Six times the cube of a number

When there are 6 choices for ingredients, the combination for selection of group of 3 ingridients for the taco will be 20.

What is combination?

The definition of the combination is "An arrangement of objects where the order of the objects is irrelevant." Combining these two words indicates "Selection of things," where the order of the items is irrelevant.

The number of ingredients is n = 6

The number of selection of ingredients available r = 3

The number of ways in which r distinct objects can be selected from a group of n distinct objects is n^C_r = n!/[r!(n-r)!]

The number of combinations is -

6^C_3 = 6!/[3!(6-3)!]

Here, n! represents 1 × 2 × 3 × 4 ×.....×n and 0! = 1

Calculate the combination =

6^C_3 = (6 × 5 × 4 × 3 × 2 × 1)/[3 × 2 × 1(3)!]

6^C_3 = 720/[6(3 × 2 × 1)]

6^C_3 = 720/(6 × 6)

6^C_3 = 720/36

Use the arithmetic operations of division -

6^C_3 =  20

Therefore, the number of combinations made are 20.

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The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).

Solving the given system of equations using Gaussian elimination:

2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13

Matrix form of the system is

[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13

Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1

Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4

Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5

Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5

Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6

The solution is (x,y,z) = (6,-5,5)

Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).

The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by

A·B = |A||B|cosθ

Given,A = (2, -3,0) and B = (-1,0,5)

Magnitude of A is |A| = √(2²+(-3)²+0²) = √13

Magnitude of B is |B| = √((-1)²+0²+5²) = √26

Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2

Cosine of the angle between A and B is

cosθ = A·B / (|A||B|)

cosθ = -2 / (√13×√26)

cosθ = -2 / √(13×26)

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Logistic regression is a statistical method used for modeling the probability of a binary outcome. In your case, yi follows a Bernoulli distribution with probability pi. The logistic regression model ensures that the predicted probability pi ∈ (0, 1) by using the logistic function.

The logistic function, also known as the sigmoid function, is defined as:

f(x) = 1 / (1 + e^(-x))

Here, x represents the linear combination of input features and their corresponding weights (or coefficients), and f(x) is the predicted probability pi. As x ranges from negative to positive infinity, the logistic function's output varies smoothly between 0 and 1.

In logistic regression, we model the log-odds of the probability pi as a linear function of input features:

log(pi / (1 - pi)) = β0 + β1 * x1 + β2 * x2 + ... + βn * xn

Solving for pi, we get:

pi = 1 / (1 + e^(-(β0 + β1 * x1 + β2 * x2 + ... + βn * xn)))

This equation ensures that the predicted probability pi always lies within the range (0, 1). The logistic function's properties guarantee that pi will never reach the exact values of 0 or 1, which preserves the parameter restrictions required for Bernoulli distributed outcomes.

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In response to the query, we can state that We can broaden the equation to test if it corresponds to the provided table:

\(0: p(0) = 0^2 - 11(0) + 19.25 = 17\s1: p(1) = 1^2 - 11(1\)

An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.

\(ax^2 + bx^2 + c = p(x)\)

We can determine a and b by using the coordinates of any two points on the parabola. Using points (1, 7) and (2, 1) as examples

\(a(1)^2 + b(1) + c = 7\\a(2)^2 + b(2) + c = 1\)

When we simplify each equation, we obtain:

\(a + b + c = 7\\4a + 2b + c = 1\\h = -b / 2a = -(-11) / 2(1) = 5.5\)

Hence, the vertex is (5.5, p(5.5)), and to finish the equation, we merely need to determine p(5.5).

We can broaden the equation to test if it corresponds to the provided table:

\(p(x) = (x - 5.5) (x - 5.5)\\a^2 - 11\s= x^2 - 11x + 30.25 - 11\s= x^2 - 11x + 19.25\\-1: p(-1) = (-1) (-1)\\a^2 - 11(-1) + 19.25 = 31\\\)

\(0: p(0) = 0^2 - 11(0) + 19.25 = 17\s1: p(1) = 1^2 - 11(1\)

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Answer:

Look at attached.

Step-by-step explanation:

A full circle is 360 degrees. So 180 represents half of the circle and 90 represents a quarter.

Answer:

chocolate 180°

Step-by-step explanation:

chocolate=180°

vanilla=90°

othere flavor=90°

the total degrees of the pie chart 360 °

Answer:

8 + \(\sqrt{3}\)

Step-by-step explanation:

A complex conjugate is found when the signs differ, but the numerical elements remain the same.

Answer:

-16

Step-by-step explanation:

Answer:

6. (x,y) -> (x,y-4)

7. (x,y) -> (-x,y)

Step-by-step explanation:

6. You shift it 4 units down. Y makes things go up and down.

7. Youre flipping it over the Y axis. It doesnt change the Y values, only the X.

M = A + |B| is the function's highest possible value. When sin or cos x equals 1, this maximum value is reached. m = A |B| is the function's lowest possible value. If either cos x or sin x is equal to 1, this minimum will be reached.

Example :

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Answer:

You do not

have graph, child.

N 1

Remember that

the speed is equal to divide the distance by the time

s=d/t

in this problem

we have

d=100 yd

t=5.1 sec

therefore

Convert the units

1 mile=1,760 yards

1 hour=3,600 seconds

so

d=100 yd=100/1,760 miles

t=5.1 sec=5.1/3,600 hours

Find out the speed

speed=(100/1,760)/(5.1/3,600)

N 2

speed=175 miles/hour

speed=d/t

d=speed*t

For t=12 sec -----> convert to hours

1 hour=3,600 sec

12 sec=12/3,600 hours

d=175(12/3,600)

d=0.5833 miles

Convert miles to feet

1 mile=5,280 ft

0.5833 miles=0.5833*5,280=3,080 ft

Convert 12 sec to hours

1 hour=3,600 sec

so

9514 1404 393

Answer:

Step-by-step explanation:

We can use the notation a∠b to represent the (x, y) components (a·cos(b), a·sin(b)), where angle b is measured CCW from the +x direction. If we label the forces a, b, c, d clockwise from A, then we have ...

  a = 80∠0° = (80, 0)

  b = 60∠90° = (0, 60)

  c = 90∠45° = (63.640, 63.640)

  d = 150∠-110° = (-51.303, -140.954)

__

If we label point A the origin, then the clockwise torque on point A is the sum of products of the force x-component and its y location, and its y-component and the negative of its x location.

  T = (0, 0)·(80, 0) +(3, 0)·(0, 60) +(3, -8)·(63.640, 63.640) +(0, -8)·(-51.303, -140.954)

  T = 809.433 . . . . n·m, the CW torque on point A

__

The sum of forces is ...

  F = a +b +c +d = (92.337, -17.314) = 93.946∠-10.62° . . . N

__

This force, applied to the point of application, must generate the same torque as the given forces. That is ...

  F·(y, -x) = 809.433

Then the equation of the line of action is ...

  17.314x +92.337y = 809.433 . . . . . x and y in meters measured from A

Any point (x, y) on this line will serve as a point of application of the force. Unfortunately, this line of action does not pass through the rectangular plate. The attachment shows the point (D) on the line of action that is closest to point A.

_____

Additional comment

The resultant force could be decomposed into two forces acting on the rectangular plate. One could be of much larger magnitude, operating at the corner opposite point A. This force would provide the necessary torque. Another would be acting on point A, providing no torque, but with components such that the resultant has the correct magnitude and direction.

Answer:

A(-2,2),. B(−1, −2), and C(-6, 1). Graph the triangle. Then graph the triangle after a translation 7 units right and. 3 units up.

Step-by-step explanation:

After translation 7units left and 17unit up ΔXYZ become ΔX'Y'Z' with new coordinates X'(-14,4) , Y'(-10,8) an Z'(-14,12).

" Translation is defined as the moving a geometrical shape by certain distance."

According to the question,

In ΔXYZ,

Coordinates of X =(-7,-13)

Coordinates of Y = (-3 ,-9)

Coordinates of Z = ( -7, -5)

After translation 7units left and 17units up and rotation 270° counterclockwise around the origin

New coordinates as shown in the drawn graph of ΔX'Y'Z'

Coordinates of X' = (-14, 4)

Coordinates of Y' = (-10, 8)

Coordinates of Z' = (-14,12)

Hence, translation 7units left and 17unit up ΔXYZ gives ΔX'Y'Z' with new coordinates X'(-14,4) , Y'(-10,8) an Z'(-14,12).

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The correct option is the mean for set 2 is equal to the mean for set 1. (option A).

Mean is a measure of central tendency that is used to determine the average of a set of numbers.  

Mean = sum of the numbers / total number

Mean of set 1 = (29 + 31 + 27 + 33 + 30) / 5

= 150 / 5 = 30

Mean of set 1 = (33 + 31 + 26 + 31 + 29) / 5

= 150 / 5 = 30

Median is the measure of center of a dataset. It determines the value that is at the center of a dataset that is arranged in either ascending or descending order.

Set 1 arranged in ascending order : 27, 29, 30, 31, 33

Median of set 1 = 30

Set 2 arranged in ascending order : 26, 29, 31, 31, 33

Median of set 2 = 31

Differnce in the median = 31 - 30 = 1

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The square root property to the equation will be (x – 4)² = 25. And the solutions will be the negative 1 and 9.

The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2. Then we have

The equation is given below.

x² – 8x + 16 = 9 + 16

Then the equation can be written as

(x – 4)² = 25

x – 4 = ±5

x = 4 ± 5

x = -1, 9

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If the variables are not quantitative we cannot do the arithmetic required in the formulas for r.

Quantitative order:

Therefore, if the variables are not quantitative we cannot do the arithmetic required in the formulas for r.

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The solution of the equations using elimination method is x = 2.5, y = 5.25

The elimination method is a method used to solve systems of linear equations. It involves manipulating the equations in such a way that one of the variables is eliminated, resulting in an equation in one variable that can be easily solved.

8x+4y = 49 --- (1)

3x+2y = 21  ----(2)

To eliminate x, multiply (1) by 3 and multiply (2) by 8. Then subtract the result. That is:

3 × (8x+4y = 49)   = 24x + 12y = 147

8 ×(3x+2y = 21)    = 24x + 16y = 168

.......................................................................

                                          4y = 21

.........................................................................

4y = 21

y = 21/4

y = 5.25

Put y = 5.25 into (1):

8x+4y = 49

8x + 4(5.25) = 49

8x + 21 = 49

8x = 49 -21

8x = 28

x = 28/8

x = 3.5

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The value of the sample proportionThe sample proportion is the percentage of individuals in a sample who have the attribute of interest. As a result, the sample proportion is computed by dividing the number of students who answered "yes" by the total number of students surveyed.

Here's the computation:Sample proportion= 220/400= 0.55Therefore, the sample proportion is 0.55.b. The standard error of the sample proportionThe standard error of the sample proportion can be determined using the following formula:Standard error of Standard error of the sample proportion= √[(0.55 * 0.45)/400]= √(0.00061875)= 0.0249Therefore, the standard error of the sample proportion is 0.0249.c. Constructing an approximate 95% confidence interval for the true proportion

A confidence interval is a range of values around a sample statistic, such as the sample proportion, that is expected to contain the true value of the population parameter with a certain degree of confidence. A 95 percent confidence interval implies that we are 95 percent certain that the true population parameter is within the specified interval.Let's first compute the margin of error:Margin of error= z* √[(p*q)/n]wherez= critical value of the standard normal distribution for a 95% confidence level= 1.96Margin of error= 1.96* √[(0.55*0.45)/400]= 0.0487Therefore, the margin of error is 0.0487. Now that we have the margin of error, we can construct the confidence interval using the following formula:Confidence interval= sample proportion ± margin of error= 0.55 ± 0.0487= (0.5013, 0.5987)Therefore, an approximate 95 percent confidence interval for the true proportion is (0.5013, 0.5987).

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\(\text{Given that,}\\\\\text{Width =w}, \\\\\text{Length,}~ l = \dfrac 52 +2w\\\\\text{Perimeter of rectangle}\\\\ =2( l+w)\\\\=2\left(\dfrac 52 + 2w +w\right)\\\\\\=2\left(\dfrac 52 +3w\right)\\\\\\=6w+5~~ \text{units}\)

Answer:

$3.87

Step-by-step explanation:

$123.84 / 32 = $3.87

So, each individual person's lunch costs $3.87

The length of the missing leg of the right triangle is 8sqrt(5) inches. To find the length of the missing leg of the right triangle, we can use the Pythagorean theorem.

It states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. This is Pythagorean theorem

In this case, we know that one leg measures 8 inches, and the hypotenuse measures 12 inches. Let's call the missing leg x, then we have:

8^2 + x^2 = 12^2

Simplifying, we have:

64 + x^2 = 144

Subtracting 64 from both sides, we get:

x^2 = 80

Taking the square root of both sides, we get:

x = sqrt(80)

Simplifying, we get:

x = 8sqrt(5)

Therefore, the length of the missing leg of the right triangle is 8sqrt(5) inches.

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The multiplication equation to find 5 divided by 1/3 is 5 x 3 = 15.

The division is one of the four basic mathematical operations, the other three being addition, subtraction, and multiplication.

At an elementary level the division of two natural numbers is, among other possible interpretations, the process of calculating the number of times one number is contained within another.

Unlike the other basic operations, when dividing natural numbers there is sometimes a remainder that will not go evenly into the dividend.

Division has two parts dividend and divisor.

Division is not commutative, meaning that a / b is not always equal to b / a.

Division is also not, in general, associative.

Division is traditionally considered as left-associative.

Division is right-distributive over addition and subtraction.

Division is shown in algebra and science by placing the dividend over the divisor with a horizontal line, also called a fraction bar, between them. For example, "a divided by b" can written as:

a/b

Now it is given that,

5 divided by 1/3

This can be expressed as,

5 divided by 1/3 = 5 ÷ 1/3

Since to convert the division of fraction into multiplication, we reciprocate the fraction

So, applying division we get,

5 ÷ 1/3 = 5 x 3

So, the multiplication equation is,

5 x 3

Now multiplying 5 and 3 we get,

5 x 3 = 15

this is the required multiplication equation of 5 divided by 1/3.

Thus, the multiplication equation to find 5 divided by 1/3 is 5 x 3 = 15.

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The probability of the weather forecast being correct on the randomly chosen day is 0.6, and the probability of it not being correct is 0.4.

To find the probability of the weather forecast being correct or not correct on a randomly chosen day, we need to use the information given:
Total number of days: 300
Number of days the weather forecast was correct: 180
First, let's find the probability that the weather forecast was correct on the randomly chosen day:
Probability of correct forecast = (Number of correct forecasts) / (Total number of days)
Probability of correct forecast = 180 / 300
Probability of correct forecast = 0.6
Now, let's find the probability that the weather forecast was not correct on the randomly chosen day:
Probability of incorrect forecast = 1 - Probability of correct forecast
Probability of incorrect forecast = 1 - 0.6
Probability of incorrect forecast = 0.4

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Answer:

4 km per second so 20 to 30 = 20+30=50÷4=12.5 or 12km

Answer:

Step-by-step explanation:

the line given is

\(x + 3y = 6\\3y = -x + 6\\y = \frac{-1}{3} (x) + 2\\\)

parallel lines have the same slope

\(y = \frac{-1}{3} (x) + b\\3 = \frac{-1}{3}(5) + b\\\frac{9}{3} = \frac{-5}{3} + b\\ b = \frac{14}{3}\\\)

\(y = \frac{-1}{3} (x) + \frac{14}{3}\)

The equation of line passes through the point (5, 3) will be;

⇒ y = - x/3 + 14/3

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The point on the line are (5, 3).

And, The parallel line is,

⇒ x + 3y = 6

⇒ y = - x/3 + 2

Now,

Since, The equation of line passes through the point (5, 3).

So, We need to find the slope of the line.

Since, The slope of the parallel line is same.

Hence, Slope of the line is,

⇒ y = - x/3 + 2

⇒ m = dy/dx = - 1/3

⇒ m = - 1/3

Thus, The equation of line with slope - 1/3 is,

⇒ y - 3 = - 1/3 (x - 5)

⇒ y - 3 = - 1/3 (x - 5)

⇒ y - 3 = - x/3 + 5/3

⇒ y = - x/3 + 5/3 + 3

⇒ y = - x/3 + 14/3

Therefore, The equation of line passes through the point (5, 3) will be;

⇒ y = - x/3 + 14/3

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The total area of the diamond is 19.5 square cm.

The total area of the diamond can be calculated by finding the area of the trapezoid and triangle separately and adding them together.

The area of the trapezoid can be calculated using the formula for the area of a trapezoid:

Area = (base1 + base2) / 2 × height

Where base1 and base2 are the lengths of the parallel sides and height is the distance between the parallel sides. In this case, base1 and base2 are both 4 cm, and height is 2 cm, so:

Area = (4 + 4) / 2 × 2 = 4 × 2 = 8 square cm

The area of the triangle can be calculated using the formula for the area of a triangle:

Area = (base × height) / 2

In this case, the base is 4 cm, and the height is 5.75 cm, so:

Area = (4 × 5.75) / 2 = 11.5 square cm

Adding the area of the trapezoid and triangle together:

Area = 8 + 11.5 = 19.5 square cm

So the total area of the diamond is 19.5 square cm.

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Answer:

f(3)=21

g(-4)=-14

Step-by-step explanation:

Answer:

Step-by-step explanation:

f(x) = 6x + 3

f(3) =6*3 +3

f(3) = 18 + 3

f(3) = 21

g(x) = 3x - 2

g(-4) = 3*-4 - 2

g(-4) = - 14

f(3)*f(-4) = 21 * -14= -294

Answer:

y = -4x + 12

Step-by-step explanation:

For a line to be parallel, it needs to have the same slope.

Point intercept form: y - y₁ = m (x - x₁)

Where y and x are just kept as y and x, y₁ and x₁ are the parts of a coordinate, and m = slope.

So, in order for the line to be parallel, it needs to have the same slope as the first equation. The slope of the line (which is the "m" in y = mx + b) is..

4x + y = 7

y = -4x + 7

So, m, or the slope, is -4.

Plug this, along with the coordinate the problem gives you into point-intercept form.

y - y₁ = m (x - x₁)

y - 8 = -4 (x - 1)

Simplify.

y - 8 = -4x + 4

Add 8 to both sides.

y = -4x + 12