MATHEMATICS COLLEGE

The board of a large company is made up of 7 women and 9 men. 6 of them will go as a delegation to a national conference. a) How many delegations are possible?

b) How many of these delegations have all men?

c) How many of these delegations have at least one woman?

Answers

Answer 1
Answer:

Answer:

a) 5765760

b) 60480

c) 5705280

Step-by-step explanation:

Assuming that order is not important:

Number of women = 7

Number of men = 9

Members of the delegation = 6

a) How many delegations are possible?

n=(16!)/((16-6)!)=16*15*14*13*12*11\n n= 5765760

b) How many of these delegations have all men?

n_(men) = (9!)/((9-6)!)=9*8*7*6*5*4 \nn_(men) = 60480

c) How many of these delegations have at least one woman?

n_(women >0)=n-n_(men)\nn_(women >0) =5765760-60480\nn_(women >0) =5705280

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Determine if 25110 is divisible by 45​
Please answer this correctly
Use the following to answer Sean takes two 250 mg chewable calcium tablets each day, 6) How many milligrams of calcium will Sean take in a week? 7) How many grams of calcium will Sean take in a week?​

jewelry box with a square base is to be built with silver plated sides, nickel plated bottom and top, and a volume of 44 cm3. If nickel plating costs $1 per cm2 and silver plating costs $2 per cm2, find the dimensions of the box to minimize the cost of the materials. (Round your answers to two decimal places.) The box which minimizes the cost of materials has a square base of side length cm and a height of cm.

Answers

Answer:

The box which minimizes the cost of materials has a square base of side length 4.45cm and a height of 2.22 cm.

Step-by-step explanation:

Volume of the jewellery box=44cm³

The box has a square base and is to be built with silver plated sides and nickel plated top and base.

Therefore: Volume  = Square Base Area X Height = l²h

l²h=44

h=44/l²

Total Surface Area of a Cuboid =2(lb+lh+bh)

Since we have a square base

Total Surface Area =2(l²+lh+lh)

The Total Surface Area of the box =2l²+4lh

Nickel plating costs $1 per cm³

Silver Plating costs $2 per cm³

Since the sides are to be silver plated and the top and bottom nickel plated:

Therefore, Cost of the Material for the jewellery box =1(2l²)+2(4lh)

Cost, C(l,h)=$(2l²+8lh)

Recall earlier that we derived:

h=44/l²

Substituting into the formula for the Total Cost

Cost, C(l)=2l²+8l(44/l²)

C=2l²+352/l

C=(2l³+352)/l

The minimum costs for the material occurs at the point where the derivative equals zero.

C'=(4l³-352)/l²

4l³-352=0

4l³=352

Divide both sides by 4

l³=88

l=4.45cm

Recall:

h=44/l²=44/4.45²=2.22cm

The box which minimizes the cost of materials has a square base of side length 4.45cm and a height of 2.22 cm.

What is the first step to solve this equation:
11 - 3x = 44

Answers

Answer:

Subtract 11 from both sides

Step-by-step explanation:

X has to be alone

Answer:

Subtract 11 from sides

Step-by-step explanation:

You have to get the x by itself first

Make m the subject when g=square root sign over m-5

Answers

Answer:

m = g² + 5

Step-by-step explanation:

Step 1: Write equation

g = √(m - 5)

Step 2: Solve for m

  1. Square both sides: g² = m - 5
  2. Add 5 to both sides: g² + 5 = m
  3. Rewrite: m = g² + 5

A parabola has a minimum value of 0, a y-intercept of 4, and an axis of symmetry at x = -2.Select the graph that matches the description.

Answers

Answer:

Graph represented by option D is the correct choice.

Step-by-step explanation:

We have been given that a parabola has a minimum value of 0, a y-intercept of 4, and an axis of symmetry at x=-2.

Since the minimum value of our given parabola is 0, so y-coordinate of vertex of parabola would be 0. This means that vertex of parabola will be at x-axis.

Since Since the minimum value of our given parabola is 0, so our parabola will be upward opening.

We are also told that parabola has an axis of symmetry at x=-2. This means that parabola will be symmetric about line x=-2.

The y-intercept of parabola is 4. This means that parabola will intersect y-axis at point (0,4).

Upon looking at our given choices, we can see that option D is the correct choice as it meets all the given conditions.

The answer is d. The y-intercept is at 4, the parabola is at 0 and the axis of symmetry is x=-2.

Which property is illustrated by the equation –8 + 8 = 0?additive inverse
additive identity
commutative property
distributive property

Answers

The property additive inverse is illustrated in this equation.

Valerie wants to take out a discount loan of $569. The rate is 4.5% for 250 days. How much interest will she pay? (Be sure to round the time to the nearest hundredth.

Answers

The interest is computed from

... I = Prt

where P is the principal amount ($569), r is the rate (0.045) and t is the time in years (250/360).

... I = $569×0.045×250/360 ≈ $17.78

Please note that time is not rounded. Rather, the exact value (25/36) is used in the calculation. The only rounding of any number is done at the end, where the amount is rounded to the nearest cent. (Your text authors should know this.)

_____

If you follow the problem instructions (which Valerie's lender will not do), the interest is calculated as ...

... t = 250/360 = 0.6944444... ≈ 0.69 . . . . years

... I = $569×0.045×0.69 ≈ $17.67

_____

Note the rounding of intermediate numbers (time) introduces an error of about $0.11 in the answer.

Answer:$17.41 (A+)


Step-by-step explanation:
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