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3 years ago

In a surey of 375 dog and cat owners there were 215 dog owners and 193 cat owners. how many in the survey own a dog

Mathematics

2 answers:

VARVARA [1.3K]3 years ago

4 0

First, draw venn diagram and determine how many people own both cat and dog. See image attached.
x represents the number of people own both cat and dog
dog only owner + cat only owner + both cat and dog owner = 375
215 - x + 193 - x + x = 375
408 - x = 375
x = 408 - 375
x = 33
The number of people own both cat and dog is 33

Second, find the number of people own dog only
dog only = 215 - 33
dog only = 182
The number of people own dog only is 182

spin [16.1K]3 years ago

3 0

Percent wise, 57.3% own a dog

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3 years ago

I am having trouble with this relative minimum of this equation.<br>

Norma-Jean [14]

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So the approximate relative minimum is (0.4,-58.5).

Step-by-step explanation:

Ok this is a calculus approach. You have to let me know if you want this done another way.

Here are some rules I'm going to use:

$(f+g)'=f'+g'$ (Sum rule)

$(cf)'=c(f)'$ (Constant multiple rule)

$(x^n)'=nx^{n-1}$ (Power rule)

$(c)'=0$ (Constant rule)

$(x)'=1$ (Slope of y=x is 1)

$y=4x^3+13x^2-12x-56$

$y'=(4x^3+13x^2-12x-56)'$

$y'=(4x^3)'+(13x^2)'-(12x)'-(56)'$

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$y'=4(3x^2)+13(2x^1)-12(1)$

$y'=12x^2+26x-12$

Now we set y' equal to 0 and solve for the critical numbers.

$12x^2+26x-12=0$

Divide both sides by 2:

$6x^2+13x-6=0$

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$a=6$

$b=13$

$c=-6$

We are going to use the quadratic formula to solve for our critical numbers, x.

$x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$

$x=\frac{-13 \pm \sqrt{13^2-4(6)(-6)}}{2(6)}$

$x=\frac{-13 \pm \sqrt{169+144}}{12}$

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Let's separate the choices:

$x=\frac{-13+\sqrt{313}}{12} \text{ or } \frac{-13-\sqrt{313}}{12}$

Let's approximate both of these:

$x=0.3909838 \text{ or } -2.5576505$ .

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The relative maximum is at approximately -2.5576505.

So the relative minimum is at approximate 0.3909838.

We could also verify this with more calculus of course.

Let's find the second derivative.

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