6(a+2b+3c) USE THE DISTRIBUTIVE PROPERTY TO CREATE AN EQUIVALENT EXPRESSION!!!!!!!!

Answer:

28

Step-by-step explanation:

Let x be the missing segment

We will use the proportionality property to find x

24/16 = 42/x

Simplify 24/16

24/16= (4×6)/(4×4)= 4/6 = 3/2

So 3/2 = 42/x

3x = 42×2

3x = 84

x = 84/3

x= 28

Answer:

H0: μ=2; Ha: μ>2

Step-by-step explanation:

The null hypothesis is the default hypothesis while the alternative hypothesis is the opposite of the null and is always tested against the null hypothesis.

In this case study, the null hypothesis is that adults were eating, on average, the recommended 2 cups of vegetables a day: H0: μ=2 while the alternative hypothesis is adults were eating, on average, more than the recommended 2 cups of vegetables a day Ha: μ>2.

The lines of the inequalities are parallel, and the system of inequalities do not have any solution.

The system of inequalities are  given as:

The inequality y ≥ 2x + 1 has the following characteristics:

The inequality y ≤ 2x – 2 has the following characteristics:

See attachment for the graphs of the system of inequalities

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Answer: 6 / √26

Step-by-step explanation:

Given that f(x, y, z) = xe^y + ye^z + ze^x

so first we compute the gradient vector at (0, 0, 0)

Δf ( x, y, z ) = [ e^y + ze^x,  xe^y + e^z,  ye^z + e^x ]

Δf ( 0, 0, 0 ) = [ e⁰ + 0(e)⁰, 0(e)⁰ + e⁰, 0(e)⁰ + e⁰ ] = [ 1+0 , 0+1, 0+1 ] = [ 1, 1, 1 ]

Now we were also given that  V = < 4, 3, -1 >

so ║v║ = √ ( 4² + 3² + (-1)² )

║v║ = √ ( 16 + 9 + 1 )

║v║ = √ 26

It must be noted that "v"  is not a unit vector but since ║v║ = √ 26, the unit vector in the direction of "V" is ⊆ = ( V / ║v║)

so

⊆ =  ( V / ║v║) = [ 4/√26, 3/√26, -1/√26 ]

therefore by equation   D⊆f ( x, y, z ) = Δf ( x, y, z ) × ⊆

D⊆f ( x, y, z ) = Δf ( 0, 0, 0 ) × ⊆ = [ 1, 1, 1 ] × [ 4/√26, 3/√26, -1/√26 ]

= ( 1×4 + 1×3 -1×1 ) / √26

= (4 + 3 - 1) / √26

= 6 / √26

Answer:

A sample of at least 541 is needed if we wish to be 98% confident that our sample mean will be within 4 hours of the true mean.

Step-by-step explanation:

We are given that an electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 40 hours.

We have to find a sample such that we are 98% confident that our sample mean will be within 4 hours of the true mean.

As we know that the Margin of error formula is given by;

The margin of error =  [tex]Z_(_\frac{\alpha}{2}_) \times \frac{\sigma}{\sqrt{n} }[/tex]

where, [tex]\sigma[/tex] = standard deviation = 40 hours

            n = sample size

            [tex]\alpha[/tex] = level of significance = 1 - 0.98 = 0.02 or 2%

Now, the critical value of z at ([tex]\frac{0.02}{2}[/tex] = 1%) level of significance n the z table is given as 2.3263.

So, the margin of error =  [tex]Z_(_\frac{\alpha}{2}_) \times \frac{\sigma}{\sqrt{n} }[/tex]

                 [tex]4=2.3263 \times \frac{40}{\sqrt{n} }[/tex]

                 [tex]\sqrt{n}= \frac{40 \times 2.3263}{ 4}[/tex]

                  [tex]\sqrt{n}=23.26[/tex]

                   n = [tex]23.26^{2}[/tex] = 541.03 ≈ 541

Hence, a sample of at least 541 is needed if we wish to be 98% confident that our sample mean will be within 4 hours of the true mean.

Answer:

The answer is 5th angle = [tex]\bold{42^\circ}[/tex]

Step-by-step explanation:

Given that pizza is divided into six unequal slices.

Largest slice has an angle of [tex]90^\circ[/tex].

He eats the pizza from largest to smallest.

Let the difference in angles in each slice = [tex]d^\circ[/tex]

1st angle = [tex]90^\circ[/tex]

2nd angle = 90-d

3rd angle = 90-d-d = 90 - 2d

4th angle = 90-2d-d = 90 - 3d

5th angle = 90-3d-d = 90 - 4d

6th angle = 90-4d -d = 90 - 5d

We know that the sum of all the angles will be equal to [tex]360^\circ[/tex] (The sum of all the angles subtended at the center).

i.e.

[tex]90+90-d+90-2d+90-3d+90-4d+90-5d=360\\\Rightarrow 540 - 15d = 360\\\Rightarrow 15d = 540 -360\\\Rightarrow 15d = 180\\\Rightarrow d = 12^\circ[/tex]

So, the angles will be:

1st angle = [tex]90^\circ[/tex]

2nd angle = 90- 12 = 78

3rd angle = 78-12 = 66

4th angle = 66-12 = 54

5th angle = 54-12 = 42

6th angle = 42 -12 = 30

So, the answer is 5th angle = [tex]\bold{42^\circ}[/tex]

Answer:

range of the function F(x) is  (-infinity, 3)

Step-by-step explanation:

I do not see the graph function F(x), so will assume that it is a graph of the function F(x) over the complete domain (-inf,inf).

As you can see from the attached graph, the function reaches a maximum at y=+3, and extends all the way to -infinity.

So the range of the function F(x) is  (-infinity, 3)

Answer:

20cm it's is the answers

Step-by-step explanation:

5*4=20

Answer:

The variance of the data is 15.

σ² = 15

Step-by-step explanation:

The mean is given as

X = 8

х        |    (x - X)    |    (x - X) ²

12       |        4         |    16

9        |        1         |     1    

11        |        3         |    9

5       |        -3        |    9

3       |        -5        |    25

The variance is given by

[tex]\sigma^2 = \frac{1}{n-1} \sum (x - X)^2[/tex]

[tex]\sigma^2 = \frac{1}{5 - 1} (16 + 1 + 9 + 9 +25) \\\\\sigma^2 = \frac{1}{4} ( 16 + 1 + 9 + 9 +25) \\\\\sigma^2 = \frac{1}{4} (60) \\\\\sigma^2 = 15[/tex]

Therefore, the variance of the data is 15.

Answer: 1. [tex]-\dfrac{5}{6}[/tex]  2. [tex]-\dfrac{1}{3}[/tex] . 3. [tex]-3[/tex]

Step-by-step explanation:

Formula: Slope[tex]=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

1. (-2,2) (3,-3)

Slope [tex]=\dfrac{-3-2}{3-(-2)}[/tex]

[tex]=\dfrac{-5}{3+2}\\\\=\dfrac{-5}{6}[/tex]

Hence, slope of line passing through  (-2,2) (3,-3) is [tex]-\dfrac{5}{6}[/tex] .

2. (-5,1) (4,-2)

Slope [tex]=\dfrac{-2-1}{4-(-5)}[/tex]

[tex]=\dfrac{-3}{4+5}\\\\=\dfrac{-3}{9}\\\\=-\dfrac{1}{3}[/tex]

Hence, slope of line passing through  (-2,2) and (3,-3) is [tex]-\dfrac{1}{3}[/tex] .

3. (-1,5) (2,-4)

Slope [tex]=\dfrac{-4-5}{2-(-1)}[/tex]

[tex]=\dfrac{-9}{2+1}\\\\=\dfrac{-9}{3}\\\\=-3[/tex]

Hence, slope of line passing through (-1,5) and (2,-4) is -3.

Step-by-step explanation:

Let us assume that 1/2+root 3 is rational . So 1/2+root 3 = a/b where a and b are irrationals. since rhs is a rational number root 3 should be also rational .

Answer:

√41

Step-by-step explanation:

Considering the sides with lengths 48 and 52 units, we would use Pythagoras theorem to find the third side. Let that side be t

52² = 48² + t²

t² = 52² - 48²

= 2704 - 2304

= 400

t = √400

= 20

Considering the next triangle with sides t (20 units) and 12 units, again using the theorem

20² = 12² + y²

where y is the third side

400 = 144 + y²

y² = 400 - 144

= 256

y = √256

= 16 units

Considering the triangle with two sides given as 5 and 13 units, the third side (which is part of the 16 units calculated earlier)

13² = 5² + u²

where u is the 3rd side

169 = 25 + u²

u² = 169 - 25

u² = 144

u = √144

u = 12

The other part of the side of that triangle

= 16 - 12

= 4

Considering the smallest triangle whose sides are x, 5 and 4,

x² = 5² + 4²

= 25 + 16

= 41

x = √41

Answer:

√3/2

Explanation:

The directional derivative at the given point is gotten using the formula;

∇f(x,y)•u where u is the unit vector in that direction.

∇f(x,y) = f/x i + f/y j

Given the function f(x, y) = y cos(xy),

f/x = -y²sin(xy) and

f/y = -xysin(xy)+cos(xy)

∇f(x,y) = -y²sin(xy) i + (cos(xy)-xysin(xy)) j

∇f(x,y) at (0,1) will give;

∇f(0,1) = -0sin0 i + cos0j

∇f(0,1) = 0i+j

The unit vector in the direction of angle θ is given as u = cosθ i + sinθ j

u = cos(π/3)i+ sin(π/3)j

u = 1/2 i + √3/2 j

Taking the dot product of both vectors;

∇f(x,y)•u = (0i+j)•(1/2 i + √3/2 j)

Note that i.i = j.j = 1 and i.j = 0

∇f(x,y)•u = 0 + √3/2

∇f(x,y)•u = √3/2

The directional derivative of [tex]f[/tex] at the given point in the direction indicated is [tex]\frac{\sqrt{3}}{2}[/tex].

The directional derivative is represented by the following formula:

[tex]\nabla_{\vec v} f = \nabla f(x_{o},y_{o}) \cdot \vec v[/tex]    (1)

Where:

The gradient of [tex]f[/tex] is calculated below:

[tex]\nabla f (x_{o},y_{o}) = \left[\begin{array}{cc}\frac{\partial f}{\partial x} (x_{o}, y_{o}) \\\frac{\partial f}{\partial y} (x_{o}, y_{o})\end{array}\right][/tex] (2)

Where [tex]\frac{\partial f}{\partial x}[/tex] and [tex]\frac{\partial f}{\partial y}[/tex] are the partial derivatives with respect to [tex]x[/tex] and [tex]y[/tex], respectively.

If we know that [tex](x_{o}, y_{o}) = (0, 1)[/tex], then the gradient is:

[tex]\nabla f(x_{o}, y_{o}) = \left[\begin{array}{cc}-y^{2}\cdot \sin xy\\\cos xy -x\cdot y\cdot \sin xy\end{array}\right][/tex]

[tex]\nabla f (x_{o}, y_{o}) = \left[\begin{array}{cc}-1^{2}\cdot \sin 0\\\cos 0-0\cdot 1\cdot \sin 0\end{array}\right][/tex]

[tex]\nabla f (x_{o}, y_{o}) = \left[\begin{array}{cc}0\\1\end{array}\right][/tex]

If we know that [tex]\vec v = \cos \frac{\pi}{3}\,\hat{i} + \sin \frac{\pi}{3} \,\hat{j}[/tex], then the directional derivative is:

[tex]\Delta_{\vec v} f = \left[\begin{array}{cc}0\\1\end{array}\right]\cdot \left[\begin{array}{cc}\cos \frac{\pi}{3} \\\sin \frac{\pi}{3} \end{array}\right][/tex]

[tex]\nabla_{\vec v} f = (0)\cdot \cos \frac{\pi}{3} + (1)\cdot \sin \frac{\pi}{3}[/tex]

[tex]\nabla_{\vec v} f = \frac{\sqrt{3}}{2}[/tex]

The directional derivative of [tex]f[/tex] at the given point in the direction indicated is [tex]\frac{\sqrt{3}}{2}[/tex]. [tex]\blacksquare[/tex]

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Complete Question:

Which statement about the following equation is true?

[tex]2x^2-9x+2 = -1[/tex]

A) The discriminant is less than 0, so there are two real roots

B) The discriminant is less than 0, so there are two complex roots

C) The discriminant is greater than 0, so there are two real roots

D) The discriminant is greater than 0, so there are two complex roots

Answer:

C) The discriminant is greater than 0, so there are two real roots

Step-by-step explanation:

The given equation is [tex]2x^2-9x+2 = -1[/tex] which by simplification becomes

[tex]2x^2 - 9x + 3 = 0[/tex]

For a quadratic equation of the form [tex]ax^2 + bx + c = 0[/tex], the discriminant is given by the equation, [tex]D = b^2 - 4ac[/tex]

If the discriminant D is greater than 0, the roots are real and different

If the discriminant D is equal to 0, the roots are real and equal

If the discriminant D is less than 0, the roots are imaginary

For the quadratic equation under consideration, a = 2, b = -9, c = 3

Let us calculate the discriminant D

D = (-9)² - 4(2)(3)

D = 81 - 24

D = 57

Since the Discriminant D is greater than 0, the roots are real and different.

Answer:

Step-by-step explanation:

C) The discriminant is greater than 0, so there are two real roots

Answer:

y = x+3

Step-by-step explanation:

First step is to find the slope

m = ( y2-y1)/(x2-x1)

   = ( 7-9)/(4 - 6)

   = -2 / -2

  = 1

The we can put is in slope intercept form

y = mx+b where m is the slope and b is the y intercept

y = 1x+b

Putting in one of the points

9 = 1*6+b

Subtracting 6

9-6 = b

3=b

y = 1x+3

y = x+3

Answer:

[tex]\boxed{y=x+3}[/tex]

Step-by-step explanation:

Solve for slope first.

The slope can be found through 2 points.

[tex]slope=\frac{change \: in \: y}{change \: in \: x}[/tex]

[tex]slope=\frac{7-9}{4-6}[/tex]

[tex]slope=\frac{-2}{-2}[/tex]

[tex]slope=1[/tex]

Using slope-intercept form.

[tex]y=mx+b\\m=slope\\b=y \: intercept[/tex]

[tex]y=1x+b[/tex]

Let x = 6 and y = 9.

[tex]9=1(6)+b[/tex]

[tex]9-6=b[/tex]

[tex]3=b[/tex]

[tex]y=1x+3[/tex]

Answer:

61% i think

Step-by-step explanation:

if you have 39% and it 10 out of a 100 well you have a 39/100 and then n would be 61/100 so 61%

0.39  is the value of n for the video games on their smartphones. Thus option A is correct.

The mathematical discipline known as probability specializes in determining the possibility of an event occurring. Probability, which expresses the probability of a risk, is calculated by dividing the total possible combinations by the frequency of favorable events. Composite reliabilities vary from 0 to 1, with 1 representing certainty and 0 representing hesitation.

In a binomial distribution, p stands for the success probability. It refers to the likelihood that a certain number of experiments will result in favorable results. For all binomial attempts, the probability of winning stays constant.

This suggests that there will be a distribution of 39/100. The result after the calculation will be 0.39. Therefore, option A is the correct option.

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The question is incomplete, the complete question will be :

A survey found that  39 % of all gamers play video games on their smartphones. Ten frequent gamers are randomly selected. The random variable represents the number of frequent games who play video games on their smartphones. What is the value of n ?

A) 0.39

B) 0.10

C) 10

D) x

Answer:

The measure of each angle:

152.8°   and     27.2°

Step-by-step explanation:

Supplementary angles sum 180°

then:

a + b = 180°

a - b = 125.6°

then:

a = 180 - b

a = 125.6 + b

180 - b = 125.6 + b

180 - 125.6 = b + b

54.4 = 2b

b = 54.4/2

b = 27.2°

a = 180 - b

a = 180 - 27.2

a = 152.8°

Check:

152.8 + 27.2 = 180°

Answers:

Step-by-step explanation:

Let x and y be the measures of each angle.

x + y = 180°

x - y = 125.6°

180 - 125.6 = 54.4

Now we divide 54.4 evenly to get y.

y = 27.2°

To get x, we substitute y into the equation.

x = 27.2 + 125.6

x = 152.8°

To check, we plug these in to see if they equal 180°.

27.2 + 152.8 = 180° ✅

Answer: 14

Step-by-step explanation:

12/4 times 3 +5

= 3 times 3 + 5

= 9 + 5

= 14

Answer:

The answer is below

Step-by-step explanation:

A sugar refinery has three processing plants, all receiving raw sugar in bulk. The amount of raw sugar (in tons) that one plant can process in one day can be modelled using an exponential distribution with mean of 4 tons for each of three plants. If each plant operates independently,a.Find the probability that any given plant processes more than 5 tons of raw sugar on a given day.b.Find the probability that exactly two of the three plants process more than 5 tons of raw sugar on a given day.c.How much raw sugar should be stocked for the plant each day so that the chance of running out of the raw sugar is only 0.05?

Answer: The mean (μ) of the plants is 4 tons. The probability density function of an exponential distribution is given by:

[tex]f(x)=\lambda e^{-\lambda x}\\But\ \lambda= 1/\mu=1/4 = 0.25\\Therefore:\\f(x)=0.25e^{-0.25x}\\[/tex]

a) P(x > 5) = [tex]\int\limits^\infty_5 {f(x)} \, dx =\int\limits^\infty_5 {0.25e^{-0.25x}} \, dx =-e^{-0.25x}|^\infty_5=e^{-1.25}=0.2865[/tex]

b) Probability that exactly two of the three plants process more than 5 tons of raw sugar on a given day can be solved when considered as a binomial.

That is P(2 of the three plant use more than five tons) = C(3,2) × [P(x > 5)]² × (1-P(x > 5)) = 3(0.2865²)(1-0.2865) = 0.1757

c) Let b be the amount of raw sugar should be stocked for the plant each day.

P(x > a) = [tex]\int\limits^\infty_a {f(x)} \, dx =\int\limits^\infty_a {0.25e^{-0.25x}} \, dx =-e^{-0.25x}|^\infty_a=e^{-0.25a}[/tex]

But P(x > a) = 0.05

Therefore:

[tex]e^{-0.25a}=0.05\\ln[e^{-0.25a}]=ln(0.05)\\-0.25a=-2.9957\\a=11.98[/tex]

a  ≅ 12

Answer:

Hey there!

The common ratio is 5, because you multiply by 5 to get from one term to the next.

Hope this helps :)

Answer:

5

Step-by-step explanation:

To find the common ratio take the second term and divide by the first term

55/11 = 5

The common ratio would be 5

Answer:

1-{0.2(m-3)+¼}=0

1{0.2m-0.6+¼}=0

1-{(0.8m-2.4+1)/4}=0

1-(0.8m-1.4)/4=0

lcm

(4-0.8m-1.4)/4=0

(2.6-0.8m)/4=0

cross multiply

2.6-0.8m=0

m=2.6/0.8

m=3.25

The solution of the expression are,

⇒ m = 3.25

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Expression is,

⇒ 1 - | 0.2 (m - 3) + 1/4 | = 0

Now, We can simplify as;

⇒ 1 - | 0.2m - 0.6 + 1/4| = 0

⇒ 1 - |0.2m - 0.6 + 0.25| = 0

⇒ 1 - |0.2m - 0.35| = 0

⇒ 1 = 0.2m + 0.35

⇒ 1 - 0.35 = 0.2m

⇒ 0.2m = 0.65

⇒ m = 3.25

Thus, The solution of the expression are,

⇒ m = 3.25

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Answer:

a=6, b=5.5

Step-by-step explanation:

By looking at the sides of the triangles it can easily be seen that some of the sides match up. Side b is similar to the side of 11 and same with side a and the side of 3. Since one side is 16 and the other side on the smaller triangle is 8, the bigger triangle is twice as large than the smaller one. So 3 x 2 = 6 and 11 / 2 = 5.5

The average rate of change between two input values is the total change of the function values (output values) divided by the change in the input values.

Answer:  4

Step-by-step explanation:

Simply rotate the graph 1-turn to the left to see where the triangle lands. The x-axis will be the horizontal line and the y-axis will be the vertical line.

The attachment shows the graph rotated 1-turn to the left (90°).

Notice it is in the exact same position as #4.

Answer:

the probability that one parachute of the  five parachute is damaged is 0.156

Step-by-step explanation:

From the given information;

Let consider X to be the altitude above the  ground that a parachute opens

Then; we can posit that the probability that the parachute is damaged is:

P(X ≤ 100 )

Given that the population mean μ = 155

the standard deviation σ = 30

Then;

[tex]P(X \leq 100 ) = ( \dfrac{X- \mu}{\sigma} \leq \dfrac{100- \mu}{\sigma})[/tex]

[tex]P(X \leq 100 ) = ( \dfrac{X- 155}{30} \leq \dfrac{100- 155}{30})[/tex]

[tex]P(X \leq 100 ) = (Z \leq \dfrac{- 55}{30})[/tex]

[tex]P(X \leq 100 ) = (Z \leq -1.8333)[/tex]

[tex]P(X \leq 100 ) = \Phi( -1.8333)[/tex]

From standard normal tables

[tex]P(X \leq 100 ) = 0.0334[/tex]

Hence; the probability of the given parachute damaged is 0.0334

Let consider Q to be the dropped parachute

Given that the number of parachute be n= 5

The probability that the parachute opens in each trail be  p = 0.0334

Now; the random variable Q follows the binomial distribution with parameters n= 5 and p = 0.0334

The probability mass function is:

Q [tex]\sim[/tex] B(5, 0.0334)

Similarly; the event that one parachute is damaged is :

Q ≥ 1

P( Q ≥ 1 ) = 1 - P( Q < 1 )

P( Q ≥ 1 ) = 1 - P( Y = 0 )

P( Q ≥ 1 ) = 1 - b(0;5; 0.0334 )

P( Q ≥ 1 ) = [tex]1 -(^5_0)* (0.0334)^0*(1-0.0334)^5[/tex]

P( Q ≥ 1 ) = [tex]1 -( \dfrac{5!}{(5-0)!}) * (0.0334)^0*(1-0.0334)^5[/tex]

P( Q ≥ 1 ) = 1 -  0.8437891838

P( Q ≥ 1 ) = 0.1562108162

P( Q ≥ 1 ) [tex]\approx[/tex] 0.156

Therefore; the probability that one parachute of the  five parachute is damaged is 0.156

Answer:

b = 4/3

Step-by-step explanation:

In an exponential equation:

f(x) = a (b)ˣ

Evaluated at x+1:

f(x+1) = a (b)ˣ⁺¹

The ratio between them is:

f(x+1) / f(x)

= (a (b)ˣ⁺¹) / (a (b)ˣ)

= b

So the decay factor b can be found by dividing the consecutive y values.

b = 16 / 12

b = 4/3

Answer: 8.5 sq. units.

Step-by-step explanation:

Formula:

Area of triangle : [tex]\dfrac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]

Given: Triangle IJK, with vertices I(3,-7), J(7,-4), and K(4,-2)

Then, Area of triangle  IJK = [tex]\dfrac{1}{2}|3(-4-(-2))+7(-2-(-7))+4(-7-(-4))|[/tex]

[tex]\dfrac{1}{2}|3(-2)+7(5)+4(-3)|\\\\=\dfrac{1}{2}|-6+35-12|\\\\=\dfrac{1}{2}(17)\\\\=8.5\text{ sq. units}[/tex]

Hence, the area of this triangle  IJK on a Coordinate Grid = 8.5 sq. units.

Answer:

Step-by-step explanation:

The null hypothesis is described as the default hypothesis while the alternative hypothesis us always tested against this null ie the opposite of the null hypothesis.

In this case study, Let the proportion of houses that have home security be p

Thus, the null hypothesis is proportion of houses that have home security is 45% : p = 45%

The alternative hypothesis is proportion of houses that have home security is different than 45%: p =/ 45%

Store T sells apples at the lowest rate

Step-by-step explanation:

1st We need to make every statement in order of 1 pound. Then We will easily find the lowest rate of apple.

i) R sell 1.20 $ per pound.

ii) S sell 4 pounds for 5$

i.e S sell 1 pound for 5/4 = 1.25$

iii) T sell 3 pound for 3.48$

i.e T sell 1 pound for 3.48/3 = 1.16$

Analysing the above data I get,

Store T sells apples at the lowest rate

Answer:

The probability that all three people on the subcommittee are men

= 20%

Step-by-step explanation:

Number of members in the committee = 15

= 8 men + 7 women

The probability of selecting a man in the committee

= 8/15

= 53%

The probability of selecting three men from eight men

= 3/8

= 37.5%

The probability that all three people on the subcommittee are men

= probability of selecting a man multiplied by the probability of selecting three men from eight men

= 53% x 37.5%

= 19.875%

= 20% approx.

This is the same as:

The probability of selecting 3 men from the 15 member-committee

= 3/15

= 20%