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2 months ago

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2 months ago

We can suppose the equation of the plane is in the form ...

ax +by +cz = 1

By using the given point coordinates for x, y, and z, we end up with three equations in 3 unknowns. These can be described by the augmented matrix ...

Putting this in reduced row-echelon form, we find

a = 54/35

b = -63/35

c = 43/35

The equation of the plane through is ...

54x -63y +43z = 35

ax +by +cz = 1

By using the given point coordinates for x, y, and z, we end up with three equations in 3 unknowns. These can be described by the augmented matrix ...

Putting this in reduced row-echelon form, we find

a = 54/35

b = -63/35

c = 43/35

The equation of the plane through is ...

54x -63y +43z = 35

Question

In a family with 8 children, excluding multiple births, what is the probability of having 7 boys and 1 girl, in any order? assume that a boy is as likely as a girl at each birth

Solution 1

There is a 7/8 chance there will be boys and a 1/8 chance there will be a girl

Question

For the particular problem raised in the introduction, assume that the total bill is $44. to answer the question "how should the bill be split?" we will create a linear equation. the unknown is how much money a single person (besides anika) must pay, so call that x. although four people (you plus three friends) went to dinner, only three are paying the unknown amount x for a total of 3x. since anika is paying $2, the total amount paid is 3x+2 dollars, which must equal the amount of the bill, $44. thus, the equation to find x is 3x+2=44. the steps for solving a linear equation are as follows: move all of the constants to the right side. move all of the variable terms (terms containing x) to the left side. divide both sides by the coefficient of the variable to isolate the variable. you will go through these steps one at a time to solve the equation and determine how much each person should pay.

Solution 1

3x+2=44

3x+2(-2)=44-2

3x=42

3x/3=42/3

x=14

So each person would have to pay $14, except Anika

3x+2(-2)=44-2

3x=42

3x/3=42/3

x=14

So each person would have to pay $14, except Anika

Question

A pair of two distinct dice are rolled six times. suppose none of the ordered pairs of values (1, 5), (2, 6), (3, 4), (5, 5), (5, 3), (6, 1), (6, 2) occur. what is the probability that all six values on the first die and all six values on the second die occur once in the six rolls of the two dice?

Solution 1

The **probability** that all six **values** on the first die and all six **values** on the second die occur once in the **six **rolls of the **two **dice is 1/6.

It is defined as the **ratio **of the number of **favorable** outcomes to the total number of **outcomes**, in other words, the **probability **is the **number **that shows the happening of the event.

It is given that:

A pair of **two **distinct dice are rolled **six **times. suppose none of the ordered **pairs **of values (1, 5), (2, 6), (3, 4), (5, 5), (5, 3), (6, 1), (6, 2) occur.

Total **number** of outcomes = 6x6

Total number of **outcomes** = 36

Total favourable outcome = 6

The **probability **that all six values on the first die and all **six** values on the second die **occur **once in the **six **rolls of the **two **dice:

P = 6/36 = 1/6

Thus, the **probability** that all six **values** on the first die and all six **values** on the second die occur once in the **six **rolls of the **two **dice is 1/6.

Learn more about the **probability **here:

#SPJ2

Solution 2

But them in order of add them all up i guess

Question

If the numerator of a fraction is increased by 3, the fraction becomes 3/4. If the denominator is decreased by 7, the fraction becomes 1. Determine the original fraction. Which of the following equations represents "If the numerator of a fraction is increased by 3, the fraction becomes 3/4"?

Solution 1

For this case, the original fraction is:

x / y

Where,

x = numerator

y = denominator:

If the numerator of a fraction is increased by 3, the fraction becomes 3/4:

(x + 3) / y = 3/4

If the denominator is decreased by 7, the fraction becomes 1:

x / (y-7) = 1

Solving the system of equations we have:

x = 9

y = 16

The original fraction is:

9/16

**Answer:**

**the original fraction is:**

**9/16**

** "If the numerator of a fraction is increased by 3, the fraction becomes 3/4" is:**

** ****(x + 3) / y = 3/4**

x / y

Where,

x = numerator

y = denominator:

If the numerator of a fraction is increased by 3, the fraction becomes 3/4:

(x + 3) / y = 3/4

If the denominator is decreased by 7, the fraction becomes 1:

x / (y-7) = 1

Solving the system of equations we have:

x = 9

y = 16

The original fraction is:

9/16

Solution 2

Let n = numerator

d = denominator

n+3/d = 3/4

n/(d-7) = 1

Which of the following equations represents "If the numerator of a fraction is increased by 3, the fraction becomes 3/4"?

The equation is**(****n+3)/d = 3/4**

d = denominator

n+3/d = 3/4

n/(d-7) = 1

Which of the following equations represents "If the numerator of a fraction is increased by 3, the fraction becomes 3/4"?

The equation is

Question

A single fair die is tossed. find the probability of rolling a number greater than 55.

Solution 1

0% no # greater than 6

Question

A jar contains 8 large red marbles, 5 small red marbles, 7 large blue marbles, and 4 small blue marbles. if a marble is chosen at random, which of the conditional probabilities is larger, p(red|large) or p(large|red)?

Solution 1

8 large red, 5 small red, 7 large blue, 4 small blue:

totally = 24 marbles

P(red)= 13/24

let A red and B large

P(A/B)= P(A∩B)/P(B)

P(B)= 15/24 =.625

P(A∩B)= 8/24 = .333

P(A/B) =.333/.625 =.533

P(B/A) =.625/.333= 1.875

so the probability of p(large/red) is larger.

totally = 24 marbles

P(red)= 13/24

let A red and B large

P(A/B)= P(A∩B)/P(B)

P(B)= 15/24 =.625

P(A∩B)= 8/24 = .333

P(A/B) =.333/.625 =.533

P(B/A) =.625/.333= 1.875

so the probability of p(large/red) is larger.

Question

"a fair coin is tossed 5 times. what is the probability of exactly 4 heads?"

Solution 1

5 flips render40 % 4 will turn up heads

Question

Evaluate the surface integral. s xyz ds, s is the cone with parametric equations x = u cos(v), y = u sin(v), z = u, 0 ≤ u ≤ 3, 0 ≤ v ≤ π 2

Solution 1

**Answer:**

**Step-by-step explanation:**

Let

Differentiate partially with respect to u, v.

To find f, put in xyz.

So,

Integrate with respect to u.

Integrate with respect to v.

Solution 2

Let's capture the parameterization of the surface by the vector function

Then the surface element is given by

So the surface integral is equivalent to

Then the surface element is given by

So the surface integral is equivalent to

Question

Determine the values of the constants b and c so that the function given below is differentiable. f(x)={2xbx2+cxx≤1x>1

Solution 1

Assuming the function is

For to be differentiable, it necessarily has to be continuous. For this condition to be met, we need

For the derivative to exist, the one-sided limits of the derivative must also exist and be equal. We have

Now we solve for and :

For to be differentiable, it necessarily has to be continuous. For this condition to be met, we need

For the derivative to exist, the one-sided limits of the derivative must also exist and be equal. We have

Now we solve for and :

Question

A tank with a capacity of 100 gallons initially contains 50 gallons of water with 10 pounds of salt in solution. fresh water enters at a rate of 2 gallons per minute and a well-stirred mixture is pumped out at the rate of 1 gallon per minute. compute the amount of salt (in pounds) in the tank at the first moment when the tank is filled.

Solution 1

Let be the amount of salt (in pounds) in the tank at time . We're given that.

The rate at which the amount of salt in the tank changes is given by the ODE

Given that , we find that

so that the amount of salt in the tank is described by

The tank will be filled when , or after minutes. At this time, the amount of salt in the tank is

The rate at which the amount of salt in the tank changes is given by the ODE

Given that , we find that

so that the amount of salt in the tank is described by

The tank will be filled when , or after minutes. At this time, the amount of salt in the tank is

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