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3 years ago

.Write the following number in expanded form using powers of 10: 67.938

Mathematics

1 answer:

HACTEHA [7]3 years ago

8 0

Answer:

67.938 =

(6 * 10^1) + (7 * 10^0) + (9 * 10^-1) + (3 * 10^-2) + (8 * 10^-3)

Step-by-step explanation:

Here, we want to write the given number in expanded form

Mathematically that will be ;

60 + 7 + 0.9 + 0.03 + 0.008

Using the power of 10, that will be;

(6 * 10^1) + (7 * 10^0) + (9 * 10^-1) + (3 * 10^-2) + (8 * 10^-3)

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Consider the probability distribution of a random variable x. Is the expected value of the distribution necessarily one of the p

pav-90 [236]

Answer:

yes . The Expected value must always be one of its possible values of x

Step-by-step explanation:

<u>For example</u> :-

Download docx

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3 years ago

Solve the following equation for a: -g + 3/4a = y

matrenka [14]

9514 1404 393

Answer:

a = (4/3)(y+g)

Step-by-step explanation:

Isolate 'a' term, then multiply by the reciprocal of its coefficient.

$-g+\dfrac{3}{4}a=y\qquad\text{given}\\\\\dfrac{3}{4}a=y+g\qquad\text{add $g$}\\\\\boxed{a=\dfrac{4(y+g)}{3}}\qquad\text{multiply by $4/3$}$

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4 years ago

let f(x) = 2x^2+5-e^x , use the intermediate value theorem to show that the f(x) has a root in the interval [3,4]?

sergiy2304 [10]

9514 1404 393

Answer:

sign(f(3)) ≠ sign(f(4))

Step-by-step explanation:

The intermediate value theorem tells you that a sign change between f(a) and f(b) means there is a root in the interval [a, b].

Here, we have f(3) ≈ +2.9 and f(4) ≈ -17.6, so there is a root in [3, 4].

_____

The root is approximately 3.27560108885.

7 0

3 years ago

Two complex numbers are given byz1= 3 +j4 andz2= 2 +j3. Determine in both polar andCartesian forms

Marat540 [252]

Answer:

Cartesian

z₁= 3 +4*j

z₂= 2 +3*j

Polar

z₁=5 * e^ (0.927*j)

z₁=√13 * e^ (0.982*j)

Step-by-step explanation:

for the complex numbers z the cartesian form of is

z= x + y*j

then

1) z₁= 3 +4*j (cartesian form)

2) z₂= 2 +3*j (cartesian form)

the polar form is

z= r* e^jθ

where

r= √(x²+y²) → r₁ = √(3²+4²) = 5 , r₂ = √(2²+3²) = √13

and

θ = tan⁻¹ (y/x) → θ₁ = tan⁻¹ (4/3)= 0.927 rad , θ₂ = tan⁻¹ (3/2)= 0.982 rad

then

z₁=5 * e^ (0.927*j)

z₁=√13 * e^ (0.982*j)

3 0

4 years ago

Cora says he dosen't need to know the y-interce of a line to write its equation,just its slope and some other point on the line.

Soloha48 [4]

Answer:

Yes, Cora is correct.

The equation of line with point (2,6) and slope of line (-1/3)

is x + 3y - 20 = 0

Step-by-step explanation:

Yes, the equation of a line can be written using a point and a slope of the line equation.

Cora has used the POINT SLOPE FORMULA, to represent the line equation.

In <u>Point Slope formula</u>:

The equation with slope m and points (x0,y0) can be written as:

(y-y0) =m (x-x0)

Here, the point (x0,y0) = (2,6)

and slope m = (-1/3)

So, the equation can be written as: $( y - 6) =\frac{-1}{3} (x-2) \\\implies 3( y-6) = (2-x)\\or, 3y - 18 -2 + x = 0\\or, x + 3y - 20 = 0$

Hence, the equation of line with point (2,6) and slope of line (-1/3)

is x + 3y - 20 = 0

4 0

3 years ago