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3 years ago

A the fraction one half kilogram of flour is packed equally into 8 bags. How much flour is in each bag

Mathematics

1 answer:

marissa [1.9K]3 years ago

6 0

Answer:

0.0625 kg per bag

or 1/16th of a kilogram per bag

Step-by-step explanation:

You'd need to divide the total amount the the number of sections.

In this case, it'd be 0.5 kg/8 bags, resulting in 0.0625 kg of flour per bag.

I hope this helps!

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In a process that manufactures bearings, 90% of the bearings meet a thickness specification. A shipment contains 500 bearings. A

vredina [299]

Answer:

c) P(270≤x≤280)=0.572

d) P(x=280)=0.091

Step-by-step explanation:

The population of bearings have a proportion p=0.90 of satisfactory thickness.

The shipments will be treated as random samples, of size n=500, taken out of the population of bearings.

As the sample size is big, we will model the amount of satisfactory bearings per shipment as a normally distributed variable (if the sample was small, a binomial distirbution would be more precise and appropiate).

The mean of this distribution will be:

$\mu_s=np=500*0.90=450$

The standard deviation will be:

$\sigma_s=\sqrt{np(1-p)}=\sqrt{500*0.90*0.10}=\sqrt{45}=6.7$

We can calculate the probability that a shipment is acceptable (at least 440 bearings meet the specification) calculating the z-score for X=440 and then the probability of this z-score:

$z=(x-\mu_s)/\sigma_s=(440-450)/6.7=-10/6.7=-1.49\\\\P(z>-1.49)=0.932$

Now, we have to create a new sampling distribution for the shipments. The size is n=300 and p=0.932.

The mean of this sampling distribution is:

$\mu=np=300*0.932=279.6$

The standard deviation will be:

$\sigma=\sqrt{np(1-p)}=\sqrt{300*0.932*0.068}=\sqrt{19}=4.36$

c) The probability that between 270 and 280 out of 300 shipments are acceptable can be calculated with the z-score and using the continuity factor, as this is modeled as a continuos variable:

$P(270\leq x\leq280)=P(269.5$

d) The probability that 280 out of 300 shipments are acceptable can be calculated using again the continuity factor correction:

$P(X=280)=P(279.5$

8 0

3 years ago

Plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz

statuscvo [17]

9514 1404 393

Answer:

(a) x = (3 -ln(3))/5 ≈ 0.819722457734

(b) y = 10

Step-by-step explanation:

(a) Taking the natural log of both sides, we have ...

2x +1 = ln(3) +4 -3x

5x = ln(3) +3 . . . . . . . . add 3x-1

x = (ln(3) +3)/5 ≈ 0.820

(b) Assuming "lg" means "log", the logarithm to base 10, we have ...

log(y -6) +log(y +15) = 2

(y -6)(y +15) = 100 . . . . . . . taking antilogs

y^2 -9x -190 = 0 . . . . . . . . eliminate parentheses, subtract 100

(y -19)(y +10) = 0 . . . . . . . . factor

The values of y that make these factors zero are -19 and 10. We know from the first term that (y-6) > 0, so y > 6. That means y = -19 is an extraneous solution.

The solution is ...

y = 10

When solving equations using a graphing calculator, it often works well to define a function f(x) such that the solution is f(x) = 0, the x-intercept(s). That form is easily obtained by subtracting the right side of the equation from both sides of the equation. In part (a) here, that is ...

f(x) = e^(2x+1) -3e^(4-3x)