In how many ways can alice give 12 apples to 3 children if each child must get at least 1 apple

Answer:

2 solutions

Step-by-step explanat

ion:|2x-3|-|3x-2|=0

<=>|2x-3|=|3x-2|

<=>2x-3=3x-2

Or 2x-3=-3x+2

<=>2x-3x=-2+3

or 2x+3x=2+3

<=>x=-1

Or x=1

Answer:

H. 40 inches

Step-by-step explanation:

On Wednesday, he is 40 inches taller. ... That would make 5 days of growth, for 100 inches. But this is only 3 days therefore he would grow 40 inches taller

Answer:

2.5L of 10% salt solution and 7.5L of the 30% salt solution

Step-by-step explanation:

let the amount of L in the 10% solution be 'x'

let the amount of L in the 30% solution be '10-x'

* because they add up to a total of 10L

10%(x) + 30%(10-x) = 25%(10)

0.1x + 3 - 0.3x = 2.5

-0.2x = -0.5

x = 2.5

x =2.5

10-x = 7.5

2.5 of 10% solution and 7.5% of 30% solution

Answer:

17

Step-by-step explanation:

8+2+(3×3-2)=8+2+(9-2)=8+2+7=17

mistake in the first step

firstly we do × and ÷

then + and -

Answer:

See below.

Step-by-step explanation:

When Brian passes Alex they both have travelled the same distance.

Call this distance d.

Let the speed that Brian passes = x miles/hour.

Distance = speed * time  so:

For Alex:

d = (x - 5) * 1.5        ( Alex cycles for 1 + 30 minutes =  1.5 hours)

For Brian:

d = x * 1

So substituting d = x in Alex's equation:

x = 1.5(x - 5)

x = 1.5x - 7.5

7.5 = 0.5x

7/5 / 0.5 = x

15 = x.

ANSWER:

Brian's speed is 15 miles/hour.

Alex's speed is 15 - 5 = 10 miles/hour.

Answer:

0.1294

Step-by-step explanation:

Number of chocolates in box = 38

Number of nuts = 8

Number of caramel = 16

Number of solid chocolate = 14

Since 2 are selected in a row and not replaced, then;

Probability of first being solid chocolate = 14/38

Probability of second being solid chocolate after first one = 13/37

Thus;

P(2 selected in a row being solid chocolate) = 14/38 × 13/37 = 0.1294

9514 1404 393

Answer:

  A.  x = ±2

Step-by-step explanation:

Add 14, then take the square root.

  x^2 -14 +14 = -10 +14

  x^2 = 4

  x = ±√4

  x = ±2

Answer:

A

Step-by-step explanation:

X^2-14=-10

X^2=14-10

X^2=4

√X2=√4

X=±2

Answer:

[tex]Max\ z = 1[/tex]

[tex]Min\ z = -9[/tex]

Step-by-step explanation:

Given

[tex]z = 4x + 5y[/tex]

[tex]x \ge -1[/tex]

[tex]y \le 2x +3[/tex]

[tex]y \le -1[/tex]

Required

The maximum and minimum of z

To do this, we make use of the graphical method

See attachment for graphs of

[tex]x \ge -1[/tex]

[tex]y \le 2x +3[/tex]

[tex]y \le -1[/tex]

The corner points of the function are:

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

[tex](x,y) = (-1,0)[/tex]

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

We have:

[tex]z = 4x + 5y[/tex]

Calculate z with  the above values

[tex]z = 4(-1) + 5(1) = 1[/tex]

[tex]z = 4(-1) + 5(0) = -4[/tex]

[tex]z = 4(-1) + 5(-1) = -9[/tex]

So, we have:

[tex]Max\ z = 1[/tex]

[tex]Min\ z = -9[/tex]

I don't know how you want it solved but, I am giving u -2 I hope this helps

Answer:

Card picked=2

P(factors of 28)={1,2,4,7,14,28}

total cards=4

in percentage=4 x 20 + 20

80+20=100

Therefore 2 in percentage will be

2 x 20 + 20

=40+20=60%

Answer:

156,567

Step-by-step explanation:

782,835 ÷ 5 = 156,567

Answer:

it is 165,567

Step-by-step explanation:

u divide

Answer:

(6) the letter n : intersection which means the number you will find at the first bracket and has the same number at the other bracket

ANSWER:

the conditions are the angle a is equal to angle c and ab = bc . Hence we need to prove that the triangles is congruent to the triangle cbe. ... angle A =angle C and AB=BC.

Answer:

[tex]=\frac{1}{8568}\ = .00011\\\ =\frac{7}{8568} = .00081[/tex]

Step-by-step explanation:

[tex]5/18\cdot \:4/17\cdot \:3/16\cdot \:2/15\cdot \:1/14=\frac{1}{8568}[/tex]

Answer:

since Sal washed 5 cars in 50 minutes, we can express his time as follow:

[tex] \frac{5 \: cars}{50 \: minutes} [/tex]

simplifying it by diving by 5, we get:

[tex] \frac{1 \: car}{10 \: minutes} [/tex]

Thus the rate will be 10 minutes per car (10 min/car)

Answer:

10 mins / car

Step-by-step explanation:

50 / 5 = 10

Answer:

C. Complex

Step-by-step explanation:

A complex number consists of a real part (-4.8) and an imaginary part (56i)

Answer:

3300cm²

Step-by-step explanation:

30cm+30cm=60cm 60cm is the lengh of the whole joint structure.We will put it in the equation as "a".

heigh stays the same(10cm) because the pieces are not stacked one on top of the other.They are joined on their sides.We will put it as "c".

Widht also stays the same.its 15 cm and we will put it as letter "b".

So

a=60cm

b=15cm

c=10cm

We need to calculate the surface area of the entire joint structure.

1.First thing to do is to calculate the top part which is:

a*b=15*60=900cm²

2.The bootom side is the same 900cm².

3.The front side is:

a*c=60*10=600cm²

4.The back side is the same as front so it is 600cm².

5.The left side is:

c*b=10*15=150cm²

6.The right side is the same as the left and it is 150cm²

Now we just add it up.

S(surface)=900*2+600*2+150*2=3300cm²

If you want the whole exercise in one equation:

S=2*(a*b)+2*(a*c)+2*(b*c)

Answer:

864

Step-by-step explanation:

A=6a^2=6·12^2=864

Answer:

864 in^2

Step-by-step explanation:

2(144+144+144) = 2(432) = 864 in^2.

Hope this helped!

Answer:

y = -3/4x + 3

Step-by-step explanation:

Answer:

(1, 2)

Step-by-step explanation:

Given the equation of the lines x + 2y = 5 and 2x - 3y = -4

First we need to make x the subject of the formulas

For x+2y = 5

x = 5 - 2y ... 1

For 2x - 3y = -4

2x = -4+3y

x = (-4+3y)/2 ... 2

Equate 1 and 2

5 - 2y =  (-4+3y)/2

2(5-2y) = -4+3y

10 - 4y = -4+3y

-4 -3y = -4-10

-7y = -14

y = 14/7

y = 2

Substitute y = 2 into 1

x = 5 = 2y

x = 5 - 2(2)

x = 5 - 4

x = 1

Hence the point where the lines meet will be at (1, 2)

Answer:

B

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

Here [ a, b ] = [ 1, 3 ] , then

f(3) = 18 ← value of y when x = 3

f(1) = 2 ← value of y when x = 1

Then

average rate of change = [tex]\frac{18-2}{3-1}[/tex] = [tex]\frac{16}{2}[/tex] = 8 → B

Answer:

The correct answer is - A.(112.86, 127.14)

Step-by-step explanation:

Given:

mean = $120

sd = $17.50

n = 40

Solution:

Confidence interval for a populationcan be express as mean +/- margin of error (E)

degree of freedom = n-1 = 40-1 = 39

confidence level (C) = 99% = 0.01

significance level = 1 - C = 1 - 0.01 = 0.99 = 99%

 by margin of error E = t×sd/√n = 2.58*17.50/√40

= 2.58*2.76

= 7.138 or 7.14

then the lower limit of mean = mean - E = 120 - 7.14 = $112.86

and, the upper limit of population mean = mean + E = 120 + 7.14 = $127.14

Answer:

The orginal number is 26.

Step-by-step explanation:

So the units digit can be 3 6 or 9

The tens digit can be 1 2 or 3

So the original number can be 13

31 = 2*13+ (1+3) + 2

31 =? 26 + 4 + 2    

This doesn't work. The right side is 32

26

62 = 2*26 + 8 + 2

62 = 52 + 8 + 2

This is your answer.

3 and 9 won't work because 39 is odd and so is 93. The result has to be even.

after each year it's 83% of it's value from last year (100%-17%=83%)

the function in 19000 * (0.83) ^x

3 will be filled in for x

19000 * (0.83) ^3= 10863.953

$10863.95

Answer:

$10,863.95

Step-by-step explanation:

y = 19,000[tex](.83)^{t}[/tex]

y = 19,000[tex](.83)^{3}[/tex]

y =$10,863.95

Answer:

D

Step-by-step explanation:

The median goes from the vertex to the midpoint of the opposite side, so

LN = NM , that is

3x - 7 = 5 ( add 7 to both sides )

3x = 12 ( divide both sides by 3 )

x = 4

Then

KL = 2x + 3 = 2(4) + 3 = 8 + 3 = 11 → D

Answer:

5/8 boxes

Step-by-step explanation:

1/3 ⋅ 1 7/8 = ?

1/3 ⋅ 15/8 = 15/24

15/24 = 5/8

5/8 boxes

Add the ratio: 3 + 5 = 8

Divide total students by that:

32/8 = 4

The ratio for girls is 3, multiply the 4 by 3:

4 x 3 = 12

There are 12 girls

Answer:

12

Step-by-step explanation:

If the ratio of girls to boys is 3:5, that means that for every 8 total students, 3 would be girls and 5 would be boys. Therefore 3/8 of the students are girls and 5/8 are boys. If 3/8 are girls, then:

[tex]\frac{3}{8}[/tex] of 32

= [tex]\frac{3}{8} * 32[/tex]

[tex]=\frac{3 * 32}{8} \\= \frac{96}{8} \\= 12[/tex]

There are 12 girls.

Answer:

C.

0.5; 13.5; 1093.5

Step-by-step explanation:

Answer:

a) 30

b)600pi

Step-by-step explanation:

For the first questions, since the arc is 240°, the area of the sector and circumference will be 240/360 or 2/3 of the total of the circles'. Therefore 125.6 x 3/2 is the circumference, which is 188.4. When we divide this by 6.28, we get 30

Now, since the area is pi r^2 where we know that r=30, we get 900pi as the area of the whole thing, however since the sector is 2/3 of the whole circle, 2/3 x 900pi = 600pi

We know

[tex]\boxed{\sf cos\Theta=\dfrac{b}{h}}[/tex]

[tex]\\ \sf\longmapsto cos22=\dfrac{x}{47}[/tex]

[tex]\\ \sf\longmapsto 0.9=\dfrac{x}{47}[/tex]

[tex]\\ \sf\longmapsto x=47(0.9)[/tex]

[tex]\\ \sf\longmapsto x=42.3[/tex]