A smoke-detector system uses three devices, A, B and C. If smoke is present, the probability that it will be detected by device A is 0.92; by device B is 0.98; and by device C is 0.93. If smoke is present, find the probability that the smoke will be detected by the three devices. Round your answer to 4 decimal places.

A counterexample to show that the statement is false is -1<x<0 or >1

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.

EXPLANATION;

Rearrange unknown terms to the left side of the equation: x^3-x>0

Factor the expression:x(x+1)(x-1)>0

Convert inequality to equation:x(x+1)(x-1)=0

Apply Zero Product Property: x=0 or x+1=0 or x-1=0

Rearrange unknown terms to the left side of the equation:x=-1

Rearrange unknown terms to the left side of the equation:x=1

Combine the results: :x=0 or :x=1  or- :x=1

Order x-intercepts from smallest to greatest: x1=-1or x2=0  or x3=1

EXPLANATION;

Rearrange unknown terms to the left side of the equation:

Factor the expression:

Convert inequality to equation:

Apply Zero Product Property: or  or

Rearrange unknown terms to the left side of the equation:

Rearrange unknown terms to the left side of the equation:

Combine the results: or  or

Order x-intercepts from smallest to greatest: or  or

Plot: As shown in figure

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Answer:2√5

Step-by-step explanation:

5. If OR is perpendicular to PQ and O its the center of the cincunference it means that RP has the same size of QR, then all you have to do its a Pythagorean theorem

H^2=C^2+C^2

OP^2=(2√3)^2+(2√2)^2

(=)OP^2= 12+8

(=)OP^2=20

(=)OP=±√20 ∧ OP>0

(=)OP=2√5

I'm Sorry for the bad english

Answer:

Step-by-step explanation:

The company will need to hire approximately 200 freelancers in order to complete the remaining 40,000 hours of work. This is because each freelancer works 200 hours per month, so in order to complete the 40,000 hours of work in the last 4 months, the company will need to hire 200 freelancers.

Answer:

52

Step-by-step explanation:

RTQ is 52 because if PTR is a right angle, right angles equal 90 degrees. So if PTQ is 38 degrees, we subtract 38 from 90 to get RTQ. 90-38 equals 52.

Answer:

52 degrees

Step-by-step explanation:

right angle = 90

90-38=52

So RTQ = 52 degrees

Answer:

62.5%

Step-by-step explanation:

(mass of solute/mass of solution) x 100 = 62.5%

Answer: 4

Step-by-step explanation: Amplitude has to do with how high and low the function goes according to the midline. The midline for this function is at -3. The maximum point is 1, and the minimum point is -7. The function goes up 4 units and down 4 units

Answer:

Amplitude = 4

Step-by-step explanation:

The amplitude of a sinusoidal function is the height (vertical distance) from the midline to the peak (or trough).

To calculate the amplitude, simply divide the vertical distance between the maximum and minimum y-values by 2.

From inspection of the given graph:

Therefore:

[tex]\implies \sf Amplitude = \dfrac{1-(-7)}{2}=\dfrac{8}{2}=4[/tex]

Answer:

1:3 5/9

18/18=1 64/18=3 5/9

Answer:

Below  

Step-by-step explanation:

Vertex at 8,1      and includes point 9,-1    <=====given

Vertex form :

y = a (x-8)^2 + 1

Plug in the point (9,-1)  to find 'a'

  -1 = a ( 9-8) + 1

    a = -2

                   Parabola equation is then  y = -2(x-8)^2 + 1

Answer:

IT is 245 pounds

Step-by-step explanation:

The solution is: 0.1225 tons  is 245 pounds.

Here, we have,

given that,

245 pounds

we need to find the value in ton

we know that,

1 pound = 1/2000 ton

             = 0.0005 ton

let, 245 pounds = x ton

so, we get,

1 pound = 0.0005 ton

245 pounds = 0.0005 * 245  tons

                    = 0.1225 tons

so, x = 0.1225 tons

Hence, The solution is: 0.1225 tons  is 245 pounds.

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Answer:

3/10

This is to reach the character limit

Answer:

3/10

Step-by-step explanation:

0.3 =

3/10  ==> since there is a non-zero number before the decimal, the

number is being divided by 10. If there was an extra 0, add a 0 to 10 and divide the number by 100. (0.3 = 3/10. 0.03 = 3/100)

Add another 0 to make 0.003, which is 3/1000 (add an extra 0 to 100 to make 1000, 10->100->1000).

The amount Erica earned (in dollars) from her job at the college is 16400.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Let, The amount she earned from her college job is, 'x'.

Therefore, The numerical form of the statement can be formed as,

(3x + 1550) + x = 67150.

4x = 65600.

x = 65600/4.

x = 16400.

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The 1st table is proportional and the 2nd table is not proportional.

The equation y = 3x is proportional and the equation y = 2x + 1 is not proportional.

The 1st graph is not proportional and the 2nd graph is proportional.

A proportional relationship is a type of mathematical relationship in which two variables are directly proportional to each other. This means that as one variable increases, the other also increases in a consistent ratio.

The equation for a proportional relationship is typically written as y = kx, where y and x are the variables and k is a constant ratio of proportionality. In other words, y is always k times x.

From the 1st table, let's the ratios of pencils to students (k). That:

k = 3/1 = 3

k = 6/2 = 3

k = 9/3 = 3

12/4 = 3

Thus, this is proportional.

From the 2nd table, the ratios y to x are not the same. Thus, this is not proportional.

The equation y = 3x is proportional.

The equation y = 2x + 1 is not proportional.

The 1st graph is not proportional because it does not start from the origin.
The 2nd graph is proportional because it starts from the origin.

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Reason:

1% converts to the decimal form 0.01

0.01*800 = 8

Basically we move the decimal point two spots to the left

So the 800.0 becomes 8.000 or simply 8

Answer:

8

Step-by-step explanation:

Anything in percentage format can be expressed as a fraction by dividing by 100

Thus

[tex]\textrm{1\% }= \dfrac{1}{100}[/tex]

1% of 800 is found by multiplying 800 by the above fraction
[tex]\textrm{1\% of 800 } = 800\cdot \dfrac{1}{100} = 8[/tex]

The graph solution of the function is attached below;

For a solution to be solution to a system, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs, so solution to a system is the intersection of all its equation at single point(as we need common point, which is going to be intersection of course)(this can be one or many, or sometimes none)

Given in the question;

points to be plotted;

(-4,9) , (-1,3) , (0,1) , (2,-3)

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Answer: We can use the Squeeze theorem to find the limit.

We know that:

x^2 + y^2 >= 0 for all (x, y)

Also,

|3xy| <= 3|x||y| <= 3x^2 + 3y^2

So,

|3xy/(x^2 + y^2)| <= 3(x^2 + y^2)/(x^2 + y^2) = 3

As we approach (x, y) = (0, 0), x^2 + y^2 becomes arbitrarily close to 0, so the right-hand side of the inequality becomes arbitrarily close to 3, and the left-hand side becomes arbitrarily close to 0.

Therefore,

lim[(x,y)->(0,0)] (3xy/(x^2+y^2)) = 0

Hence, by the sandwich theorem, we can say that the limit of the function is 0.

Step-by-step explanation:

230p – 1010 = 650p – 400 – p and 2.3p – 10.1 = 6.49p – 4 are the equations after rewriting their properties have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p.

As with other words like "equal," "equality," and "equate," the word "equa" at the start of the equation will sound familiar to you. Making things balance out is the theme of all these words. A statement of two quantities' equality is expressed by an equation.

You might still attempt to make the two sides equal even if the equation is not mathematical but rather, say, interpersonal. It might be simpler for two people to decide to remain together for a while if marriage is removed from the picture, for instance.

Given the equation 2.3p – 10.1 = 6.5p – 4 – 0.01p

When multiplied by 100, it becomes

230p – 1010 = 650p – 400 – p

And 6.5p - 0.01p = 6.49p

So, 2.3p – 10.1 = 6.49p – 4

Thus, 230p – 1010 = 650p – 400 – p and 2.3p – 10.1 = 6.49p – 4 are the equations after rewriting their properties have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p.

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The pair of parallel lines intersected by a transversal so at least one angle is 45 degrees has an angle B'EB as 45 degrees.

In terms of geometry, parallel lines are two separate lines that never cross each other and are located in the same plane. They may be vertical or horizontal.

They are referred to be intersecting lines when two or more lines in a plane cross each other. The point of intersection, which can be found on all intersecting lines, is the common point shared by the intersecting lines.

The pair of parallel lines intersected by transversal is as shown:

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Answer:

x = √52

Step-by-step explanation:

Triangle PLM and JLK are connected together at L, which means that they share the same vertex L and therefore, the angle at L is the same for both triangles.

Since PLM and JLK are both triangles, we know that the sum of the angles in each triangle is always 180 degrees.

Let's call the angle at L as a. So we have:

a + (180-a) = 180

We know that PL = 6 and PM = 12, so we can use the Law of Cosines to find the value of the angle a:

c^2 = a^2 + b^2 - 2ab*cos(C)

where c is the hypotenuse, a and b are the other two sides and C is the angle opposite to c.

c = PL = 6

a = PM = 12

b = JL = 4

c^2 = 12^2 + 4^2 - 2124cos(a)

36 = 144 - 48cos(a)

cos(a) = (144 - 36)/48 = (108/48) = 9/4

a = arccos(9/4)

Now we know the measure of angle a and we can use it in the equation of the sum of angles in a triangle.

a + (180-a) = 180

We also know that JL = 4 and JK = x and we can use the Law of Cosines again to find the value of x.

x^2 = 4^2 + 6^2 - 246cos(a)

x^2 = 16 + 36 - 24(9/4)

x^2 = 52

x = √52

The correct statement regarding the addition of the fractions is given as follows:

A. (3x² + 14x + 196)/[(x + 14)(x - 14)], x ≠ -14, x ≠ 14.

The addition of fractions for this problem is given as follows:

[tex]\frac{2x}{x + 14} + \frac{x + 14}{x - 14}[/tex]

They have different denominators, hence the least common factor of the denominator is used.

The terms at the denominator have no common factor, hence the least common factor is the multiplication of them.

Dividing the least common factor by the denominator and multiplying at the numerator, the addition of the fractions is given as follows:

[2x(x - 14) + (x + 14)(x + 14)]/[(x + 14)(x - 14)]

Expanding the numerator, we have that:

2x² - 14x + x² + 28x + 196.

Combining the like terms, the added fraction is given as follows:

(3x² + 14x + 196)/[(x + 14)(x - 14)]

The denominator cannot be zero, hence the restrictions are given as follows:

x ≠ -14, x ≠ 14.

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Answer:

(x−h)2+(y−k)2=r2

Step-by-step explanation:

Standard form for the equation of a circle is (x−h)2+(y−k)2=r2. The center is (h,k) and the radius measures r units. To graph a circle mark points r units up, down, left, and right from the center.

The rectangular bin has a depth of 20 feet.

A cuboid is a three-dimensional shape with rectangles on all sides. A cuboid has six faces, eight vertices, and twelve edges. All of the angles formed at a cuboid's vertices are right angles. The opposing edges are perpendicular to each other.

For the given situation,

A rectangular bin is in the shape of a cuboid.

Volume of the rectangular bin, V = 1200 cubic feet

Length of the rectangular bin ,l = 10 feet

Width of the rectangular bin,w = 6 feet

Let the height of the rectangular bin be h.

The formula of volume of cuboid is

[tex]v=lwh[/tex]

Now substitute the above values,

⇒ 1200= (10)(6)h

⇒ [tex]h=\frac{1200}{60}[/tex]

⇒ h= 20

Hence we can conclude that the rectangular bin is 20 feet deep.

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The depth of the box is found through the volume formula for a rectangular prism, which involves multiplying the length, width and depth. Knowing the volume when half-filled, and the length and width, we can calculate the box is 10 feet deep.

This problem deals with the concept of volume in mathematics. First, the formula for the volume of a rectangular prism (or a box) is length multiplied by width multiplied by height. In this case, we know that the box is half filled with grain and that the total volume of that grain is 200 cubic feet. So, if the box was filled completely, it would have a volume of twice that, or 400 cubic feet.

Now we know that the box's volume is 400 cubic feet and its length is 8 feet and width is 5 feet. So to find the height (which is what we're calling 'depth' in this case), we can use our volume formula. We divide the total volume by the product of the length and width (400/40) to find the height or depth, resulting in a depth of 10 feet.

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Using the rate of the exponential growth to calculate the exponential function, the number of subscribers after 10 years is 3446

An exponential function is a function in which the variable appears in an exponent. It is of the form f(x) = aˣ, where a is a constant and x is the independent variable. The graph of an exponential function is a curve that increases or decreases at an increasing rate.

To solve this problem, we have to find the rate and then calculate the number subscribers after 10 years.

In a given exponential function;

A = P(1 + x)ⁿ

Since this is an exponential growth, we can calculate the rate as;

1 year = 250 subscriber

2 years = 3 * 250

rate = (250 / 750) * 100

rate = 30%

We can substitute the values into the formula and solve

A = 250(1 + 0.3)¹⁰

A = 3446.46

They are expected to have 3446 subscribers after 10 years

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The minimum and maximum values, over the interval x ≥ 3, for the function f(x) = -|x - 1| + 1 graphed are -36 and 64 respectively.

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

Here Relative minimum are the minimum values  in the interval

Looking at the graph, we find the lowest point in the interval

Relative minimum : (-3, -36) and (3,-36)  

y value -36

Looking at the graph, we can find the highest point in the interval

Relative maximum : (0,64)  

y value 64

The minimum and maximum values, over the interval x ≥ 3, are -36 and 64 respectively.

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The equivalent expression to the given expression; 30 / 100 is; 3 / 10.

It follows from the task content that the equivalent expression to the given fraction 30 / 100 is to be determined.

Since the given expression is; 30 / 100.

It follows that the greatest common factor to the numerator and denominator is 10.

Hence, by dividing the numerator and denominator each by 10; the resulting equivalent fraction is; 3 / 10.

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Answer: -5

Step-by-step explanation:

y2 - y1/x2 - x1

3 + 2/3 - 4

5/-1

-5

Answer: 9 inches of wire may be botten.

Step-by-step explanation: First I divided 72 by 12 to find the rate of cents for every inch of wire. I found the rate was 6 cents per inch so I did 6x9= 54.

Pls mark me brainiest if this was right and it helped you (;

Answer: If 34,500 copies sold in the first month of release represent 9.8% of the number of copies sold to date, we can use this information to find the total number of copies sold to date. We can set up the equation as:

(34,500 copies) / (9.8%) = (Total number of copies sold to date)

To solve for the total number of copies sold to date, we can cross-multiply and divide by 0.098:

(34,500 copies) * (100%) / (9.8%) = (Total number of copies sold to date)

(34,500 copies) * (100/9.8) = (Total number of copies sold to date)

This simplifies to:

(34,500 copies) * 10.20408163 = (Total number of copies sold to date)

Total number of copies sold to date = 353878.163.

Rounding the answer to the nearest whole number we get:

Total number of copies sold to date = 353878.

So the book has sold 353878 copies to date.

Step-by-step explanation:

352,041

Take 34,500 and divide it be 9.8.

Next, multiply it by 100.

not sure if this is the answer

40cm as a fraction of 2.4m is 1/6

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. In a proper fraction, the numerator is less than the denominator. e.g . 2/7, 4/5, 3/10 e.t.c

An improper fraction had it's numerator higher than it's denominator .Example is 5/2 , 7/3 e.tc.

By expressing 40 cm as a fraction of 2.4m. The first thing we have to do is making both of thesame unit. therefore ;

2.4m = 2.4×100 = 240cm

40 as a fraction of 240 = 40/240

divide through by 40

= 1/6

therefore the fraction of 40 in 240 is 1/6 i.e 240×1/6 = 40

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In mathematics, the value for x is 9.38 in Example 1 and 11.40 in Example 2.

What are the value signifies?

The value in mathematics refers to the numerical representation of a quantity or concept. It represents the numerical magnitude of a mathematical expression, equation, or quantity.

For example, in the expression 2 + 3 = 5, the value of 2, 3, and 5 all represent specific numerical magnitudes. The value of a variable, such as x or y, can change depending on the context or equation it is used in, but it still represents a specific numerical value.

Values can be represented in different forms, such as integers, fractions, decimals, or real numbers, and they are used to perform mathematical operations and solve mathematical problems.

a) Example 1

AB  is a diameter

PQ is a chord

AO = 13

AO is perpendicular to PQ (2AP=AQ)

In Δ APO

[tex](AO)^2 =(AP)^2+ (PO)^2[/tex]

[tex](13)^2 = (9)^2 + X^2[/tex]

[tex]169 = 81 +X^2[/tex]

X^2 = 169-81

X^2 = 88

X = √88

X = 9.38

As a consequence, 9.38 is equal to x.

b) Example 2

LM = 18

KN = 7

LK = ?

LN = 9

In Δ LKN:

[tex]X^2 = (KN)^2 + (LN)^2[/tex]

[tex]X^2 = (7)^2 + (9)^2[/tex]

X^2 = 49 + 81

X^2 = 130

X =√ 130

X = 11.40

As a consequence, 11.40 is equal to x.

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