A gallon of water weighs 8 1/3 lb. How much does 1 1/5 gallon of water weigh?

Transformations can be thought of as functions that take the points from one object (the pre-image) to the corresponding points

sweet-ann [11.9K]

1. Translation of a units to the right and b units up has rule:

(x,y)→(x+a,y+b).

Then the function is

$T(x,y)=(x+a,y+b).$

2. Reflection across the y-axis acts in following way:

(x,y)→(-x,y).

Then the function is

$R_y(x,y)=(-x,y).$

3. Reflection across the x-axis acts in following way:

(x,y)→(x,-y).

Then the function is

$R_x(x,y)=(x,-y).$

4. Rotation of 90 degrees counterclockwise about the origin, point O acts bu the rule:

(x,y)→(-y,x).

Then the function is

$R_{O,90^{\circ}}(x,y)=(-y,x).$

5. Rotation of 180 degrees counterclockwise about the origin, point O acts bu the rule:

(x,y)→(-x,-y).

Then the function is

$R_{O,180^{\circ}}(x,y)=(-x,-y).$

6. Rotation of 270 degrees counterclockwise about the origin, point O acts bu the rule:

(x,y)→(y,-x).

Then the function is

$R_{O,270^{\circ}}(x,y)=(y,-x).$

4 0

3 years ago

Help me plz I neeed

dybincka [34]

AnsWER:

shaded: 40% unshaded 60%

Step-by-step explanation:

ONLY 4 ROWS ARE SHADED

non shaded are 6 rows

10 rows in total

8 0

3 years ago

Read 2 more answers

Below is the graph of y = |x| . .Translate it to make it the graph of of y=|x-2|+4

sineoko [7]

Explanation

Given a function f(x) we translate the function:

• a units horizontally (a > 0 to the right, a < 0 to the left),

,

• b units vertically (b > 0 up, b < 0 down),

by the transformation:

$f(x)\rightarrow g(x)=f(x-a)+b.$

In this case, we have:

$\begin{gathered} f(x)=|x|, \\ g(x)=|x-2|+4=f(x-2)+4. \end{gathered}$

Comparing f(x) and g(x) with the general transformation above, we see that the graph of g(x) is the graph of f(x) translated:

• a = 2 units to the right,

,

• b = 4 units up.

Translating the graph of f(x), we get:

Answer

The translated graph is the graph in red:

7 0

1 year ago

Lake Okeechobee’s water level was at sea level in April. In May, the lake’s level rose 4 inches and in June it rose 2 more inche

Mice21 [21]

Answer:

Just here for points XD.

Step-by-step explanation:

7 0

3 years ago

Construct a 99% confidence interval for the population mean, mu. Assume the population has a normal distribution. A group of 1

Zarrin [17]

Answer:

99% confidence interval for the population mean is [19.891 , 24.909].

Step-by-step explanation:

We are given that a group of 19 randomly selected students has a mean age of 22.4 years with a standard deviation of 3.8 years.

Assuming the population has a normal distribution.

Firstly, the pivotal quantity for 99% confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean age of selected students = 22.4 years

s = sample standard deviation = 3.8 years

n = sample of students = 19

$\mu$ = population mean

<em>Here for constructing 99% confidence interval we have used t statistics because we don't know about population standard deviation.</em>

So, 99% confidence interval for the population mean, $\mu$ is ;

P(-2.878 < $t_1_8$ < 2.878) = 0.99 {As the critical value of t at 18 degree of

freedom are -2.878 & 2.878 with P = 0.5%}

P(-2.878 < $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ < 2.878) = 0.99

P( $-2.878 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X - \mu}$ < $2.878 \times {\frac{s}{\sqrt{n} } }$ ) = 0.99

P( $\bar X -2.878 \times {\frac{s}{\sqrt{n} }$ < $\mu$ < $\bar X +2.878 \times {\frac{s}{\sqrt{n} }$ ) = 0.99

<u>99% confidence interval for</u> $\mu$ = [ $\bar X -2.878 \times {\frac{s}{\sqrt{n} }$ , $\bar X +2.878 \times {\frac{s}{\sqrt{n} }$ ]

= [ $22.4 -2.878 \times {\frac{3.8}{\sqrt{19} }$ , $22.4 +2.878 \times {\frac{3.8}{\sqrt{19} }$ ]

= [19.891 , 24.909]

Therefore, 99% confidence interval for the population mean is [19.891 , 24.909].

6 0

3 years ago