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Zina [86]
3 years ago
9

15, Evaluate 6 choose 4.

Mathematics
1 answer:
Novosadov [1.4K]3 years ago
4 0

Answer:  The required result is 15.

Step-by-step explanation:  We are given to evaluate the following :

"6 choose 4".

Since we are to choose 4 from 6, so we have to use the combination of 6 different things chosen 4 at a time.

We know that

the formula for the combination of n different things chosen r at a time is given by

^nC_r=\dfrac{n!}{r!(n-r)!}.

For the given situation, n = 6  and  r = 4.

Therefore, we get

^6C_4=\dfrac{6!}{4!(6-4)!}=\dfrac{6!}{4!2!}=\dfrac{6\times5\times4!}{4!\times2\times1}=15.

Thus, the required result is 15.

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What is the explicit formula for the sequence -9,-3,3,9,15​
astra-53 [7]

Answer:

B

Step-by-step explanation:

The difference between each term is six and the numbers are increasing so the only one that is in the correct format, which is an = a1 + (n-1)d, is B

please give Brainliest

3 0
3 years ago
Complete this proof.<br><br> Given: EC AC, DB AC, ∠A = ∠F<br> Prove: ΔMDF ∼ ΔNCA
Gelneren [198K]

Answer:

Proved

Step-by-step explanation:

Given: EC || AC, DB || AC, ∠A = ∠F

Prove: ΔMDF ∼ ΔNCA

Solution

See diagram attached to the solution to better understand the following workings.

Redrawing ΔMDF or rotating to be facing the same direction.

EC is parallel to AC

DB parallel to AC

Using similar triangle theorem:

If ΔMDF ∼ ΔNCA

Ratio of Corresponding sides would be equal

(adjacent of ΔMDF)/(adjacent of ΔNCA) = (Opposite of ΔMDF)/(opposite of ΔNCA) = (hypotenuse of ΔMDF)/(hypotenuse of ΔNCA)

DF/ CA = MD/NC = FM/AN

∠A = ∠F

∠M = ∠N

∠D = ∠C

Since the ratio of Corresponding sides and angle are equal, ΔMDF is similar to ΔNCA.

ΔMDF ∼ ΔNCA

6 0
3 years ago
Read 2 more answers
Suppose that 12% of test scores for the unit 1 test were above 85 and 8% were below 70. Assuming a normal
Doss [256]

Answer:

Mean = 78.2

Standard deviation = 5.8

Step-by-step explanation:

Mathematically z-score;

= (x-mean)/SD

From the question;

12% of test scores were above 85

Thus;

P( x > 85) = 12%

P(x > 85) = 0.12

Now let’s get the z-score that has a probability of 0.12

This can be obtained from the standard normal distribution table and it is = 1.175

Thus;

1.175 = (85 - mean)/SD

let’s call the mean a and the SD b

1.175 = (85-a)/b

1.175b = 85 - a

a = 85 - 1.175b ••••••••(i)

Secondly 8% of scores were below 70

Let’s find the z-score corresponding to this proportion;

We use the standard normal distribution table as usual;

P( x < 70) = 0.08

z-score = -1.405

Thus;

-1.405 =( 70-a)/b

-1.405b = 70-a

a = 70 + 1.405b ••••••(ii)

Equate the two a

70 + 1.405b = 85 - 1.175b

85 -70 = 1.405b + 1.175b

15 = 2.58b

b = 15/2.58

b = 5.81

a = 70 + 1.405b

a = 70 + 1.405(5.81)

a = 78.16

So mean = 78.2 and Standard deviation is 5.8

4 0
3 years ago
A triangle was dilated by a scale factor of 6. If sin aº
Pavlova-9 [17]

Answer:

24 units

Step-by-step explanation:

A triangle was dilated by a scale factor of 6. If sin a° = four fifths and segment DE measures 30 units, how long is segment EF?

triangle DEF in which angle F is a right angle, angle D measures a degrees, and angle E measures b degrees

15.5 units

24 units

30 units

37.5 units

From the description:

angle D measures a degrees

opposite to angle D is side EF

side DE (which measures 30 units) is the hypotenuse of the triangle.

We also know that

\sin (a) = \frac{4}{5}

\sin (a) = \frac{opposite}{hypotenuse}

From definition:

\sin (a) = \frac{opposite}{hypotenuse}

Replacing:

\frac{4}{5} =\frac{ EF}{DE} \\\\EF = \frac{4}{5} *DE\\\\EF = \frac{4}{5} *30 \\\\= 24 units

8 0
3 years ago
How will you graphically represent data in cyber security with math?
qaws [65]

Answer:

Step-by-step explanation:

another math-based concept used in cybersecurity is hexadecimal math. Rather than having only two options, as in binary math, hexadecimal math is based on the idea that you can count up to any one of 16 different options. ... Cryptography is the science of codes and encryption and is based on mathematical theory

3 0
2 years ago
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