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Varvara68 [4.7K]
2 years ago
10

casey has the forgotten combination to a lock. the lock has three dials with numbers 1, 2, and 3 What is the probability that th

e combination starts with 2?
Mathematics
1 answer:
olga nikolaevna [1]2 years ago
4 0

The probability that the combination starts with 2 is 1/3

<h3>Probability</h3>

Probability is the likelihood or chance that an event will occur.

Probability = expected/total outcome

The total outcome  = 3! = 6

The expected outcome if the combination starts with 2 is given as 2! = 2

Pr(the combination starts with 2) = 2/6 = 1/3

Hence the probability that the combination starts with 2 is 1/3

Learn more on probability here: brainly.com/question/25870256

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4) The line -3x + 4y = 8 is transformed by a dilation centered at the origin. Which linear equation could represent its image?
Dimas [21]

Answer:

4) The linear equation which could represent its image is y = \frac{3}{4} x + 8 ⇒ (2)

5) The equation of the image of the line is y = \frac{3}{2} x - 3 ⇒ (4)

Step-by-step explanation:

Dilation does not change the slope of a line but changes the y-intercept

Dilation of a line segment is longer or shorter by ratio that equal to the scale factor of dilation

4)

The slope-intercept form of the linear equation is y = m x + b, where m is the slope of the line and b its y-intercept

Let us put the given equation in the slope-intercept form to find its slope

∵ The line -3x + 4y = 8 is transformed by a dilation centered at

   the origin

- Add 3x to both sides

∴ 4y = 3x + 8

- Divide both sides by 4

∴ y = \frac{3}{4} x + 2 ⇒ the equation of the line before dilation

- By comparing it with the form above, then m =  \frac{3}{4} , so the

   equation after dilation has the same slope

∵ The slope of the line before dilation is  \frac{3}{4}

∴ The slope of the line after dilation is  \frac{3}{4}

∵ The equation that has the slope  \frac{3}{4}  is y =

∴ The equation of the image of the line is y = \frac{3}{4} x + 8

The linear equation which could represent its image is y = \frac{3}{4} x + 8

5)

∵ The equation of the line is y = \frac{3}{2} x - 4

∵ The scale factor of dilation is \frac{3}{4}

- Dilation dose not change the slope of the line

∴ The slope of the image after dilation is \frac{3}{2}

- Dilation changes the y-intercept, to find it multiply the scale

  factor of dilation by the y-intercept of the line before dilation

∵ The y-intercept of the line is (0 , -4)

- Multiply it by \frac{3}{4}

∵  \frac{3}{4} × -4 = -3

∴ The y-intercept of the image is (0 , -3)

∴ The equation of the image of the line is y = \frac{3}{2} x - 3

3 0
3 years ago
Use the formula to find the standard error of the distribution of differences in sample means, x¯1-x¯2. Samples of size 100 from
garri49 [273]

Answer:

standard error = 2.11

Step-by-step explanation:

First we stablish the data that we have for each sample:

<u>Population 1</u>                                          <u>Population </u>2

n₁ = 100                                                     n₂ = 90

x¯1= 95                                                    x¯2 = 75

σ₁ = 14                                                        σ₂ = 15                  

To calculate the standard error of each sample we would use the formulas:

σ = σ₁/√n₁

σx¯2 =  σ₂/√n₂

Now, in order to obtain the standard error of the differences between the two sample means we combine those two formulas to obtain this:

σx¯1 - σ x¯2  = √(σ₁²/n₁ + σ₂²/n₂ )

So as you can see, we used the square root to simplify and now we require the variance of each sample (σ²):

σ₁² = (14)² = 196

σ₂² = (15)² = 225

Now we can proceed to calculate the standard error of the distribution of differences in sample means:

σx¯1 - σx¯2  = √(196/100 + 225/90) =  2.11

This gives an estimate about how far is the difference between the sample means from the actual difference between the populations means.

6 0
3 years ago
Solve question ( x + 4 ) ( x+2 )
nexus9112 [7]
X^2+6x+8 if you multiply
8 0
3 years ago
Read 2 more answers
(10n-5)÷(5)=2n-1 the left of the parentheses has to equal the right
daser333 [38]
(10n-5)/(5)= 2n-1
just divide
10/5 = 2 and -5/5 =-1
and you get the answer
2n-1= 2n-1
8 0
3 years ago
6 - 3x = 5x - 10x + 8
Jet001 [13]

Answer:

x=1

Step-by-step explanation:

6-3x=5x-10x+8=

move all terms to the left:

6-3x-(5x-10x+8)=0

add all the numbers together, and all the variables

-3x-(-5x+8)+6=0

get rid of parentheses

-3x+5x-8+6=0

add all the numbers together, and all the variables

2x-2=0

move all terms containing x to the left, all other terms to the right

2x=2

x=2/2

x=1

3 0
3 years ago
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