which polynomial represents the difference below 12x^3+7x+3-(3x^7+4x)

a. The probability of no insect contaminants in a 225-gram bar from a brand at the mean contamination level can be found using the Poisson probability formula:

[tex]P(X = 0) = \frac{ (e^{-λ})(λ^0)}{0!} = \frac{(e^{-14.4})(14.4^0)}{0!}= 0.000000831[/tex]

b. If you consume a bar that is one-fifth the size tested (45 grams) from a brand at the mean contamination level, the mean number of insect fragments would be one-fifth of 14.4, or 2.88. The probability of no insect contaminants can be found using the Poisson probability formula:

[tex]P(X = 0) = \frac{(e^-λ)(λ^0)}{0!} = \frac{(e^-2.88)(2.88^0)}{0!} = 0.056032[/tex]

c. If you consume seven 28.35 gram (one-ounce) bars this week from a brand at the mean contamination level, the mean number of insect fragments would be (7 * 28.35/225) * 14.4 = 5.4336.

The probability of consuming one or more insect fragments in more than one bar can be found using the Poisson probability formula and the complement rule:

[tex]$$\begin{aligned}& P(X>1) \\& =1-P(X \hat{a} 1) \\& =1-\left[\left(e^{-} \hat{I}\right)\left(\hat{I}^0\right) / 0 !+\left(e^{-} \hat{I}\right)\left(\hat{I}^1\right) / 1 !\right] \\& =1-\left[\left(e^{-} 5.4336\right)\left(5.4336^0\right) / 0 !+\left(e^{-} 5.4336\right)\left(5.4336^1\right) / 1 !\right] \\& =0.994784\end{aligned}$$[/tex]

d. The probability of contamination more than twice the mean of 14.4 can be found using the Poisson probability formula and the complement rule:

[tex]P(X > 28.8) = 1 - P(X ≤ 28.8) \\= 1 - ∑(e^-λ)(λ^x)/x!\\ = 1 - 0.999999999999999 \\= 0.000000000000001[/tex]

This probability is extremely small, so it can be considered unusual and not typical variation.

https://brainly.in/question/39769270

#SPJ1

Answer:

84 deg

Step-by-step explanation:

cos(x)=sin(90-x)

90-x=6

x=84

The value of expression 50% of 36 is,

⇒ 50% of 36 = 18

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

The expression is,

⇒ 50% of 36

Now, We can simplified as;

The expression is,

⇒ 50% of 36

By definition of percent we get;

⇒ 50/100 × 36

⇒ 1/2 × 36

⇒ 36/2

⇒ 18

Thus, The value of 50% of 36 is,

⇒  50% of 36 = 18

Learn more about the percent visit:

https://brainly.com/question/24877689

#SPJ9

Answer:

Brian hiked 6 1/2 more miles than Christine.

Step-by-step explanation:

Ok. 5.25+4.75+6-2*4.75=6.5 or 6 1/2 more miles.

Answer:

S$ 250

Step-by-step explanation:

we can solve this by dividing 20,000 NRs by 80 since S$1.00 = NRs 80

Answer: To graph this system of inequalities, we can first graph each inequality separately and then find the region where they overlap.

Starting with the first inequality, x - y ≥ 7, we can rearrange it to y ≤ x - 7 and graph the line y = x - 7. Since the inequality includes the line, we will use a solid line to represent it, and shade below the line to show the region where y is less than or equal to x - 7.

Next, for the second inequality, x + 2y < 5, we can rearrange it to y < (-1/2)x + 5/2 and graph the line y = (-1/2)x + 5/2. Since the inequality excludes the line, we will use a dashed line to represent it, and shade below the line to show the region where y is less than (-1/2)x + 5/2.

Now we can combine the two shaded regions to find the overlapping region where both inequalities are satisfied. This region is shown in the graph below:

     |          /

     |        /

     |      /

     |    /  

     |  /    

     |/      

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

The point that represents a solution to the system is the point where the two lines intersect. To find this point, we can solve the system of equations:

y = x - 7

y = (-1/2)x + 5/2

Substituting the first equation into the second, we get:

x - 7 = (-1/2)x + 5/2

Simplifying this equation, we get:

(3/2)x = 19/2

x = 19/3

Substituting this value of x into either of the original equations, we get:

y = 19/3 - 7 = 2/3

So the point that represents a solution to the system is (19/3, 2/3).

Step-by-step explanation:

To match the terms to their correct definitions, we have:

A quadrilateral refers to a two-dimensional shape that has four sides, four vertices, and four angles.

There are different categories of quadrilaterals, such as trapezium, kite, parallelogram, rectangle, rhombus, and square.

The sides of a quadrilateral can be of different lengths and the angles can be of different measures.

Some types of quadrilaterals such as squares, rectangles, rhombus, etc. are special with some of their sides and angles being equal.

Learn more about a quadrilateral at brainly.com/question/1190071.

#SPJ1

a) Let x denote the quality rating and y denote the meal price.

b. From the above table, the marginal density function of x is 1.94

c. From the probability table, the marginal density function of y is 2.09

The probability distribution table for quality and meal price is obtained by dividing each and every frequency by the total frequency of 300 is attached in the image.

The probability distribution is obtained in the attached image below.

The expected value of x is,

1 x 0.28  + 2 x 0.50 + 3 x 0.22

= 1.94

To find the marginal density function of y

1 x 0.26  + 2 x 0.39 + 3 x 0.35

= 2.09

Given that var(x+y)=1.6691

var(x)=0.4964 and var(y)=0.6019

var(x+y) =1.6691

var(x) + var(y) +2* cov(x,y)=1.6691

0.4964+0.6019+ 2 *cov(x,y) =1.6691

1.0983+ 2 * cov(x,y) =1.6691

2 * cov(x,y) =1.6691-1.0983

2* cov(x,y)=0.5708

cov(x,y) =(0.5708)/2

cov(x,y)= 0.2854

Thus, the covariance of x and y is, 0.2854.

Here, the covariance of x and y is positive.

Thus, the relationship between quality and meal price is positive.

If the quality of the meal increases then the meal price also increases.

Yes, the expected result is positive because if the quality of the meal is good then meal price increases.

Read more about probability here:

https://brainly.com/question/24756209

#SPJ1

The cost of the burger and the cost of an order of fries to Lynn would be :

From the problem, we know that Lynn spent $20.00 and purchased 4 hamburgers and 5 orders of fries. Similarly, we know that Ricardo spent $41.20 and purchased 10 hamburgers and 7 orders of fries, which gives us the equations:

4h + 5f = 20

10h + 7f = 41.20

Using substitution, we can express h in form of f to be :

4h + 5f = 20

4 [ ( 3 f + 1. 20 ) / 2] + 5 f = 20

6 f + 2 . 40 + 5 f = 20

11 f = 17. 60

f = $ 1. 60

We can then find the cost of hamburgers using the first equation :

4h + 5f = 20

4h + 5 ( 1. 60 ) = 20

4h + 8 = 20

4h = 12

h = $ 3

Find out more on cost at https://brainly.com/question/26850134

#SPJ1

We have shown that the product of two rational numbers is rational.

A number system is defined as a system of writing to express numbers.

Let a and b be two rational numbers, such that:

a = p/q

b = r/s

where p, q, r, and s are integers and q, s are non-zero.

We need to show that the product ab is also a rational number.

We have:

ab = (p/q) x (r/s)

= (p x r) / (q x s)

Since p, q, r, and s are all integers,

ab = m/n

where m = p x r and n = q x s.

Since both m and n are integers and n is non-zero ,we can conclude that ab is a rational number.

Therefore, we have shown that the product of two rational numbers is rational.

To learn more on Number system click:

https://brainly.com/question/22046046

#SPJ1

Answer:

Step-by-step explanation:

is -2(-12y+5)+4=8(3y+2)-22 a conditional equation an identity or a contradiction

-2(-12y + 5) + 4 - 8(3y - 2) + 22 = 0

24y - 10 + 4 - 24y - 16 + 22 = 0

-6 - 16 + 22

- 22 + 22 = 0

0 = 0   (All real numbers are solutions.)

The linear equations represented by graph are y=6-2.5x and y=0.8x.

What is a linear equation, exactly?

When the greatest power of a variable is 1, the equation is said to be linear. Other term used for it is a one-degree equation. The standard form of a linear equation with one variable is Ax + B = 0. There are three variables in this equation: x, A, and B. A denotes a coefficient. A linear equation with only two variables is commonly written as Ax + By = C. There is three more constants added to the constant C: the variables x and y, the coefficients A and B, and the variables.

Now,

In given graph for y=6-2.5x

when  x        y

          1        3.5

          2       1

and for y=0.8x

when  x   y

          1    0.8

          2   1.6

hence,

           The linear equations represented by graph are y=6-2.5x and y=0.8x as shown in the image.

To know about linear equations visit the link

https://brainly.com/question/29739212

#SPJ1

Answer: C) (1, -1)

Step-by-step explanation:

[tex]\boldsymbol{\sf{\underline{\diamond System \ of \ equations \ by \ the \ reduction \ method:} }}[/tex]

   [tex]\boldsymbol{\sf{We\:have\:the\:system\:of\:equations \ --\to \ \left \{ {{x+2y=1 \ } \atop {2x-3y=5 }} \right. }}[/tex]

Multiply the first equation by 2, and the second equation by -1, then both equations must be added.

             [tex]\boldsymbol{\sf{\star \ 2(x+2y=-1) }}\\ \boldsymbol{\sf{\star -1(2x-3y=5) }}[/tex]

We add these equations to eliminate x.

             [tex]\boldsymbol{\sf{\star \ 7y=-7 }}[/tex]

Then we solve 7y=-7 for y (divide by 7).

               [tex]\boldsymbol{\sf{\star \ \dfrac{7y}{7}=\dfrac{-7}{7} }}\\ \\ \boxed{\boldsymbol{\sf{\star \ y=-1}}}[/tex]

We place the found value of y, in one of the original equations y to solve for x.

                  [tex]\boldsymbol{\sf{\star \ x+2y=-1}} \\ \\ \boldsymbol{\sf{\star \ x+2(-1)=-1}}\\ \\ \boldsymbol{\sf{\star \ 0=-x+1 }}[/tex]

Simplify (We add x to both sides.)

                  [tex]\boldsymbol{\sf{\star \ 0+(x)=-x+1+(x) }}\\ \\ \boldsymbol{\sf{\star \ x=1}}\\ \\ \boldsymbol{\sf{\star -2=-1-x}}[/tex]

Add (2) to both sides.

                   [tex]\boldsymbol{\sf{\star \ -2+(2)=-x-1+(2) }}\\ \\ \boldsymbol{\sf{\star \ 0=-x+1 }}[/tex]

We divide by 1.

                      [tex]\boldsymbol{\sf{\star \ \dfrac{x}{1}=\dfrac{1}{1} }}\\ \\ \boxed{\boldsymbol{\sf{\star \ x=1}}}[/tex]

                                     [tex]\underline{\bf{ \ \ x,y \ answer\ \ \ \ }}\\\boxed{\boldsymbol{\sf{x=1,y=-1 }}}[/tex]

Learn more about systems of equations in https://brainly.com/question/20178040

[-1.5, 3.5] and [-2, infty) are the range and domain of the equation.

Quadratic function are functions that have a leading degree of 2.

The domain of the function are values that lies along the x-axis of the graph. Hence the domain of the curve will be [-1.5, 3.5]

The range of the function are values that lies along the y-axis of the graph. Hence the domain of the curve will be [-2, infty)

Hence the range and domain of the graph are [-1.5, 3.5] and [-2, infty)

Learn more on domain and range here: https://brainly.com/question/10197594

#SPJ1

450, 46, 12

46, 12, 10

450, 10, 12

46,450,10

Step-by-step explanation:

The mixture of any three would be the possibilities

450, 46, 12

46, 12, 10

450, 10, 12

46,450,10

Percentage of amount paid towards principal = 70.37%

Percentage of amount paid towards interest = 29.63%

APR is abbreviation Annual Percentage Rate. APR is estimate cost over a year of borrowing, It is expressed in percentage of the money borrowed. The higher it is, the more expensive to borrow. The lower it is, the cheaper it'll be to borrow.

Given,

Principal amount (P) = $95000

APR (R) = 5% = 0.05

Time (T)= 25 years

Amount paid monthly $450 for 25 years

There are 12 payments every year for 25 years

No. of payments,

12 × 25 = 300.

Total amount paid

3000 × $450 = $135000.

Amount paid toward Principal = $95,000

In percentage

= (95000/135000)×100

= 70.37%

Toward Interest = $135000 - $95000 = $40000

In percentage

= (95000/135000)×100

= 29.63%

Hence, 70.37% of amount is paid toward principal and 29.63% is paid for interest.

Learn more about APR here:

https://brainly.com/question/14184570

#SPJ1

Answer:

Step-by-step explanation:

To determine what percentage of the total amount paid is applied towards the principal and interest, we first need to calculate the total amount paid over the 25-year term.

The monthly payment can be calculated using the formula for a loan payment:

P = (r(PV)) / (1 - (1+r)^(-n))

where P is the monthly payment, r is the monthly interest rate (APR / 12), PV is the present value of the loan (or the amount borrowed), and n is the total number of payments (25 years * 12 months/year = 300).

Plugging in the given values, we get:

P = (0.05/12 * $95,000) / (1 - (1+0.05/12)^(-300)) = $536.82

This means that the total amount paid over the 25-year term is:

Total amount paid = 300 * $536.82 = $161,046

The amount borrowed (or the principal) is $95,000. Therefore, the amount of interest paid over the 25-year term is:

Total interest paid = $161,046 - $95,000 = $66,046

To find the percentage of the total amount paid that is applied towards the principal, we can divide the principal by the total amount paid and multiply by 100:

Percentage of total amount paid towards principal = ($95,000 / $161,046) x 100% = 59.03%

To find the percentage of the total amount paid that is applied towards interest, we can divide the interest paid by the total amount paid and multiply by 100:

Percentage of total amount paid towards interest = ($66,046)

Answer:

x = 10

Step-by-step explanation:

We know that it's a right triangle and it's two sides, which are 6 and 8

So we can find the third side, the Hypotenuse or x, using the Pythagoras Theorem

6² + 8² = Hypotenuse ²

36 + 64 = Hypotenuse²

100 = Hypotenuse²

Hypotenuse = root100

Hypotenuse = 10

Therefore x = 10

The probabilities are given as follows:

1) Blue eyes: 0.132.

2) Female with green eyes: 0.09.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

The total number of people is given as follows:

20 + 25 + 30 + 15 + 10 + 12 + 15 + 20 + 10 + 10 = 167.

10 + 12 = 22 people out of 167 have blue eyes, hence the probability is given as follows:

p = 22/167 = 0.132.

15 people out of 167 are female with green eyes, hence the probability is given as follows:

p = 15/167 = 0.09.

More can be learned about probability at https://brainly.com/question/24756209

#SPJ1

The magnitude of the earthquake, as measured on the Richter Scale, is 2.5.

What is Richter Scale ?

The Richter Scale is a logarithmic scale used to measure the magnitude of earthquakes. It was developed by seismologist Charles Richter in the 1930s and is named after him.

The Richter Scale measures the amplitude of the seismic waves produced by an earthquake, which are detected by seismographs. The amplitude is a measure of the size of the earthquake, and is related to the amount of energy released by the earthquake.

Given by the question:
The Richter Scale equation for the magnitude (R) of an earthquake is:

R = log(A/A0)

where A is the amplitude of the earthquake and A0 is a standard wave amplitude.

We are given that the earthquake amplitude (A) is 288 times as great as the standard wave amplitude (A0):

A = 288 A0

Substituting this into the Richter Scale equation, we get:

R = log(288 A0 / A0)

R = log(288)

Using a calculator or a logarithm table, we can evaluate the logarithm of 288 to get:

R = 2.46

Rounding this to one decimal place, we get:

R ≈ 2.5

Therefore, the magnitude of the earthquake, as measured on the Richter Scale, is 2.5.

To know more about Richter Scale visit:
https://brainly.com/question/18765411
#SPJ1

Answer:

the Rhine River is approximately 1216 km long

Step-by-step explanation:

a) If the Mississippi River is 19% longer than the Indus River, we can find its length by multiplying the length of the Indus River by 1.19:

Length of Mississippi River = 3200 km x 1.19 = 3808 km

Therefore, the Mississippi River is approximately 3808 km long.

b) If the Rhine River is 62% shorter than the Indus River, we can find its length by multiplying the length of the Indus River by 0.38 (100% - 62% = 38%):

Length of Rhine River = 3200 km x 0.38 = 1216 km

Therefore, the Rhine River is approximately 1216 km long.

Answer:

Step-by-step explanation:

Item: $15

on sale:$15 -35% or 15*7/20=

$9.75~

The area that will be frosted on the bottom layer 680

What are the basic mathematical operations?

The four basic mathematical operations are Addition, subtraction, multiplication, and division.

1. Find the smaller cake first with (lw*amount of sides) and then add it to the larger cake using the same formula.

6*6*6+10*10*6

This equals 816

2. Find the amount not frosted. The bottom and the connection. Simply, (lw).

6*6+10*10

This equals 136

3. Subtract 136 from 816.

816-136= 680 sq inches

Hence, The area that will be frosted on the bottom layer 680

To learn more about basic mathematical operations, Visit

https://brainly.com/question/20628271

#SPJ1

The average is 9.99, the very first percentile is 8.01, as well as the upper quartile is 13.33 as a result.

From smallest to highest number, 25% is the first quartile. Second quartile: 25.1% to 50% (till median) 51% to 75%, third quartile (above the median) 25% of the biggest values are in the fourth quartile.

The data must first be arranged in ascending order before we can calculate the median or quartiles of the provided data:

5.24, 6.02, 6.67, 7.30, 7.59, 7.99, 8.03, 8.35, 8.81, 9.45, 9.61, 10.37, 10.39, 11.86, 12.22, 12.71, 13.07, 13.59, 13.89, 15.42

There are a total of 20 data points, and the median is calculated as that of the average of a 10th and 11th pieces of data:

(9.61 + 10.37) / 2 = 9.99; median

The very first quartile (Q1) must be determined in order to determine.

To know more about Quartiles visit:

https://brainly.com/question/7039036

#SPJ1

Answer:

Let M be the minimum monthly payment and A be the additional monthly payment of $30. Let B be the balance on the store credit card.

From the problem, we have:B = M * 58 (if only minimum payments are made)

B = (M + A) * 24 (if an additional $30 is paid each month)

Simplifying these equations, we get:M = B / 58

M + A = B / 24

Substituting the first equation into the second equation, we get: B / 58 + A = B / 24

Solving for A, we get:A = B / 24 - B / 58

A = B * (58/24 - 1/58)

Simplifying, we get:A = B * 0.08275862

To find the percent of time that Haddad will save by paying the extra $30 per month, we need to find the difference in time between the two scenarios and divide by the longer time (58 months).

The time it takes to pay off the balance with only the minimum payments is 58 months, while the time it takes to pay off the balance with the additional $30 each month is 24 months.

The difference in time is:58 - 24 = 34

So Haddad will save 34 / 58 = 0.5862, or 58.62% of the time by paying the extra $30 per month.

Based on the given information, we can make the following conclusions: Both means are shorter than their respective medians. The median-to-mean increase is greater in the case of bypass surgery

In statistics, the median is a measure of central tendency that represents the middle value of a dataset when the data is arranged in ascending or descending order. It is the value that separates the lower 50% of the data from the upper 50% of the data. To find the median of a dataset, the data is first arranged in order. If the number of data points is odd, the median is the middle value. If the number of data points is even, the median is the average of the two middle values. The median is a useful measure of central tendency because it is less sensitive to outliers than the mean, which makes it a better indicator of the typical or central value of a dataset when the data is skewed or contains extreme values.

Here,

1. Both means are shorter than their respective medians, suggesting that both distributions are skewed to the right. This means that there are some patients who wait for a very long time, causing the right tail of the distribution to be longer.

2. The fact that the median is greater for angioplasty and the mean is greater for bypass surgery tells us that the median-to-mean increase is greater in the case of bypass surgery, suggesting that the skewness is more pronounced for bypass surgery than for angioplasty. This means that there are relatively more patients who wait for a very long time for bypass surgery compared to angioplasty, which is reflected in the longer right tail of the distribution for bypass surgery.

To know more about median,

https://brainly.com/question/29156884

#SPJ1

The area of the irregular figure to the nearest tenth is 8.12 sq. ft.

Shapes classified as irregular lack both equal sides and equal angles. The entire area occupied by an irregular shape on a two-dimensional plane is referred to as the shape's area. An irregular form can be split into a number of regular shapes, such as triangles, squares, and rectangles, to determine its area. The area of those smaller shapes can then be added to determine the total area.

Given that, the diameter of the semicircle= 2.8 ft.

The radius of the semicircle = 1.4 ft.

The area of the semicircle is:

A = πr² / 2

A = (3.14)(1.4)²/2

A= 3.077 sq. ft

The area of the triangle is given as:

A = 1/2(b)(h)

A = 1/2(2.8)(3.6)

A = 5.04 sq. ft

The area of the irregular figure is:

A = Area of semicircle + area of triangle

A = 3.077 + 5.04

A = 8.117 sq. ft

Hence, the area of the irregular figure to the nearest tenth is 8.12 sq. ft.

Learn more about shapes here:

https://brainly.com/question/28756579

#SPJ1

A claw arcade machine contains stuffed animals and mystery boxes.

A claw arcade machine is a popular type of game machine found in many arcades and amusement parks. It typically consists of a glass cabinet that contains a variety of stuffed animals and other prizes, such as mystery boxes, that can be won by using a mechanical claw.

The player inserts a designated amount of money and then uses the joystick to position the claw over the desired prize. Once the player is satisfied with the claw's position, they press a button to make the claw descend and attempt to grab the prize. If the claw is successful in grabbing the prize, it will lift it up and drop it into the prize chute, where the player can then collect it.

The prizes in a claw machine can vary from small plush toys to larger stuffed animals, and even mystery boxes that contain unknown items or a chance to win a bigger prize. The claw's strength and grip are adjustable, which can make winning a prize more difficult or easier depending on the machine's settings.

Claw machines are a popular form of entertainment for all ages, and the thrill of successfully grabbing a coveted prize can be a source of excitement and satisfaction for players.

To more about machine :https://brainly.com/question/2555822

#SPJ1

The interpretation of the solution of the graph can be: the solution (6, 64) on the graph represents that after 6 minutes, there are 64 gallons of water.

The solution to a system that is plotted on a graph is the coordinates of the point interception of the graph.

Therefore, the solution (6, 64) represents a point on the graph of a relationship between time in minutes (represented by the x-axis) and water in gallons (represented by the y-axis).

The solution tells us that at 6 minutes, the water level is 64 gallons. In other words, (6, 64) on the graph, represents the amount of water in the tank over time.

Learn more about the solution of a graph on:

https://brainly.com/question/25799000

#SPJ1

The length of the apothem of the pentagon is approximately 11 meters.

Polygon is defined as a geometric shape that is composed of 3 or more sides these sides are equal in length, and an equal measure of angle at the vertex,

Examples of polygons, equilateral triangles, squares, pentagons etc.

Here, we have,

To solve this problem, we can use the formula for the area of a regular pentagon:

A = (5/2) × s × a

Where A is the area of the pentagon, s is the length of one side, and a is the apothem (the distance from the center of the pentagon to the midpoint of a side).

We know that the area of the pentagon is 118.25 square meters and the length of one side is 4.3 meters. We can substitute these values into the formula and solve for the apothem:

118.25 = (5/2) × 4.3 × a

Divide both sides by (5/2) x 4.3:

a = 118.25 / ((5/2) × 4.3)

 = 118.25 / 10.75 ≈ 11 meters

Therefore, the length of the apothem of the pentagon is approximately 11 meters.

Learn more about polygon here:

brainly.com/question/24464711

#SPJ1