Suppose the daily customer volume at a call center has a normal distribution with mean 5,500 and standard deviation 1,000. What is the probability that the call center will get between 4,800 and 5,000 calls in a day

Terminal point for 4π/3

(cos4π/3 ,sin4π/3)

{cos(π+π/3) ,sin(π+π/3)}= (-cosπ/3 ,-sinπ/3)

or ,(- 1/2, -√3/2)

OPTION C

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Answer:

  (d)  1/4

Step-by-step explanation:

The scale factor is the ratio of lengths of corresponding sides:

  XZ/AC = 3/12 = 1/4

_____

Additional comment

I find the wording of the question a bit ambiguous. To transform ΔABC to ΔXYZ, every linear dimension of ΔABC is multiplied by 1/4. This is the sense of "ΔABC to ΔXYZ" that is used in the above answer.

On the other hand, one of the ways ratios are written is using the word "to," as in "12 to 3". Using this idea, we might interpret the question to be asking for ...

  ΔABC to ΔXYZ = AC to XZ = 12 to 3 = 12/3 = 4

Answer:

We can construct a 90º angle either by bisecting a straight angle or using the following steps.

Step 1: Draw the arm PA.

Step 2: Place the point of the compass at P and draw an arc that cuts the arm at Q.

Step 3: Place the point of the compass at Q and draw an arc of radius PQ that cuts the arc drawn in Step 2 at R.

Step-by-step explanation:

Answer:

12.9 miles

Step-by-step explanation:

Formula: (x/360)×dπ(circumference)

90/360=1/4

1/4×16.4π

1/4×51.496

12.874

Answer:

[tex]m JM=90 =\Theta[/tex]

[tex]Radius=dimeter/2=16.4/2[/tex]

[tex]\longrightarrowr=8.2[/tex]

The length of arc JM=

[tex]=\frac{\Theta }{360} \times\pi r[/tex]

[tex]=\frac{90}{360} \times2\times\ 3.14\times 8.2[/tex]

[tex]=12.874[/tex]

[tex]\approx 12.9 \; miles[/tex]

[tex]OAmalOHopeO[/tex]

Work Shown:

1 pound = 16 ounces

4*(1 pound) = 4*(16 ounces)

4 pounds = 64 ounces

Answer:

25288

Step-by-step explanation:

shown in the picture

Answer:

Step-by-step explanation:

One solution, at the point of intersection, (3,3)

Answer:

mean=21.17

mode=20,22

median=3.5

range=15

Step-by-step explanation: MEAN=sum of all observations/ no. of observations

mean=22+20+14+22+29+20/6

mean=127/6

mean=21.17

MODE= most frequent observations

mode=22,20

MEDIAN=1/2(n/2+n+2/2)

=1/2(6/2+6+2/2)

=1/2(3+4)

=1/2(7)

=7/2

=3.5

RANGE=X max -X min

=29-14

=15

let dogs be heads. Let cats be tails. A coin has two sides, in which you are flipping two of them. Note that there can be the possible outcomes  

h-h, h-t, t-h, t-t.  

How this affects the possibility of two dogs & two cats. Note that there are 1/2 a chance of getting those two (with the others being one of each), which means that out of 4 chances, 2 are allowed.  

2/4 = 1/2  

50% is your answer

Heads represents cats and tails represents dogs. There is two coins because we are checking the probability of two pets. You have to do the experiment to get your set of data, once you get your set of data, you will be able to divide it into the probability for cats or dogs. To change the simulation to generate data for 3 pets, simply add a new coin and category for the new pet.

Hope this helps you out!

Answer:

is the second answer 2x+1/x-1

Answer:

1because the occasion of cases

Step-by-step explanation:

V= IR --> R = V/I = (220 V)/(3.6 A) = 61.1 ohms

Answer:

61.11 ohms

Step-by-step explanation:

R=V/I

R=220/3.6

R=61.11 ohms

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Answer:

  3x

Step-by-step explanation:

If x represents the number, then "3 times a number" is 3x.

__

Additional comment

"The quotient of the number and 4" is x/4.

The sum of those two expressions is ...

  3x + x/4

Answer:

0.0728177272

Step-by-step explanation:

Given :

Number of flips = 80

Probability of landing on tail at most 33 times ;

Probability of landing on tail on any given flip = 1 / 2 = 0.5

This a binomial probability problem:

Hence ;

P(x ≤ 33) = p(x=0) + p(x=1) +... + p(x = 33)

Using a binomial probability calculator :

P(x ≤ 33) = 0.0728177272

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Answer:

  a) domain bounds are -1 ≤ x ≤ 1, x > 1

Step-by-step explanation:

In considering the definition of any piecewise function, the domain descriptions in the function definition must match the pieces shown in the graph.

Here, the right segment has no upper bound, so x > 1 is an appropriate description of its domain.

The left segment has the points at x=-1 and x=1 included, so the appropriate domain description for that is -1 ≤ x ≤ 1.

The one answer choice that combines these domain descriptions is ...

  [tex]\displaystyle f(x)=\begin{cases}x^2,&\text{if }-\!1\le x\le1\\\sqrt{x},&\text{if }x>1\end{cases}[/tex]

Answer: the numbers are 10 and 5

Step-by-step explanation:

10 times 5 is 50

10 plus 5 is 15

Answer:

Step-by-step explanation:

Answer:

0.2405 = 24.05% probability that the sample proportion of households spending more than $125 a week is less than 0.31.

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.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Assume the population proportion is 0.34 and a simple random sample of 124 households is selected from the population.

This means that [tex]p = 0.34, n = 124[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.34[/tex]

[tex]s = \sqrt{\frac{0.34*0.66}{124}} = 0.0425[/tex]

What is the probability that the sample proportion of households spending more than $125 a week is less than 0.31?

This is the p-value of Z when X = 0.31, so:

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

[tex]Z = \frac{0.31 - 0.34}{0.0425}[/tex]

[tex]Z = -0.705[/tex]

[tex]Z = -0.705[/tex] has a p-value of 0.2405.

0.2405 = 24.05% probability that the sample proportion of households spending more than $125 a week is less than 0.31.

Answer:

Answer:

Option D

Step-by-step explanation:

Generally the equation for Margin of Error is mathematically given by

[tex]M.E=Z*sqrt{\frac{p*(1-p)}{n}}[/tex]

Condition for Largest M.E

n has to be smallest and Z value has to be largest.

Where

From options

Smallest [tex]n=300[/tex]

Largest Z value respects to [tex]\alpha=95\%[/tex]

Therefore

n= 300, confidence level 95%

Option D

Answer:

0.01375 = 1.375% probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2.

Step-by-step explanation:

We have the mean during the interval, which means that the Poisson distribution is used.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

Lost-time accidents occur in a company at a mean rate of 0.8 per day.

This means that [tex]\mu = 0.8n[/tex], in which n is the number of days.

10 days:

This means that [tex]n = 10, \mu = 0.8(10) = 8[/tex]

What is the probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2?

This is:

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

In which

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-8}*8^{0}}{(0)!} = 0.00034[/tex]

[tex]P(X = 1) = \frac{e^{-8}*8^{1}}{(1)!} = 0.00268[/tex]

[tex]P(X = 2) = \frac{e^{-8}*8^{2}}{(2)!} = 0.01073[/tex]

So

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.00034 + 0.00268 + 0.01073 = 0.01375[/tex]

0.01375 = 1.375% probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2.

the answer is d. my shlime

Answer:

12

Step-by-step explanation:

Answer:

B. 28, 32, 36 millions

Step-by-step explanation:

Given:

P(t) = 24 + 0.4t

Where,

P(t) = population in millions

t = number of years

✔️Value of the population when t = 10:

Plug in t = 10 into P(t) = 24 + 0.4t

P(t) = 24 + 0.4(10)

P(t) = 24 + 4

P(t) = 28 million

✔️Value of the population when t = 20:

Plug in t = 20 into P(t) = 24 + 0.4t

P(t) = 24 + 0.4(20)

P(t) = 24 + 8

P(t) = 32 million

✔️Value of the population when t = 30:

Plug in t = 30 into P(t) = 24 + 0.4t

P(t) = 24 + 0.4(30)

P(t) = 24 + 12

P(t) = 36 million

Answer:

0.2358 = 23.58% probability that at least 18 of the 75 sampled employees would like to move into management.

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

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

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

20% of employees would like to move into management and be the boss.

This means that [tex]p  = 0.2[/tex]

Sample of 75:

This means that [tex]n = 75[/tex]

Mean and standard deviation:

[tex]\mu = E(X) = np = 75(0.2) = 15[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{75*0.2*0.8} = 3.4641[/tex]

Find the probability that at least 18 of the 75 sampled employees would like to move into management.

Using continuity correction, this is [tex]P(X \geq 18 - 0.5) = P(X \geq 17.5)[/tex], which is 1 subtracted by the p-value of X = 17.5. So

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

[tex]Z = \frac{17.5 - 15}{3.4641}[/tex]

[tex]Z = 0.72[/tex]

[tex]Z = 0.72[/tex] has a p-value of 0.7642.

1 - 0.7642 = 0.2358

0.2358 = 23.58% probability that at least 18 of the 75 sampled employees would like to move into management.

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Answer:

  (b)  x = 1

Step-by-step explanation:

A graph shows the solution to f(x) = g(x) is x = 1.

__

We want to solve ...

  g(x) -f(x) = 0

  x^3 +2x^2 -x -2 -(-11/3x +11/3) = 0

  x^2(x +2) -1(x +2) +11/3(x -1) = 0 . . . . . factor first terms by grouping

  (x^2 -1)(x +2) +11/3(x -1) = 0 . . . . .  . the difference of squares can be factored

  (x -1)(x +1)(x +2) +(x -1)(11/3) = 0 . . . . we see (x-1) is a common factor

  (x -1)(x^2 +3x +2 +11/3) = 0

The zero product rule tells us this will be true when x-1 = 0, or x = 1.

__

The discriminant of the quadratic factor is ...

  b^2 -4ac = 3^2 -4(1)(17/3) = 9 -68/3 = -41/3

This is less than zero, so any other solutions are complex.

Answer:

[tex]P(S&G) =0.7941[/tex]

Step-by-step explanation:

From the question we are told that:

Sample size [tex]n=16+18=>34[/tex]

N0 of  Large [tex]L=16[/tex]

N0 of Small [tex]S=18[/tex]

N0 large Green [tex]L_g=9[/tex]

N0 of small White [tex]S_w=3[/tex]

Therefore

Number of green marbles [tex]N0(G)=9+(18-3)[/tex]

Number of green marbles [tex]N0(G)=24[/tex]

Generally the Number of both small and green Marble is

[tex]N0 of (S&G)= 18 - 3 = 15[/tex]

Generally the  probability that it is small or green P(S&G) is mathematically given by

[tex]P(S&G) = \frac{(18 + 24 - 15)}{(18 + 16)}[/tex]

[tex]P(S&G) =0.7941[/tex]

Answer:

13.5% is the increase in percentage

Answer:

74%

Step-by-step explanation:

To get the answer, divide 800 by 1080, and you will get a decimal. That decimal is 0.74074074074. Then, move the decimal point two times two the right, so you should have 074.074074074. Ignore everything after the decimal point as well as the 0 before the decimal point, and if done correctly, it should be 74%.

So, the final answer would be 74%.

Hope this helped!

Answer: D' = (1, -1)

Step-by-step explanation:

When dilating by a 1/2 you take a point and divide the x and y of the point in half. So D before is (2,-2) and then divide that by a 1/2, which gives us our answer (1, -1).