Are these proportional? 10 books for $4.50; 15 books for $6.00

Answer:

The answer is below

Step-by-step explanation:

Expansion using pascal triangle:

a)  (x + 2)⁶ = x⁶2⁰ + 6(x⁵)(2)¹ + 15(x⁴)(2²) + 20(x³)(2³) + 15(x²)(2⁴) + 6(x)(2⁵) + 1(2⁶)

                 = x⁶ + 12x⁵ + 60x⁴ + 160x³ + 240x² + 192x + 64

b) (x-4)⁴ = x⁴ + 4(x³)(-4) + 6(x²)(-4)² + 4(x)(-4)³ + 1(x⁰)(-4)⁴

              =x⁴-16x³+96x²-256x+256

c) (2x + 3)⁵ = (2x)⁵ + 5(2x)⁴(3) + 10(2x)³(3)² + 10(2x)²(3)³ + 5(2x)(3)⁴ + 1(2x)⁰(3)⁵ =

                  = 32x⁵ + 240x⁴ + 720x³ + 1080x² + 810x + 243

d) (2x-3y)⁴ = 1(2x)⁴(-3y)⁰ + 4(2x)³(-3y) + 6(2x)²(-3y)² + 4(2x)(-3y)³ + 1(2x)⁰(-3y)⁴

                  = 16x⁴- 96x³ + 216x² - 216x + 81

Expansion using binomial where [tex]C(n,r)=\frac{n!}{(n-r)!r!}[/tex]

a)  (x + 2)⁶ = C(6,0)[x⁶2⁰] + C(6,1)[(x⁵)(2)¹] + C(6,2)[(x⁴)(2²)] + C(6,3)[(x³)(2³)] + C(6,4)[(x²)(2⁴)] + C(6,5)[(x)(2⁵)] + C(6,6)[(2⁶)]

                = x⁶2⁰ + 6(x⁵)(2)¹ + 15(x⁴)(2²) + 20(x³)(2³) + 15(x²)(2⁴) + 6(x)(2⁵) + 1(2⁶)

                 = x⁶ + 12x⁵ + 60x⁴ + 160x³ + 240x² + 192x + 64

b) (x-4)⁴ = C(4,0)[x⁴] + C(4,1)[(x³)(-4)] + C(4,2)[(x²)(-4)²] + C(4,3)[(x)(-4)³] + C(4,4)[(x⁰)(-4)⁴]

              = x⁴ + 4(x³)(-4) + 6(x²)(-4)² + 4(x)(-4)³ + 1(x⁰)(-4)⁴

              =x⁴-16x³+96x²-256x+256

c) (2x + 3)⁵   = C(5,0)[(2x)⁵] + C(5,1)[(2x)⁴(3)] + C(5,2)[(2x)³(3)²] + C(5,3)[(2x)²(3)³] + C(5,4)[(2x)(3)⁴] + C(5,5)[(2x)⁰(3)⁵]

                   = (2x)⁵ + 5(2x)⁴(3) + 10(2x)³(3)² + 10(2x)²(3)³ + 5(2x)(3)⁴ + 1(2x)⁰(3)⁵

                  = 32x⁵ + 240x⁴ + 720x³ + 1080x² + 810x + 243

d) (2x-3y)⁴ = C(4,0){(2x)⁴(-3y)⁰} + C(4,1)[(2x)³(-3y)] + C(4,2)[(2x)²(-3y)²] + C(4,3)[(2x)(-3y)³] + C(4,4)[(2x)⁰(-3y)⁴]

                  = 1(2x)⁴(-3y)⁰ + 4(2x)³(-3y) + 6(2x)²(-3y)² + 4(2x)(-3y)³ + 1(2x)⁰(-3y)⁴

                  = 16x⁴- 96x³ + 216x² - 216x + 81

In the expansion of (3a + 4b)⁸, the only possible variable terms are a⁵b³, b⁸, a⁴b⁴, a⁸, ab⁷ because for each of them, the sum of there powers is eight. If the sum of the powers is not 8 then it is not correct.

For a²b³, the sum of the power is 5, for ab⁸ the sum of power is 9 and for a⁶b⁵ the sum of the power is 11 therefore thy are not correct.

As per the question expand the bimonoidal theorem and the pascal triangle. Showing the (x+2)6 (x-4)4 (2x+3)5 (2x-3y)4.

Learn more about the use the binomial theorem.

brainly.com/question/11995132.

Answer:

Explained below.

Step-by-step explanation:

The question is:

Please answer me these questions or one: v please. My math class room is 700 m2, how much is 1/4 of the room? How long is 3/4 of the room? . How many minutes is 3/5 of a half hour? . It takes 4/7 of a liter of paint to paint a square meter of wall, if we want to paint 2/5 of a square meter of wall, how much paint will we need? . If it takes 2/5 of an orange to make a glass of orange juice, how many oranges do you need to make 2 and a half glasses?

(1)

Compute 1/4th of the math class room as follows:

[tex]=700\times\frac{1}{4}\\=175[/tex]

Thus, 1/4th of the math class room is 175 m².

(2)

Compute 3/4th of the math class room as follows:

[tex]=700\times\frac{3}{4}\\=525[/tex]

Thus, 3/4th of the math class room is 525 m².

(3)

Compute 3/5th of half an hour as follows:

[tex]=30\times \frac{3}[5}\\=18[/tex]

Thus, 3/5th of half an hour is 18 minutes.

(4)

A square meter of wall required 4/7 liter of paint.

Then 2/5 of a square meter will require,

[tex]=\frac{4}{7}\times \frac{2}{5}\\\\=\frac{8}{35}[/tex]

Thus, 8/35 liter of paint will be used to pain /5 of a square meter of the wall.

(5)

1 glass of orange juice can be made using 2/5 of an orange.

Then 2 and half glass will require,

[tex]=\frac{2}{5}\times 2\frac{1}{2}\\\\=\frac{2}{5}\times \frac{5}{2}\\\\=1[/tex]

Thus, 1 orange will be required to make 2 and half glass of orange juice.

what should we do??? the question isn't there!

Answer:

He cut 6 slices

3/4 (leftover bread) equals to six eights (6/8)

Answer:

18 feet

Step-by-step explanation:

to find the frame around the widow means need to find the perimeter around the window:

P=2l+2w

P= 2(5+4)

P=18 feet

Answer:

340 im pretty sure

Step-by-step explanation:

Answer:

26.5 liters

Step-by-step explanation:

We know that 1 gallon is 4 quarts, and 1 gallon is approx. 3.78 liters. There's 7 days in a week, so 7 gallons of water is being flowed through. Multiplying 3.78  by 7, we get 26.46 liters per week. Rounding to the nearest tenth, and we get 26.5 liters.

Answer:

2/5 (because the chance winning the race is 3/5 and the remaining is 3/5 when we add 3/5 , 2/5 the answere is 5/5 when we subtract 3/5 from 5/5 the answere is 2/5

Answer:

[tex]5 \frac{1}{9}[/tex]

[tex]6 \frac{2}{5}[/tex]

Step-by-step explanation:

We can convert these improper fractions into mixed numbers by seeing how many times the denominator goes into the numerator.

In [tex]\frac{46}{9}[/tex], 9 goes into 46 5 times, with a remainder of 1. So:

[tex]5 \frac{1}{9}[/tex].

In [tex]\frac{32}{5}[/tex], 5 goes into 32 6 times with a remainder of 2, so:

[tex]6 \frac{2}{5}[/tex].

Hope this helped!

Answer:

5 1/9 and 6 2/5

Step-by-step explanation:

The simplest way to convert improper fractions into mixed fractions is by long division (see attached).

Answer:

27π inch^3

Step-by-step explanation:

Answer:  A

Step-by-step explanation:

Notes: Dividing by a fraction means to multiply by its reciprocal.

           The denominator cannot equal zero.

[tex]\dfrac{5a^3bc}{8ab^3}\div\dfrac{-ab^2}{6a^5b}\cdot \dfrac{2a^2b^3}{3b}\qquad \rightarrow a\neq 0,b\neq 0\\\\\\=\dfrac{5a^3bc}{8ab^3}\cdot\dfrac{6a^5b}{-ab^2}\cdot \dfrac{2a^2b^3}{3b}\\\\\\=\dfrac{5\cdot 6\cdot 2\quad a^3\cdot a^5\cdot a^2\quad b\cdot b\cdot b^3\quad c}{8\cdot -1 \cdot 3\quad a\cdot a\qquad b^3\cdot b^2\cdot b \quad}\\\\\\=\dfrac{-60a^{10}b^5c}{-24a^2b^6}\\\\\\=\dfrac{-5a^8c}{2b}[/tex]

Answer:

4 maximum extrema

Step-by-step explanation:

5th degree means that it can change direction 5 times, therefore creating a maximum of 4 extrema

Answer:

B

Step-by-step explanation:

The rules for reflecting across the x axis are just multiply the y value by -1

your answer is the second answer choice

For y axis refection, it is the same but for the x value, not the y .

Answer:

The volume of the cylinder is 163.3 m³.

Step-by-step explanation:

Given that,

Height = 13 cm

Base = 4 cm

So, radius = 2 cm

We need to calculate the volume of the cylinder

Using formula of cylinder

[tex]V=\pi r^2h[/tex]

Where, r = radius

h = height

Put the value into the formula

[tex]V=\pi\times(2)^2\times13[/tex]

[tex]V=163.3\ cm^3[/tex]

Hence, The volume of the cylinder is 163.3 cm³.

Given that:-

→ 1 sandwich = 2 slices of bread.

→ 1 hiker = 1 sandwich.

→ Then we have to find number of bread slices for n hikers .

→ Number of bread slices for 1 hiker = 2

→ Number of bread slices for 2 hikers = 2 × 2

→ For 3 hikers = 3 × 2

So in similar way

→ Number of bread slices for n hikers = 2×n → 2n

So 2n is the answer.

Answer:

3,440 strawberries

Step-by-step explanation:

Because of PEMDAS you want to start with the parentheses, and want to treat them like the distributive property.

So,

43 x 2 = 86

Then,

86 x 40 = 3440.

I hope that helps!!

Answer: 3440 strawberries on the farm.

Step-by-step explanation: (43)(2)⋅40                                                                     (86)(40)                                                                                                                     3440

Answer:

a. [tex]\mathbf{P(Y \leq 60) = 0.3333}[/tex]

b. P(Y>50) = 0.8889

c. E(y) = 67.5 and  Standard deviation [tex]\sigma[/tex] = 12.99

Step-by-step explanation:

From the information given :

an automobile body paint shop, has determined that the painting time of automobiles is uniformly distributed and that the required time ranges between 45 minutes to [tex]1\frac{1}{2}[/tex]hours.

The objective is to determine  the probability that the painting time will be less than or equal to an hour?

since 60 minutes make an hour;

[tex]1\frac{1}{2}[/tex]hours = 60 +30 minutes = 90 minutes

Let Y be the painting time of the automobile; then,

the probability that  the painting time will be less than or equal to an hour ca be  computed as :

[tex]P(Y \leq 60) = \int ^{60}_{45} f(y) dy \\ \\ \\ P(Y \leq 60) = \int ^{60}_{45} \dfrac{1}{45} dy \\ \\ \\ P(Y \leq 60) = \dfrac{1}{45} \begin {pmatrix} x\end {pmatrix}^{60}_{45} \\ \\ \\ P(Y \leq 60) = \dfrac{60-45}{45 } \\ \\ \\ P(Y \leq 60) = \dfrac{15}{45} \\ \\ \\ P(Y \leq 60) = \dfrac{1}{3} \\ \\ \\ P(Y \leq 60) = 0.3333[/tex]

What is the probability that the painting time will be more than 50 minutes?

The probability that the painting will be more than 50 minutes is P(Y>50)

So;

[tex]P(Y>50) = \int \limits ^{90}_{50} f(y) dy[/tex]

[tex]P(Y>50) = \int \limits ^{90}_{50} \dfrac {1}{45} dy[/tex]

[tex]P(Y>50) = \dfrac{1}{45}[x]^{90}_{50}[/tex]

[tex]P(Y>50) = (\dfrac{90-50}{45})[/tex]

[tex]P(Y>50) = \dfrac{40}{45}[/tex]

P(Y>50) = 0.8889

Determine the expected painting time and its standard deviation.

Let consider E to be the expected painting time

Then :

[tex]E(y) = \int \limits ^{90}_{45} y f(y) dy \\ \\ \\ E(y) = \int \limits ^{90}_{45} y \dfrac{1}{45} dy \\ \\ \\ E(y) = \dfrac{1}{45} [\dfrac{y^2}{2}]^{90}_{45} \\ \\ \\ E(y) = \dfrac{1}{45}[\dfrac{(90^2-45^2)}{2}] \\ \\ \\ E(y) = \dfrac{1}{45} (\dfrac{6075}{2}) \\ \\ \\ E(y) = \dfrac{1}{45} \times 3037.8 \\ \\ \\ \mathbf{E(y) = 67.5}[/tex]

[tex]E(y^2) = \int \limits ^{90}_{45} y^2 f(y) dy \\ \\ \\ E(y^2) = \int \limits ^{90}_{45} y^2 \dfrac{1}{45} dy \\ \\ \\ E(y^2) = \dfrac{1}{45} [\dfrac{y^3}{3}]^{90}_{45} \\ \\ \\ E(y^2) = \dfrac{1}{45}[\dfrac{(90^3-45^3)}{3}] \\ \\ \\ E(y^2) = \dfrac{1}{45} (\dfrac{637875}{3}) \\ \\ \\ E(y^2) = \dfrac{1}{45} \times 2126.25 \\ \\ \\ \mathbf{E(y^2) = 4725}[/tex]

To determine the standard deviation, we need to first know what is the value of our variance,

So:

Variance [tex]\sigma^2[/tex] = E(x²) - [E(x)]²

Variance [tex]\sigma^2[/tex] = 4725 - (67.5)²

Variance [tex]\sigma^2[/tex] = 4725 - 4556.25

Variance [tex]\sigma^2[/tex] = 168.75

Standard deviation [tex]\sigma[/tex] = [tex]\sqrt{variance}[/tex]

Standard deviation [tex]\sigma[/tex] = [tex]\sqrt{168.75}[/tex]

Standard deviation [tex]\sigma[/tex] = 12.99

Answer:

therefore, 33 divided by 13 equals 2 and 7 thirteenths (can be rewritten as 2 7/13)  

Step-by-step explanation:

Long division:

13  33

13*2 = 26

33 - 26 = 7

we have: 33/13 = 2 r7

we know that we can rewrite the remainder as 7/13

therefore, 33 divided by 13 equals 2 and 7 thirteenths (can be rewritten as 2 7/13)  

Answer:

If the order doesn't matter then we have a combination, if the order do matter then we have a permutation. One could say that a permutation is an ordered combination. The number of permutations of n objects taken r at a time is determined by the following formula: P(n,r)=n!

Step-by-step explanation:

To calculate the probability of a combination, you will need to consider the number of favorable outcomes over the number of total outcomes. Combinations are used to calculate events where order does not matter. In this lesson, we will explore the connection between these two essential topics.

Answer:

combination : If the order of numbers  or  operations does not matter

Permutation : when the order of numbers matter ( common example most teachers use : a code of 4 numbers has to be in a certain order and the numbers are from 0 to 9 , how many permutation can you make if you use the number one time)

P=n!/(n-r)!

n! ( are number from 0-9 we have 10 numbers)

r is the number of digits in the code = 4

n!=10*9*8*7*6*5*4*2*1

(n-r)!=(10-4)!=6!=6*5*4*3*2*1

P=5040 ways ( if the order matter)

If the order does not matter

Combination C(n,r)=n!/(n-r)!r!

C(10,4)=(10*9*8*7*6*5*4*2*1)/[(6*5*4*3*2*1)(4*3*2*1)]

Answer:

18 m

Step-by-step explanation:

Answer:

18m

Step-by-step explanation:

Plot point F where angle alpha is located.

Triangle ABF has two interior angles x and 80. They add to the exterior angle alpha due to the remote interior angle theorem.

alpha = x+80

Answer:

y = - 140

Step-by-step explanation:

Given that y varies jointly as x and z then the equation relating them is

y = kxz ← k is the constant of variation

To find k use the condition y = - 180 when z = 15 and x = - 3, thus

- 180 = k × - 3 × 15 = - 45k ( divide both sides by - 45 )

4 = k

y = 4xz ← equation of variation

When x = 7 and z = - 5, then

y = 4 × 7 × - 5 = - 140

Answer:

7 and 1

Step-by-step explanation:

Let the numbers be a and b.

A positive number is 7 times another number:

If 3 is added to both the numbers then one of the new number becomes 5 by 2 times the other new number:

To solve this we substitute a with 7b in the second equation:

Then, finding a:

So the numbers are 7 and 1

we can subtract the trapezium (white part) formed after from the trapezium (including white and grey) to get area of striped part

area of trapezium is [tex]\frac H2(a+b)[/tex] where $a$ and $b$ are parallel sides.

for bigger trapezium, $h=4$ parallel sides are $5$ and $5$

hence area is $\frac{4(5+5)}{2}=20$

similarily area of white trapezium, $\frac{4(3+3)}{2}=12$

and area of striped part is $20-12=8$

No they are not the same.

We can plug in x = 0 to get

11-2x = 11-2(0) = 11-0 = 11

2x-11 = 2(0)-11 = 0-11 = -11

We get the results 11 and -11 for the expressions 11-2x and 2x-11 respectively. Since we got different outputs, this is enough to show that the expressions are not the same. They would need to produce the same outputs for any given x value.

On a graph, y = 11-2x and y = 2x-11 are two different lines to show they are not the same expression.

note: if you plug in x = 11/2 = 5.5, then both outputs are the same; otherwise, you'll get different outputs.

Answer:

5.3

Step-by-step explanation:

A rational number is a number that can be written as the quotient of two integers.

5.2 and 5.5 are both rational since they can be written as quotients of integers as shown below.

5.2 = 52/10

5.5 = 55/10

5.3 is a number between 5.2 and 5.5, and since 5.3 can be written as 53/10, it is rational.

Answer: 5.3

Answer:

Step-by-step explanation:

rational numbers can be written in form a/b where b≠0

5.2 and 5.5

52/10 and 55/10

so some rational numbers could be

53/10, 54/10

irrational numbers  most likely the square root numbers

square them

5.2^2=27.04

5.5^2=30.25

5.2<?<5.5

square everybody

27.04<?²<30.25

so pick a number between 27.04 and 30.25

29 or 30 are 2 numbers

I'll pick 29

?²= 29

square root

?=√29

the irrational number can be √29

it is 5.39 to the hundredth

Answer:

y = 3x+13

Step-by-step explanation:

y-3x=13

Add 3x to each side

y-3x+3x=3x+13

y = 3x+13

The value of y for the given equation y - 3x = 13 is calculated to be y = 3x + 13.

Given that:

y - 3x = 13

It is required to find the value of y.

In order to find the value of y, the equation has to be solved in such a way that y has to be kept on one side.

Consider:

y - 3x = 13

Add 3x on both sides.

y - 3x + 3x = 13 + 3x

y = 13 + 3x

Hence, the value of y is 13 + 3x.

Learn more about Equations here :

https://brainly.com/question/29657992

#SPJ6

Answer:

It will depend on how many euros they intend to convert. If they were only converting one euro they would get $1.35 whichever rate they used, but imagine it was a thousand euros - at the correct rate they would get $1352.61, at the proposed rate they would only get $1350.

Step-by-step explanation:

No, by rounding the conversion ratio, the Ruiz family will not be getting the most accurate answer. Using the more accurate conversion ratio will give an answer with more than 2 decimal places so the answer can accurately be rounded after the conversion.

Answer:

No, by rounding the conversion ratio, the Ruiz family will not be getting the most accurate answer. Using the more accurate conversion ratio will give an answer with more than 2 decimal places so the answer can accurately be rounded after the conversion.

Step-by-step explanation:

just copy/paste

Answer:

28\3

Step-by-step explanation: