The probability of writing the first 7 digits of your phone number is 1/604,800.
Given data ,
To determine the probability of writing the first 7 digits of your phone number, we need to consider the total number of possible outcomes and the favorable outcomes.
Total number of possible outcomes:
When picking 7 digits without replacement from the set of 10 digits (0-9), the total number of possible outcomes is given by 10P7 (permutations of 10 objects taken 7 at a time):
10P7 = 10! / (10 - 7)! = 10! / 3! = 10 * 9 * 8 * 7 * 6 * 5 * 4 = 604,800.
Favorable outcomes:
To have written the first 7 digits of your phone number, you need to pick those specific digits in the correct order. Since the phone number has no repeated digits, there is only one specific order that satisfies this condition.
Therefore, the number of favorable outcomes is 1.
Probability:
The probability is given by the ratio of favorable outcomes to total possible outcomes:
Probability = Favorable outcomes / Total possible outcomes
= 1 / 604,800.
Hence, the probability is 1/604,800.
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A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below:
The probability of landing on purple to the nearest hundredth: 0.15
How to solveThe total number of spins is 84, and the probability of landing on purple is 13/84 = 0.15476.
Rounding to the nearest hundredth, this is 0.15.
Elaborating:
Number of times the spinner landed on purple: 13
Total number of spins: 84
Probability of landing on purple: (13/84) = 0.15476
Probability of landing on purple to the nearest hundredth: 0.15
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The Complete Question
A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below:
Spinner Results
Color Frequency
Red 18
Blue 15
Green 20
Yellow 18
Purple 13
Based on these results, express the probability that the next spin will land on purple as a decimal to the nearest hundredth.
Can someone help me with this?
The value of sinθ is √17/7 and the value of [?] is √17
According to The Pythagorean identity,
Sin²θ + Cos²θ = 1
This is a Trigonometric equation, where 'sin' refers to 'sine' and 'cos' refers to 'cosine' which are functions revealing the shape of a right-angled triangle.
Given, cosθ=4√2/7
Cos²θ = 32/49
From equation 1 we get,
Sin²θ = 1 - Cos²θ
Sin²θ = 1 - (32/49)
Sin²θ = (49-32)/49
Sin²θ = 17/49
Sinθ = √(17/49)
Sinθ = √17 / 7
Given, sinθ = √[?] / [ ]
[?] = 17
Therefore, The value of sinθ is √17/7 and the value of [?] is √17
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Amy opened a savings account and deposited $300.00. The account earns 2% interest, compounded continuously. If she wants to use the money to buy a new bicycle in 1 year, how much will she be able to spend on the bike?
Use the formula A=Pert, where A is the balance (final amount), P is the principal (starting amount), e is the base of natural logarithms (≈2.71828), r is the interest rate expressed as a decimal, and t is the time in years.
The final amount is $2203. 2
How to determine the valueFrom the information given, the formula for finding the amount is expressed as;
A=Pert
Such that the parameters are;
A is the balance (final amount), P is the principal (starting amount) e is the base of natural logarithms (≈2.71828) r is the interest rate expressed as a decimal t is the time in years.Substitute the values, we have;
A = 300 × [tex]2.71^(^2^*^1^)[/tex]
Multiply the exponents, we have;
A = 300 × [tex]2.71^2[/tex]
Find the square value and multiply, we get;
A = $2203. 2
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A spinner with three equal size sections labeled red, green, and yellow is
spun once. Then a coin is tossed, and one of two cards labeled with a 1 or
a 2 is selected. What is the probability of spinning yellow, tossing heads,
and selecting the number 2?
FASTTT (ASAPPP!)
Use cramer's rule to solve this system: 8x+5y= 2x - 4y = - 10
The solution to the system of equations using Cramer's rule is x = -1 and y = 2.
To solve the system of equations using Cramer's rule, we'll need to determine the values of x and y by calculating the determinants of various matrices.
The given system of equations is:
8x + 5y = 2 (Equation 1)
2x - 4y = -10 (Equation 2)
First, let's calculate the determinant of the coefficient matrix, D:
D = |8 5|
|2 -4|
D = (8 * -4) - (5 * 2)
D = -32 - 10
D = -42
Next, we'll calculate the determinant of the matrix formed by replacing the x coefficients with the constants from the right side of the equations, Dx:
Dx = |2 5|
|-10 -4|
Dx = (2 * -4) - (5 * -10)
Dx = -8 + 50
Dx = 42
Similarly, we'll calculate the determinant of the matrix formed by replacing the y coefficients with the constants, Dy:
Dy = |8 2|
|2 -10|
Dy = (8 * -10) - (2 * 2)
Dy = -80 - 4
Dy = -84
Now, we can find the values of x and y:
x = Dx / D
x = 42 / -42
x = -1
y = Dy / D
y = -84 / -42
y = 2
Therefore, the solution to the system of equations is x = -1 and y = 2.
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Simplify each expression. Write your answer in exponential notation.
13. [(-0.5) (-0.5)²12²
14. (3.3³)3
تبر4 + 2( 20) .15
16. (a¹. a)³
(a^)³
Help I really need the extra credit
For simplification the exponent rules must be known to us .
The exponent rules are mentioned below:
a^0 = 1a^1 = aa^m × a^n = a^m+na^m / a^n = a^m−na^−m = 1/a^m(a^m)^n = a^mn(ab)m = a^mb^m(a/b)m = a^m/b^m1)
Now,
Simplifying,
[(-0.5)² *(-0.5)²]²
Apply property 3,
[(-0.5)^4]^2
(-0.5)^8
2)
(3.3³)3
Simplify by property 3
= 3 ^12
3)
(y² × y)²÷4y²
Simplify by rule 3 and 4,
= y^6 ÷ 4 y²
= y^4/4
4)
(a^3 × a^6)^3/(a^4)^5
Simplify by rule 3 and 4,
=a^7
Hence with the use of exponent rules the expressions can be simplified.
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A Ferris wheel with a diameter of 60 completes 2 revolutions in one minute. The center of the wheel is 30 feet above the ground. If a person taking a ride starts at the lowest point, which trigonometric function can be used to model the riders height, h(t), above the ground after t seconds?
Answer:
define the height above the ground, h, as a function of time, t, using the sine function:
h(t) = A * sin(B * t + C) + D
A represents the amplitude of the function, which is half of the vertical distance covered by the rider (in this case, 30 feet).
B represents the frequency of the function, which is related to the number of complete cycles or revolutions in a given time period. In this case, the Ferris wheel completes 2 revolutions per minute, so B = 2π (since 2π radians represents one complete revolution).
C represents the phase shift of the function, which accounts for the initial position of the rider. Since the rider starts at the lowest point, there is no phase shift, so C = 0.
D represents the vertical displacement of the function, which is the average height above the ground. In this case, the center of the wheel is 30 feet above the ground, so D = 30.
Putting it all together, the trigonometric function that can be used to model the rider's height, h(t), above the ground after t seconds is:
h(t) = 30 * sin(2π * t) + 30
Therefore, the sine function can be used to model the rider's height
What is the meaning of "it is a subset of any X ∈ C"?
The phrase "it is a subset of any X ∈ C" indicates that the subject in question (denoted by "it") is a subset of every element X that belongs to the set C. In other words, whatever "it" refers to is contained within every element of the set C.
The phrase "it is a subset of any X ∈ C" indicates that the subject in question (denoted by "it") is a subset of every element X that belongs to the set C. In other words, whatever "it" refers to is contained within every element of the set C.
To provide a clearer understanding, let's break it down further:
"Subset": A subset is a collection of elements that are all contained within another set. If set A is a subset of set B, it means that every element of A is also an element of B.
"Any X ∈ C": Here, X represents a generic element of the set C. The phrase "X ∈ C" denotes that X belongs to the set C. It implies that X is one of the elements within the set C.
Combining the two parts, "it is a subset of any X ∈ C" means that "it" (referring to a specific set or collection of elements) is included in every element X of the set C. In other words, every element of C contains "it" as a subset.
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A 13 km 13km13, start text, k, m, end text stretch of road needs repairs. Workers can repair 3 1 2 km 3 2 1 km3, start fraction, 1, divided by, 2, end fraction, start text, k, m, end text of road per week. How many weeks will it take to repair this stretch of road?
you can start by dividing the total length of the road by the distance that can be repaired per week:
13 km ÷ 3 1/2 km/week = 3.71 weeks
Rounding up, it will take 4 weeks to repair the entire 13 km stretch of road.
one serving of vegetables has 96 grams of protein witch is 30% of the recommended daily amount find the recommended daily amount of protein
Answer:
320 g
Step-by-step explanation:
To find the recommended daily amount of protein, we can set up a proportion using the given information:
30% of the recommended daily amount = 96 grams
Let "x" represent the recommended daily amount of protein. We can set up the proportion as:
30/100 = 96/x
To solve for x, we can cross-multiply and solve the equation:
30x = 100 * 96
30x = 9600
Dividing both sides by 30:
x = 9600 / 30
x ≈ 320
simplify and write in usual form ((5.5 * 10 ^ - 4)(6 * 10 ^ 7))/((3.3 * 10 ^ - 6) * (2 * 10 ^ 4) ^ 2)
Step-by-step explanation:
Expand the given 10 n and multiply it by the given number. 2. Then the result will be in the usual form.
2021: Sales Revenues = $800,000. Cost of good sold = $350,000
2020: Sales Revenues = $795,000. Cost of good sold = $600,000
Answer:
Step-by-step explanation:
Sales Revenue: $800.00
Cost of good sold: $350,000.00
Subtract: $450,000.00
Sales Revenue: $795,000.00
Cost of good sold: $600,000.00
Subtract Sales $195,000.00
Revenue from Cost
of goods sold.
Find the standard deviation of the sampling distribution of sample means using the given information. Round to one decimal place, if necessary. μ = 64 and o = 12; n = 9
The standard deviation of the data sample is 2.55.
What is the standard deviation of the data sample?The standard deviation of the data sample is calculated by applying the following formula;
S.D = √ (x - μ)²/(n - 1)
where;
μ is the mean of the distributionx is the sample datan is the number of sample dataThe given parameters;
mean, μ = 64
x, = 12
number of samples = 9
The standard deviation of the data sample is calculated as;
S.D = √ (12 - 64)²/(9 - 1)
S.D = 2.55
Thus, the standard deviation of the data sample is calculated by applying the formula for standard deviation.
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Match the histogram with the description that best fits the distribution of the data
shown in the histogram.
1. Uniform
2. Approximately Bell-Shaped
3. Skewed Left
4. Skewed Right
The correct matches are 1) Approximately Bell-Shaped, 2) Skewed Right, 3) Uniform and 4) Skewed Left.
Uniform: In a uniform distribution, the data is evenly spread across the entire range, resulting in a rectangular-shaped histogram. All values have roughly the same frequency or probability. It suggests that there is an equal chance of observing any value within the given range.
Approximately Bell-Shaped: This description refers to a distribution that closely resembles a bell curve or a normal distribution. The data is symmetrically distributed around a central peak, with most values clustered near the mean. The histogram will have a characteristic bell shape, with the highest frequency at the center and gradually decreasing frequencies on both sides.
Skewed Left: A left-skewed distribution, also known as negatively skewed or left-tailed, is characterized by a long tail extending towards the lower values. The majority of the data is concentrated on the right side of the distribution, and the tail extends to the left. The histogram will show a longer tail on the left side and a shorter right side.
Skewed Right: A right-skewed distribution, also known as positively skewed or right-tailed, has a long tail extending towards the higher values. The majority of the data is concentrated on the left side of the distribution, and the tail extends to the right. The histogram will exhibit a longer tail on the right side and a shorter left side.
Hence the correct matches are 1) Approximately Bell-Shaped, 2) Skewed Right, 3) Uniform and 4) Skewed Left.
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What is the co-interior angle x in the drawing below? Type in numerical answer only
Answer:
[tex]58 + x = 180[/tex]
[tex]x = 122[/tex]
Angle x measures 122°.
What is the angle of o in the drawing below? Type in numerical answer only
Answer:
[tex]52 + o = 180[/tex]
[tex]o = 128[/tex]
Angle o measures 128°.
An investor was afraid that he would become like King Lear in his retirement and beg hospitality from his children, so he purchased grain "tithes," or shares in farm output, for 800 pounds. The tithes paid him 78 pounds per year for 30 years. What interest rate did the he receive on this investment?
as far as I can read it, he bought £800 in shares, who knows how many, is irrelevant in this case, however we also know that he got £78 for 30 years, what was the rate?
well, we can nevermind the 30 years part and keep an eye that every year his earned interest was £78 flat, so we're looking at a simple interest rate, since it's not compounding, so let's reword all that
with an initial investment of £800 yielding £78 per year, what's the interest rate?
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \pounds 78\\ P=\textit{original amount deposited}\dotfill & \pounds 800\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &1 \end{cases} \\\\\\ 78 = (800)(\frac{r}{100})(1) \implies 78=8r\implies \cfrac{78}{8}=r\implies \stackrel{ \% }{9.75}=r[/tex]
if y is directly porportional to x^2 and the difference in the values of y when x=1 and x=3 is 32, find the value of y when x=-2
Answer:
Step-by-step explanation:
y=kx²
y₁=k(1)²=k
y₃=k(3)²=9k
y₁-y₃=k-9k=32
-8k=32
k=-4
y=-4x²
y₋₂=-4(-2)²=-16
a racer is traveling 150 miles per hour how many feet dose it travel in 5 seconds
150 miles is the same as 150*5280 = 792000 feet, and one hour is equivalent to 60*60 = 3600 seconds. Now we divide 792000 feet by 3600 seconds to get the equivalent rate: 792000 ft/3600 sec = 220 ft/second. Now, we multiply the rate by 5 and get 1100 feet per 5 seconds. So, our answer is 1100 feet.
Geometry
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Please answer fast
Applying the Angle Addition Postulate, the measure of angle BDC is calculated as: 57 degrees.
How to Apply the Angle Addition Postulate?The Angle Addition Postulate establishes that when two angles are adjacent, the measure of the resulting angle formed by their combination is equal to the sum of their individual measures.
Therefore, according to the Angle Addition Postulate, we would have:
(-6x + 11) + (-7x + 15) = 104
Solve for x:
-6x + 11 - 7x + 15 = 104
-13x + 26 = 104
-13x = 104 - 26
-13x = 78
x = -6
Measure of angle BDC = -7x + 15
Plug in the value of x:
Measure of angle BDC = -7(-6) + 15 = 57°
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HELP QUICK PLS, For each of the figures, write Absolute Value equation in the form
|x−c=d|, where c and d are some numbers, to satisfy the given solution set.
pls answer!
x = -8; x = -4
The absolute value equation for x = -4 can be written as:
|x - (-2)| = 2
We have,
For x = -8, the absolute value equation can be written as:
|x - c| = d
Substituting x = -8 into the equation, we have:
|-8 - c| = d
To satisfy the given solution set, we need to determine the values of c and d that make the equation true.
Since x = -8, the absolute value of -8 minus c should be equal to d.
For x = -8, a suitable choice of c would be -12 and d would be 4.
This gives us:
|-8 - (-12)| = 4
|4| = 4
Therefore, the absolute value equation for x = -8 can be written as:
|x - (-12)| = 4
Similarly, for x = -4, the absolute value equation can be written as:
|x - c| = d
Substituting x = -4 into the equation, we have:
|-4 - c| = d
To satisfy the given solution set, we need to determine the values of c and d that make the equation true.
Since x = -4, the absolute value of -4 minus c should be equal to d.
For x = -4, a suitable choice of c would be -2 and d would be 2. This gives us:
|-4 - (-2)| = 2
|-2| = 2
Therefore,
The absolute value equation for x = -4 can be written as:
|x - (-2)| = 2
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if i were to make 126 dollars a week and i were to work for one year, how much money would i have when the year is over? please hurry
Help me plssss 5 stars to whoever answers
Answer:
f = 65
s = 144
t = 144
u = 77
Step-by-step explanation:
the sum of a triangles angles will always be 180
so we can subtract 37 and 78 from 180 to find f which is 65
in regards to s and t, the sum of those 4 angles will be 360, and we can assume the opposite sides of the angles are the same.
so the other side of the 36 angle will also be 36, so we subtract 36 and 36 from from 380 which gives us 288
then we divide it by 2 because we have 2 unknown angles that are the same size, then we get 144 for s and 144 for t
the sum of the angles of a polygon will always be 360
so we can subtract 86 and 53 and t (which we now know is 144) from 360 to find u
so u = 77
If you’re walking on icream
Answer: clean your shoes
Step-by-step explanation:
since you're walking on ice cream , your shoes will be sticky so one should clean them shoes with water.
Solve the following system of equations with the substitution method:
y=10/3x-121
y=5/4x-46
Answer:
x = 36
y = -1
Step-by-step explanation:
The substitution method is when the value of one variable from one equation is substituted in the other equation.
y = 10/3x - 121
y = 5/4x - 46
In this case you substitute one of the equations for y.
5/4x - 46 = 10/3x - 121
Lets set the coefficient being multiplied by x to a number with a common demoninator.
15/12x - 46 = 40/12x - 121
Next isolate x and combine like terms.
15/12x - 46 = 40/12x - 121
-15/12x -15/12x
-46 = 25/12x - 121
+121 +121
75 = 25/12x
*12/25 12/25
36 = x
------
Now lets plug x in to solve for y
(you pick either equation to do this)
y = 5/4(36) - 46
y= 45 - 46
y = -1
A steel manufacturer wants to produce a container in the shape of a rectangular solid with volume 84 m3 . The manufacturer wants the length of the container to be one meter longer than the width, and the height to be one meter greater than twice the width. What should the dimensions of the container be?
Answer:
Step-by-step explanation:
Find the volume
1.Cone whose radius is 10cm and the height is 5cm.
2.Sphere whose radius is 5m.
3.Cone whose radius is 6m and the height is 20m.
Answer:
The answers are all in 2d.p
1)523.81cm³
2)166.67m³
3)754.29m³
Step-by-step explanation:
1)V=1/3pir²h
V=1/3×10²×5×22/7
V=523.81cm³
2)V=4/3pir³
V=4/3×5³
V=166.67m³
3)V=1/3pir²h
V=1/3×22/7×6²×20
V=754.29m³
5/6x - 1/3 > 1 1/3
Solve for x
Answer:
First subtract (4) and (3x) from each side of the equation to isolate the x ... 5x-4=3x-8 One solution was found : x = -2 Rearrange: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation
Step-by-step explanation:
Answer:
x > 2
Step-by-step explanation:
To solve for x, we will first simplify the left side of the inequality by finding a common denominator for the fractions:
5/6x - 1/3 > 4/3
Multiplying both sides by 6 to eliminate the fractions, we get:
5x - 2 > 8
Adding 2 to both sides, we have:
5x > 10
Dividing both sides by 5, the final answer is:
x > 2
Hope this helps!
A cylinder has a base diameter of 20 inches and a height of 2 inches. What is its volume in cubic inches, to the nearest tenths place?
Answer:
628.3 cubic inches
Step-by-step explanation:
Since the base diameter of the cylinder is d=20 inches, so its radius r is:
[tex]r=\frac{d}{2}=\frac{20}{2}=10[/tex]
Then, the volume V of the cylinder with radius r=10 inches and height h=2 inches is:
[tex]V=\pi r^{2} h=\pi\times 10^{2}\times 2=628.3[/tex]
Answer:
To find the volume of a cylinder, we need to use the formula V = πr^2h, where V is the volume, r is the radius of the base, and h is the height. Since we are given the diameter of the base, which is 20 inches, we can find the radius by dividing it by 2. So, r = 20 / 2 = 10 inches. The height is given as 2 inches. Plugging these values into the formula, we get:
V = π(10)^2(2)
V = π(100)(2)
V = 200π
To get the volume in cubic inches, we need to multiply this by the conversion factor of 1 cubic inch per cubic inch. This does not change the value, but it gives us the correct units. So,
V = 200π cubic inches
To round this to the nearest tenths place, we need to look at the hundredths digit. If it is 5 or more, we round up; if it is less than 5, we round down. Using a calculator, we can approximate π as 3.14. So,
V ≈ 200(3.14) cubic inches
V ≈ 628 cubic inches
The hundredths digit is 0, which is less than 5. So we round down and keep the tenths digit as it is. Therefore,
V ≈ 628.0 cubic inches
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Calculate the dimensions of an irregular hexagon whose perimeter in 98 cm. Answer will vary.
The dimensions of the irregular hexagon are 17 cm, 15 cm, 14 cm, 13 cm, 22 cm and 17 cm
Calculating the dimensions of the irregular hexagonFrom the question, we have the following parameters that can be used in our computation:
Shape = irregular hexagon
Also, we have
Perimeter = 98 cm
The perimeter of a shape is the sum of its side length
An irregular hexagon has six unequal sides
using the above as a guide, we have the following:
17 + 15 + 14 + 13 + 17 + 22 = 98
This means that the side lengths are 17 cm, 15 cm, 14 cm, 13 cm, 22 cm and 17 cm
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