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2 years ago

Let P(2, 3) be a point on a figure. The figure is dilated by a scale factor of 4.

1 answer:

5 0

Hi there!

If (2,3) is a point and 4 is the scale factor, we need to multiply both x and y by 4 to dilate the figure. Doing this gives us (8,12).

Hope this helps!! :)
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Solve the following equation |x – 3| = 4. Show all work.

Igoryamba

<h2>Solving Equations with Absolute Values</h2><h3>Answer:</h3>

$x = 7$ and $x = -1$

<h3>Step-by-step explanation:</h3>

Solving for the Positive Absolute Value:

$|x -3| = 4 \\ x -3 = 4 \\ x -3 +3 = 4 +3 \\ x = 7$

Solving for the Negative Absolute Value:

$|x -3| = 4 \\ -(x -3) = 4 \\ -(x -3) \cdot -1 = 4 \cdot -1 \\ x -3 = -4 \\ x -3 +3 = -4 +3 \\ x = -1$

8 0

3 years ago

Read 2 more answers

Although cities encourage carpooling to reduce traffic congestion, most vehicles carry only one person. For example, 64% of vehi

ira [324]

Answer:

a) 0.7291 is the probability that more than half out of 10 vehicles carry just 1 person.

b) 0.996 is the probability that more than half of the vehicles carry just one person.

Step-by-step explanation:

We are given the following information:

A) Binomial distribution

We treat vehicle on road with one passenger as a success.

P(success) = 64% = 0.64

Then the number of vehicles follows a binomial distribution, where

$P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}$

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 10

We have to evaluate:

$P(x \geq 6) = P(x =6) +...+ P(x = 10) \\= \binom{10}{6}(0.64)^6(1-0.64)^4 +...+ \binom{10}{10}(0.64)^{10}(1-0.79)^0\\=0.7291$

0.7291 is the probability that more than half out of 10 vehicles carry just 1 person.

B) By normal approximation

Sample size, n = 92

p = 0.64

$\mu = np = 92(0.64) = 58.88$

$\sigma = \sqrt{np(1-p)} = \sqrt{92(0.64)(1-0.64)} = 4.60$

We have to evaluate the probability that more than 47 cars carry just one person.

$P(x \geq 47)$

After continuity correction, we will evaluate

$P( x \geq 46.5) = P( z > \displaystyle\frac{46.5 - 58.88}{4.60}) = P(z > -2.6913)$

$= 1 - P(z \leq -2.6913)$

Calculation the value from standard normal z table, we have,

$P(x > 46.5) = 1 - 0.004 = 0.996 = 99.6\%$

0.996 is the probability that more than half out of 92 vehicles carry just one person.

5 0

2 years ago

Military radar and missile detection systems are designed to warn a country of enemy attacks. A reliability question deals with

Nadusha1986 [10]

Answer:

Step-by-step explanation:

Given that a particular detection system has a 0.83 probability of detecting a missile attack.

Also each system is independent of the other to detect missile attack.

a) the probability that a single detection system will detect an attack= $0.83$

b) the probability that at least one of the systems will detect the attack given two systems= 1-Prob no system detects

= $1-(1-0.83)(1-0.83)\\\\=1-0.0289\\=0.9711$

c) If three systems are installed, the probability that at least one of the systems will detect the attack

= 1- none of the three systems detect attack

$= (1-0.17^3)\\=1-0.004913\\=0.995087$

d) We find that probability of detecting is more if we increase the system form 1 to 2 and 2 to 3.

Hence for safety and defence purpose multiple detection system is recommended.

7 0

3 years ago

Explain how you would write 423,090,709,000 in word form

vfiekz [6]

Four hundred twenty-three billion, ninety million, seven hundred nine thousand

Hope this helped:))

8 0

3 years ago

BRAINLIEST FOR CORRECT ANSWER

user100 [1]

2 times 2.5 times 1.5 times 10 equals to 75 square meters.

4 0

3 years ago