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3 years ago

Anyone? please help asap i really want to finish this

Mathematics

1 answer:

bekas [8.4K]3 years ago

4 0

Answer:

Question 6a: $p \leq 16$

Question 6b: option d

Step-by-step explanation:

Question 6a: $6p \leq 96\\6p/6 \leq 96/6\\p \leq 16$

Question 6b:

- closed dot since its equal to 16

- p is less than 16 (arrow pointing left)

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8 0

3 years ago

Read 2 more answers

PLEASE HELP WILL GIVE BRAINLY FAST!!:)

Rus_ich [418]

Answer:

I attached a picture for the answer.

Step-by-step explanation:

Hope this helps!! Please make me Brainliest!

8 0

3 years ago

In October of 2012, Apple introduced a much smaller variant of the Apple iPad, known at the iPad Mini. Weighing less than 11 oun

sveticcg [70]

Answer:

a. $f_X(x) = \dfrac{1}{3.5}8.5$

b. the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286 which is about 42.86%

c. the probability that the battery life for an iPad Mini will be at least 11 hours is 0.2857 which is about 28.57 %

d. the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours is 0.5714 which is about 57.14%

e. 86 should have a battery life of at least 9 hours

Step-by-step explanation:

From the given information;

Let X represent the continuous random variable with uniform distribution U (A, B) . Therefore the probability density function can now be determined as :

$f_X(x) = \dfrac{1}{B-A}A$

where A and B are the two parameters of the uniform distribution

From the question;

Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours

So; Let A = 8,5 and B = 12

Therefore; the mathematical expression for the probability density function of battery life is :

$f_X(x) = \dfrac{1}{12-8.5}8.5$

$f_X(x) = \dfrac{1}{3.5}8.5$

b. What is the probability that the battery life for an iPad Mini will be 10 hours or less (to 4 decimals)?

The probability that the battery life for an iPad Mini will be 10 hours or less can be calculated as:

F(x) = P(X ≤x)

$F(x) = \dfrac{x-A}{B-A}$

$F(10) = \dfrac{10-8.5}{12-8.5}$

F(10) = 0.4286

the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286 which is about 42.86%

c. What is the probability that the battery life for an iPad Mini will be at least 11 hours (to 4 decimals)?

The battery life for an iPad Mini will be at least 11 hours is calculated as follows:

$P(X\geq11) = \int\limits^{12}_{11} {\dfrac{1}{3.5}} \, dx$

$P(X\geq11) = {\dfrac{1}{3.5}} (x)^{12}_{11}$

$P(X\geq11) = {\dfrac{1}{3.5}} (12-11)$

$P(X\geq11) = {\dfrac{1}{3.5}} (1)$

$P(X\geq11) = 0.2857$

the probability that the battery life for an iPad Mini will be at least 11 hours is 0.2857 which is about 28.57 %

d. What is the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours (to 4 decimals)?

$P(9.5 \leq X\leq11.5) =\int\limits^{11.5}_{9.5} {\dfrac{1}{3.5}} \, dx$

$P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} \, (x)^{11.5}_{9.5}$

$P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} (11.5-9.5)$

$P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} (2)$

$P(9.5 \leq X\leq11.5) =0.2857* (2)$

$P(9.5 \leq X\leq11.5) =0.5714$

Hence; the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours is 0.5714 which is about 57.14%

e. In a shipment of 100 iPad Minis, how many should have a battery life of at least 9 hours (to nearest whole value)?

The probability that battery life of at least 9 hours is calculated as:

$P(X \geq 9) = \int\limits^{12}_{9} {\dfrac{1}{3.5}} \, dx$

$P(X \geq 9) = {\dfrac{1}{3.5}}(x)^{12}_{9}$

$P(X \geq 9) = {\dfrac{1}{3.5}}(12-9)$

$P(X \geq 9) = {\dfrac{1}{3.5}}(3)$

$P(X \geq 9) = 0.2857*}(3)$

$P(X \geq 9) = 0.8571$

NOW; The Number of iPad that should have a battery life of at least 9 hours is calculated as:

n = 100(0.8571)

n = 85.71

n ≅ 86

Thus , 86 should have a battery life of at least 9 hours

3 0

4 years ago

First, rewrite 9/10 and 11/12 so that they have a common denominator

Licemer1 [7]

Step-by-step explanation:

Find common denominators:

$\frac{9}{10} \times \frac{12}{12} = \frac{108}{120}$

$\frac{11}{12} \times \frac{10}{10} = \frac{110}{120}$

Now compare:

$\frac{108}{120} < \frac{110}{120}$

$so \: \frac{9}{10} < \frac{11}{12}$

6 0

3 years ago

A random sample of 1000 people was taken. Four hundred fifty of the people in the sample favored Candidate AT. The 95% confidenc

azamat

Answer:

$0.45 - 1.96 \sqrt{\frac{0.45(1-0.45)}{1000}}=0.419$

$0.45 + 1.96 \sqrt{\frac{0.45(1-0.45)}{1000}}=0.481$

And the 95% confidence interval would be given (0.419;0.481). And the best option would be:

b. .419 to .481

Step-by-step explanation:

We know the following info:

$n = 1000$ sample size selected

$X= 450$ represent the number of people who favored Candidate AT

The sample proportion would be:

$\hat p=\frac{450}{1000}=0.45$

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

And replacing into the confidence interval formula we got:

$0.45 - 1.96 \sqrt{\frac{0.45(1-0.45)}{1000}}=0.419$

$0.45 + 1.96 \sqrt{\frac{0.45(1-0.45)}{1000}}=0.481$

And the 95% confidence interval would be given (0.419;0.481). And the best option would be:

b. .419 to .481

4 0

3 years ago