Solve for b to the nearest hundredth:

You need to know the band between 5.48 g and 5.82 g, the mean is 5.67 g and the standard deviation is .0.070 g, with that information you can calculate the percentage to the left of the mean and the percentage to the right of the mean and add them.

To know its percentage you have to calculate the z score for both values.

$z = \frac{x-\mu}{\sigma}$

x is the value being evaluated

μ is the mean

σ is the standard deviation

For 5.48 g:

$z = \frac{5.48-5.67}{0.070} =-2.714$

and is equivalent to 0.0034

For 5.82 g:

$z = \frac{5.82-5.67}{0.070} = 2.143$

and is equivalent to 0.9838

Those numbers mean that the percentage below 5.48 is equivalent to the 0.34% of the values and the percentage below 5.82 is equivalent to 98.38% of the values. Then the percentage rejected is the percentage above 5.82, 100 - 98.38 = 1.62% plus the percentage below 5.48, 0.34%.

Percentage rejected = 1.62% + 0.34% = 1.96%

7 0

3 years ago

Find the sum of all positive integers less than 200 that are divisible by 7.

Troyanec [42]

Step-by-step explanation:

the positive integer numbers that are divisible by 7 are an arithmetic sequence by always adding 7 :

a1 = 7

a2 = a1 + 7 = 7+7 = 14

a3 = a2 + 7 = a1 + 7 + 7 = 7 + 2×7 = 21

...

an = a1 + (n-1)×7 = 7 + (n-1)×7 = n×7

the sum of an arithmetic sequence is

n/2 × (2a1 + (n - 1)×d)

with a1 being the first term (in our case 7).

d being the common difference from term to term (in our case 7).

how many terms (what is n) do we need to add ?

we need to find n, where the sequence reaches 200.

200 = n×7

n = 200/7 = 28.57142857...

so, with n = 29 we would get a number higher than 200.

so, n=28 gives us the last number divisible by 7 that is smaller than 200 (28×7 = 196).

the sum of all positive integers below 200 that are divisible by 7 is then

28/2 × (2×7 + 27×7) = 14 × 29×7 = 2,842

6 0

2 years ago

sam is eating a hamburger. He at 20% of the hamburger with his first bite, 20% of what is left in his second bite, and so on, ea

ryzh [129]

The hamburger will weigh 250 g, if there was originally 160g of it remaining after the second bite given that 20% of the hamburger with his first bite, 20% of what is left in his second bite, and so on, eating 20% of what remains with each bite. This can be obtained by assuming the total weight as x and multiplying the percentages.

<h3>How much did the hamburger weigh?</h3>

Let the total weight of the hamburger be x.

First it is given that Sam ate 20% of the hamburger.

The first bite will be,

20% of the hamburger = 20% × x

20% of the hamburger = 20/100 × x

20% of the hamburger = 20x/100

⇒ first bite = 20x/100

Therefore the remaining hamburger will be,

remaining hamburger = x - 20x/100

remaining hamburger = (100x - 20x)/100

⇒ remaining hamburger after first bite = 80x/100

Next it is given that Sam ate 20% of the remaining hamburger.

The second bite will be,

20% of the remaining hamburger = 20% × 80x/100

20% of the remaining hamburger = 20/100 × 80x/100

20% of the remaining hamburger = 16x/100

⇒ second bite = 16x/100

Therefore the remaining hamburger will be,

remaining hamburger = 80x/100 - 16x/100

remaining hamburger after second bite = 64x/100

It is given that there was originally 160g of it remaining after the second bite.

Then, 64x/100 = 160

x = 160 × 100/64

x = 250 g

Hence the hamburger will weigh 250 g, if there was originally 160g of it remaining after the second bite given that 20% of the hamburger with his first bite, 20% of what is left in his second bite, and so on, eating 20% of what remains with each bite.

Learn more about percentages here:

brainly.com/question/25395

#SPJ4

5 0

1 year ago