Nathan is collecting aluminum cans for charity. One empty 355 ml can weighs about 17 g. It takes 59 cans to get about 1 kg of 100% recyclable aluminum.



Over one month, he collected 1978 cans.


What is the mass, in kilograms, of these cans?

Answer:

[tex]\displaystyle y = 2sin\:1\frac{1}{3}\pi{x} + 3[/tex]

Step-by-step explanation:

[tex]\displaystyle \boxed{y = 2cos\:(1\frac{1}{3}\pi{x} - \frac{\pi}{2}) + 3} \\ \\ y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 3 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\frac{3}{8}} \hookrightarrow \frac{\frac{\pi}{2}}{1\frac{1}{3}\pi} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{1\frac{1}{2}} \hookrightarrow \frac{2}{1\frac{1}{3}\pi}\pi \\ Amplitude \hookrightarrow 2[/tex]

OR

[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 3 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{1\frac{1}{2}} \hookrightarrow \frac{2}{1\frac{1}{3}\pi}\pi \\ Amplitude \hookrightarrow 2[/tex]

You will need the above information to help you interpret the graph. First off, keep in mind that although the exercise told you to write the sine equation based on the speculations it gave you, if you plan on writing your equation as a function of cosine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 2cos\:1\frac{1}{3}\pi{x} + 3,[/tex]in which you need to replase "sine" with "cosine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the sine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the cosine graph [photograph on the right] is shifted [tex]\displaystyle \frac{3}{8}\:unit[/tex]to the left, which means that in order to match the sine graph [photograph on the left], we need to shift the graph FORWARD [tex]\displaystyle \frac{3}{8}\:unit,[/tex]which means the C-term will be positive, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{\frac{3}{8}} = \frac{\frac{\pi}{2}}{1\frac{1}{3}\pi}.[/tex]So, the cosine graph of the sine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 2cos\:(1\frac{1}{3}\pi{x} - \frac{\pi}{2}) + 3.[/tex]Now, with all that being said, in this case, sinse you ONLY have the exercise to wourk with, take a look at the above information next to [tex]\displaystyle Wavelength\:[Period].[/tex]It displays the formula on how to define each wavelength of the graph. You just need to remember that the B-term has [tex]\displaystyle \pi[/tex]in it as well, meaning both of them strike each other out, leaving you with just a fraction. Now, the amplitude is obvious to figure out because it is the A-term, so this is self-explanatory. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 3,[/tex]in which each crest is extended three units beyond the midline, hence, your amplitude. So, no matter what the vertical shift is, that will ALWAYS be the equation of the midline, and if viewed from a graph, no matter how far it shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

Answer:

-7

Step-by-step explanation:

3 v + 2 x

3 ( - 1) + 2 ( -2)

-3 - 4

-7

Answer:

61º

Step-by-step explanation:

sin= opp/hyp

sin∅ = 35/40

∅ = arcsin35/40

use calculator

∅ = 61.044975628140152

∅ ≈ 61º

Answer:

g(x) = 2x + 1

Step-by-step explanation:

f(x)= 3x - 5 when it is translated 6 units up

Translating a function a units is adding a to the function. So

[tex]3x - 5 + 6 = 3x + 1[/tex]

Horizontal stretch by a factor of 3/2.

This means that [tex]g(x) = f(\frac{2x}{3})[/tex], that is. So

[tex]g(x) = 3(\frac{2x}{3}) + 1 = 2x + 1[/tex]

Then

g(x) = 2x + 1

Answer: Hello your question is incomplete below is the missing part of the question

The Bureau of the Census reports that the median family income for all families in the United States during the year 2003 was $43,318. That is, half of all American families had incomes  exceeding this amount, and half had incomes equal to or below this amount. Suppose that four  families are surveyed and that each one reveals whether its income exceeded $43,318 in 2003.

answer :

P(A) = 11 / 16

P(B)  = 3/8

and P(C) = 1/4

Step-by-step explanation:

Making use of the given interpretation for the median we can assign probabilities to simple events as

P(A) = | A | / | sample space |

where | A | = 11

sample space = 16

P(A) = 11 / 16

∴ P(B) = 6/16 = 3/8

and P(C) = 4/16 = 1/4

Answer:

[tex](\frac{13}{5};\frac{6}{5}).[/tex]

Step-by-step explanation:

[tex]1)\left \{ {{5x=13} \atop {y=2x-4}} \right. \ 2)\left \{ {{x=\frac{13}{5} } \atop {y=\frac{6}{5} }} \right.[/tex]

short explanation: 1) to add the 1st equation to the 2d; 2) to calculate the value of 'x', then to substitute x=13/5 into the 2d equation and calculate the value of 'y'.

Answer:

$78.12

Step-by-step explanation:

10÷62×100%

=16.12

Therefore price of gold necklace ($62) + 10% tax ($16.12) will be equal to total cost which is $78.12

Answer:

[tex]a) x = k \times \frac{1}{y^2} \ , \ where \ k \ is \ a \ constant\\\\b) x = 3, \ when\ y\ =\ 10\\\\c) y = 10, \ when \ x = 3[/tex]

Step-by-step explanation:

a)

[tex]x \ \alpha \ \frac{1}{y^2}\\\\x = k \times \frac{1}{y^2}\\\\[/tex]                [tex][ \ where \ k \ is \ a \ constant \ ][/tex]

Find k.

Given x = 12, y = 5,

[tex]12 = k \times \frac{1}{5^2}\\\\k = 12 \times 25 = 300[/tex]

b)

Find x.

Given y = 10

We have k = 300

[tex]x = k \times \frac{1}{y^2}\\x = 300 \times \frac{1}{10^2} \\\\x= \frac{300}{100} = 3[/tex]

c)

Find y

Given x = 3

We have k = 300

[tex]x = k \times \frac{1}{y^2}\\\\3 = 300 \times \frac{1}{y^2}\\\\\frac{1}{y^2} = \frac{3}{300}\\\\\frac{1}{y^2} = \frac{1}{100}\\\\y^2 = 100\\\\y = \sqrt{100} = 10[/tex]

Answer:

The minimum sample size needed 64 monthly U.S. rental car mileages.

Step-by-step explanation:

Note: This question is not complete as all the important data are omitted. The complete question is therefore provided before answering the question as follows:

A consumer advocacy group is doing a large study on car rental practices. Among other things, the consumer group would like to estimate the mean monthly mileage, u, of cars rented in the U.S. over the past year. The consumer group plans to choose a random sample of monthly U.S. rental car mileages and then estimate u using the mean of the sample. Using the value 850 miles per month as the standard deviation of monthly U.S. rental car mileages from the past year, what is the minimum sample size needed in order for the consumer group to be 95% confident that its estimate is within 175 miles per month of u?

The explanation of the answer is now given as follows:

The minimum sample size needed can be calculated using the following sample size formula:

n = ((Z * S) / E)^2 ………………………… (1)

Where:

n = sample size or minimum sample size = ?

Z = Confidence interval at 95% = 1.645

S = Standard deviation = 850

E = Accepted magnitude of error = 175

Substituting all the relevant values into equation (1), we have:

n = ((1.645 * 850) / 175)^2 = (1,398.25 / 175)^2 = 7.99^2 = 63.8401, or 64.

Therefore, the minimum sample size needed 64 monthly U.S. rental car mileages.

Answer:

2

Step-by-step explanation:

it has 2 in the equation

Answer:

64 pounds of the $8.10 Mexican Shade Grown

36 pounds of the $14.10 Tanzanian

Step-by-step explanation:

8.1x + 14.1(100 - x) = 10.26(100)

Distribute

8.1x + 1410 - 14.1x = 1026

Combine like terms

1410 - 6x = 1026

Subtract 1410 from both sides

-6x = -384

Divide both sides by -6

x = 64 pounds of the $8.10

100 - x = 36 pounds of the $14.10

Answer:

9 is the answer

Answer:

2n=18

Step-by-step explanation:

Double means multiply by 2. A number can be represented by n.

So the equation is

2n=18

BONUS:

2n=18

/2    /2

n=9

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hope it helps

Answer:

pls complete your question. what exactly are we supposed to calculate?

Answer:

a) = 7/10

b)= 9/10

c)= 1  1/10

Step-by-step explanation:

a) green and a 2 = 1/2 + 1/5 = 0.7 = 7/10

b) red and an even number = 1/2 + 2/5 = 0.9 = 9/10

c) green and a prime number = 1/2 + 3/5 = 1.1 = 1  1/10

An angle of depression is measured from the horizon downwards and an angle of elevation is measured from the horizon upwards.

When solving for the sides or angles of a right triangle you can use trigonometry. The sine of an angle is found by the ratio of the opposite side and the hypotenuse. The cosine of an angle is found by the ratio of the adjacent side and the hypotenuse. The tangent of an angle is found by the ratio of the opposite side and the adjacent side.

The opposite side is always the leg opposite the angle that you are using. The adjacent side is the leg that forms one of the sides of the angle you are talking about and the hypotenuse is always across from the right angle.

If you know two lengths you can find the third leg length by using the Pythagorean Theorem.

Answer:

lower limit : 36.44

upper limit : 39.56

Step-by-step explanation:

Given :

s = 9

n = 90

x = 38.9

Alpha, α = 0.10

∴ [tex]$z_{\alpha/2}=z_{0.05} = 1.645$[/tex]

The confidence interval is :

[tex]$=x \pm\left(z_{\alpha /2} \times \frac{s}{\sqrt{n}}\right)$[/tex]

[tex]$=38.9 \pm\left(1.645 \times \frac{9}{\sqrt{90}}\right)$[/tex]

[tex]$=38.9 \pm 1.56$[/tex]

[tex]$=(36.44, 39.56)$[/tex]

Therefore,

lower limit : 36.44

upper limit : 39.56

Undefined

Order of matrix Q is 4 by 3

whereas order of R is 4by 4

In order to add two matrices , they should be of same order.

Answer:

DOES NOT EXIST.

Step-by-step explanation:

The sum of two matrices exists only if the matrices are of the same order.

Here Q is 3x3 and R is 4x4, so they do not have the same order, hence the sum DOES NOT EXIST.

Answer:

2396

Step-by-step explanation:

Let the diameter = d

Let the height = h

Formula

Metric Tons = k * d^4 / h^2

Solution

Metric Tons = 64

d = 2

h = 9

k = ?

(You can't do the second part by not using a ratio unless you  put k in and solve for it)

64 = 2^4 k / 9^2

64 = 8 *k / 81

64 * 81 / 8 = k

5184 / 8 = k

k = 648

Solve for the second example

Metric Tons = d^4 * k / h^2

Metric Tons = ?

d = 5

h = 13

k = 648

Metric Tons = 5^4 * 648 / 13^2

Metric Tons = 625 * 648 / 169

Metric Tons = 2396 rounded.

Step-by-step explanation:

p^2+b^2=h^2

or, 16+9=h^2

or, 25=h^2

or h=5

again, p^2 +b^2=h^2

or, 25+b^2=36

or, b^2=11

or. b=√11 therefore b=x=√11

Answer:

obtuse

Step-by-step explanation:

A circle is 360 degrees

Divide by 3

360/3 =120

This is greater than 90 and less than 180 so it is obtuse

Given:

A company wants to select 1 project from a set of 4 possible projects.

Consider the options are:

a. [tex]X_1+X_2+X_3+X_4=1[/tex]

b. [tex]X_1+X_2+X_3+X_4\leq 1[/tex]

c. [tex]X_1+X_2+X_3+X_4\geq 1[/tex]

d. [tex]X_1+X_2+X_3+X_4\geq 0[/tex]

To find:

The constraints that ensures only 1 will be selected.

Solution:

It is given that the company wants to select 1 project from a set of 4 possible projects. It means the sum of selected projects must be equal to 1.

[tex]X_1+X_2+X_3+X_4=1[/tex]

Therefore, the correct option is (a).

Answer:

this is the correct answer

please mark brainliest

A translação é o movimento que a Terra realiza em torno do Sol, sendo que ela demora 365 dias, 5 horas e 48 minutos para completá-lo. Esse movimento é o responsável direto pela existência das estações do ano. Como o eixo de inclinação do nosso planeta é de 23º27', há períodos em que os dias são maiores que as noites (solstícios de verão), períodos em que as noites são maiores que os dias (solstícios de inverno) e períodos em que eles possuem a mesma duração (equinócios de primavera e outono).

Answer:

Hope this helps. If it doesn't then I apologize.

Answer:

[tex]H_0[/tex] : [tex]\mu \leq 445.99[/tex]

[tex]H_a[/tex] : [tex]\mu > 445.99[/tex]

Step-by-step explanation:

It is given the average cost of the flight nationwide is $ 445.99

I wanted to [tex]\text{perform the hypothesis test}[/tex] to determine that the true average is greater than $ 445.99

Let the hypothesis that the true average is actually greater than $445.99

Therefore,

the [tex]\text{null hypothesis}[/tex] for the test is :

[tex]H_0[/tex] : [tex]\mu \leq 445.99[/tex]

And the alternate hypothesis is :

[tex]H_a[/tex] : [tex]\mu > 445.99[/tex]

Answer:

-2 and 3

Step-by-step explanation:

From the graph, the solution is the points where the curve cuts the x axis. From the graph, you can see that the equation cuts the x axis at two points that is at x=-2 and 3.

Hence the solutions to the equation is -2 and 3

Answer:

A 91.

Step-by-step explanation:

[tex]\frac{75+87+90+88+79+x}{6}=85\\\\\frac{419+x}{6}=85\\\\(\frac{419+x}{6})6=85*6\\\\419 + x = 510\\\\419-419+x=510-419\\\\\boxed{x = 91}[/tex]

Answer:

336 ft³ or 336 cubic feet

Step-by-step explanation:

Volume = Area triangle * height

Area triangle = 1/2(8 x 14)

Area triangle = 1/2(112) = 56 ft²

56 ft² * 6 ft = 336 ft³

If my answer is incorrect, pls correct me!

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-Chetan K

Answer:

I think it is 65 because we can divide it by 5

Answer:

i think there is only one multiple which is 65