If Rick buys a remote control car for $29.00, what is his selling price?

The equation x2 − xy + y2 = 3 represents a "rotated ellipse," that is, an ellipse whose axes are not parallel to the coordinate

Setler [38]

Answer:

the points where the ellipse crosses the x- axis are (1.73, 0) and (-1.73, 0)

Step-by-step explanation:

To find the points at which a graphic crosses the x-axis we need to find the values for x where y = 0.

Therefore, in the equation x²- xy + y² = 3 we are going to make y = 0 and solve for x

x² - xy + y² = 3

x²- x(0) + (0)² = 3

x² = 3

x = ±√3

x₁ = 1.73 and x₂ = -1.73

Therefore, the points where the ellipse crosses the x- axis are (1.73, 0) and (-1.73, 0)

3 0

3 years ago

Assume that 63% of people are left-handed. If we select 5 people at random, find the probability of each outcome described below

mash [69]

Answer:

a. 0.9931

b. 0.3423

c. 0.3907

d. 0.2670

e. 3.15

f. 1.0796

Step-by-step explanation:

The probability of the variable that said the number of left-handed people follow a Binomial distribution, so the probability is:

$P(x)=nCx*p^{x}*(1-p)^{n-x}$

nCx is calculated as:

$nCx=\frac{n!}{x!(n-x)!}$

Where x is the number of left-handed people, n is the number of people selected at random and p is the probability that a person is left--handed. So P(x) is:

$P(x)=5Cx*0.63^{x}*(1-0.63)^{5-x}$

Then the probabilities P(0), P(1), P(2), P(3), P(4) and P(5) are:

$P(0)=5C0*0.63^{0}*(1-0.63)^{5-0}=0.0069$

$P(1)=5C1*0.63^{1}*(1-0.63)^{5-1}=0.0590$

$P(2)=5C2*0.63^{2}*(1-0.63)^{5-2}=0.2011$

$P(3)=5C3*0.63^{3}*(1-0.63)^{5-3}=0.3423$

$P(x)=5C4*0.63^{4}*(1-0.63)^{5-4}=0.2914$

$P(x)=5C5*0.63^{5}*(1-0.63)^{5-5}=0.0993$

Then, the probability P(x≥1) that there are some lefties among the 5 people is:

P(x≥1) = P(1) + P(2) + P(3) + P(4) + P(5)

P(x≥1) = 0.0590 + 0.2011 + 0.3423 + 0.2914 + 0.0993 = 0.9931

The probability P(3) that there are exactly 3 lefties in the group is:

P(3) = 0.3423

The probability P(x≥4) that there are at least 4 lefties in the group is:

P(x≥4) = P(4) + P(5) = 0.2914 + 0.0993 = 0.3907

The probability P(x≤2) that there are no more than 2 lefties in the group is:

P(x≤2) = P(0) + P(1) + P(2) = 0.0069 + 0.0590 + 0.2011 = 0.2670

On the other hand, the expected value E(x) and standard deviation S(x) of the variable that follows a binomial distribution is:

$E(x)=np=5(0.63)=3.15\\S(x)=\sqrt{np(1-p)}=\sqrt{5(0.63)(1-0.63)}=1.0796$

6 0

3 years ago

A pair of pants that regularly costs $55 are on sale for 35% off the regular price. What is the sale price of the pants?

fomenos

Answer:

$35.75

Step-by-step explanation:

100-35=65

.65 x 55 = 35.75

6 0

2 years ago

Read 2 more answers

What is the LCM of 12,30 and 42

Hoochie [10]

Answer:

420

Step-by-step explanation:

We can find the prime factors of each of the numbers first before finding their LCM.

12: 2 × 2 × 3

30: 2 × 3 × 5

42: 2 × 3 × 7

To find the LCM, we need to see if they are any common prime factors between all three numbers. The common prime factors are 2 and 3. Then, we multiply 2 and 3 with the remaining outstanding factors, which are 2, 5, and 7.

LCM: 2 × 2 × 3 × 5 × 7 = 420

7 0

2 years ago

Read 2 more answers

20 POINTS AND BRAINLIEST

emmainna [20.7K]

To solve this equation we must first plug in 5 for x.

$\frac{1}{3}$ (5 - 4x)
↓
$\frac{1}{3}$ (5 - 4 · 5)

The next step would be to multiply 4 by 5 to get rid of the parenthesis within our main parenthesis.

$\frac{1}{3}$ (5 - 4 · 5)

$\frac{1}{3}$ (5 - 20)

The next step would be to subtract both of the numbers within the parenthesis.

$\frac{1}{3}$ (-15)

Now we must multiply.

- $\frac{1}{3}$ · 15 = - $\frac{1×15}{3}$

- $\frac{15}{3}$

Now we simplify our answer to get our final answer.

-5

8 0

3 years ago