A rectangular tank measures 60cm by 50cm by 40cm. Water flows into the tank at a rate of 8 litres per minute. At this rate, how long will it take to fill the tank?

Answer: 254.34

Step-by-step explanation: 3.14(9*9)=254.34

Answer:

When x = -4 and y = -6, p = 37.75

Step-by-step explanation:

Given that p = x² - y²/x² + x·y, we have;

p = (x² × x² -y² + x·y×x²)/x²

p = (x²⁺² - y² + x¹⁺² × y)/x²

p = (x⁴ - y² + x³·y)/x²

Therefore, p in the simplest form is given as follows;

[tex]p = \dfrac{x^4 - y^2 + x^3 \cdot y }{x^2}[/tex]

To find the value of p when x = -4 and y = -6, we plug in the value of x and y into the above equation to get the following equation;

[tex]p = \dfrac{(-4)^4 - (-6)^2 + (-4)^3 \cdot (-6) }{(-4)^2} = 37.75[/tex]

Therefore, the value of p when x = -4 and y = -6 is equal to 37.75.

Answer:

[tex]\frac{(^3_1)*(^{37}_4)}{(^{40}_5)}[/tex]

Step-by-step explanation:

The total number of ways in which 5 specimens can be selected from the  dish at random is given as C(40, 5).

Since only one of the five specimens would have the trait, the number of ways of selecting the one specimen out of the 3 specimens with the trait is C(3, 1).

3 specimens have the trait therefore 37 specimens (40 - 3) do not have the trait. The number of ways in which the remaining 4 specimens out of the 5 spemimens that do not have the trait is C(37, 4).

Therefore, the probability that only 1 of the 5 specimens selected will have the trait = [tex]\frac{C(3,1)*C(37,4)}{C(40,5)} =\frac{(^3_1)*(^{37}_4)}{(^{40}_5)}[/tex]

Total weight required is half pound, so let the amount of cashews be [tex] a[/tex] , and amount of peanuts be $b$

$\therefore a+b=0.5$ (1)

And we want this to cost $2.80$

Cost of $a$ pound of cashews will be $5.50\times a$ and cost of $b$ pound peanuts will be $2.30\times b$

$\therefore 5.5a+2.3b=2.8$ (2)

Substitute $a=0.5-b$ from equation (1) in equation (2)

$5.5(0.5-b)+2.3b=2.8$

$\implies -3.2b=2.8+5.5\times0.5 $

$\implies -3.2b=0.05$

$b$ comes out to be negative. That means there's no solution with the given conditions.

I checked once , I don't think there's any mistake. Can someone else verify too?

EDIT

I verified all the given options from calculator, and no option gives 2.80

Answer: 79

Concept:

Here, we need to understand the idea of evaluation.  

When encountering questions that gave you an expression with variables, then stated: "If x = a, y = b, z = c" (a, b, c are all constants), this means you should substitute the value given for each variable back to the expression.

Solve:

Given information

10x² - 7x + 10

x = 3

Substitute the value into the expression

= 10 (3)² - 7 (3) + 10

Simplify by multiplication

= 10 (9) - 21 + 10

= 90 - 21 + 10

Simplify by subtraction

= 69 + 10

Simplify by addition

= 79

Hope this helps!! :)

Please let me know if you have any questions

Answer:

92

Step-by-step explanation:

The variable 'x' shows up twice in this expression.  Replace each instance of 'x' with 3:

10(3)^2 - 7(3) + 10  =  10(9) - 21 + 19  =  92

Answer:

D.

Step-by-step explanation:

[tex]\frac{x^{2/3}}{y^{-3/4}}[/tex]

= [tex]x^{2/3}y^{3/4}[/tex]

= [tex]\sqrt[3]{x^2} * \sqrt[4]{y^3}[/tex]

So, D is your answer.

Hope this helps!

Answer:

a= Apple = 3

b= Banana =5

v= Lollypop=1

Step-by-step explanation:

36 is divided into 2 giving us 18

Let apple=a

Banana=b

Lollypop=c

In the first half

An apple + 3 bananas=18

a+3b=18 (1)

Second half is further divided into 2

That is,

18÷2=9

First half of the second half

3apples=9

3a=9 (2)

Second half of the second half

1 apple + 1 banana + 1 lollypop=9

a+b+c=9 (3)

a+3b=18 (1)

3a=9 (2)

a+b+c=9 (3)

From (2)

3a=9

Divide both sides by 3

a=9/3

a=3

Substitute a=3 into 1

a+3b=18

3+3b=18

3b=18-3

3b=15

Divide both sides by 3

b=15/3

=5

b=5

Substitute the value of a and b into (3)

a+b+c=9

3+5+c=9

8+c=9

c=9-8

c=1

Therefore,

a= Apple = 3

b= Banana =5

v= Lollypop=1

Answer:

6b^2 +4b

Step-by-step explanation:

The area of a triangle is

A = 1/2 bh

A = 1/2 * (3b+2) * (4b)

    =1/2 (12 b^2 +8b)

   = 6b^2 +4b

Answer:

√20 units.

Step-by-step explanation:

Please see attached photo for diagram.

The other leg of the triangle is x as shown in the attached photo.

Using the pythagoras theory, we can obtain the the value of x as follow:

x² = 4² + 2²

x² = 16 + 4

x² = 20

Take the square root of both side.

x = √20 units

Therefore, the value of the other leg x of the triangle is √20 units

Answer:

[tex]\sqrt{} 20[/tex] is your answer hope this helps

Step-by-step explanation:

Answer:

This means you would plug in g(x) into f(x).

Step-by-step explanation:

It would look like this:

[tex]3(x^{2} + 1) + 2[/tex]

Answer:

∠ 2 = 70°

Step-by-step explanation:

∠ 13 and ∠ 14 are adjacent angles and sum to 180° , then

12x - 22 + 9x - 29 = 180

21x - 51 = 180 ( add 51 to both sides )

21x = 231 ( divide both sides by 21 )

x = 11

Then

∠ 14 = 9x - 29 = 9(11) - 29 = 99 - 29 = 70°

∠ 7 = ∠ 14 = 70° ( Alternate angles )

∠ 2 = ∠ 7 = 70° ( Alternate angles )

Answer:

1. (4)

2. (2)

Step-by-step explanation:

Answer:

33.14 ft^2

Step-by-step explanation:

First find the area of the circle

The diameter is 20 ft so the radius is 1/2 of the diameter of 20*1/2 = 10 ft

A = pi r^2 = pi ( 10)^2 = 100 pi

The central angle is 38

That is a fraction of the circle, which is 360 degrees

38/360 = 19/180

Multiply the fraction of the circle by the area

19/180 * 100 pi

19/9 * 5 pi

Using 3.14 for pi

33.144444

To the nearest hundredth

33.14 ft^2

The area of the slice of pie that was cut, rounded to the nearest hundredth   33.14 ft^2.

We have to first find the area of the circle.

The diameter is 20 ft so the radius is 1/2 of the diameter of

20*1/2 = 10 ft.

The area of a circle [tex]A = \pi r^2[/tex]

By using the formula we have,

A= pi ( 10)^2

A = 100 pi

The central angle is 38.

That is a fraction of the circle, which is 360 degrees

38/360 = 19/180

Multiply the fraction of the circle by the area

19/180 * 100 pi

19/9 * 5 pi

Using 3.14 for pi

33.144444

To the nearest hundredth, it is 33.14 ft^2.

To learn more about the circle visit:

https://brainly.com/question/24375372

Cost of 1 kg = $9

So, cost of 5 kg = $9 × 5 = $45

Answer:

Surface Area = 85.75 ft²

Step-by-step explanation:

Surface area of pyramid = ½(Perimeter of triangular base * slant height of pyramid) + Area of triangular base

Perimeter of triangular base = sum of all sides of the triangular base = 5+5+5 = 15 ft

Slant height of pyramid = 10 ft

Area of triangular base = ½*base of triangle*height of triangle = ½*5*4.3 = 10.75 ft²

Plug in the above values:

Surface Area = ½(15*10) + 10.75

= (15*5) + 10.75

= 75 + 10.75

Surface Area = 85.75 ft²

Answer:

x/4+10=2

x/4=2-10

x/4=-8

x=-8 x 4

x=-32

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

So, we are given a right triangle and we know that 2x+4 is the length of the hypotenuse and 8 is the length of one of the sides.

Remember that the hypotenuse in a right triangle will always always be the longest side. Therefore, we can write the following inequality:

[tex]2x+4>8\\2x>4\\x>2[/tex]

The answer is A.

Answer:x>2

Step-by-step explanation:

2x+4>8

2x>8-4

2x>4

x>4/2

x>2

Answer:

96 people were coming

Step-by-step explanation:

In this question, we want to determine the number of people who were coming to the party.

First of all, we were made to know that this number is between 50 and 100. So whatever figure we will be giving as answer will be something within that range.

We were told that if 8 or 12 people sat at a table, there would be no remainder left. So basically what we need to do here is to calculate the highest multiple of 8 and 12 which is between 50 and 100.

we could have 24, 48 and 96 as multiples of both. But that multiple that sits between 50 and 100 is 96. So therefore, our answer is 96.

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Answer:

commutative properties

Answer:

A. Total weight of the fruits is 2.25 kg

B. There are no more fruits left.

Step-by-step explanation:

A.

To get the total weight of the fruits, we will first of all have to sort out the fruits and multiply the weight of the fruits by the number available.

Weight of apples:

we have one 1apple weighing 1/2 kg. The weight will be 1 |X 1/2 = 1/2 kg

Weight of mangoes:

We have five mangoes weighing 1/4 kg. Total weight will be 5 X 1/4 = 5/4 kg

Weight of oranges:

We have one orange weighing 1/2 kg. Total weight will be 1X 1/2 = 1/2 kg

Total weight of the fruits will be total weight of Mangoes + oranges + apples

= 1/2 + 5/4 + 1/2 = 2.25kg

B.

If her family begins to eat off some portions of the fruits, we will have to calculate the sum total of all the weights of fruits eaten

The portion eaten will be 3/4 + (2 X 1/2) + 1/2 = 2.25kg

If this happens the family would have eaten all of the fruits because

the original weight present is only 2.25kg of fruits to start with

Answer:

The term a⁴-3a²b²+b⁴ can't be factorised

Answer:

√2=1.414

then :√8 +2√32 +3√128+4√50

√8=√2³ =2√2

2√32=√2^5 = 4*2√2 = 8√2

3√128 = 3√2^6*2=8*3√2 =24√2

4√50 =4√5²*2= 20√2

add results : 2√2+8√2 +24√2+20√2=54√2

x=7-4√3

√x+ 1/√x

√(7-4√3) +1/√(7-4√3) =

(8-4√3)/√(7-4√3)

(8-6.93)/√(7-6.93) = 4 ( after rounded to the nearest whole number)

4 is your answer

Answer:

D

Step-by-step explanation:

Note that I will be using a, b, and y instead of their Greek counterparts.

First, we know that sin(c+d) = sin(c)cos(d) + cos(d)sin(a) and sin(c-d) = sin(c)cos(d) - cos(d)sin(a). We can apply these here to get

sin(b+y) = sin(b)cos(y) + cos(b)sin(y)

sin(b-y) = sin(b)cos(y) - cos(b)sin(y)

sin(a+y) = sin(a)cos(y) + cos(a)sin(y)

sin(a-y) = sin(a)cos(y) - cos(a)sin(y)

Plugging these into our equation, we get

(sin(b)cos(y) + cos(b)sin(y) - (sin(b)cos(y) - cos(b)sin(y)))

/

(sin(a)cos(y) + cos(a)sin(y)-(sin(a)cos(y) - cos(a)sin(y)))

=

2cos(b)sin(y) / 2cos(a)sin(y)

= cos(b)sin(y)/cos(a)sin(y)

= cos(b)/cos(a)

Next, we can see that a+b = π, so we can subtract b from both sides to get a = π -b. Plugging that in for a in our equation, we get

cos(b) / cos(π-b)

After that, we know that cos(c-d) = cos(c)cos(d) - sin(c)sin(d). Plugging that in here, we get

cos(π-b) = cos(π)cos(b) - sin(π)sin(b)

= -cos(b) + 0

= -cos(b)

Plugging that back into our equation, we get

cos(b) / -cos(b) = -1

Answer:

Mr. Lim will have $2500

Step-by-step explanation:

Given:

The total amount of money which Mr. Lim, Mr. Tan and Mr. Chan is $8650;

Mr. Lim has $450 more than what Mr. Tan has;

Mr. Chan has double the amount of money than what Mr. Tan has.

Therefore, if we assume that the amount of money Mr. Tan has as x, then...

Total money = Mr. Tan + Mr. Lim + Mr. Chan

therefore,

8650 = x + (x + 450) + 2x

8650 = x + 2x + x + 450

8650 = 4x + 450

8650 - 450 = 4x

8200 = 4x

8200/4 = x

2050 = x

As we assumed earlier, x will be equal to the amount of money Mr. Tan has and the question is asking us how much money Mr. Lim has. To find this out, you have to add $450 to the amount of money Mr. Tan has which is $2050. This is because the question also gives us that Mr. Lim has $450 more that Mr. Tan.

I hope this helped you :)

Answer:

20cm

Step-by-step explanation:

If each side of the square = 5 cm, 5 cm times 4 sides = 20 cm.

Answer:

P=20cm

Step-by-step explanation:

To find the perimeter of a square, you just add all the four sides.

Because it says the sides are 5cm, and squares always have the same length, you just:

5+5+5+6=20cm

So, the perimeter of this square is 20cm.

Hope this helps, and have a nice day:)

Answer:

45 is the father's age

Step-by-step explanation:

Answer:

-1.666666...

Step-by-step explanation: