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Alexandra [31]
2 years ago
11

If the letters in the word poker are rearranged, what is the probability that the word will begin with the letter k and end with

the letter p?
Mathematics
1 answer:
GarryVolchara [31]2 years ago
3 0
The probability is 6/120 or 1/20, which can be expressed as a percentage of 5%.

You can find this by first deciding how many possibilities there are. With a number of items being arranged in a set, the easiest way to solve this is by using the factorial function on your calculator (the button that looks like "!"). It denotes That number by all of the integers lower than it down to 1 multiplied together. 

So since there are 5 letters in poker, we would use 5! or written out:
1*2*3*4*5 = 120. 

Then we would have to find all of the options that start with k and end with p, of which there are exactly 6. 

koerp
korep
kreop
kroep
kerop
keorp

So then we divide the number of possibles by the total number of options. 


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Bill and Pete shared 1/2 of a cake. Bill got to eat twice as much cake as Pete. What fraction of the whole cake did Bill eat?
KatRina [158]

Answer:

Step-by-step explanation:

Total cake shared=1/2

Pete share=x

Bill= twice as much as Pete

=2x

Pete's share+ Bill's share=total share

x+2x=1/2

3x=1/2

x=1/2÷3

x=1/2×1/3

=1/6

Pete's share=x=1/6

Bill's share=2x

=2(1/6)

=2/6

=1/3

3 0
2 years ago
Diagonal cross-section of a sphere produces which two dimensional shape
Leni [432]
Every cross-section of a sphere will  be a circle. 

Answer: circle

Any further questions about this? Or how I got my answer?

7 0
2 years ago
A newsletter publisher believes that 55% of their readers own a Rolls Royce. Is there sufficient evidence at the 0.05 level to r
melomori [17]

Set up hypotheses:

The null hypotheses is that the proportion of readers who own a Rolls Royce is equal to 0.55

Null hypotheses = H₀: p = 0.55

The alternate hypotheses is that the proportion of readers who own a Rolls Royce is not equal to 0.55

Alternate hypotheses = H₁: p ≠ 0.55

Determine the  type of test:

Since the alternate hypothesis states that the proportion of readers who own a Rolls Royce is different, therefore it is a two-tailed test.

Determine the level of significance and Critical Z-score:

Given level of significance = 0.05

Since it is a two-tailed test,

Z-score = 1.960 (two tailed)

Set up decision rule:

Since it is a two-tailed test, using a Z statistic at a significance level of 5%

We Reject H₀ if Z < -1.960 or Z > 1.960

We Reject H₀ if p ≤ α

Compute the test statistic:

The test statistic may be calculated using,

$ Z =  \frac{\hat{p} - p}{ \sqrt{\frac{p(1-p)}{n} }}  $

We are not given enough information to find out the test statistic.

Conclusion:

We do not have enough information to accept or refuse the publisher's claim.

4 0
2 years ago
Devon and his friends bought strawberry wafers for $3 per packet and chocolate wafers for $1 per packet at a carnival. They spen
Irina-Kira [14]
Hi there!

PART A:
The system of equations we would use would be:
x + y = 22 (amount of items)
3x + 1y = 30 (cost)

Variables:
x = the amount of strawberry wafers bought at the price of $3
y = the amount of chocolate wafers bought at the price of $1

PART B:
To solve, we'll use substitution because we can easily isolate a variable using the first equation.

Work:
x + y = 22 (first equation)
y = 22 - x (isolating a variable)
3x + 1y = 30 (second equation)
3x + (22 - x) = 30 (substituting into the second equation)
2x + 22 = 30 (simplifying)
2x = 8 (subtracting)
x = 4 strawberry wafers
4 + y = 22 (substituting x into the first equation to solve for y)
y = 18 chocolate wafers

ANSWER:
They bought 4 strawberry wafers and 18 chocolate wafers.

Hope this helps!! :)
If there's anything else that I can help you with, please let me know!
8 0
2 years ago
A new car is purchased for 15300 dollars. The value of the car depreciates at 14.25% per year. What will the value of the car be
Andrei [34K]

Answer:

\$6,082.70  

Step-by-step explanation:

we know that

The  formula to calculate the depreciated value  is equal to  

V=P(1-r)^{x}  

where  

V is the depreciated value  

P is the original value  

r is the rate of depreciation  in decimal  

x  is Number of Time Periods  

in this problem we have  

P=\$15,300\\r=14.25\%=0.1425\\x=6\ years

substitute in the formula

V=15,300(1-0.1425)^{6}  

V=15,300(0.8575)^{6}  

V=\$6,082.70  

3 0
3 years ago
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