On the package for a certain brand of spinach seeds there is a guarantee that, if the printed instructions are followed, of planted seeds will germinate. A random sample of seeds is chosen. If these seeds are planted according to the instructions, find the probability that of them germinate.

Answers

Answer 1

Answer:

The question is incomplete. Here is the complete question.

On the package for a certain brand of spinach seeds there is a guarantee that, if the printed instructions are followed, 63% of planted seeds will germinate. A random sample of 9 seeds is chosen. If these seeds are planted according to the instructions, find the probability that 4 or 5 of them germinate. Do not round your intermiediate computations, and round your answer to three decimal places.

Answer: P(4<X<5) = 0.624

Step-by-step explanation: The probability of a seed germinate is a BinomialDistribution, i.e., a discrete probability distribution of the number of successes in a sequence of n independents experiments.

This distribution can be approximated to normal distribution by determining the values of mean and standard deviation population:

$\mu=np$

$\sigma=√(np(1-p))$

where

n is the sample quantity

p is proportion of successes

For the spinach seeds:

Mean is

$\mu=9(0.65)$

$\mu=$ 5.85

Standard deviation is

$\sigma=√(9.0.65(1-0.65))$

$\sigma=$ 1.431

Now, use

$z=(x-\mu)/(\sigma)$

to convert into a standard normal distribution.

The probability we want is between 2 values: P(4<X<5).

Therefore, we have to convert those two values:

For X = 4:

$z=(4-5.85)/(1.431)$

z = -1.29

For X = 5:

$z=(5-5.85)/(1.431)$

z = -0.59

Using z-table:

P(X>4) = 1 - P(z< -1.29) = 0.9015

P(X<5) = P(z< -0.59) = 0.2776

The probability will be

P(4<X<5) = P(X>4) - P(X<5)

P(4<X<5) = 0.9015 - 0.2776

P(4<X<5) = 0.624

The probability of 4 or 5 seeds germinate is0.624.

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The State Police are trying to crack down on speeding on a particular portion of the Massachusetts Turnpike. To aid in this pursuit, they have purchased a new radar gun that promises greater consistency and reliability. Specifically, the gun advertises ± one-mile-per-hour accuracy 75% of the time; that is, there is a 0.75 probability that the gun will detect a speeder, if the driver is actually speeding. Assume there is a 1% chance that the gun erroneously detects a speeder even when the driver is below the speed limit. Suppose that 72% of the drivers drive below the speed limit on this stretch of the Massachusetts Turnpike. a. What is the probability that the gun detects speeding and the driver was speeding? b. What is the probability that the gun detects speeding and the driver was not speeding? c. Suppose the police stop a driver because the gun detects speeding. What is the probability that the driver was actually driving below the speed limit?
Write an equation of a line that passes through (-3,1), perpendicular to Y=-3x-3

Y<-2/3 x-1 graphing the inequality

Answers

Answer:

y < − 2/3x − 1

Step-by-step explanation:

Which expression is equivalent to 3/56x^7y^5 , if x ≠0 and y≠0

Answers

Answer:

$2x^2y\sqrt[3]{7xy^2}$

Step-by-step explanation:

Given

$\sqrt[3]{56x^7y^5}$

Required

Solve

Expand

$\sqrt[3]{8*7*x^6*x*y^3*y^2}$

Rewrite as:

$\sqrt[3]{8*x^6*y^3*7*x*y^2}$

Split

$\sqrt[3]{8*x^6*y^3} *\sqrt[3]{7*x*y^2}$

Express 8 as 2^3

$\sqrt[3]{2^3*x^6*y^3} *\sqrt[3]{7*x*y^2}$

Apply law of indices

$2^((3/3))*x^((6/3))*y^((3/3)) *\sqrt[3]{7*x*y^2}$

$2*x^2*y *\sqrt[3]{7*x*y^2}$

$2x^2y *\sqrt[3]{7xy^2}$

$2x^2y\sqrt[3]{7xy^2}$

9+9+3=21
1234+1234+1234= 30
9+1224+12=?

Answers

Answer:

Mathematically,

9+1224+12 = 1245

But, Logically, here:

9+1224+12 = 21

Answer:

9+1224+12=1245

Hope this helps

A rock falls off a balcony. It's height (in feet) is given by the formula f(x)=-16t^2+13.4t+120, where t is measured in seconds. How long will it take the rock to hit the ground? Round your answers to the nearest three decimal places.

Answers

Answer:

3.189 seconds

Step-by-step explanation:

You want f(t) = 0, so ...

0 = -16t^2 +13.4t +120

0 = t^2 -0.8375t -7.5 . . . . divide by -16

0 = (t^2 -0.8375t +0.41875^2) -7.5 -0.41875^2 . . . . complete the square*

0 = (t -0.41875)^2 -7.6753515625 . . . . write as a square

√7.6753515625 = t -0.41875 . . . . . . . . add 7.67... and take positive root

t = 0.41875 +√7.6753515625 ≈ 3.189192 . . . . add 0.41875

It will take the rock about 3.189 seconds to hit the ground.

_____

* We complete the square by adding the square of half the coefficient of the linear term (= (-0.8375/2)^2) inside parentheses and subtracting the same amount outside parentheses. This gives a form inside parentheses that is ...

(t^2 -2at +a^2) = (t -a)^2

Completing the square is complicated a little bit by a leading coefficient that is not 1. That is why we divided by -16 first.

_____

Comment on the question

We note that the rock "falls" from the 120 foot high balcony by first traveling upward at a rate of 13.4 feet per second. We also note that the height function is written f(x), but uses t as the variable. That is, it should be f(t) = ...

In the expression 4X +2, what do we call the 2