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Catalina skates 40 feet due north in a skating rink. Then she skates 30 feet due west, before skating diagonally across the rink

Andre45 [30]

Answer:

Catalina skates a total of 120 feet

Step-by-step explanation:

In order to determine how far she skates, create a right triangle. We know each legs' value with one being 30 and the other 40. Now we can find the hypotenuse by using the Pythagorean Theorem.

a^2 + b^2 = c^2

30^2 + 40^2= c^2

900 + 1600 = c^2

2500 = c^2

50 = c

Now that we have all 3 sides of the right triangle, add them together for the total distance.

30 + 40 + 50 = 120 feet

7 0

3 years ago

In the past you paid $800 per month to rent your apartment. You now pay $900 per month for your rent. What is the percent increa

Leni [432]

The percent increase is 12.5%, 800 multiplied by 0.125 equals 100 and 100+800=900.

6 0

3 years ago

Read 2 more answers

You always need some time to get up after the alarm has rung. You get up from 10 to 20 minutes later, with any time in that inte

Mama L [17]

Answer:

a) P(x<5)=0.

b) E(X)=15.

c) P(8<x<13)=0.3.

d) P=0.216.

e) P=1.

Step-by-step explanation:

We have the function:

$f(x)=\left \{ {{\frac{1}{10},\, \, \, 10\leq x\leq 20 } \atop {0, \, \, \, \, \, \, otherwise }} \right.$

a) We calculate the probability that you need less than 5 minutes to get up:

$P(x$

Therefore, the probability is P(x<5)=0.

b) It takes us between 10 and 20 minutes to get up. The expected value is to get up in 15 minutes.

E(X)=15.

c) We calculate the probability that you will need between 8 and 13 minutes:

$P(8\leq x\leq 13)=P(10\leqx\leq 13)\\\\P(8\leq x\leq 13)=\int_{10}^{13} f(x)\, dx\\\\P(8\leq x\leq 13)=\int_{10}^{13} \frac{1}{10} \, dx\\\\P(8\leq x\leq 13)=\frac{1}{10} \cdot [x]_{10}^{13}\\\\P(8\leq x\leq 13)=\frac{1}{10} \cdot (13-10)\\\\P(8\leq x\leq 13)=\frac{3}{10}\\\\P(8\leq x\leq 13)=0.3$

Therefore, the probability is P(8<x<13)=0.3.

d) We calculate the probability that you will be late to each of the 9:30am classes next week:

$P(x>14)=\int_{14}^{20} f(x)\, dx\\\\P(x>14)=\int_{14}^{20} \frac{1}{10} \, dx\\\\P(x>14)=\frac{1}{10} [x]_{14}^{20}\\\\P(x>14)=\frac{6}{10}\\\\P(x>14)=0.6$

You have 9:30am classes three times a week. So, we get:

$P=0.6^3=0.216$

Therefore, the probability is P=0.216.

e) We calculate the probability that you are late to at least one 9am class next week:

$P(x>9.5)=\int_{10}^{20} f(x)\, dx\\\\P(x>9.5)=\int_{10}^{20} \frac{1}{10} \, dx\\\\P(x>9.5)=\frac{1}{10} [x]_{10}^{20}\\\\P(x>9.5)=1$

Therefore, the probability is P=1.

3 0

3 years ago

Can you please help,I will mark the Brainlest too!<br> Picture below<br> Thanks :)

8_murik_8 [283]

Answer:

55

Step-by-step explanation:

That’s a ninety degree angle

90-35=55

4 0

3 years ago

Read 2 more answers

Find the image of (–7, –3) reflected across the x-axis. A. (–7, 3) B. (7, –3) C. (7, 3) D. (–7, –3)

Naddika [18.5K]

Answer:

(-7, -3) (Answer A)

Step-by-step explanation:

We start with the point (-7, -3). The x-coordinate does not change at all if we reflect this point across the x-axis. Whereas the y-value of (-7, -3) is -3, we end up with +3 after this reflection. The desired image is (-7, +3) (Answer A)

8 0

3 years ago