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vovangra [49]
2 years ago
15

A polar vortex causes the temperature to decrease from 3 degrees Celsius at 3:00 P.M. to -2 degrees Celsius at 4:00 P.M. The tem

perature continues to change by the same amount each hour until 8:00 P.M. Find the total change in temperature from 3:00 P.M. to 8:00 P.M.
Mathematics
1 answer:
sergey [27]2 years ago
5 0

Answer:

Wait

Step-by-step explanation:

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Three interior angles of a quadrilateral measure 55, 117 and 120 degrees. What is the measure of the fourth interior angle?
Salsk061 [2.6K]

4 angles = 360

120 + 117 +55 = 292

360-292 = 68

4th angle = 68 degrees

8 0
2 years ago
Sean and his sister, Betty equally mow 8/9th the total area of a lawn. What fraction of the total area did each of them mow? (Sh
Alexxx [7]
Since they mowed \frac{8}{9} of the lawn in two equal parts, we need to split the pieces that were mowed into two equal groups. We know that in total they mowed 8 out of the total 9 pieces of lawn, so two equal groups that make 8 would be of size 4, since \frac{8}{2}=4. Then they each mowed \frac{4}{9} of the lawn.
8 0
2 years ago
7 girls audition for 12 roles in a school play. What is the probability that at least 2 of the girls audition for the same part?
Sophie [7]

Answer:

Step-by-step explanation:

This is one minus the probability that all the girls audition for different roles. The total number of ways of assigning roles to the girls is 12^7, because to each of the 7 girls, you have a choice of 12 roles.

Then if each girl is to receive a different role, then there are 12!/5! possibilities for that. If you start assigning roles to the girls, then for the first girl, there are 12 choices, but for the next you have to choose one of the 11 different ones, so 11 for the next, and then one of the 10 remaining for the next etc. etc., and this is 12*11*10*...*6 = 12!/(12-7)! =12!/5!

The probability that a random assignment of one of the 12^7 roles would happen to be one of the 12!/5! roles where each girl has a different role, is

(12!/5!)/12^7 = 12!/(12^7 5!)

Then the probability that two or more girls addition for the same part is the probability that not all the girls are assigned different roles, this is thus:

1 - 12!/(12^7 5!)

6 0
2 years ago
Triangle KLM represents a section of a park set aside for picnic tables. The picnic area will take up approximately 400 square y
svetoff [14.1K]
Given triangle KLM with two sides given as 45 yd and 20 yd and a 25 degree angle opposite the 20 yd side.

We find the angle made at the opposite of the 45 yd side using the sine rule as follows.
\frac{\sin{A}}{a} =  \frac{\sin{B}}{b}  \\  \frac{\sin{25^o}}{20} = \frac{\sin{B}}{45}  \\ \sin{B}= \frac{45\sin{25^o}}{20} = \frac{19.0178}{20} =0.9509 \\ B=\arcsin{(0.9509)}=71.97^o

Thus, the third angle is given by 180 - 25 - 71.97 = 83.03 degrees.

We also use the sine rule to find the third side of the triangle as follows.
\frac{\sin{A}}{a} = \frac{\sin{C}}{c} \\ \frac{\sin{25^o}}{20} = \frac{\sin{83.03^o}}{c} \\ c= \frac{20\sin{83.03^o}}{\sin{25^o}} = \frac{19.8522}{\sin{25^o}} =46.97 yds

Therefore, amount of fencing needed to surround the perimeter of the picnic area = 45 + 20 + 46.97 = 111.97 ≈ 120 yds
6 0
2 years ago
Read 2 more answers
Find the area of the shape below.
lawyer [7]

9514 1404 393

Answer:

  164π cm²

Step-by-step explanation:

The area of a circle is given by the formula ...

  A = πr²

The radius (r) is half the diameter (d), so the area of a semicircle in terms of its diameter is ...

  1/2A = (1/2)(π)(d/2)² = (π/8)d²

The given shape is the combination of three (3) semicircles. The smallest has a diameter of 6 cm; the middle-sized one has a diameter of (32 cm -6 cm -8 cm) = 18 cm. The largest has a diameter of 32 cm.

The total area will be ...

  area of largest + area of middle-size - area of smallest

  = (π/8)(32² +18² -6²) = (π/8)(1312) . . . . cm²

The area of the shape is 164π cm².

4 0
1 year ago
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