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Arlecino [84]
3 years ago
10

En red socks and ten blue socks are all mixed up in a dresser drawer. The 20 socks are exactly alike except for their colour. Th

e room is in pitch darkness and you want two matching socks. What is the smallest number of socks you must take out of the drawer in order to be certain that you have a pair that match?
Mathematics
1 answer:
Gennadij [26K]3 years ago
5 0

Answer:

3 socks

Step-by-step explanation:

Given that, there are 10 red socks and 10 blue socks which are mixed up in the dresser drawer.

The socks are identical except the color.

We need to find out, the minimum number of socks to be taken out from the dark room so that there is at least a pair of matching socks comes out of the drawer.

Let us consider the cases:

First Two socks pulled out of the drawer.

Case 1: Both are red or both are blue.

In this case, the matching pair is ready.

But there can be other case as well.

Case 2:

One red and one blue color taken out.

Now, when we pull the third, there will be either red or blue.

That will make a pair.

Therefore, to cover up all the cases and to be certain to get a matching pair out of the drawer, <em>at least 3 socks must be taken out</em>.

So, the answer is:

We need to take out at least 3 socks.

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Mila graphs the point A
melamori03 [73]
Answers:
B. <span>The x-coordinate of point A is 5.
</span>E. <span>Point A is on the x-axis.
</span>
Explanation:
Any point drawn on the coordinates has the general notation of (x,y).
The given point is (5,0). This means that:
The x-coordinate of the point is 5
The y-coordinate of the point is 0

Now, let's check the place of this point.
The x-coordinate of the point is 5. This means that we will move 5 points to the right of the origin on the x-axis
The y-coordinate of the point is 0. This means that we will not move along the y-axis which means that the point stays on the x-axis.

Now, comparing the deduced results with the given choices, we will find that the correct choices are B and E

Hope this helps :)
6 0
3 years ago
Determine if the two triangles are congruent if they are state how do you know SSS,SAS,HL,ASA, OR AAS. Be sure to include any ex
dlinn [17]
1: yes AAS
2: yes SSS reflective
3: yes ASA
4: yes HL reflective
5: no SSA vertical
6: yes SAS vertical

Not sure on vocabulary for 1 and 3 sorry:(
7 0
2 years ago
What is the exact value of the expression the square root of 486. − the square root of 24. + the square root of 6.? Simplify if
kenny6666 [7]
Sqrt(486) - sqrt(24) + sqrt(6)

find the factors of 486 that we can remove from under the square root sign
 2 * 243
 2 * 3 * 81
 2 * 3 * 9 * 9 (we have 2 nines, we can move a 9 outside the sqrt sign)
sqrt(486) = 9 sqrt(6)

Repeating for sqrt(24)
2 * 12
2 * 2 * 6
2 * 2 * 2 * 3 (we can move a 2 outside the sqrt
sqrt(24) = 2 sqrt(6)

Finally, add all 3 terms together

9 sqrt(6) - 2 sqrt(6) + sqrt(6)
8 sqrt(6)

8 times square root of 6 is the final answer
8 0
3 years ago
Determine the value of x for the following isosceles triangle.
andrew11 [14]

Given :

▪︎This triangle is an isosceles triangle.

▪︎Measure of one of its legs = 6 inches

▪︎Measure of its equivalent leg = \tt \frac{x}{9} inches

▪︎Measure of its base = \tt \frac{5}{2} inches

Which means :

=\tt 6 =  \frac{x}{9}

=\tt  \frac{6}{1}  =  \frac{x}{9}

=\tt 6 \times 9  = x \times 1

\hookrightarrow\color{plum}\tt 54 = x

Let us check whether or not we have found out the correct value of x by placing 54 in the place of x :

=\tt 6 =  \frac{54}{9}

= \tt6 = 6

Since the Left Hand Side of the equation is equivalent to the Right Hand Side of the equation, we can conclude that we have found out the correct value of x.

▪︎Therefore, the value of <u>x = 54</u>

8 0
2 years ago
A data set includes 103 body temperatures of healthy adult humans having a mean of 98.1 F and a standard deviation of 0.56 F. Co
Ira Lisetskai [31]

Answer:

The 99​% confidence interval estimate of the mean body temperature of all healthy humans is (97.955F, 98.245F).

98.6F is above the upper end of the interval, which means that the sample suggests that the mean body temperature could be lower than 98.6F.

Step-by-step explanation:

The first step is finding the confidence interval

The sample size is 103.

The first step to solve this problem is finding how many degrees of freedom there are, that is, the sample size subtracted by 1. So

df = 103-1 = 102

Then, we need to subtract one by the confidence level \alpha and divide by 2. So:

\frac{1-0.99}{2} = \frac{0.01}{2} = 0.005

Now, we need our answers from both steps above to find a value T in the t-distribution table. So, with 102 and 0.005 in the t-distribution table, we have T = 2.63.

Now, we need to find the standard deviation of the sample. That is:

s = \frac{0.56}{\sqrt{103}} = 0.055

Now, we multiply T and s

M = T*s = 2.63*0.055 = 0.145

For the lower end of the interval, we subtract the mean by M. So 98.1 - 0.145 = 97.955F.

For the upper end of the interval, we add the mean to M. So 98.1 + 0.145 = 98.245F.

The 99​% confidence interval estimate of the mean body temperature of all healthy humans is (97.955F, 98.245F).

98.6F is above the upper end of the interval, which means that the sample suggests that the mean body temperature could be lower than 98.6F.

5 0
3 years ago
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