The combination lock has three wheels each numbered from 0 to 9 what is the possibility that someone randomly guesses the correct combination in five attempts?

[tex]x {}^{2} - 9 = 8x \\ x {}^{2} - 8x - 9 = 0 \\ x = \frac{ - ( - 8) + \sqrt[]{( - 8) {}^{2} - 4(1)( - 9)} }{2( {1}^{}) } [/tex]

[tex]x = \frac{8 + \sqrt{64 + 36} }{2} = \frac{8 + \sqrt{100} }{2} = \frac{8 + 10}{2} = 9[/tex]

Answer: x = 9

Step-by-step explanation:

The difference of the square of a number and 9 is equal to 8 times that number. Find the positive solution.

let x = a number

[tex]x^2-9=8x\\x^2-8x-9\\(x-9)(x+1)\\x-9 = 0\\x=9\\x+1=0\\x=-1[/tex]

taking only the positive solution, we get x = 9

The rise is the difference in y-coordinates:

The run is the difference in x-coordinates:

The slope is the quotient of rise over run:

========================

If two points on a line are A(10, −3) and B(12, 9), the rise is 12, and the run is 2, so the slope of the line is 6.

Answer:

x = 117

Step-by-step explanation:

Foremost, we know that the three angles of the triangle always add up to 180 degrees.

So, there are two sides which are 27 degrees and 36 degrees, we need to find the third one's degree.

Add 27 and 36 (27 + 36 = 63)

Two sides equal 63.

Then, subtract 180 - 63 = 117

So the third angle's measurement is 117 degrees. The answer is 117.

To check, add 117 + 27 + 36 = 180

Hope it helps.

Answer:

no

Step-by-step explanation:

Answer:

Step-by-step explanation:

6(3x-5)≤2(9x+7)+10

divide by 2

3(3x-5)≤9x+7+5

3(3x-5)≤9x+12

divide by 3

3x-5≤3x+4

-5≤4

which is true.

answer

symbolic materials ?

The domain of the function is the set of all real numbers and the range of the function is the set of all values greater than -2

The function is given as:

f(x) = 2(x -4)^2 - 2

A quadratic function can take any real number as its input.

So, the domain of the function is the set of all real numbers

The vertex of the above function is:

Vertex = (4, -2)

And the leading coefficient is:

a = 2

The y value of the vertex is;

y = -2

Because the value of a is positive, then the vertex is a minimum.

This means that the range of the function is the set of all values greater than -2

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See below for the algebraic expressions of the scenarios.

The given parameters are:

Scenario 1

Represent the speed with x.

So, we have:

Speed = Distance/Time

The time is given as:

Time = 10 minutes

Since he did not stop at all;

The speed is

x = 2400/10

Multiply both sides by 10

10x = 2400

The above expression represents the scenario 1.

Scenario 2

Represent the speed with x, and time with t

So, we have:

Speed = Distance/Time

The time to reach halfway is given as:

Time = 6 minutes

He stopped for 1 minute, before continuing at the same initial speed

So, the total time it 13 minutes

The speed is represented as:

x = 2400/13

Multiply both sides by 13

13x = 2400

The above expression represents the scenario 2.

Scenario 3

Represent the speed with x, and time with t

So, we have:

Speed = Distance/Time

The time to reach halfway is given as:

Time = 6 minutes

He stopped for 1 minute, before continuing at twice the initial speed

So, the total time is

t = 6 + 1 + 1/2 * 6 minutes

t = 10 minutes

The speed is represented as:

x = 2400/10

Multiply both sides by 10

10x = 2400

The above expression represents the scenario 3.

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Answer:

A∩B = { 1 }

Step-by-step explanation:

Consider the sets :

A = {1, 2, 6}

B = {x  ;where x is an odd whole number less than 8}

Suppose the numbers of B are natural numbers (not integers).

Then

B = {1 , 3 , 5 , 7}

We obtain :

A = {1, 2, 6}  and  B = {1 , 3 , 5 , 7}

The intersection of A and B or the set A∩B :

is the set of the common numbers of A and B.

Then

A∩B = { 1 }

The set A intersection B(or, A∩B) for the given set A and set B exists {1}.

"The set A intersection B(or, A∩B) exists described as the set composed of all elements that belong to both A and B".

The intersection of a set A with a B exists the set of elements that exist in both sets A and B. The intersection exists represented as A∩B.

The intersection of two mathematical objects exists where they overlap. For geometric objects, the intersection exists as a point or group of points where the objects cross.

For numerical or non-numerical sets, the intersection exists every number or object the two sets contain in common.

Given: A = {1, 2, 6}

B = {x | x is an odd whole number less than 8}.

From the above information, we get

⇒ B = {1, 3, 5, 7}

If A = {1, 2, 6} and B = {1, 3, 5, 7}

then A∩B = {1, 2, 6} ∩ {1, 3, 5, 7}

A∩B = {1}

Therefore, the correct answer A∩B exists {1}.

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Answer:

-24

Step-by-step explanation:

-6 × f(3) - 6 × g(-1) = ?

to answer this we need to find the functional values of the functions at the specified points.

f(3) = -2

we find this easily : we go to x = 3 on the x-axis, and then see there at what y value a vertical line is intersecting the functional graph. the intersection is below the x-axis, so the y value is negative.

g(-1) = 6

we go to x=-1, and we find that a vertical line there will intersect the g curve at y = 6.

and that's really it.

now we need to calculate it all in the main expression :

-6 × -2 - 6 × 6 = 12 - 36 = -24

you remember, that multiplications and divisions have to happen before any addition of subtraction ?

Answer: A shift 16 units down

Step-by-step explanation:

See attached image.

The transformation of the function f(x) = x is (x, y) → (x + 16, y). This transformation is said to be the translation rule and the translation is 16 units towards the right.

The translation rule for a function f(x) is given by

(x, y) → (x + a, y + b)

Where a, and b are constant.

(x, y) → (x + a, y); translation towards right

(x, y) → (x - a, y); translation towards left

It is given that the function f(x) = x and g(x) = x - 16

So, the variation is

x - a = x - 16

⇒ - a = x - x - 16

∴ a = 16

Thus, the transformation is (x, y) → (x + 16, y)

Therefore, the transformation of the function f(x) = x is (x, y) → (x + 16, y) i.e., the translation of 16 units towards the right .

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Answer:

-5

Step-by-step explanation:

The y coordinate of the vertex is -5.

The algebraic expression is 20b

The statement is given as:

$20 a ticket

This means that the cost of 1 ticket is $20.

So, the cost of b tickets is

Cost = 20 * b

Evaluate

Cost = 20b

Hence, the algebraic expression is 20b

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The net that represents a cube is (b) net b

A cube has 6 faces

This means that the net must have 6 faces

For a net to represent a cube, there must be four adjacent faces

And 2 two adjacent faces

Where

The net that represents the above scenario is net (b)

Hence, the net that represents a cube is (b) net b

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It's 4 buns & 5 cakes

Hope my explanation to the other one helps, if not, you can draw them; while following the steps & you may get it better.

E.g draw a box for the bun & a circle for the cake, then, adding them up to get the 95p. Also, you keep taking away from 435p

Answer:

d.

Step-by-step explanation:

Given a length [tex]l[/tex] and a width [tex]w[/tex], we can express the perimeter of a rectangle as [tex]2(l+w)[/tex].

Therefore the perimeter [tex]P[/tex] can be expressed as

[tex]2\times[(x-8)+(x-9)]\\=2\times(2x-17)\\=4x-34[/tex]

The inequality graphed is the one in the first option.

On the graph we can see a solid parabola, the parabola opens downwards, and we can see that the vertex of the parabola is on the point (-1, 5).

And the shaded region is above the parabola.

Then the inequality is of the form:

y  ≥  parabola.

By knowing where is the vertex, we know that:

parabola = -a*(x + 1)^2 + 5

Then the correct option is the first one.

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Answer:[tex]\sqrt{303.51}[/tex]

Step-by-step explanation:

The difference in the radii of the two circles is [tex]4.3-1.8=2.5[/tex] inches.

Since the tangent has a length of 2.5 inches, by the Pythagorean theorem, the required distance is

Answer:

Discount: $30 off

New Sale Price: $270

Step-by-step explanation:

$300*10% =

30

$300-30=

$270

or

$300*.1=

30

$300-30=

$270

The domain of the composite function is given as follows:

[–3, 6) ∪ (6, ∞)

The composite function of f(x) and g(x) is given as follows:

[tex](f \circ g)(x) = f(g(x))[/tex]

In this problem, the functions are:

The composite function is of the given functions f(x) and g(x) is:

[tex]f(g(x)) = f(\sqrt{x + 3}) = \frac{1}{\sqrt{x + 3} - 3}[/tex]

The square root has to be non-negative, hence the restriction relative to the square root is found as follows:

[tex]x + 3 \geq 0[/tex]

[tex]x \geq -3[/tex]

The denominator cannot be zero, hence the restriction relative to the denominator is found as follows:

[tex]\sqrt{x + 3} - 3 \neq 0[/tex]

[tex]\sqrt{x + 3} \neq 3[/tex]

[tex](\sqrt{x + 3})^2 \neq 3^2[/tex]

[tex]x + 3 \neq 9[/tex]

[tex]x \neq 6[/tex]

Hence, from the restrictions above, of functions f(x), g(x) and the composite function, the domain is:

[–3, 6) ∪ (6, ∞)

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The amount that Ross report as taxable income will be $31965.

Taxable income refers to the base upon which an income tax system imposes the tax.

In other words, the taxable income is the income over which the government imposed tax. It includes some or all items of income and is reduced by expenses and other deductions.

From the information:

Gross salary = $56,145

Interest earnings = $205

Dividend income = $65

Standard deduction = $12,000

Itemized deductions = $11,250

Adjustments to income = $1,200

The taxable income is given by:

= Gross salary + Interest earnings + Dividend income - Standard deduction - Itemized deductions - Adjustment to income

= 56145 + 205 + 65 - 12000 - 11250 - 1200

= $31965

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From the given information,

a. The length of the belt is 180.28 ft

b. The height of the window from the ground is 100 ft

c. The length of the ramp needed is 141.42 ft

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two legs of the triangle. I.e., (hypotenuse)² = (opposite)² + (adjacent)²

It is given that,

The height of the silo is 150 feet

The distance from the belt to the silo is 100 feet

With the given measurements, a right-angled triangle is formed.

a. Finding the length of the belt:

From the diagram,

The height of the silo, sh = 150 ft

The base distance, sb = 100 ft

So, the length of the conveyor belt is the hypotenuse (bh) of the triangle formed.

On applying the Pythagorean theorem,

bh² = sb² + sh²

⇒ bh² = (100)² + (150)²

⇒ bh² = 32500

⇒ bh = √32500 = 50√13

∴ bh = 180.28 ft

Thus, the length of the belt is 180.28 ft.

b. Finding the height of the window from the ground:

It is given that the angle of elevation from the lower end of the belt(b) to a window(w) on the side of the silo is 45°.

This creates a special right-angled triangle. I.e.,

The angles of the new triangle are 90°- 45°. So, the third angle also becomes 45° (Since the sum of angles in a triangle is 180°)

So, the new triangle has angles of 90°- 45°- 45°

Thus, the new triangle is said to be an isosceles right angled triangle.

So, the two legs of the triangle are equal. I.e., sb = sw = 100 ft

Therefore, the height of the window from the ground(sw) is 100 ft

c. Finding the length of the ramp(bw) to the window:

Since we have

sw = 100 ft and sb = 100 ft

On applying Pythagora's theorem,

bw² = sb² + sw²

⇒ bw² = (100)² + (100)²

⇒ bw = √20000 = 141.42 ft

Therefore, the length of the ramp to the window is 141.42 ft.

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Answer: [tex]8\pi[/tex]

Step-by-step explanation:

The period is [tex]\frac{2\pi}{1/4}=8\pi[/tex].

Answer:

a) 10/21 b) 5/21 c)1/21

Step-by-step explanation:

a) your have 7 choice and 5 or them or red, 5/7.  You do not replace the red marble, so for your second draw, you now only have 6 choices and of those 6 choices only 4 of them are now red or 4/6 or 2/3.  We multiple these two numbers together:

5/7(2/3) = 10/21

b) For the first draw, you have 5 red marbles available out of a total 7 marbles or 5/7.  The second draw now only has 6 marbles and 2 of them or yellow to make 2/6 or 1/3 (simplified).  We multiply these together.

5/7(1/3) =5/21

c)  I am assuming that you are still selecting 2 marbles.  The first draw would be 2/7.  This time I am selecting yellow and there are only 2 choices for yellow.  My next draw will only have 6 marbles and only 1 of them will be yellow, so 1/6.  We multiply these together

2/7(1/6) = 2/42 or 1/21

Answer:

[tex]\frac{15}{2}[/tex]

Step-by-step explanation:

The absolute value of a number is just its distance from zero. In other words, if it's negative, the absolute value would make the number positive. This makes the absolute value [tex]\frac{45}{6}[/tex]. Now, reduce to get[tex]\frac{15}{2}[/tex].

Considering the Central Limit Theorem, we have that:

a) The probability cannot be calculated, as the underlying distribution is not normal and the sample size is less than 30.

b) The probability can be calculated, as the sample size is greater than 30.

It states that the sampling distribution of sample means of size n is approximately normal has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex], as long as the underlying distribution is normal or the sample size is greater than 30.

In this problem, the underlying distribution is skewed right, that is, not normal, hence:

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Based on the student's grades, and the credit hours, their grade point average is 2.60.

First, find the grade points earned:

= (4 x 3) + (1 x 3) + (3 x 3) + (2 x 1)

= 12 + 3 + 9 + 2

= 26

The GPA is:

=Grade points earned / total number of credits

= 26 / (3 + 3 + 3 + 1)

= 26 / 10

= 2.6

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[tex]\\ \rm\Rrightarrow \dfrac{x^2+3x+2}{x^2-4x-5}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{x^2+2x+x+2}{x^2-5x+x-5}[/tex]

[tex]\\ \rm\Rrightarrow {(x+2)(x+1)}{(x-5)(x+1)}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{x+2}{x-5}[/tex]

And

[tex]\\ \rm\Rrightarrow \dfrac{x^2+7x+12}{x^2-3x-28}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{x^2+4x+3x+12}{x^2-7x+4x-28}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{(x+4)(x+3)}{(x-7)(x+4)}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{x+3}{x-7}[/tex]