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QUESTION GUIDE EXIT TEST
3. A wedge of cheese is in the shape of a triangular prism. The dimensions of the wedge
are shown below.
30.5 cm
TAAR
as olles
em Readiness
16 cm
12 cm
20 cm
What is the volume of the wedge of cheese?

Answer:

The fifteenth term of the binomial expansion of [tex](a+b)^{20}[/tex] is [tex]38760\cdot a^{6}\cdot b^{14}[/tex].

Step-by-step explanation:

Let be a binomial of the form [tex](a+b)^{n}[/tex], where [tex]a, b\in \mathbb{R}[/tex] and [tex]n\,\in\mathbb{N}^{+}[/tex]. The expansion of this polynomial is defined below:

[tex](a+b)^{n} = \Sigma\limits_{k=0}^{n}\,\frac{n!}{k!\cdot (n-k)!}\cdot (a^{n-k}\cdot b^{k})[/tex] (1)

Where:

[tex]n[/tex] - Number of terms of the expanded polynomial.

[tex]k[/tex] - Index associated to [tex]k[/tex]-th term of the expanded polynomial.

For all [tex]n[/tex]-th binomial, we a sum of [tex]n+1[/tex] terms. If the given binomial has a term of [tex]20[/tex], then we have 21 terms and the fifteenth term of the polynomial corresponds to the [tex]14[/tex]-th term. Then, the fifteenth term of the binomial is:

[tex]c_{14} = \frac{20!}{14!\cdot 6!}\cdot (a^{6}\cdot b^{14})[/tex]

[tex]c_{14} = 38760\cdot a^{6}\cdot b^{14}[/tex]

The fifteenth term of the binomial expansion of [tex](a+b)^{20}[/tex] is [tex]38760\cdot a^{6}\cdot b^{14}[/tex].

Answer:

It's B

Step-by-step explanation:

Answer:

(a + b) / n

Step-by-step explanation:

Pounds of apple in box = a

Pounds of plum in box = b

Number of boxes used in packing = n

The amount fruit in pounds that are in each box :

Total pound of fruits / number of boxes used

Total pounds of fruit = a + b

Number of boxes used = n

Hence, we have ;

(a + b) / n

Answer:

The distance in one sweep is 100 cm approximately

Step-by-step explanation:

Here, we want to calculate the distance the wiper covers in one sweep

Mathematically;

we have a structure like an arc of a circle. It is the length of this arc we want to calculate.

The formula for the length of an arc is;

theta/360 * 2 * pi * r

r is the radius which in this case is 50 cm

We have ;

115/360 * 2 * 3.1412 * 50 = 100 cm approximately

Answer: 38

Step-by-step explanation:

3 (2/3) +(9)(4)

3 (2/3) +(9)(4) Again=38

If I Helped Please Mark Me As Brainliest, Have A Great Day :D

Answer:

1 foot

Step-by-step explanation:

1 meter = 3 feet

3 feet divided by 3 = 1 foot

The length of each section of the rope is 1 foot.

The piece of rope is 1m long.

Carter divided the ropes into three equal parts by tying up the knot.

1 meter = 3 foot.

Therefore, divide 3 by 3.

[tex]\frac{3}{3} =1[/tex] foot.

Therefore, each section is 1 foot long.

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This doesn’t include the Einstein problem cause I didn’t have that one.

Answer:

1)0.125

2)127.825

Step-by-step explanation:

Answer:

50 :)

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

Answer:

Step-by-step explanation:

6.    x² + 8x + 7

   = x² + 7x + x + 7

   = x (x + 7) + 1 (x + 7)

  = (x + 1) (x + 7)

Option D is the answer.

7.    x² - x - 72

  = x² - 9x + 8x - 72

  = x(x - 9) + 8(x - 9)

Option B is the answer.

8.   x² - 49

  = (x - 7) (x + 7)    [formula used a² - b² = (a-b)]

 Option D is the answer.

9.   9x² - 54x + 72

 =  9(x² - 6x + 8)

 =  9(x² - 4x - 2x + 8)

 =  9[x(x-4) -2 (x-4)]

 =  9[(x - 2) (x - 4)]

 = Option A is the answer.

10.   x⁴ - 3x³ - 10x²

   =  x² (x² - 3x - 10)

   =  x² (x² - 5x + 2x - 10)

   =  x² [x (x-5) + 2 (x-5)]

   =  x² (x+2) (x-5)

Option A is the answer.

Answer: Nick needs to sell 20 treats to break even.

Answer:

I think it would be 216cm

Step-by-step explanation:

how I got this answer?:

cubes are mostly the same in all sides due to all the sides being equal

Answer:

the answer is B

Step-by-step explanation:

when you take the first answer and subtract the second answer from it you get a negitive number of -1.1080325x10+28

Answer:10

Step-by-step explanation:u have to see how many time can a number go into it

Answer:

Option A ) Cylinder is correct.

Step-by-step explanation:

The important information need to consider is

1. Circular cross section when cut parallel to the base

2. Rectangular cross section when cut perpendicular to the base.

Let's consider each options.

Cylinder would have circular cross section when parallel to base and rectangle when it cut perpendicular to the base.

Yes! The cylinder works.

Answer:

[tex]1\frac{7}{10}[/tex] kg of sugar

Step-by-step explanation:

Amount of sugar on Wednesday: [tex]3\frac{2}{3}[/tex] kg

Convert the mixed number fraction to an improper fraction (multiply the whole number by the numerator)

[tex]3\frac{2}{3}[/tex] ⇒ [tex]\frac{6}{3}[/tex] ⇒ [tex]2[/tex]

Therefore, Emila bought 2 kg of sugar on Wednesday.

Because Emila bought [tex]\frac{3}{10}[/tex] kg less sugar on Thursday, subtract [tex]\frac{3}{10}[/tex] from [tex]2[/tex].

[tex]2-\frac{3}{10}[/tex]

Convert 2 into a fraction with 10 as the denominator

[tex]=\frac{20}{10} -\frac{3}{10}\\=\frac{17}{10}[/tex]

Convert the fraction into a mixed number

[tex]= 1\frac{7}{10}[/tex]

Therefore, Emila bought [tex]1\frac{7}{10}[/tex] kg of sugar on Thursday.

I hope this helps!

Answer:

x=23

Step-by-step explanation:

set them equal to each other since its not same sides

these are alternative exterior

8x-77=3x=38

5x=115

x=23

Answer:

23

Step-by-step explanation:

8x-77=3x+38 > 8x=3x+115 > 5x=115 > x=23

Answer:

Compound

Step-by-step explanation:

Answer:

16 inch³

Step-by-step explanation:

Given that :

Length = 2 2/6 = 14/6 inches

Width = 3 3/7 = 24 /7 inches

Height = 2

The volume of a rectangular prism is given by :

Volume = Length * width * height

Volume = (14/6) * (24/7) * 2

Volume = 16 inch³

Answer:

x= - 7/2

Step-by-step explanation:

Decimal Form: -3.5

Mixed Number Form: -3 1/2

Answer:

There are two possibilities of determine which solution is the smallest one:

(i) The smallest solution is the value of [tex]x[/tex] has the smallest distance with respect to origin: [tex](x_{2},y_{2}) = (0.18,0)[/tex]

(ii) The smallest solution is the most negative value: [tex](x_{1},y_{1}) = (-1.577,0)[/tex]

Step-by-step explanation:

Let [tex]f(x) = g(x)[/tex], [tex]f(x) = \ln (x+5)-1[/tex] and [tex]g(x) = x^{3}-2\cdot x + 1[/tex], then we have the following implicit equation:

[tex]\ln (x+5)-x^{3}+2\cdot x -2 = 0[/tex] (1)

This equation cannot be solved by analytical means. There are two different strategies to solve this expression: (i) Numerical methods, (ii) Graphical methods. We decide to use the second method:

Let suppose that we use this function [tex]h(x) = \ln (x+5) -x^{3}+2\cdot x - 2[/tex]. By the help of a graphing tool, we find the smallest solution such that [tex]h(x) = 0[/tex]. There are three possible solutions: [tex](x_{1},y_{1}) = (-1.577,0)[/tex], [tex](x_{2},y_{2}) = (0.18,0)[/tex], [tex](x_{3}, y_{3}) = (1.376, 0)[/tex]

There are two possibilities of determine which solution is the smallest one:

(i) The smallest solution is the value of [tex]x[/tex] has the smallest distance with respect to origin: [tex](x_{2},y_{2}) = (0.18,0)[/tex]

(ii) The smallest solution is the most negative value: [tex](x_{1},y_{1}) = (-1.577,0)[/tex]

The smallest smallest solution of f(x) = g(x) will be [tex]\rm \left(-1.577,0.223\right)[/tex]

A function is a statement, rule, or law that specifies the connection between two variables. Functions are common in mathematics and are required for the formulation of physical connections.

Given functions;

f(x) = ln(x + 5) – 1

g(x) = x³ – 2x + 1

After graphing both the function, we get the three solutions of the given equation,

[tex]\rm \left(-1.577,0.223\right)[/tex]

[tex]\left(0.18,0.645\right)[/tex]

[tex]\left(1.376,0.853\right)[/tex]

Hence,the smallest smallest solution of f(x) = g(x) will be [tex]\rm \left(-1.577,0.223\right)[/tex]

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Answer:

Step-by-step explanation:

mean = total / amount of numbers

= 15/5 = 3

median = 4 middle number

mode = most common numbers = 3,2

Answer:

6

Step-by-step explanation:

3+3 = 6

Answer:

There is 1 cat for each dog so the ratio would be 1:1 together.

Step-by-step explanation:

This means there are twice as many cats as dogs, or half as ... The ratio of 6:3 reduces to the ratio of 1:1

Answer:

2(b+6)

Step-by-step explanation:

Answer:

$12,150

Step-by-step explanation:

I = Prt

I = (40500)(0.03)(10)

I = 12150

I'm pretty sure you have to write how much they are

Pink heart is 2

Green square is 2

Blue moon 1

Answer:

Pink Heart = 2 Green Square = 6  Blue Moon = 4

Step-by-step explanation:

h ( h x g) = (b x g) = 24    left side of table

2 (2 x  3)  = (4 x 6) = 24   right side of table

h(h x g ) = 2(2 x 3) = (4 x 6) = (b x g) = 24   equivalent outcomes

Answer: $5

Step-by-step explanation: