A company selling cell phones has a total inventory of 900 phones. Of these phones, 450 are smartphones and 270 are black. If 225 phones are not black and not a smartphone, how many of the phones are black smartphones

Answers:

[tex]\displaystyle \lim_{x\to -3^{+}} h(x) = 1\\\\\displaystyle \lim_{x\to -3^{-}} h(x) = 1\\\\\displaystyle \lim_{x\to -3} h(x) = 1\\\\\displaystyle \lim_{x\to 0^{+}} h(x) = 0\\\\\displaystyle \lim_{x\to 0^{-}} h(x) = 3\\\\\displaystyle \lim_{x\to 2^{-}} h(x) = \infty\\\\\displaystyle \lim_{x\to 2^{+}} h(x) = \infty\\\\[/tex]

The limit exists at -3

The limit does not exist at 0

The limit exists at 2, assuming your teacher allows positive infinity to be an answer (otherwise, the limit doesn't exist).

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Explanation:

If we start on the left side of x = -3, and approach toward x = -3 itself, then we will approach y = 1. Imagine it's like a car on a roller coaster able to move along the curve. If the car is to the left of x = -3, then it goes uphill slowly approaching that limiting value.

If we start on the right side of x = -3, and approach -3 itself, then we approach the same y value as before

So that's how I'm getting

[tex]\displaystyle \lim_{x\to -3^{+}} h(x) = 1\\\\\displaystyle \lim_{x\to -3^{-}} h(x) = 1\\\\\displaystyle \lim_{x\to -3} h(x) = 1\\\\[/tex]

The third limit is basically the combination of the first two limits. If the LHL (left hand limit) and the RHL (right hand limit) are equal, then the limit exists.

--------------------------------------

We see that the LHL and RHL at x = 0 aren't the same. So the limit does not exist at x = 0

The LHL for x = 0 is 3 while the RHL for x = 0 is 0.

That explains why

[tex]\displaystyle \lim_{x\to 0^{+}} h(x) = 0\\\\\displaystyle \lim_{x\to 0^{-}} h(x) = 3\\\\\\\displaystyle \lim_{x\to 0} h(x) = \text{DNE}\\\\\\[/tex]

DNE means does not exist

-------------------------------------

Lastly, when we approach x = 2 from the left, we head upward toward positive infinity.

So [tex]\displaystyle \lim_{x\to 2^{-}} h(x) = \infty\\\\[/tex]

Also, [tex]\displaystyle \lim_{x\to 2^{+}} h(x) = \infty\\\\[/tex] because we're heading upward forever when approaching x = 2 from the right side.

We can then say [tex]\displaystyle \lim_{x\to 2} h(x) = \infty\\\\[/tex]

Answer:

a) The 99% confidence interval for the proportion of all students who had use of a computer at home and give it in interval notation is (0.709, 0.911).

b) 0.81

c) 0.039.

d) 0.101

Step-by-step explanation:

Question a:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

In a randomly selected sample of 100 students at a University, 81 of them had access to a computer at home.

This means that [tex]n = 100, \pi = \frac{81}{100} = 0.81[/tex]

99% confidence level

So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.81 - 2.575\sqrt{\frac{0.81*0.19}{100}} = 0.709[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.81 + 2.575\sqrt{\frac{0.81*0.19}{100}} = 0.911[/tex]

The 99% confidence interval for the proportion of all students who had use of a computer at home and give it in interval notation is (0.709, 0.911).

b) Give the value of the point estimate described in this scenario.

Sample proportion of [tex]\pi = 0.81[/tex]

c) Give the value of the standard error for the point estimate.

This is:

[tex]s = \sqrt{\frac{\pi(1-\pi)}{n}} = \sqrt{\frac{0.81*0.19}{100}} = 0.039[/tex]

The standard error is of 0.039.

d) Give the value of the margin of error if you were to calculate a 99% confidence interval.

This is:

[tex]M = zs = 2.575*0.039 = 0.101[/tex]

Answer: [tex]\dfrac{x^2+1}{2}[/tex]

Step-by-step explanation:

Given

[tex]f(x)=\sqrt{2x-1}[/tex]

We can write it as

[tex]\Rightarrow y=\sqrt{2x-1}[/tex]

Express x in terms of y

[tex]\Rightarrow y^2=2x-1\\\\\Rightarrow x=\dfrac{y^2+1}{2}[/tex]

Replace y be x to get the inverse

[tex]\Rightarrow f^{-1}(x)=\dfrac{x^2+1}{2}[/tex]

To prove, it is inverse of f(x). [tex]f(f^{-1}(x))=x[/tex]

[tex]\Rightarrow f(f^{-1}(x))=\sqrt{2\times \dfrac{x^2+1}{2}-1}\\\\\Rightarrow f(f^{-1}(x))=\sqrt{x^2+1-1}\\\\\Rightarrow f(f^{-1}(x))=x[/tex]

So, they are inverse of each other.

Answer:

they would have bike 544 miles together with each other.

Step-by-step explanation:

since Elsa went more than Linda Linda had to stop while Elsa kept going.

Answer:

- 8

Step-by-step explanation:

56 ÷ (- 7)

56 ÷ - 7

- 8

Answer:

-8

Step-by-step explanation:

A positive number divided by a negative one results in a negative quotient.

Thus, 56 ÷ (–7) = -8

Answer:

282.12 ft

Step-by-step explanation:

Please find attached a graphical illustration of the question

We are given the value of the opposite side and we are to determine the value of the adjacent side. Thus, tan would be used

Tan 65 = opposite / adjacent

2.1445 = 605 / x

x = 605 / 2.1445

x = 282.12 ft

Answer: 34767.2

Step-by-step explanation:

given p = $16,000, n = 14 years, y = 5.7%

amount in bank after 14 years = p ( 1 + </100)

= 16,000 (1 + 5.7/ 100) 14

= 34767.2

Answer:

Step-by-step explanation:

Required formula:

Substitute values and solve:

Answer:

42

Step-by-step explanation:

20/100*210

20/100=1/5 or 0.2

1/5 or 0.2*210= 42

Answer:

Yes there is alternative way in solving and arithmetic sequence .An arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence.

Answer:

-15

Step-by-step explanation:

So it's a-1-2x.

rewrite as -4-1-(2*5)

-4-1-10

-4+-1-10

-5+-10

-15

Answer:

- 15

Step-by-step explanation:

a - 1 - 2 x

- 4 - 1 - 2 ( 5 )

- 5 - 10

- 1 5

9514 1404 393

Answer:

  x = (10√3)/3 ≈ 5.7735 m

Step-by-step explanation:

The 30°-60°-90° right triangle is one of the "special" right triangles, so you know its side ratios are ...

  BC : AB : AC = 1 : √3 : 2

Then ...

  x = BC = AB/√3 = (10 m)/√3 = (10√3)/3 m ≈ 5.7735 m

Answer:

36

Step-by-step explanation:

Simple:

(4)(3)+2((5)(3)−2)−2

=12+2((5)(3)−2)−2

=12+2(15−2)−2

=12+(2)(13)−2

=12+26−2

=38−2

=36

Answer:a

Step-by-step explanation:

Answer:

182

2.0239

3.97

(178, 186)

Step-by-step explanation:

Given :

Sample mean, n = 250

Sample mean, xbar = 182

Sample standard deviation, s = 32

Point estimate for the mean ;

According to the central limit theorem ; for n > 30, the sample mean equal to the population mean.

Hence, point estimate of mean cholesterol level for men is 182

B.) The standard error = s/√n

s= 32 ; n = 250

Standard error = 32/√250 = 2.0239

C.) Margin of error :

TCritical * standard error

TCritical at 95% ; df =250 -1 = 249 = 1.96

1.969 * 2.0239 = 3.966 = 3.97

D.) The confidence interval :

Point estimate ± margin of error

182 ± 3.97

182 - 3.97 = 178.03

182 + 3.97 = 185.97

(178, 186)

The required value of function g is (-4x - 5)/(x+2) and graph is shown below.

The parent function of a function is the simplest form of the function, which satisfies all the conditions of the given function.

Given that,

Parent function f(x) = 3/x,

And function g(x) = f(x + 2) - 4.

To find the graph of function g(x), first determine the value of function g(x),

Substitute x = x+2 in function f(x), to determine g(x),

g(x)  = 3/(x+2) -4

       = 3-4(x+2)/x+2

       = 3 - 4x - 8/(x + 2)

       = (-4x - 5)/(x+2)

The required function g(x) is (-4x - 5)/(x+2) .

The graph of function g(x) is shown below.

To learn more about Parent function on:

https://brainly.com/question/17939507

#SPJ2

Step-by-step explanation:

5

Sigma (10(n-1) + 3)

n=1

Answer:

4x^2-9x+7+\frac{x-2}{x^2+x+1}

Step-by-step explanation:

Here is a hopefully helpful answer! :)

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Answer:

70

Step-by-step explanation:

X is equal to 70 degrees because angle x and the angle that is 70 degrees are alternate interior angles.

These are alternate interior angles. If two angles are alternate interior angles they are congruent. That means x is also 70 degrees.

Answer:

0.9452 = 94.52% probability that their mean length is less than 16.8 inches.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 15.4 inches, and standard deviation of 3.5 inches.

This means that [tex]\mu = 15.4, \sigma = 3.5[/tex]

16 items are chosen at random

This means that [tex]n = 16, s = \frac{3.5}{\sqrt{16}} = 0.875[/tex]

What is the probability that their mean length is less than 16.8 inches?

This is the p-value of Z when X = 16.8. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{16.8 - 15.4}{0.875}[/tex]

[tex]Z = 1.6[/tex]

[tex]Z = 1.6[/tex] has a p-value of 0.9452.

0.9452 = 94.52% probability that their mean length is less than 16.8 inches.

9514 1404 393

Answer:

  B.  F(-9/2, 0), x = 9/2

Step-by-step explanation:

One definition of a parabola is that it is all of the points that are equidistant from the focus and the directrix. Among other things, this means the parabola "wraps around" the focus, and opens away from the directrix.

The focus is on the axis of symmetry, so shares a coordinate with the vertex. Since the vertex is a point on the parabola, it is equidistant from the focus and directrix—halfway between them.

The given equation has x get more negative as y increases, so the parabola opens to the left. This means the focus will be a point on the -x axis. Only one answer choice meets that requirement:

  focus: (-9/2, 0), directrix: x = 9/2

__

The equation of a parabola with its vertex at the origin can be written as ...

  x = 1/(4p)y^2

In this case, we have 4p = -18, so p = -9/2. This is the distance from the vertex to the focus. The negative sign means the focus is to the left of the vertex, and its x-coordinate is -9/2 (as noted above).

Answer:

209

Step-by-step explanation: guyci you y tf7itfit 6tuit6yci7v uvtfi7ftyvg hkvyucoyvyvhj gku citctvo utictgvuk h jh hj vvuk

c A hotel spent $504 on new hair dryers. The hair dryers cost $8 each. The hotel has 6 floors with the same number of rooms on each floor. If every room gets a new hair dryer, how many hair dryers will be left over?

vvvv A hotel spent $504 on new hair dryers. The hair dryers cost $8 each. The hotel has 6 floors with the same number of rooms on each floor. If every room gets a new hair dryer, how many hair dryers will be left over?

vv A hotel spent $504 on new hair dryers. The hair dryers cost $8 each. The hotel has 6 floors with the same number of rooms on each floor. If every room gets a new hair dryer, how many hair dryers will be left over?

A hotel spent $504 on new hair dryers. The hair dryers cost $8 each. The hotel has 6 floors with the same number of rooms on each floor. If every room gets a new hair dryer, how many hair dryers will be left over?

A hotel spent $504 on new hair dryers. The hair dryers cost $8 each. The hotel has 6 floors with the same number of rooms on each floor. If every room gets a new hair dryer, how many hair dryers will be left over?

v A hotel spent $504 on new hair dryers. The hair dryers cost $8 each. The hotel has 6 floors with the same number of rooms on each floor. If every room gets a new hair dryer, how many hair dryers will be left over?

A hotel spent $504 on new hair dryers. The hair dryers cost $8 each. The hotel has 6 floors with the same number of rooms on each floor. If every room gets a new hair dryer, how many hair dryers will be left over?

Answer:

28.5

Step-by-step explanation:

X*2/3=19, X=19/(2/3)=57/2=28.5

Answer:

The number is 28.5

Step-by-step explanation:

Let the number be x

Two - third of the number is 19 means

                                                            [tex]\frac{2}{3} \ of \ x = 19[/tex]

Solve for x

[tex]\frac{2}{3} \times x = 19\\\\2 \times x = 19 \times 3\\\\x = \frac{19 \times 3}{2} = 28.5[/tex]

Answer:

4xy² + 3x -5 polynomial example

example of a polynomial

this one has 3 terms

Dividing

polynomial division

Polynomials can sometimes be divided using the simple methods shown on Dividing Polynomials.

But sometimes it is better to use "Long Division" (a method similar to Long Division for Numbers)

Numerator and Denominator

We can give each polynomial a name:

x² + 2x -7 (numerator)

_________

x-2 (denominator)

[tex] \times - {}^{2} \sqrt{ \times {}^{2} } + 2 \times - 7[/tex]

Both polynomials should have the "higher order" terms first (those with the largest exponents, like the "2" in x2).

then :

divide: the first term of the numerator

by the first term of denominator and put that answer

multiply the denominator by that answer, put that below the numerator

subtract to create a new polynomial

repeat using the polynomial

Answer:

Hence the correct option is Option b that is the same for each interval.

Step-by-step explanation:

The PDF for Uniform distribution in [a,b] is given by  

[tex]f(x)=\frac{1}{b-a}~~~~~~a\leq x\leq b[/tex]  

So the probability that the random variable assumes a value in​ [a,b] is given by  

[tex]\int_{a}^{b}f(x)dx=\int_{a}^{b}\frac{1}{b-a}dx=1[/tex]

Therefore the correct option is b. the same for each interval.

Answer:

[tex]\bar x = 1.4896[/tex]

[tex]Median = 1.525[/tex]

7 is an outlier

Step-by-step explanation:

Given

See comment for dataset

Solving (a): The mean

The mean is calculated as:

[tex]\bar x = \frac{\sum x}{n}[/tex]

So, we have:

[tex]\bar x = \frac{2.53 +1.33 +0.64 +2.55 +0.67 +0.57 +............+2.03 +1.78}{50}[/tex]

[tex]\bar x = \frac{74.48}{50}[/tex]

[tex]\bar x = 1.4896[/tex]

Solving (b): The median

First, we sort the data:

[tex]0.01, 0.01, 0.08, 0.14, 0.24, 0.35, 0.57, 0.64, 0.65, 0.67,[/tex]

[tex]0.69, 0.74, 0.81, 0.82, 0.92, 0.99, 1.01, 1.04, 1.15, 1.16, 1.33,[/tex]

[tex]1.41, 1.45, 1.48, 1.52, 1.53, 1.58, 1.61, 1.62, 1.73, 1.77, 1.78, 1.84,[/tex]

[tex]1.98, 2.01, 2.02, 2.03, 2.06, 2.06, 2.31, 2.41, 2.53, 2.55, 2.59,[/tex]

[tex]2.66, 2.74, 2.74, 2.77, 2.77, 2.91[/tex]

The median position is:

[tex]Median = \frac{n + 1}{2}[/tex]

[tex]Median = \frac{50 + 1}{2}[/tex]

[tex]Median = \frac{51}{2}[/tex]

[tex]Median = 25.5th[/tex]

This means that the median is the average of the 25th and the 26th item.

So:

[tex]Median = \frac{1.52+1.53}{2}[/tex]

[tex]Median = \frac{3.05}{2}[/tex]

[tex]Median = 1.525[/tex]

Solving (c): Is 7 an outlier

Yes; 7 is an outlier.

Because the range of the dataset (0.01 to 2.92) is far from 7.

Answer:

A = 2.1 ft^2

Step-by-step explanation:

The area of a triangle is

A = 1/2 bh where b is the base and h is the height

A = 1/2 ( 2.8)(1.5)

A = 2.1 ft^2

Answer:2.1

Step-by-step explanation:

The formula of finding the area of a triangle is A=. 1/2*b*h

A=1/2*2.8*1.2

A=1/2* 4.2

A=2.1