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3 years ago

13

1) write down a different ratio equivalent to 12 : 3

2 answers:

Alina [70]3 years ago

7 0

1) 24:6
2) 60:48
I just multiplied by 2

Dennis_Churaev [7]3 years ago

4 0

Answer: 1) 4:1 2) 60/48

Step-by-step explanation:

1. 12: 3 is the same as 12/3 so you can diving both side by 3.

12:3 ÷ 3/3=4/1

2. 30:24 is the same as 30/24 so you can divide both sides by 6 or multiply both sides by 2.

30/24 * 2/2= 60/48

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Katrina buys a 42-ft roll of fencing to make a rectangular play area for her dogs.

vekshin1

Answer:

(a) $l = -w + 21$

(b) Domain: $0$ <em>(See attachment for graph)</em>

(c) $f(w) = -w + 21$

Step-by-step explanation:

Given

$2(l + w) = 42$

$l = length$

$w = width$

Solving (a): A function; l in terms of w

All we need to do is make l the subject in $2(l + w) = 42$

Divide through by 2

$l + w = 21$

Subtract w from both sides

$l + w - w = 21 - w$

$l = 21 - w$

Reorder

$l = -w + 21$

Solving (b): The graph

In (a), we have:

$l = -w + 21$

Since l and w are the dimensions of the fence, they can't be less than 1

So, the domain of the function can be $0$

--------------------------------------------------------------------------------------------------

To check this

When $w = 1$

$l = -1 + 21$

$l = 20$

$(w,l) = (1,20)$

When $w = 20$

$l = -20 + 21$

$l = 1$

$(w,l)= (20,1)$

--------------------------------------------------------------------------------------------------

<em>See attachment for graph</em>

<em></em>

Solving (c): Write l as a function $f(w)$

In (a), we have:

$l = -w + 21$

Writing l as a function, we have:

$l = f(w)$

Substitute $f(w)$ for l in $l = -w + 21$

$l = -w + 21$ becomes

$f(w) = -w + 21$

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3 years ago

The function f(x) = -6x. The graph of g(x) is f(x)vertically stretched by a factor of 7 and reflected in the x-axis. What is the

Vera_Pavlovna [14]

we are given a function

$f(x)=-6x$

First translation:

The graph of function is vertically stretched by a factor of 7

Whenever we vertically stretch any function by 'a' units

so, we can write it as

$g(x)=a\times f(x)$

Here, it is vertically stretch by 7

so, we get

$g(x)=7\times -6x$

$g(x)=-42x$

Second translation:

Whenever we reflect any function about x-axis

we multiply y-value by -1

so, we can write it as

$g(x)=-f(x)$

Here , it is reflected in the x-axis

so, we can multiply by -1 to y-value

we get

$g(x)=-1\times -42x$

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Out of 100 people sampled, 42 had kids. Based on this, construct a 99% confidence interval for the true population proportion of

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Answer:

The 99% confidence interval for the true population proportion of people with kids is (0.293, 0.547).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

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This means that $n = 100, \pi = \frac{42}{100} = 0.42$

99% confidence level

So $\alpha = 0.01$ , z is the value of Z that has a p-value of $1 - \frac{0.01}{2} = 0.995$ , so $Z = 2.575$ .

The lower limit of this interval is:

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The upper limit of this interval is:

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