There are 31 flavors of ice cream, 2 choices of cones, 1 scoop, 2 scoops, or 3 scoops. How many different choices are there?

Answer:

a) 0.0065 = 0.65% probability of receiving no emails during an hour.

b) 0.1212 = 12.12% probability of receiving at least three emails during an hour

c) The expected number of emails received during 15 minutes is 1.2604.

d) 0.2835 = 28.35% probability that no emails are received during 15 minutes

Step-by-step explanation:

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 time interval.

In this question.

121 emails per day.

A day has 24 hours, so per hour, 121/24 = 5.0417, which means that [tex]\mu = 5.0417n[/tex], in which n is the number of hours.

A. What is the probability of receiving no emails during an hour?

n = 1, so [tex]\mu = 5.0417[/tex]

This is P(X = 0).

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

[tex]P(X = 0) = \frac{e^{-5.0417}*(5.0417)^{0}}{(0)!} = 0.0065[/tex]

0.0065 = 0.65% probability of receiving no emails during an hour

B. What is the probability of receiving at least three emails during an hour?

Either you receive less than three emails during an hour, or you receive at least 3. The sum of the probabilities of these events is decimal 1. So

[tex]P(X < 3) + P(X \geq 3) = 1[/tex]

We want [tex]P(X \geq 3)[/tex]

Then

[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]

In which

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

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

[tex]P(X = 0) = \frac{e^{-5.0417}*(5.0417)^{0}}{(0)!} = 0.0065[/tex]

[tex]P(X = 1) = \frac{e^{-5.0417}*(5.0417)^{1}}{(1)!} = 0.0326[/tex]

[tex]P(X = 2) = \frac{e^{-5.0417}*(5.0417)^{2}}{(2)!} = 0.0821[/tex]

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0065 + 0.0326 + 0.0821 = 0.1212[/tex]

0.1212 = 12.12% probability of receiving at least three emails during an hour

C. What is the expected number of emails received during 15 minutes?

15 minutes is a fourth of an hour, so n = 1/4 and [tex]\mu = \frac{5.0417}{4} = 1.2604[/tex]

The expected number of emails received during 15 minutes is 1.2604.

D. What is the probability that no emails are received during 15 minutes?

[tex]P(X = 0) = \frac{e^{-1.2604}*(1.2604)^{0}}{(0)!} = 0.2835[/tex]

0.2835 = 28.35% probability that no emails are received during 15 minutes

Answer:

-399

Step-by-step explanation:

21=b/-19

b=21 x -19

b=-399

Answer:

-399

explanation

b=21×-19

b=-399

Answer:

X = 9

Step-by-step explanation:

1. Subtract 72 from both sides.

24x = 216

2. Divide 24 on both sides

x = 9

Answer:

X = 9

Step-by-step explanation:

We have to separate the like terms

72 + 24x = 288

24x = 288 - 72

24x = 216

We then divide both sides by 24

X = 9

Answer:

g(x) = 4x - 1

Step-by-step explanation:

We have that:

[tex]g(x) = ax + b[/tex]

So

[tex]g(2t) = a*(2t) + b[/tex]

Equaling both sides:

[tex]g(2t) = 8t - 1[/tex]

[tex]a*(2t) + b = 8t - 1[/tex]

b = -1.

And

[tex]2a = 8[/tex]

[tex]a = \frac{8}{2}[/tex]

[tex]a = 4[/tex]

Then

g(x) = 4x - 1

Answer:

26.39

Step-by-step explanation:

sin B = 4/9

B = inverse sin 4/9 = 26.387

Answer:

E[X]= [tex]2 + 3 e^{(-2/3)[/tex]

Step-by-step explanation:

The objective of this question is to determine E[X].

T is defined (0,infinity)

X=max(c,T)

where; c=constant

E[X]=c+function (c,infinity) Sf(t)dt

E[X] =[tex]e^{-t/3[/tex]

E[X]=2+function (2,infinity)[tex]e^{-t/3[/tex]dt

E[X] =[tex](2+e^{-t/3})/(1/3)[/tex] function (2,infinity)

E[X]= [tex]2 + 3 e^{(-2/3)[/tex]

If X = T   if T ≥ 2 and X = 2    if 0 ≤ T < 2,

So Since T is  exponentially distributed with mean 3,  the density function of T is  [tex]f(t) = (1/3)e^{(-t/3)[/tex]

Answer:

The 95% confidence interval for the standard deviation of the diameter is (0.0014; 0.0036).

Step-by-step explanation:

We have to calculate a confidence interval for the standard deviation.

The confidence level is 95%.

The size of the sample is n=10.

The sample standard deviation is s=0.002.

The lower limit is calculated as:

[tex]LL=s\sqrt{\dfrac{n-1}{\chi_{(1-\alpha)/2;n-1}}}\\\\\\LL=0.002\sqrt{\dfrac{10-1}{19.02}}=0.002\sqrt{0.473}=0.002*0.688=0.0014[/tex]

[tex]UL=s\sqrt{\dfrac{n-1}{\chi_{\alpha/2;n-1}}}\\\\\\UL=0.002\sqrt{\dfrac{9}{2.7}}=0.002\sqrt{3.33}=0.002*1.826=0.0036[/tex]

The 95% confidence interval for the standard deviation of the diameter is (0.0014; 0.0036).

Answer:

r = sqrt of 5 or 2.2

Step-by-step explanation:

(1)²+(2)²=r²

5 = r²

r = sqrt of 5 or 2.2

Answer:

I'm pretty sure it would be B; go 2 units to the right and 12 units up.

Step-by-step explanation:

the question is asking for the percentage that got it right not the number of letters in the word, and 9 is the number of letters, and 12 is the number that got it right.

The correct data for 2 in coordinate grid will be from the origin, go 9units to the right and 12units up.

How to locate a point on graph?

To locate a point having coordinate (x,y) in graph, we have to go x direction right or left depending on the sign of x-coordinate(for right +,for left -), then we have to go y direction up or down depending on the sign of y-coordinate(for up +,for down -).

The graph is done by taking Number of letters in the word in x axis and Percentage of students who spelled the word correctly in y axis.

According to the table, it is clear that for data 2 Number of letters in the word is 9. so x=9

And Percentage of students who spelled the word correctly is 12

so y=12

So the coordinate of the point for data 2 is (9,12)

To locate the point (9,12) in coordinate grid we have to go 9units to the right in x axis and then we have to go 12units up in y axis direction.

Therefore The correct data for 2 in coordinate grid will be from the origin, go 9units to the right and 12units up.

Learn more about the location of point in graph

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Answer:

7719

Step-by-step explanation:

2,573*3=7719

Answer:

[tex] \boxed{C. \: 7,719} [/tex]

Step-by-step explanation:

Amount saved by Kate's family last year = 2,573 pennies

Amount saved by Zoe's family last year = 3 × Amount saved by Kate's family last year

= 3 × 2,573

= 7,719 pennies

Answer:

1/2 or 0.5

Step-by-step explanation:

Within 1 to 6,

Even numbers are 2, 4, 6

While odd numbers are 1, 3, 5

Assuming cards are mixed up properly and the probabilities of drawing a card with any number from 1 to 6 is constant,

Probability of drawing even number cards = number of units of even number cards ÷ total number of units of cards from 1 to 6 aka total number of cards

= 3 / 6

= 1 / 2

The probability of drawing even number cards is 1/2.

Probability is "possibility that deals with occurrence of random events".

According to the question,

Lucy places five cards that are labeled 1 to 6 face down on the table and mixes them up.

Numbers of space = 1,2,3,4,5,6

Even numbers are 2, 4, 6 and odd numbers are 1, 3, 5.

To find Probability of drawing even number cards is equal to number of units of even number cards is divided by total number of units of cards.

Probability of even numbers of cards = 3/6

= 1/2

Hence, Probability of even numbers of cards is 1/2.

Learn more about probability here

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Answer:

And for this case we can begin completing the square like this:

[tex] f(x) = x^2 +10x + (10/2)^2 +21 -(10/2)^2[/tex]

And after aggrupate the terms we got:

[tex] f(x) = (x+5)^2 +21 -25 [/tex]

And finally we have:

[tex] f(X)= (x+5)^2 -4[/tex]

And for this case our vertex would be:

[tex] (h,k) = (-5,-4) [/tex]

Step-by-step explanation:

For this case we have the following equation given:

[tex] f(x) = x^2 +10x +21[/tex]

And we want to find a formula in terms in the vertex form given by:

[tex] f(x) = a(x-h)^2 +k[/tex]

And for this case we can begin completing the square like this:

[tex] f(x) = x^2 +10x + (10/2)^2 +21 -(10/2)^2[/tex]

And after aggrupate the terms we got:

[tex] f(x) = (x+5)^2 +21 -25 [/tex]

And finally we have:

[tex] f(X)= (x+5)^2 -4[/tex]

And for this case our vertex would be:

[tex] (h,k) = (-5,-4) [/tex]

Answer:

Bicycle : $117

Tricycle : $87

Unicycle : $183

Step-by-step explanation:

Write a system of equations:

x + 3y + z = 561

7x + y = 906

2x + 7y + 5z = 1758

Where:

x = price of bicycle

y = price of tricycle

z = price of unicycle

Solve for x, y, and z.

Answer:

The test statistic Z = 1.844 < 1.96 at 0.05 level of significance

Null hypothesis is accepted

Yes he is right

The manager claims that at least 95 % probability that the plant is operating properly

Step-by-step explanation:

Explanation:-

Given data Population mean

                                           μ     = 885 tons /day

Given random sample size

                                          n = 60

mean of the sample

                                        x⁻  = 875 tons/day

The standard deviation of the Population

                                      σ = 42 tons/day

Null hypothesis:- H₀: The manager claims that at least 95 % probability that the plant is operating properly

Alternative Hypothesis :H₁: The manager do not claims that at least 95 % probability that the plant is operating properly

Level of significance =  0.05

The test statistic

 [tex]Z = \frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }[/tex]

[tex]Z = \frac{875 -885}{\frac{42}{\sqrt{60} } }[/tex]

[tex]Z = \frac{-10}{5.422} = -1.844[/tex]

|Z| = |-1.844| = 1.844

The tabulated value

                         [tex]Z_{\frac{0.05}{2} } = Z_{0.025} = 1.96[/tex]

The calculated value Z = 1.844 < 1.96 at 0.05 level of significance

Null hypothesis is accepted

Conclusion:-

The manager claims that at least 95 % probability that the plant is operating properly

Answer:

[tex](f-g)(x) = -12x^{2} - 8x + 9[/tex]

(f-g)(-4) = -151

Step-by-step explanation:

To find f-g(x) we subtract the common terms. So

[tex]f(x) = -9x^{2} - 2x[/tex]

[tex]g(x) = 3x^{2} + 6x - 9[/tex]

(f-g)(x)

[tex](f-g)(x) = f(x) - g(x) = -9x^{2} - 2x - (3x^{2} + 6x - 9) = -9x^{2} - 2x - 3x^{2} - 6x + 9 = (-9 - 3)x^{2} + (-2 - 6)x + 9 = -12x^{2} - 8x + 9[/tex]

(f-g)(-4)

[tex](f-g)(x) = -12x^{2} - 8x + 9[/tex]

We replace x by -4

[tex](f-g)(-4) = -12(-4)^{2} - 8(4) + 9= -151[/tex]

(f-g)(-4) = -151

Answer:

La ecuación química necesita ser equilibrada para que siga la ley de conservación de la masa.

Step-by-step explanation:

Answer:

Option C is correct.

Step-by-step explanation:

The area of 1 side of the divider is approximately 8 x 3 = 24 < 25  

Hope this helps!

:)

Answer:

a = 4

Step-by-step explanation:

Multiply by 2 on each side

6a = 24

a = 4

Answer:

$ 71.83  

Step-by-step explanation:

This year's earnings=last year's earnings*(1+growth rate)=$2*(1+20%)=$2.4

This year's dividend=2.4 *payout ratio=2.4 *20%=$0.48

Next year's earnings=$2.4*1.2=$2.88

Next year's dividend=2.88 *0.2=$ 0.58  

Year 3 earnings=$2.88*1.2=$ 3.46  

Year three dividend= 3.46*0.2=$0.69  

year 4 earnings =$3.46*1.08=$ 3.74  

Dividend from year 4 onward= 3.74  *0.5=1.87

From year 4 terminal value=1.87 /(cost of equity-growth rate)=1.87/(10%-8%)=$93.5

Share price is present value of the above dividends amnd terminal value=0.48/(1+0.1)^0+0.58/(1+0.1)^1+0.69/(1+0.1)^2+93.5/(1+0.1)^3=$ 71.83  

Answer:

B. Jazz and opra

Step-by-step explanation:

40 percent of 55 is 22. Find whatever is equal to 22

B) Jazz & Opera music combo were chosen by 40% of people surveyed

Given : Total respondents = 55

So, 40% of total respondents = 40% of 55 = 22

County & Opera are chosen by 15 + 10 = total 25 respondents, ie not equal to 40%

Jazz & Opera are chosen by 12 + 10 = total 22 respondents, ie equal to 40%

Jazz, Opera, Rock & Country, Jazz, Rock are totally more respondents.

To learn more about Percentage Respondents, refer https://brainly.com/question/8191920?referrer=searchResults

Answer:

Step-by-step explanation:

Given:-

- The following system of equations is given:

                       [tex]6x_1 - 6x_2 -4x_3 = 0\\\\x_1 - 7x_2 -6x_3 = 0\\\\x_1 - 5x_2 -nx_3 = 0\\[/tex]

Solution:-

- The matrix equation consists of coefficient matrix "A" and a variable matrix " x ". These two matrices undergo multiplication to yield a solution column vector "b".

- The matrix A, is a symmetrical square matrix with its elements representing the coefficients of each variable as follows:

            [tex]A = \left[\begin{array}{ccc}a_1_1&a_1_2&a_1_3\\a_2_1&a_2_2&a_2_3\\a_3_1&a_3_2&a_3_3\end{array}\right][/tex]

- Where the elements first subscript denotes the equation number and second subscript denotes the variable number.

             [tex]A = \left[\begin{array}{ccc}6&-6&-4\\1&-7&-6\\1&5&n\end{array}\right][/tex]

- Similarly, the variable matrix " X " is a column vector that lists all the variables in the the system of equations in a ascending order.

             [tex]X = \left[\begin{array}{c}x_1&x_2&x_3\end{array}\right][/tex]

- The solution vector " b " is the corresponding solution or any number written on the right hand side of the equals to sign " = " :

              [tex]b = \left[\begin{array}{c}0&2&-2\end{array}\right][/tex]

- Now, we can express the given system in the asked format:

            [tex]A*X = b\\\\\left[\begin{array}{ccc}6&-6&-4\\1&-7&-6\\1&5&n\end{array}\right]*\left[\begin{array}{c}x_1&x_2&x_3\end{array}\right] = \left[\begin{array}{c}0&2&-2\end{array}\right][/tex]

- The augmented matrix is a matrix that combines the coefficient matrix " A " and the solution vector " b ". A solution vector "b" as an extra column to the coefficient matrix:

            [tex][ A | b ]\\\\ \left[\begin{array}{ccccc}6&-6&-4&|&0\\1&-7&-6&|&2\\1&5&n&|&-2\end{array}\right][/tex]

- Now we will perform row reduction operation such that the system is consistent and has infinite number of solution.

- Row operation: R3 - R2 & R1/6

            [tex]\left[\begin{array}{ccccc}1&-1&-\frac{2}{3} &|&0\\1&-7&-6&|&2\\0&12&n+6&|&-4\end{array}\right][/tex]  

- Row operation: R2 - R1 & R3 / 12

            [tex]\left[\begin{array}{ccccc}1&-1&-\frac{2}{3} &|&0\\0&-6&-\frac{16}{3} &|&2\\0&1&\frac{n+6}{12} &|&-\frac{1}{3}\end{array}\right][/tex]

- Row operation: R2 / 6

           [tex]\left[\begin{array}{ccccc}1&-1&-\frac{2}{3} &|&0\\0&-1&-\frac{8}{9} &|&\frac{1}{3} \\0&1&\frac{n+6}{12} &|&-\frac{1}{3}\end{array}\right][/tex]

For the above system to be consistent and have infinite many solution then the coefficient of " x3 " for the 2nd and 3rd row must be equal:

           [tex]-x_2 - ( \frac{n+6}{12})*x_3 = \frac{1}{3}[/tex]

           [tex]-x_2 - ( \frac{8}{9})*x_3 = \frac{1}{3}[/tex]

The coefficient of " x_3 " must be equal:

           [tex]( \frac{n+6}{12}) = \frac{8}{9} \\\\\\\n = \frac{14}{3}[/tex]

- The augmented matrix in reduced form becomes:

           [tex]\left[\begin{array}{ccccc}1&-1&-\frac{2}{3} &|&0\\0&1&\frac{8}{9} &|&-\frac{1}{3} \\0&0&0 &|&0\end{array}\right][/tex]

Answer: Rank = Number of non-zero rows = 2

- The number of linearly independent rows are equal to the rank of the augmented matrix.

Hence,

Answer: Number of linearly independent rows = 2

Row operation: R1 + R2

             [tex]\left[\begin{array}{ccccc}1&0&\frac{2}{9} &|&-\frac{1}{3} \\0&1&\frac{8}{9} &|&-\frac{1}{3} \\0&0&0 &|&0\end{array}\right][/tex]

- The variable "x_3" will take any arbitrary value for which the solution holds infinitely many solutions.

           [tex]x_2 + \frac{8}{9}*x_3 = -\frac{1}{3} \\\\x_2 = - ( \frac{8}{9}*x_3 + \frac{1}{3} )\\\\x_1 + \frac{2}{9}*x_3 = -\frac{1}{3} \\\\x_1 = - ( \frac{2}{9}*x_3 + \frac{1}{3} )\\[/tex]

- Taking x_3 = α:

Answers:

           [tex]x_1 = -\frac{1}{3} + \frac{2}{9} \alpha \\\\x_2 = -\frac{1}{3} + \frac{8}{9} \alpha[/tex]

Answer:

Step-by-step explanation:

Considering story 1,

The weight of each book is x pounds. The weight of 5 books would be 5x pounds. Since the weight of the empty bag is 3 pounds and the weight of the bag and the books is 17 pounds, then the equation is

5x + 3 = 17

Considering story 2

x represents the increase in length of each rectangle. The new length of each rectangle would be x + 5. Since the three identical triangles has a total length of 17 feet, the equation would be

3(x + 5) = 17

Considering story 3,

x represents the cost of each bookmark. The cost of a $3 book and 5 booksmarks is 5x + 3. Since the amount spent is $17, the equation is

5x + 3 = 17

Considering story 4,

x represents the weight of each packet of paper. The weight of each bag is x + 3. Since the weight of 5 bags is 17 pounds, the equation is

5(x + 3) = 17

Considering story 5,

x represents the number of pencils that Noah has. The number of pencils that Andre has is 3x. Since he has 17 pens and pencils altogether, the equation would be

3x + 5 = 17

Answer:

Step-by-step explanation: first you take x and multiply it by z and u start taking the guys p and start blowing. if u dont know how 2 pls look it up<33 then ur answer should end up at 69

<3333

Answer:

0.136m

This is because if you draw a diagram, and label all the sides of the triangle (opp, hyp, adj), the adjacent angle is 3m. You can now use the sine rule to find the hypotenuse (length of ladder) by doing: cos 20= 3/h. You divide cos(20) by 3 and you get the answer of 0.13602m

Answer:

Step-by-step explanation:

Hi Sorry this took so long!

1. True

A=hbb /2 or Half of Base times Height.

2.False it would be 63

A= b * h

3.True

A=a+b/2 * h

Hope this helps!

Answer:

All parallelograms are squares

Step-by-step explanation:

Reasoning:

You can have a parallelogram with side lengths, i dont know, 5 and 3, right? That isn't a square :)

Answer:

d.

Step-by-step explanation:

x^2 because their is no other x^2

2x because their is no more x.

-7+1 equals -6

Answer:

D

Step-by-step explanation:

(f + g)(x) means that you add the two functions together, which results in (f + g)(x) = 2x + 1 + x² - 7 = D) x² + 2x - 6. Hope this helps!

Answer:

The minimum number of widgets for the company to earn more than 50 dollars = 104 widgets.

Step-by-step explanation:

Complete Question

Inequality

Imagine the polynomial function shown represents the profits, in y dollars, earned by the production of x widgets.

y = -0.04x² + 40x - 3600

What is the minimum number of widgets for the company to earn more than 50 dollars?

Solution

For the profit to be more than 50

y > 50

-0.04x² + 40x - 3600 > 50

-0.04x² + 40x - 3650 > 0

0.04x² - 40x + 3650 < 0

(x - 898.4) (x - 101.6) < 0

Using the inequality table to obtain the required solution to this inequality

Eqn | x < 101.6 | 101.6 < x < 898.4 | x > 898.4

(x - 898.4) | -ve | - ve | + ve

(x - 101.6) | -ve | + ve | + ve

(x-898.4)(x-101.6) | +ve | - ve | +ve

Hence, the inequality that satisfies the equation of (x - 898.4) (x - 101.6) < 0, that is, negative, is 101.6 < x < 898.4.

And from this range, the minimum number of widgets for the company to earn more than 50 dollars = 102 widgets.

But 102 widgets give a profit of 13 dollars, 103 widgets give a profit of 47 dollars and it is until 104 widgets that the profits exceed 50 dollars truly.

Hope this Helps!!!

Answer:4

Step-by-step explanation:

The above questions answer is 8 and 14