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2 years ago

11. A company plans to have coffee mugs produced with the company logo on them. The cost of each

Mathematics

1 answer:

vovikov84 [41]2 years ago

6 0

Answer:

Step-by-step explanation:

The cost of each mug depends on the number of mugs that are ordered and is modeled by :

$y =0.0001x^2+ 0.1x + 30$ ...(1)

We need to find the minimum cost of each mug.

For minimum cost, dy/dx = 0

So,

$\dfrac{d(0.0001x^2- 0.1x + 30)}{dx}=0\\\\2x(0.0001)-0.1=0\\\\0.0002x=0.1\\\\x=\dfrac{0.1}{0.0002}\\\\x=500$

Put the value of x in equation (1).

$y =0.0001(500)^2- 0.1(500) + 30\\\\y=5$

So, the minimum cost of each mug is $5.

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two observers, Anna and Bryan. sight a kite at angles 44 degrees and 66 degrees. respictively. if anna is located 20m from the k

Arada [10]

Answer:

28.6m

Step-by-step explanation:

this question is very incomplete. it requires a number of assumptions to give an answer. the main one - where is Bryan located relative to Anna ? I assume diametrically on the opposite side of the kite. because he has the steeper angle, it is clear that he is nearer to the kite.

so, I guess, we have to add his distance to the kite to her distance to the kite to get the distance between her and him.

but he could be on any point on a circle around the kite to have the same viewing angle, and we would have no clue about where on that circle.

as the other extreme alternative, he could be on the same line to the kite as Anna. and then we would have to subtract his distance from her distance.

but again, we assume he is exactly on the other side of the kite.

anyway, each person creates a right-angled triangle with the kite:

there is the direct line of sight as the base line or Hypotenuse (c).

there is the line on the ground from the person to the point on the ground directly under the kite as one side.

there is the line representing the height of the kite above ground as the other side. we let this start at the height of the eyes of the watching person.

and we assume that both persons are of the same height (so the height of the kite relative to their eyes is the same for both).

let's start with Anna.

the side a of Anna's triangle is

a = 20m

angle between a and c = 44 degrees

we know the angle between a and b is 90 degrees.

therefore the angle between b and c = 180-90-44 = 46 degrees.

now we use the law of sines :

a/sin(bc) = b/sin(ac) = c/sin(ab)

we know sin(ab) = sin(90) = 1

20/sin(46) = b/sin(44)

b = 20×sin(44)/sin(46) = 19.31... m = height of the kite

now to Bryan.

now we know his b (height of the kite) = 19.32... m

his angle between a and c is 66 degrees.

his angle between a and b is also 90 degrees.

therefore his angle between b and c = 180-90-66 = 24 degrees.

19.31/sin(66) = a/sin(24)

a = 19.31×sin(24)/sin(66) = 8.6 m

based on our assumption that they are standing opposite from each other in relation to the kite their distance is

20 + 8.6 = 28.6m

3 0

3 years ago

There is a bag filled with 4 blue, 3 red and 5 green marbles.

Vsevolod [243]

<h2>The chances of receiving two greens are 5/31.</h2>

<em>Given a bag containing four blue, three red, and five green marbles, the total result is:</em>

<em>Total number of balls = 4 + 3 + 5 = 12</em>

<em>If green is chosen first, the chances of picking a green are 5/12.</em>

<em>The probability that the second stone is green is 4/11 if it is picked and not replaced (4 greens remaining)</em>

<em>The chance of earning two greens is 5/12 4/11.</em>

<em>The chance of getting two greens is 20/132.</em>

<em>The chance of earning two greens is 5/31.</em>

<h3><em>As a result, the chance of getting two greens is 5/31.</em></h3>

7 0

2 years ago

Find m∠LKE. m∠LKJ = 150° m∠LKE = (x + 32)° m∠EKJ = (x + 94)° A) 40° B) 44° C) 46° Eliminate D) 48°

Luden [163]

Answer:

B) 44°

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

A Statistics professor has observed that for several years students score an average of 106 points out of 150 on the semester ex

tekilochka [14]

Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 106

For the alternative hypothesis,

µ > 106

It is a right tailed test because of >.

Since no population standard deviation is given, the distribution is a student's t.

Since n = 241,

Degrees of freedom, df = n - 1 = 241 - 1 = 240

t = (x - µ)/(s/√n)

Where

x = sample mean = 109

µ = population mean = 106

s = samples standard deviation = 8.3

a) test statistic, t = (109 - 106)/(8.3/√241) = 5.61

We would determine the p value using the t test calculator. It becomes

p = 0.00001

Since alpha, 0.05 > than the p value, 0.00001, then we would reject the null hypothesis. Therefore, At a 5% level of significance, this improvement seem to be practicallysignificant.

b) Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean.

Margin of error = z × s/√n

Where

s = sample standard deviation

n = number of samples

From the information given, the population standard deviation is unknown, hence, we would use the t distribution to find the z score

df = 240

Since confidence level = 95% = 0.95, α = 1 - CL = 1 – 0.95 = 0.05

α/2 = 0.05/2 = 0.025

the area to the right of z0.025 is 0.025 and the area to the left of z0.025 is 1 - 0.025 = 0.975

Looking at the t distribution table,

z = 1.6512

Margin of error = 1.6512 × 8.3/√241

= 0.88

Confidence interval = 109 ± 0.88

7 0

2 years ago

I don't understand word problems can someone please answer it for me and I need it ASAP.

maksim [4K]

Answer:

Inequality: 3 + 1.2c

What you'd put on graph: 1 ≥ 13.50

5 0

3 years ago