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4 years ago

7

At a factory, a machine puts tops on bottles at a rate of 80 bottles per minute. How many tops can be put on bottles between 8:0

0 a.m. and 3:30 p.m.?

1 answer:

timama [110]4 years ago

6 0

Answer:

= 36000 caps

Step-by-step explanation:

First we need to figure out how many minutes between 8 am and 3:30 pm

There are 7 hours and 30 minutes.

1 hour = 60 minutes

Multiply each by 7

7 hours = 7*60 minutes = 420 minutes

So 7 hours 30 minutes = 420 + 30 = 450 minutes

Bottle caps = rate * minutes

= 80 caps/minute * 450 minutes

= 36000 caps

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ra1l [238]

3x27=81 so 81 is a multiple of 3

there is no integer x for which 4x=46 so 46 is not a multiple of 4

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there is no integer x for which 6x=45 hence 45 is not a multiple of 6

6 0

4 years ago

Franchise Business Review stated over 50% of all food franchises earn a profit of less than $50,000 a year. In a sample of 130 c

nydimaria [60]

Answer:

We need a sample size of 564.

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 zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

$\pi = \frac{81}{130} = 0.6231$

The margin of error is:

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

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

Based upon a 95% confidence interval with a desired margin of error of .04, determine a sample size for restaurants that earn less than $50,000 last year.

We need a sample size of n

n is found when $M = 0.04$

So

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

$0.04 = 1.96\sqrt{\frac{0.6231*0.3769}{n}}$

$0.04\sqrt{n} = 1.96\sqrt{0.6231*0.3769}$

$\sqrt{n} = \frac{1.96\sqrt{0.6231*0.3769}}{0.04}$

$(\sqrt{n})^{2} = (\frac{1.96\sqrt{0.6231*0.3769}}{0.04})^{2}$

$n = 563.8$

Rounding up

We need a sample size of 564.

4 0

3 years ago

What is 40% as a whole number

maksim [4K]

% is a number over 100, so 40% is 40/100, which is 0.40.

5 0

3 years ago

Read 2 more answers

Find the critical numbers of the function f(x) = x6(x − 2)5.x = (smallest value)x = x = (largest value)(b) What does the Second

Marrrta [24]

Answer:

$a) x=0, x=\frac{12}{11}, x=2 \:$ b) The 2nd Derivative test shows us the change of sign and concavity at some point. c) At which point the concavity changes or not. This is only possible with the 2nd derivative test.

Step-by-step explanation:

a) To find the critical numbers, or critical points of:

$f(x)=x^{6}(x-2)^{5}$

1) The procedure is to calculate the 1st derivative of this function. Notice that in this case, we'll apply the <em>Product Rule</em> since there is a product of two functions.

$f(x)=x^{6}(x-2)^{5}\Rightarrow f'(x)=(f*g)'(x)\\=f'g+fg'\Rightarrow (fg)'(x)=6x^{5}(x-2)^{5}+5x^{6}(x-2)^{4} \Rightarrow 6x^{5}(x-2)^{5}+5x^{6}(x-2)^{4}=0\\f'(x)=6x^{5}(x-2)^{5}+5x^{6}(x-2)^{4}$

2) After that, set this an equation then find the values for x.

$x^{5}(x-2)^{4}[6(x-2)+5x]=0\Rightarrow x^{5}(x-2)^{4}[11x-12]=0\Rightarrow x_{1}=0\\(x-2)^{4}=0\Rightarrow \sqrt[4]{(x-2)}=\sqrt[4]{0}\Rightarrow x-2=0\Rightarrow x_{2}=2\\(11x-12)=0\Rightarrow x_{3}=\frac{12}{11}$

$x=0\:(smallest\:value)\:x_{3}=\frac{12}{11}\:x=2 (largest value)$

b) The Second Derivative Test helps us to check the sign of given critical numbers.

Rewriting f'(x) factorizing:

$f'(x)=(11x-12)(x-2)^4x^{5}$

Applying product Rule to find the 2nd Derivative, similarly to 1st derivative:

$f''(x)>0 \Rightarrow Concavity\: Up\\\\f''(x)$

$f''(x)=11\left(x-2\right)^4x^5+4\left(x-2\right)^3x^5\left(11x-12\right)+5\left(x-2\right)^4x^4\left(11x-12\right)\\f''(x)=10\left(x-2\right)^3x^4\left(11x^2-24x+12\right)$

1) Setting this to zero, as an equation:

$10\left(x-2\right)^3x^4\left(11x^2-24x+12\right)=0\\\\$

$10\left(x-2\right)^3x^4\left(11x^2-24x+12\right)=0\\(x-2)^{3}=0 \Rightarrow x_1=2\\x^{4}=0 \therefore x_2=0\\11x^{2}-24x+12=0 \Rightarrow x_3=\frac{12+2\sqrt{3}}{11}\:,x_4=\frac{12-2\sqrt{3}}{11}\cong 0.78$

2) Now, let's define which is the inflection point, the domain is as a polynomial function:

$D=(-\infty$

Looking at the graph.

Plugging these inflection points in the original equation $f(x)=x^{6}(x-2)^{5}$ to get y coordinate:

We have as Inflection Points and their respective y coordinates (Converting to approximate decimal numbers)

$(1.09,-1.05)$ Inflection Point and Local Minimum

$(2,0)$ Inflection Point and Saddle Point

$(0,0)$ Inflection Point Local Maximum

(Check the graph)

c) At which point the concavity changes or not. This is only possible with the 2nd derivative test.

At

$x=\frac{12}{11}\cong1.09$ Local Minimum

$At\:x=0,\:Local \:Maximum$

$At\:x=2, \:neither\:a\:minimum\:nor\:a\:maximum$ (Saddle Point)

5 0

3 years ago

Can I get some help

Cloud [144]

The answer should be B.

4 0

3 years ago