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3 years ago

In a standard deck of playing cards, one-fourth of the cards are hearts.

Mathematics

1 answer:

makkiz [27]3 years ago

7 0

Answer:

$\sf D) \quad \dfrac{1}{64}$

Step-by-step explanation:

$\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}$

Probability of drawing a heart from one deck:

$\sf \implies P(heart)=\dfrac{1}{4}$

Therefore, probability of drawing a heart from each of 3 decks:

$\sf \implies P(heart)\:and\:P(heart)\:and\:P(heart)=\dfrac{1}{4} \times \dfrac{1}{4} \times \dfrac{1}{4}=\dfrac{1}{64}$

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Suppose you and a friend each choose at random an integer between 1 and 8, inclusive. For example, some possibilities are (3,7),

Bezzdna [24]

Answer and explanation:

Given : Suppose you and a friend each choose at random an integer between 1 and 8, inclusive.

The sample space is

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (1,7) (1,8)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (2,7) (2,8)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (3,7) (3,8)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (4,7) (4,8)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (5,7) (5,8)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6) (6,7) (6,8)

(7,1) (7,2) (7,3) (7,4) (7,5) (7,6) (7,7) (7,8)

(8,1) (8,2) (8,3) (8,4) (8,5) (8,6) (8,7) (8,8)

Total number of outcome = 64

To find : The following probabilities ?

Solution :

The probability is given by,

$\text{Probability}=\frac{\text{Favorable outcome }}{\text{Total outcome}}$

a) p(you pick 5 and your friend picks 8)

The favorable outcome is (5,8)= 1

$\text{Probability}=\frac{1}{64}$

b) p(sum of the two numbers picked is < 4)

The favorable outcome is (1,1), (1,2), (2,1)= 3

$\text{Probability}=\frac{3}{64}$

c) p(both numbers match)

The favorable outcome is (1,1), (2,2), (3,3), (4,4), (5,5), (6,6), (7,7), (8,8) = 8

$\text{Probability}=\frac{8}{64}$

$\text{Probability}=\frac{1}{8}$

7 0

4 years ago

In a study of the accuracy of fast food drive-through orders, one restaurant had orders that were not accurate among orders obs

Lesechka [4]

Complete Question

In a study of the accuracy of fast food drive-through orders, one restaurant had 32 orders that were not accurate among 367 orders observed. Use a 0.05 significance level to test the claim that the rate of inaccurate orders is equal to 10%. Does the accuracy rate appear to be acceptable?

Answer:

The decision rule is

Fail to reject the null hypothesis

The conclusion is

There is sufficient evidence to show that the rate of inaccurate orders is equal to 10%

Step-by-step explanation:

Generally from the question we are told that

The sample size is n = 367

The number of orders that were not accurate is $k = 32$

The population proportion for rate of inaccurate orders is p = 0.10

The null hypothesis is $H_o : p = 0.10$

The alternative hypothesis is $H_a : p \ne 0.10$

Generally the sample proportion is mathematically represented as

$\^ p = \frac{k}{n}$

=> $\^ p = \frac{32}{367}$

=> $\^ p = 0.0872$

Generally the test statistics is mathematically represented as

$z= \frac{ \^ p - p }{ \sqrt{ \frac{ p(1 - p)}{ n} } }$

=> $z= \frac{ 0.0872 - 0.10 }{ \sqrt{ \frac{ 0.10 (1 - 0.10 )}{367} } }$

=> $z= -0.8174$

From the z table the area under the normal curve to the left corresponding to -0.8174 is

$P(z < -0.8173 ) = 0.20688$

Generally the p-value is mathematically represented as

$p- value = 2 * 0.20688$

=> $p- value = 0.4138$

From the value obtained we see that $p-value > \alpha$ hence

The decision rule is

Fail to reject the null hypothesis

The conclusion is

There is sufficient evidence to show that the rate of inaccurate orders is equal to 10%

4 0

3 years ago

Factor the trinomial 2x^2+15x+7

Mashutka [201]

Answer:

(2x+1)(x+7)

Step-by-step explanation:

2x2+15x+7

For a polynomial of the form ax2+bx+c

, rewrite the middle term as a sum of two terms whose product is a⋅c=2⋅7=14 and whose sum is b=15

Tap for more steps...

2x2+x+14x+7

Factor out the greatest common factor from each group.

Tap for more steps...

x(2x+1)+7(2x+1)

Factor the polynomial by factoring out the greatest common factor, 2x+1

(2x+1)(x+7)

3 0

3 years ago

Tarik rides a stationary bike and Janet rides her bike on a trail. Their data is shown

KiRa [710]

Answer:

Part a. The graph does not model a proportional relationship.

Part b. The values in table model a proportional relation.

3.5 minutes per mile.

Step-by-step explanation:

Part a.

The graph shown in the question representing Janet's data is not a straight line although it passes through the origin.

That is why the rate of change of distance with time is not constant.

Therefore, the graph does not model a proportional relationship.

Part b.

If we plot the data in the table using distance in miles along the y-axis and time in minutes along the x-axis, then we will get a straight line passing through the origin.

So, the values in the table model a proportional relation.

Now, Tarik's unit rate in minutes per miles will be $\frac{7-0}{2-0} =3.5$ minutes per mile. (Answer)

6 0

3 years ago

Math<br> Can someone please explain what I need to do here to find answer?<br> Thanks

zmey [24]

Answer:

Step-by-step explanation:

First of all their is an easier way solving this 2l/ + l^2

but how you need it is c because the base is 100 and each face is 40 how 10x8=80 80/2=40

6 0

3 years ago