Suppose that a department contains 10 men and 12 women. How many ways are there to form a committee with six members if it must have the same number of men and women

Answer:

yes , k = 9

Step-by-step explanation:

The equation of a proportional relationship is

y = kx ← k is the constant of proportion

To find k divide both sides by x

[tex]\frac{y}{x}[/tex] = k

Check each ordered pair in the table

k = [tex]\frac{18}{2}[/tex] = 9

k = [tex]\frac{45}{5}[/tex] = 9

k = [tex]\frac{63}{7}[/tex] = 9

Thus the relationship is proportional with k = 9

Answer is x=50.1

Step 1

Tanx=opposite/adjacent

Step2

Tanx=6.1/5.1

x=arctan(6.1/5.1)

x=50.1

Answer in degrees as required

Answer:

Haley simplified correctly

Step-by-step explanation:

According to indices rule, if we have the same base and we are to multiply two numbers raised to exponent, we are to add the powers on the bases

So, it is expected that;

x^3 * x^2 = x*(3 + 2) = x^5

However, x^3 + x^2 stays the same (but of course can only be factorised)

So we can conclude that only Haley’s answer is correct

Answer:

x = 50.6

Step-by-step explanation:

Answer:

31.80°

Step-by-step explanation:

In ∆ ABC :-

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Answer:

Number of terms: 2

Degree: 1

Step-by-step explanation:

✔️A term can either be a coefficient with a variable, a variable, or a constant.

In the polynomial given, 10y + 2, there are two terms:

First term is a coefficient with a variable = 10y

Second term is a constant = 2

The two terms are: 10y and 2

✔️Degree of a polynomial is the highest exponents possessed by any of its term.

10y has an exponent of 1.

The degree of the polynomial therefore will be 1

Answer:

[tex]{ \tt{h(t) = - 10t + 6}} \\ - 44 = - 10t + 6 \\ - 10t = - 50 \\ t = 5[/tex]

Answer:

h(5)

Step-by-step explanation:

Equate - 10t + 6 and - 44 and solve for t

- 10t + 6 = - 44 ( subtract 6 from both sides )

- 10t = - 50 ( divide both sides by - 10 )

t = 5 , that is

h(5) = - 44

Answer:

Arc XY = 180- 43

= 137º

answer is C

Step-by-step explanation:

Answer:

It should be option c, [tex]\sqrt 37 - \sqrt26\\\\[/tex]

Step-by-step explanation: i hope this helps

Step-by-step explanation:

12/3.75 = 3.2 a gallon

Answer:

You'll have a closed circle at x = 2, and shading to the left

See the diagram below

=========================================================

Explanation:

The fractions here are 3/7 and 21/2. The denominators of which are 7 and 2 respectively. The LCD is 7*2 = 14.

If we multiply both sides by 14, then this will clear out the denominators and make the fractions go away.

So if we multiplied both sides by 14, then we have these steps

[tex]\frac{3}{7}(35x-14) \le \frac{21x}{2}+3\\\\14*\frac{3}{7}(35x-14) \le 14*\left(\frac{21x}{2}+3\right)\\\\14*\frac{3}{7}(35x-14) \le 14*\left(\frac{21x}{2}\right)+14*\left(3\right)\\\\6(35x-14) \le 147x+42\\\\[/tex]

--------------------------

Let's isolate x

[tex]6(35x-14) \le 147x+42\\\\6(35x)+6(-14) \le 147x+42\\\\210x-84 \le 147x+42\\\\210x-147x \le 42+84\\\\63x \le 126\\\\x \le 126/63\\\\x \le 2\\\\[/tex]

The graph of this will consist of a closed or filled in circle at x = 2. We shade to the left to represent numbers smaller than 2.

So either x = 2 or x < 2.

If we used an open hole at 2, then we wouldn't be including 2 (but we want to include this endpoint).

See the diagram below.

Given:

A point on a graph.

To find:

The location of the point.

Solution:

From the given graph it is clear that the point lies in the third quadrant, it means both coordinates are negative.

The distance between point and y-axis = 1

The distance between point and x-axis = 2

It means, the x-coordinate is -1 and the y-coordinate is -2. So, the location of the given point is (-1,-2).

Therefore, the correct option is B.

Answer:

x ≈ 8.8

Step-by-step explanation:

Using the sine ratio in the right triangle

sin20° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{PQ}{OQ}[/tex] = [tex]\frac{3}{x}[/tex] ( multiply both sides by x )

x × sin20° = 3 ( divide both sides by sin20° )

x = [tex]\frac{3}{sin20}[/tex] ≈ 8.8 ( to the nearest tenth )

Answer:

D.  I or II only

Step-by-step explanation:

By a small online search, I've found that the equation is:

6x + 7 = 3x - 5

And the options are:

I. Combining the 6x and 3x terms

II. Combining the 7 and 5

III. Dividing both sides of the equation  by 6

A.  I only

B.  II only

C.  III only

D.  I or II only

E.   I or II or III

So, let's solve the equation in such a way that we can prevent the use of fractions:

6x + 7 = 3x - 5

We can use I and II, combining one in each side, so we get (so we use I and II at the same time)

6x - 3x = -5 - 7

solving these, we get:

(6 - 3)*x = -12

3*x = -12

and -12 is divisible by 3, so if we divide in both sides by 3, we get:

x = -12/3 = -4

x = -4

So we avoided working with fractions, and we used I and II.

Then the first step could be either I or II (the order does not matter)

Then the correct option is:

D.  I or II only

[tex]\bold{{Answer}}[/tex]

B.2.And30

What is the means of a proportion?

1 : harmonious relation of parts to each other or to the whole : balance, symmetry. 2a : proper or equal share each did her proportion of the work. b : quota, percentage. 3 : the relation of one part to another or to the whole with respect to magnitude, quantity, or degree : ratio.

A proportion is simply a statement that two ratios are equal. It can be written in two ways: as two equal fractions a/b = c/d; or using a colon, a:b = c:d. The following proportion is read as "twenty is to twenty-five as four is to five."

please correct me if im wrong

Answer:

D

Step-by-step explanation:

Given the proportion

[tex]\frac{a}{b}[/tex] = [tex]\frac{c}{d}[/tex]

Then a and d are the extremes of the proportion

and b, c are the means of the proportion

Then for

[tex]\frac{2}{3}[/tex] = [tex]\frac{20}{30}[/tex]

3 and 20 are the means → D

Answer:

4,5,5,7

Step-by-step explanation:

The answer is 4,5,5,7

9514 1404 393

Answer:

  p = 30

  angles 30°, 45°; exterior: 75°

Step-by-step explanation:

The exterior angle is equal to the sum of the remote interior angle:

  3p -15 = p + (p +15)

  p = 30 . . . . . . . . . . . . . add 15-2p

The interior angles are 30°, 45°; the exterior angle is 75°.

Answer:

d. 20

Step-by-step explanation:

28 ÷ (100%+40%)

= 28 ÷ 140%

= 28 ÷ 1.4 = 20

Answer:

option d

Step-by-step explanation:

Let the number be x

40% of x = 0.40x

Increased by 40% = 28

That is ,

           x + 0.40x = 28

               1.40x = 28

                   [tex]x = \frac{28}{1.40}\\[/tex]

                  [tex]x = \frac{28 \times 100}{1.40 \times 100 } = \frac{28 \times 100}{140} =\frac{4 \times 100}{20} = 4 \times 5 = 20[/tex]

Therefore, the number is 20

Answer:

both are equal is 0

Step-by-step explanation:

After substituting, the answer is 0 to both

Answer:

-4sin(4x-3)

Step-by-step explanation:

Given y = cos u, u = 4x - 3

dy/dx = dy/du * du/dx

dy/du = -sinu

du/dx = 4

dy/dx = -4sinu

since u = 4x - 3

dy/dx = -4sin(4x-3)

Answer:

80 square units

536.6 [tex]cm^{2}[/tex]

Step-by-step explanation:

First one.

2 Trapezoids

A = [tex]\frac{(base_{1} +base_{2}) }{2}[/tex] x h

A = [tex]\frac{10 + 6}{2}[/tex] x 2

A = 16

One rectangle

A = b x h

A = 6 x 8

A = 48

Total Area = 16 + 16 + 48 = 80

Second one:

Two triangles:

A = [tex]\frac{(b)(h)}{2}[/tex]

A = [tex]\frac{10(8.66)}{2}[/tex]

A = [tex]\frac{86.6}{2}[/tex]

A = 43.3

One large rectangle

A = b x h

A = 30 x 15

A = 450

Total Area = 450 + 43.3 + 43.3 = 536.6

Answer:

A=80

Step-by-step explanation:

A=1/2(6+10)2

A=16(2)

A=32

A=8x6

A=48+32

A=80

Answer:

3 x + 2 y + z/ x + y + z ,  x = 2 ,  y = 3 ,  z = 1

tan ( x ) ,  x = − π

cot ( 3 x ) ,  x = 2 π /3

Step-by-step explanation:

Answer:

88%

Step-by-step explanation:

to initial price (100%) was increased by 10% (resulting in 110% of the initial price).

then these 110% were decreased by 20%.

so, the final price is actually 80% of 110% of the initial price

20/100 = 1/5

80/100 = 4/5

so, the customer pays only 4/5 of the 110% price.

110 × 4/5 = 22 × 4 = 88%

so, the final price was 88% of the initial price

Answer:

g(x) = |x-7|+4

Step-by-step explanation:

If we imagine trying to find the vertex of f(x) or the lowest part, we can always input x and y into each equation and see if they equal on either side.

The vertex is at points (7,4)

4=|7-7|+4 : 4=4.

Answer:

exact form: x=-1/2

decimal form: x=-0.5

Answer: 3/4 is the answer.

Step-by-step explanation:

(2/3)/(8/9)

(doing reciprocal)

2/3 * 9/8

= 18/24

= 6/8

= 3/4

Answer:

3/4

Step-by-step explanation:

2/3 ÷ 8/9 = 2/3 ×9/8 = (2×9)/(3×8) =3/4

Answer:

[tex]f^{-1}(f(58))=58[/tex]

[tex]f(f(5))=11[/tex]

Step-by-step explanation:

We are given that the table which shows some inputs and outputs of the invertible function f with domain all real numbers.

We are given that

x         f(x)

5         9

3         -2

1          -5

18          -1

0           1

9           11

We have to find

[tex]f^{-1}(f(58))[/tex] [tex]f(f(5))[/tex]

We know that

[tex]f^{-1}(f(x))=x[/tex]

Using the property

[tex]f^{-1}(f(58))=58[/tex]

[tex]f(5)=9[/tex]

[tex]f(f(5))=f(9)[/tex]

[tex]f(f(5))=11[/tex]