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Sergio [31]
3 years ago
5

Q5: The probability that event A occurs is 5/7 and the probability that event B occurs is 2/3 . If A and B are independent event

s, what is the probability that A and B both occur?
Mathematics
1 answer:
bekas [8.4K]3 years ago
7 0

Answer:

P(A \cap B)

And we can use the following formula:

P(A \cap B)= P(A)* P(B)

And replacing the info we got:

P(A \cap B) = \frac{5}{7} \frac{2}{3}= \frac{10}{21}=0.476

Step-by-step explanation:

We define two events for this case A and B. And we know the probability for each individual event given by the problem:

p(A) = \frac{5}{7}

p(B) = \frac{2}{3}

And we want to find the probability that A and B both occurs if A and B are independent events, who menas the following conditions:

P(A|B) = P(A)

P(B|A) = P(B)

And for this special case we want to find this probability:

P(A \cap B)

And we can use the following formula:

P(A \cap B)= P(A)* P(B)

And replacing the info we got:

P(A \cap B) = \frac{5}{7} \frac{2}{3}= \frac{10}{21}=0.476

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Lyrx [107]

Answer:

21 times 21

Step-by-step explanation:


5 0
4 years ago
A jumping spider's movement is modeled by a parabola. The spider makes a single jump from the origin and reaches a maximum heigh
aleksklad [387]

The spider's movement is an illustration of a parabola.

  • The equation of a parabola is: \mathbf{y = -\frac{1}{160}(x - 40) + 10}
  • The focus of a parabola is: (40,-30)
  • The axis of symmetry is: \mathbf{x = 40}
  • The directrix is:\mathbf{y = 50}

<u>(a) The equation</u>

The spider passes through the origin.

So, we have:

\mathbf{(x,y) = (0,0)}

The spider jumps to a maximum height of 10mm, midway 80mm.

So, the vertex is:

\mathbf{(h,k) =  (40,10)}

The equation of a parabola is:

\mathbf{y = a(x - h)^2 + k}

So, we have:

\mathbf{0 = a(0 - 40)^2 + 10}

Subtract 10 from both sides

\mathbf{a(0 - 40)^2 =- 10}

\mathbf{1600a =- 10}

Solve for a

\mathbf{a =- \frac{1}{160}}

Substitute \mathbf{a =- \frac{1}{160}} and \mathbf{(h,k) =  (40,10)} in \mathbf{(h,k) =  (40,10)}

\mathbf{y = -\frac{1}{160}(x - 40) + 10}

<u>(b) The focus, directrix and the axis of symmetry</u>

The focus of a parabola is:

\mathbf{Focus= (h, k + p)}

Where:

\mathbf{p = \frac{1}{4a}}

So, we have:

\mathbf{p = \frac{1}{4 \times -1/160}}

\mathbf{p = -\frac{160}{4}}

\mathbf{p = -40}

So, we have:

\mathbf{Focus = (40,10-40)}

\mathbf{Focus = (40,-30)}

The axis of symmetry is:

\mathbf{x = h}

So, we have:

\mathbf{x = 40}

The directrix is:

\mathbf{y = k - p}

\mathbf{y = 10 + 40}

\mathbf{y = 50}

Read more about parabolas at:

brainly.com/question/25237745

4 0
3 years ago
2. the average battery life of 2400 manufactured cell phones is recorded
Cloud [144]

A Z-score helps us to understand how far is the data from the mean. The number of phones who have battery life in the range of 11.4 to 13 range is 1145.

<h3>What is Z-score?</h3>

A Z-score helps us to understand how far is the data from the mean. It is a measure of how many times the data is above or below the mean. It is given by the formula,

Z = \dfrac{X- \mu}{\sigma}

Where Z is the Z-score,

X is the data point,

μ is the mean and σ is the standard variable.

The percentage of phones who have battery life in the range of 11.4 to 13 range is,

P(11.4 < X < 13) = P(Z < \dfrac{13-13}{0.8}) - P(Z < \dfrac{11.4-13}{0.8})

                            = 0.50 - 0.0228

                            = 0.4772

Now, the number of phones who have battery life in the range of 11.4 to 13 range is,

Number of phones = 0.4772 × 2400 = 1145.28 ≈ 1145

Hence, the number of phones who have battery life in the range of 11.4 to 13 range is 1145.

Learn more about Z-score:

brainly.com/question/13299273

#SPJ1

3 0
2 years ago
70 meters increased by 80%
hram777 [196]
I think the answer is 126;
3 0
4 years ago
Jen and Jason recently opened a savings account. Jen made an inital deposit of $350 and will put in an additional $25 every week
ycow [4]
Find how long it take to have the same balance
Write the expressions represent the savings of Jen and the savings of Jason
For an instance, w stands for the number of weeks they take to have the same balance.

Jen ⇒ initial $350, additional $25/week, the expression will be
350 + 25w
Jason ⇒ initial $470, additional $15/week, the expression will be
470 + 15w

Then find the value of w using equation Jen's expression and Jason's expression
350 + 25w = 470 + 15w
25w - 15w = 470 - 350
10w = 120
    w = 120/10
    w = 12

They have the same balance in 12 weeks

Find how much each of them has in 12 weeks
350 + 25w
= 350 + 25(12)
= 350 + 300
= 650

They have each $650 in 12 weeks
5 0
3 years ago
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