Given the objective function C=3x−2y and constraints x≥0, y≥0, 2x+y≤10, 3x+2y≤18, identify the corner point at which the maximum value of C occurs.

Answer:

7)x=20 8)x=19

Step-by-step explanation:

7)4x-40=2x

4x-2x=40

2x=40

x=20

8)

2x+19=3x

3x-2x=19

x=19

Answer:

A)[tex]^{28}P_4}=491400[/tex]

Step-by-step explanation:

Total number of members = 28

We are supposed to find the no. of ways the four offices of chairman, vice chairman, secretary, and treasurer be filled from a club with 28 members

When 1 member is selected for Chairman position

So, 27 members will be left for the selection for the position of Vice chairman

When 1 member out of 27  is selected for Vice chairman position

So,26 members will be left for the selection for the position of secretary

When 1 member out of 26  is selected for secretary position

So,25 members will be left for the selection for the position of treasurer

Permutation relates to the act of arranging all the members of a set into some sequence or order,

The combination is a way of selecting items from a collection, such that (unlike permutations) the order of selection does not matter.

So, we will use permutation over here

Formula [tex]^nP_r=\frac{n}{(n-r)!}[/tex]

Substitute n = 28 and r = 4

So,[tex]^{28}P_4=\frac{28!}{(28-4)!}=491400[/tex]

So, Option A is true

A)[tex]^{28}P_4}=491400[/tex]

Hence There are 491400 ways the four offices of chairman, vice chairman, secretary, and treasurer be filled from a club with 28 members.

The number of ways the four offices of chairman, vice chairman, secretary, and treasurer be filled from a club with 28 members is 491,400.

The given parameters

[tex]nP_r =\frac{n!}{(n- r)!}[/tex]

[tex]28 P4 = \frac{28!}{(28-4)!} = \frac{28!}{24!} = 491,400[/tex]

Thus, the number of ways the four offices of chairman, vice chairman, secretary, and treasurer be filled from a club with 28 members is 491,400.

Learn more about permutation here: https://brainly.com/question/3086912

Answer:

42

Step-by-step explanation:

During the season, 40% of the goals are scored the by the star player.  This means that 60% of the goals are scored by everyone else.

100% - 40% = 60%

To find how many goals are scored by the rest of the team, convert the percentage to a decimal.  You then have to multiply the decimal by the total goals scored.

60% = 0.6

70 × 0.6 = 42

The rest of the team scored 42 goals.  

Answer:

42

Step-by-step explanation:

40% of 70=28

70-28=42

Answer:

210cm2

Step-by-step explanation:

Area of rectangle: HxW

Area of Triangle: 1/2 x bx h

There are 3 rectangles with the length of 14x3

14x3x3

= 14x9

= 126cm2

There are two triangles with the height of 12 and base of 14.

1/2x 14x 12

= 1/2x 168

= 168/2

= 84cm2

Now finally add them together:

84+126

= 210cm2

Answer:

4

Step-by-step explanation:

Answer:

in thirds so Dena gets 1/3 and Sue gets 2/3 which is half

Step-by-step explanation:

y = v₀t - gt²/2

For y=0 (back to where we started),

0 = t(v₀ - gt/2)

t=0 (which we knew) or v₀ - gt/2 = 0

v₀ = gt/2

2v₀ = gt

t = 2v₀/g

t = 2 (35.7 m/s) / (9.8 m/s/s) = 7.3 seconds

Answer: 7.3 seconds

Answer:

[tex]13 \: \: \: \: : \: \: \: \: 9[/tex]

Step-by-step explanation:

[tex]plates = 13 \\ cups = 9[/tex]

So the ratio of the number of plates to the number of cups.

[tex]plates \: \: \: \: \: : \: cups \\ \: \: \: \: \: \: \: \: 13 \: \: \: \: \: \: \: \: : \: \: 9[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

[tex]x=15^\circ[/tex]

Step-by-step explanation:

In a right triangle:

[tex]\sin \theta =cos(90^\circ-\theta) $ (Complementary angles)[/tex]

Therefore, given:

[tex]Sin (30 + x) \º = Cos (3x) \º\\30+x+3x=90^\circ\\30+4x=90^\circ\\4x=90^\circ-30^\circ\\4x=60^\circ\\$Divide both sides by 4\\x=15^\circ[/tex]

Answer:

6 out of 13 (6/13)

Step-by-step explanation:

30/65

Simplify by dividing both sides by 5

6/13

Tada!

hi this is my first answer

a straight angle has 180°,

here your given angle is 60+60=120°

so your missing angle is 180-120=60°

Step-by-step explanation:

The missing angle is 60° (180 - 60 - 60=60)

Its name: equilateral triangle

Answer:

In fig. 9, angle Y = angle 110° (vertically opposite angles )

Angle x = angle z = 180 - 110 = 70° (angles on a straight line)

In fig 10, angle y = 78°

Angle x = angle z = 180-78 = 102°

In fig 11, angle x = 83°

Angle y = angle z = 180-83 = 97°

In fig 12, angle y = 37°

Angle x = angle z = 180-37 = 143°

Answer:

64

Step-by-step explanation:

When two angles are supplementary, their measures must add up to 180 degrees. Therefore:

x+y=180

x+116=180

x=180-116=64 degrees

Hope this helps!

Answer:

∠x = 64°

Step-by-step explanation:

∠x+∠y=180°

∠x+116°=180°

Subtract 116° from both sides

∠x=64°

Answer:

Your answer is seven

the correct answer is 15 + 8.

Answer:

The answer is B.

Step-by-step explanation:

Mark me brainiiest.

Answer:

(–4, –1)

Step-by-step explanation:

Since, S is translated left 8 and down 4, therefore x and y coordinates would be - 4 and - 1 respectively.

Hence, the coordinate pair for the translated point S' are (–4, –1).

Answer:

24 square units

Step-by-step explanation:

You apply area of a trapezium

Answer:

C) 32.6%

Step-by-step explanation:

Given:

Total number of cards = 52

3 Cards already drawn = 5 of spades, 9 of spades, and 9 of hearts.

To win the next card drawn must be greater than the highest card already drawn.

Required:

Find the probability of winning

Here, the highest card already drawn is 9 of spades or 9 of hearts.

The cards higher than 9 of spades or 9 of hearts are four in number (10, J, Q, K). Since, we have 4 suits, the highest cards remaining are 4 * 4 = 16.

Also, a total of 49 cards are remaining since 3 cards are already drawn (52 - 3 = 49).

Therefore, the probability that the next card the player draws is a winning card: [tex]\frac{16}{49} = 0.326[/tex]

Convert to percentage:

0.326 * 100 = 32.6%

Answer:

The second figure is rhombus but the first figure is square

Answer:

17

-12 - -5 = -17

-17 is 17 numbers away from 0 so 17 is the answer

Hope this helps

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Square root of 3 is between 1 and 2

1^2 =1

(sqrt(3)) ^2 =3

2^2 = 4

So it must be point B

Answer:

B

Step-by-step explanation:

Answer:

B: 24 cm

Step-by-step explanation:

The triangle is ((4*3)/2). The squares are 12 (3*4) and 6 (1.5*4)

Answer:

24 cm^2

Step-by-step explanation:

We can find the area of the figure, surface area is for three dimensional figures

The area of the triangle is

A = 1/2 bh

A = 1/2 (3) *4 = 6

The area of the top rectangle is

A = l*w = 3 * (8-4) = 3* 4 = 12

And the area of the bottom rectangle

A = l*w = 1.5 ( 8-4) = 1.5*4 =6

The total area is the sum of the individual areas

6+12+6 = 24

24 cm^2

Answer:

Step-by-step explanation:

Given sin α = –4∕5 and sin β = 1∕2

To get α from sin α = –4∕5,

α = arcsin(-4/5)

α = arcsin (-0.8)

α = -53.13°

If angle α is in quadrant III, then α = 180+53.13 = 233.13° (sin is negative in the 3rd quadrant)

Similarly for sin β = 1∕2

β = arcsin(1/2)

β = arcsin(0.5)

β = 30°

Since  β is in quadrant II,  β = 180-30 = 150°

To find  cos (α + β). where α = 233.13° and  β = 30°

cos (α + β)= cos (233.13 + 150)

= cos 383.13°

cos (α + β) = 0.9196

Answer:

3/4

Step-by-step explanation:

There are 8 outcomes and 6 of them are odd.

6/8 = 3/4

Thus probability is 3/4

Answer:

3/4

Step-by-step explanation:

No. of sections = 8

No. of odd numbers = 6

Probability of getting an odd no. = 6÷8 = 3/4

Answer:

Step-by-step explanation:

1) Kate:

Number tickets  = x

Cost of 10 tickets = 10x

Parking fee = $ 5

Total money spend = $ 35

10x + 5 = 35

2)Ram:

Number of pen given to a friend =x

Number of pen given to 5 friends = 5*x = 5x

Number of pens left with him = 10

Total pens he had before giving to his friends = 35

5x + 10 = 35

Answer:

Left. Right

1. - c

2. - b

3 - a

Answer:

[tex]72[/tex]

Step-by-step explanation:

Jeremy is [tex]x[/tex] years-old.

Jeremy's grandfather is [tex]4x[/tex] years-old.

Adding their ages together will get [tex]90[/tex]

[tex]4x+x=90\\5x=90\\x=90 \div 5\\x=18[/tex]

Jeremy's grandfather age would be:

[tex]4x\\4(18)\\72[/tex]

Answer: 72

Step-by-step explanation:

Let Jeremy age be x

Granfather' age is 4x

x + 4x = 90

5x = 90

x = 90/5 = 18

Jeremy' age is 18

Granfather age is 4x = 4*18 = 72

The distance between (6,-2) and (1,-2) is 5.

Answer:

The distance:

[tex]d = 5[/tex]

Step-by-step explanation:

To find the distance between points [tex](6,-2)[/tex] and [tex](1,-2)[/tex], you need the distance formula:

[tex]d = \sqrt{(x_{2} - x_{2})^{2} + (y_{2} - y_{1})^{2}}[/tex]

-Use the given points [tex](6,-2)[/tex] and [tex](1.-2)[/tex] for the distance formula:

[tex]d = \sqrt{(1 - 6)^{2} + (-2 + 2)^{2}}[/tex]

-Then, solve the formula:

[tex]d = \sqrt{(1 - 6)^{2} + (-2 + 2)^{2}}[/tex]

[tex]d = \sqrt{(-5)^{2} + (0)^{2}}[/tex]

[tex]d = \sqrt{25 + 0^{2}}[/tex]

[tex]d = \sqrt{25 + 0}[/tex]

[tex]d = \sqrt{25}[/tex]

[tex]d = 5[/tex]

So, the distance is [tex]5[/tex].

Answer:

x = 0.9333333

Step-by-step explanation:

-4x - 4/3 = x - 6                    Multiply through by 3

-12x - 4 = 3x - 18                  Add 12x to both sides

-12x+12x-4 = 3x+12x - 18     Combine like terms

-4 = 15x - 18                         Add 18 to both sides

-4+18=15x - 18 + 18              Combine like terms

14 = 15x                                Divide by 15

14/15 = x

x = 0.933333

Answer:

V = 10 in^3

Step-by-step explanation:

The volume of a sphere is given by

V = 4/3 pi r^3

We have the diameter

r = d/2 = 2.7/2 =1.35

V = 4/3 ( 3.14) (1.35)^3

V =10.30077

Rounding to the nearest whole number

V = 10 in^3

Answer:

10 in^3

Step-by-step explanation:

Answer:

None, unless c was a typo

Step-by-step explanation:

Distributing gets us xy+2x=5

None of the options is that

If you meant option c as xy+2x = 5 though, then it would be correct