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2 years ago

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Peter has one of each of the following coins in his pocket: a penny, a nickel, a dime, a quarter, and a half-dollar. Four of the

se coins are taken out of the pocket and the sum of their values is calculated. How many different sums are possible?

1 answer:

DochEvi [55]2 years ago

3 0

Answer:

10

Step-by-step explanation:

This is a combinations problem, involving factorials.

5!/3!*2!=5*4/2=20/2=10

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. Given f(x) = e 2x e 2x + 3e x + 2 : (a) Make the substitution u = e x to convert Z f(x) dx into an integral in u (HINT: The ea

MrRa [10]

Answer:

Step-by-step explanation:

Given;

$f(x)=\frac{e^{2x}}{e^{2x}+3e^x+2}$

a)

substitute $u=e^x\\du=e^x dx\\\\\int\frac{e^{2x}}{e^{2x}+3e^x+2}dx=\int\frac{e^x\dot e^x}{e^x^{2x}+3e^x+2}dx\\\\=\int\frac{udu}{u^2+3u+2}$

b)

Apply partial fraction in (a), we get;

$\frac{u}{u^2+3u+2}=\frac{2}{u+2}-\frac{1}{u+1}\\\\\therefore u^2+3u+2\\=u^2+2u+u+2\\=u(u+2)+1(u+1)\\=(u+2)(u+1)\\\\Now\,\int\frac{u}{u^2+3u+2}\,du=\int\frac{2}{u+2}du-\int\frac{1}{u+1}du\\\\=2ln|u+2|-ln|u+1|+c\\=2ln|e^x+2|-lm|e^x+1|+c$

where C is an arbitrary constant

8 0

2 years ago

Three boards are placed end to end to make a walkway. The first board is 4 feet 5 inches long, the second board is 6 feet 9 inch

Kazeer [188]

Answer:

15 feet and 1 inch long

Step-by-step explanation:

add up the feet: 4+6+3= 13 feet

add up the inches: 5+9+11 = 25 inches

25/12= 2 feet 1 inch

13 feet + 2 feet + 1 inch= 15 feet 1 inch

7 0

2 years ago

The graph shows the side view of a waterslide. Dimensions are in feet. Two points on slide: (0, ), ( , 40)

nika2105 [10]

Answer:

Whats the question

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

12. If a manufacturer conducted a survey among randomly selected target market households and wanted to be 95% confident that th

atroni [7]

Answer:

$n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11$

And rounded up we have that n=1068

Step-by-step explanation:

We have the following info given:

$Confidence= 0.95$ the confidence level desired

$ME =0.03$ represent the margin of error desired

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

The confidence level is 95% or 0.95, the significance is $\alpha=0.05$ and the critical value for this case using the normal standard distribution would be $z_{\alpha/2}=1.96$

Since we don't have prior information we can use $\hat p= 0.5$ as an unbiased estimator

Also we know that $ME =\pm 0.03$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11$

And rounded up we have that n=1068

6 0

2 years ago

Terrence is folding paper cranes at a constant rate. Write an equation to describe the relationship between c, the number of cra

Vanyuwa [196]

Answer:

It is c = kt.

Step-by-step explanation:

This is direct variation . As the time increases the number of cranes increases.

The equation is c = kt where k is the constant of variation. In this case it will be a positive value because c is increasing with time.

If they make 20 cranes in 10 minutes then we can find the value of k by plugging in these values;

20 = k * 10

g = 20/10

k = 2.

So they make 2 cranes per minute.

7 0

2 years ago