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Eduardwww [97]
3 years ago
15

A 47-foot-long piece of pipe is to be cut into three pieces. The second piece is three times as long as the first piece, and the

third piece is two feet more than five times the length of the first piece. What is the length of the longest piece?
Mathematics
1 answer:
DanielleElmas [232]3 years ago
7 0
A = first piece, b = second piece, c = third piece

a + b + c = 47
b = 3a
c = 5a + 2

a + (3a) + (5a + 2) = 47.....combine like terms
9a + 2 = 47
9a = 47 - 2
9a = 45
a = 45/9
a = 5 ft

b = 3a.....b = 3(5)....b = 15 ft
c = 5a + 2....c = 5(5) + 2.....c = 25 + 2....c = 27 ft

longest piece (c) = 27 ft
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The graph of the sequence M , we define M recursively using function notation

f(n+1)=f(n)-2

Given :

the graph of the sequence M

Lets write the recursive function using the given points

First point is (1,7) and second point is (2,5) then (3,3) and so on

For recursive function , we use the initial point (1,7)

when n=1, f(n)=7

the y values of the point are decreasing by 2. Common difference is -2

Recursive function is

f(n+1)=f(n)-diffeference \\f(n+1)=f(n)-2

where n=2,3,4...

Learn more : brainly.com/question/10676131

8 0
2 years ago
Question 7(Multiple Choice Worth 1 points)
lana66690 [7]

Answer:

Option A.

Step-by-step explanation:

The given function is

f(x)=0.15x^2-6x+400

Leading coefficient is positive, so it is an upward parabola. Vertex of an upward parabola is the point of minima.

Vertex of a parabola f(x)=ax^2+bx+c is

Vertex=\left(\dfrac{-b}{2a},f(\dfrac{-b}{2a})\right)

In the given function a=0.15, b=-6 and x=400.

-\dfrac{b}{2a}=-\dfrac{-6}{2(0.15)}=20

At x=20,

f(20)=0.15(20)^2-6(20)+400=340

So, minimum value of f(x) is 340 at x=20.

From the given table it is clear that the minimum value of g(x) is 55 at x=70.

Since 55 < 340, therefore, g(x) has a lower minimum values, i.e, (70,55).

Hence, option A is correct.

4 0
4 years ago
A communications company has developed three new designs for a cell phone. To evaluate consumer response, a sample of n = 120 co
defon

Answer:

The answer is "Its results are not consistent with its three designs Yes. Its results show significant differences between both the three designs."

Step-by-step explanation:

Following are the distribution of preference:  

Design 1 =54 \\\\ Design 2=38 \\\\\ Design 3=28 \\\\

Design \ \ \ \ \ \ \ \ \ \ O_i \\ 1 \ \ \ \ \ \  \ \ \ \ \ \ \ \ \ \ \ 54 \\2  \ \ \ \ \ \  \ \ \ \ \ \ \ \ \ \ \ 38\\3 \ \ \ \ \ \  \ \ \ \ \ \ \ \ \ \ \  28 \\Total \ \ \ \ \ \ \ \ \ \ 120

An expected frequency(E_i) has 40 Null hypotheses to take n=120.to each design:  

The effects of the three designs are standardized  

Inaccurate.  

Hypothesis Alternative:  

The effects of the three prototypes are not uniform

Degrees Of freedom =(n-1)=(3-1)=2

H_o, x^2  \ test\  statistic \  \sum_i {\frac{(O_i -E_i)^2}{E_i}} \\

= \frac{(54 -40)^2}{40}+\frac{(38-40)^2}{40} + \frac{(28-40)^2}{40}\\\\=49+0.1+3.6\\\\=8.6

Chi-squared distribution critical value at \alpha = 0.05 (x^2 _{0.052})=5.99  

Since x^2, a value > x^2 -table of \alpha =0.05 =5.99is determined.  

SoH_o is rejected.

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3 years ago
I really need help of 39 !!!! Lots of points
Reil [10]
The answer is C ! :)
6 0
3 years ago
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Figure ABC is to be translated to Figure A'B'C' using the rule (x, y) → (x−3, y+4). Triangle ABC on the coordinate plane with th
KIM [24]
The translation P<span>(x, y) → P'(x−3, y+4) 

means that every point P(x, y) is shifted :

3 units left (because of the -) and 4 units up (because of the +).


We say P was "mapped" onto P'.


Point A(1,1) is mapped to </span>A'(1-3,1+4)=A'(-2, 5).


Check the picture to see where each of the points A, B and C are mapped.

6 0
3 years ago
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