The manager would like to know the probability of a stockout during replenishment lead-time. in other words, what is the probability that demand during lead-time will exceed 25 gallons?

Step-by-step explanation:

The position of the median of an even data set is 1/2(8+1)=4.5

That is between two values, 4 and 5.

(5x-10+3x+30)/2=82

(8x+20)/2=82

(8x+20)=41

8x=41-20

8x=21

x=21/8

Answer:

Below

Step-by-step explanation:

3/4 (1/6 x +16) = 3/7 (4 3/8 - 21)      expand L side and compute R side

3/24 x + 12 =  - 7.125        Subtract 12 from both sides of the equation

3/24 x = -19.125             Multiply both sides by 24/2

x = -153

THIS EQUATION DOES SHOW x = -153

PERHAPS you MEANT this :

3/4 (1/(6x) +16) = 3/7 (4 3/8 - 21)       Expand L side  and compute R side

3/(24x) + 12 = - 7.125       subtract 12 from both sides

3/(24x) = -19.125      re-arrange

3 / (-19.125)    = 24 x      divide both sides by 24

3/ (-19.125 * 24) = x = - 1/153      

     Don't know how to find a different answer......check the equation you posted......

(a+4) (a-4)

according to formula,

x square - y square : (x+y) (x-y)

(a+4) (a-4)

xy : a square - 4

Hypotheses are always statements about population parameters.

A hypothesis is a statement or assumption about the value of a population parameter, such as the population mean or proportion.

The hypotheses are formulated based on the research question or problem being investigated.

They provide a framework for conducting statistical tests and drawing conclusions about the population based on sample data.

For example, if we want to test whether a new drug is effective in reducing blood pressure, the null hypothesis might state that the population mean blood pressure is equal to a certain value (e.g., no change), while the alternative hypothesis would state that the population mean blood pressure is different from that value (e.g., there is a decrease or increase).

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Answer:

a) 72

b) 1/72

c) 1/36

Step-by-step explanation:

a) number of ways she can choose route= 3C1 = 3

   number of ways she can choose parking lots= 4C1 = 4

number of ways she can choose entrances= 3C1 = 3  

number of ways she can choose elevators= 2C1 = 2

number of ways she can go to office= number of ways she can choose route×number of ways she can choose parking lots×number of ways she can choose entrances×number of ways she can choose elevators

      number of ways she can go to office= 3×4×3×2

                                                                      = 72

b) Probability of morning side= number of morning side/ total number of routes=  1/3

probabiltiy of Parking lot A=  number of parking lot A/ total number of parking lot= 1/4

probability of south entrance= number of south entrance/ total number of entrances=  1/3

probablity of elevator 1=  number of elevator 1/ total number of elevator= 1/2

combine probability= 1/3× 1/4×1/3×1/2 = 1/72

c) Probability of Industrial Avenue= number of industrial avenue/ total number of avenue= 1/3

Probability of parking lot D= number of parking lot D/ total number of parking lot after deducting number of parking lots A and B = 1/2

Probability of north entrance= number of north entrance/ total number of entrance= 1/3

probablity of elevator 2= number of elevator 2/ total number of elevator

                                      = 1/2

combine probability= 1/3 × 1/2 × 1/3 ×1/2

                                  = 1/36

Answer:

See explanation

Step-by-step explanation:

We can see that the sequence is 90, 86,82,.......

The common difference is  86 - 90 = -4

                                             82 - 86 = -4

Hence the sequence is arithmetic

The function is;

t(n) = 90 + (n - 1)(-4) = 90 + 4 - 4n

t(n) = 94 - 4n

Since it is AP, we have the sequence as;

90, 86, 82, 78, 74, 70, 66, 62......

He will no longer play football after the eighth quiz.

The total points earned is the sum of the first eight terms of the AP

Sn =n/2[2a + (n - 1) d]

Sn = 8/2[2(90) + (8 - 1) (-4)]

Sn = 608 points

Step-by-step explanation:

rearrange the equation so that the unknown you are r trying to calculate is on its own on one side of the equation

The system of equations are solved and x = -4 and y = -1

Given data ,

Let the system of equations be represented as A and B

where 3x + 8y = -20   be equation (1)

And , -5x + y = 19   be equation (2)

Multiply equation (2) by 8 , we get

-40x + 8y = 152   be equation (3)

Subtracting equation (1) from equation (3) , we get

-40x - 3x = 152 - ( -20 )

-43x = 172

Divide by -43 on both sides , we get

x = -4

Substituting the value of x in equation (2) , we get

-5 ( -4 ) + y = 19

20 + y = 19

Subtracting 20 on both sides , we get

y = -1

Hence , the equation is solved and x = -4 and y = -1

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a) Each person would receive 1/6 of the cake

b) If there are 49 balls in total and each person is to get seven balls, How many persons can share the balls?

We know that we can be able to make us of the principles of algebra so as to be able to obtain the problems that we have to deal with in the question that appears in the image that is attached.

Given that we have the total amount of the cake as 2 1/2 and then we are told that there are 15 persons in the class thus the amount that everyone should receive would be x.

2 1/2 = 15 x

5/2 = 15x

5 = 2 * 15x

x = 5/2 * 15

x = 1/6

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Using the exponential growth formula, the population in 2005 was 161 million.

The equation f(x) = a(1 + r)^x can also be used to compute exponential growth, where: The function is represented by the word f(x). The initial value of your data is represented by the a variable. The growth rate is represented by the r variable. To calculate growth rates, divide the difference between the starting and ending values for the period under study by the starting value.

Growth factor = (159/154) for the eleven-year period between 1990 and 2001.

The population growth might thus be described by the exponential equation

p(t) = 154(159/154)^(t/11), where t is the number of years since 1990.

The model forecasts a population of... p(15) = 154(159/154)^(15/11)

= 160.86 = 161 million

In 2005, there were about 161 million people living there.

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Correct Question:

A country's population in 1990 was 154 million. In 2001 it was 159 million. Estimate the population in 2005 using the exponential growth formula. Round your answer to the nearest million.

Answer:

The constant of variation is ¹/₄.

Step-by-step explanation:

When n varies jointly with f and g, we can write the following equation:

\(\boxed{n \propto fg \implies n = kfg}\)

where k is the constant of variation.

We are given that f = 2, g = 8, and n = 4.  

Substitute these values into the equation:

\(\implies 4 = k \cdot 2 \cdot 8\)

Solve for k:

\(\implies 4 = 16k\)

\(\implies \dfrac{4}{16} = \dfrac{16k}{16}\)

\(\implies \dfrac{1}{4}=k\)

Therefore, the constant of variation is ¹/₄.

\(\blue{\huge {\mathrm{CONSTANT \; VARIATION}}}\)

\(\\\)

\({===========================================}\)

\({\underline{\huge \mathbb{Q} {\large \mathrm {UESTION : }}}}\)

\({===========================================}\)

\( {\underline{\huge \mathbb{A} {\large \mathrm {NSWER : }}}} \)

\({===========================================}\)

\({\underline{\huge \mathbb{S} {\large \mathrm {OLUTION : }}}}\)

If n varies jointly with f and g, the relationship between them can be written as:

where:

Using the given information, we can solve for k as follows:

Therefore, the constant of variation is 1/4.

\({===========================================}\)

The probability of answering all three questions correctly by random guessing is 1/64. The probability of a random guess on one question yielding the correct answer is 1/4.

Using the idea of independent occurrences, it is possible to determine the likelihood that a random guess will accurately respond to all three questions. Given that there are four possible answers for each question and that you make a random guess, the likelihood that you will choose the right response is one in four (1/4).

The odds of each event occurring must be multiplied in order to determine the likelihood of successfully answering all three questions. The odds of the events can be multiplied together because they are independent.

P(answer all three correctly) = P(correctly guess the first question) P(correctly guess the second question) P(correctly guess the third question).

P(give the right answers to all three) = (1/4) (1/4) (1/4)

P(give correct answers to all three) = 1/64

As a result, the likelihood of properly answering all three questions by chance is 1/64.

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Answer:

15.4269444444

Step-by-step explanation:

The change in air pressure when the pure tone is produced is mathematically given as

p(1/2000) =0 mP

This pressure is referred to as the atmospheric pressure, air pressure, or simply pressure. It is the force that is exerted on a surface by the air that is above it due to the gravitational pull that gravity has on the surface. A barometer is an instrument most often used to measure the pressure of the atmosphere. When the pressure in the atmosphere changes, a column of mercury contained inside a glass tube in a barometer will either rise or sink.

Generally, the equation for is pressure  mathematically given as

\(p(t) =2sin (4000\pi t)\)

Therefore

p(1/2000) =2sin (4000\pi *1/2000)

p(1/2000) = 2sin (2\pi)

p(1/2000) = 2*0

p(1/2000) =0 mP

In conclusion, the pressure

p(1/2000) =0 mP

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Answer:

2. y = x + 13

Step-by-step explanation:

Your points are: (-4, 9) and (2, 15)

To write an equation of a line from two ordered pairs, you first find the slope (m)

To find the slope, you do y2 - y1 / x2 - x1

(-4 is x1, 9 is y1) (2 is x2, 15 is y2)

Plug in the numbers:

15 - 9 / 2 - (-4) ----------------------> 6/6 ----------> 1, m = 1

The next equation we'll use is y - y1 = m(x - x1)

and slope intercept form is y = mx + b

Pick either ordered pair to plug in the coordinates, but this time I'll use

(2, 15) -----> 2 is x1, 15 is y1

y - 15 = m(x - 2)

Since we already know the slope, m, we can simplify the equation.

y - 15 = 1(x - 2)

Distributive property

y - 15 = x - 2

Add 15 on both sides,

y = x + 13

The graph of the function is attached below.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given a function x +4y -3 = 0

To graph the equation x + 4y - 3 = 0, we need to find at least two points that satisfy the equation and plot them on a coordinate plane. To do this, we can use the intercept method.

First, we can find the x-intercept by setting y = 0 in the equation and solving for x:

x + 4(0) - 3 = 0

x = 3

So the x-intercept is (3, 0).

Next, we can find the y-intercept by setting x = 0 in the equation and solving for y:

0 + 4y - 3 = 0

4y = 3

y = 3/4

So the y-intercept is (0, 3/4).

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Answer:

Range: \(\:f\left(x\right)\ge \:-\frac{68}{11}\)

Interval notation \([-\frac{68}{11},\:\infty \:)\)

Step-by-step explanation:

I got a little confused with the x - 1/2x^2 term and I am taking to to be:

\(x\:-\frac{1}{2}x^2\)  . If this is incorrect please mention the correct term in your comment and I will edit this post. Or you can re-post the question

We have
\(f\left(x\right)=6x^2+x\:-\frac{1}{2}x^2+\:x\:-\:6\)

Simplify by grouping like terms:
\(=-\frac{1}{2}x^2+6x^2+x+x-6\)

\(= \frac{1}{2}x^2+6x^2+2x-6\)

Add similar elements
\(-\frac{1}{2}x^2+6x^2\)\(= -\frac{1x^2}{2}+\frac{12x^2}{2} = \frac{11x^2}{2}\)

So the original function expression becomes
\(y=\frac{11}{2}x^2+2x-6\)

This is the equation of a parabola which in standard form is \(ax^2 + bx + c\)

Here
\(a=\dfrac{11}{2},\:b=2,\:c=-6\)

We can compute the vertex of this parabola using the fact that the x, y coordinates of the vertex are given by
\(x_v =-\dfrac{b}{2a}\)

Plugging in values for b and a give us
\(x_v =-\dfrac{b}{2a} = -\dfrac{2}{2\left(\dfrac{11}{2}\right)} =-\dfrac{2}{11}\)

Plugging in this value of \(x_v\) into the parabola equation will give the value for \(y_v\) which is the function value at the vertex

Plug in \(x_v = -\frac{2}{11}\) t find the \(y_v\) value:
\(y_v=\dfrac{11\left(-\dfrac{2}{11}\right)^2}{2}+2\left(-\dfrac{2}{11}\right)-6\)

Simplify
\(\dfrac{11\left(-\dfrac{2}{11}\right)^2}{2} =\dfrac{2}{11}\)

\(2\left(-\dfrac{2}{11}\right) = -\dfrac{4}{11}\)

Combining the terms we get
\(y_v =\) \(\dfrac{2}{11}-\dfrac{4}{11}-6\) \(= -\dfrac{68}{11}\)

\(\textsf{Therefore the parabola vertex is at }\) \(\left(-\dfrac{2}{11},\:-\dfrac{68}{11}\right)\)
For a parabola of the form \(ax^2 + bx + c\) with vertex \(\left(x_v,\:y_v\right)\)

\(\circ \;\mathrm{If}\:a < 0\:\mathrm{the\:range\:is}\:f\left(x\right)\le \:y_v\)
\(\circ \;\mathrm{If}\:a > 0\:\mathrm{the\:range\:is}\:f\left(x\right)\ge \:y_v\)

Here \(a=\frac{11}{2}\) so the range is \(f\left(x\right)\ge \:-\dfrac{68}{11}\)

Answer range of f(x) is
\(f\left(x\right)\ge \:-\dfrac{68}{11}\)

In interval notation it is \([-\frac{68}{11},\:\infty \:)\)

It is much easier if you visualize it in a graph

Hope that helps

The linear inequality in two variables is  3x + 6y ≤ 9 . Option B

Linear inequalities are inequalities that involve at least one linear algebraic expression, that is, a polynomial of degree 1 is compared with another

Inequalities are math expressions or statements that use the inequalities "less than or equal to", "greater than or equal to", "less than", "greater than", and "not equal to".

Linear expressions are math statements or expressions whose expressions of a degree 1 (Highest exponent).

Variables are mathematical symbol or term that represents the unknown values.

In the problem, the question asks for a linear inequality in two variables. As you can see, all of the choices are linear expressions. The only option that uses one of the inequality symbols and has two unknown variables is the third option. So, it's the option B.

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The  examples that would constitute a discrete random variable are;

I. Total number of points scored in a football game

III. Number of near collisions of aircraft in a year

A discrete random variable has only a countable number of different values that it can assume. Usually, but not always, discrete random variables are counts. A random variable is discrete if it can only take a finite number of different values. A variable whose value is determined by counting is referred to as a discrete variable.

A continuous variable is one whose value may be determined through measurement. A random variable is a variable whose value is the resultant number of an unpredictable event.

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The equation \((sin(x)cos(x))^2 = sin(2x)\) is verified to be an identity.

Simplify LHS and RHS?

To verify whether the equation \((sin(x)cos(x))^2 = sin(2x)\) is an identity, we can simplify both sides of the equation and see if they are equivalent.

Starting with the left side of the equation:

\((sin(x)cos(x))^2 = (sin(x))^2(cos(x))^2\)

Now, we can use the trigonometric identity \(sin(2x) = 2sin(x)cos(x)\) to rewrite the right side of the equation:

\(sin(2x) = 2sin(x)cos(x)\)

Substituting this into the equation, we have:

\((sin(x))^2(cos(x))^2 = (2sin(x)cos(x))\)

Next, we can simplify the left side of the equation:

\((sin(x))^2(cos(x))^2 = (sin(x))^2(cos(x))^2\)

Since both sides of the equation are identical, we can conclude that the given equation is indeed an identity:

\((sin(x)cos(x))^2 = sin(2x)\)

Hence, the equation \((sin(x)cos(x))^2 = sin(2x)\) is verified to be an identity.

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A tip of 18% was given to the restaurant after the meal and tax to the nearest percentage.

Cost of the food = $25.30

Tax on the food cost = 8%

Tax amount

= 8% of 25.30

= 0.08  × 25.30

= 2.204

Total cost of food before tip = 25.30 + 2.204 = $27.504

Tip given = 32.24 - 27.504 = 5.036

Tip percentage

= 5.036 / 27.504 × 100%

= 18.31%

≈ 18%

Hence a tip of 18% was given to the restaurant after the meal and tax to the nearest percentage.

Percentage increases and decreases are calculated by computing the difference between two numbers or by comparing that difference to the starting value.

One can calculate how significantly the initial value has changed mathematically by dividing the result by the starting value and using the absolute value of the difference between the two values.

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Answer:

15x^2−14xy−8y^2−x−y

Step-by-step explanation:

Combine like units.

Answer:

hope it helped

have a good day

Answer:

equilateral

Step-by-step explanation:

equilateral sides are equal and the angles aswell

Answer:

A.

Step-by-step explanation:

22+(2x + 16)+90=180

combine like terms: 90+22+16=128

180-128=52

52=2x

52/2 = 2x/2

26 = x

(2*26+16) - angle B

The correct options according given identity of tangent are;

1) Write tan(x + y) as sin(x + y) over cos(x + y)

2) Use the sum identity for sine to rewrite the numerator

3) Use the sum identity for cosine to rewrite the denominator

4) Divide both the numerator and denominator by cos(x)·cos(y)

5) Simplify fractions by dividing out common factors or using the tangent quotient identity

According to the statement

we have given that the a identity and we have to use in the given conditions.

So, For this purpose, we know that the

Given that the required identity of Tangent is Tangent (x + y) = (tangent (x) + tangent (y))/(1 - tangent(x) × tangent (y)),

we have:

tan(x + y) = sin(x + y)/(cos(x + y))

sin(x + y)/(cos(x + y)) = (Sin(x)·cos(y) + cos(x)·sin(y))/(cos(x)·cos(y) - sin(x)·sin(y))

(Sin(x)·cos(y) + cos(x)·sin(y))/(cos(x)·cos(y) - sin(x)·sin(y)) = (Sin(x)·cos(y) + cos(x)·sin(y))/(cos(x)·cos(y))/(cos(x)·cos(y) - sin(x)·sin(y))/(cos(x)·cos(y))

(Sin(x)·cos(y) + cos(x)·sin(y))/(cos(x)·cos(y))/(cos(x)·cos(y) - sin(x)·sin(y))/(cos(x)·cos(y)) = (tan(x) + tan(y))(1 - tan(x)·tan(y)

∴ tan(x + y) = (tan(x) + tan(y))(1 - tan(x)·tan(y)

After solving this identity according to the statement it is clear that all the options are correct.

So, The correct options according given identity of tangent are;

1) Write tan(x + y) as sin(x + y) over cos(x + y)

2) Use the sum identity for sine to rewrite the numerator

3) Use the sum identity for cosine to rewrite the denominator

4) Divide both the numerator and denominator by cos(x)·cos(y)

5) Simplify fractions by dividing out common factors or using the tangent quotient identity

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Disclaimer: This question was incomplete. Please find the full content below.

Question:

Examine the following steps. Which do you think you might use to prove the identity Tangent (x) = StartFraction tangent (x) + tangent (y) Over 1 minus tangent (x) tangent (y) EndFraction question mark

Check all that apply.

-Write tan(x + y) as sin (x + y) over cos(x +y).

-Use the sum identity for sine to rewrite the numerator.

-Use the sum identity for cosine to rewrite the denominator.

-Divide both numerator and denominator by cos(x)cos(y).

-Simplify fractions by dividing out common factors or using the tangent quotient identity.

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Answer:

n=27

Step-by-step explanation:

x=3x(-3)^2

x=3x3^2

x=3^3

x=27

I hope that helped I'm sorry if It didn't!!

Answer:

Im pretty sure its 27

Step-by-step explanation:

simplified \(3(4-7)^{2}\)

n=27

Answer:

B. -2

Step-by-step explanation:

A relation that is not a function would have one x-value having two different corresponding y-values.

If we choose -2 to represent b I the relation, the relation would not be a function. This is because, we there would be two different y-values, 8 and 1, that are assigned to one x-value, which is -2 ==> (-2, 8) and (-2, 1).

Answer:

x = 1

Step-by-step explanation:

Both equations can be set equal to each other since they are both equal to y:

\(x-10=-4x-5\\5x-10=-5\\5x=5\\x=1\)

equate both equations !

x - 10 = -4x - 5

5x - 10 = -5

5x = 5

x = 1

therefore x = 1

Answer:

h(-3) = -3

Step-by-step explanation:

h(-3) = -(-3)2 + 3(-3)

h(-3) = 6 - 9

h(-3) = -3

Answer:

h(-3)= -18

Step-by-step explanation:

Substitute -3 for x

-(-3)^2 + 3(-3)

Simplify

-(9) - 9

Answer: -18