5/7+1/2+3/4

i need help please

The spherical coordinates for the point (0, -3, -3) are (3√2, -π/2, π/4).

(a) To change from rectangular coordinates to spherical coordinates, we use the following formulas:

rho = √(x² + y² + z²)

theta = atan2(y, x)

phi = acos(z / rho)

Given the rectangular coordinates (5, 5√3, 10√3), we can substitute the values into the formulas to find the corresponding spherical coordinates:

rho = √((5)² + (5√3)² + (10√3)²)

= √(25 + 75 + 300)

= √(400)

= 20

theta = atan2(5√3, 5)

= atan(√3)

≈ 1.0472 radians

phi = acos((10√3) / 20)

= acos(√3 / 2)

= π/6 radians

Therefore, the spherical coordinates for the point (5, 5√3, 10√3) are (20, 1.0472, π/6).

(b) Given the rectangular coordinates (0, -3, -3), we can apply the formulas for spherical coordinates:

rho = √((0)² + (-3)² + (-3)²)

= √(0 + 9 + 9)

= √(18)

= 3√2

theta = atan2(-3, 0)

= -π/2 radians

phi = acos((-3) / (3√2))

= acos(-1/√2)

= π/4 radians

Hence, the spherical coordinates for the point (0, -3, -3) are (3√2, -π/2, π/4).

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Answer:

B = 48.7°

C = 61.3°

b = 12

Step-by-step explanation:

Given:

A = 70°

a = 15

c = 14

Required:

B, C, and b

Solution:

✔️Using the law of sines, let's find C:

Sin C/c = Sin A/a

Plug in the values

Sin C/14 = Sin 70/15

Cross multiply

Sin C × 15 = Sin 70 × 14

Divide both sides by 15

Sin C = (Sin 70 × 14)/15

Sin C = 0.8770

C = Sin^{-1}(0.8770)

C = 61.282566° = 61.3° (nearest tenth)

✔️Find B:

B = 180 - (70 + 61.3) (sum of triangle)

B = 48.7°

✔️Find b using the law of sines:

b/sinB = a/sinA

Plug in the values

b/sin 48.7 = 15/sin 70

Cross multiply

b*sin 70 = 15*sin 48.7

Divide both sides by sin 48.7

b = (15*sin 48.7)/sin 70

b = 11.9921789

b = 12.0 (nearest tenth)

Answer:

angle 1 = 124

angle 2 = 56

angle 3 = 124

angle 4 = 56

Step-by-step explanation:

This problem is a bit like a puzzle. To make notation easier I'm going to do this:

angle 1 = a

angle 2 = b

angle 3 = c

angle 4 = d

Now, let's start with what we know from the image.

All angles added together form a circle or 360 degrees

a + b + c + d = 360

In the same regard a + d = 180, and b + c = 180

Also,

a = c

and

b = d

It also tells us angle 4 is 25 degrees greater than one fourth of angle 1. Which is written as.

d = 1/4(a) + 25

If we look at all the equations we have, we can see that two of the equations have two of the same variables:

a + d = 180

and

d = 1/4(a) + 25

Using substitution we can take the second equation substitute it for d in the first equation giving us:

a + (1/4(a) + 25) = 180

Now we just solve for a

[tex]\frac{4}{4} a+ \frac{1}{4} a + 25 = 180\\\\\frac{5}{4}a + 25 = 180 \\\\(\frac{5}{4}a + 25) - 25 = (180) -25\\\\\frac{5}{4} a = 155\\\\\frac{5}{4} a * \frac{4}{5} = 155 * \frac{4}{5}\\\\a = 124[/tex]

Therefore a, or angle 1, is 124

Since a = c, then c, or angle 3, is also 124

Since a + d = 180 and a = 124 then

d = 180 -124

d = 56

So, d, or angle 4, is 56

And because b = d then b, or angle 2, is also 56

a = 124

b = 56

c = 124

d = 56

For extra measure, we can check our work by using the first equation

a + b + c + d = 360

124 + 56 + 124 + 56 = 360

Answer:

16%

Step-by-step explanation:

(174-150)/150= 0.16

0.16*100 = 16%

Answer:

3/10 inches apart

Step-by-step explanation:

total miles based on 2" equals 33 miles can be found by solving this proportion:

2/33 = 6/x

2x = 198

x = 99

99 miles divided by 11 rest stops means each stop is 9 miles apart

now use new ratio of 1" equals 30 miles

1/30 = x/9

30x = 9

x = 9/30 or 3/10 inches

The correct statement is : M spans P2.

The set M = {[tex]x+1, x^2-2, 3x[/tex]} consists of three polynomials in the variable x.

To determine whether M spans P3 or P2, we need to consider the highest degree of the polynomials in M.

The highest degree of the polynomials in M is 2 (from [tex]x^2-2[/tex]), which means that M can span at most the space of polynomials of degree 2 or less, i.e., P2.

To check whether M spans P2 or not, we need to see if any polynomial of degree 2 or less can be expressed as a linear combination of the polynomials in M.

We can write any polynomial of degree 2 or less as [tex]ax^2 + bx + c[/tex], where a, b, and c are constants.

To express this polynomial as a linear combination of the polynomials in M, we need to solve the system of equations:

[tex]a(x^2-2) + b(x+1) + c(3x) = ax^2 + bx + c[/tex]

This can be written as:

[tex]ax^2 + (-2a+b+3c)x + (b+c) = ax^2 + bx + c[/tex]

Equating the coefficients of [tex]x^2, x,[/tex] and the constant term, we get:

[tex]a = a,\\-2a+b+3c = b,\\b+c = c.[/tex]

The first equation is always true, and the other two equations simplify to:

[tex]-2a+3c = 0,\\b = 0.[/tex]

Solving for a, b, and c, we get:

[tex]a = 3c/2,\\b = 0,\\c = c.[/tex]

Therefore, any polynomial of degree 2 or less can be expressed as a linear combination of the polynomials in M. This means that M spans P2.

However, M cannot span P3, because P3 includes polynomials of degree 3, which cannot be expressed as a linear combination of the polynomials in M (since the highest degree polynomial in M is [tex]x^2[/tex]).

Therefore, the correct statement is: M spans P2.

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Answer:

(x - 3)^2 + (y - 6)^2 = 17

Step-by-step explanation:

The standard form of a circle's equation is (x-h)² + (y-k)² = r² where (h,k) is the center and r is the radius.

(x - 3)^2 + (y - 6)^2 = 17

Answer:

Where is the question so that I can help you with it

a. For the function f(x) = (x + x)(log(x) + 3x) is O(x) with the witnesses C = 7 and k = 1.

b. It is proved that f(x) = (x + x)(log(x) + 3x) is (x) with the witnesses C = 1 and k = 1.

c. The obtained witnesses C = 1, C' = 10, and k =[tex]10^C.[/tex] such that g(x)log(x) < Cg(x) whenever x > k. And g(x) = 1.

a) To show that f(x) = (x + x)(log(x) + 3x) is O(x),

find witnesses C and k such that f(x) ≤ C × x for all x > k.

Let's simplify the expression for f(x):

f(x) = 2x × (log(x) + 3x)

= 2x × log(x) + 6x²

Now, find a witness C and a value k such that f(x) ≤ C × x for all x > k.

Let's choose C = 7 and k = 1.

This means show that f(x) ≤ 7x for all x > 1.

For x > 1,

f(x) = 2x × log(x) + 6x²

< 2x × log(x) + 6x² + 7x

= 2x × log(x) + 6x² + 7x

= x(2log(x) + 6x + 7)

≤ x(2log(x) + 13x)

≤ x × 7

= 7x

This implies,

f(x) = (x + x)(log(x) + 3x) is O(x) with the witnesses C = 7 and k = 1.

b) To show that f(x) = (x + x)(log(x) + 3x) is (x),

find witnesses C and k such that f(x) ≥ C × x for all x > k.

Let us simplify the expression for f(x):

f(x) = 2x × (log(x) + 3x)

= 2x × log(x) + 6x²

Now, find a witness C and a value k such that f(x) ≥ C × x for all x > k.

Let us choose C = 1 and k = 1.

This means show that f(x) ≥ x for all x > 1.

For x > 1,

f(x) = 2x × log(x) + 6x²

> x × log(x) + 6x²

= x(log(x) + 6x)

≥ x(log(x) + x)

≥ x × log(x)

≥ x

Therefore, we have shown that f(x) = (x + x)(log(x) + 3x) is (x) with the witnesses C = 1 and k = 1.

c) To find the obtained witnesses C, C', and k .

such that g(x)log(x) < Cg(x) whenever x > k,

Examine the expression f(x) = (x + x)(log(x) + 3x) and determine the function g(x).

Let us simplify the expression for f(x),

f(x) = 2x × (log(x) + 3x)

= 2x × log(x) + 6x²

From the given condition, we have g(x)log(x) < Cg(x) rewrite this as,

log(x) < C

Since log(x) is an increasing function, if log(x) < C, it means x < [tex]10^C.[/tex]Therefore, the witness k is [tex]10^C.[/tex]

Now let us determine g(x).

Since g(x)log(x) appears in the inequality, we can take g(x) = 1.

C = 1, C' = 10, and k = [tex]10^C.[/tex] for g(x)log(x) < Cg(x) whenever x > k. And g(x) = 1.

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A class interval refers to option b) a division used for grouping a set of observations.

The correct answer is (b) a division used for grouping a set of observations. In statistics, when dealing with a large set of data, it is often helpful to group the data into intervals or classes to better understand the distribution. A class interval represents a range of values that are grouped together. It is defined by specifying the lower and upper boundaries of each interval.

For example, if we are analyzing the heights of individuals, we may create class intervals such as 150-160 cm, 160-170 cm, and so on. The purpose of using class intervals is to simplify the data and provide a clearer picture of the distribution. It allows us to summarize the data and identify patterns or trends within specific ranges. Therefore, option (b) is the correct description of a class interval.

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Answer:

5.318 * 10 to power of 8

Step-by-step explanation:

Answer:

5.318 × [tex]10^{8}[/tex]

Step-by-step explanation:

The expected value of the given random variable is 8.3. This means that, on average, if we repeatedly sample from this random variable, we can expect the resulting values to be around 8.3.

To find the expected value of a random variable, you multiply each possible value by its corresponding probability and sum them up. In this case, we have a combination of probabilities and numerical values. Let's calculate the expected value:

Multiply each numerical value by its corresponding probability:

(0.35 * 8) + (0.3 * 9) + (0.05 * 10) + (0.1 * 11) + (0.05 * 11) + (0.15 * 11)

Perform the calculations:

2.8 + 2.7 + 0.5 + 1.1 + 0.55 + 1.65

Sum up the results:

8.3

Therefore, the expected value of the given random variable is 8.3. This means that, on average, if we repeatedly sample from this random variable, we can expect the resulting values to be around 8.3. The expected value provides a measure of central tendency for the random variable.

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To have a horizontal asymptote at y = 3 and vertical asymptotes at x = 4 and x = -3, the rational function should have the following form:

f(x) = (a polynomial in x) / ((x - 4)(x + 3))

The polynomial in the numerator can have any degree, but it must be of lower degree than the denominator.

Therefore, among the given rational functions, the one that satisfies these conditions would be the one in the form:

f(x) = (a polynomial) / ((x - 4)(x + 3))

Please provide the specific options you have, and I can help you determine which of those options matches this form.

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Answer:

x = 12 the correct answer

Answer:

38

Step-by-step explanation:

(10*2)+(9*2)

Answer:

B. 9

Step-by-step explanation:

Proportions are just like fractions and to figure them out sometimes you can use simplification in different forms.

[tex]\frac{x}{6}[/tex] = [tex]\frac{36}{24}[/tex]

Now to get to 6, 24 had to be divided by 4...in proportions and fractions usually, the top and bottom are both simplified or proportioned to the same number or scale

36 ÷ 4 = 9

Check your answer by inserting it there to see if it works

9*4 = 36            6*4 = 24

Answer:

[tex]\boxed {\boxed {\sf B. \ 9}}[/tex]

Step-by-step explanation:

We are given this proportion:

[tex]\frac {x}{6}=\frac{36}{24}[/tex]

We want to solve for x, so we must isolate the variable using inverse operations.

It is being divided by 6. The inverse of division is multiplication, so we multiply both sides of the proportion by 6.

[tex]6*\frac {x}{6}=\frac{36}{24}*6[/tex]

[tex]x=\frac{36}{24}*6[/tex]

[tex]x=1.5*6 \\x=9[/tex]

Another way to solve is with cross multiplication. Multiply the first numerator by the second denominator, then the first denominator by the second numerator.

[tex]\frac { x}{6}=\frac{36}{24}[/tex]

[tex]24*x=6*36[/tex]

[tex]24x=216[/tex]

The variable is being multiplied by 24. The inverse of multiplication is division, so we divide both sides of the equation by 24.

[tex]24x/24=216/24\\x=9[/tex]

The value of x that makes this proportion true is 9.

(a) If there are 4 candidate,  the smallest number of votes that a plurality candidate could have is 33.

(b) If there are 8 candidate,  the smallest number of votes that a plurality candidate could have is 17.

The smallest number of votes that a plurality candidate could have is calculated as follows;

(a) If there are 4 candidate, the number of votes for each candidate;

= 129 / 4

= 32.25

The least number of votes for the plurality candidate = 33

(b) If there are 8 candidate, the number of votes for each candidate;

= 129 / 8

= 16.125

The least number of votes for the plurality candidate = 17

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Answer:

Tens digit, x = 3

Unit digit, y = 8

Number = 38

Step-by-step explanation:

Let the 2 digit number = xy

y = x + 5 - - - (1)

10x + y = 4(x + y) - 6

10x + x + 5 = 4(x + x + 5) - 6

11x + 5 = 4(2x + 5) - 6

11x + 5 = 8x + 20 - 6

11x + 5 = 8x + 14

11x - 8x = 14 - 5

3x = 9

x = 9/3

x = 3

From (1)

y = x + 5

y = 3 + 5

y = 8

I think that the answer would be two triangles.

Answer:

50

Step-by-step explanation:

this can be solved by ratio   15/x = 30/100.  Cross multiply and solve for x.  The answer is 50.

Answer:

12.6

Step-by-step explanation:

divide the length value by 3

Answer:

x=-2

Step-by-step explanation:

Answer:

60 mins

Step-by-step explanation:

15+45=60

The time needed to make 138 pancakes if both Mark and Charlotte work together is 227.142 minutes.

A fraction is a way to describe a part of a whole. such as the fraction 1/4 can be described as 0.25.

As it is given that Mark can make 9 pancakes in 15 minutes, therefore, the number of pancakes that Mark can make in one minute,

[tex]\text{Number of Pancake in one minute} = \dfrac{9}{15}[/tex]

Now, for Charlotte, it is given that he makes 42 pancakes in 45 minutes, therefore, the number of pancakes that Charlotte can make in one minute,

[tex]\text{Number of Pancake in one minute} = \dfrac{42}{45} = \dfrac{12}{15}[/tex]

Further, the total pancakes that can be made in one minute,

[tex]\text{Total Number of Pancake in one minute} = \dfrac{9}{15} +\dfrac{12}{15} = \dfrac{21}{15}[/tex]

As they both need to make 138 pancakes together, therefore, the time they need is,

[tex]\rm Time\ Needed = \dfrac{\text{Total number of pancakes}}{\text{Total number of pancakes in one minute}}[/tex]

[tex]\rm Time\ Needed = \dfrac{138}{\frac{21}{15}} = \dfrac{138\times 15}{21} = 227.142[/tex]

Hence, the time needed to make 138 pancakes if both Mark and Charlotte work together is 227.142 minutes.

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I hope the answer is helpful

Answer:

50 units

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

[Right Triangles Only] Pythagorean Theorem: a² + b² = c²

Step-by-step explanation:

Step 1: Define

a = 48

b = 14

c = ?

Step 2: Solve for c

Ok. So 14% of 18.00 can be figured out without a calculator. 18.00 / 10 = 1.80 = 10%.

(18.00 / 100) x 4 = 0.72

1.80 + 0.72 = $2.52 is the tip.

$18 + $2.52 = $20.52

⭐ Answered by Foxzy0⭐

⭐ Brainliest would be appreciated, I'm trying to reach genius! ⭐

⭐ If you have questions, leave a comment, I'm happy to help! ⭐

Answer:

9/2 = 4 1/2

Step-by-step explanation:

Given that a hockey tournament consists of 16 teams. In the first round, every team is randomly assigned to one of 8 games (2 teams per game). We are supposed to find the probability that all three Alberta teams are randomly assigned to different games. Let A be the event of assigning all three Alberta teams to different games.

Then the number of ways to select 3 teams from 16 teams is $\ dbinom {16}{3}$, the number of ways to assign 3 teams to different games is $8\times7\times6$, and the number of ways to assign the remaining 13 teams to games is $(13!) / (2^6\times6!)$.The probability of event A is given by;$$

P(A) = \frac{\text{number of ways to assign 3 teams from Alberta to different games}}{\text{number of ways to assign all teams to games}} = \frac{8\times7\times6 \times (13!) / (2^6\times6!)}{\dbinom{16}{3} \times (14!) / (2^7\times7!)}
$$Simplifying the above expression,$$
P(A) = \frac{8\times7\times6 \times 13! \times 2}{\dbinom{16}{3} \times 14!} = \frac{8\times7\times6 \times 2}{\dbinom {16}{3}} = \frac{336}{560} = \frac{3}{5}

Therefore, the probability that all three Alberta teams are randomly assigned to different games is $\frac{3}{5}$.

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Answer:The diagram that models the ratio in the story is:

Mermaid book: Princess book = 3:2

To find out how many times Nolan has read the mermaid book, we can set up the following proportion:

3/2 = x/20

Cross-multiplying, we get:

2x = 3 * 20

2x = 60

Dividing both sides by 2, we find:

x = 60/2

x = 30

Therefore, Nolan has read the mermaid book 30 times this month.