3!+0!
____
2!x1!
A. 3/2
B. 3
C. 7/2

Given: The angle with a measure of 2.8 degrees.

To calculate the percentage, we need to determine how many degrees are in a full rotation around the circle. A full rotation is equivalent to 360 degrees.

Now we can calculate the percentage:

Percentage = (Angle measure / Full rotation measure) * 100

Percentage = (2.8 degrees / 360 degrees) * 100

Percentage ≈ 0.7778%

Therefore, the angle with a measure of 2.8 degrees is approximately 0.7778% of a full rotation around the circle.

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\(\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=8\\ \theta =135 \end{cases}\implies A=\cfrac{(135)\pi (8)^2}{360}\implies A=24\pi \implies A\approx 75.4\)

The equation of the function d(t) is d(t) = -2sin(π/2 t) + 5

The function is given as:

d(t) = a * sin(b * t) + d

The bob is 5 cm away from the wall implies that the vertical shift is 5.

This means that

d = 5

So, we have

d(t) = a * sin(b * t) + 5

The bob reaches the closest point to the wall, which is 3 cm from the wall.

So, the amplitude is

A = 3 - 5

Evaluate

A= -2

So, we have:

d(t) = -2 * sin(b * t) + 5

The period is calculated as:

B = 2π/t

Where

t = (5 + 3)/2

This gives

t = 4

Substitute t = 4 in B = 2π/t

B = 2π/4

Evaluate

B = π/2

So, we have:

d(t) = -2sin(π/2 t) + 5

Hence, the equation of the function d(t) is d(t) = -2sin(π/2 t) + 5

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Hi, you've asked an incomplete question. However, I provided a brief explanation about surface areas.

Explanation:

Surface area is a term commonly used in mathematics, and other branches of science, and it basically refers to a calculation of the total space that an object occupies.

For example, you can find the surface areas of a cuboid using the formula:

\(6s^{2}\) where s= side length.

Answer:

34.7647058824

Step-by-step explanation:

Answer:

300

Step-by-step explanation:

Total= 40+96+2*30+104= 300

Each hippo receives 0.6 pumpkins, according to an expression.

Mathematical operators such as addition, subtraction, multiplication, and division are used to form an expression using numbers or variables. For instance, "4 added to 2" in mathematics will be expressed as 2+4.

An expression in mathematics is made up of a mixture of variables, numbers, and functions (such as addition, subtraction, multiplication or division etc.) In some ways, phrases and expressions are comparable.

3/5 = 0.6.

Each hippo receives 0.6 pumpkins, according to an expression.

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Step-by-step explanation:

If they are similar, then 10 is to 3      as  x is to 15

10/3 = x/15    multiply both sides by 15

 50 mm = x

Using the combination, 1716 are 7 digit phone numbers in which the digits are non-increasing and every digit is less than or equal to the previous one.

In the given question,

We have to find how many 7 digit phone numbers are there in which the digits are non-increasing and that is, every digit is less than or equal to the previous one.

We have to write 7 digit phone number.

Let the 7 digit are

A, B, C, D, E, F, G

Every digit is less than or equal to the previous one.

A ≥ B ≥ C ≥ D ≥ E ≥ F ≥ G

The sum of these number is 7.

So |A| + |B| + |C| + |D| + |E| + |F| + |G| = 10

We always have precisely one non-increasing digit for any given set of seven digits. Therefore, the solution to our problem is to make it simpler to calculate the total number of combinations where 7 digits must be chosen from a set of 7 digits where each digit is repeatable.

So the solution should be

= \(^{7+7-1}C_{7}\)

= \(^{13}C_{7}\)

We know that \(^nC_{r}=\frac{n!}{r!(n-r)!}\)

= \(\frac{13!}{7!(13-7)!}\)

= \(\frac{13!}{7!6!}\)

Simplifying

= \(\frac{13\times12\times11\times10\times9\times8\times7!}{7!\times6\times5\times4\times3\times2\times1}\)

Simplifying

= 13×11×2×3×2

= 1716

Hence, 1716 are 7 digit phone numbers in which the digits are non-increasing and every digit is less than or equal to the previous one.

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The given equation 3x^2 - y^2 + z^2 = 0 represents a surface known as an elliptic paraboloid. To sketch this surface using traces, we can fix one variable (either x, y, or z) and vary the other two to observe the resulting curve.

Let's fix x at a constant value of 0. Substituting x = 0 into the equation, we get -y^2 + z^2 = 0. This equation represents a pair of intersecting lines, forming a trace. By varying x and fixing y or z, we can obtain additional traces, which are also pairs of intersecting lines.

Thus, by considering multiple traces, we can sketch the elliptic paraboloid surface, which resembles a bowl or a saddle. The traces consist of intersecting lines that form a grid-like pattern on the surface.

Now, moving on to the second question, we are given two skew lines with parametric equations. To find the distance between these lines, we can use the closest distance formula.

First, we need to find a point on each line. By setting t = 0 in the first line's equations, we find a point (2, 3, 0). Similarly, setting s = 0 in the second line's equations gives us a point (1, 6, -2).

Next, we find the direction vectors for both lines. The direction vector for the first line is <1, 6, 2>, and for the second line is <2, 14, 5>.

Using the closest distance formula, we can calculate the distance between the two lines as follows:

distance = |(2-1, 3-6, 0+2) · (1, 6, 2) x (2, 14, 5)| / |(1, 6, 2) x (2, 14, 5)|

Simplifying this expression will give us the distance between the skew lines.

Please note that the exact calculations are omitted here, but following the steps outlined above will provide the desired distance.

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Answer:

No

Step-by-step explanation:

The function is not one to one because there are multiple x-values for each y-value.

Diagonals of a parallelogram measure 16cm and 14cm respectively. The shorter side measures 10cm. The longer side of the parallelogram measures 2 * sqrt(13) cm.

To find the length of the longer side of the parallelogram, we can use the properties of parallelograms. In a parallelogram, opposite sides are equal in length.

Let's assume that the longer side of the parallelogram measures x cm. Since the shorter side is given as 10 cm, we have two sides of the parallelogram: 10 cm and x cm.

We are also given the lengths of the diagonals, which are 16 cm and 14 cm. In a parallelogram, the diagonals bisect each other. This means that the diagonal divides the parallelogram into two congruent triangles.

Using the properties of these triangles, we can apply the Pythagorean theorem. The diagonals, shorter side, and longer side of the parallelogram form a right triangle.

Using the Pythagorean theorem, we can set up the following equation:

(14/2)^2 + (16/2)^2 = 10^2 + (x/2)^2

Simplifying the equation, we have:

49 + 64 = 100 + (x/2)^2

113 = 100 + (x/2)^2

(x/2)^2 = 13

x/2 = sqrt(13)

x = 2 * sqrt(13)

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Answer:

A = 2 1/2 ft^2

Step-by-step explanation:

The area of a rectangle is given by

A = l*w

A = 3 * 5/6

A = 5/2 ft^2

A = 2 1/2 ft^2

Answer:

A=2.5 ft^2

Step-by-step explanation:

A=3

A=3(5/6)

A=2.5 ft^2

Answer:

see explanation

Step-by-step explanation:

the legs and diagonals of an isosceles trapezoid are congruent , then

EH = FG ( substitute values )

4x - 27 = x + 9 ( subtract x from both sides )

3x - 27 = 9 ( add 27 to both sides )

3x = 36 ( divide both sides by 3 )

x = 12

and

FH = EG ( substitute values )

11y - 21 = 3y + 19 ( subtract 3y from both sides )

8y - 21 = 19 ( add 21 to both sides )

8y = 40 ( divide both sides by 8 )

y = 5

Then

EH = 4x - 27 = 4(12) - 27 = 48 - 27 = 21

EG = 3y + 19 = 3(5) + 19 = 15 + 19 = 34

Part A: Width = 9.3 ft; Height = 16.5 ft; Area =  153.45 sq ft.

Part B: Width = 38.25 ft ; Height = 91 ft; Area =  3503.5 sq ft.

Part A: conversion factor: 1 in = 3 ft

Width = 3.1 in

Width = 3.1 x 3

Width = 9.3 ft

Height = 5.5 x 3 ft

Height = 16.5 ft

Area = Width x Height

Area = 9.3 ft x  16.5 ft

Area = 153.45 sq ft

Part B: conversion factor: 1 in = 6.5 ft

Width = 8.5 in

Width = 8.5 x 6.5

Width = 38.25 ft

Height = 14 x 6.5 ft

Height = 91 ft

Area = Width x Height

Area = 38.5 ft x  91 ft

Area =  3503.5 sq ft

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The number of arrangements of the letters in mathematics such the last vowel in the arrangement is an i are 30,240.

To find the number of arrangements of the letters in "mathematics" such that the last vowel in the arrangement is an "i". Counting the vowels, we have three vowels that are a, e, and i.

Count the number of ways to arrange the three vowels in the word. This is a permutation problem, and we can use the formula for permutations of n objects taken r at a time, which is:

P(n, r) = n! / (n-r)!

So, putting the values,

P(3, 3) = 3! / (3-3)! = 3! / 0! = 6

There are 6 methods to arrange a, i and e in the word. Now, we have to arrange the consonants. There are 7 consonants in "mathematics", but we have already placed the last vowel as "i", so we only need to arrange the remaining 6 letters. This is again a permutation problem, and we can use the formula for permutations of n objects taken r at a time:

P(n, r) = n! / (n-r)!

Putting values,

P(7, 6) = 7! / (7-6)!

= 7! / 1!

= 5040

There are 5040 ways to arrange the remaining 6 letters in the word.

Finally, we can multiply the number of arrangements of the vowels and the number of arrangements of the remaining consonants to get the total number of arrangements that meet the given condition:

6 * 5040 = 30,240

Therefore, there are 30,240 arrangements of the letters in "mathematics" such that the last vowel in the arrangement is an "i".

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Answer:

-6/5

Step-by-step explanation:

The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the slope formula:

slope = (y2 - y1) / (x2 - x1)

Plugging in the given points, we get:slope = (14 - 8) / (-3 - 2) = 6 / (-5)

To write this in simplest form, we can divide the numerator and denominator by their greatest common factor, which is 1 in this case. So the slope in simplest form is:

slope = 6 / (-5) = -6/5

Using the rise/run notation, we can say that the slope of the line passing through the points (2, 8) and (-3, 14) is -6/5, or -6 over 5.

The rise is -6 (since we move down 6 units from y1 to y2), and the run is 5 (since we move 5 units to the left from x1 to x2).

The total time required taken by the bell to ring 20 times is equal to 180 seconds, or 3 minutes.

If it takes the bell 90 seconds to ring 10 times, we can calculate the average time it takes for each ring,

Average time per ring

= Total time / Number of rings

= 90 seconds / 10 rings

= 9 seconds per ring

To find out how long it will take the bell to ring 20 times,

we can multiply the average time per ring by the number of rings,

Time to ring 20 times

= Average time per ring × Number of rings

= 9 seconds per ring × 20 rings

= 180 seconds

Therefore, it will take the bell 180 seconds, or 3 minutes, to ring 20 times.

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Answer:

\(\cos(\theta_1)=-\dfrac{\sqrt{15}}{4}\)

Step-by-step explanation:

The angle \(\theta_1\) is located in Quadrant II.

\(\sin(\theta_1)=\dfrac{1}{4}\)

From trigonometry, we know that:

\(\sin(\theta)=\dfrac{Opposite}{Hypotenuse}\\$Therefore:\\Opposite=1\\Hypotenuse=4\\Using Pythagorean theorem:\\Hypotenuse^2=Opposite^2+Adjacent^2\\4^2=1^2+Adjacent^2\\Adjacent^2=16-1\\Adjacent^2=15\\Adjacent=\sqrt{15}\)

Now, in Quadrant II,

Therefore, the Adjacent angle to \(\theta_1 =-\sqrt{15}\)

Therefore:

\(\cos(\theta_1)=\dfrac{Adjacent}{Hypotenuse}=\dfrac{-\sqrt{15}}{4}\\\\\cos(\theta_1)=-\dfrac{\sqrt{15}}{4}\)

To determine A we will use the inverse function of the sine ( the arcsine):

Now, we convert A from degrees to degrees and minutes:

Answer:

Answer:

78.5

Step-by-step explanation:

Answer:

6 gallons per month

Step-by-step explanation:

Company A     Company B

     $15                  $25            Gallon 1

    $23                  $31             Gallon 2

    $31                   $37            Gallon 3

    $39                  $43            Gallon 4

    $47                  $49            Gallon 5

    $55                  $55           Gallon 6

Answer:

The slope is -4/3

I hope this helps :)

Answer:

-8(3x-8)

Step-by-step explanation:

Factor -8 out of -24x+64

Answer:

The british

Step-by-step explanation:

Answer:

The Britsh

Step-by-step explanation:

Formal colonialism first came to the region we today call Ghana in 1874, and British rule spread through the region into the early twentieth century. The British called the territory the “Gold Coast Colony."

Answer:

n = 7

n = -3

Step-by-step explanation:

4n+6 = n²-15

4n = n² - 21

n² - 4n - 21 = 0

(n-7)(n+3) = 0

n = 7

n = -3

Step-by-step explanation:

The actual square root value is

12.7671453348...

But we Have taken only significant

figure and it is as 12.76

Answer:

x=5

Step-by-step explanation:

Simplifying 5x + -7 = 2x + 8 Reorder the terms: -7 + 5x = 2x + 8 Reorder the terms: -7 + 5x = 8 + 2x Solving -7 + 5x = 8 + 2x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2x' to each side of the equation. -7 + 5x + -2x = 8 + 2x + -2x Combine like terms: 5x + -2x = 3x -7 + 3x = 8 + 2x + -2x Combine like terms: 2x + -2x = 0 -7 + 3x = 8 + 0 -7 + 3x = 8 Add '7' to each side of the equation. -7 + 7 + 3x = 8 + 7 Combine like terms: -7 + 7 = 0 0 + 3x = 8 + 7 3x = 8 + 7 Combine like terms: 8 + 7 = 15 3x = 15 Divide each side by '3'. x = 5 Simplifying x = 5

Answer:

x = 8

Step-by-step explanation:

Given

- 4 + 3x = 20 ( add 4 to both sides )

3x = 24 ( divide both sides by 3 )

x = 8

\(\huge\text{Hey there!}\)

\(\large\textsf{-4 + 3x = 20}\\\rightarrow\large\textsf{3x - 4 = 20}\\\\\large\text{ADD 4 to BOTH SIDES}\\\large\textsf{3x - 4 + 4 = 20 + 4}\\\large\text{CANCEL out: \textsf{-4 + 4} because that gives you \textsf 0}\\\large\text{KEEP: \textsf{20 + 4}} \text{ because it gives you the \textsf{x-value}}}\\\\\large\textsf{20 + 4 = \bf 24}\\\\\large\text{DIVIDE 3 to BOTH SIDES}\\\\\mathsf{\dfrac{3x}{3}= \dfrac{24}{3}}\\\large\text{CANCEL out: }\mathsf{\dfrac{3}{3}}\large\text{ because that gives you \textsf 1}\)

\(\large\text{KEEP: }\mathsf{\dfrac{24}{3}}\large\text{ because it helps gives you the result of the \textsf{x-value}}\\\\\mathsf{x = \dfrac{24}{3}}\\\\\large\textsf{x= 24}\div \large\textsf{3}}\\\large\textsf{x = \bf 8}\\\\\boxed{\boxed{\huge\text{Therefore, your answer is: \textsf{x = 8}}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

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