A rectangular fish tank is 70 cm long, 30 cm wide, and 20 cm high.
How many cubic centimeters of water will the tank hold?
How many milliliters of water will the tank hold?
How many liters of water will the tank hold?

Solution :

From the given equation :

E[ E (X|Y) ] = E (X)

a). Then,

   E[ E [ X|Y,Z] | Z] = E [ X|Z ]

     ----  True

   E [ E [ X|Y ] | Z ] = E [ X|Z ]

    ---- False

  E [E [X | Y,Z ]] = E [X|Y ]

    ----  False

b). Th quantity E [ g (X,Y) | Y,Z ] is ,

The low of iteration tell the following statement are true E[ E [ X|Y,Z] | Z] = E [ X|Z ] . A random variable y . A function of (Y,Z)

From the given equation the law of iterated expectations

\(E[ E (X|Y) ] = E (X)\)

Therefore We have to find a)

Iteration is the repetition of a process in order to generate a sequence of outcomes.

So by using the low of iteration we can say that,

E[ E [ X|Y,Z] | Z] = E [ X|Z ]     ----  True

E [ E [ X|Y ] | Z ] = E [ X|Z ]  ---- False

E [E [X | Y,Z ]] = E [X|Y ]   ----  False

b). Th quantity E [ g (X,Y) | Y,Z ] is ,

For a random variable y this is  -----  True

For a number ----- False

For a function of (X,Y)  -----   False

For a function of (Y,Z) -----   True

For function of Z only  -------   False

Therefore,The low of iteration tell the following  statement are true E[ E [ X|Y,Z] | Z] = E [ X|Z ] . A random variable y . A function of (Y,Z)

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Answer:

x = 2/5

Step-by-step explanation:

x is equal to 2/5

5/2 • x = 1

Answer:

A.4.16

B. 4 R 12

Step-by-step explanation:

I'm justing going around answering my friends question Imao

The value of the expression is 16x(x+1) / 10x² -14x -12

In mathematics, an algebraic expression is an expression built up from constant algebraic numbers, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)

The given expression is

16/(x-2)  ÷ 4/(x+1) + 6/x

Simplify this to have

16 / (x-2) ÷ (10x + 6) / (x+1)(x)

this implies that 16/(x-2) * (x+1)(x)/(10x +6)

16(x² + x)/(x-2)(10x+6)

Therefore the value of the expression is

16x(x+1) / 10x² -14x -12

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The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

From the figure, the area of triangles can be calculated using the:

Area = (1/2)height×base length

Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)

Area of three triangle = 1/2(24×3) = 36 square units

Area of the figure = area of three triangle + area of the rectangle

= 36 + 6×4

= 60 square units

Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

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Answer:

x = 11/2 = 5.5

Step-by-step explanation:

2x-6 = 5

2x = 11

x = 11/2 = 5.5

The given expression expressed in the form (x+A)^2+B is (x - 6)² + 65

A = -6 and B = 65

From the question, we are to express the given expression in the form (x + A)^2+B by completing the square

The given expression is

x² -12x + 101

Using the completing the square method

x² -12x + 101

Divide the coefficient of x by 2 and then square it

The coefficient of x is -12

Dividing by 2, we get

-12/2 = -6

Squaring

(-6)²

Now, add and subtract this value from the expression

x² -12x + (-6)² + 101 - (-6)²

Then, we can write that

(x - 6)² + 101 - (-6)²

(x - 6)² + 101 - 36

(x - 6)² + 65

Thus,

The given expression expressed in the form (x+A)^2+B is (x - 6)² + 65

By comparison,

A = -6

and

B = 65

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Quickly does a cube's diagonal grow if its edges increasing at a rate of 19.9 cm/s.

d(Df)/dt = 19.9 √2   [cm/s]

and d(Dc)dt = 19.9√3  [cm/s]

Given that,

We have to find how quickly does a cube's diagonal grow if its edges grow at a rate of 19.9 cm/s.

Two diagonals exist in a cube, if you think about it. One is a cube diagonal (Dc) while the other is a face diagonal (Df) (Dc). Let's say that the edge's length is x.

Then, Df = √(x₂ + x₂) = x √2 ----------------------(1)

        Dc = √(x₂ + x₂ + x₂) = x √3 ---------------(2)

Therefore, if you separate out each equation for time t,

        d(Df)/dt = dx/dt times √2   -------------------(3)

        d(Dc)/dt = dx/dt times √3 --------------------(4)

The edges are growing at a rate of 2 cm/s, hence in equation (3), dx/dt = 19.9 cm/s (4).

Therefore, d(Df)/dt = 19.9 √2   [cm/s]

               and d(Dc)dt = 19.9√3  [cm/s]

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Answer: his lunch will cost him 45 dollar

Step-by-step explanation:

Answer:The reciprocal of 2/3 is 3/2. The product of 2/3 and its reciprocal 3/2 is 1.

Step-by-step explanation:

Answer:

Step-by-step explanation:

(-4*5 - 1) + (-4)

(-20 - 1) - 4

-21 - 4

-25

Answer:

3/14

Step-by-step explanation:

1st subtract the y's

the subtract the x's in the same order

-9 - 5 = -14

put the first result over the second

-3/-14 = 3/14

A, B, and C's interest rates are 49.96, 296.32 and 102.96, respectively. Since the total interest is $449.24.

The annual percentage rate (APR) on a credit card indicates that the interest you pay over a year is generally equivalent to your balance.

The balances and annual percentage rates for Jimmy's credit cards are shown below.

If Jimmy pays the same amount each month, he will be free of his credit card debt in a year.

We know that the formula

\($P V=\frac{P M T\left[1-\left(1+\frac{r}{12}\right)^{12 n}\right]}{\frac{r}{12}}$\)

Where, PV be present value

PMT be monthly payment

r be interest rate

n be time

For credit card A, we have

\($\begin{aligned} 563 & =\frac{{PMT}\left[1-\left(1+\frac{0.16}{12}\right)^{12}\right]}{\frac{0.16}{12}} \\ \text { PMT } & =51.08\end{aligned}$\)

Total payment will be, 51.08 × 12 = 612.96

The interest charge will be, 612.96 − 563 = 49.96

For credit card B, we have

\($\begin{aligned} & 2525=\frac{{PMT}\left[1-\left(1+\frac{0.21}{12}\right)^{12}\right]}{\frac{0.21}{12}} \\ & \mathrm{PMT}=235.11\end{aligned}$\)

Total payment will be, 235.11 × 12 = 2821.32

The interest charge will be, 2821.32 − 2525 = 296.32

For credit card C, we have

\($\begin{aligned} 972 & =\frac{\text { PMT }\left[1-\left(1+\frac{0.19}{12}\right)^{12}\right]}{\frac{0.19}{12}} \\ \text { PMT } & =89.58\end{aligned}$\)

Total payment will be, 89.58 × 12 = 1074.96

The interest charge will be, 1075.96 − 972 = 102.96

Total interest = 102.96 + 296.32 + 49.96

Total interest = 449.24

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Answer:

Polly used 15 bags to fill this sack of rice.

Step-by-step explanation:

Each kilogram has 1000 grams.

Polly has a full 5 kg sack of rice. Each full bag contains 350 g of rice. How many bags did Polly fill from this sack of rice?

We solve this by rule of three, using proportions.

Each bag has 350g of rice. In all, x bags will have 5kg = 5*1000 = 5000g of rice. So

1 bag - 350g

x bags - 5000g

Applying cross multiplication

\(350x = 5000\)

\(x = \frac{5000}{350}\)

\(x = 14.3\)

Since a decimal part of a bag is not possible, Polly used 15 bags to fill this sack of rice. 14 complete, and the last bag the remaining part.

The LCM of A = 3² × 5⁴ × 7 and B = 3⁴ × 5³ × 7 × 11 is 3898125 using Prime factorization.

Given are two numbers which are showed in the prime factorized form.

A = 3² × 5⁴ × 7

B = 3⁴ × 5³ × 7 × 11

Prime factorization is the factorization of a number in terms of prime numbers.

In order to find the LCM of these two numbers, we have to first match the common primes and write down vertically when possible and then bring down the primes in each column.

A = 3² ×         5³ × 5 × 7

B = 3² × 3² × 5³ ×       7 × 11

Bring down the primes in each column.

LCM = 3² × 3² × 5³ × 5 × 7 × 11

        = 3898125

Hence the LCM is 3898125.

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S = √2+√8+√18+√32+……………… n terms.

or, S = √2 + 2√2 +3√2 +4√2.+………………….+ n terms.

This is an A.P. in which a = √2. , d = √2.

Sn = n/2.[2.a +(n-1).d].

or, Sn = n/2.[ 2√2 +(n-1).√2].

or, Sn = (n/2).√2.[ 2 +n-1].

or, Sn = n.(n+1)/√2. Answer.

Given AP :√2,√8,√18,√32,...

First term = √2

Common difference = √8-√2

⇛ √(2×2×2)-√2

⇛ 2√2-√2

⇛√2

We know that

Sum of first n terms of an AP

⇛ Sn = (n/2)[2a+(n-1)d]

⇛ Sn = (n/2)[2√2+(n-1)(√2)]

⇛ Sn = (n/2)[2√2+√2 n -√2]

⇛ Sn = (n/2)[√2 n +√2)

⇛ Sn = (n/2)×(√2)(n+1)

⇛Sn = (n/√2)(n+1)

⇛ Sn = n(n+1)/√2

Additional comment:

nth term of an AP = a+(n-1)d

Sum of first n terms of an AP

Sn = (n/2)[2a+(n-1)d]

Sum of the first n terms = Sn =

(n/2)(a+an)

If a,b,c are the three consecutive terms in an AP then b = (a+c)/2

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The sum of the 8th & 4th of an Ap is 24 and sum of and sum of 6th & 10th term is 44 Find the Ap

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Answer:

19.6

Step-by-step explanation:

According to the

Cosine Theorem

e² = d² + f² - 2dfcos /_E

°Cos 13° = 0.974

e² = (7.1) 2 + (26.5) 2-2 × 26 = 5 × 7.1 × 0.974

=752.66 - 366.516

= 386.14

e = 386.14 = 19.6

Answer:

$8.22

Step-by-step explanation:

Items purchased :

Banana = 3 pounds

Price per pound of banana = $0.69

Cost of 3 pounds of banana = (3 * 0.69) = $2.07

Apple = 5 pounds

Price per pound of apple = $1.23

Cost of 5 pounds of apple = (5 * 1.23) = $6.15

Total cost :

$(2.07 + 6.15) = $8.22

The length of pregnancy does play a role in the education level of the baby. A significant relationship can be established using the chi square test.

A chi square ( χ2) test is performed in order to find a co relation between two unrelated variables. The main objective of the test is to prove whether the relationship holds true or is just a product of mere chance. For example, if we are conducting a survey of two different parameters, first being the population of people who are married and the other about their educational qualification, we will get two distinct table of values without any significant co relation. But now if we want to establish a relationship, lets say that married people have less educational qualifications, we need to prove our statement by performing a chi square test. The final value can either be a null hypothesis which states that their is no convincing relationship between the two parameters or can be a alternate hypothesis with significant co relation.

Following data can be represented on tabular form and calculated:

                                                  Gestation Period (Observed)

                                     22-27       28-32       33-36       37-42       43+    Tot

Less than high   YES    14              34            140           1010         81     1279

school degree     NO    26             65            343          3032      208   3674

                                      40             99            483          4042      289   4953

                                                   Gestation Period (Expected)

                              YES   10.32     25.56        124.72    1043.75    74.62

                              NO     29.67    73.43        358.27    2998.24   214.37

χ2 = ∑ \(\frac{(Observed-Expected)^2}{Expected}\)

= \(\frac{13.54}{10.32} +\frac{71.23}{25.56} +\frac{233.47}{124.72} +\frac{1139.06}{1043.75} +\frac{40.70}{74.62} +\frac{13.46}{29.67} +\frac{233.17}{358.27} +\frac{1139.73}{2998.24}+\frac{40.57}{214.37}\)

= 1.31+2.78+1.87+1.09+0.54+0.45+0.96+0.65+0.38+0.18 = 10.21

Now, calculating the degree of freedom= (coulmn-1)(row-1)= (5-1)(2-1) = 4

Looking at the reference table at 0.05 significance level, the value is 9.488

As the calculated value is more than the table value/critical value, null hypothesis can be rejected proving the alternate hypothesis that there might be a relationship between gestation period of a mother and the education level of her kid.

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6 hours

Explanation:

30 divide by 4 = 7.5

7.5 multiplied by 48 = 360 minutes / 6 hours

Answer:

6.4 miles

Step-by-step explanation:

Set up a ratio.

4 miles is to 30 minutes as x miles is to 48 minutes.

4/30 = x/48

X=4(48)/30

x 96/15 or x = 6.4 miles.

Two years ago, an investment of R1 500000 has increased to R1 700000 and has delivered R40 000 worth of dividends over the two years. Then the return on investment would be 16%.

We can use the following formula to calculate ROI:

ROI = (gain from investment - cost of investment) / cost of investment

where, gain from investment is the total value of the investment (including dividends), and cost of investment is the initial investment.

Using the values given in the question, we can calculate the ROI as:

ROI = ((R1,700,000 + R40,000) - R1,500,000) / R1,500,000 = R240,000 / R1,500,000

ROI = 0.16 or 16%

Therefore, the return on the investment is 16%.

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Answer:

a

Step-by-step explanation:

Answer:

54 girls

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

first, 0 is a whole number so it can only be C or D; then -8.5 is an integer so D

Answer:

d

Step-by-step explanation:

The required piecewise linear relations are f(x) = 4 if [0, 2), and f(x) = -2x + 8 if [2, 4).

A piecewise-defined function (also known as a piecewise function or a hybrid function) is a function defined by multiple sub-functions, each of which applies to a different interval of the main function's domain (a sub-domain).

The graph is given in the question, as shown

f(x) = 2x + 4 if [-2, 0]

This the sub-function define between the interval [-2, 0].

f(x) = 4 if [0, 2)

This the sub-function define between the interval [0, 2).

f(x) = -2x + 8 if [2, 4)

This the sub-function define between the interval [2, 4).

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Answer:

4x² + 22x - 12

Step-by-step explanation:

A = bh/2

A = (4x - 2)(2x + 12)/2

A = (8x² + 48x - 4x - 24)/2

A = (8x² + 44x - 24)/2

A = 4x² + 22x - 12

Answer: C

Step-by-step explanation:

Answer:

events at A and B are independent because P(A)(B)≠P(A)

Answer:

B) 6.68

Step-by-step explanation:

Use Cosine.

Cosine= Adjacent ÷ Hypotenuse

In this case the base you want to find is adjacent to the angle, 42°. Hence,

Cos (42)= adjacent ÷ hypotenuse

Cos (42) = x ÷ 9

x = Cos (42) × 9. Input that into your calculator.

x= 6.68

To remember the trigonometric ratios/formulas

Use the acronym, SOHCAHTOA

Hope this helps!!!!