Which of the following expressions are polynomials? Select all that apply.

Answer:

A)

\(\left \{ {{80} \atop {20}} \} * \left \{ {{60} \atop {20}} \} * \left \{ {{40} \atop {20}} \} * \left \{ {{20} \atop {20}} \}\)

B)

\(\left \{ {{20+4-1} \atop {4-1}} \} = \left \{ {{23} \atop {3}} \}\)

C)

= \(\left \{ {{17+4+1} \atop {4-1}} \} = \left \{ {{20} \atop {3}} \}\)

D)

= \(\left \{ {{20} \atop {3}} \} - \left \{ {{17} \atop {3}} \}\)

Step-by-step explanation:

A) How many ways can you put all Jellybeans in a row

Total number of Jellybeans = 80

The first jellybeans = 20 yellow , second is 20 orange jellybeans , third is 20 red jellybeans , fourth is 20 green jellybeans

Therefore the number of ways the Jellybeans can be put in a row is :

\(\left \{ {{80} \atop {20}} \} * \left \{ {{60} \atop {20}} \} * \left \{ {{40} \atop {20}} \} * \left \{ {{20} \atop {20}} \}\)

B) How many ways are there to select a handful of 20 jellybeans

lets assume:

yellow jellybeans = a , orange jellybeans = b , red jellybeans = c , green jellybeans = d

a + b + c + d = 20

This is the number Non-negative integer solutions

= \(\left \{ {{20+4-1} \atop {4-1}} \} = \left \{ {{23} \atop {3}} \}\)

C) This is also the number of Non-negative integer solutions but in this case the value of C ≥ 3

hence the number of ways to select a handful of 20 jellybeans that contains at least 3 red

= \(\left \{ {{17+4+1} \atop {4-1}} \} = \left \{ {{20} \atop {3}} \}\)

D) In this case the value of C ≥ 3 and B ≤ 2

Hence the number of ways to select a handful of 20 jellybeans that contains at least 3 red and at most 2 orange

= \(\left \{ {{20} \atop {3}} \} - \left \{ {{17} \atop {3}} \}\)

Answer:

500 times

Step-by-step explanation:

Divide the thickness of a cat hair by the thickness of a human hair.

4.0 × 10^-1 / 8.0 × 10^-4 =

= 0.5 × 10^3

= 500

500 times

Answer:

not just you

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

18+27= 45

8+7=15

2+1= 3

15x3= 45

Answer:

129 degrees

Step-by-step explanation:

When we add a right angle (90 degrees) to an acute 39 degree angle we get 129 degrees.

azb = 129 degrees

Answer:

Substract by 2: n+8, 2n+8, 2n+8

Divide by 2: (n+8)/2, (n+8)/2, (n+8)/2

Step-by-step explanation:

Answer:

\(\boxed{\boxed{\pink{\bf \leadsto It \ will \ take \ 5 hours \ to \ travel \ 300 \ miles. }}}\)

According to Question , a plane travels 120 miles in 2 hours. So here we will use unitary method .

\(\bf\implies If \ it \ covers \ 120 \ miles \ in \ 2 \ hours \\\\\bf\implies Then \ one \ mile \ will \ be \ covered \ in \ \dfrac{120}{2} hrs \\\\\bf\implies Hence \ 300 \ miles \ will \ be \ covered \ in \ \dfrac{2}{120}\times 300 hrs = \red{5 \ hours } \)

Here it was a case of direct proportion in which if two things are directly proportional to each other. If one thing thing increases then the value of second also increases. Here if the time increases then the distance also increases

Answer:

9). 15 miles

10). 12880.8 in²

Step-by-step explanation:

9). Total distance to be covered by Kelly = Perimeter of the given triangle

                                                                    = Sum of three sides of the triangle

    To know the length of Laurel drive (Hypotenuse of the triangle), we will apply Pythagoras theorem in the given triangle,

    (Hypotenuse)² = (Leg 1)² + (Leg 2)²

                             = (2.5)²+ 6²

                             = 6.25 + 36

     Hypotenuse = \(\sqrt{42.25}\)

                           = 6.5 mi.

     Therefore, total distance covered by Kelly = 6.5 + 2.5 + 6

                                                                             = 15 mi.

10). Amount of paper required to cover one desk of the class

     = Area of the trapezoid shown in the figure

     = \(\frac{1}{2}(b_1+b_2)h\)

      Here, \(b_1\) and \(b_2\) are the parallel sides of the trapezoid

      And 'h' is the distance between the parallel sides.

      By applying Pythagoras theorem in ΔPRT,

      PR² = RT² + PT²

      PT = \(\sqrt{PR^2-RT^2}\)

      PT = \(\sqrt{(18)^2-2^2}\)

            = \(\sqrt{324-4}\)

            = \(\sqrt{320}\)

            = 17.89 in.

      Area of the trapezoid PQRS = \(\frac{1}{2}(PQ+RS)(PT)\)

                                                      = \(\frac{1}{2}(22+26)(17.89)\)

                                                      = 429.36 in²

      Therefore, paper required to cover 30 desks = 30 × 429.36

                                                                                   = 12880.8 in²

107.4972. No problem..............

5x+7x=660;

12x=660;

x=660:12;

x=55 (kg).

Then 5x=5×55=275 kg and 7x=7×55= 385 kg.

The required ratio is therefore

660= 275:385.

Given the expressions:

Using FOIL:

Similarly, given the expression provided, we obtain:

Answer:

200

Step-by-step explanation:

If 40% are roses than 60% must be sunflowers (40% + 60% = 100%)

We are trying to find 60% of some number is 120.

Let n = the total number of flowers

.6n = 120  Divide both sides by .6

n = 200

Answer:

The net of a triangular pyramid with an equilateral triangle for the base consists of four triangles, and at least three of them are congruent to each other.

Step-by-step explanation:

we cannot conclude that the volume of the prism is half the volume of the cylinder, twice the volume of the cylinder, or not equal to the volume of the cylinder.

How to solve the problem ?

The given information states that the cross-sectional areas of a triangular prism and a right cylinder are congruent, and both have a height of 5 units. Based on this information, we can conclude that the volumes of the two shapes may be equal, but we cannot conclude that the volume of the prism is half or twice the volume of the cylinder.

To determine the volumes of the two shapes, we need to know their respective formulas. The volume of a triangular prism is given by V = (1/2)bh, where b is the length of the base of the triangular cross-section and h is the height of the prism. The volume of a right cylinder is given by V = πr²h, where r is the radius of the circular cross-section and h is the height of the cylinder.

Since the cross-sectional areas of the two shapes are congruent, we can assume that their bases are similar. Therefore, the base of the triangular prism must be a triangle with the same area as the circular base of the cylinder. However, without further information about the shape and size of the cross-section, we cannot determine the values of b and r.

Therefore, we cannot conclude that the volume of the prism is half the volume of the cylinder, twice the volume of the cylinder, or not equal to the volume of the cylinder. The only conclusion that can be made is that the volume of the prism is equal to the volume of the cylinder, assuming that the cross-sectional areas are congruent.

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The student's percentile will be 28.

Calculating percentiles is a common practise. The majority of the time, we can define percentile as a score below which a predetermined percentage of other scores fall. We might be able to tell when someone received a test score of 65 out of 90. But without knowing what percentile he belongs to, this number is meaningless. When a score is in the 90th percentile, it signifies that it is higher than the scores of 90% of test-takers.

Given : Student's rank = 144 out of 200

So, there are 56 (200-144) students whose rank is below that student.

We know that, percentile

= no. of ranks below that rank / total no. of ranks * 100

So, his percentile = 56/200 * 100

                             = 28 percentile.

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Answer:

Attached is an example of a circle with a radius of 5 and a diameter of 10.

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Have a GREAT day!!!

I believe the it would be 2x^2 + 6x + 20 = 0.

Answer:

Rental cost for each movie = $3.25

Rental cost for each video game = $5.25

Step-by-step explanation:

We can find the rental cost for each movie and each video game using a system of equations where:

First equation:

Since Jina rented 6 movies and 2 video games for a total of $30, our first equation is given by:

6M + 2V = 30

Second equation:

Since Jina also rented 3 movies and 5 video games for a total of $36, our second equation is given by:

3M + 5V = 36

Method to solve:  Elimination:

We can solve this with eliminate.  First, we need to multiply the second equation by -2.  Then, we must add the two equations to eliminate the Ms and solve for V:

Multiplying the entire second equation by -2:

-2(3M + 5V = 36)

-6M - 10V = -72

Adding the two equations:

    6M + 2V = 30

+

   -6M - 10V = -72

(6M - 6M) + (2V - 10V) = (30 - 72)

-8V = -42

Solving for V:

(-8V = -42) / -8

V = 5.25

Thus, the rental cost for each video game is $5.25.

Solving for M:

We can now find M by plugging in 5.25 for V in any of the two equations in our system.  

Let's use the first equation:

Plugging in 5.25 for V in 6M + 2V = 30 to solve for M:

6M + 2(5.25) = 30

(6M + 10.50 = 30) - 10.50

(6M = 19.50) / 6

M = 3.25

Thus, the rental cost for each movie is $3.25.

The informal negation for each of the following statements:

1) No dog is ferocious.

2) Noboby is sad.

4) No suspicions were unsubstantiated.

5) No estimate is incorrect.

It is sometimes necessary in mathematics to determine the inverse of a given mathematical statement. This is commonly known as "negating" a statement. Keep in mind that if a statement is true, then its negation is false (and if a statement is false, then its negation is true). A conditional statement's negation is logically equivalent to a conjunction of the antecedent and the negation of the consequent. The logical negation symbol or is one of the statement connectives or operators that can be used to combine two or more statements to form new compound statements. It simply flips the truth value of any statement it appears in front of.

Here,

Each of the following statements has an informal negation:

1) No dog is ferocious.

2) Noboby is sad.

4) No suspicions were unsubstantiated.

5) No estimate is incorrect.

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Answer:

x=-0.9375

Step-by-step explanation:

x= - \(\frac{3}{4}\)-\(\frac{3}{16}\)

x=-0.9375

Answer:

The equation of the plane is

8(x - 5) - 7(y - 4) - 5(z - 5) = 0

8x - 7y - 5z + 13 = 0

Step-by-step explanation:

Given 3 points, P(x₁, y₁, z₁), Q(x₂, y₂, z₂), and R(x₃, y₃, z₃).

We can calculate the equation of the plane through those points as

a(x - x₀) + b(y - y₀) + c(z - z₀) = 0, where (x₀, y₀, z₀) are the coordinates of any one of the points P, Q, or R, and <a,b,c> is a vector perpendicular to the plane.

The vector perpendicular to the plane is obtained by writing vector PQ and PR and taking the cross or vector product.

For this question,

P = (5, 4, 5)

Q = (-5, -1, -4)

R = (-2, 1, -2)

PQ = (-5, -1, -4) - (5, 4, 5) = (-10, -5, -9)

= (-10î - 5ĵ - 9ķ)

PR = (-2, 1, -2) - (5, 4, 5) = (-7, -3, -7)

= (-7î - 3ĵ - 7ķ)

PQ × PR is then

| î ĵ ķ |

|-10 -5 -9|

|-7 -3 -7|

= î [(-5×-7) - (-9×-3)] - ĵ [(-10×-7) - (-9×-7)] + ķ [(-10×-3) - (-7×-5)]

= î (35 - 27) - ĵ (70 - 63) + ķ (30 - 35)

= 8î - 7ĵ - 5ķ

Hence, (a, b, c) = (8, -7, -5)

And using point P as (x₀, y₀, z₀) = (5, 4, 5)

The equation of the plane is

a(x - x₀) + b(y - y₀) + c(z - z₀) = 0

8(x - 5) - 7(y - 4) - 5(z - 5) = 0

8x - 40 - 7y + 28 - 5z + 25 = 0

8x - 7y - 5z = 40 - 28 - 25 = -13

8x - 7y - 5z + 13 = 0

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The 2 : 5 scaled version of the deck Sam plans to build and the dimensions of the original deck indicates;

Part A; Base length of the new deck = 7.2 feet

Height of the new deck = 2.8 feet

Part B; The area of the original deck is 63 square feet

The area of the new deck is 10.08 square feet

Part C; The ratio of the areas is the square of the scale factor

A scale factor is a number or factor that is used to enlarge or reduce the dimensions a shape or size of a figure.

The base length of the triangular deck = 18 feet

The height of the triangular deck = 7 feet

The scale factor for the scaled version Sam intends to build = 2 : 5

Part A; The dimensions of the new deck are;

Base length of the new deck using the the 2 : 5 ratio is; (2/5) × 18 = 7.2 feet

The height of the new deck = (2/5) × 7 = 2.8 feet

Part B; The area of the original deck = (1/2) × 18 × 7 = 63 square feet

Area of the new dec = (1/2) × 7.2 × 2.8 = 10.08 square feet

Part C; The ratio of the areas is; 10.08/63

Ratio of the area = 10.08/63 = 4/25 = 4 : 25

The scale factor is; 2 : 5

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If the train travels at an average speed of 50 Km/h, it would be late by 10 minutes.

Speed is simply referred to as distance traveled per unit time.

It is expressed as:

Speed = distance / time

Given that the train running between two stations 50 Km apart arrives on time if it travels at an average speed of 60 km/h.

The time taken by the train to travel 50 km at an average speed of 60 km/h can be calculated using the formula:

Speed = distance / time

time = distance / speed

time = 50 km / 60 km/h

time = 5/6 hour

Next, if the train travels at an average speed of 50 km/h, the time taken to cover the same distance of 50 km would be:

Speed = distance / time

time = distance / speed

time = 50 km / 50 km/h

time = 1 hour

Now, the difference in time between the two scenarios would be:

time difference = 1 hour - 5/6 hour

time = 1/6 hour

Convert to minutes

time = 1/6 × 60

time = 10 minutes

Therefore, the train would be late by 10 minutes.

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Answer:

25 and 8) = 200

(32,24 and 18) =288

(22 and 4)=44

(14 and 12) = 84

(9,8 and 7)= 504

(27,12 and 36) =108

Answer:

  top down: 200, 288, 44, 84, 504, 108

Step-by-step explanation:

The least common multiple (LCM) can be figured a couple of ways.

a) factor the numbers, then form the product of unique factors (to their highest powers)

b) divide the product of the numbers by their greatest common factor (GCF). Factoring or Euclid's method can be used to find the GCF.

When there are more than two numbers, the LCM can be figured for two of them, then for that result and the next number, and so on.

__

25 and 8 have no common factors, so their LCM is their product: 200

__

32 and 24 have 8 as their GCF, so their LCM is 32·24/8 = 96. 96 and 18 have 6 as their GCF, so their LCM is 96·18/6 = 288

__

22 and 4 have 2 as their GCF, so their LCM is 22·4/2 = 44

__

14 and 12 have 2 as their GCF, so their LCM is 14·12/2 = 84

__

9, 8, 7 have no common factors, so their LCM is their product: 9·8·7 = 504

__

27 and 12 have 3 as their GCF, so their LCM is 27·12/3 = 108. 108 is a multiple of 36, so their LCM is 108.

The dancers in the ballroom have approximately 113.1 square meters of area to move around on.

The area of a circle is given by the formula A = π\(r^2\), where A is the area and r is the radius. In this case, the radius of the dance floor is 6 meters, so we can plug that into the formula:

A = π\((6)^2\)

Simplifying the expression, we get:

A = 36π

To find the approximate area, we can use 3.14 as an approximation for π and calculate:

A ≈ 113.1 square meters

Rounding to the nearest tenth, we get:

A ≈ 113.1 ≈ 113.1 square meters

Therefore, the dancers in the ballroom have approximately 113.1 square meters of area to move around on.

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Answer:

the correct answer is 193

Step-by-step explanation:

25×1-0=25

25×2-1=49

49×2-1=97

97×2-1=193

The expression for y is given as y = (7x - π)/2

Linear equation are equation that has a degree of 1.

Given the linear equation

π=7x-2y

Subtract 7x from both  sides

π-7x = -2y + 7x - 7x
π-7x = -2y

2y = 7x - π

Divide both sides by 2

2y/2 = (7x - π)/2

y = (7x - π)/2

Hence the expression for y is given as y = (7x - π)/2

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Explanation:

Let's list the ways to roll a 6.

There are A = 5 items listed above.

Now let's list the ways to roll a sum of 7.

There are B = 6 items listed above.

Lastly, let's list the ways to roll a sum of 8.

There are C = 5 items listed above.

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

Summary so far:

We found there are

Therefore, we have A+B+C = 6+7+8 = 21 ways to roll either of those three sums. Each event is mutually exclusive.

This is out of 6*6 = 36 ways to roll two dice (whether we get those sums or not).

21/36 = (7*3)/(12*3) = 7/12 is the probability of getting any of those three sums mentioned.

7/12 = 0.5833 = 58.33% approximately

Answer:1 2/4

Step-by-step explanation: