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2 years ago

Help A)38 B)62 C)80 D)100

Mathematics

2 answers:

olganol [36]2 years ago

8 0

Answer:

80 degrees

Step-by-step explanation:

Veseljchak [2.6K]2 years ago

5 0

Answer:

Step-by-step explanation:

∠5 +∠6 +∠7 = 180 {straight line angle}

38 + 62 + ∠7 = 180

100 +∠7 = 180

∠7 = 180 - 100

∠7 = 80°

l // m

∠3 = ∠7 {Alternate interior angles are congruent}

∠3 = 80°.

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Digiron [165]

What I gather from the question is that $X$ has second moment $E(X^2)=81$ and variance $V(X) = 58$ , and you're asked to find the expectation and variance of the random variable $Y=2X+10$ .

From the given second moment and variance, we find the expectation of $X$ :

$V(X) = E(X^2) - E(X)^2 \implies E(X) = \sqrt{E(X^2) - V(X)} = \sqrt{23}$

Expectation is linear, so

$E(Y) = E(2X+10) = 2 E(X) + 10 = \boxed{2\sqrt{23} + 10}$

Using the same variance identity, we have

$V(Y) = V(2X+10) = E((2X+10)^2) - E(2X+10)^2$

and

$E((2X+10)^2) = E(4X^2 + 40X + 100) = 4E(X^2) + 40E(X) + 100 = 424 + 40\sqrt{23}$

so that

$V(Y) = V(2X+10) = (424 + 40\sqrt{23}) - (2\sqrt{23} + 10)^2 = \boxed{232}$

Alternatively, we can use the identity

$V(aX+b) = a^2 V(X) \implies V(2X+10) = 4V(X) = 232$

5 0

2 years ago

two blocks of wood are shaped as right rectangle prisms the smaller block has a length of 9 cm a width of 3 cm and a height of 7

dolphi86 [110]

Answer:

1,512 cm³

Step-by-step explanation:

The general formula for the volume of a prism is:

V= Bh, where B = the area of the base and h = height of the prism

Given the dimensions of the smaller block as 9cm x 3cm x 7cm, then the dimensions of the larger block (double the dimensions of the smaller block) must be 18cm x 6cm x 14cm. Using these measurements:

V = (18)(6)(14) = 1,512 cm³

3 0

3 years ago

Binomial (x - 6) and trinomial (-2x2 + x + 9) are the factors of which of the

djyliett [7]

Answer:

Option (3)

Step-by-step explanation:

If binomial (x - 6) and trinomial (-2x² + x + 9) are the factors of a polynomial then their multiplication will be equal to the polynomial.

(x - 6)(-2x² + x + 9) = x(-2x² + x + 9) - 6(-2x² + x + 9)

= -2x³ + x² + 9x + 12x² - 6x - 54

= -2x³ + 13x² + 3x - 54