Find the surface area of each triangular prism.
Also don't mind my writing on the paper

Therefore, the expression that represents the area of the rectangle is A(x) = mnx² + (mc + bn)x + bc.

In mathematics, a polynomial is a mathematical expression consisting of variables (also known as indeterminates) and coefficients, which are combined using only the operations of addition, subtraction, multiplication, and non-negative integer exponents.

Here,

Part A:

Let's assume that the length of the rectangle is represented by the linear polynomial L(x) = mx + b, where m is the slope of the line and b is the y-intercept. Similarly, let's represent the width of the rectangle by the linear polynomial W(x) = nx + c, where n is the slope of the line and c is the y-intercept.

The area of the rectangle is given by multiplying the length and width of the rectangle, so we can express the area A(x) as:

A(x) = L(x) * W(x)

= (mx + b) * (nx + c)

= mnx² + (mc + bn)x + bc

Part B:

The degree of the polynomial A(x) is 2, which makes it a quadratic polynomial. The classification of the polynomial A(x) is that of a concave upward parabola. The degree of the polynomial is 2 because of the presence of the quadratic term mnx² in the expression for the area. The classification of the polynomial as a concave upward parabola is because the coefficient of the x² term is positive (i.e., mn > 0), and this causes the graph of the polynomial to curve upwards.

Part C:

Closure under multiplication means that if we multiply two numbers in a certain set, the result is always within that same set. In the context of the dimensions and area of a rectangle, closure under multiplication applies because if we multiply the length and width (which are both represented by linear polynomials), the resulting area (which is represented by a quadratic polynomial) is still within the same set of polynomial functions. Specifically, multiplying two linear polynomials results in a quadratic polynomial, and since polynomial functions are closed under multiplication, the resulting area polynomial is still a polynomial function. This means that the area of the rectangle can be represented by a single polynomial function, which is useful for various mathematical computations and applications.

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Answer:

You're right -- it's B!

Step-by-step explanation:

When raising a power to a power, multiply exponents. The answer would be D if it were 4^6 times 4^3, but it's (4^6)^3, so I'm not sure what is happening to the computer.

Step-by-step explanation:

Height = - 16 t^2  + 96 t + 4

   max will occur at   t =  - b/2a   =   -  96/(2*-16) = 3 seconds

The max height at t = 3

   Height = -16 (3^2) + 96 (3) + 4 = 148 ft

Answer: y= -6

Step-by-step explanation: use the slope formula and slope intercept; y=mx+b

The type of control chart should be used here is equals to C-chart. So, the right answer is option (c). The upper and lower control limits are 10 and 0 respectively.

We have a quality style manufactures self-assembling furniture.

Average Defect rate = 4 per day

Now, here we are checking the number of defective packages per day which is independent day to day and have a mean or average of 4 per day. So, we use here the C- chart one of type of control chart. Also, we have to draw control chart with 3-sigma control limits. Average defect Rate, c' = 4

We determine the control limits,

CL = 3 ( 3-sigma )

The upper control limit , UCL = c' + 3 √c'

= 4 + 3 √4 = 10

The lower limit, LCL= max ( 0, c' - 3 √c')

c' - 3 √c' = 4 - 3√4 = -2, as it is less than zero, So, lower control limit, LCL= 0.00.

The construction of control chart always consists,

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Complete question:

quality style manufactures self-assembling furniture. to reduce the cost of returned orders, the manager of its quality control department inspects the final packages each day using randomly selected samples. the defects include wrong parts, missing connection parts, parts with apparent painting problems, and parts with rough surfaces. the average defect rate is four per day. owhich type of control chart should be used?

i) R chart

ii) p chart

iii) c chart

construct a control chart with 3-sigma control limits.

The sum of the given algebraic expression is =6g²-9g +4

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.

The given expression is

=3g²-g+(3g²-8g+4)

=3g²-g + 3g² -8g +4

=6g²-9g +4

The sum of the given algebraic expression is =6g²-9g +4

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Answer:

Step-by-step explanation:

Answer: 15.4% (rounded to the nearest tenth)

Step-by-step explanation:

The population of bacteria after I days is P(I) = 3700 * e^(0.11 * I) and  percentage rate of change per hour is 0.4285%

Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function.

The population of bacteria in the petri dish is growing exponentially at a rate of 11% per day. This means that the daily growth rate r is 0.11, or 11/100.

The formula for exponential growth is:

P(t) = P0 * e^(rt)

Where:

P(t) is the population after t days

P0 is the initial population

r is the growth rate per day

e is the mathematical constant approximately equal to 2.71828

Using the given information, we have:

P0 = 3700

r = 0.11

So, the formula for the population of bacteria after I days is:

P(I) = 3700 * e^(0.11 * I)

To find the percentage rate of change per hour, we need to convert the daily growth rate to an hourly growth rate. There are 24 hours in a day, so the hourly growth rate h is:

h = (1 + r)^(1/24) - 1

Substituting the value of r, we get:

h = (1 + 0.11)^(1/24) - 1

Simplifying this expression, we get:

h = 0.004285

So, the hourly growth rate is 0.4285%, or 0.004285 expressed as a decimal.

Therefore, the population of bacteria after I days is:

P(I) = 3700 * e^(0.11 * I)

And the percentage rate of change per hour is:

0.4285% (rounded to the nearest hundredth of a percent)

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The percentage rate of change per hour is approximately 0.46%.

How to calculate percentage?

The formula for exponential growth is:

N(t) = N0 * e raise to the power (r*t)

where:

N(t) is the population at time t

N0 is the initial population

r is the growth rate

e is the mathematical constant approximately equal to 2.71828

t is the time elapsed

In this case, we have:

N0 = 3700

r = 11% per day, or 0.11/24 = 0.0045833 per hour (since there are 24 hours in a day)

t is the time elapsed in days

To convert the time elapsed in days to hours, we can multiply t by 24. Therefore, the function for the population of bacteria after t days is:

f(t) = 3700 * e raise to the power (0.004583324t)

To round the coefficients in the function to four decimal places, we can use the round() function in Python:

f(t) = round(3700 * e**(0.004583324t), 4)

To determine the percentage rate of change per hour, we can calculate the percentage increase in the population per hour using the formula:

Percentage increase = (e raise to the power (r*h) - 1) * 100

where:

r is the growth rate per day

h is the time elapsed in hours

In this case, we have:

r = 11% per day, or 0.11/24 = 0.0045833 per hour

h = 1 hour

Plugging these values into the formula, we get:

Percentage increase = (e raise to the power (0.0045833*1) - 1) * 100 = 0.4646%

Therefore, the percentage rate of change per hour is approximately 0.46%.

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Answer: 24,500 ways

Step-by-step explanation:

The number of ways to select 4 appetizers out of 8 is given by the combination C(8,4) = 70. Similarly, the number of ways to select 3 main courses out of 5 is given by C(5,3) = 10, and the number of ways to select 3 desserts out of 7 is given by C(7,3) = 35.

To find the total number of ways to select the full meal consisting of 4 appetizers, 3 main courses, and 3 desserts, we can use the multiplication principle of counting, which states that the total number of ways to perform a sequence of independent tasks is equal to the product of the number of ways to perform each individual task.

Therefore, the total number of ways to select the full meal is given:

70 x 10 x 35 = 24,500

Hence, there are 24,500 ways to select 4 appetizers, 3 main courses, and 3 desserts from the given options.

Answer:

Step-by-step explanation:

The number of ways to select 4 appetizers out of 8 is given by the combination C(8,4) = 70.
Similarly, the number of ways to select 3 main courses out of 5 is given by C(5,3) = 10, and the number of ways to select 3 desserts out of 7 is given by C(7,3) = 35.

To find the total number of ways to select the full meal consisting of 4 appetizers, 3 main courses, and 3 desserts, we can use the multiplication principle of counting, which states that the total number of ways to perform a sequence of independent tasks is equal to the product of the number of ways to perform each individual task.

Therefore, the total number of ways to select the full meal is given:70 x 10 x 35 = 24,500.

Hence, there are 24,500 ways to select 4 appetizers, 3 main courses, and 3 desserts from the given options.

The given wood length does not satisfied the property of triangle through which it unable to create a triangle.

What about length of triangle?

The length of a triangle depends on the specific triangle you are referring to and the measurements of its sides. A triangle is a three-sided polygon, and its length is typically measured as the length of its sides.

There are different types of triangles based on their side lengths, such as equilateral triangles with three equal sides, isosceles triangles with two equal sides, and scalene triangles with no equal sides. The length of each side in these triangles can be determined using various methods, such as the Pythagorean theorem, the Law of Cosines, or trigonometric functions.

Define triangle property:

A triangle is a polygon with three sides and three angles. The properties of a triangle include:

According to the given information:

As, we know the property of triangle that sum of two side always greater than third side of the triangle. But when add 16 inch and 14 inch we get 30 inch as a result that is same length of the third side.

Hence, it is not greater than third side so, through the given length we can't create a triangle.

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To find the number that 495 is 55% of, we can use the percent proportion or percent equation.

Using the percent proportion:

Part/Whole = Percent/100

Let x be the whole (or total) number we are looking for. Then:

495/x = 55/100

We can cross-multiply to solve for x:

49500 = 55x

Dividing both sides by 55:

x = 900

Therefore, 495 is 55% of 900.

Using the percent equation:

Percent * Whole = Part

Let x be the whole (or total) number we are looking for. Then:

55% * x = 495

We can divide both sides by 0.55 to solve for x:

x = 495 / 0.55

Simplifying:

x = 900

Therefore, 495 is 55% of 900.

Answer: 55 %

Step-by-step explanation:

To find the number that $495 is 55% of, we can use the following proportion:

part/whole = percent/100

Let x be the number we are trying to find, then we can write:

495/x = 55/100

To solve for x, we can cross-multiply:

55x = 49500

Dividing both sides by 55, we get:

x = 900

Therefore, $495 is 55% of 900.

The area of triangle in given figure is = 60 cm²

A triangle is a three-sided polygon that is formed by connecting three non-collinear points in a plane.The sum of the interior angles of a triangle is always 180 degrees, and the length of each side can be determined by the application of the Pythagorean theorem or other trigonometric functions, depending on the given information. Triangles can also be classified based on the size of their angles and the lengths of their sides, which give rise to various types of triangle such as equilateral, isosceles, scalene, acute, right, and obtuse triangles.

According to quesrtion

Given height = 3cm

Base = 10cm

if the height is quadrupled then height = 4 × 3 = 12cm

Area = 1/2 × base × height

= 1/2 × 70 × 12

to solve this we get

Area = 60cm²

So, the area of this triangle is 60cm²

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The area of a triangle whose sides have lengths √70,√70,√and 28 is 10.45.

What is the area of the triangle?

A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.

The area of the triangle is defined as the product of half the base and the height of the triangle.

The area of the triangle =  (0.5)x b x h

Length of its base = b units

Its height = h units long,

Given;

The sides of the triangle √70,√70,√28

Now,

H²=70-28/4

H²=70-7

H=7.9

[tex]Area= b *\frac{ h}{2}[/tex]

[tex]=\sqrt{28}\frac{7.9}{2}[/tex]

=10.45

Therefore, the area of the triangle will be 10.45.

The complete question is-

What is the area of a triangle whose sides have length √{70},√{70}, and √{28} ?

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Answer:

13

Step-by-step explanation:

Evaluate the expression:

[tex]6-(5 \div a)^3 +8[/tex]

a = 5, plug in the value

[tex]6-(5\div 5)^3 + 8[/tex]

Divide in parentheses

[tex]6-1^3+8[/tex]

1^3 = 1, then subtract 6 and 1

[tex]5+8[/tex]

Add

[tex]13[/tex]

value of side x in the triangle is 6 ( simplest radical form with a rational denominator is 6/1).

A right triangle is a triangle that has one angle measuring 90 degrees, which is also called a right angle. The hypotenuse is the side that faces the right angle, while the legs are the other two sides.

Trigonometric functions are a set of mathematical functions used to relate the angles and sides of a right triangle. Sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent are the six fundamental trigonometric functions (cot).

In the given right angles triangle

Using trigonomteric function

Tan30°=√12/x

1/√3=√12/x

x=√12×√3

x=√36

x=6

Hence, value of side x in the triangle is 6.

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The measure of following values for the given circle is:

Sector AE = (2/3)π square units

Sector AB = (10/9)π square units

Sector ECB = (1/3)π square units

Angle BOC = 160 degrees

In geometry, a circle is a two-dimensional shape that is defined as the set of all points in a plane that are equidistant from a given point called the center. The distance from the center to any point on the circle is called the radius of the circle.

Here,

Sector AE:

The central angle of 60 degrees represents one-sixth (60/360) of the circle, so the sector AE has an area of one-sixth of the total area of the circle. The area of the circle is πr² = 4π square units, so the area of sector AE is:

(1/6) x 4π = (2/3)π square units

Sector AB:

The central angle of 50 degrees represents 5/18 (50/360) of the circle, so the sector AB has an area of 5/18 of the total area of the circle. The area of the circle is πr² = 4π square units, so the area of sector AB is:

(5/18) x 4π = (10/9)π square units

Sector ECB:

Since angles EOC and BOC are complementary (they add up to 90 degrees), the central angles they subtend are also complementary. Therefore, the central angle of sector ECB is 90 - 60 = 30 degrees. This represents one-twelfth (30/360) of the circle, so the sector ECB has an area of one-twelfth of the total area of the circle. The area of the circle is πr² = 4π square units, so the area of sector ECB is:

(1/12) x 4π = (1/3)π square units

Angle BOC:

Since angles AOB and COE are both right angles (as they subtend diameters of the circle), we know that angle AOC is 90 degrees. Therefore, angle BOC is:

360 - 90 - 60 - 50 = 160 degrees

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The probability that Sean will make more than Evan on a randomly selected week is approximately 0.3446 or 34.46%.

To calculate the probability that Sean will make more than Evan in a randomly selected week, we need to compare their incomes in terms of standard deviations from the mean.

First, we need to calculate the difference between their means:

Mean difference = Sean's mean income - Evan's mean income = $225 - $240 = -$15

Next, we need to calculate the standard deviation of the difference between their incomes:

Standard deviation of difference = √[(Sean's standard deviation)^2 + (Evan's standard deviation)^2] = √[(35)^2 + (15)^2] = 37.42

Now, we can use a z-score table to find the probability that Sean's income will be higher than Evan's income:

Z-score = (Sean's income - Evan's income - Mean difference) / Standard deviation of difference = (225 - 240 - (-15)) / 37.42 = 0.40

From the z-score table, we find that the probability of a z-score of 0.40 or higher is 0.3446.

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The number which could be added to both sides of the quadratic equation to complete the square is; -2.25.

What in mathematics is a quadratic equation?

ax² + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. Real or complicated solutions are also possible.

The quadratic equations give in the task content is; 1=x²-3x. Hence, to express the equation by completing the square method; we have;

1 - 2.25 = (x -3/2)² - 2.25

Hence, the number which should be added to both sides of the equation is; -2.25.

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We have to solve all of the parts of the given problem using our understanding of a sample and a population. It is given below.

A sample is taken when you want to take data from a specific set and then make observations based on that. A population is, on the other hand, the complete set that you want to make your observations from.

In the given problem -

A. To find how many books are published in one week by a famous publishing company - We are going to use a sample because we need to observe under s set category - one week.

B. To test a new drug produced by a biotech company - We are going to use a population because we need to monitor all individuals who take this drug.

C. To find the number of men and women working in an IT company with 600 people - We use a population here because we are going to use the data of all the people in the company.

D. To estimate the average salary of doctors in California - We use a sample here because the set category is California.

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Answer:

To find the slope between two points (x1, y1) and (x2, y2), we use the formula:

slope = (y2 - y1) / (x2 - x1)

Using the given points P(-11, -24) and Q(21, 40), we can substitute the values into the formula:

slope = (40 - (-24)) / (21 - (-11))

slope = 64 / 32

Therefore, the slope between points P(-11, -24) and Q(21, 40) is 2.

Answer:

2

Step-by-step explanation:

To find the slope, we can use the slope formula

m = ( y2-y1)/(x2-x1)

    = ( 40 - -24)/(21 - -11)

    = ( 40+24)/(21+11)

    = 64/32

    = 2

Kim must receive 75 stickers if Jim gets 60 stickers.

1. Since Kim receives 4 stickers more than Jim, and Kim receives 20 stickers,

we can determine the number of stickers Jim receives:
Jim's stickers = Kim's stickers - 4
Jim's stickers = 20 - 4
Jim's stickers = 16
2. The ratio of Kim's stickers to Jim's stickers is:
Kim's stickers : Jim's stickers
20 : 16
3. To simplify the ratio, divide both numbers by their greatest common divisor (4):
(20/4) : (16/4)
5 : 4
So, the ratio of Kim's stickers to Jim's stickers is 5:4.
4. If Jim receives 60 stickers, we can determine how many stickers Kim must receive using the ratio 5:4:
4 units = 60 stickers (Jim's)
1 unit = 60 stickers / 4
1 unit = 15 stickers
Since Kim has 5 units in the ratio:
Kim's stickers = 5 units * 15 stickers/unit
Kim's stickers = 75 stickers.

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(a) (i) 0.3174 = 31.74% probability of a defect

(ii) The expected number of defects for a 1,000-unit production run is 317.

(b) (i) 0.0026 = 0.26% probability of a defect

(ii) The expected number of defects for a 1,000-unit production run is 3.

(C) Reduces the process standard deviation and causes no change in the number of defects.

When the distribution is normal, we use the z-score formula.

In a set with mean  and standard deviation, the score of a measure X is given by:

         Z = X-μ /σ

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Question a:

We have that: μ = 10 and σ = 0.12

(i). Calculate the probability of a defect.

Less than 9.88 or greater than 10.12. These probabilities are equal, so we find one and multiply by 2.

Probability of less than 9.88:

This is the p-value of Z when X = 9.88. Thus,

  Z = X-μ /σ

⇒ Z = 9.88 - 10/0.12

⇒ Z = -1, has a p-value of 0.1587

⇒ 2× 0.1587 = 0.3174

This means 0.3174 = 31.74% probability of a defect

(ii)  Calculate the expected number of defects for a 1,000-unit production run.

The expected number of defects is 31.74% of 1000. So

0.3174*1000 = 317.4

Rounding to the nearest integer

The expected number of defects for a 1,000-unit production run is 317.

Question (b):

The mean remains the same, but the standard deviation is now

(i) Calculate the probability of a defect.

Less than 9.88 or greater than 10.12. These probabilities are equal, so we find one and multiply by 2.

Probability of less than 9.88:

This is the p-value of Z when X = 9.88. Thus,

   Z = X-μ /σ

⇒ Z = 9.88 -10/0.04

⇒ Z = -3

⇒ Z = -3, has a p-value of 0.0013

which means 2× 0.0013 = 0.0026

from which 0.0026 = 0.26% probability of a defect

(ii) Calculate the expected number of defects for a 1,000-unit production run. The expected number of defects is 31.74% of 1000. Thus,

⇒ 0.0026*1000 = 2.6

Rounding to the nearest integer

The expected number of defects for a 1,000-unit production run is 3.

(C) The advantage of reducing process variation, thereby causing problem limits to be at a greater number of standard deviations from the mean Reduces the process standard deviation and causes no change in the number of defects.

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So, the largest angle in quadrilateral PQRS is < 120 degrees.

A cyclic quadrilateral is what?

A quadrilateral that may be encircled by a circle is known as a cyclic quadrilateral.

Considering that,<P=3x , <Q=4x and <R=5x

∠P + ∠R = 180º            ∠Q + ∠S = 180º

Then we can write

3x+4x+5x+<S=360

12x+<S=360

<S=360-12x

We are aware that in a cyclic quadrilateral, the largest angle lies opposite the smallest angle.

Hence, in order to determine the largest angle, we must first determine the smallest angle.

P being the smallest angle leads us to believe that it is equal to x.

Therefore:

x+4x+5x+<s=360

10x+<s=360

<S=360-10x

therefore, Largest angle

- 10x < 360 - (10 * 24) = 120

So, the largest angle in quadrilateral PQRS is less than 120 degrees.

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To test if p - 1 is a factor of p^2 + p + p - k, we can use synthetic division.

Place the coefficients of p^2 + p + p - k in the top row of the division table, and write (p - 1) to the left, outside of the table:

       | 1   1   1   -k

    1  |__________

       |  

Bring down the first coefficient of 1:

       | 1   1   1   -k

    1  |__________

       |      1  

Multiply the 1 by (p - 1) to get p - 1:

       | 1   1   1   -k

    1  |__________

       |      1  

       |__________

Add the entries diagonally (1 and 1) to get 2 and write the result under the next coefficient of 1:

       | 1   1   1   -k

    1  |__________

       |      1  

       |__________

             2  

Multiply the 2 by (p - 1) to get 2p - 2:

       | 1   1   1   -k

    1  |__________

       |      1  

       |__________

             2  

       -2p+2      

Add the entries diagonally (2 and 1) to get 3 and write the result under the next coefficient of 1:

       | 1   1   1   -k

    1  |__________

       |      1  

       |__________

             2  

       -2p+2      

       ________

            3  

Multiply the 3 by (p - 1) to get 3p - 3:

       | 1   1   1   -k

    1  |__________

       |      1  

       |__________

             2  

       -2p+2      

       ________

            3  

       -3p+3    

Add the entries diagonally (3 and 1) to get 4 and write the result under the next coefficient of -k:

       | 1   1   1   -k

    1  |__________

       |      1  

       |__________

             2  

       -2p+2      

       ________

            3  

       -3p+3    

       ________

                 4

The remainder is 4, which means that p - 1 is a factor of p^2 + p + p - k if k = 4.

Therefore, the value of k is 4.

The first, second, and third one.

Emily has to pay $41.31 for the shirt after adding coupon and discount.

How to find the Cost Price (CP) of any discounted item?

Lets say CP = 54 and the discount is of 15% i.e. marked price

So, Marked Price= 85% of CP = 45.9

Lets apply the additional coupon of 10% on Marked Price.

Therefore, the payment amount = 90% of MP

payment amount = $41.31

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