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2 years ago

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A lock has 5 buttons. The lock is opened by pushing two buttons simultaneously and then by pushing one button alone. How many co

mbinations are possible?

1 answer:

Pavel [41]2 years ago

7 0

We first must calculate how many ways 2 oblects can be chosen from 5.

combinations = 5! / 2! * (5-2)!

combinations = 5*4 / 2

combinations = 10

There are 10 ways to choose the 2 buttons and 5 ways to choose the final butto so there are 10 * 5 = 50 different ways.

Source

1728.com/combinat.htm

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Boden is making a prize wheel for the school fair. The ratio of winning spaces to losing spaces is shown in the diagram. The tab

IceJOKER [234]

The correct answers are Losing 12; Winning 15

Explanation:

The ratio of winning to losing is 5: 6 or 5/6. This means for every 5 winning spaces in the wheel there are 6 losing spaces. This ration should be used to complete the values of the table.

1. The first row shows there are 10 winning and you need to calculate the number of losing spaces. The process is shown below.

$\frac{5}{6} = \frac{10}{x}$ - Express the ratios using fractions; use x to show the missing value

$5x = 60$ - Cross multiply to find the value of x

$x = 60 / 5$ - Solve the equation to find x

$x = 12$ - The number of losing is 12 if there are 10 winning spaces

2. The second row shows there are 18 losing spaces, and you need to calculate the number of winning spaces. Repeat the process.

$\frac{5}{6} = \frac{x}{18}$

$6x = 90$

$x = 90 / 6$

$x =15$ - The number of winning spaces is 15 if there are 18 losing spaces

6 0

2 years ago

Read 2 more answers

What are the x- and y- coordinates of point E, which partitions the directed line segment from J to K into a ratio of 1:4? (–13,

Lana71 [14]

I added a screenshot of the complete question.

<u><em>Answer:</em></u>

(-7, -1)

<u><em>Explanation:</em></u>

<u>The formulas given to calculated the x and y coordinates are as follows:</u>

$x = (\frac{m}{m+n})(x_{2}-x_{1}) + x_{1}\\\\y = (\frac{m}{m+n})(y_{2}-y_{1}) + y_{1}$

<u>Let's define the variables used:</u>

(x₁ , y₁) are the coordinates of the first point while (x₂ , y₂) are the coordinates of the second point.

<u>We are given that the segment is directed from J to K, therefore:</u>

First point is J ..........> (x₁ , y₁) is (-15, -5)

Second point is K ....> (x₂ , y₂) is (25, 15)

m and n defined the portion of the partitioned segment (JE : EK). It is given that this ratio is 1:4. <u>Therefore:</u>

m = 1 and n = 4

<u>Finally, let's substitute with these variables in the equations as follows:</u>

$x = (\frac{1}{1+4})(25-(-15)) + (-15) = -7\\\\y = (\frac{1}{1+4})(15-(-5)) + (-5) = -1$

Based on the above, the coordinates of point E are (-7, -1)

Hope this helps :)

8 0

2 years ago

Read 2 more answers

The value -1 is a lower bound for the zeros of the function shown below.

BlackZzzverrR [31]

Answer:

false

Step-by-step explanation:

3 0

2 years ago

A thin sheet of ice is in the form of a circle. If the ice is melting in such a way that the area of the sheet is decreasing at

elena-14-01-66 [18.8K]

Answer:

dx/dt = 0,04 m/sec

Step-by-step explanation:

Area of the circle is:

A(c) =π*x² where x is a radius of the circle

Applying differentiation in relation to time we get:

dA(c)/dt = π*2*x* dx/dt

In this equation we know:

dA(c)/dt = 0,5 m²/sec

And are looking for dx/dt then

0,5 = 2*π*x*dx/dt when the area of the sheet is 12 m² (1)

When A(c) = 12 m² x = ??

A(c) = 12 = π*x² ⇒ 12 = 3.14* x² ⇒ 12/3.14 = x²

x² = 3,82 ⇒ x = √3,82 ⇒ x = 1,954 m

Finally plugging ths value in equation (1)

0,5 = 6,28*1,954*dx/dt

dx/dt = 0,5 /12.28

dx/dt = 0,04 m/sec

7 0

2 years ago

Read 2 more answers

A theatre has the capacity to seat people across two levels, the Circle and

andriy [413]

Answer: $76.19\%$

Step-by-step explanation:

<h3> The complete exercise is: " A theatre has the capacity to seat people across two levels, the Circle, and the stalls. The ratio of the number of seats in the circle to a number of seats in the stalls is 2:5. Last Friday, the audience occupied all the 528 seats in the circle and $\frac{2}{3}$ of the seats in the stalls. What is the percentage of occupancy of the theatre last Friday?"</h3>

Let be "s" the total number of seats in the Stalls.

The problem says that the ratio of the number of seats in the Circle to the number of seats in the Stalls is $2:5$ .

Since the number of seats that were occupied last Friday was 528 seats, we can set up the following proportion:

$\frac{2}{5}=\frac{528}{s}$

Solving for "s", we get:

$s*\frac{2}{5}=528\\\\s=528*\frac{5}{2}\\\\s=1,320$

So the sum of the number of seats in the Circle and the number of seats in the Stalls, is:

$Total=1,320\ seats+528\ seats=1,848\ seats$

We know that $\frac{2}{3}$ of the seats in the Stalls were occupied. Then, the number of seat in the Stalls that were occupied is:

$(1,320)(\frac{2}{3})=880$

Therefore, the total number of seats that were occupied las Friday is:

$Total\ occupied=880\ seats+528\ seats=1,408\ seats$

Knowing this, we can set up the following proportion, where "p" is the the percentage of occupancy of the theatre last Friday:

$\frac{100}{1,848}=\frac{p}{1,408}$

Solving for "p", we get:

$(1,408)(\frac{100}{1,848})=p\\\\p=76.19\%$

8 0

2 years ago