When you arrive at the family reunion, Uncle Ta-Nehisi has already started eating mini hot dogs. 2 minutes
later, he has eaten a total of 43 hot dogs. 4 minutes after you arrived he finished 73 of them.

Answer:

If a function has an axis of symmetry x = a,

Step-by-step explanation:

then f (x) = f (- x + 2a). The following graph is symmetric with respect to the origin. In other words, it can be rotated 180o around the origin without altering the graph. Note that if (x, y) is a point on the graph, then (- x, - y) is also a point on the graph.The graph of a quadratic function is a parabola. The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves. The axis of symmetry always passes through the vertex of the parabola . The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola.

Answer:

8n+7

Step-by-step explanation:

Performance relative to the whole class refers to an individual's academic achievement in comparison to the rest of their peers in a particular subject or course.

We describe performance relative to the whole class.

To do this, we'll be using the terms "average", "percentile rank", and "standard deviation".
Average:

Calculate the average performance of the whole class by adding all students' scores and then dividing by the number of students.

This will give you a baseline to compare individual performances against the class average.
Percentile Rank:

Determine the percentile rank of a student by calculating the percentage of students in the class who scored lower than them.

For example, if a student is in the 75th percentile, it means they performed better than 75% of the class.
Standard Deviation:

Calculate the standard deviation, which measures the spread of scores within the class.

A low standard deviation indicates that most students have similar performances, while a high standard deviation shows more variability in scores.
By considering these three factors, you can effectively describe a student's performance relative to the whole class. For example, you might say: "John scored above the class average, placing him in the 80th percentile with a moderate standard deviation, indicating that his performance is better than the majority of his classmates."

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Answer:

x = 3

Measurement of angle b: 70 degrees

Measurement of angle c: 70 degrees

Step-by-step explanation:

120° = (15x + 5) + (22x + 4)         (ext. ∠ of △)

120° = 15x + 22x + 5 + 4

(120 - 9)° = 37x

x = (111/37)

x = 3

Measurement of angle b: 22x = 4 = 22(3) + 4 = 66 + 4 = 70 degrees

Measurement of angle c: 15x + 5 = 15(3) + 5 = 45 + 5 = 50 degrees

Hope this helped!

Answer:

x = 3, ∠ B = 70°, ∠ C = 50°

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ ADC is an exterior angle of the triangle , then

15x + 5 + 22x + 4 = 120 , that is

37x + 9 = 120 ( subtract 9 from both sides )

37x = 111 ( divide both sides by 37 )

x = 3

Thus

∠ B = 22x + 4 = 22(3) + 4 = 66 + 4 = 70°

∠ C = 15x + 5 = 15(3) + 5 = 45 + 5 = 50°

Answer:

9 months

Step-by-step explanation:

$500 - $240 = $260

$260/$30 = 8.67(3s.f.) ≈ 9 months

Recheck:

Balance after 9 months = 240 + (30×9) = 240 + 270 = $510

                                      ∴ $510 > $500

The total number of starting lineups (of 5 players) can coach yells lot make, if the starting lineup can't contain both bob and yogi is 672.

An official list of the players who will take part in the event when the game starts is known as a starting lineup in sports. The players who are in the starting lineup are frequently referred to as starters, while the rest are known as bench players or replacements.

Case 1: Bob starts (and Yogi doesn't). In this case, the coach must choose 4 more players from the 10 remaining players (remember that Yogi won't play, so there are only 10 players left to select from). Thus there are 10C4 lineups that the coach can choose.

⇒ ¹⁰C₄ = 10!/4!(10-4)! = 10!/4!6!

⇒ ¹⁰C₄ = (10*8*9*7)/(4*3*2*1)

⇒ ¹⁰C₄ = 210

Case 2: Yogi starts (and Bob doesn't). As in Case 1, the coach must choose 4 more players from the 10 remaining players. So there are 10C4 lineups in this case.

⇒ ¹⁰C₄ = 210

Case 3: Neither Bob nor Yogi starts. In this case, the coach must choose all 5 players in the lineup from the 10 remaining players. Hence there are 10C5 lineups in this case.

⇒ ¹⁰C₅ = 10!/5!(10-5)! = 10!/5!5!

⇒ ¹⁰C₅ = (10*8*9*7*6)/(5*4*3*2*1)

⇒ ¹⁰C₅ = 252

To get the total number of starting lineups, we add the number of lineups in each of the cases:

Case 1 + Case 2 + Case 3

= 210 + 210 + 252 = 672

The total number of starting lineups (of 5 players) can coach yells lot make, if the starting lineup can't contain both bob and yogi is 672.

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Answer:

\((x^{-3} )^{2}\)

\(x^6 x^{-12}\)

Step-by-step explanation:

\((x^{3} x^{-6} )^{2}\) is the expression given to be solved.

First of all let us have a look at 3 formulas:

\(1.\ p^a \times p^b = p^{(a+b)}\\2.\ (p^a \times q^b)^c = (p^{a})^c \times (q^{b})^c\\3.\ (p^a)^b = p^{a\times b}\)

Both the formula can be applied to the expression(\((x^{3} x^{-6} )^{2}\)) during the first step while solving it.

Applying formula (1):

\((x^{3} x^{-6} )^{2}\)

Comparing the terms of \((x^{3} x^{-6} )\) with \(p^a \times p^b\)

\(p=x, a =3, b=-6\)

\(\Rightarrow x^{3+(-6)}\\\Rightarrow x^{3-6}\\\Rightarrow x^{-3}\)

So, \((x^{3} x^{-6} )^{2}\) is reduced to \((x^{-3} )^{2}\)

Applying formula (2):

Comparing the terms of \((x^{3} x^{-6} )^{2}\) with \((p^a \times q^b)^c\)

\(p=q=x, a =3, b=-6, c=2\)

\(\Rightarrow (x^{3})^2\times (x^{-6})^2\\\text{Applying Formula (3)}\\x^6 x^{-12}\)

So, \((x^{3} x^{-6} )^{2}\) is reduced to \(x^6 x^{-12}\).

So, the answers can be:

\((x^{-3} )^{2}\)

\(x^6 x^{-12}\)

Answer:

b d

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

hope it helps....

it's 100% correct

Answer:

24

Step-by-step explanation:

simplify 48/16

3 = X/8

Multiply both sides by 8

3 × 8 = 24

Given:

m is directly proportional to the cube of h.

m = 525 when h= 5.

To find:

The equation connecting m and h.

Solution:

m is directly proportional to the cube of h.

\(m\propto h\)

\(m=kh\)            ...(i)

Where, k is the constant of proportionality.

Putting m = 525 and h= 5, we get

\(525=k(5)\)

\(\dfrac{525}{5}=k\)

\(105=k\)

Putting k=105 in (i), we get

\(m=105h\)

Therefore, the required equation is \(m=105h\).

Given:

There are given that the triangle ABC.

Where,

Explanation:

According to the question:

We need to find the value for BC:

So,

To find the value of BC, we need to use the cosine rule:

From the cosine rule:

Then,

Put the all values into the given formula:

Then,

Then,

Final answer:

Hence, the value of BC is 6.016 km.

Answer:

20

Step-by-step explanation:

2x - 5 = x + 15

2x - x = 5 + 15

x = 20

Answer:

b=-3

Step-by-step explanation:

Answer:

(0, 12)

Step-by-step explanation:

To find the y-intercept of the quadratic function f(x) = (x - 6)(x - 2), we need to substitute x = 0 in the equation and solve for f(0).

f(x) = (x - 6)(x - 2)

f(0) = (0 - 6)(0 - 2) // Substitute x = 0

f(0) = 12

Therefore, the y-intercept of the quadratic function f(x) = (x - 6)(x - 2) is 12, which means the graph of the function intersects the y-axis at the point (0, 12).

Answer:

C

Step-by-step explanation:

\(\frac{6y }{x^{8} } . \frac{4y}{x^{14} }\\\\\frac{24y^{2} }{x^{8+14} } \\\\\frac{24y^{2} }{x^{22} }\)

Therefore , the solution of the given problem of inequality comes out to be add any amount of water up to 30 liters to the tub and still not exceed its capacity of 45 liters.

A mathematics inequality is a relationship or set of variables, minus the equal sign. Equity usually comes after equilibrium. When two parameters are not equal, inequality results. Between equality and inequality, there are differences. Since the values are not the same or equal, it was determined to use the most common symbol (). Any disparity, no mater how few or numerous, can be utilized to compare values.

Here,

Given :

The given inequality is:

w + 15 ≤ 45

To isolate w, we need to subtract 15 from both sides:

w + 15 - 15 ≤ 45 - 15

w ≤ 30

Therefore, the inequality that represents all possible values of w is:

w ≤ 30

This means that Matthew can add any amount of water up to 30 liters to the tub and still not exceed its capacity of 45 liters.

Therefore , the solution of the given problem of function comes out to be add any amount of water up to 30 liters to the tub and still not exceed its capacity of 45 liters.

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Answer:

s = 25.33m

θ = 60.65°

12.37m

A = 160m^2

Step-by-step explanation:

The pyramid has a side base of 35m and a height of 22m.

side base = b = 35m

height of the pyramid = h = 22m

To calculate the slant edge of the pyramid, you first calculate the diagonal of the squared base of the pyramid.

You use the Pythagoras theorem:

\(d=\sqrt{(\frac{35}{2})^2+(\frac{35}{2})^2}=24.74\)

With the half of the diagonal and the height, and by using again the Pythagoras theorem you can calculate the slat edge:

\(s=\sqrt{(\frac{24.74}{2})^2+(22)^2}=25.23\)

The slant edge of the pyramid is 25.33m

The angle of the base is given by:

\(\theta=sin^{-1}(\frac{h}{s})=sin^{-1}(\frac{22}{25.23})=60.65\°\)

The angle of the base is 60.65°

The distance between the corner of the pyramid and its center of its base is half of the diagonal, which is 24.74/2 = 12.37m

The area of one side of the pyramid is given by the following formula:

\(A=\frac{(b/2)l}{2}\)        (1)

l: height of the side of pyramid

then, you first calculate l by using the information about the side base and the slant.

\(l=\sqrt{s^2-(\frac{b}{2}^2)}=\sqrt{(25.33)^2-(\frac{35}{2})^2}\\\\l=18.31m\)

Next, you replace the values of l and b in the equation (1):

\(A=\frac{(35/2)(18.31)}{2}=160m^2\)

The area of one aside of the pyramid is 160m^2

Answer:

8x+3y=-6

Step-by-step explanation:

Convert to slope-intercept form

8x+3y=-6

3y=-8x-6

y=-8/3x-2, The slope is the same, therefore the lines are parallel.

The equation of a line parallel to given line is 8x+3y=-6. Therefore, option A is the correct answer.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The given equation is y=-8/3x-8.

Here, slope of a line is -8/3

The slope of a line parallel to given line is m1=m2

Then, the slope of parallel line is -8/3.

Now,

A) 8x+3y=-6

3y=-8x-6

y=-8/3x-2

B) 8x-3y=3

3y=8x-3

y=8/3x-1

C) 8y-3x=-48

8y=3x-48

y=3/8x-6

D) 3x+8y=48

8y=-3x+48

y=-3/8c+6

Therefore, option A is the correct answer.

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Answer:

f(g(0)) = 12

Step-by-step explanation:

to find f(g(0)) , evaluate g(0), then substitute the value obtained into f(x)

g(0) = 0 + 4 = 4 , then

f(4) = 3(4) = 12

The required elementary matrix E such that EA = B is

\(\left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right]\).

Any matrix obtained by performing a single elementary row operation on the identity matrix is called an elementary matrix.

The elementary operations are as follows:

1. Interchange the two rows of a matrix

2. Multiply a row of a matrix by the non-zero scalar k.

3. Add k-times of a row into another row of the matrix.

Each type of elementary operation may be performed by matrix multiplication, using square matrices called elementary operators.To perform an elementary row operation on A, an n×m matrix, take the following steps:

1. To find E, the elementary row operator, apply the operation to an n×n identity matrix.

2. To carry out the elementary row operation, premultiply A by E.

We want to interchange the first and second rows of A, a 3×3 matrix to  get B. To create the elementary row operator E, we interchange the first and second rows of the identity matrix I3:

\(\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]\) is changed to  \(\left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right]\).

So, \(\left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right]\)\(\left[\begin{array}{ccc}2&1&3\\-2&4&5\\3&1&4\end{array}\right]\) = \(\left[\begin{array}{ccc}2&1&3\\3&1&4\\-2&4&5\end{array}\right]\)

Thus, the required elementary matrix E such that EA = B is

\(\left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right]\)

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a. there are 524,288 frames in the system. b. the maximum number of frames is determined by the number of bits required to represent the page number, and the number of pages that can be addressed is limited by the size of the logical address space. c. 3 bits are needed to represent the page number 8, and 12 bits are needed to represent the offset 12.

a) The system has 524,288 frames. This can be calculated by dividing the maximum size of the logical address space (1MB) by the size of each frame (4KB).

1MB = 2^20 bytes

4KB = 2^12 bytes

Number of frames = (1MB / 4KB) = (2^20 / 2^12) = 2^(20-12) = 2^8 = 256

Therefore, there are 524,288 frames in the system.

b) The maximum number of frames that can be allocated to a process in this system is 256. This is because the maximum number of frames is determined by the number of bits required to represent the page number, and the number of pages that can be addressed is limited by the size of the logical address space.

c) i. The page number 8 can be represented using 3 bits. This is because there are 2^3 = 8 possible page numbers (0 to 7).

ii. The offset 12 can be represented using 12 bits. This is because there are 2^12 = 4,096 possible offsets (0 to 4,095).

Therefore, 3 bits are needed to represent the page number 8, and 12 bits are needed to represent the offset 12.

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========================================================

Explanation:

The base faces are the two triangles that are parallel to one another. We'll be ignoring those faces when computing the lateral surface area.

Instead, we focus on the three rectangles that form the sides. We can think standing the prism on one of the triangular faces, so that one triangle is the floor and the other triangle is the ceiling. The rectangular pieces are the walls of this room.

The three areas then combine to 128+96+96 = 320 square cm which is the lateral surface area.

------------------

As a different approach, we can use this formula

LSA = p*h

where LSA is the lateral surface area, p is the perimeter of the base polygon, h is the height of the prism.

The base triangle has sides of 8, 6 and 6. So the perimeter is p = 8+6+6 = 20 cm. The height is h = 16 cm. The LSA is therefore,

LSA = p*h = 20*16 = 320 square cm.

Answer:

Step-by-step explanation:

In the first triangle, using Pythagorean's theorem, x^2+3^2=5^2, x = 4

In the second triangle, using Pythagorean's theorem, x^2+7^2=24^2, x = 25

In the third triangle, using Pythagorean's theorem, 8^2+15^2=x^2, x = 17

In the fourth triangle, using Pythagorean's theorem, x^2+8^2=10^2, x = 6

In the fifth triangle, using Pythagorean's theorem, 5^2+12^2=x^2, x = 13

Answer:

Slope: m = (y2 - y1)/(x2 - x1) = (-5 - 3)/(14 - 6) = -8/8 = -1

The equation of the line is y = -x + b

Substitute (6,3) into the equation:

3 = -6 + b

b = 9

Therefore, the equation of the line is y = -x + 9

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

The area of a square is given by

A = s^2 where s is the side length

36 = s^2

Taking the square root of each side

sqrt(36) = sqrt(s^2)

6 = s

The side length of the pen is 6 ft

To find the perimeter of a square

P = 4s

P = 4*6 = 24

He will need 24 ft of fencing

If the Woodward Corporation would like to donate 20 computers and 30 printers to local schools. the greatest number of schools that The Woodward Corporation can donate to is: 10 schools.

We need to first of all find the common factors

20 = 1 × 20 = 2 ×10 = 2× 5 ×2

30 = 1 × 30 = 3 × 10

Common factors are 1 and 10.

Highest common factor is 10.

20 / 10 = 2

30 / 10 = 3

Each school will receive 2 computers and 3 printers.

The total number of schools  that will receive them is 10 schools  which is the  highest number of schools that will receive the same set of both computers and printers.

Therefore the  greatest number of schools is 10.

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To find the maximum volume of a cylinder inscribed in a sphere of radius r, we need to use optimization techniques. The cylinder should be such that its height is equal to its diameter and both should be equal to the diameter of the sphere. This means that the cylinder should be a cube with its diagonal equal to the diameter of the sphere.

Let the diameter of the sphere be 2r. The diagonal of the cube is equal to the diameter of the sphere, so its side is r√3. The volume of the cube is (r√3)^3 = 27r^3.

Since the cylinder is inscribed in the sphere, its radius is r and its height is 2r. The volume of the cylinder is πr^2(2r) = 2πr^3.

To maximize the volume of the cylinder, we need to differentiate the volume equation with respect to r and set it equal to zero:

d/dx (2πr^3) = 6πr^2 = 0

This gives us r = 0, which is not a valid solution. Therefore, the maximum volume of the cylinder inscribed in the sphere of radius r is 2πr^3, when the cylinder is a cube with its diagonal equal to the diameter of the sphere.

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Hence, the minimum number of at-the-door tickets she needs to sell to make her goal is (B) 334.

Given information: Anna is in charge of the alumni fundraiser for her alma mater. She is selling pre-sale tickets for $10 and at-the-door tickets $25. The venue has the capacity to hold 400 people.

The graph represents the number of tickets Anna needs to sell to offset her upfront costs and raise at least $5,000 for her school.

The minimum number of at-the-door tickets she needs to sell to make her goal can be calculated as follows;

Let's suppose that x represents the number of pre-sale tickets, and y represents the number of at-the-door tickets Anna needs to sell.

Then the following equation represents the total amount of money Anna will earn after selling the given number of tickets;

10x + 25y ≥ 5,000

If she sells all the tickets, she will have sold a total of x + y tickets. But, we know that the venue has a capacity of 400 people.

So, we also know that;

x + y ≤ 400

Solving the two equations for y gives;

10x + 25y ≥ 5,00025y ≥ 5,000 - 10x y ≥ (5,000 - 10x)/25y ≥ 200 - 0.4xy ≤ 333.3 - 0.4x

Answer: B.334.

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A straight line = 180°. You have: 58° , 40°, and q so:

q = 180° - (58° + 40°)

q = 82°

Answer:

82

Step-by-step explanation:

180 i s the line length so

180-40=140

140-58=82

Born: 582 BCE

Died: 497 BCE

582-497= 85

Answer: 85 years old