What set of reflections and rotations would carry rectangle ABCD onto itself?

rjkz [21]

1) start with (x-h)^2 + (y-k)^2 = r^2. Insert the given info: center at (-1,8) and radius 5:

(x+1)^2 + (y-8)^2 = 5^2 (answer)

7 0

3 years ago

A 20-gallon salt-water solution contains 15% pure salt. How much pure water should be added to it to produce a 10% solution?

Elanso [62]

15% of 20 gal = 0.15 * 20 gal = 3 gal, so the solution contains 3 gal of salt.

If we add x gal of water to the solution, we end up with (20 + x) gal of solution. We want the new mixture to have a concentration of 10%, or

10% of (20 + x) gal = 0.1 * (20 + x) gal = 2 + 0.1x gal

of salt.

The amount of salt in the tank hasn't changed. Solve for x :

2 + 0.1x = 3

0.1x = 1

x = 10 gal

3 0

3 years ago

For the function y = -10x find the matching y-value when x = 3

Alchen [17]

Answer:

y= -30

Step-by-step explanation:

THis is because you substitue 3 for X and then multiply -10 and 3 and a negative times a positive is a negative so -10 times 3 is -30

6 0

3 years ago

Read 2 more answers

Find the slope Thxxxx

Helga [31]

Answer:

-The slope:

$m = \frac{3}{2}$

Step-by-step explanation:

-To find the slope, you need this trick:

$m= \frac{rise}{run}$

-So, according to the graph, start to the first doted point which is (0,1) to get to the second doted point, which is (2,4) on the graph, by counting how far up and how far across:

Rise: 3

Run: 2

$m= \frac{3}{2}$

So, therefore the slope is $\frac{3}{2}$ .

6 0

3 years ago

Customers arrivals at a checkout counter in a department store per hour have a Poisson distribution with parameter λ = 7. Calcul

IgorLugansk [536]

Answer:

(1)14.9% (2) 2.96% (3) 97.04%

Step-by-step explanation:

Formula for Poisson distribution: $P(k) = \frac{\lambda^ke^{-k}}{k!}$ where k is a number of guests coming in at a particular hour period.

(1) We can substitute k = 7 and $\lambda = 7$ into the formula:

$P(k=7) = \frac{7^7e^{-7}}{7!}$

$P(k=7) = \frac{823543*0.000911882}{5040} = 0.149 = 14.9\%$

(2)To calculate the probability of maximum 2 customers, we can add up the probability of 0, 1, and 2 customers coming in at a random hours

$P(k\leq2) = P(k=0)+P(k=1)+P(k=2)$

$P(k\leq2) = \frac{7^0e^{-7}}{0!} + \frac{7^1e^{-7}}{1!} + \frac{7^2e^{-7}}{2!}$

$P(k \leq 2) = \frac{0.000911882}{1} + \frac{7*0.000911882}{1} + \frac{49*0.000911882}{2}$

$P(k\leq2) = 0.000911882+0.006383174+0.022341108 \approx 0.0296=2.96\%$

(3) The probability of having at least 3 customers arriving at a random hour would be the probability of having more than 2 customers, which is the invert of probability of having no more than 2 customers. Therefore:

$P(k\geq 3) = P(k>2) = 1 - P(k\leq2) = 1 - 0.0296 = 0.9704 = 97.04\%$

4 0

3 years ago