If a rectangular prism is sliced vertically by a plane, what is the shape of the resulting two dimensional figure?

Fill in the missing numbers I need an answer ASAP

mamaluj [8]

Answer:

the missing numbers be 60 and 6 respectively

Step-by-step explanation:

The computation of the missing numbers are shown below:

Let us assume the missing numbers be x

a/

, $\frac{1}{2} \times 30 = \frac{1}{4} \times x\\\\15 = \frac{1}{4} \times x\\\\x = 60$

b.

$\frac{1}{3} \times 12 = \frac{2}{3} \times x\\\\4 = \frac{2}{3} \times x\\\\x = 6$

Hence, the missing numbers be 60 and 6 respectively

4 0

3 years ago

400 Suppose a particular surveillance system has a 99% chance of correctly identifying a future terrorist and a 99.8% chance of

alexgriva [62]

Answer:

1.236 × 10^(-3)

Step-by-step explanation:

Let A be the event that the person is a future terrorist

Let B the event that the person is identified as a terrorist

We are told that there are 1,000 future terrorists in a population of 400 million. Thus, the Probability that the person is a terrorist is;

P(A) = 1000/400000000

P(A) = 0.0000025

P(A') = 1 - P(A)

P(A') = 1 - 0.0000025

P(A') = 0.9999975

We are told that the system has a 99% chance of correctly identifying a future terrorist. Thus; P(B|A) = 0.99

Thus, P(B'|A) = 1 - P(B|A)

P(B'|A) = 1 - 0.99

P(B'|A) = 0.01

We are told that there is a 99.8% chance of correctly identifying someone who is not a future terrorist. Thus; P(B'|A') = 0.998

Hence: P(B|A') = 1 - P(B'|A')

P(B|A') = 1 - 0.998

P(B|A') = 0.002

We want to find the probability that someone who is identified as a terrorist, is actually a future terrorist. This is represented by: P(A|B)

We can find it from bayes theorem as follows;

P(A|B) = [P(B|A) × P(A)]/[(P(B|A) × P(A)) + (P(B|A') × P(A')]

Plugging in the relevant values;

P(A|B) = [0.99 × 0.0000025]/[(0.99 × 0.0000025) + (0.002 × 0.9999975)]

P(A|B) = 0.00123597357 = 1.236 × 10^(-3)

8 0

3 years ago

When Klorina swims with the current, she swims 10 km in 2 h. Against the current, she can swim only 8 km in the same time. How f

nasty-shy [4]

Answer:

Klorina's rate in still water is 4.5 km/h

Current's rate is 0.5 km/h

Step-by-step explanation:

Let

x km/h = Klorina's rate in still water

y km/h = current's rate

With the current (current helps):

Distance = 10 km

Time = 2 hours

Rate = x + y km/h

$10=2(x+y)$

Against the current:

Distance = 8 km

Time = 2 hours

Rate = x - y km/h

$8=2(x-y)$

Divide both equations by 2:

$x+y=5\\ \\x-y=4$

Add these equations:

$x+y+x-y=5+4\\ \\2x=9\\ \\x=4.5\ km/h$

Subtract these two equations:

$(x+y)-(x-y)=5-4\\ \\x+y-x+y=1\\ \\2y=1\\ \\y=0.5\ km/h$

4 0

3 years ago

Suppose that the distribution of typing speed in words per minute (wpm) for experienced typists using a new type of split keyboa

KengaRu [80]

Answer:

a. 0.5 or 50%

b. 0.496 or 49.6%

c. 0.8185 or 81.85%

d. Yes, it would be just 0.0013 or 0.13% of probability to find a typist whose speed exceeds 105 wpm

e. 0.0252 or 2.52%

f. The qualifying speed would be 47.4 wpm.

Step-by-step explanation:

a. Let's find the z-score this way:

μ = 60 σ= 15

z-score = (x - μ)/σ

z-score = (60 - 60)/15

z-score = 0

Now, let's calculate the p value for z-score = 0, using the z-table:

p (z=0) = 0.5 or 50%

b. z-score = (x - μ)/σ

z-score = (59.9 - 60)/15

z-score = -0.01

Now, let's calculate the p value for z-score = -.0.01, using the z-table:

p (z = -0.01) = 0.496 or 49.6%

If the question were less or equal than 60, a and b would have the same answer. But in this case, the question is "less than 60 wpm".

c.

z-score = (x - μ)/σ

z-score = (45 - 60)/15

z-score = - 1

Now, let's calculate the p value for z-score = -1, using the z-table:

p (z = -1) = 0.1587

z-score = (x - μ)/σ

z-score = (90 - 60)/15

z-score = 2

Now, let's calculate the p value for z-score = 2, using the z-table:

p (z = 2) = 0.9772

In consequence,

p (-1 ≤ z ≤ 2) = 0.9772 - 0.1587 = 0.8185 or 81.85%

d. z-score = (x - μ)/σ

z-score = (105 - 60)/15

z-score = 3

Now, let's calculate the p value for z-score = 3, using the z-table:

p (z = 3) = 0.9987

In consequence,

p (z > 3) = 1 - 0.9987 = 0.0013

Yes, it would be just a 0.13% of probability to find a typist whose speed exceeds 105 wpm.

e. z-score = (x - μ)/σ

z-score = (75 - 60)/15

z-score = 1

Now, let's calculate the p value for z-score = 1, using the z-table:

p (z = 1) = 0.8413

In consequence,

p (z > 1) = 1 - 0.8413 = 0.1587

and if the two typists are independently selected, then

p = 0.1587 * 0.1587

p = 0.0252 or 2.52%

f. p = 0.2, using the z-table, the z-score is -0.84, then:

z-score = (x - μ)/σ

-0.84 = (x - 60)/15

-12.6 = x - 60

-x = -60 + 12.6

-x = - 47.4

x = 47.4

The qualifying speed would be 47.4 wpm.

8 0

3 years ago

The area of this parallelogram is 120 ft. Find the value of h

julsineya [31]

are you going to show a picture??? its impossible to answer otherwize

4 0

4 years ago