At the airport, each piece of luggage to be checked in must not weigh more than 50
pounds.
Use w to represent the weight (in pounds) of a piece of luggage that can be checked in.

Answer:

19/20 miles

Step-by-step explanation:

3/4 + 1/5

3/4 = 0.75

1/5 = 0.2

3/4 + 1/5

= 0.75 + 0.2

= 0.95

= 95/100

= 19/20

Therefore,

the miles you have walked in all is 19/20.

Answer:

Step-by-step explanation:

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

The 8 degree polynomial for the given roots can be written as  p(x) =  x⁸ - x⁷- 12x⁶ - 4x⁵ + 30x⁴ + 51x³ + 18x².

The factor theorem states that for a polynomial p(x) if there exists a real number a such that p(a) = 0, then (x - a) is one of the factors of p(x).

The roots of the polynomial are given as follows,

Number of roots at -2 = 1

Number of roots at 3 = 2

Number of roots at 0 = 2

And, number of roots at -1 = 3.

Now, the polynomial can be written using factor theorem as,

p(x) = x²(x + 2)(x - 3)²(x + 1)³

      = x²(x + 2)(x²- 6x + 9)(x³ + 3x² + 3x + 1)

      = x⁸ - x⁷- 12x⁶ - 4x⁵ + 30x⁴ + 51x³ + 18x²

Hence, the polynomial for given roots can be written as p(x) =  x⁸ - x⁷- 12x⁶ - 4x⁵ + 30x⁴ + 51x³ + 18x².

To know more about factor theorem click on,

https://brainly.com/question/13547729

#SPJ2

Answer:

Continuous

Step-by-step explanation:

Answer:

213 crates

Step-by-step explanation:

There is enough space for 26000 kg - 13200 kg = 12800 kg. Divide this by 60 and you get 213 and 1/3. You cannot put 1/3 of a crate, so it is 213 crates.

Answer:

1470 inches cubed

Step-by-step explanation:

Vol=length × width × height

But ALSO,

length × width = Area,

So we find another Volume equation,

Vol = BaseArea × height

This is the information you are given in the question.

Vol = 210 × 7

Vol = 1470 inches cubed

Answer:

don't know

Step-by-step explanation:

Answer:

The explicit formula for the nth term of the sequence is [tex]a_n=9+8(n-1)[/tex]

Step-by-step explanation:

Recall:

The explicit formula for a sequence is [tex]a_n=a_1+(n-1)d[/tex] where [tex]a_n[/tex] is the [tex]n[/tex]th term, [tex]a_1[/tex] is the first term, and [tex]d[/tex] is the common difference

Given:

First term --> [tex]a_1=9[/tex]

Common Difference --> [tex]d=8[/tex]

Substitute:

[tex]a_n=9+(n-1)(8)[/tex]

[tex]a_n=9+8(n-1)[/tex]

Answer:

Step-by-step explanation:

The progression of sums is ...

  1, 5, 15, 34, 65, ...

So, first differences are ...

  4, 10, 19, 31

Second differences are ...

  6, 9, 12, ...

Third differences are constant:

  3, 3, ...

This means the expression for Sn will be a cubic expression. If dn is the first of the n-th differences, then the equation can be written as ...

  Sn = S1 +(n -1)(d1 +(n -2)/2(d2 +(n -3)/3(d3)))

And this simplifies a little bit to ...

  Sn = 1 +(n -1)(4 +(n -2)(n +3)/2)

In simpler form, we have ...

  Sn = 1/2(n³ +n)

Then the two terms we're interested in are ...

  S7 = (1/2)(7³ +7) = 175

  S17 = (1/2)(17³ +17) = 2465

Each term Sₙ consists of the sum of a triangular number of terms, which are given by

[tex]T_n = \displaystyle \sum_{k=1}^n k = 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}2[/tex]

The triangular numbers are given recursively for n ≥ 1 by

[tex]T_n = T_{n-1} + n[/tex]

starting with T₀ = 0.

For example,

• S₁ = 1 and

[tex]\displaystyle S_1 = \sum_{k=T_0+1}^{T_1} k = \sum_{k=1}^1 k = 1[/tex]

• S₂ = 2 + 3 and

[tex]\displaystyle S_2 = \sum_{k=T_1+1}^{T_2} k = \sum_{k=2}^3 k = 2 + 3[/tex]

• S₃ = 4 + 5 + 6 and

[tex]\displaystyle S_3 = \sum_{k=T_2+1}^{T_3} k = \sum_{k=4}^6 k = 4 + 5 + 6[/tex]

Then the n-th term of the sequence we're considering is

[tex]S_n = \displaystyle \sum_{k=T_{n-1}+1}^{T_n} k = \sum_{k=T_{n-1}+1}^{T_{n-1}+n} k[/tex]

Expanding this sum, we have

[tex]S_n = \left(T_{n-1}+1\right) + \left(T_{n-1}+2\right) + \left(T_{n-1}+3\right) + \cdots + \left(T_{n-1}+n\right)[/tex]

There are n terms on the right side, and hence n copies of [tex]T_{n-1}[/tex], and the rest of the terms make up the next triangular number [tex]T_n[/tex] :

[tex]S_n = nT_{n-1} + 1 + 2 + 3 + \cdots + n[/tex]

[tex]S_n = nT_{n-1} + \displaystyle \sum_{k=1}^n k[/tex]

[tex]S_n = nT_{n-1} + T_n[/tex]

We have a closed form for [tex]T_n[/tex], so we end up with

[tex]S_n = n \cdot \dfrac{(n-1)n}2 + \dfrac{n(n+1)}2 \implies \boxed{S_n=\dfrac{n^3+n}2}[/tex]

From here it's easy to find S₇ and S₁₇.

[tex]S_7 = \dfrac{7^3+7}2 \implies \boxed{S_7 = 175}[/tex]

[tex]S_{17} = \dfrac{17^3+17}2 \implies \boxed{S_{17} = 2465}[/tex]

Answer:

Hello There!

According to the question,

Base=6

And

Height =4

Let's know the formula

[tex] \frac{1}{2} \times base \times height \\ so \\ \frac{1}{2} \times 6 \times 4 \\ [/tex]

simplify 2 with 6 then it will look like this

[tex] \frac{1}{1} \times3 \times 4 \\ \\ [/tex]

1 has no value so

[tex]3 \times 4 = 12 {ft}^{2} \\ [/tex]

So third option

[tex]a = 12 {ft}^{2} [/tex]

is correct.

[tex]\Large\textsf{Hope \: It \: Helped}[/tex]

Answer:

Area = 12 sq ft

Step-by-step explanation:

The formula to find the area of a triangle is

1/2 bh so we will replace the letters with their number value

1/2 (6x4)

1/2 x 24 = 12

So, 12 is your answer!

Answer:

Step-by-step explanation:

Answer:

x = 36

Step-by-step explanation:

3x+2x=180

5x=180

x=36

Answer:

x=36 degrees

Step-by-step explanation:

Answer: the answer is 600 or the letter C

Answer:

3) 600

Step-by-step explanation:

Answer:

arrange them: -9x^3+2x^3-4x^2+x^2-6x-5x

the simplified is: -7x^3-3x^2-11x

Answer:

Dividend: Number on top

Divisor: Number on bottom

Quotient: Answer

Dividend ÷ Divisor = Quotient

The distance Jen is from the base of the lighthouse is 86.6 meters.

Trigonometric ratio is used to show the relationship between the sides of a and angles of a right angled triangle.

Let d represent the distance Jen is from the base of the lighthouse.

Using trigonometric ratios:

[tex]tan(30)=\frac{50}{d} \\\\d=\frac{50}{tan(30)} \\\\d=86.6\ m[/tex]

The distance Jen is from the base of the lighthouse is 86.6 meters.

Find out more on Trigonometric ratio at: https://brainly.com/question/10417664

Answer:

It'd be a rational number

Step-by-step explanation:

Real numbers are a set of numbers containing all of the rational numbers and all of the irrational numbers.

Types of numbers in the rational number "section" are decimals, whole, mixed, and fraction numbers whether they are negative or positive they are rational numbers.

Irrational numbers are numbers that cannot be expressed as the ratio of two integers. So they would be square root, pi and more.

Answer:

The man traveled 20km by train.

Step-by-step explanation:

If x is the distance he traveled by train, you can write this equation to represent the situation:

[tex]10+x+2x=70[/tex]

Then, you can simply solve for x:

[tex]10+3x=70\\3x=60\\x=20[/tex]

The man traveled 20km by train.

[tex]10+(20)+2(20)=70\\10+20+40=70\\70=70[/tex]

Answer:

See answer below.

Step-by-step explanation:

This is true for all right triangle a² + b² = c²    were c = the largest number

9, 12, 15           A right triangle

21, 28, 35       A right triangle

9, 13, 16          Not a right triangle

10, 11, 15          Not a right triangle

Answer:

13 ft^2

Step-by-step explanation:

Area = Base * Height

= 3 * (4+1/3)

=3*(13/3)

=13

Answer:

0.14

Step-by-step explanation:

brainliest please

Answer:

|-5| absolute be always + so 5

Answer:

[tex]5[/tex]

Step-by-step explanation:

Step 1:  Determine what absolute value does

Taking the absolute value of a number just returns how far a specific value is from 0.  So in this case we see a number -9 and although it's negative it's still 9 away from 0 therefore that would be the absolute value.

We are missing the absolute value of -5 or 5 so we know that taking the absolute value would just give us the distance from 0.  In this case that would just be 5.

Answer: [tex]5[/tex]

Answer:

d

Step-by-step explanation:

same explanation as before just replace the current values with the previous explanation

Answer:

After a quick stint of attempting to read the graphs I would speculate D

Using the binomial distribution, it is found that the variance of the number that pass inspection in one day is 5.7.

For each component, there are only two possible outcomes, either it passes inspection, or it does not. The probability of a component passing inspections is independent of any other component, hence, the binomial distribution is used to solve this question.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability, and has variance given by:

[tex]V(X) = np(1 - p)[/tex]

In this problem:

The variance is given by:

[tex]V(X) = np(1 - p) = 120(0.95)(0.05) = 5.7[/tex]

The variance of the number that pass inspection in one day is 5.7.

To learn more about the binomial distribution, you can take a look at https://brainly.com/question/24863377

Answer:

LETS

GO

BRANDON

Step-by-step explanation:

Answer:

x=41

Step-by-step explanation:

9²+40²=x²

81+1600=x²

1681=x²

√1681=√x²

41=x

Answer:

x<=-12

Step-by-step explanation:

1/4x<=-3

*Multiply both sides by 4

x<=-12

and it's solved :)