And of course 1i = i, so we have the expression 8(0 + i ). Distributing the " 8, " 8( 0 ) = 0, and 8(i) = 8i, making the fourth answer the correct solution.

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3 years ago

How many 3s are in 48?

Nitella [24]

To find the answer, all you need to do is divide 48 by 3. This shall get you the answer 16. This means that there are sixteen(16) 3s in 48.

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3 years ago

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Hatshy [7]

Answer:

Step-by-step explanation: