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4 years ago

I need help with number 7 can someone explain how u get the answer?

Mathematics

1 answer:

Svet_ta [14]4 years ago

5 0

Answer:

5 months

Step-by-step explanation:

Set up an inequality, using x to represent months.

(The 35 and 40 represent the cost per month, and you add the 100 and 75 just once because it's a one-time fee and not monthly)

35x + 100 < 40x + 75

Now solve for x.

5x > 25

x > 5

This means that the membership will be less expensive after 5 months.

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A state vector X for a four-state Markov chain is such that the system is four times as likely to be in state 2 as in 4, is not

GREYUIT [131]

All the components in the state vector need to sum to 1. You're given that component corresponding to state 1 is 0.2, and that the component for state 3 is 0.

That leaves states 2 and 4, for which you're told that the component for state 2 is four times as large. If $x_i$ is the component for state $i$ , then you have

$x_1+x_2+x_3+x_4=1\iff 0.2+4x_4+0+x_4=1\implies5x_4=0.8\implies x_4=0.16$

which means $x_2=4x_4=0.64$ . So the state vector is $\mathbf x=(0.2,0.64,0,0.16)$ .

8 0

3 years ago

1) For the following problem: Let f={(-2,3),(-1,1),(0,0),(1,-1), (2,-3)} and let g-{-3,1),(-1,-2), (0, 2),(2, 2),(3,1)}.Find the

N76 [4]

Answer:

1. f(1)=-1 and g(-1)=-2.

2. (gof)(1)=-2.

3. (gofof)(-1)=-2

4. (fog)(3)=-1

Step-by-step explanation:

The given functions are defined as

f={(-2,3),(-1,1),(0,0),(1,-1), (2,-3)}

g={(-3,1),(-1,-2), (0, 2),(2, 2),(3,1)}

The value of function f at x=1 is -1, So, f(1)=-1.

The value of function g at x=-1 is -2, So, g(-1)=-2.

Therefore the value of f(1) is -1 and the value of g(-1) is -2.

$(g\circ f)(1)=g(f(1))$ $[\because (g\circ f)(x)=g(f(x))]$

$(g\circ f)(1)=g(-1)$ $[\because f(1)=-1]$

$(g\circ f)(1)=-2$ $[\because g(-1)=-2]$

Therefore the value of (gof)(1) is -2.

$(g\circ f\circ f)(-1)=(g\circ f)(f(-1))$ $[\because (g\circ f)(x)=g(f(x))]$

$(g\circ f\circ f)(-1)=(g\circ f)(1)$ $[\because f(-1)=1]$

$(g\circ f\circ f)(-1)=-2$ $[\because \text{From part 2}, (g\circ f)(1)=-2]$

Therefore the value of (gofof)(1) is -2.

$(f\circ g)(3)=f(g(3))$ $[\because (f\circ g)(x)=f(g(x))]$

$(f\circ g)(3)=f(1)$ $[\because g(3)=1]$

$(f\circ g)(3)=-1$ $[\because f(1)=-1]$

Therefore the value of (fog)(3) is -1.

6 0

3 years ago

Increase £120 by 40%

leonid [27]

Answer:

£168

Step-by-step explanation:

To increase £120 by 40%, multiply 120 by 1.4

120(1.4)

= 168

So, £120 increased by 40% is £168

4 0

3 years ago

Seth has a garden with dimensions 9 feet long times 8 feet wide he wants to enlarge the garden to an area of 120 ft.² how much f

ziro4ka [17]

Answer:

6 ft longer (total length of 15ft)

Step-by-step explanation:

the initial dimensions are:

length: $l=9ft$

width: $w=8ft$

the area area of the garden is given by:

$a=l*w$

so the original area is:

$a=9ft*8ft=72ft^2$

Since we need the area to be $120ft^2$ , and we can only change the length, the width will still be 8ft.

We substitute the value of the new area and the width to the equation for the area:

$a=l*w\\120ft^2=l*8ft$

and we clear for the new length:

$l=\frac{120ft^2}{8ft}\\ \\l=15$

The length of the garden for the area to be $120ft^2$ , must be 15ft.

This means that if originally the length was 9 ft, now it has to be 6 ft longer.

5 0

3 years ago

Suppose that a rectangle has a perimeter of 17 meters. Express the area A(x) of the rectangle in terms of the length x of one of

Simora [160]

<span>Let the length of one side of the rectangle be x. Then the opposite side of the rectangle also has a length of x. The sum of the other two sides must be 17 - 2x. So the length of one of these sides is 8.5 - x. The length of two sides of the rectangle are x and 8.5 - x. To find the area, we need to multiply these two values. A(x) = (x) (8.5 - x) = 8.5x - x^2</span>

4 0

4 years ago