The number of peanuts in a 16-ounce can of nut munchies is normally distributed with a mean of 96.3 and a standard deviation of 2.4 peanuts. the number of peanuts in a 20-ounce can of gone nuts is normally distributed with a mean of 112.6 and a standard deviation of 2.8 peanuts.
(a) carmen purchased a 16-ounce can of nut munchies and counted 100 peanuts.
what is the z-score for this can of peanuts?
(b) angelo purchased a 20-ounce can of gone nuts and counted 116 peanuts.
what is the z-score for this can of peanuts?
(c) carmen declares that purchasing her can of nut munchies with 100 peanuts is less likely than angelo purchasing a can of gone nuts with 116 peanuts. is carmen’s statement correct? use the definition of a z-score to support or refute carmen’s claim.

To calculate for the z-score we use the formula:

z=(x-μ)/σ

thus the answers to questions will be as follows:

Step-by-step explanation:

a]Carmen purchased a 16-ounce can of Nut Munchies and counted 100 peanuts. What is the z-score for this can of peanuts?

x=100

μ=96.3

σ=2.4

z=(100-96.3)/2.4

z=1.542

b]Angelo purchased a 20-ounce can of Gone Nuts and counted 116 peanuts. What is the z-score for this can of peanuts?

x=116

μ=112.6

σ=2.8

thus

z=(116-112.6)/2.8

z=1.214

c]Carmen declares that purchasing her can of Nut Munchies with 100 peanuts is less likely than Angelo purchasing a can of Gone Nuts with 116 peanuts. Is Carmen’s statement correct? Use the definition of a z-score to support or refute Carmen’s claim.

This is very correct because because by definition of z-score, Munchies with 100 peanuts is 1.542 away from the mean as compared to Munchies with 116 peanuts which is 1.214 standard deviations from the mean hence the higher likelihood. 

hello from mrbilldoesmath!

answer:   x^2 + y^2 = 1024

discussion:

the equation of a circle with center (h,k) and radius "r" is

(x-h)^2 + (y-k)^2 = r^2.

in our case

(x-0)^2 + (y-0) ^2 = 32^2 = 1024

you,

mrb

the speed is   miles per hour > is false

step-by-step explanation:

we know that  

a relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form or

in a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

the graph shown in the figure represent a direct variation

the slope of the line represent the speed

for the point

substitute the values of x and y

the linear equation is equal to

statements

case a) it takes hours to go miles

the statement is true

because

substitute

for

find the value of y in the linear equation

> is correct

case b) the speed is   miles per hour

the statement is false

because the speed is

case c) the unit rate for the trip is

the statement is true

because the speed is equal to the slope of the linear equation

case d) it took minutes to go the first miles

the statement is true

because

substitute

for

find the value of y in the linear equation

> is correct