show that if 16 people are seated in a row of 20 chairs, then some group of 4 consecutive chairs must be occupied.

Answer:

x = - 1

Step-by-step explanation:

P = \(\frac{x-2}{x+1}\)

the denominator of the rational function cannot be zero as this would make it undefined. Equating the denominator to zero and solving gives the value that x cannot be.

x + 1 = 0 ( subtract 1 from both sides )

x = - 1

P is undefined when x = - 1

The fraction of those who were delivered by car will be 1/6.

It should be noted that from the information given, the students were questioned on how they got to schoo and half of the students said they walk, one-third said they take a taxi,and the rest claimed they drive.

Therefore, the fraction of those who were delivered by car will be:

= 1 - (1/2 + 1/3)

= 1/2 - 5/6

= 1/6

In conclusion, the fraction of those who were delivered by car will be 1/6.

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Answer:

x,y(0,12)

Step-by-step explanation:

Y=mx+c

4=2X+4

4=2x+4

2x=0

X=0

Y=mx+c

Y=2(4)+4

Y=8+4

Y=12

Answer:

1. V = 157in³, so the volume of the sugar container is 157in³

2. h = 12in, so the height of the rice container is 12in

3. The rice container's height is 12in and the height of the sugar container is 8in, which means the rice container is taller by 4in. The rice container's volume is 235.5in and the sugar container's volume is 157in, so the rice container's volume is greater than the volume of the sugar container's volume by 78.5in.

4. V = 50.24in³, so the volume of the flour container is 50.24in³

5.  The rice container's volume is 235.5in, the sugar container's volume is 157in, and the flour container's volume is 50.24in. This means the container that contains the greatest volume is the rice container and the container that contains the smallest volume is the flour container.

Step-by-step explanation:

1. to find the volume of a cylinder, we use the formula:

V = πr²h

V = 3.14(2.5² × 8)

V = 3.14(6.25 × 8)

V = 3.14(50)

V = 157in³

2. To find the height of a cylinder when given the volume and radius, you use the formula:

h = V / πr²

h = 235.5/3.14(2.5²)

h = 235.5/3.14(6.25)

h = 235.5/19.625

h = 12in

h = height

3. The rice container's height is 12in and the height of the sugar container is 8in, which means the rice container is taller by 4in. The rice container's volume is 235.5in and the sugar container's volume is 157in, so the rice container's volume is greater than the volume of the sugar container's volume by 78.5in.

4.

V = bh

V = 12.56 × 4

V = 50.24in³

5. The rice container's volume is 235.5in, the sugar container's volume is 157in, and the flour container's volume is 50.24in. This means the container that contains the greatest volume is the rice container and the container that contains the smallest volume is the flour container.

Answer: I do, do you have a question

Answer:

e

Step-by-step explanation:

Answer:

x=-1

Step-by-step explanation:

Answer:

186.

Step-by-step explanation:

By multiplying six by thirty one, you'll get every single way the instructor can choose six students from a class of thirty one students for a field trip.

The number of different ways that an instructor can choose 6 students from a class of 31 students for a field trip is 186.

We have a number of different ways that an instructor can choose 6 students from a class of 31 students for a field trip.

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.

By multiplying six by thirty-one, you'll get every single way the instructor can choose six students from a class of thirty-one students for a field trip.

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The length of AE¯¯¯¯¯ is 5√2 cm.

Since quadrilateral ABCD is a square, all four sides are congruent. Let's denote the length of one side as s. Therefore, the length of BD¯¯¯¯¯ is equal to s.

Given that the length of BD¯¯¯¯¯ is 10 cm, we can conclude that s = 10 cm.

Now, we need to find the length of AE¯¯¯¯¯. Looking at the square, AE¯¯¯¯¯ is the diagonal connecting opposite corners.

In a square, the diagonal divides the square into two congruent right triangles. We can use the Pythagorean theorem to find the length of the diagonal.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the diagonal (the hypotenuse) is the same as the side length, s.

Applying the Pythagorean theorem:

s^2 = AE¯¯¯¯¯^2 + AE¯¯¯¯¯^2

10^2 = AE¯¯¯¯¯^2 + AE¯¯¯¯¯^2

100 = 2 * AE¯¯¯¯¯^2

AE¯¯¯¯¯^2 = 50

Taking the square root of both sides:

AE¯¯¯¯¯ = √50

Simplifying the square root:

AE¯¯¯¯¯ = √(25 * 2) = 5√2 cm

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Answer:

d) 1/12

Step-by-step explanation:

Answer:

If it is a fair die then it should have 6 faces, each one having a number 1-6. The probability of landing on a single number is 1/6. Because the die is fair there should be an equal probability of landing on a number 1-6 giving you a probability of 1/6. However, if the number of times rolled is changed, then the answer would be multiplied or added (depending on the question).

Answer:

4

Step-by-step explanation:

Lets plug these points in:

\(\frac{((-2)-10)}{(2-5)} =\frac{-12}{-3} =4\)

Answer:

375 ft

Step-by-step explanation:

Given:

Length of deck on drawing = 11 in

Width of deck on drawing = 4 in

Scale of drawing: 2 in : 25 ft

Required:

Permitted of the actual deck

Solution:

First, find the actual length and width of the deck using the scale of the drawing given.

Scale = 2 in : 25 ft

Actual length = (11*25)/2 = 137.5 ft

Actual width = (4*25)/2 = 50 ft

Perimeter of actual deck = 2(length + width)

Perimeter = 2(137.5 + 50) = 2(187.5)

Perimeter = 375 ft

Answer:

375

Step-by-step explanation:

Answer:A.The triangles are similar but not congruent

Step-by-step explanation:

In a congruent traingle:

the both triangles are same in shape and size

There are five theorems to see if the triangles are congruent

and neither particularly applies here

sss: the sides are not equal

as none of the sides are equal, then despite the angles, congruence is not possible

However it is evident that one of the triangles is proportionally bigger than the other but similar. Hence A is correct.

Step-by-step explanation:

The correct answer is that the data set {3, 7, 4} is represented in the given histogram.(option-a)

The given histogram represents the number of children in each age group who need to travel to school. Since the histogram has only three bars, we can conclude that there are only three age groups.

The first bar represents children aged 5-10, of which there are 3. The second bar represents children aged 11-13, of which there are 7. The third bar represents children aged 14-18, of which there are 4.

Therefore, the data set that is represented in the histogram is:

{3, 7, 4}

None of the other data sets given match the values in the histogram. The first data set has duplicate values and is not sorted by age group. The second data set includes ages that are not represented in the histogram. The third data set has values for ages 6, 11, 12, 13, 14, 15, 17, and 18, but the histogram does not have bars for all those ages. (option-a)

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Answer:2.8

Step-by-step explanation:add 3.5 to the 10.5 which equals 14 then you divide 5 by 14 to get the y alone and it equals 2.8

Answer:

the answer is y=3 I hope I helped

Answer:

\(x = 3\)

Step-by-step explanation:

\(y + 3 = - y + 9\)

\(y + y = 9 - 3\)

\(2y = 6\)

\( \frac{2y}{2} = \frac{6}{2} \)

\(x = 3\)

Answer:

The given graph shows the relationship between the f(x) and g(x).

Since the problem is to find the points where f(x) becomes equal to g(x) then we will be focusing only to the x-axis and ignore the points of y-axis.

Out of the four choices, the correct answer for the given functions of x will be f(2) = g(2) and f(0) = g(0), f(0) and g(0) is located at the origin. So the points where the curve and line are intersecting is at f(2) and g(2) and the other point is at f(0) and g(0), neglecting the y-axis.

Step-by-step explanation:

9514 1404 393

Answer:

  y -2 = 2(x -30)

Step-by-step explanation:

The point-slope equation is ...

  y -k = m(x -h) . . . . . line through (h, k) with slope m

The slope formula is ...

  m = (y2 -y1)/(x2 -x1)

  m = (-28 -2)/(15 -30) = -30/-15 = 2

Using this slope and the first point, the equation of the line is ...

  y -2 = 2(x -30)

Answer:

The selling price of the diamond necklace at Shamin Jewelers after 10% discount is:

$442 * 0.9 = $397.80

The selling price of the same necklace at the competitor's store after 34% and 14% discount is:

$527 * 0.66 * 0.86 = $247.08

So, Shamin Jewelers needs to offer an additional discount to meet the competitor's price:

$397.80 - $247.08 = $150.72

To calculate the additional rate of discount, we divide the difference by the original selling price at Shamin Jewelers and multiply by 100:

($150.72 / $442) * 100 = 34.11%

Therefore, Shamin Jewelers must offer an additional 34.11% discount to meet the competitor's price.

Step-by-step explanation:

Answer:

Step-by-step explanation: well, you will more than likely get it at least 60%-80% of the time! If this doesn't help i can try to explain in a lot more detail unless someone does for me!

Answer:

C

Step-by-step explanation:

trust me c is the correct answer

The dimensions of the rectangular garden to maximize the area is length = width = 75 meters.

Let l be the length and w be the width of the rectangular garden.

We need to find the dimensions of the rectangular garden of greatest area that can be fenced off (all four sides) with 300 meters of fencing.

The perimeter of the  rectangular garden = 300 meters

We know that the perimeter of the rectangle =2(length + width)

300 = 2(l + w)

l + w = 150               .......(1)

Now, the maximum area of a  rectangular garden is when Length  = width

So, for equation 1

l + l = 150

l = 75 meters

So, w = 75 meters

And the area of the rectangular garden = length * width

                                                               = 75 * 75

                                                               = 5625 m²

So the maximum area of the  rectangular garden is 5625 m²

Therefore, the dimensions of the garden to maximize the area is length = width = 75 meters and maximum area is  5625 m²

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The surface area of the prism include the following: C. two hundred seventy-five and one-eighth cm².

In Mathematics and Geometry, the surface area of a rectangular prism can be calculated and determined by using this mathematical equation or formula:

Surface area of a rectangular prism = 2(LH + LW + WH)

Where:

By substituting the given side lengths into the formula for the surface area of a rectangular prism, we have the following;

Surface area of rectangular prism = 2[(23/4 × 4) + (23/4 × 47/4) + (4× 47/4)]

Surface area of rectangular prism = 2[23 + 1081/16 + 47]

Surface area of rectangular prism = 275 1/8 cm².

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Answer:

40 pizzas in total

Step-by-step explanation:

10×4=40

The difference between their yearly incomes is $31,304.

To calculate each person's yearly income, we need to multiply their weekly income by the number of weeks in a year. Assuming there are 52 weeks in a year, the yearly income can be calculated as follows:

For the student who drops out of high school:

Yearly Income = Weekly Income x Number of Weeks

= 451 x 52

= 23,452

For someone with a bachelor's degree:

Yearly Income = Weekly Income x Number of Weeks

= 1053 x 52

= 54,756

The difference between their yearly incomes can be found by subtracting the student's yearly income from the bachelor's degree holder's yearly income:

Difference = Bachelor's Yearly Income - Student's Yearly Income

= 54,756 - 23,452

= 31,304

Therefore, the difference between their yearly incomes is $31,304.

It is important to note that these calculations are based on the given information and assumptions. The actual yearly incomes may vary depending on factors such as work hours, additional income sources, deductions, and other financial considerations.

Additionally, it is worth considering that educational attainment is just one factor that can influence income, and there are other variables such as experience, job type, and market conditions that may also impact individuals' earnings.

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Answer:

(48b 2) 3

Step-by-step explanation:

The answer is  A) The simplified expression is a polynomial. & B)The simplified expression has a constant term.

Polynomials are sums of phrases of the form okay⋅xⁿ, where ok is any range and n is an effective integer. as an instance, 3x+2x-5 is a polynomial. Introduction to polynomials. This video covers commonplace terminology like phrases, diploma, fashionable form, monomial, binomial and trinomial.

Here, we have,

A polynomial is described as an expression that consists of variables, constants, and exponents, which can be mixed with the usage of mathematical operations including addition, subtraction, multiplication, and department (No department operation by way of a variable).

t³(8 + 9t) - (t² + 4)(2 - 3t)

=   8t³ + 9t⁴ - (2t² - 3t³ + 8 - 12t)

=   8t³ + 9t⁴ - 2t² + 3t³ - 8 + 12t

=   9t⁴ + 11t³ - 2t² + 12t - 8.

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complete question;

T^3(8 + 9t) - (t2 + 4) (2 – 3t)

The simplified expression is a polynomial.

The simplified expression has a constant term.

The simplified expression is cubic.

The simplified expression has four terms.

The simplified expression is a trinomial

Answer:

288π or 904.78

Step-by-step explanation:

We know that the diameter of this beach ball is 12 inches and we want to determine how much air it can hold using the formula for the volume of a sphere which is \(\frac{4}{3}\) × π × r³ where 'r' is the radius. In the question we are given the diameter not the radius but we can half the diameter to find the radius so 12 ÷ 2 = 6. The radius of the beach ball is 6 inches so let's work out how much air it can hold.

Volume = \(\frac{4}{3}\) × π × r³

→ Let's substitute in the values

Volume = \(\frac{4}{3}\) × π × 6³

→ Simplify

Volume = \(\frac{4}{3}\) × π × 216

→ Simplify further

Volume = 288π or 904.78

The amount of air can the sphere shape beach ball hold is 208π or 904.78 inches.

The "set of all  points  in 3 dimensional space is lying the same distance from the given points or center" is called sphere.

According to the question,

Diameter of sphere shape beach ball is 12inches

Radius of sphere shape beach ball is 12/2 = 6inches

Volume of sphere = \(\frac{4}{3}\) × π × r³  

= \(\frac{4}{3}\) × \(\frac{22}{7}\) × (6)³

= 904.78inches

Hence, the amount of air can the sphere shape beach ball hold is 208π or 904.78 inches.

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Answer:

yes

Step-by-step explanation:

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