a circuit system is given . assume the components fail independently. (a) what is the probability that the entire system works? (b) given that the system works, what is the probability that the component a is not working?

Answer:

Table 3

Step-by-step explanation:

A linear relationship will have constant rate of change(slope) for all x values

Rate of change = Δf(x)/Δx

where Δf(x) = change in values of f(x)

and Δx = corresponding change in values of x

Only table 3 has this constant rate of change:

This slope of 2 is the same if you take any two pairs of x, f(x) values in that table

Hence constant slope = linear relation

Answer: Let's call the number of hours worked h.

The cost of hiring Carmony is $255 + $85h.

The cost of hiring Holliday is $115h.

We want to find the number of hours h such that $255 + $85h is less than $115h.

We can write this as:

$255 + $85h < $115h

Subtracting $115h from both sides:

$255 < $115h - $85h

Combining like terms:

$255 < $30h

Dividing both sides by $30:

8.5 < h

So, it is cheaper to hire Carmony for more than 8.5 hours. For 8.5 hours or less, it is cheaper to hire Holliday.

Step-by-step explanation:

Answer:

630 ft

Step-by-step explanation:

[tex]\frac{x}{140}=\frac{18}{4}\\ \\4x=2520\\\\x=630[/tex]

Hence, the height of the building is 630 feet.

Answer:

4. 175

5. 2

6. 72

7. 48

8. 45

9. 5

10. 18

11. 3

12. 10

13. 30

14. 12

15. 1

16. 2

17. 2

18. 8

[tex]90 \sqrt{72} [/tex]

which is equal to 763.6753236815

The total cost of the dinner is given by the equation A = $ 161.19

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total cost of the dinner be represented as A

Now , the equation will be

The cost of the dinner without tax and tip = $ 128.95

The sales tax percentage = 7.5 %

So , the sales tax amount = ( 7.5 % ) x cost of the dinner without tax and tip

Substituting the values in the equation , we get

The sales tax amount = ( 7.5/100 ) x 128.95

The sales tax amount = $ 9.0265

Now , the percentage of tip = 18 %

So , the tip amount = ( 18 % ) x 128.95

The tip amount = $ 23.211

And , the total cost of the dinner A = cost of the dinner without tax and tip + sales tax amount + tip amount

On simplifying the equation , we get

The total cost of the dinner A = $ 128.95 + $ 9.0265 + $ 23.211

The total cost of the dinner A = $ 161.1875

Hence , the total amount of dinner is $ 161.19

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Answer: x = 18

Step-by-step explanation:

Rearrange the terms

70 = 7 + 3.5 × x

Calculate

-3.5x = 7 -70

Divide Both Sides

-3.5x = -63

x = [tex]\frac{-63}{-3.5}[/tex]

x = 18

Number of bottles of paint needed to paint 70 ornaments is 112.

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

Each ornament is made up of two identical cones.

A cone has a circular base and a lateral surface

Surface area of base = πr², where r is the radius

Lateral surface area of the cone = πrl, where r is radius and l is slant height.

Total surface area of a cone = πr² + πrl = πr (r + l)

There are 2 identical cones for an ornament.

Surface area of an ornament = 2πr (r + l)

                                                = 2π × 3.3 (3.3 + 8.6)

                                                = 246.6156 cm²

Surface area of 70 ornaments = 70 × 246.6156 cm²

                                                  = 17263.092 cm²

Bottle of paint for 155 cm² = 1

Bottle of paint for 17263.092 cm² = 17263.092 / 155

                                                        = 111.374

                                                        ≈ 112

Hence Dona needs approximately 112 bottles of paint.

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Answer: x=6

Step-by-step explanation :

4x+10=34

Subtract 10 on both sides :

4x=24

Divide by 4 on both sides

X=6

Answer:

x = 6

Step-by-step explanation:

4x + 10  =   34

    -  10  = - 10

        4x  =  24

         /4      /4

          x  =  6

Answer:

19 meters

Step-by-step explanation:

209/11 = 19 meters per second

Answer: 19

209 divided by 11 is 19, which means that car moves 19 meters per second.

Hope this helped <3 !!

A mathematical puzzle, where the rational numbers are used is attached with the answer.

A puzzle is a game, problem, or toy that tests a person's ingenuity or knowledge.

In a puzzle, the solver is expected to put pieces together in a logical way, in order to arrive at the correct or fun solution of the puzzle.

Given is to investigate a mathematical puzzle where rational numbers are used.

Refer to the image attached. It shows a mathematical puzzle attached where the rational numbers are used.

Therefore, a mathematical puzzle, where the rational numbers are used is attached with the answer.

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{Question in english -

Investigate a mathematical puzzle where rational numbers are used.}

Edwin run 1.48 kilometers on  tuesday  as he run 4 lap for 370 meter as given in question.

As given in question that edwin usually does laps on a 370 meter indoor track

its means the total distance he cover on 1 round is 370 meter

and we have to find it on kilometers so to convert meter to kilometer we will do

1  kilometers = 1000 meter

so 370 meter = 370 /1000 km

= 0.37 km in 1 round

and he completer 4 round as given in question so

for 4 round = 0.37 * 4 = 1.48 kilometers

in this Question we already given the total distance which is 1480 meter which he run on tuesday and we just convert it on kilometers only

= 1480 meter = 1480/1000

= 1.48 kilometers

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Answer: For this version of the question its  1.48 kilometers

but for the people on study island or the other version of the question it will be 2.25 km

Step-by-step explanation:

a) The probability of selecting a jury of all​ students is  792 / 245, 157.

b) The  probability of selecting a jury of all​ faculty us 330/ 245157

c) The  probability of selecting a jury of of students and ​faculty is 0.0000043

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.

Given:

Out of 12 students and 11 faculty, a jury of six individuals can be select C(23,  7).

A) The probability of selecting a jury of all​ students

= C( 12, 7) / C(23,  7).

= 792 / 245, 157

B) The  probability of selecting a jury of all​ faculty

=  C( 11, 7) / C(23,  7).

= 330/ 245, 157

C) The probability of selecting a jury of students and ​faculty

=  792 / 245, 157 x 330/ 245, 157

= 0.0000043

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The statements can be used to compare the characteristics of the functions is:

If the values in a set of data are distinct and separate, the set is said to be discrete (unconnected values).

"All the values" that are input into a function are referred to as the domain of a function. A function's domain is the set of all potential inputs. Consider this box to represent the f(x) = 2x function. When the input values are x = 1,2,3,4,..., the domain is merely the collection of natural numbers, and the values that are returned are referred to as the range.

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Complete question:

The table shows three unique, discrete functions. Which statements can be used to compare the characteristics of the functions? Select three options.

has the greatest maximum. f(x)

has the greatest x-intercept. h(x)

has the smallest minimum value. g(x)

All three functions share the same domain.

All three functions share the same y-intercept.

The probability of being dealt two aces and one of them being the ace of spades is 1 in 221, or 0.45%.

The probability of being dealt two aces and one of them being the ace of spades is 1/221. This is because the chance of the first card being the ace of spades is 1/52 and the chance of the second card being an ace, given that the first card is an ace, is 3/51. Thus, the probability of both cards being aces and one of them being the ace of spades is 1/221.

Mathematically, this can be expressed as P(Ace of Spades, Ace) = P(Ace of Spades) x P(Ace|Ace of Spades) = (1/52) x (3/51) = 1/221.

This means that the probability of being dealt two aces and one of them being the ace of spades is 1 in 221, or 0.45%.

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Note that the most precise name for quadrilateral ABCD with vertices a(-2, -1), b(2, 2), c(1, -2), and d(-3, -3) is an Irregular Quadilateral. See the image attached.

An irregular quadrilateral is a polygon with four sides, but all four (opposite) sides and angles are incongruent.

Rectangles, parallelograms, kites, and isosceles trapezoids are examples of irregular quadrilaterals. There are several formulas for calculating the area of these quadrilaterals. Set formulae may be used to compute the area of rectangles, parallelograms, kites, and isosceles trapezoids.

There is just one angle attribute for an irregular quadrilateral: the sum of the angles equals 360° 360° 360°. Add all internal angles that are known.

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Relations of the line with the given equation of line are:

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given an equation of line y = 1/5x +1

Comparing with the slope-intercept general formula of line

the slope of the given line = 1/5

And the slope of the line that is perpendicular to this will be = -1/slope

the slope of the line that is perpendicular to this will be = -5

For A) y = 5x +1

Slope = 5

this line has no relation with the equation of the line given

For B) y = 1/5x -2

Slope = 1/5

thus, this line is parallel to the given line.

For c)

10x + 2y = 10

In slope intercept

y = -5x +5

Slope = -5

Thus this line is perpendicular to the line given

For D)

x - 5y = 20

In slope intercept

y = 1/5x -4

Slope = 1/5

thus, this line is parallel to the given line.

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He has to pay $1.05 in taxes for the meal.

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”

Given here: Sales tax

A sales tax is a consumption tax imposed by the government on the sale of goods and services. A conventional sales tax is levied at the point of sale, collected by the retailer, and passed on to the government.

Now it costs $15.00 and the tax is 7%

Treating the taxable amount as $15 and now to find 7% equivalent we get

Now 7%×15=$1.05

Thus he has to pay $1.05 in taxes

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Refer to the attached image.

The chance of observing Mississippi after permuting the letters of it and randomly picking a word from that set is 1 in 34032.

The number of words that can be constructed from the letters of the word "Mississippi" is given by the number of permutations of those letters. Since the letters are not unique, we use the formula for permutations with repetition:

n! / (n₁! ×  n₂! ×  ... × nk!)

where n is the total number of letters, and n₁, n₂, ..., nk are the number of times each letter is repeated.

In this case, n = 11 and n₁ = 4, n₂ = 4, n₃ = 2, n₄ = 1.

So, the number of words that can be constructed is 11! / (4! × 4! × 2! × 1!) = 34, 032.

Thus, the chance of observing "Mississippi" is 1 in 34, 032 or approximately 1/34.

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The value of x is 38.

Parallelogram is a quadrilateral that has two pairs of parallel sides.

In a parallelogram, opposite sides and angles are equal.

The adjacent angles add up to 180 degrees.

We have,

EB = x - 7

DE = 31

From the figure, we see that,

(1/2)BD = EB = DE

Since the diagonal of a parallelogram bisects each other at its midpoint.

Now,

x - 7 = 31

Adding 7 on both sides.

x = 31 + 7

x = 38

Thus,

x = 38.

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Answer: -135

Step-by-step explanation:

90 + 45 = 135

90 - 135 = -45

I hope this helps

Faults are planar features in rocks where the two sides move past each other due to tectonic forces. However, not all planar features in rocks are faults, as there are other types of planar features that do not involve movement. A planar feature that does not involve movement is called a joint.

A planar feature refers to a surface or boundary within a rock that has a relatively consistent orientation or direction. These features can be caused by a variety of geological processes, such as deformation, metamorphism, or sedimentation. Some examples of planar features in rocks include bedding planes, foliation, and cleavage.

A fault, in particular, is a type of planar feature that forms when tectonic forces cause two sides of a rock to move past each other. This movement can be horizontal, vertical, or a combination of both. Faults can range in size from small fractures in the rock to large features that extend for kilometers. They are a common feature in regions where tectonic forces are actively shaping the Earth's crust, such as along plate boundaries or in areas with active volcanism.

On the other hand, a planar feature that does not involve movement is called a joint. Joints are fractures in rocks that do not result in any significant displacement of the rock on either side of the fracture. They can be caused by a variety of factors, such as cooling and contraction of magma or shrinkage of sediments. Joints can be important in geology because they can influence the way that rocks weather and erode over time.

In summary, a planar feature refers to a surface or boundary within a rock that has a relatively consistent orientation or direction. While faults are a type of planar feature that involves movement between two sides of a rock, joints are planar features that do not involve any significant displacement of the rock on either side of the fracture. Understanding these different planar features is important in geology, as they can provide insight into the geological history of a region and can be used to predict future geological activity.

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Answer:

x=65

y=25

Step by step explanation:

90+90+25+x+x+y= 360

2x+y=155  (1)

90+25+x= 180

x= 65   (2)

sub (2) into (1):

2(65)+y=155

y= 25

Answer:

8/5

Step-by-step explanation:

divide numerator and denominator by 8 (GCF)

Answer:

8/5

Step-by-step explanation:

Divide into halves (3 steps):

[tex]\frac{64}{40} =\frac{32}{20} =\frac{16}{10} =\frac{8}{5}[/tex]

Or divide by eight (1 step):

[tex]\frac{64}{40} =\frac{8}{5}[/tex]

Hope this helps

In part (a), the y-intercept is (0,3), which means that when x = 0, the value of f(x) is 3. In part (b), the y-intercept is (0,0), which means that when x = 0, the value of f(x) is 0. In part (c), the y-intercept is (0,-6), which means that when x = 0, the value of f(x) is -6.

A transformation of a function is a process that changes the position or shape of the function on a coordinate plane. There are several types of transformations, including:

Translation: A translation moves the graph of a function horizontally or vertically, but does not change its shape. This can be accomplished by adding or subtracting a constant to the input or output of a function.

Scaling: A scaling changes the size of a function's graph, but not its shape. This can be accomplished by multiplying the input or output of a function by a constant.

Reflection: A reflection flips the graph of a function over a line. This can be accomplished by negating either the input or the output of a function.

Stretching or Compression: A stretching or compression changes the height or width of a function's graph, but not its shape. This can be accomplished by multiplying the output of a function by a constant greater than 1 for stretching, or by a constant between 0 and 1 for compression.

These transformations can be used to shift, scale, reflect or distort the graph of a function, allowing for greater understanding and analysis of its properties.

a. f(x) = [tex]3(2)^{x}[/tex] + 3 is an exponential function that has been vertically shifted up by 3 units. The y-intercept is (0,3), which means that when x = 0, the value of f(x) is 3.

b. f(x) = [tex]6(4)^{x}[/tex] * 0.5 is an exponential function that has been vertically stretched by a factor of 0.5 and horizontally stretched by a factor of 6. The y-intercept is (0,0), which means that when x = 0, the value of f(x) is 0.

c. f(x) = [tex]4(0.5)^{x}[/tex] - 6 is an exponential function that has been vertically shifted down by 6 units. The y-intercept is (0,-6), which means that when x = 0, the value of f(x) is -6.

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Answer:

a =

Step-by-step explanation:

Line is straight across so you just

8 - a =

a =

The equation y = 2(kx - 1)^5 represents a curve. To find the equation of the curve, we need to determine the value of the constant k. To do this, we can use the two points given, (0,1) and (1,8), to find two equations and solve for k.

First, we'll substitute the x-coordinate and y-coordinate of the first point, (0,1), into the equation:

1 = 2(k * 0 - 1)^5

Expanding the right-hand side:

1 = 2(-1)^5

1 = -32

This equation is clearly false, so the point (0,1) does not lie on the curve represented by y = 2(kx - 1)^5.

Next, we'll substitute the x-coordinate and y-coordinate of the second point, (1,8), into the equation:

8 = 2(k * 1 - 1)^5

Expanding the right-hand side:

8 = 2(k - 1)^5

Dividing both sides by 2:

4 = (k - 1)^5

Taking the fifth root of both sides:

2 = k - 1

Adding 1 to both sides:

3 = k

Now that we have the value of k, we can write the equation of the curve:

y = 2(kx - 1)^5

= 2(3x - 1)^5

This is the equation of the curve that passes through the points (0,1) and (1,8).

It's important to note that the original equation y = 2(kx - 1)^5 is only one of an infinite number of curves that can pass through the points (0,1) and (1,8). The process of finding the equation of a curve that passes through specific points is known as curve fitting. The specific equation found in this case is just one possible representation of the curve that passes through the given points.

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Answer: 12

Step-by-step explanation: So, if 6 is 50% of x, x must be 12. Why? Because 50% is also equal to 1/2, so if 6 is only half of x, the other half must also be 6 - so its 6 + 6 = 12.

0.00426 is the probability of being dealt six clubs and three cards with one card .

Describe probability using an example?

A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

                                 The likelihood of an event occurring increases as its probability increases. The flip of a fair (impartial) coin serves as a straightforward illustration.

We will get 9 cards out of 52 cards

Probability of getting 6 clubs is

total we have 13 clubs

no of chances = 13C6

chances of getting 3 cards from 3 other suits

= 39C3

Now, the total probability

= 13C6 * 39C3 / 52C9

= 1716 * 9139 / 3679075400

= 0.00426

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