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IrinaVladis [17]
2 years ago
6

A number in which each digit except 0 appears exactly 3 times is divisible by 3. for​ example, 777,555,222 and​ 414,143,313 are

divisible by 3. explain why this is true
Mathematics
1 answer:
balandron [24]2 years ago
4 0
The sum of digits of such a number is a multiple of 3. According to the divisiblity rule for 3, that is all that is required for a number to be divisible by 3.
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A batter strikes a baseball. the equation y = -0.005^2 +0.7x + 3.5 models its path, where x is the horizontal distance, in feet,
hram777 [196]

Answer:

(D)144.8 feet

Step-by-step explanation:

Given the equation which models the path of the baseball

y = -0.005x^2 +0.7x + 3.5

where x is the horizontal distance, in feet, the ball travels and y is the height, in feet, of the ball.

To determine how far from the batter the ball will land, we determine the distance x at which the height, y=0.

y = -0.005x^2 +0.7x + 3.5=0

-0.005x^2 +0.7x + 3.5=0

We use the quadratic formula to solve.

In the quadratic equation above, a=-0.005, b=0.7, c=3.5

x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a} \\=\dfrac{-0.7\pm\sqrt{0.7^2-4(-0.005*3.5)} }{2*-0.005} \\=\dfrac{-0.7\pm\sqrt{0.49+0.07} }{-0.01}\\=\dfrac{-0.7\pm\sqrt{0.56} }{-0.01}\\x=\dfrac{-0.7+\sqrt{0.56} }{-0.01} \: or\: x=\dfrac{-0.7-\sqrt{0.56} }{-0.01}\\x=-4.83 \: or\: x=144.83

Since x cannot be negative, x=144.8 feet to the nearest tenth of a foot.

<u>The correct option is D.</u>

6 0
2 years ago
Ethan Makes $6 per hour mowing lawns and $7.50 per hour bagging groceries. last week, he made a total of $129. the difference be
zlopas [31]
Let x be the number of hours of nagging groceries spent by Ethan. With this representation, the number of hours for moving lawns will be x + 10. The equation that would let us solve this item is,

                6x + 7.50(x + 10) = 129

The value of x from the equation is 4. Thus, the number of hours spent for moving lawns is 14 hours. 
4 0
2 years ago
Read 2 more answers
Player V and Player M have competed against each other many times. Historical data show that each player is equally likely to wi
Helen [10]

Answer:

0.46 (46%)

Step-by-step explanation:

We have the following data:

- Probability that player V wins the first set:

p(1)=0.50

(because the text says the two players are equally likely to win the first set)

- Probability that player V wins the 2nd set if he has won the 1st set:

p(2|1)=0.60

So, the probability that player V wins the first 2 sets is:

p(12)=p(1)\cdot p(2|1)=(0.50)(0.60)=0.30 (1)

Instead, the probability that player V loses the 2nd set if he has won the 1st set is 0.40 (=1-0.60), so

p(2^c|1)=0.40

So, the probabiity that player V winse the 1st set but loses the 2nd set is

p(12^c)=p(1)\cdot p(2^c|1)=(0.50)(0.40)=0.20 (2)

Also, we have:

- Probability that player V loses the 1st set:

p(1^c)=0.50

- Probability that she will lose the 2nd set in this case is 0.70, it means that the probability that she will win the 2nd set if she lost the 1st set is 0.30, so:

p(2|1^c)=0.30

So, the probability that she will lose the 1st set and win the 2nd set is:

p(1^c2)=p(1^c)\cdot p(2|1^c)=(0.50)(0.30)=0.15 (3)

Combined together (2) and (3), this means that the probability that player V wins exactly 1 set out of the first two sets is:

p(1/2)=p(12^c)+p(1^c2)=0.20+0.15=0.35 (4)

At this point, the probability that she will win the 3rd set is

p(3)=0.45

This means that the overall probability that she will win the 3rd set if she won exacty 1 of the first 2 sets is:

p(1/2,3) = p(1/2)\cdot p(3)=(0.35)(0.45)=0.16 (5)

So, the overall probability that player V will win a match against player M is the sum of (1) and (5):

p(W)=p(12)+p(1/2,3)=0.30+0.16=0.46

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2 years ago
Point A has coordinates (7,2). Point B has coordinates (2,-10). Find the coordinates of point P that partition AB in the ratio o
aleksklad [387]
You have to use section formula for internal division.

4 0
1 year ago
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The ceiling of Katie’s living room is a square that is 10 ft long on each side. Katie knows the diagonal of the ceiling from cor
CaHeK987 [17]

Answer:

Answer: 14 feet. a. The Pythagorean theorem is a^2 + b^2 = c^2, where a and b are the sides of a right angle. By plugging in the sides of the wall, and solving for c, you can find the answer. 10^2 + 10^2 = c^2

| 100 + 100 = c^2 | 200 = c^2 | c = sqrt 200 | c = 14. The other way to solve this would be using the trig functions. You know that the angle between the hypotenuse and the wall side is 45 degrees, so you can use Sine to determine the hypotenuse. Sine is equal to opposite over hypotenuse. Sin (45) = 10/h | Sin (45) * h = 10 | h = 10/Sin (45) | h = 14. Both of the methods result in 14.

Read more on Brainly.com - brainly.com/question/16274528#readmore

Step-by-step explanation:

5 0
1 year ago
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