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dsp73
4 years ago
10

A standard deck of 52 cards contains four suits: clubs, spades, hearts, and diamonds. Each deck contains an equal number of card

s in each suit. Rochelle chooses a card from the deck, records the suit, and replaces the card. Her results are shown in the table.
How does the experimental probability of choosing a heart compare with the theoretical probability of choosing a heart?

A.The theoretical probability of choosing a heart is 1/16 greater than the experimental probability of choosing a heart.

B.The experimental probability of choosing a heart is 1/16 greater than the theoretical probability of choosing a heart.

C.The theoretical probability of choosing a heart is 1/26 greater than the experimental probability of choosing a heart.

D.The experimental probability of choosing a heart is 1/26 greater than the theoretical probability of choosing a heart.

Mathematics
2 answers:
Simora [160]4 years ago
7 0

52 cards  / 4 suits  = 13 cards of each suit.

Theoretically picking a heart would be 13/52 = 1/4 probability.

Experimentally she picked 15 hearts out of 80 total tries. for a 15/80 = 3/16 probability, which is less than the theoretical probability.

1/4 - 3/16 = 1/16

The answer is A.

sergey [27]4 years ago
6 0

Answer:

The right answer is A -<em> The theoretical probability of choosing a heart is StartFraction 1 over 16 EndFraction greater than the experimental probability of choosing a heart.</em>

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Sasha works at the farmers market. She packs fifteen pounds of apples equally into 6 bags. How many pounds of apples are in each
Irina-Kira [14]

Answer:

2\frac{1}{2} pounds

The number lies 2\frac{1}{2} between 2 and 3.

Step-by-step explanation:

She packs 15 pounds of apples equally into 6 bags.

The amount of apples in each bag is gotten by dividing the total amount of apples by the number of bags.

Therefore:

N = 15 / 6 = 5/2 = 2\frac{1}{2} pounds

There are 2\frac{1}{2} pounds of apples in each bag.

The number lies 2\frac{1}{2} between 2 and 3.

7 0
4 years ago
Let C be the curve of intersection of the parabolic cylinder x^2 = 2y, and the surface 3z = xy. Find the exact length of C from
Maslowich
I've attached a plot of the intersection (highlighted in red) between the parabolic cylinder (orange) and the hyperbolic paraboloid (blue).

The arc length can be computed with a line integral, but first we'll need a parameterization for C. This is easy enough to do. First fix any one variable. For convenience, choose x.

Now, x^2=2y\implies y=\dfrac{x^2}2, and 3z=xy\implies z=\dfrac{x^3}6. The intersection is thus parameterized by the vector-valued function

\mathbf r(x)=\left\langle x,\dfrac{x^2}2,\dfrac{x^3}6\right\rangle

where 0\le x\le 4. The arc length is computed with the integral

\displaystyle\int_C\mathrm dS=\int_0^4\|\mathbf r'(x)\|\,\mathrm dx=\int_0^4\sqrt{x^2+\dfrac{x^4}4+\dfrac{x^6}{36}}\,\mathrm dx

Some rewriting:

\sqrt{x^2+\dfrac{x^4}4+\dfrac{x^6}{36}}=\sqrt{\dfrac{x^2}{36}}\sqrt{x^4+9x^2+36}=\dfrac x6\sqrt{x^4+9x^2+36}

Complete the square to get

x^4+9x^2+36=\left(x^2+\dfrac92\right)^2+\dfrac{63}4

So in the integral, you can substitute y=x^2+\dfrac92 to get

\displaystyle\frac16\int_0^4x\sqrt{\left(x^2+\frac92\right)^2+\frac{63}4}\,\mathrm dx=\frac1{12}\int_{9/2}^{41/2}\sqrt{y^2+\frac{63}4}\,\mathrm dy

Next substitute y=\dfrac{\sqrt{63}}2\tan z, so that the integral becomes

\displaystyle\frac1{12}\int_{9/2}^{41/2}\sqrt{y^2+\frac{63}4}\,\mathrm dy=\frac{21}{16}\int_{\arctan(3/\sqrt7)}^{\arctan(41/(3\sqrt7))}\sec^3z\,\mathrm dz

This is a fairly standard integral (it even has its own Wiki page, if you're not familiar with the derivation):

\displaystyle\int\sec^3z\,\mathrm dz=\frac12\sec z\tan z+\frac12\ln|\sec x+\tan x|+C

So the arc length is

\displaystyle\frac{21}{32}\left(\sec z\tan z+\ln|\sec x+\tan x|\right)\bigg|_{z=\arctan(3/\sqrt7)}^{z=\arctan(41/(3\sqrt7))}=\frac{21}{32}\ln\left(\frac{41+4\sqrt{109}}{21}\right)+\frac{41\sqrt{109}}{24}-\frac98

4 0
4 years ago
Please help me with 1,2,3 and show me how you get it the answers and how you get it do not send me link please I need help someo
elena-s [515]

Answer:

1) 20 cm

2) 22.4 in

3) 15 ft

Step-by-step explanation:

For this question, you have to use the <u>Pythagorean theorem.</u>

Why?

Well, because it is a <u><em>right triangle</em></u> and you have <u><em>2 sides given</em></u> and you want to find the third side.

Now let's solve this problem!

<u>For number 1 we have:</u>

a = 16 cm and B = 12 cm

you need to find the 3rd side which is c (aka the hypothenuse)

so let's write the equation:

a^2 + b^2 = c^2

Then we substitute with what we have given.

16^2 + 12^2 = c^2

Using a calculator solve the equation

400 = c^2

Now we have to find the square root from both sides of the equation.

c = 20 cm (That's the final answer)

<u>For number 2 we have:</u>

a = 10 in and b = 20 in

we follow the same steps as in number 1

a^2 + b^2 = c^2

10^2 + 20^2 = c^2

500 = c^2

c = 22.4 in (That's the final answer)

<u>For number 3 we have:</u>

a = 9 ft and b = 12 ft

a^2 + b^2 = c^2

9^2 + 12^2 = c^2

225 = c^2

c = 15 ft (That's the final answer)

<u></u>

8 0
3 years ago
What is the correct written expression for the variable expression: (3 - x)/7
Nonamiya [84]
<h2>The answer is:</h2>

<h3>The difference if 3 divided by 7 and x</h3>

<h2>Hope it was helpful to you </h2>
3 0
3 years ago
You’re working at a theater where you are evaluating attendance at several events. From the first event to the second event, att
viktelen [127]
The percent decrease is 8 percent

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