In how many ways can a committee of 3 men and 2 women can be formed from 7 men and 5 women?​

Answer:

Answer is 2√37

Step-by-step explanation:

since a+bi = sqrt(144+4) = sqrt(148) = 2sqrt37

Answer:

In a class of 50 students, 30 participated in athletics and 25 participated in music. Drawing a Venn- diagram , calculate how many students ...

Answer:

ok

Step-by-step explanation:

t7y7y8 I am not going out for the

Answer:

a) 0.0156 = 1.56% probability that all children will develop the disease.

b) 0.4219 = 42.19% probability that only one child will develop the disease.

c) 0.1406 = 14.06% probability that the third children will develop the disease, given that the first two did not.

Step-by-step explanation:

For each children, there are only two possible outcomes. Either they carry the disease, or they do not. The probability of a children carrying the disease is independent of any other children, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The probability that their offspring will develop the disease is approximately .25.

This means that [tex]p = 0.25[/tex]

Three children:

This means that [tex]n = 3[/tex]

Question a:

This is P(X = 3). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 3) = C_{3,3}.(0.25)^{3}.(0.75)^{0} = 0.0156[/tex]

0.0156 = 1.56% probability that all children will develop the disease.

Question b:

This is P(X = 1). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 1) = C_{3,1}.(0.25)^{1}.(0.75)^{2} = 0.4219[/tex]

0.4219 = 42.19% probability that only one child will develop the disease.

c. The third child will develop Tay–Sachs disease, given that the first two did not.

Third independent of the first two, so just multiply the probabilities.

First two do not develop, each with 0.75 probability.

Third develops, which 0.25 probability. So

[tex]p = 0.75*0.75*0.25 = 0.1406[/tex]

0.1406 = 14.06% probability that the third children will develop the disease, given that the first two did not.

Answer:

A) 8/ 3(x-5)

Step-by-step explanation:

1) 2x+14/x^2-25 • 8x+40/6x+42=2(x+7)/ (x-5)(x+5) * 8(x+5)/ 6(x+7)

2)

after expressing every part of every fraction as product you should reduce the fraction. You can get rid of common divisor (x+5) in the denominator of the first fraction and the numerator of the second one and the common divisor (x+7) for the numerator of the first fraction and denominatorof the second one.

Then you'll get 2*8/ 6(x+5)   reduce it again, 2 and 6 have the common divisor 2

Then 8/3(x-5) is the correct answer

Step-by-step explanation:

D

*not sure about this answer pls tell me i ak right or wrong

Answer: c. A function that acts as a placeholder and returns a simple value so another function can be tested.

Step-by-step explanation:

A stub simply means a function which has an expected signature but has an incomplete implementation. It is put in place in order for codes to be tested before the functions are fully written.

A stub is a function that acts as a placeholder and returns a simple value so another function can be tested. Therefore, the correct option is C.

Answer:

9 and 20

Step-by-step explanation:

x = one number

y = 2x+2 = other number

xy = 190

x(2x+2) = 180

2x^2 +2x = 180

2x^2 +2x- 180 = 0

Factor out 2

x^2 +x -90 = 0

(x+10)(x-9) =0

Using the zero product property

x+10 = 0  x-9=0

x= -10  x=9

But they have to be positive

x = 9

y = 2x+2 = 2(9)+2 = 18+2 = 20

Answer:

1/36

Step-by-step explanation:

When you roll a die the possible outcomes are 1,2,3,4,5,6

P(1) = number of outcomes that are 1 / total outcomes

       =1/6

The events are independent so we can multiply the probabilities

P(1,1) = 1/6*1/6 = 1/36

Answer:

53 by 83.5.

just divided the two numbers by 1/4

Answer:

848 and 1336

Step-by-step explanation:

You would actually multiply 212 and 334 by 4.

You need to multiply 1/4 by 4 to get 1.

212 x 4 = 848

334 x 4 =1336

Answer:

C. 325.

Step-by-step explanation:

The last term a5 = 85

a1 = 45

Sum of n terms = n/2 (a1 + l)

So here we have n = 5, a1 = 45 and the last term l = 85

= (5/2)(45 + 85)

= 5/2 * 130

= 325.

The required sum of the arithmetic series is 325.

Arithmetic series is defined as a sequence of numbers arranged in a particular pattern.

The sum of the nth term of an arithmetic sequence is expressed as:

[tex]S_n = \frac{n}{2}[a+l]\\[/tex] where:

n is the number of terms

a is the first term

l is the last term

Given the following

a = 45

n = 5

an = l = 85

Substitute the given values in the formula above:

[tex]S_5= \frac{5}{2}(45+85)\\ S_5=\frac{5}{2}(130)\\ S_5=5 \times 65\\S_5=325[/tex]

Hence the sum of the arithmetic series is 325

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Answer:

The ratio of the perimeters of the first nonagon to the second is 3.6 to 1.

Step-by-step explanation:

Given that a regular nonagon has an area of 90 square feet, and a similar nonagon has an area of 25 square feet, to determine what is the ratio of the perimeters of the first nonagon to the second, the following calculation must be performed:

25 = 1

90 = X

90/25 = X

3.6 = X

Therefore, the ratio of the perimeters of the first nonagon to the second is 3.6 to 1.

Answer:

Step-by-step explanation:

It's geometric. The nth term differs by -5 when compared to the n+1 term.

Sum 0 to n a(-5)^n-1 where a = 2

I think this is what you want, but there is also a formula. See below.

Sum = a (r^n - 1)/(r - 1)

Answer:

67/18

Step-by-step explanation:

Find common denominator:

7 9/54 - 3 24/54

Convert to improper fraction

387/54 - 186/54

201/54

67/18

Answer:

3 15/18

Step-by-step explanation:

We start by looking at the problem, and by trying to change the denominator by finding out what number than can both go into 6 and 9.

6 x 3 = 18  9 x 2 = 18

We then change the denominator to 18.

Next, we change the whole number into a fraction. If we convert 2 whole numbers into 7 1/18, we get 5 37/18. If we convert 1 into 3 4/18, we get 2 22/18.

If we then subtract the whole numbers and fractions, the answer is

3 15/18. (It can not simplify).

Answer:

Step-by-step explanation:

y = ½(x-4)² + 13

y = ½(x² - 8x + 16) + 13

y = ½x² - 4x + 21

Answer:

yes

Step-by-step explanation:

The total amount of time university students in the United States spend sleeping, eating and drinking, and doing leisure and sports is about: Average weekday time used for full-time college and university students in the US Sleeping 36.2% Leisure and sports 17.1% 3.3% Grooming 4.2% Eating and drinking 13.8% 5.8% Educational activities 9.6% Traveling 10.0% Other Work and related activities A A 1/3 of their total time 3/5 of their total time C) 1/2 of their total time 3/4 of their total time

"Our data was consistent with what researchers have found in academic studies — that students are in bed, on average, seven to eight hours per weeknight," says Brian Wilt, Jawbone's head of data science and analytics.

On average, college students get a whopping six hours of sleep a night according to a study by the University of Georgia. Lack of sleep can take a toll on your mental health, cause a reduction in cognitive performance and affect your memory capacity!

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Step-by-step explanation:

the inequality is

[tex]c + 8 > 30[/tex]

dy/dx = 4 + √(y - 4x + 6)

Make a substitution of v(x) = y(x) - 4x + 6, so that dv/dx = dy/dx - 4. Then the DE becomes

dv/dx + 4 = 4 + √v

dv/dx = √v

which is separable as

dv/√v = dx

Integrating both sides gives

2√v = x + C

Get the solution back in terms of y :

2√(y - 4x + 6) = x + C

You can go on to solve for y explicitly if you want.

√(y - 4x + 6) = x/2 + C

y - 4x + 6 = (x/2 + C )²

y = 4x - 6 + (x/2 + C )²

Answer:

27%

Step-by-step explanation:

Let x = simple interest rate

$9000 / 36 = $250 per month

$250x = 317.5

Divide both sides by 250

250x/250 = 317.5/250

x = 1.27

Let's check

250 x 1.27 = 317.5

If you were to multiply by .27 then it would just go down

250 x .27 = 67.5

Answer:

0.47

Step-step explanation:

Add 8+7 which gives you 15. So 7/15. Then turn it into decimal form which is 0.47. Hope this helps!

Answer:

HJ = FG

Step-by-step explanation:

SAS means side - (included) angle - side.

we have one angle confirmed (at H and at G).

we have actually one side confirmed (HG), because the graphic shows that this side is shared between the triangles. so, implicitly it is not only congruent but really identical.

so, we need the confirmation of the second side enclosing the confirmed angle.

Step-by-step explanation:

D correct answer Trust me

Answer:

4

Step-by-step explanation:

The given data is :

8, 10, 12,14,16,18,20

We need to find the standard deviation. Here,

Count = 7

Sum, Σx: 98

Mean, μ: 14

The standard deviation is given by :

[tex]\sigma=\sqrt{\dfrac{1}{N}\Sigma(x_i-\mu)^2}[/tex]

or

[tex]\sigma^2=\dfrac{1}{N}\Sigma(x_i-\mu)^2\\\\=\dfrac{(8-14)^2+...+(20-14)^2}{7}\\\\=\dfrac{112}{7}\\\\\sigma^2=16\\\\\sigma=4[/tex]

So, the standard deviation of the given data is 4.

Step-by-step explanation:

Hey there!

[tex]f(x) = 3. {4}^{x} [/tex]

Then;

[tex]f(3) = 3. {4}^{3} [/tex]

[tex]f(3) = 192[/tex]

Therefore, f(3) = 192.

Hope it helps!

Answer:

LHS.= Sin 2x /( 1 + cos2x )

We have , sin 2x = 2 sinx•cosx

And. cos2x = 2cos^2 x - 1

i.e . 1+ cosx 2x = 2cos^2x

Putting the above results in the LHSwe get,

Sin2x/ ( 1+ cos2x ) =2 sinx•cosx/2cos^2x

=sinx / cosx

= Tanx

.•. sin2x/(1 + cos2x)= tanx

Step-by-step explanation:

9514 1404 393

Answer:

  (a)  M = 0.25n +100

Step-by-step explanation:

The distance between the dots on the graph is a rise of 1 grid square and a run of 2 grid squares. If we extend the sequence of dots to the left, we expect to place one at (0, 100). That is, the y-intercept of this function is 100 (eliminates choices C and D).

The rise of 1 grid square represents 25 kg, and the run of 2 grid squares represents 100 CDs. Then the slope of the function (rate of change) is ...

  slope = rise/run = 25/100 kg/CD = 0.25

Then the equation describing the points on the graph will be ...

  M = 0.25n +100

Answer:

[tex](x,y) = (1,2)[/tex] -------- [tex]R_{y-axis}[/tex]

[tex](x,y)=(2,-1)[/tex] --------- [tex]R_{y=x}[/tex]

Step-by-step explanation:

Given

[tex](x,y) = (-1,2)[/tex]

Required

[tex]R_{y-axis}[/tex]

[tex]R_{y=x}[/tex]

[tex]R_{y-axis}[/tex] implies that:

[tex](x,y) = (-x,y)[/tex]

So, we have: (-1,2) becomes

[tex](x,y) = (1,2)[/tex]

[tex]R_{y=x}[/tex] implies that

[tex](x,y) = (y,x)[/tex]

So, we have: (-1,2) becomes

[tex](x,y)=(2,-1)[/tex]

Answer:

64

Step-by-step explanation:

the different sum of money is 64

John can make 6 different sums of money. He can make $0.05 from $2, $0.15 from $1, $0.40 from $0.50, $0.90 from #0.25, $1.90 from $0.10, and $3.90 from $0.05 coins

To discover the different sums of money John can make, we are able to utilize a strategy called "coin alter" or "category" issue.

John has a $2, $1, $0.50, $0.25, $0.10, and $0.05 coin in his pocket

Step 1: Begin with a purge entirety (0).

Step 2: Include each coin group in its entirety, one at a time.

Step 3: Rehash Step 2 for all possible combinations of coins.

Let's go through the method:

With $0.05 coin: total sum = (+ $0.05) = $0.05

With $0.10 coin: total sum = ($0.05 + $0.10) = $0.15

With $0.25 coin: total sum = ($0.15 + $0.25) = $0.40

With $0.50 coin: total sum = ($0.40 + $0.50) = $0.90

With $1 coin: total sum = ($0.90 + $1) = $1.90

With $2 coin: total sum = ($1.90 + $2) = $3.90

Presently, John can make the following different sums of money from the coins:

$0.05

$0.15

$0.40

$0.90

$1.90

$3.90.

There are 6 diverse wholes of cash John can make.

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