Use this for question 6 to 8:
Four machines A, B, C and D produce respectively 30%, 30%, 15% and 25% of the total number of
items from a factory. The percentage of defective output from these machines are 1%, 1.5%, 3% and
2% respectively. Given that an item is to be selected at random from the total output.
6: Find the probability that the item will be defective.
(a) 0.105
(2 marks)
(b) 0.017
(c) 0.007
(d) 0.170
7: If an item selected at random is found defective, what is the probability that it is produced by
machine A
(2 marks)
(2 marks)
(d) 0.007
(a) 0.018
(b) 0.015
(c) 0.111
8: Find the probability that the item is produce by machine D
(a) 0.294
(b) 0.034
(c) 0.118
(d) 0.253

Therefore , the solution of the given problem of inequality comes out to be x ≤ 48.

A relationship or collection of numbers without the equal sign is known as a mathematical inequality. Equilibrium is typically followed by equity. Inequality happens when two factors are not equal. Differences exist between variable equity and inequality. Because the digits are not identical or similar, the most typical symbol was selected (). Any difference, regardless of how small or large, can be used to evaluate values.

Here,

If each side of the frame can be at most 12 inches long, then the perimeter of the frame can be at most 4 x 12 = 48 inches.

So, the inequality that describes the problem is:

x ≤ 48.

Therefore , the solution of the given problem of inequality comes out to be x ≤ 48.

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The cost of nails can be represented as 12.99n, and the cost of screws can be represented as 14.99s.

The cost of buying nails and screws can be represented by a system of inequalities where "n" represents the number of boxes of nails and "s" represents the number of boxes of screws.

The cost of one box of nails is $12.99 and the cost of one box of screws is $14.99. Hence, the cost of "n" boxes of nails is represented by 12.99n and the cost of "s" boxes of screws is represented by 14.99s. The carpenter has a budget of $60 and can spend no more than that.

Therefore, the combined cost of buying nails and screws must be less than or equal to $60. This requirement can be represented by the inequality 12.99n + 14.99s <= 60.

To make the calculation easier, we can also express the inequality as n + s <= 4.62, where 4.62 is obtained by dividing $60 by $12.99. This system of inequalities represents the carpenter's budget constraint and helps to determine the number of boxes of nails and screws that can be purchased within the budget.

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Answer:

With a volume of 700 cubic feet and a height of 9 feet , the radius of cylinder is 3.49 feet after rounding to nearest hundredth.

To find the radius of a right cylinder, you need to know its volume and height. The formula for the volume of a cylinder is given by:

V = πr^2h

Where r is the radius, h is the height, and π is approximately equal to 3.14.

Given that the volume is 700 cubic feet and the height is 9 feet, we can substitute these values into the formula:

700 = πr^2 * 9

Dividing both sides by π * 9:

700 / (π * 9) = r^2

Taking the square root of both sides:

√(700 / (π * 9)) = r

Using a calculator and rounding to the nearest hundredth, we find that:

r ≈ 3.49

So the radius of the cylinder is approximately 3.49 feet.

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Match each quotient of the complex numbers accordingly as shown below.

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1. The real part of a complex number is represented by a, while the imaginary part is represented by bi.

No. 1

Multiply the numerator and denominator by 3-4i:

1/(3 + 4i) = 1/(3 + 4i)  * (3 - 4i)/(3 - 4i)  

             =  (3 - 4i)/(9 + 16)

             =  (3 - 4i)/25

             =  3/25 - 4/25 i

No. 2

Multiply the numerator and denominator by 3+4i:

1/(3 - 4i) = 1/(3 - 4i)  * (3 + 4i)/(3 + 4i)  

             =  (3 + 4i)/(9 + 16)

             =  (3 + 4i)/25

             =  3/25 + 4/25 i

No. 3

i/i = 1

   = 1 + 0i

No. 4

Multiply the numerator and denominator by 3-4i:

(3 - 4i)/(3 + 4i) = (3 - 4i)/(3 + 4i) * (3 - 4i)/(3 - 4i)

                       = (9 - 24i -16) / (9 + 16)

                       = (-7 - 24i) / 25

                       = -7/25 - 24i/25

No. 5

(3 - 4i)/ 1 = 3 - 4i

No. 6

Multiply the numerator and denominator by 3+4i:

(3 + 4i)/(3 - 4i) = (3 + 4i)/(3 - 4i) * (3 + 4i)/(3 + 4i)

                       = (9 + 24i -16) / (9 + 16)

                       = (-7 + 24i) / 25

                       = -7/25 + 24i/25

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Answer: 0.75

Step-by-step explanation:

The area of the lateral surfaces will be 192.55 square centimetres.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the prism in a two-dimensional plane is called as the area of the prism.

Given that there is a triangular prism having sides the height of the triangular side is 4.3 cm and its base is 5 cm.

The lateral surface area will be calculated as:-

SA = 2 x ( 5 x W ) + 10 x 50 + ( 1 / 2 ) x 5 x 4.3

W = √ ( 5² + 4.3²)

W = √43.49

W = 6.59 cm

SA = 2 x ( 10 x W ) + 10 x 50 + ( 1 / 2 ) x 5 x 4.3

SA = 2 x ( 10 x 6.59 ) + 10 x 5 + ( 1 / 2 ) x 5 x 4.3

SA = 131.8 + 50 + 10.75

SA = 192.55 square centimetres

Therefore, the area of the prism will be 192.55 square centimetres.

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Answer:

y = -17

Step-by-step explanation:

None

A negative number that have a value greater then 8 does not exist

From the question, we have the following parameters that can be used in our computation:

negative number that have a value greater then 8

The number 8 is a positive number

As a general rule:

No negative number is greater than a positive number

Hence, the negative number does not exist (DNE)

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This value can be rounded to 3 decimal places, which would be 3.800°F.

Values relative what made it up importance of something if can refer to an intangible concepts such as person principle of it tangible objects such as rare coin value where body widely across culture society and individual can even vary within the same individual over time.

To find the change in temperature during a 1.5-hour period after a storm began, it would be necessary to take two temperature readings, one before the storm began and one after the storm ended. By subtracting the two readings, the change in temperature can be determined. For example, if the temperature before the storm began was 75.4°F and the temperature after the storm ended was 79.2°F, the change in temperature would be 3.8°F. This value can be rounded to 3 decimal places, which would be 3.800°F.

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Answer:

16+X is the answer because 16 has no variable beside it X is also standing on it's own so they can't even group like terms

Answer:

Step-by-step explanation:

The actual length of the dragonfly if the drawing is 8. 5 cm, can be found to be 6. 375 mm

The scale on the science textbook is such that every 4 cm of the drawing of an insect is the same as 3 mm of the actual insect.

If a drawing is 8. 5 cm therefore, the actual length of the dragonfly would be :

= ( Drawing length of dragonfly x Scale of insect ) / Drawing scale of insect

The actual length is therefore :

= ( 8. 5 x 3 ) / 4

= 6. 375 mm

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Answer:

Step-by-step explanation:

The expression "11 increased by twice Grogan's height" can be written as:

11 + 2Grogan's height

For example, if Grogan's height is 5 feet, the expression would be:

11 + 2(5) = 11 + 10 = 21

21 is 18.75% of 112. Percentage is widely used to represent a difference or contrast between two numbers.

A percentage is a way to express a number as a fraction of 100. It is often used to express a change or a comparison between two numbers. The symbol for percentage is %, and it represents the fraction of 100. For example, 50% means 50 out of 100, or 1/2.

Percentages are often used to represent increases or decreases in a quantity, as well as ratios and proportions. For example, if the price of a product increases by 20%, it means the new price is 120% of the original price, or 1.2 times the original price. If a student scores 80% on a test, it means they answered 80 out of 100 questions correctly.

Percentages can be easily converted to decimals or fractions by dividing by 100. For example, 50% can be written as 0.5 as a decimal or 1/2 as a fraction. Similarly, 75% can be written as 0.75 as a decimal or 3/4 as a fraction.

To find what percent 21 is of 112, we can use the formula:

Percent = (Part ÷ Whole) x 100

In this case, the part is 21 and the whole is 112, so:

Percent = (21 ÷ 112) x 100

Percent = 0.1875 x 100

Percent = 18.75

Therefore, 21 is 18.75% of 112.

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The number of distinct 10-letter arrangements that can be formed from the letters in the word "statistics" is 40320, which can be calculated by finding the permutation of 8 objects taken 8 at a time

Permutation is a mathematical concept that deals with counting the number of ways to arrange a set of objects in a particular order.

The number of permutations of a set of n objects taken r at a time can be calculated using the formula:

=> n! / (n - r)!.

Where "n!" represents n factorial, which is the product of all positive integers less than or equal to n.

In this case, we are going to find out the number of distinct 10-letter arrangements that can be formed from the letters in the word "statistics".

In our case, the number of objects is 8 (the letters in the word "statistics") and we are taking 10 at a time, so the formula becomes:

=> 8! / (8 - 10)! = 8! / (-2)!.

The factorial of a negative number is undefined, so this case is not possible.

Since we cannot take more objects than the number of available objects, we have to find the number of permutations of 8 objects taken 8 at a time. The formula becomes:

=> 8! / (8 - 8)! = 8! / 0! = 8!.

Finally, 8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40320,

which means that there are 40320 distinct 10-letter arrangements that can be formed from the letters in the word "statistics".

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Answer:

Below

Step-by-step explanation:

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

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

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

x = -153

THIS EQUATION DOES SHOW x = -153

PERHAPS you MEANT this :

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

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

3/(24x) = -19.125      re-arrange

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

3/ (-19.125 * 24) = x = - 1/153      

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

Answer:

yes Priya's conclusion is incorrect

Step-by-step explanation:

x square will always be greater than the actual value of x

but in this expression

f (x ) = 10 * x²

g (x) = 3 * 2raise to the power x

priya's conclusion is incorrect because in the other expression the power of x is increasing exponentially so eventually g(x) will be greater than f(x)

as for x = 10

f(x) = 10 * 10² = 1000

g(x) = 3 * 2raise to power 10 = 3 * 1024 = 3072

For the triangle ABC the interior angles measures ∠A = 80°, ∠B = 58°, and ∠C = 42°.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

According to the angles of a triangle theorem, the sum of angles of a triangle is 180°.

The measure of ∠A = 80°.

The measure of ∠B = 8x + 2.

The measure of ∠C = 6x.

The equation is -

∠A + ∠B + ∠C = 180°

Substitute the values into the equation -

80° + 8x + 2 + 6x = 180

Collect the like terms -

8x + 6x = 180 - 80 - 2

14x = 98

x = 98/14

x = 7°

So, the measure of ∠B = 8(7) + 2 = 58°

The measure of ∠C = 6(7) = 42°

The interior angles of the triangle are 80°, 58° and 42°.

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A correlation coefficient of 0.8 or higher indicates a strong association between two variables, while a coefficient between 0.5 and 0.7 indicates a moderate association and a coefficient of 0.4 or lower indicates a weak association.

0.8 - Strong Association

0.25 - Weak Association

0.9 - Strong Association

0.65 - Moderate Association

The strength of a correlation is determined by its correlation coefficient. A correlation coefficient of 0.8 or higher is considered strong, a correlation coefficient between 0.5 and 0.7 is considered moderate, and a correlation coefficient of 0.4 or lower is considered weak. A correlation coefficient of 0.8 indicates a strong association between two variables, a correlation coefficient of 0.25 indicates a weak association, a correlation coefficient of 0.9 indicates a strong association, and a correlation coefficient of 0.65 indicates a moderate association.

A correlation coefficient of 0.8 or higher indicates a strong association between two variables, while a coefficient between 0.5 and 0.7 indicates a moderate association and a coefficient of 0.4 or lower indicates a weak association. For the given correlation coefficients, 0.8 and 0.9 indicate strong associations, 0.25 indicates a weak association, and 0.65 indicates a moderate association.

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Answer:

Step-by-step explanation:

36 divided by 4 is 9, so the answer would be 9

Part A: Each block will have an area of 128 square inches (8 in. x 16 in.), but the outside border of each block will be covered with blue paint.

Area is the measurement of the space contained within a two-dimensional surface.

The outside border of each block is 8 in. long and 16 in. high, for a total of 128 square inches of each block that is covered in blue paint.

Part B: The entire mural will have 25 identical blocks, so the total number of square inches of the entire mural that will be covered by white paint is 3,200 square inches (25 blocks x 128 square inches per block).

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Step-by-step explanation:

3p + (-)7.81 = -13.81

3p = -13.81 + 7.81

3p = -6

p = -6/3

p = -2

a) The sine and the cosine are given as follows:

b) The tangent is given by the sine divided by the cosine, as follows:

tan(Φ) = sin(Φ)/cos(Φ) = (8/17)/(15/17) = 8/15.

The three trigonometric ratios are defined as follows:

Applying the Pythagorean Theorem, the length of the hypotenuse is given as follows:

h² = 8² + 15²

h = sqrt(8² + 15²)

h = 17.

Considering that 8 is the opposite side and 15 is the adjacent side to the angle, the sine and the cosine are given as follows:

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The given mixed fraction can be written in decimal form as 1.5.

These are just improper fractions written as a sum of whole number and a proper fraction. (improper fraction has the upper value(also called numerator) bigger or equal to denominator(the bottom value) and proper fraction has numerator value is less than that of the denominator)

The given mixed fraction is [tex]1\frac{1}{2}[/tex].

Now, the given mixed fraction can be written as 3/2

3/2 can be written in decimal number as 1.5.

Decimal number 1.5 is between 1 and 2.

Therefore, the given mixed fraction can be written in decimal form as 1.5.

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The percentage of the students at the university which are foreign are 25% by conditional probability formula.

According to the question,  10% of all college students are foreign students who also smoke and it is also known that 40% of all foreign college students smoke.

We use the conditional probability formula to solve this question.

Let foreign students be denoted as F

Let students smoking be denoted as S

We know that 10% of all college students are foreign students who also smoke this means

P(F ∩ S) = 0.1

and 40% of all foreign college students smoke which means

P(S/F) = 0.4

So, the percentage of the students at this university who are foreign can be calculated as  

[tex]P(F) = \frac{0.1}{0.4}[/tex] = 0.25

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The surface area of the toy that is yellow is 847.8 inches², to the nearest tenth.

The area of a three dimensional object on it's outer surface is called the surface area of the object.

A square pyramid is a three dimensional object with one square base and 4 four triangular lateral faces.

Total surface area of the pyramid = Area of the base + 4(area of triangular face)

Base length = 24 inches

Base area = 24² = 576 inches²

Height of the pyramid = 20 inches

The slant height, l of the triangle can be found as,

l = [tex]\sqrt{(\frac{a}{2} )^2+h^2}[/tex], where a is the length of the base and h is the height.

l = [tex]\sqrt{12^2+20^2}[/tex]

 = √544

 = √(34 × 16)

 = 4√34 inches

Area of 4 triangular faces = 4 ([tex]\frac{1}{2}[/tex] × 24 × 4√34)

                                           = 2 × 24 × 4√34

                                           = 192√34 inches²

Total surface area = 192√34 inches² + 576 inches²

                              = (192√34 + 576) inches²

                              = 1695.5428 inches²

Surface area of toy that is yellow = 1695.5 / 2 = 847.8 inches², to the nearest tenth.

Hence the surface area of the yellow part of toy is 847.8 inches², to the nearest tenth.

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Step-by-step explanation:

=01000101

is the answer

The binary value of the given expression is 111101.

To multiply binary numbers, we use the same process as with decimal numbers, but using only 0s and 1s. We can use the distributive property of multiplication to break down the problem into simpler multiplication and addition operations.

First, we multiply 1101 by 101:

                                  1101

                                x  101

                                  -----

                                  1101

                                  1101

                                ------

                              111001

Next, we add 100 to the result:

                              111001

                            +    100

                               -------

                              111101

The decimal value of 111101 is given by,

                              (111101)₂ = (61)₁₀

Therefore, the product of 1101 and 101, plus 100, is 111101 in binary.

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Answer:

Step-by-step explanation:

I gotchu.

sinS = 2/9

S = sin^-1(2/9)

S = 12.84 = 321/25 or 12 21/25