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1 year ago

15

Lyle graphs triangle ABC on coordinate axes. He performs two transformations on this figure that result in the congruent triangl

e XYZ Which series of transformations did Lyle most likely use?
a translation left and then a dilation with a scale factor of 3
a dilation with a scale factor of 2.5 and then a rotation 180' counterclockwise
a rotation 90' clockwise and then a reflection across the y-axis
a reflection across the x-axis and then a dilation with a scale factor of 0.25
C

1 answer:

Shtirlitz [24]1 year ago

3 0

Answer:

a rotation 90˚ clockwise and then a reflection across the y-axis

Step-by-step explanation:

I'm doing the test right now

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A class in advanced physics is composed of 10 juniors, 30 seniors, and 10 graduate students. the final grades show that 3 of the

const2013 [10]

Solution: We are given:

Total students = 10 + 30 + 10 =50

Number of students who received A grade = 3 + 10 + 5 = 18

Number of senior student's who received A grade is = 10

Let A be the event that the student is senior and B be the event that he or she earned an A. Then,

$P(A \cap B)=\frac{10}{50}$

$P(B) = \frac{18}{50}$

Now the probability a student chosen at random from this class and is found to have earned an A, the probability that he or she is a senior is:

$P(A|B) = \frac{P(A \cap B}{P(B)}$

$=\frac{\frac{10}{50} }{\frac{18}{50} }$

$=\frac{10}{18}=\frac{5}{9} =0.556$

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2 years ago

At a cell phone assembly plant, 77% of the cell phone keypads pass inspection. A random sample of 111 keypads is analyzed. Find

Serggg [28]

Answer:

The probability that the proportion of passed keypads is between 0.72 and 0.80 is 0.6677.

Step-by-step explanation:

According to the Central limit theorem, if from an unknown population large samples of sizes <em>n</em> > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

$\mu_{\hat p}=p$

The standard deviation of this sampling distribution of sample proportion is:

$\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}$

Let <em>p</em> = the proportion of keypads that pass inspection at a cell phone assembly plant.

The probability that a randomly selected cell phone keypad passes the inspection is, <em>p</em> = 0.77.

A random sample of <em>n</em> = 111 keypads is analyzed.

Then the sampling distribution of $\hat p$ is:

$\hat p\sim N(p,\ \sqrt{\frac{p(1-p)}{n}})\\\Rightarrow \hat p\sim N (0.77, 0.04)$

Compute the probability that the proportion of passed keypads is between 0.72 and 0.80 as follows:

$P(0.72$

$=P(-1.25$

Thus, the probability that the proportion of passed keypads is between 0.72 and 0.80 is 0.6677.

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2 years ago

Johan works in a cafe.

Ksenya-84 [330]

Answer:

4:1

Step-by-step explanation:

The ratio at first would be 48:12, after this to simplify it we need to find the gcf (greatest/biggest common factor), which is 12. Dividing 48 by 12 gives us 4 and dividing 12 by 12 gives us 1, thus making the ratio 4:1

6 0

1 year ago

The measure of rst can be represented by the expression (6x+12)

Vitek1552 [10]

6x+12
6x=-12
-12/6
x=-2

7 0

2 years ago

Read 2 more answers

1. Maryann is tracking the change in her vertical jump over 6 months. Use the table to write a linear function that models her j

ArbitrLikvidat [17]

Answer:

Part 1) Option A. f of x equals one half times x plus 16

Part 2) Option A. x = 5

Part 3) Option C. x − 4y = −9

Part 4) Option A. The number of rides is the independent variable, and the total cost is the dependent variable.

Step-by-step explanation:

Part 1)

Let

x -----> the number of months

y ----> vertical jump in inches

step 1

Find the slope

we have the points

(0,16) and (2,17)

$m=(17-16)/(2-0)=\frac{1}{2}$

The equation of the line in slope intercept form is

$y=mx+b$

we have

$m=\frac{1}{2}$

$b=16$ -----> the point (0,16) is the y-intercept

substitute

$y=\frac{1}{2}x+16$

convert to function notation

f(x)=y

$f(x)=\frac{1}{2}x+16$

Part 2) What is the equation of a line that contains the points (5, 0) and (5, −2)?

step 1

Find the slope

we have the points

(5, 0) and (5, −2)

$m=(-2-0)/(5-5)=\frac{-2}{0}$

the slope is undefined

This is a vertical line (parallel to the y-axis)

therefore

The equation is

x=5

Part 3) Choose the equation that represents a line that passes through points (−1, 2) and (3, 1)

step 1

Find the slope

we have the points

(−1, 2) and (3, 1)

$m=(1-2)/(3+1)=-\frac{1}{4}$

step 2

Find the equation of the line into point slope form

$y-y1=m(x-x1)$

we have

$m=-\frac{1}{4}$

$point\ (3, 1)$

substitute

$y-1=-\frac{1}{4}(x-5)$

Convert to standard form

Multiply by 4 both sides to remove the fraction

$4y-4=-(x-5)$

$4y-4=-x+5$

$x-4y=-4-5$

$x-4y=-9$

Part 4) Jewels has $6.75 to ride the ferry around Connecticut. It will cost her $0.45 every time she rides. Identify the dependent variable and independent variable in this scenario

we know that

The <u>independent variable</u> is the variable whose change isn’t affected by any other variable (An example the age and time)

The <u>dependent variable</u> it’s what changes as a result of the changes to the independent variable (An example of a dependent variable is how tall you are at different ages. The dependent variable (height) depends on the independent variable (age))

Let

x ----> the number of rides

y ----> the total cost in dollars

In this problem

The independent variable or input is the number of rides

The dependent variable or output is the total cost

5 0

2 years ago