The following table provides a probability distribution for the random variable y. Y f(y) 3 0. 20 5 0. 30 6 0. 40 9 0. 10 (a) Compute Var(y) and sigma. If required round your answer to two decimal places

Answer:

m<1 = 63° (Exterior alternating Angles)

m<2 = 62°

m<3 = 118°

Step-by-step explanation:

[tex]{ \tt{m \angle 2 + 63 \degree + 55 \degree = 180 \degree}} \\ { \sf{(exterior \: corresponding \: angles)}} \\ { \tt{m \angle 2 = 180 - (63 + 55)}} \\ { \tt{ \underline{ \: m \angle 2 = 62 \degree \: }}}[/tex]

[tex]{ \tt{m \angle 3 = m \angle 1 + 55 \degree}} \\ { \tt{m \angle 3 = 63 + 55}} \\ { \tt{ \underline{ \: m \angle 3 = 118 \degree \: }}}[/tex]

The quadratic function that best matches the provided data is as follows: y = -9.38x2 - 74.8x + 186.1 with a 1594.61 squared difference total.

A function in mathematics is a connection between two groups of numbers, known as the domain and the range, where each element in the domain has a unique relationship with each element in the range. The range is the set of possible output values that the function can generate, and the domain is the set of input values for which the function is defined. Algebraic expressions or formulas that explain how the output values are arrived at based on the input values are frequently used to depict functions.

given

The greatest fit will be determined by the function with the smallest sum of squared differences.

The outcome is as follows after computing the sums of squared differences for each function:

Sum of squared differences for y = 9.38x2 + 74.8x + 186.1 is 406.27.

Sum of squared differences for y = -9.38x2 + 74.8x + 186.1 is 406.27.

Sum of squared differences for y = 9.38x2 + 274.8x + 186.1 is 18681.95.

sum of squared disparities is 1594.61 when y = -9.38x2 - 74.8x + 186.1.

The quadratic function that best matches the provided data is as follows: y = -9.38x2 - 74.8x + 186.1 with a 1594.61 squared difference total.

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the correct options are A), B), and E).

why it is and what is Gallon?

A) 2 quarts = 8 cups

B) 8 cm = 80mm

E) 96 inches = 8 feet

The number 8 cannot correctly fill in the blank for statements C and D.

C) 1 gallon = 16 cups, so 4 gallons = 64 cups, not 8 cups.

D) 1 hour = 60 minutes, so 96 minutes = 1 hour and 36 minutes, not 8 hours.

Therefore, the correct answers are A), B), and E).

A gallon is a unit of measurement for volume commonly used in the United States and some other countries. There are two different sizes of gallons: the US gallon and the imperial gallon.

The US gallon is defined as exactly 3.785411784 liters, and is used for measuring liquids such as gasoline, milk, and other beverages.

The imperial gallon, which is used in the United Kingdom and some other countries, is defined as exactly 4.54609 liters.

In both cases, a gallon is typically divided into smaller units such as quarts, pints, and fluid ounces for measuring smaller amounts of liquid.

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Let X and Y be independent random variables, uniformly distributed in the interval [0, 1 ]. The CDF of X - Y is FZ(z) = (1/2)(1+z)^2 for -1 ≤ z ≤ 0, 1 - (1/2)(1-z)^2 for 0 ≤ z ≤ 1, 0 for z < -1 or z > 1. The PDF of X - Y is fZ(z) = z + 1 for -1 < z < 0, 1 - z for 0 < z < 1, 0 otherwise.

To find the CDF of X - Y, we first note that the range of X - Y is [0, 1]. Let Z = X - Y, then:

FZ(z) = P(Z ≤ z) = P(X - Y ≤ z)

We can write this as an integral over the joint distribution of X and Y:

FZ(z) = ∫∫[X - Y ≤ z] fXY(x, y) dx dy

Since X and Y are independent, the joint distribution is simply the product of their marginal distributions:

fXY(x, y) = fX(x) fY(y) = 1 * 1 = 1

for 0 ≤ x, y ≤ 1.

Thus, we have:

FZ(z) = ∫∫[X - Y ≤ z] dx dy

= ∫∫[Y ≤ X - z] dx dy

= ∫0^1 ∫0^(x-z) 1 dy dx + ∫0^1 ∫(x-z)^1 1 dy dx

= ∫0^(1+z) (1-z) dx

= (1/2)(1+z)^2 for -1 ≤ z ≤ 0

= 1 - (1/2)(1-z)^2 for 0 ≤ z ≤ 1

Therefore, the CDF of X - Y is:

FZ(z) =

(1/2)(1+z)^2 for -1 ≤ z ≤ 0

1 - (1/2)(1-z)^2 for 0 ≤ z ≤ 1

0 for z < -1 or z > 1

To find the PDF of X - Y, we differentiate the CDF:

fZ(z) = dFZ(z)/dz =

z + 1 for -1 < z < 0

1 - z for 0 < z < 1

0 otherwise

Therefore, the PDF of X - Y is:

fZ(z) =

z + 1 for -1 < z < 0

1 - z for 0 < z < 1

0 otherwise

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Answer:

g(x) = 1/2|x - 1| + 2

Step-by-step explanation:

You were almost there, you just got the slope wrong.  

original vertex (h, k): (0, 0)

transformed vertex (h', k'): (1, 2)

original slope:  1

transformed slope: m = (3-2)/(3-1) = 1/2    pick any 2 points to find the slope

equation for the transformed function shown in the graph:

g(x) = 1/2|x - h'| + k'

g(x) = 1/2|x - 1| + 2

Answer:

0.600 or 600, 0.500 or 500, select option 2

Step-by-step explanation:

36.92 lbs. of the $3.45 tea and 43.08 lbs. of the $2.15 tea are needed.

Let x and y be the amount of tea that sells fo 3.45 and 2.15 a pound respectively:

x+y=80....................eq 1

3.45x+2.15y=2.75(80)......eq 2

:

rewrite eq 1 to x=80-y and plug that value into eq 2

:

3.45(80-y) +2.15y=2.75(80)

:

276-3.45y+2.15y=220

:

-1.3y=56

:

y=43.07 pounds of $2.15 tea

:

28x=80-43.07=36.93 pounds of $3.45 tea

Let a= the pounds of the more expensive tea needed

Let b= the pounds of the less expensive tea needed

(1) a+%2B+b+=+80

(2) 345a+%2B+215b+=+80%2A275 (in cents)

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

In words, (2) says.

(lbs of 'a' tea x price/lb) + (lbs of 'b' tea x price/lb) =

(lbs of mixture x price/lb of mixture)

-------

Multiply both sides of (1) by 215 and then.

subtract from (2)

345a+%2B+215b+=+80%2A275

-215a+-+215b+=+-80%2A215

130a+=+80%2A60

130a+=+4800

a+=+36.92

and, from (1)

(1) a+%2B+b+=+80

36.92+%2B+b+=+80

b+=+80+-+36.92

b+=+43.08

36.92 lbs. of the $3.45 tea and 43.08 lbs. of the $2.15 tea are needed.

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The mixture contains 34 pounds of black tea and 46 pounds of Earl Gray tea.

What is an algebraic expression?

An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations.

Let's denote the amount of black tea in pounds by "x" and the amount of Earl Gray tea in pounds by "y".

Since the total amount of mixture is 80 lb, we have:

x + y = 80 ----(1)

We also know that the mixture sells for $2.75 a pound, so the total revenue from selling 80 lb of mixture is:

80 x $2.75 = $220

On the other hand, the cost of the mixture is the sum of the costs of the black tea and the Earl Gray tea, which is:

3.45x + 2.15y

Since the company wants to make a profit, the revenue must be greater than the cost, so we have:

3.45x + 2.15y < $220

We can simplify this inequality by dividing both sides by 0.1:

34.5x + 21.5y < 2200 ----(2)

Now we have two equations with two unknowns (equations (1) and (2)), which we can solve using substitution or elimination.

Substitution method:

From equation (1), we have:

y = 80 - x

Substituting this into equation (2), we get:

34.5x + 21.5(80 - x) < 2200

Simplifying and solving for x, we get:

x < 34.5

Rounding x to the nearest pound, we get x = 34.

Substituting this value into y = 80 - x, we get y = 46.

Therefore, the mixture contains 34 pounds of black tea and 46 pounds of Earl Gray tea.

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The analysis of the relationship in the question and the graph of the relationship indicates that the cost of the delivery truck between 1 mile and 2 miles is a constant, therefore;

The graph of a dataset displays the relationship,  between the variables in the dataset. It is a visual representation of the connection between the variables.

The fixed base price of the delivery truck for (the first) 2 miles = $6

The additional amount the delivery truck charges after 2 miles = $2 per mile

The additional amount charged by the delivery truck after 6 miles = $4 per mile

The part of the question obtained from a similar question posted on the website, includes;

The cost of the delivery truck, between 1 mile and 2 miles based on the graph is an horizontal line.

The horizontal line of a graph, indicates that the relationship between the input and output is a constant, such that the output of the relationship, within the interval of the horizontal line is a constant. The correct option is therefore;

b). The cost of the delivery truck between 1 mile and 2 miles is constant

The possible question options includes;

a) More information is required to determine the cost of the delivery truck between 1 mile and 2 miles

b) The cost of the delivery truck between 1 mile and 2 miles, is constant

c) The cost of the delivery truck is decreasing between 1 mile and 2 miles

d) The cost of the delivery truck is increasing between 1 mile and 2 miles

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Answer:

4 + - 6 = -2

Hope this helps!

Step-by-step explanation:

The arrow closest to the line shows going forward 4 or + 4

The second arrow shows going back 6 or -6

+ 4 - 6 = -6 + 4 = -2

Answer:

Step-by-step explanation:

By choosing the LIFO method for inventory, the following items would be decreased (compared to what would have happened if they chose to use FIFO):

Net income

Taxes payable

Total assets

Owner's equity

This is because the LIFO method results in higher cost of goods sold and lower ending inventory, which in turn decreases net income and taxes payable. Lower ending inventory also decreases total assets and owner's equity.

The items that would be decreased by the choice of LIFO (compared to what would have happened if they chose to use FIFO) are Ending inventory and Net profit

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

We are given that;

Inventory costs in 2012 were rising

Now,

LIFO stands for last-in, first-out, and FIFO stands for first-in, first-out. These are two ways of assigning costs to the units of inventory that you sell. FIFO assumes that you sell the oldest units first, while LIFO assumes that you sell the newest units first1.

The choice of LIFO or FIFO has implications on a company’s financial statements as this decision impacts the value of inventory, cost of goods sold, and net profit2. If inventory costs are rising during a period, then LIFO will result in a lower value of ending inventory, a higher cost of goods sold, and a lower net profit compared to FIFO1.

Therefore, by unitary method the answer will be Ending inventory and Net profit

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In response to the stated question, we may state that Therefore, the trigonometry exact values of sin(u), cos(u), sin(2u), and cos(2u) are 4/5, 3/5, 24/25, and -7/25, respectively. The exact value of sin(t/2) is 2√5 / 5.

The study of the connection between triangle side lengths and angles is known as trigonometry. The concept first originated in the Hellenistic era, during the third century BC, due to the application of geometry in astronomical investigations. The subject of mathematics known as exact techniques deals with certain trigonometric functions and their possible applications in calculations. There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their separate names and acronyms (csc). The study of triangle characteristics, particularly those of right triangles, is known as trigonometry. As a result, geometry is the study of the properties of all geometric forms.

Using the given triangle, we can find the values of sin(u), cos(u), and tan(u) as follows:

sin(u) = opposite / hypotenuse = 4 / 5

cos(u) = adjacent / hypotenuse = 3 / 5

tan(u) = opposite / adjacent = 4 / 3

To find the values of sin(2u) and cos(2u), we can use the double angle formulas:

[tex]sin(2u) = 2 sin(u) cos(u)\\cos(2u) = cos^2(u) - sin^2(u)\\sin(2u) = 2 (4/5) (3/5) = 24/25\\cos(2u) = (3/5)^2 - (4/5)^2 = -7/25[/tex]

sin(t/2) = ± [tex]\sqrt((1 - cos(t)) / 2)[/tex]

We need to determine the sign of the square root based on the quadrant in which t/2 lies. Since 7t/2 is in the second quadrant (between pi and 3pi/2), t/2 is in the second quadrant as well (between pi/2 and pi). In the second quadrant, sine is positive and cosine is negative. Therefore, we take the positive square root:

[tex]sin(t/2) = \sqrt((1 - cos(t)) / 2)\\= \sqrt((1 - (-3/5)) / 2)\\= \sqrt(8/10)\\= \sqrt(4/5)\\[/tex]

= 2/√5

= 2√5 / 5

Therefore, the exact values of sin(u), cos(u), sin(2u), and cos(2u) are 4/5, 3/5, 24/25, and -7/25, respectively. The exact value of sin(t/2) is 2√5 / 5.

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The elements in the set  (A∩B¹) = {2,11,12,} and (B∩A¹) ={5,7,8,9,13,15,16,18}

You should understand that Set theory is a branch of mathematical logic that studies sets, which can be informally described as collections of objects such as numbers, alphabets and variables.

The universal set

S = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}

A = {1,2,6,11,12,19,20}

B = {1,5,6,7,8,9,13,15,16,18,19,20}

S = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}

B¹ = {2.3.4.10.11.12.14.17)

A = {1,2,6,11,12,19,20}

(A∩B¹) = {2,11,12,}

The elements of (B∩A¹) is

S = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}

A = {1,2,6,11,12,19,20}

A¹ = {3,4,5,7,8,9,10,13,14,15,16,17,18}

B = {1,5,6,7,8,9,13,15,16,18,19,20}

(B∩A¹)  = {5,7,8,9,13,15,16,18}

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Answer: The sale price of the dress is $45.

Step-by-step explanation:

To find the discount rate, we need to calculate the amount of the discount first. Since the dress is on sale for 25% off, the discount amount is:

Discount = 25% x $60 = $15

The discount rate is then calculated by dividing the discount amount by the original price of the dress and multiplying by 100:

Discount rate = ($15 / $60) x 100% = 25%

To find the sale price of the dress, we need to subtract the discount amount from the original price:

Sale price = $60 - $15 = $45

Therefore, the sale price of the dress is $45.

Answer:

To calculate the moles of hydrogen gas produced, we need to use the ideal gas law equation:

PV = nRT

where P is the total pressure, V is the volume of the gas, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin.

First, we need to convert the temperature to Kelvin by adding 273.15:

T = 26.0 + 273.15 = 299.15 K

Next, we need to calculate the pressure of the hydrogen gas by subtracting the vapor pressure of water from the barometric pressure:

P(H2) = P(total) - P(vapor) = 745 - 25.5 = 719.5 mmHg

Now we can plug in the values into the ideal gas law equation and solve for n:

n = PV/RT

n = (719.5 mmHg)(94.00 mL)/(62.3637 L mmHg/K mol)(299.15 K)

n = 0.00384 mol

Therefore, the moles of hydrogen gas produced by the reaction is 0.00384 mol.

Answer:

u8hiuhihihoiho'hjoihuiytrdeee

Step-by-step explanation:

The parameter an in the Lotka-Volterra predator-prey model denotes the capture efficiency (alpha).

The lotka-Volterra predator-prey model is what.

The Lotka-Volterra model makes the assumption that a predator's rate of prey consumption is inversely related to its abundance.

The parameter an in the Lotka-Volterra predator-prey model denotes the capture efficiency (alpha).

In conclusion, the lotka-volterra predator-prey model aids in estimating the rate at which prey is consumed.

We possess that

The predator population is x.

y is the number of prey.

The dy/dt equation contains the coefficient c. Hence, this coefficient is correlated with the prey population. The presence of a minus sign indicates a decline in the population of prey. It multiplies x as well, indicating a connection to the predator population.

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The correct order of the steps to test the general hypothesis is given as B, A, E, C, D, F.

A hypothesis is basically a uncertain fact that is backed by some logical and solid information. While using the hypothesis, it s important that we use the correct method to verify the credibility of the hypothesis in the system.

So, as per the given option, the correct sequence should be, B, A, E, C, D, F.

We first set up the null hypothesis and the alternative hypothesis, and then we choose the degree of significance. The next phases in hypothesis testing are choosing the test statistics and creating the decision-making rule.

When we get to a conclusion based on the hypothesis after carefully calculating and computing the hypothesis' performance, the procedure is said to be finished.

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Complete question - place the following steps in order. what is the correct order for the general procedure for hypothesis testing?

A. Select the level of significance

B. setup null and alternative hypothesis

C. Establish the decision rule

D. performance computation

E. select the test statistics

F. Draw conclusions

Answer:

Step-by-step explanation:

We can use the distributive property and FOIL method to multiply these two complex numbers:

(-4 + i)(2 - 3i) = -4(2) + (-4)(-3i) + (i)(2) + (i)(-3i)

Simplifying each term, we get:

(-4 + i)(2 - 3i) = -8 + 12i + 2i - 3i^2

Since i^2 = -1, we can replace it with -1:

(-4 + i)(2 - 3i) = -8 + 12i + 2i - 3(-1)

Simplifying further, we get:

(-4 + i)(2 - 3i) = -5 + 14i

Therefore, the product of (-4 + i) and (2 - 3i) is -5 + 14i.

Answer:

g(x)

=6x−4

=3x

2

−2x−10

Escribe (g∘f)(x) como una expresión en términos de x.

Step-by-step explanation:

Primero necesitamos conocer la función f(x). Luego podemos sustituir f(x) en g(x) para obtener (g∘f)(x).

Como la función f(x) no se proporcionó en la pregunta, asumiré que f(x) es:

f(x) = x^2 - 2x + 1

Entonces, podemos sustituir f(x) en g(x) de la siguiente manera:

g(f(x)) = 6f(x) - 4

= 6(x^2 - 2x + 1) - 4 (sustituyendo f(x))

= 6x^2 - 12x + 2

Por lo tanto, (g∘f)(x) = 6x^2 - 12x + 2.

The local tide measurement data contradict the satellite data because the number of decreasing local sea level trends is greater than the number of increasing local sea level trends. So correct option is C.

Measuring tides involves observing and recording changes in the water level of oceans, seas, and other bodies of water over time. Tides are caused by the gravitational pull of the moon and sun on the Earth's water, which results in a rhythmic rise and fall of water levels.

Tide measurements are important for a variety of reasons, including understanding ocean circulation, predicting flooding and storm surges, and planning shipping routes. Tidal data is also used in climate research, as changes in sea level can indicate long-term climate trends.

The local tide measurement data contradict the satellite data because the number of decreasing local sea level trends is greater than the number of increasing local sea level trends.

The measurement is done because the land surfaces are dynamic with some locations rising or sinking relative to sea level changes are different across world coasts.

Therefore, the Option C is correct.

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The complete question is:

OR is the perpendicular bisector and R is the vertex of a pair of congruent angles in the diagram.

What is perpendicular bisector and a pair of congruent angles ?

A perpendicular bisector is a geometric tool that is commonly used in mathematics and geometry. It is used to divide a line segment into two equal parts and is constructed by first finding the midpoint of the line segment. The perpendicular bisector is then constructed by drawing a line perpendicular to the line segment at its midpoint.

In geometry, two angles are said to be congruent if they have the same measure. This means that they have the same size and shape, even if they are oriented differently. In other words, if you were to place one angle on top of the other, they would perfectly overlap.

Explanation of the true statements:

In the given diagram ,

PR=RN and OR is perpendicular .

Hence, OR is the perpendicular bisector because a perpendicular bisector is a line that passes through the midpoint of a line segment and intersects it at a right angle, dividing the segment into two equal parts.

The vertex of a pair of congruent angles is the point where the two angle bisectors intersect.
Hence, R is the vertex of a pair of congruent angles in the diagram.

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Answer:

8(3/4y - 2) + 6(-1/2x + 4) + 1 can be simplified as:

6(-1/2x) = -3x

8(3/4y) = 6y

8(-2) = -16

6(4) = 24

1 remains as 1.

So the expression becomes:

6y - 3x - 16 + 24 + 1

which simplifies to:

6y - 3x + 9

Therefore, the expressions that are equivalent to 8(3/4y - 2) + 6(-1/2x + 4) + 1 are:

6y - 3x + 9

Answer:

a) Simple interest = PRT/100 = (800 x 1.5 x 5)/100 = $60

b) Future value = P(1 + RT) = 800(1 + 0.015 x 5) = $870

Total time of loan = 6 months

Phyllis pays $200 two months into the loan, so she still owes $800 for the remaining 4 months.

Simple interest = PRT/100 = (800 x 2 x 4)/100 = $64

Total interest = $64 + $20 = $84

a) Exact interest = PRT/365 = (500 x 4.5 x 90)/36500 = $5.48

b) Future value = P(1 + RT) = 500(1 + 0.045 x 90/365) = $508.22

a) Ordinary interest = PTR/100 = (3500 x 3.5 x 60)/360 = $183.75

b) Proceeds = P - I = 3500 - 183.75 = $3316.25

c) Amount to be paid at maturity = P = $3500

d) Due date = May 4 + 60 days = July 3

APY = (1 + R/n)^n - 1 = (1 + 0.16/4)^4 - 1 = 0.1664 or 16.64%

Future value = P(1 + R/n)^(nt) = 4500(1 + 0.04/2)^(2 x 2) = $5,011.03

P = FV/(1 + R/n)^(nt) = 8000/(1 + 0.06/4)^(4 x 5) = $5,764.44

Interest = (900 x 0.12) + (500 x 0.1) = $132

APR = (132/900) x (365/20) x 100% = 730%

Future value = PMT x ((1 + R/n)^(nt) - 1)/(R/n) = 1000 x ((1 + 0.08/4)^(4 x 4) - 1)/(0.08/4) = $47,490.08

Future value = PMT x ((1 + R/n)^(nt) - 1)/(R/n) x (1 + R/n) = 50 x ((1 + 0.06/12)^(12 x 2.5) - 1)/(0.06/12) x (1 + 0.06/12) = $1,327.10

Answer:

Step-by-step explanation:

Given,

Let length be x and breadth (x - 5).

Perimeter of rectangle is calculated by :

[tex] \: \: \boxed{ \pmb{ \sf{Perimeter_{(rectangle)} = 2(l + b)}}} \\ [/tex]

On substituting the values we get :

[tex]\dashrightarrow \: \: 130 = 2(x + x - 5) \\ [/tex]

[tex]\dashrightarrow \: \: 130 = 2(2x - 5) \\ [/tex]

[tex]\dashrightarrow \: \dfrac{130}{2} = (2x - 5) \\ [/tex]

[tex]\dashrightarrow \: \: 65 = 2x - 5 \\ [/tex]

[tex]\dashrightarrow \: \: 65 + 5 = 2x \\ [/tex]

[tex]\dashrightarrow \: \: 70 = 2x \\ [/tex]

[tex]\dashrightarrow \: \: \frac{70}{2} = x \\ [/tex]

[tex]\dashrightarrow \: \: 35 = x \\ [/tex]

Hence,

The probability that at least 3 minutes will elapse before the next telephone order is 0.797.

The probability that less than 15 minutes will elapse between orders is 0.677.

The probability that between 15 and 30 minutes will elapse between orders is 0.2275

To solve the following problem, we need to use the Poisson distribution, which is a probability distribution that describes the number of events that occur in a fixed interval of time or space, given the average rate of occurrence of those events.

The Poisson distribution has the following formula:

               [tex]P(X = k) = (\lambda\times ex^{-\lambda}) / k![/tex]    

Where:

P(X = k) is the probability that there are exactly k events in the interval

λ is the average rate of occurrence of events in the interval

e is the mathematical constant e (approximately 2.71828)

k! is the factorial of k (i.e., k * (k-1) * (k-2) * ... * 2 * 1)

Here we have

Between 11 pm and midnight on Thursday night Mystery pizza gets an average of 4.2 telephone orders per hour

A. The probability that at least 3 minutes will elapse before the next telephone order, using the complement rule:

=> P(at least 3 minutes) = 1 - P(less than 3 minutes)

Assume that the time between telephone orders follows an exponential distribution with a mean of 1/4.2 = 0.2381 hours (or 14.28 minutes).

Therefore, the Poisson distribution is λ = 1/0.2381 = 4.2/1.0 = 4.2.

Using the exponential distribution, we can find the probability of less than 3 minutes elapsing between orders as follows:

P(less than 3 minutes) = [tex]1 - e ^{(-\lambda \times t) }[/tex]

Where t = 3/60 = 0.05 hours

P(less than 3 minutes) = [tex]1 - e^{(-4.2\times 0.05) } = 0.203[/tex]

Therefore,

P(at least 3 minutes) = 1 - 0.203 = 0.797

The probability that at least 3 minutes will elapse before the next telephone order is 0.797.

B. To find the probability that less than 15 minutes will elapse between orders, we can use the same exponential distribution as before and set t = 15/60 = 0.25 hours:

P(less than 15 minutes) = [tex]1 - e ^{(-\lambda \times t) }[/tex]

P(less than 15 minutes) = [tex]1 - e^{(-4.2 \times 0.25)} = 0.677[/tex]

Hence, The probability that less than 15 minutes will elapse between orders is 0.677.

C. To find the probability that between 15 and 30 minutes will elapse between orders, we can subtract the probabilities found in less than 15 minutes and less than 30 minutes.

P(15 to 30 minutes) = P(less than 15 minutes) - P(less than 30 minutes) -

P(15 to 30 minutes) = [tex]e^{ (-\lambda0.5)} - e^{ (-\lambda 0.25)}[/tex]  

= 0.3499 - 0.1224  = 0.2275

Therefore,

The probability that at least 3 minutes will elapse before the next telephone order is 0.797.

The probability that less than 15 minutes will elapse between orders is 0.677.

The probability that between 15 and 30 minutes will elapse between orders is 0.2275

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Answer:

Step-by-step explanation:

a) One possible function that satisfies the conditions is:

f(x) = (x^2 - 25) / (x - 5)

This function is undefined when x = 5, but it is defined for all other real numbers.

b) One possible function that satisfies the conditions is:

g(x) = 1 / (x - 1)

This function is undefined when x = 1, but it is defined for all other positive numbers greater than 1.

c) One possible function that satisfies the conditions is:

h(x) = ln(x - 1)

This function is undefined when x = 1, but it is defined for all other positive numbers greater than 1. The range of this function is all real numbers.

The least common multiple (LCM) of 6 and 7 is 42. To find the LCM, we must first list out all the multiples of 6 and 7.

Number is a mathematical object used to count, measure, and label. It is also commonly used to represent a certain quantity. Numbers are a fundamental part of mathematics, and they can be used in a variety of ways. From basic arithmetic operations to complex equations, numbers are essential in the field of mathematics. Numbers can be used to represent any quantity, such as distance, size, time, or money. Numbers can also be used to represent abstract concepts, such as emotions or thoughts.

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72

Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84

The LCM is the smallest number that is a multiple of both numbers. In this case, the LCM of 6 and 7 is 42. This can be seen because both 6 and 7 have 42 as a multiple and no other number is smaller.

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The least common multiple (LCM) of 6 and 7 is 42. To find the LCM, we must first list out all the multiples of 6 and 7.

Number is a mathematical object used to count, measure, and label. It is also commonly used to represent a certain quantity. Numbers are a fundamental part of mathematics, and they can be used in a variety of ways. From basic arithmetic operations to complex equations, numbers are essential in the field of mathematics. Numbers can be used to represent any quantity, such as distance, size, time, or money. Numbers can also be used to represent abstract concepts, such as emotions or thoughts.

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72

Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84

The LCM is the smallest number that is a multiple of both numbers. In this case, the LCM of 6 and 7 is 42. This can be seen because both 6 and 7 have 42 as a multiple and no other number is smaller.

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Complete questions as follows-

How to find LCM of 6 and 7.

Where F_pivot is the magnitude of the force exerted on the pivot point.

What are perpendicular lines?

Perpendicular lines are lines that intersect at a right angle (90 degrees). In other words, if you draw a line perpendicular to another line, the two lines will form four right angles at the point where they intersect.

(a) The torque applied by the adult rider (on the left) can be calculated as the product of the force applied by the rider and the perpendicular distance from the pivot to the force. Let F_a be the force applied by the adult rider and let r_a be the perpendicular distance from the pivot to the force. Then, the torque applied by the adult rider is:

τ_a = F_a * r_a

The perpendicular distance r_a can be calculated using the Pythagorean theorem:

r_a = sqrt((L/2 - d)^2 + Xoffset^2)

Therefore, the torque applied by the adult rider is:

τ_a = F_a * sqrt((L/2 - d)^2 + Xoffset^2)

(b) Similarly, the torque applied by the child rider (on the right) can be calculated as:

τ_c = F_c * sqrt((L/2 + d)^2 + Xoffset^2)

where F_c is the force applied by the child rider and r_c is the perpendicular distance from the pivot to the force, which can be calculated using the Pythagorean theorem.

(c) The torque applied by the board can be calculated as the sum of the torques applied by the two riders:

τ_b = τ_a + τ_c

Substituting the expressions for τ_a and τ_c, we get:

τ_b = F_a * sqrt((L/2 - d)^2 + Xoffset^2) + F_c * sqrt((L/2 + d)^2 + Xoffset^2)

(d) To determine the distance d in terms of given quantities and variables, we can use the condition for static equilibrium, which requires that the sum of the torques about the pivot point is zero:

τ_a + τ_c = 0

Substituting the expressions for τ_a and τ_c and simplifying, we get:

F_a * (L/2 - d) = F_c * (L/2 + d)

Solving for d, we get:

d = (F_a/F_c - 1) * L/4

Substituting F_a = Mg and F_c = mg, where M is the mass of the adult rider, m is the mass of the child rider, and g is the acceleration due to gravity, we get:

d = (M/m - 1) * L/4

(e) The magnitude of the force exerted on the pivot point by the see-saw while in use can be calculated using the condition for static equilibrium, which requires that the sum of the forces in the vertical direction is zero:

F_a + F_c = Mg + mg

Substituting F_a = Mg and F_c = mg, we get:

F_pivot = Mg + mg

Therefore, where F_pivot is the magnitude of the force exerted on the pivot point.

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Answer:

Step-by-step explanation:

your given is not cleared repost it then post

The length of the base of the triangle is 8 yards.

The formula for calculating a triangle's area is

A = 1/2 * base * height,

where A represents the triangle's area, base its base length, and height its height measured perpendicularly from base to top.

Given that, height of triangle is half of 28 yards and an area of 56 sq. yards.

The area of triangle is given as:

A = 1/2 * base * height

Substitute the value of h = 1/2 (28) = 14 yards, and area = 56.

56 = 1/2 * base * 14

base = 56(2) / 14

base = 8 yards

Hence, the length of the base of the triangle is 8 yards.

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