Help me pls. This needs to be solved by the matrix method
To produce one unit of A requires 3 units of M1, 2 units of M2 and 6 units of M3. To produce one unit of B requires 3 units of M1, 2 units of M2, and 4 units of M3. To produce one unit of C requires 4 units of M3, 5 units of M1, and 7 units of M2. The manufacturer has an everyday available quantity of 71 thousand units of M1, 81 thousand units of M2 and 92 thousand units of M3.

The smallest possible value of k is 0.

Let's call a_n = n + k.

We see that this sequence satisfies both conditions (1) and (2).

For condition (1),

Since a_n = n + k, the sequence is non-decreasing as long as [tex]$k \ge 0$[/tex].

For condition (2),

Since a_n = n + k,

We have [tex]$n(n + 1)/2 \ge a_n = n + k$[/tex], which rearranges to [tex]$k \ge -n$[/tex].

To make sure that k is an integer,

we take the ceiling of -n, i.e., [tex]k \ge \lceil -n \rceil[/tex]

Therefore, the smallest such k is [tex]\max{0, \lceil -n \rceil} = \lceil -n \rceil[/tex]

Since we want to find the smallest k for any given n,

we need to find the smallest n such that [-n] is positive,

Since k must be positive.

The smallest positive n is n = 1, and [-1]=0,

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COMPLETE QUESTION

Military radar and missile detection systems are designed to warn a country of an enemy attack. A reliability question is whether a detection system will be able to identify an attack and issue a warning. Assume that a particular detection system has a .90 probability of detecting a missile attack. Use the binomial probability distribution to answer the following questions.

a. What is the probability that a single detection system will detect an attack?

b. If two detection systems are installed in the same area and operate independently, what is the probability that at least one of the systems will detect the attack?

c. If three systems are installed, what is the probability that at least one of the systems will detect the attack?

d. Would you recommend that multiple detection systems be used?

Explain.

ANSWER:-

a. The probability that a single detection system will detect an attack is, 0.90.

b. If two detection systems are installed, the probability that at least one of the systems will detect the attack is, 0.81

c. If three systems are installed, the probability that at least one of the systems will detect the attack is, 0.927

Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.

Probability of Event = Favorable Outcomes/Total Outcomes = X/n

a. The probability that a single detection system will detect an attack is 0.90.

b. If two detection systems are installed in the same area and operate independently, the probability that at least one of the systems will detect the attack is given by:

P(at least one detection) = 1 - P(neither detection)

where P(neither detection) is the probability that neither of the two systems detects the attack. Since the systems operate independently, the probability of neither detection can be calculated as:

P(neither detection) = (1 - 0.90)²

                                 = 0.19

P(at least one detection) = 1 - 0.19

                                         = 0.81

So the probability that at least one of the two systems will detect the attack is 0.81.

c. If three systems are installed, the probability that at least one of the systems will detect the attack is given by:

P(at least one detection) = 1 - P(neither detection)

where P(neither detection) is the probability that neither of the three systems detects the attack. Since the systems operate independently, the probability of neither detection can be calculated as:

P(neither detection) = (1 - 0.90)³

                                 = 0.073

P(at least one detection) = 1 - 0.073

                                         = 0.927

So the probability that at least one of the three systems will detect the attack is 0.927.

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MTH1W is a grade 9 mathematics course that covers key mathematical concepts and problem-solving skills. Topics covered include algebraic expressions and equations, graphs of linear relationships, solving systems of linear equations, quadratic relationships, trigonometry, similar triangles and circles, Pythagorean theorem, distance formula, area and volume of geometric shapes, and statistics and probability. This course helps students build a strong foundation in algebra and geometry, and develop important problem-solving skills for future math courses. The sections on algebraic expressions, linear and quadratic relationships, and trigonometry provide students with the skills to manipulate mathematical expressions and solve real-world problems. The sections on geometry and statistics cover key concepts in these areas, providing students with a well-rounded understanding of mathematics.

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The Dante's Inferno Test has banished you to the Eigth Level of Hell - the Malebolge! Here is how you matched up against all the levels: Level, Score. Purgatory ...

Maximum and careful attention was done to avoid any wrongly tagging any categories , but mistakes may happen.

The point slope form of the equation is y-5=4(x-3).

What is point slope form of the equation?

The slope of a straight line and a point on the line are both components of the point-slope form. The equations of infinite lines with a specified slope can be written, however when we specify that the line passes through a certain point, we obtain a singular straight line. In order to calculate the equation of a straight line in the point-slope form, only the line's slope and a point on it are needed.

Here the given point [tex](x_1,y_1)=(3,5)[/tex] and slope m=4 then using equation of line formula,

=> [tex]y-y_1=m(x-x_1)[/tex]

=> y-5 =4(x-3)

Hence the point slope form of the equation is y-5=4(x-3).

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if the area of a circle is 36.2 square inches, the radius of the circle to the nearest tenth is 3.4 inches.

The area of a circle is 36.2 square inches and we have to determine the radius of the circle to the nearest tenth.

The formula of the area of the circle is given as:

Area of circle = πR², where R is the radius of the circle.

We are given, Area of the circle = 36.2 square inches

So, πR² = 36.2 square inches

Now, π = 3.14

3.14R² = 36.2 square inches

R² = 36.2/3.14

R² = 11.53

Taking square root on both sides

R = √11.53

R = 3.39 inches

R ≈ 3.4 inch (Rounded to the nearest tenth)

Hence, the radius of the circle to the nearest tenth is 3.4 inches.

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Answer:

2.02

Step-by-step explanation:

2% annual rate

compound monthly so every month you get 2%/12 =0.167%

effectively in a year = 12 months you'll get

(1+0.167%)^12 =  2.02%

input 2.02

Answer:

Step-by-step explanation: (x*2)+(6*2)

Answer:

below

Step-by-step explanation:

1 is FIRST degree

degree of 2 would be a second degree

Why the length of the third (3) side of a triangle cannot be less than the total of any two (2) of its sides is shown in the diagram: B. by demonstrating that two sides with lengths of 4 and 3 cannot ever come together to form a vertex.

The definition of a triangle is a two-dimensional geometric figure with exactly three (3) sides, three (3) vertices, and three (3) angles. According to the length of their sides, triangles fall into one of the following three (3) categories:

By applying the Triangle Inequality Theorem to this diagram (see attachment), we have:

4 + 12 > 3 (True).

3 + 12 > 4 (True).

4 + 3 > 12 (False).

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The relationship of proportion is shown below.

In general, the term "proportion" refers to a part, share, or amount that is compared to a total.

According to the concept of proportion, two ratios are in proportion when they are equal.

According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Correlation is the term used to describe the relationship between two variables. The degree of link or correlation between two variables is known as proportionality or variation.

It comes in two types: direct variation or percentage, which indicates a positive correlation between the two variables. It occurs when the two variables change simultaneously.

In contrast, a negative relationship or correlation is shown by an indirect variation or proportion. Specifically, the reverse of what occurs with direct variation.

One rises while the other variables, you guessed it, fall. Because you can establish and identify how two variables connect to one another, correlations are crucial to take into account.

Note that y=1/x (indirect) and x = y (direct).

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Answer:

This is a system of equations problem. We can set up the equations as follows:

3x + 4y = 430 (1)

x + y = 125 (2)

Where x is the number of tacos sold and y is the number of burritos sold.

We can solve for x in equation (2) by subtracting y from both sides:

x = 125 - y

Now we can substitute this expression for x into equation (1):

3(125 - y) + 4y = 430

375 - 3y + 4y = 430

3y + 4y = 430 - 375

y = 55

So, 55 burritos were sold on Tuesday. To find the number of tacos sold, we can use equation (2) and substitute in the value we found for y:

x + 55 = 125

x = 70

Therefore, 70 tacos were sold on Tuesday.

Answer:

x = 15

Step-by-step explanation:

30 + 4x = 90   These angles are complementary which means that they add to 90.  Subtract 30 from both sides

30 - 30 + 4x = 90 - 30

4x = 60   Divide both sides by 4

x = 15

Answer:

A train traveling at a constant speed of 105 miles per hour covers a distance of 315 miles in 3 hours. To find the distance in feet, we need to convert miles to feet:

315 miles * 5,280 feet/mile = 1,654,400 feet

So, in 3 seconds, the train travels approximately:

1,654,400 feet / (60 seconds/minute * 60 minutes/hour) = 9,072 feet

Therefore, in 3 seconds, the train traveling at a constant speed of 105 miles per hour travels approximately 9,072 feet.

Answer:

To convert miles per hour to feet per second, multiply the speed in mph by 5280/3600 = 1.46667.

105 mph * 1.46667 ft/s = 153.333 ft/s

To find the distance travelled in 3 seconds, multiply the speed by time:

153.333 ft/s * 3 s = 315 ft

Answer:

this is a true statement

Step-by-step explanation:

The factor of [tex]6x^{2}y+8-30y-40[/tex] is 2 ( [tex]3x^{2}y-15y-20[/tex] ).

The factor is a number or quantity by which a given number, quantity, or expression is multiplied to produce another number, quantity, or expression. Factors are usually whole numbers, but they can also be expressions or fractions. Factors are used to simplify or solve equations and expressions. Factors can also be used to determine the greatest common factor (GCF) of two or more numbers or expressions.

The first step is to factor out the greatest common factor (GCF), which in this case is 2. The GCF of [tex]6x^{2}y+8-30y-40[/tex] is 2. Once the GCF is factored out, the expression can be written as 2([tex]3x^{2}y-15y-20[/tex]). Finally, the remaining factors can be combined to get the final factor of 2([tex]3x^{2}y-15y-20[/tex]).

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1.1. Given any negative real number s, the cube root of s is negative.

1.2. For any real number s, if s is negative, then the cube root of s is negative.

1.3. If a real number s is negative, then the cube root of s is negative.

The cube root of a real number can be either positive or negative, depending upon the sign of the original number. If the original number is positive, then the cube root can be either positive or negative.

If the original number is negative, then the cube root must and should be negative. This is because multiplying any negative number by itself three times will result in a negative number.

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To find the regular price of the item before the markdown, we can use the following formula:

Regular Price = Markdown / (1 - (Discount Percentage / 100))

Here, the discount percentage is 30%, and the markdown is $237.00.

Regular Price = 237 / (1 - (30 / 100))

Regular Price = 237 / 0.7

Regular Price = $341.43

So the regular price of the item before the markdown was $341.43.

Answer:

$341.43.

Step-by-step explanation:

Formula:

Original Price = Markdown ÷ [1 - (Discount Percentage ÷ 100)]

(The mardown would be $237.00 and the discount percentage would be 30%)

Modified Formula (to match out equation:

Regular Price = 237.00 ÷ [1 - (30 ÷ 100)]

= 237 ÷ 0.7

= $341.43

Answer: R-squared

Step-by-step explanation:

pronounced ARRRrrr-squared

As per the standard deviation, the probability of 8≤ X < 11 is 0.1429.

A random variable X is a mathematical representation of the possible values that a random process or experiment can take on. X has a normal distribution, meaning that its distribution follows a bell-shaped curve.

The standard deviation measures how spread out the values of X are around the mean.

If X has a mean of μ and a standard deviation of 2, then 68% of the values of X will fall within one standard deviation of the mean.

This means that about 68% of the values of X will fall between μ-2 and μ+2.

To find the probability that X falls between 8 and 11, we need to use the cumulative distribution function (CDF).  

Using the standard normal distribution table, we find that P(X < 8) = 0.8413 and P(X < 11) = 0.9842.

Thus, the probability that 8≤ X < 11 is

=> 0.9842 - 0.8413 = 0.1429,

which rounded off to the 4th decimal place is 0.1429.

Complete Question:

Random variable X has a normal distribution with mean μ and standard deviation 2. The pdf f(x) of X satisfies the following conditions: (A) f(6) > f(16), (B) f(1) < f(17). When u is an integer, what is P(8≤ X < 11) (round off to the 4th decimal place)?

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If 7 in every 9 packets of crisps in a box are salt and vinegar, then 9-7 = 2 packets of crisps in a box are plain.

If there are 63 packets of salt and vinegar in the box, then 63 packets / 7 = 9 groups of 9 packets in the box.

So, 9 groups * 2 plain crisps = 18 packets of plain crisps in the box.

Your Welcome :) Hope you have a great day!

Answer:

14

Step-by-step explanation:

9/9 - 7/9 = 2/9

2 in every 9 packets of ceisps in a box are plain crisps.

Then:

63*2/9 = 126/9

= 14

Answer:

A

Step-by-step explanation:

the sum of the arcs in a circle = 360°

here the major arc = 260° , then

the minor arc = 360° - 260° = 100°

the measure of the tangent- tangent angle x is half the difference of the measures of the intercepted arcs, that is

x = [tex]\frac{1}{2}[/tex] (260 - 100) = [tex]\frac{1}{2}[/tex] × 160 = 80

Given the L-shaped line

where p 1 = ( 0, 2, 2 )

L → Р = Ро + tυwhere p = ( x, y, z ) and p 0 = ( 1, 1, 0 ) and v = ( 1, 2, 2 )

The components p 1 and L constitute a plane with the normal vector n given by

→ \sn \s= \sλ \s1 \s( \sp \s0 \s− \sp \s1 \s)

when R = 1

L 1 is the desired line and is orthogonal to L, so

L 1 p = p 1 + t 1 v 1 = p 1 + t 1 v 1 where

2 v n with 2 R v 1 = 2 v n with 2 R

It is more advantageous to parameterize relations or implicit equations since they become explicit functions once parameterized.

A circle, for example, may be defined as x 2 + y 2 = r 2. When a relation passes the vertical line test, you know it is a function; a circle does not.

When you try to define the circle directly, you get: y = r 2 x 2. Again, this is not a function; it is the combination of two functions.

When we parameterize a circle, we get: x = r cos t

y \s= \sr \ssin \st

t \s∈ \sR

Both x and y are explicit functions that may be plotted, integrated, or differentiated as needed.

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The parametric equation of the plane is x = 11/6 t, y = -5/2t, z = 1 1/2 t.

(x, y, z) = (0, 2, 2) + t(i - j +2 k)

A plane that is parallel to this line will have the general equation:

x - y + 2z = c

We make it contain the point by substituting in the point and solving for c:

0 + 2 +2(2) = 4

c = 4

The plane x - y + 2z = 4 contains the point (0, 1, 2) and is perpendicular to the line.

To find the point where the line intersects the plane, substitute the parametric equations of the line into the equation of the plane:

x - y + 2z = 4

(1 + t) − (2 − t) + 2(2t) = 4

1+t-2+t+ 4t = 4

6t = 5

t = 5/6

x = 11/6, y = 7/6, z=5/3

The line intersects the plane at the point (11/6, 7/6, 5/3)

The vector, v, from the given point to the intersection point

v = (11/6 - 0)i + (7/6 - 2)j + (5/3 - 2)k

v = 11/6 i -5/2 j - 1/2 k

The vector equation of the line is:

(x, y, z) = (0, 2, 2) + t (11/6 i -5/2 j - 1/2 k)

The parametric equations are:

x = 11/6 t,

y = -5/2t,

z = 1 1/2 t

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The probability that a defective component will be detected only by the first inspector is 0.19

The probability that a defective component will be detected by exactly one of the two inspectors is 0.38

The probability that all three defective components in a batch escape detection by both inspectors is 0.

It is given that The first inspector detects 81% of all defectives that are present, and the second inspector does likewise.

Therefore P(A)=P(B)=81%=0.81

At least one inspector does not detect a defect on 38% of all defective components.

Therefore, bar P(A∩B)=0.38

As we know:

bar P(A∩B)=1-P(A∩B)=0.38

P(A∩B)=1-0.38=0.62

A defective component will be detected only by the first inspector.

P(A∩barB)=P(A)-P(A∩B)

=0.81-0.62

P(A∩barB)=0.19

The probability that a defective component will be detected only by the first inspector is 0.19

Part (B) A defective component will be detected by exactly one of the two inspectors.

This can be written as: P(A∩barB)+P(barA∩B)

As we know:

P(barA∩B)=P(B)-P(A∩B) and P(A∩bar B)=P(A)-P(A∩B)

Substitute the respective values we get:

P(A∩ barB)+P(bar A∩B)=P(A)+P(B)-2P(A∩B)

=0.81+0.81-2(0.62)

=1.62-1.24

P(A∩ barB)+P(bar A∩B)=0.38

The probability that a defective component will be detected by exactly one of the two inspectors is 0.38

Part (C) All three defective components in a batch escape detection by both inspectors

This can be written as: P(bar A∪ bar B)-P(bar A∩B)-P(A∩ barB)

As we know bar P(A∩B)=P(bar A∪ bar B)=0.38

From part (B): P(bar A∩B)+P(A∩bar B)=0.38

This can be written as:

P(bar A∪ bar B)-P(bar A∩B)-P(A∩bar B)=0.38-0.38=0

The probability that all three defective components in a batch escape detection by both inspectors is 0

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The profits at each level of bicycle production vary with the total cost, total revenue, and level of production, the profits are as follows:

One bike: -$30

Two bikes: $3

Three bikes: $40

Four bikes: $70

Five bikes: $90

Six bikes: $90

Seven bikes: $80

The profit is the amount retained by the business after paying off the expenses and other costs. It is determined by preparing the profit and loss account at the end of each financial year.

The formula used to determine the profit is:

Profit = Total revenue - Total cost

The computation of profit for each production level is shown in the image attached below.

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Answer:

Inverse

Step-by-step explanation:

The hypotenuse of a right triangle with side lengths 4cm and 5cm is √41 cm.

Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

It is expressed as;

hypotenuse = √( a² + b² )

Given that;

Plug in the given values and solve for hypotenuse.

hypotenuse = √( a² + b² )

hypotenuse = √( 4² + 5² )

hypotenuse = √( 16 + 25 )

hypotenuse = √41

Therefore, the hypotenuse is √41.

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The equation of line that is tangent to the function f is y = 8x - 6 and

y = 8x + 10.

Let's start with the generic equation of a line:

y = ax + b

This line must be parallel to the line 8x - y + 5 = 0, and it must have the same slope.

The slope of the line 8x - y + 5 = 0 is 8, so our line has a = 8 :

y = 8x + b

Now we must determine the b values that make this line tangent to the function f(x) = 2x².

First, compute the derivative of f(x) in relation to x:

4x = df(x) / dx

For any value of x, this derivative is the slope of the tangent line to the function. We require a slope of 8, so:

4x = 8

x = 8/4

x = ±2

To calculate the y-values, we have:

f(1) = 2 x 1² = 2

f(-1) = 2 x (-1)² = 2

Using the points (1,2) and (-1,2) from our parallel line, we get:

2 = 8 x 1 + b is the first line using (1,2).

b = -6

(-1,2) is used in the second line: 2 = 8 x -1 + b

b = 10

The value of b represents the line's y-intercept, so the line with a smaller y-intercept is y = 8x -6, and the line with a larger y-intercept is y = 8x + 10.

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