Ms. Foxmoore drives 130 miles in 2 hours. If she travels the same distance each hour, how many miles does she drive per hour?

The probability that a randomly selected box of a certain type of cereal has a particular prize is 0.20.

MatroZZZ [7]

Answer:

a) the probability is 0.0734 (7.34%)

b) the probability is 0.7382 (73.82%)

c) 10 boxes

Step-by-step explanation:

Since each box is independent of the others and defining the random variable X= number of boxes of cereal purchased without prices until having 2 prices , then X has a negative binomial distribution . Thus

P(X=k)= C(k+r-1,k)*p^k *(1-p)^r

where

p= probability to not obtain a price when a box is purchased = 1- 0.2 = 0.8

C ( ) = combinations

k = number of boxes without prices

r= number of boxes with prices=2

P(X=k) = probability of purchasing k boxes without prices until obtaining r boxes with prices

a) for k= 8 - r = 6

P(X=6)= C(7,6)*0.8^6*0.2^2 = 7*0.8^6*0.2^2 = 0.0734 (7.34%)

b) for k≥9-2=7

P(X≥7) = 1- P(X<7)= 1- Fn(X=7)

where Fn(X) is the cumulative negative binomial distribution. We can calculate it through its relationship with the cumulative binomial distribution Fb(X) that is easily found in tables :

Fn(k=7,r=2,p=0.8) = Fb(k=7,n=k+r=9,p=0.8) = 0.2618

thus

P(X≥7) = 1- P(X<7)= 1- Fn(X=7) = 1- 0.2618 = 0.7382 (73.82%)

c) the expected value E(X) for a negative binomial distribution is

E(X)= p*r/(1-p) = 0.8*2/0.2 = 8 boxes that do not contain prices

thus

n=k+r = 8 + 2 = 10 boxes

6 0

4 years ago

Find the standard deviation for the group of data items 4, 4, 4, 4, 6, 8 The standard deviation is (Simplify your answer. Round

marysya [2.9K]

Answer: 1.53

Step-by-step explanation:

The given data : 4, 4, 4, 4, 6, 8

Number of data values : n= 6

The mean value of the given data will be :-

$\overline{x}=\dfrac{\sum_{i=1}^{6}x_i}{n}\\\\\Rightarrow\ \overline{x}=\dfrac{30}{6}=5$

The formula to find standard deviation:_

$\sqrt{\dfrac{\sum(x-\overline{x})^2}{n}]$

Now,

$\sum_{i=1}^{6}(x_i-\overline{x})^2=(-1)^2+(-1)^2+(-1)^2+(-1)^2+(1)^2+(3)^2\\\\=1+1+1+1+1+9=14$

The standard deviation will be :-

$\sigma=\sqrt{\dfrac{14}{6}}\approx1.53$

5 0

4 years ago

Which number-line model represents the sum of 3/4 + ( - 1.75) ?

Fed [463]

Answer:

A

Step-by-step explanation:

6 0

3 years ago

Help.........................<br><br>

garri49 [273]

<h3>Answer: Choice A</h3>

$x^2\left(\sqrt[4]{x^2}\right)$

=====================================================

Explanation:

The fourth root of x is the same as x^(1/4)

I.e,

$\sqrt[4]{x} = x^{1/4}$

The same applies to x^10 as well

$\sqrt[4]{x^{10}} = \left(x^{10}\right)^{1/4}$

Multiply the exponents 10 and 1/4 to get 10/4

$\sqrt[4]{x^{10}} = \left(x^{10}\right)^{1/4} = x^{10*1/4} = x^{10/4}$

$\sqrt[4]{x^{10}} = x^{10/4}$

-----------------------

If we have an expression in the form x^(m/n), with m > n, then we can simplify it into an equivalent form as shown below

$x^{m/n} = x^a\sqrt[n]{x^b}$

The 'a' and 'b' are found through dividing m/n

m/n = a remainder b

'a' is the quotient, b is the remainder

-----------------------

The general formula can easily be confusing, so let's replace m and n with the proper numbers. In this case, m = 10 and n = 4

m/n = 10/4 = 2 remainder 2

We have a = 2 and b = 2

So

$x^{m/n} = x^a\sqrt[n]{x^b}$

turns into

$x^{10/4} = x^2\sqrt[4]{x^2}$

which means

$\sqrt[4]{x^{10}} = {x^2} \sqrt[4]{x^2}$

7 0

3 years ago

What is the value of x

nordsb [41]

Median is half of add the sum ofthe base and first side
17+5x-14=3+5x
divide it by 2
3+5x ÷2=median
(3+5x)/2=x+12
3+5x=2x+24
3x=21
x=7

Answer is D=7

8 0

4 years ago