I know this has already been answered but im still a little confused 19x+rx=-37x+w

How many $10 bills are the same as one $100 bill?

Anna11 [10]

Answer:

10

Step-by-step explanation:

10

4 0

3 years ago

Read 2 more answers

The diagonals of a rhombus have lengths of 12 centimeters and 16 centimeters. what is the length of one side of the rhombus

Yuki888 [10]

Diagonals of a rhombus are perpendicular and bisect each other. This means this rhombus is composed of four right triangles with legs of length 6 cm and 8 cm, with their hypotenuses forming the perimeter of the rhombus. The Pythagorean theorem a^2+ b^2 = c^2 can be used to find the length of the hypotenuse. 6^2+8^2 = 36+64 = 100. The square root of 100 is 10, so the length of a side of the rhombus is 10 cm.

5 0

3 years ago

The probability distribution for the rate of return on an investment is

babymother [125]

Answer:

a)0.7

b) 10.03

c) 0.0801

Step-by-step explanation:

Rate of return Probability

9.5 0.1

9.8 0.2

10 0.3

10.2 0.3

10.6 0.1

a.

P(Rate of return is at least 10%)=P(R=10)+P(R=10.2)+P(R=10.6)

P(Rate of return is at least 10%)=0.3+0.3+0.1

P(Rate of return is at least 10%)=0.7

b)

Expected rate of return=E(x)=sum(x*p(x))

Rate of return(x) Probability(p(x)) x*p(x)

9.5 0.1 0.95

9.8 0.2 1.96

10 0.3 3

10.2 0.3 3.06

10.6 0.1 1.06

Expected rate of return=E(x)=sum(x*p(x))

Expected rate of return=0.95+1.96+3+3.06+1.06=10.03

c)

variance of the rate of return=V(x)= $sum(x^2p(x))-[sum(x*p(x))]^2$

Rate of return(x) Probability(p(x)) x*p(x) x²*p(x)

9.5 0.1 0.95 9.025

9.8 0.2 1.96 19.208

10 0.3 3 30

10.2 0.3 3.06 31.212

10.6 0.1 1.06 11.236

sum[x²*p(x)]=9.025+19.208+30+31.212+11.236=100.681

variance of the rate of return=V(x)=sum(x²*p(x))-[sum(x*p(x))]²

variance of the rate of return=V(x)=100.681-(10.03)²

variance of the rate of return=V(x)=100.681-100.6009

variance of the rate of return=V(x)=0.0801

6 0

3 years ago

Allen is buying a video game that originally costs $49. He has a 10%-off

Annette [7]

The total amount Allen will need to pay for the video game is $48.96 as 49-0.1+0.06=48.96

7 0

4 years ago

The graphs of the polar curves r = 4 and r = 3 + 2cosθ are shown in the figure above. The curves intersect at θ = π/3 and θ = 5π

Gennadij [26K]

(a)

$\displaystyle \frac{1}{2} \cdot \int_{\frac{\pi}{3}}^{\frac{5\pi}{3}} \left(4^2 - (3 + 2\cos\theta)^2 \right) \, d\theta$

or, via symmetry

$\displaystyle\frac{1}{2} \cdot 2 \int_{\frac{\pi}{3}}^{\pi} \left(4^2 - (3 + 2\cos\theta)^2 \right) \, d\theta$

____________

(b)

By the chain rule:

$\displaystyle \frac{dy}{dx} = \frac{ dy/ d\theta}{ dx/ d\theta}$

For polar coordinates, x = rcosθ and y = rsinθ. Since
r = 3 + 2cosθ, it follows that

$x = (3 + 2\cos\theta) \cos \theta \\ 
y = (3 + 2\cos\theta) \sin \theta$

Differentiating with respect to theta

$\begin{aligned}
\displaystyle \frac{dy}{dx} &= \frac{ dy/ d\theta}{ dx/ d\theta} \\
&= \frac{(3 + 2\cos\theta)(\cos\theta) + (-2\sin\theta)(\sin\theta)}{(3 + 2\cos\theta)(-\sin\theta) + (-2\sin\theta)(\cos\theta)} \\ \\
\left.\frac{dy}{dx}\right_{\theta = \frac{\pi}{2}}
&= 2/3
\end{aligned}$

2/3 is the slope

____________

(c)

"distance between the particle and the origin increases at a constant rate of 3 units per second" implies dr/dt = 3

Angle θ and r are related via r = 3 + 2cosθ, so implicitly differentiating with respect to time

 $\displaystyle\frac{dr}{dt} = -2\sin\theta \frac{d\theta}{dt} \quad \stackrel{\theta = \pi/3}{\implies} \quad 3 = -2\left( \frac{\sqrt{3}}{2}}\right) \frac{d\theta}{dt} \implies \\ \\ \frac{d\theta}{dt} = -\sqrt{3} \text{ radians per second}$

5 0

3 years ago