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zimovet [89]
3 years ago
9

Enzo and Beatriz are playing games at their local arcade. Incredibly, Enzo wins 55 tickets from every game, and Beatriz wins 111

1 tickets from every game. When they stopped playing games, Enzo and Beatriz had won the same number of total tickets. What is the minimum number of games that Enzo could have played?
Mathematics
1 answer:
madam [21]3 years ago
8 0

Answer:

101

Step-by-step explanation:

Note that

  • 55=5\cdot 11;
  • 1111=11\cdot 101.

Here these two numbers have the common divisor 11. Find the least common multuply:

LCM(55,1111)=11\cdot 5\cdot 101=5555.

This means that  the minimum number of games that Enzo could have played will be

\dfrac{5555}{55}=101.

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Find four consecutive multiples of 3 such that the product of the first, third, and fourth is 1080
Dovator [93]

Answer:

<u>Therefore, we have 6, 9, 12, and 15, that are the first, second, third and fourth consecutive multiples of 3, such the product of 6, 12 and 15 is 1,080.</u>

Step-by-step explanation:

Let's find the factors of 1,080, as follows:

1,080 Dividing by 2 (1,080/2)

540 Dividing by 2 (540/2)

270 Dividing by 2 (270/2)

135 Dividing by 3 (135/3)

45 Dividing by 3 (45/3)

15 Dividing by 3 (15/3)

5 Dividing by 5 (5/5)

1

In consequence, we have:

5 * 3 * 3 * 3 * 2 * 2 * 2

Let's find out what multiples of 3 there are:

5 * 3 = 15 is a multiple of 3,

And 3 * 3 * 2 * 2 * 2 is remaining.

3 * 2 = 6 is also a multiple of 3,

And 3 * 2 * 2 is remaining

3 * 2 * 2 = 12 is also a multiple of 3.

<u>Therefore, we have 6, 9, 12, and 15, that are the first, second, third and fourth consecutive multiples of 3, such the product of 6, 12 and 15 is 1,080.</u>

7 0
3 years ago
A company pays its employees a fixed base salary and a commission based on sales. The scatter plot below shows the total earning
Monica [59]

I'm assuming the question is

A company pays its employees a fixed base salary and a commission based on sales. The scatter plot shows the total earning of an employee of the company (y) based on sales (x):

Plot the ordered pairs 0, 10 and 100, 20 and 200, 30 and 300, 40 and 400, 50 and 500, 60

Which function best represents the data in the scatter plot? (1 point)

y = 0.1x + 10

y = 0.1x − 10

y = 0.1x + 1

y = 0.2x − 1

So thus your answer would be y = 0.1x + 10

5 0
3 years ago
While conducting experiments, a marine biologist selects water depths from a uniformly distributed collection that vary between
aleksandr82 [10.1K]

Answer:

The probability that a randomly selected depth is between 2.25 m and 5.00 m is 0.55.

Step-by-step explanation:

Let the random variable <em>X</em> denote the water depths.

As the variable water depths is continuous variable, the random variable <em>X</em> follows a continuous Uniform distribution with parameters <em>a</em> = 2.00 m and <em>b</em> = 7.00 m.

The probability density function of <em>X</em> is:

f_{X}(x)=\frac{1}{b-a};\ a

Compute the probability that a randomly selected depth is between 2.25 m and 5.00 m as follows:

P(2.25

                               =\frac{1}{5.00}\int\limits^{5.00}_{2.25} {1} \, dx\\\\=0.20\times [x]^{5.00}_{2.25} \\\\=0.20\times (5.00-2.25)\\\\=0.55

Thus, the probability that a randomly selected depth is between 2.25 m and 5.00 m is 0.55.

6 0
3 years ago
On a coordinate plane, a parabola opens up. It goes through (negative 2, 4), has a vertex at (0.25, negative 6), and goes throug
serg [7]

The statements true about the the function f(x) = 2x2 – x – 6 are-

  • The vertex of the function is (one-quarter, negative 6 and one-eighth).
  • The function has two x-intercepts.

<h3>What is vertex of parabola?</h3>

The vertex of parabola is the point at the intersection of parabola and its line of symmetry.

Now the given function is,

f(x) = 2x^2 – x – 6

Also, it is given that the vertex is located at (0.25, -6)  and the parabola opens up, the function has two x-intercepts.

Comparing the given function with standard form,

f(x) = a x^2 bx + c

By comprison we get,

a = 2

b = -1

c = -6

Now, x-coordinate of vertex is given as,

x = -b/2a

put the values we get,

x = -(-1)/2*2

or, x = 1/4

Put the value of x in given function, so y-coordinate of the vertex is given as,

f(1/4) = 2(1/4)² - 1/4 - 6

        = -49/6

       = -6 1/8

Hence, The statements true about the the function f(x) = 2x2 – x – 6 are-

  • The vertex of the function is (one-quarter, negative 6 and one-eighth).
  • The function has two x-intercepts.

More about vertex :

brainly.com/question/86393

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3 0
1 year ago
WILL GIVE BRAINLIEST TO CORRECT ANSWER
Aliun [14]

Answer:

Total number of outcomes = 23

number of biology and art students = 2

number of biology students = 2

Since it is given that all the students study art,

number of possible outcomes = 2

probability = number of favorable outcomes/number of total outcomes.

= 2/23

Therefore probability that the selected student studies both art and biology is 2/23.

7 0
3 years ago
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