Please help. 4) What is the equation of the circle?

A triangle has a perimeter of 58 cm the longest side is twice as long as the shortest side the third side is 10cm longer than th

Natali [406]

Shortest side= x longest side= 2x third side= 10cm+x
58cm=x+2x+10cm+x
58cm=4x+10cm
48cm=4x
12cm=x
shortest side= 12cm longest side= 24cm third side=22cm

5 0

3 years ago

Use Gauss's approach to find the following sum (do not use formulas):5+11+17+23...+83

LUCKY_DIMON [66]

Denote the sum by S. So

S = 5 + 11 + 17 + 23 + ... + 83

There's a constant difference of 6 between consecutive terms in S, so the 3 terms before 83 are 77, 71, and 65. So

S = 5 + 11 + 17 + 23 + ... + 65 + 71 + 77 + 83

Gauss's approach involves inverting the sum:

S = 83 + 77 + 71 + 65 + ... + 23 + 17 + 11 + 5

If we add terms in the same position in the sums, we get

2S = (5 + 83) + (11 + 77) + ... + (77 + 11) + (83 + 5)

and we notice that each grouped term on the right gives a total of 88. So the right side consists of several copies n of 88, which means

2S = 88n

and dividing both sides by 2 gives

S = 44n

Now it's a matter of determining how many copies get added. The terms in the sum form an arithmetic progression that follows the pattern

11 = 5 + 6

17 = 5 + 2*6

23 = 5 + 3*6

and so on, up to

83 = 5 + 13*6

so n = 13, which means the sum is S = 44*13 = 572.

8 0

3 years ago

Make a tree diagram and find each probability.

Dafna11 [192]

Answer: a) probability that the game will be canceled= 45%

b) probability there will be a light drizzle and the game will not be canceled=20%

Step-by-step explanation:

Since we have given that

Probability of heavy fog is given by

$P(F)=0.70$

Probability of a light drizzle is given by

$P(D)=0.30$

Probability of getting canceled a softball game due to light drizzle is given by

$P(C\mid D)=0.80$

Probability of getting canceled a softball game due to heavy fog is given by

$P(C\mid F)=0.30$

a. Find the probability that the game will be canceled.

Probability of getting the game be cancelled is given by

$P(C)=P(F)\times P(C\mid F)+P(D)\times P(C\mid D)\\\\P(C)=0.70\times 0.30+0.30\times 0.80\\\\P(C)=0.45\\\\P(C)=45\%$

b. Find the probability there will be a light drizzle and the game will not be canceled.

Probability that there will be a light drizzle and the game will not be canceled is given by

$P(C'\mid D)=1-P(C\mid D)\\\\P(C'\mid D)=1-0.80\\\\P(C'\mid D)=0.20\\\\P(C'\mid D)=20\%$

Hence, a) probability that the game will be canceled= 45%

b) probability there will be a light drizzle and the game will not be canceled=20%

8 0

3 years ago

An ice cream store with 12 different flavors sell one and two scoop ice cream cones. A boy sitting outside the store counted 11

eduard

The answer is b and e

6 0

3 years ago

Read 2 more answers

What is the equation that matches this table?

12345 [234]

Answer:

y = –1 + 3x

Step-by-step explanation:

To know which option is correct, we shall use the equation given in each option to see which will validate the table. This is illustrated below:

Option 1

y = –1x + 3

x = –2

y = –1(–2) + 3

y = 2 + 3

y = 5

This did not give the required value of y (i.e –7) in the table.

Option 2

y = 1 + 3x

x = –2

y = 1 + 3(–2)

y = 1 – 6

y = –5

This did not give the required value of y (i.e –7) in the table.

Option 3

y = –3 + 1x

x = –2

y = –3 + 1(–2)

y = –3 – 2

y = –5

This did not give the required value of y (i.e –7) in the table.

Option 4

y = –1 + 3x

x = –2

y = –1 + 3(–2)

y = –1 – 6

y = –7

This gives the required value of y (i.e –7) in the table.

Thus, the equation that matches the table is:

y = –1 + 3x

6 0

3 years ago