The possibility that someone randomly guesses the correct combination in five attempts is 1/200
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
P(E) = Number of favorable outcomes / total number of outcomes
Given;
There are three wheels
Each numbered from 0 to 9
For the first wheel, you have 10 possible digits.
For the second wheel, you have 10 possible digits.
For the third wheel, you have 10 possible digits.
10 x 10 x 10 = 1000
For 5 attempts= 5/1000
=1/200
Therefore, the probability will be 1/200
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Ross Martin arrived at the following tax information gross salary 56,145 interest earnings 205 dividend income 65 standard deduction 12,000 itemized deductions 11,250 adjustments to income 1200 what amount with Ross report as taxable income income
The amount that Ross report as taxable income will be $31965.
What is a taxable income?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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The difference of the square of a number and 9 is equal to 8 times that number. Find the positive solution.
[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
Conveyor belts called grain elevators are used to move grain into a silo. Answer the following questions knowing that the lower end of the belt is 100 feet from the base of the silo and that the silo is 150 feet tall.
a. How long is the belt?
b. If we know the angle of elevation from the lower end of the belt to a window on the side of the silo is 45°, use special right triangle ratios to calculate the height of the window from the ground.
c. We need a ramp to the window. How long would it need to be?
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
What is the Pythagorean theorem's formula?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
Calculation: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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7. (05.02 MC)
Luciana's laptop has 3,000 pictures. The size of the pictures is skewed to the right, with a mean of 3.7MB and a standard deviation of 0.78MB
Part A: Can you accurately calculate the probability that the mean picture size is more than 3.8MB for an SRS of 20 pictures? Explain.
Part B: If you take a random sample of 60 pictures instead of 20, explain how the Central Limit Theorem allows you to find the probability that the mean picture size is more than 3.8MB.
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.
What does the Central Limit Theorem state?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:
For item a, the probability cannot be calculated, as the underlying distribution is not normal and the sample size is less than 30.For item b, the probability can be calculated, as the sample size is greater than 30.More can be learned about the Central Limit Theorem at https://brainly.com/question/16695444
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If two points on a line are A(10, −3) and B(12, 9), the rise is __________, and the run is __________, so the slope of the line is __________.
The rise is the difference in y-coordinates:
y₂ - y₁ = 9 - (-3) = 12The run is the difference in x-coordinates:
x₂ - x₁ = 12 - 10 = 2The slope is the quotient of rise over run:
m = 12/2 = 6========================
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.
Complete the function for this graph.
-5
ertificati...
5
-5
y = |x|+ [?]
Hint: y = |x-h| + v
Answer:
-5
Step-by-step explanation:
The y coordinate of the vertex is -5.
guys can you help me with this i just dont understand how to plot it so u just have to tell me how
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.
What is the domain and range of the quadratic function given by the equation /(x) = 2(x-4)] - 2
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
How to determine the domain and the range?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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Imagine the center of the London Eye Ferris Wheel is located at (0, 0) on a coordinate grid, and the radius lies on the x-axis. Write an equation of a circle for the ferris wheel, and sketch an image of what the ferris wheel would look like on the grid. Now graph a circle that is similar to the Ferris Wheel. Discuss the transformations needed to show that both circles on your graph are similar.
answer
symbolic materials ?
2. Grade points are assigned as follows: A = 4, B = 3, C = 2, D = 1, and F = 0. Grades are weighted according to credit hours. If a student receives one A in three-credit class, one D in three-credit class, three B in three-credit class and two C in one-credit class, what is the student’s grade point average?
Based on the student's grades, and the credit hours, their grade point average is 2.60.
What does the student get as their GPA?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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Imogen buys some sandwiches costing £3.50.
She has a 20% off coupon.
How much discount will Imogen receive?
K
4
4. Identify a transformation of the function f(x) = x by observing the equation of the function g(x) = x - 16.
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.
What is the translation rule of transformations?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
Calculation: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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Please help me answer this question, 20 POINTS!
Buns,cost 40p each. Cakes cost 55p each. I spend exactly £4.35 on buns and cakes.
How many of each did I buy?
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
The cost of b tickets at $20 a ticket algebraic expression
The algebraic expression is 20b
How to determine the algebraic expression?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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Select the correct answer.
Which of the nets below will make a closed cube?
Mariatu Yakubu
The net that represents a cube is (b) net b
How to determine the net?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
One of the two adjacent faces is at the end of the fourth faceThe other is at the 3rd positionBoth 2 faces do not face the same directionThe net that represents the above scenario is net (b)
Hence, the net that represents a cube is (b) net b
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Dave leaves his office in Padelford Hall on his way to teach in Gould Hall. Below are several different scenarios. Take distance units to be “feet” and time units to be “minutes.” Assume Dave’s path to Gould Hall is along a straight line which is 2400 feet long.
I. Dave leaves Padelford Hall and walks at a constant spend until he reaches Gould Hall 10 minutes later.
II. Dave leaves Padelford Hall and walks at a constant speed. It takes him 6 minutes to reach the halfway point. Then he gets confused and stops for 1 minute. He then continues on to Gould Hall at the same constant speed he had when he originally left Padelford Hall.
III. Dave leaves Padelford Hall and walks at a constant speed. It takes him 6 minutes to reach the half-way point. Then he gets confused and stops for 1 minute to figure out where he is. Dave then continues on to Gould Hall at twice the constant speed he had when he originally left Padelford Hall.
g. Using all three scenarios, represent each scenario as an algebraic function.
See below for the algebraic expressions of the scenarios.
How to represent the scenarios?The given parameters are:
Distance = 2400 feetUnit of time = MinutesScenario 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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PLEASE HELP EDGE2022 Which inequality is represented by the graph?
y ≥ –2(x + 1)2 + 5
y ≤ –2(x + 1)2 + 5
x ≥ –2(y + 1)2 + 5
x ≤ –2(y + 1)2 + 5
The inequality graphed is the one in the first option.
Which inequality is represented by the graph?
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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what is the absolute value of -45/6. I need serious help
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].
Factor the greatest common binomial factor from each polynomial
Please help!!! 24 points!!!
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 ?
A rectangle has a length of x-8 and a width of x-9. Which equation below describes the perimeter, P, of the rectangle in terms of x?
a. P=x² - 17x+72
b. P=x-17
c. P = 2x-17
d. P = 4x - 34
*show your work*
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]
What is the frequency of the function f (x). f (x) = -2sin x/4 +3
Answer: [tex]8\pi[/tex]
Step-by-step explanation:
The period is [tex]\frac{2\pi}{1/4}=8\pi[/tex].
Simplify:
x² + 3x + 2 /x² - 4x - 5
x² + 7x + 12 / x²-3x - 28
[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]
A = {1, 2, 6}
B = {x|x is an odd whole number less than 8}.
Find An B.
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}.
What is A intersection B, (A∩B)?"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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What is the discount and sale price of a $300 item that has been discounted at 10%?
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
Please help with this geometry question!
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
Dana believes that she needs to study for at least 14 hours to be prepared for her monthly accounting test. If she can study for 4 hours per day, what is the minimum number of days that she should allow to study for the test?
Instructions: Find the missing side of the triangle 27,36,x
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.
A box contains 5 red marbles and 2 yellow marbles. Consider the two–stage experiment of randomly selecting a marble from a box, NOT replacing it, and then selecting a second marble. Determine the probabilities of the following events:
a. Selecting 2 red marbles.
P (red) =
b. Selecting a red marble on the first draw and a yellow marble on the second.
P (red then yellow) =
c. Selecting at least 1 yellow marble.
P (at least 1 yellow) =
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
Given f of x is equal to 1 over the quantity x minus 3 end quantity and g of x is equal to the square root of the quantity x plus 3 end quantity comma what is the domain of f (g(x))?
[–3, ∞)
[–3, 6) ∪ (6, ∞)
(–∞, 3) ∪ (3, ∞)
ℝ
The domain of the composite function is given as follows:
[–3, 6) ∪ (6, ∞)
What is the composite function of f(x) and g(x)?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:
[tex]f(x) = \frac{1}{x - 3}[/tex].[tex]g(x) = \sqrt{x + 3}[/tex]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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