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3 years ago

A bowl of Halloween candy has 17 Kit-Kats, 23 Hershey bars, 11 Starbursts, and 14 Skittles packets.

Mathematics

1 answer:

gladu [14]3 years ago

5 0

Answer:

a.) 8/13 = 0.6154.

b) 11/65 = 0.1692

c.) 0.0267

d.) 0.0222

Step-by-step explanation:

firstly, we determine total number of candies.

17 kit kat(K)+ 23 hershey(H) + 11 starburst(B) + 14 skittles(S) = 65 candies.

Since, Probability = favourable outcome / possible outcome.

With replacement,

a.) probability of chocolate candy (kitkat or hershey) = 17/65 or 23/65

= 17/65 + 23/65

=40/65 = 8/13

b.) probability of selecting a starburst = 11/65

When without replacement:,

c) 2 kit kats, 1 skittles as first three picks and one chocolate candy as the last pick, = [KKSK], [KSKK], [SKKK], [KKSH], [KSKH], [SKKH]

[(17/65 * 16/64 * 14/63 * 15/62) × 3] + [(17/65 * 16/64 * 14/63 * 23/62) ×3]

Note: first bracket and fourth brackets are multiplied by 3 because the value of the first bracket is same for the first three brackets and the second three brackets also have the same values.

Re:chocolate candy means either KitKat or Hershey.

=[(51720/16248960) × 3] + [(87584/16248960) ×3]

=0.0105 +0.0162

= 0.0267.

d.) 1 kitkat, 1 skittles and 1 hershey as first 3 picks and one Starburst as the last pick.

= [KSHB], [KHSB], [SKHB], [SHKB], [HKSB], [HSKB]

= [(17/65 * 14/64 * 23/63 * 11/62) × 6]

note: multiplied by 6 because we will have the same value for all 6 brackets

= 60214/16248960 * 6

= 0.0222.

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Write the name of the period that has the digits 486

kogti [31]

1. The name of period that has 486 in the given number which is 751 486 is hundreds.
period is considered to a group of places of the digits, like the given number 486 is the group of hundred because the highest number it contains is 400.
=> 400 + 80 + 6
=> 4 hundreds + 8 tens + 6 ones
=> 486
while 751 is the period of hundred thousands.
=> 700 000 + 50 000 + 1 000
=> 751 000

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3 years ago

EXAMPLE 5 If F(x, y, z) = 4y2i + (8xy + 4e4z)j + 16ye4zk, find a function f such that ∇f = F. SOLUTION If there is such a functi

Valentin [98]

If there is such a scalar function f, then

$\dfrac{\partial f}{\partial x}=4y^2$

$\dfrac{\partial f}{\partial y}=8xy+4e^{4z}$

$\dfrac{\partial f}{\partial z}=16ye^{4z}$

Integrate both sides of the first equation with respect to x :

$f(x,y,z)=4xy^2+g(y,z)$

Differentiate both sides with respect to y :

$\dfrac{\partial f}{\partial y}=8xy+4e^{4z}=8xy+\dfrac{\partial g}{\partial y}$

$\implies\dfrac{\partial g}{\partial y}=4e^{4z}$

Integrate both sides with respect to y :

$g(y,z)=4ye^{4z}+h(z)$

Plug this into the equation above with f , then differentiate both sides with respect to z :

$f(x,y,z)=4xy^2+4ye^{4z}+h(z)$

$\dfrac{\partial f}{\partial z}=16ye^{4z}=16ye^{4z}+\dfrac{\mathrm dh}{\mathrm dz}$

$\implies\dfrac{\mathrm dh}{\mathrm dz}=0$

Integrate both sides with respect to z :

$h(z)=C$

So we end up with

$\boxed{f(x,y,z)=4xy^2+4ye^{4z}+C}$

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3 years ago

When a number is decreased by 18, the result is 14. what is the number

Serggg [28]

X is the number

when x is decreased by 18, we say 18-x

the result is 14

18-x=14
minus 18 both sides
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times both sides by -1
x=32

6 0

4 years ago

Read 2 more answers

A company compiles data on a variety of issues in education. In 2004 the company reported that the national college freshman-to

nasty-shy [4]

Answer:

1) Randomization: We assume that we have a random sample of students

2) 10% condition, for this case we assume that the sample size is lower than 10% of the real population size

3) np = 500*0.66= 330 >10

n(1-p) = 500*(1-0.66) =170>10

So then we can use the normal approximation for the distribution of p, since the conditions are satisfied

The population proportion have the following distribution :

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

And we have :

$\mu_p = 0.66$

$\sigma_{p}= \sqrt{\frac{0.66(1-0.66)}{500}}= 0.0212$

Using the 68-95-99.7% rule we expect 68% of the values between 0.639 (63.9%) and 0.681 (68.1%), 95% of the values between 0.618(61.8%) and 0.702(70.2%) and 99.7% of the values between 0.596(59.6%) and 0.724(72.4%).

Step-by-step explanation:

For this case we know that we have a sample of n = 500 students and we have a percentage of expected return for their sophomore years given 66% and on fraction would be 0.66 and we are interested on the distribution for the population proportion p.

We want to know if we can apply the normal approximation, so we need to check 3 conditions:

1) Randomization: We assume that we have a random sample of students

2) 10% condition, for this case we assume that the sample size is lower than 10% of the real population size

3) np = 500*0.66= 330 >10

n(1-p) = 500*(1-0.66) =170>10

So then we can use the normal approximation for the distribution of p, since the conditions are satisfied

The population proportion have the following distribution :

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

And we have :

$\mu_p = 0.66$

$\sigma_{p}= \sqrt{\frac{0.66(1-0.66)}{500}}= 0.0212$

And we can use the empirical rule to describe the distribution of percentages.

The empirical rule, also known as three-sigma rule or 68-95-99.7 rule, "is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ)".

On this case in order to check if the random variable X follows a normal distribution we can use the empirical rule that states the following:

• The probability of obtain values within one deviation from the mean is 0.68

• The probability of obtain values within two deviation's from the mean is 0.95

• The probability of obtain values within three deviation's from the mean is 0.997

8 0

3 years ago

A family wants to rent a car to go on vacation. Company A charges $50.50 and 9c per mile.

hjlf

<h3>Answer: 0.05x+10</h3>

Work Shown:

x = number of miles

Cost of company A = 0.09x+50.50

Cost of company B = 0.14x+60.50

Subtract the two expressions (B-A) to find the difference in price

B-A = (0.14x+60.50)-(0.09x+50.50)

B-A = 0.14x+60.50-0.09x-50.50

B-A = (0.14x-0.09x) + (60.50-50.50)

B-A = 0.05x+10

8 0

2 years ago