There are 210 ways we can give 4 different prizes to any 4 of 10 people if no person receives more than 1 prize.
To calculate the number of ways we can do this, we can use the formula for combinations. The formula for the number of ways to choose r objects from a set of n objects is:
ⁿCₓ = n! / x!(n-x)!
where n! represents the factorial of n, which is the product of all positive integers up to n.
5! = 5 x 4 x 3 x 2 x 1 = 120.
In this problem, we want to choose 4 people from a set of 10, so we can use the formula:
¹⁰C₄ = 10! / 4!(10-4)!
Simplifying this expression, we get:
¹⁰C₄ = (10 x 9 x 8 x 7) / (4 x 3 x 2 x 1)
¹⁰C₄ = 210
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a research team conducted a survey to check what proportion of preschool children in the hillsborough county who are not vaccinated. a random sample of 150 preschool children in hillsborough county revealed that only 60 had been vaccinated. what is the point estimate for the true proportion? [ select ] what is maximal margin of error (e) at 95% confidence? [ select ] construct a 95% confidence interval for the true proportion of interest.
The point estimate for the proportion of preschool children in Hillsborough County who are not vaccinated is 0.6 or 60%.
The point estimate for the true proportion of preschool children in Hillsborough County who are not vaccinated can be calculated by dividing the number of unvaccinated children in the sample by the total number of children in the sample
Point estimate = Number of unvaccinated children / Total number of children in sample
Since the sample size is 150 and the number of vaccinated children is 60, the number of unvaccinated children can be found by subtracting the number of vaccinated children from the total sample size
Number of unvaccinated children = Sample size - Number of vaccinated children
Number of unvaccinated children = 150 - 60 = 90
Therefore, the point estimate for the proportion of preschool children in Hillsborough County who are not vaccinated is
Point estimate = 90/150 = 0.6 or 60%
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The given question is incomplete, the complete question is:
A research team conducted a survey to check what proportion of preschool children in the hillsborough county who are not vaccinated. a random sample of 150 preschool children in hillsborough county revealed that only 60 had been vaccinated. what is the point estimate for the true proportion?
what is the contrapositive of if a radio station is playing music, then the radio station is playing an elvis song.
The original statement simply makes a conditional assumption and does not specifically declare that all of the music play by a radio station was Elvis music.
The declaration "If a station of radio plays music, then that radio station are playing the Elvis song" has the contrapositive "If it's a radio station refuses to play a Elvis song, then this radio station is without playing music."
A conditional statement's contrapositive reverses the premise and conclusion and rejects both. The original assertion and the contrapositive are logically equal, thus if the former is true, the latter is likewise true, but vice versa.
In this instance, the contrapositive argument claims that a radio station can't be playing music if it isn't playing an Elvis song. This could be taken to mean that whenever the radio station plays music, it must be an Elvis song.
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Which question can be answered by solving the inequality 7x < 50?
Answer:
The inequality 7x < 50 can be used to answer questions that involve finding the maximum value of x that satisfies the inequality. Specifically, we can solve this inequality to find the largest value of x such that 7x is less than 50.
For example, if x represents the number of hours you can work in a week and you are paid $7 per hour, then 7x represents your weekly earnings. If you want to earn less than $50 per week, the inequality 7x < 50 would be relevant. Solving this inequality would tell you the maximum number of hours you can work per week to earn less than $50.
Another example could be finding the maximum number of items you can purchase if each item costs $7 or less and you have $50 to spend. In this case, x would represent the number of items you can purchase, and 7x represents the total cost of the items. Solving the inequality 7x < 50 would give you the maximum number of items you can purchase while spending less than $50.
So, the question that can be answered by solving the inequality 7x < 50 depends on the context in which it is being used.
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Estimate the measure of this angle within 15°.
Answer:
Step-by-step explanation:
Which expression is equivalent to -3(2x - 8) + 4x?
A
B
C
D
-2x-8
-2x + 24
-10x8
-10x + 24
We distribute -3 to 2x and -8, and then we calculate the two multiplications.
We calculate -6x + 4x = -x(6 - 4) = -2x
[tex] \bf - 3(2x - 8) + 4x = \\ \\ \bf = - 3 \cdot 2x - 3 \cdot ( - 8) + 4x = \\ \\ \bf = - 6x + 24 + 4x = \\ \\ \bf = - 6x + 4x + 24 = \\ \\ \bf = - 2x + 24[/tex]
The answer is B -2x + 24
Hope that helps! Have a nice day! :)
The standard error of the mean for a sample of size 153 is 25. in order to cut the standard error of the mean in half (to 12.5) we must select a sample size of?
In order to cut the standard error of the mean in half (to 12.5), you must select a sample size of 612.
To find the new sample size required to cut the standard error of the mean in half, you can use the following formula:
New Standard Error = (Old Standard Error) / √(New Sample Size / Old Sample Size)
We know the old standard error (25) and want to find the new standard error (12.5). So, we can rewrite the formula as:
12.5 = 25 / √(New Sample Size / 153)
First, divide both sides of the equation by 25:
0.5 = 1 / √(New Sample Size / 153)
Next, square both sides of the equation:
0.25 = 1 / (New Sample Size / 153)
Now, take the reciprocal of both sides:
4 = New Sample Size / 153
Finally, multiply both sides by 153 to find the new sample size:
New Sample Size = 4 * 153
New Sample Size = 612
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i need help with What are some benefits to private ownership? Select three answers.
Answer: Private ownership provides land or goods for all citizens to use. Private ownership can make it possible for a business to earn money. Private ownership might help a person move to another economic class. Private ownership allows a person to own goods that may increase in value.
Step-by-step explanation:
consider a modified sat problem, sat’ in which given a cnf formula having m clauses and n variables x1, x2, . . . , xn, the output is yes if there is an assignment to the variables such that exactly m − 2 clauses are satisfied, and no otherwise. prove that sat’ is np-complete.
Since 3-SAT is NP-complete and we have a polynomial-time reduction from 3-SAT to SAT', it follows that SAT' is NP-hard. Thus, SAT' is NP-complete, as required.
To prove that SAT' is NP-complete, we need to show that it is in NP and that it is NP-hard.
First, we show that SAT' is in NP. Given a CNF formula, we can verify in polynomial time whether a proposed assignment to the variables satisfies exactly m-2 clauses. Specifically, we can evaluate each clause in the formula under the proposed assignment, count the number of clauses that are satisfied, and compare it to m-2. If the count is exactly m-2, then the assignment satisfies exactly m-2 clauses, and we can verify this in polynomial time. Therefore, SAT' is in NP.
Next, we show that SAT' is NP-hard. We do this by reducing an NP-complete problem to SAT'. We choose 3-SAT, which is known to be NP-complete.
Given an instance of 3-SAT with m clauses and n variables, we construct an instance of SAT' as follows. We add two new variables, y and z, and construct the following CNF formula:
(a1 ∨ b1 ∨ y) ∧ (a2 ∨ b2 ∨ ¬y) ∧ (a3 ∨ b3 ∨ ¬z) ∧ (a4 ∨ b4 ∨ z) ∧ C1 ∧ C2 ∧ ... ∧ Cm,
where C1, C2, ..., Cm are the m clauses of the 3-SAT instance, and each clause in the 3-SAT instance has exactly three literals.
We claim that this construction is a polynomial-time reduction from 3-SAT to SAT'. First, note that the CNF formula has n+2 variables and m+4 clauses, which can be constructed in polynomial time. Second, note that any assignment that satisfies exactly m-2 clauses in the CNF formula must assign y to true and z to false. This is because the first two clauses require y to be true and false, respectively, and the last two clauses require z to be false and true, respectively. Thus, the assignment to the original n variables satisfies exactly m-2 clauses in the 3-SAT instance. Conversely, any assignment to the original n variables that satisfies exactly m-2 clauses in the 3-SAT instance can be extended to an assignment that satisfies exactly m-2 clauses in the CNF formula by setting y to true and z to false. Therefore, there is a 1-1 correspondence between solutions to the 3-SAT instance and solutions to the SAT' instance.
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A website is selling balance beams for $84, but mentions that they originally cost $112. What
is the discount percentage?
Write your answer using a percent sign (96)
Answer:
25%
Step-by-step explanation:
$112 × X =$84
X= 84/112
X=0.75
Converting to a percent is to multiply by 100
75%
$112-$84 = $28
25%
Answer: 25%
Step-by-step explanation: $112 × X =$84 X= 84/112 X=0.75 Converting to a percent is to multiply by 100 75% $112-$84 = $28 25%
can i please have brainliest i need it
Need help now please.
A construction worker on the ground tosses an apple to a fellow worker who is 20. ft. above
the ground. The starting height of the apple is 5 ft. Its initial upward velocity is 32 ft/s. At
what time(s) will the apple be at the same height as the worker? (h=-161² + vt +c, where h
is the height, v is the initial velocity and c is the starting height.)
The apple will be at the same height as the worker at 0.75 seconds and 1.25 seconds
At what time will the apple be at the same height as the worker?Given that
The starting height of the apple is 5 ft. Its initial upward velocity is 32 ft/s.So, the function is
h = -16t² + 32t +5
The worker's height is 20
So, we have
h = 20
This gives
-16t² + 32t +5 = 20
Evaluate the like terms
-16t² + 32t - 15 = 0
When solved on a graph, we have
t = 0.75 and 1.25
Hence, the times are 0.75 seconds and 1.25 seconds
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Find the surface area of this shape
The total surface area of the square based prism using the net is 119 square meters
Calculating the total surface area using the net.From the question, we have the following parameters that can be used in our computation:
The net of a square based prism
The surface area of the square based prism from the net is calculated as
Surface area = sum of areas of individual shapes that make up the net of the triangular prism
Using the above as a guide, we have the following:
Area = Square + 4 * triangle
So, we have
Area = 7 * 7 + 4 * 1/2 * 5 * 7
Evaluate
Area = 119
Hence, the surface area is 119 square meters
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L 2.2.3 Quiz: Adding and Subtracting Like Fractions
Question 4 of 15
When fractions have the same denominator, their also has the same
denominator.
A. sum
B. numerator
C. product
D. dividend
SUBMIT
Answer:
A: sum
Step-by-step explanation:
For adding or subtracting fractions, the denominators of the concerned fractions need to be equal.
Using the graph, determine the coordinates of the vertex of the parabola.
Answer:
(-5,1)
Step-by-step explanation:
The vertex of a parabola is either the top most point or the bottom most, depending on which parabola is being talked about.
Step-by-step explanation:
look in thr comments and have a great day
Find the surface area of a hexagonal pyramid with a apothem of 3 square root of 2 and height of 3
The surface area of the hexagonal pyramid is 54√3 + 18√6 square units.
The base of the pyramid is a regular hexagon, so we can use the formula for the area of a regular hexagon:
Area of hexagon = (3√3/2)a^2, where a is the length of one side of the hexagon
Since the apothem of the hexagon is 3√2, we can use the relationship between the apothem and the side length:
apothem = (1/2)√3a
Solving for a,
a = 2√6
Substitute the value of a = 2√6 into the formula,
Area of hexagon = (3√3/2)(2√6)^2
= 54√3
Each face is a triangle with a base equal to one side of the hexagon and a height equal to the height of the pyramid, which is given as 3.
Using the formula for the area of a triangle,
Area of one face = (1/2)bh
= (1/2)(2√6)(3)
= 3√6
There are six identical faces, so the total area of the lateral faces is:
Total lateral area = 6(3√6)
= 18√6
Finally, we add the area of the base and the lateral faces to get the total surface area of the pyramid:
= 54√3 + 18√6
Therefore, the surface area of the hexagonal pyramid is 54√3 + 18√6 square units.
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PLEASE HELPPPPPPPPPPP MEEEEEEE
The following are the measures of angles and sides using the sine and cosine rules:
1). QR = 15, m∠P = 52°, m∠Q = 43°
2). BC = 21, DC = 10.4, m∠C = 22°
3). VX = 10.7, WX = 10.2, m∠V = 39°
4). HF = 18.4, m∠H = 28.7, m∠F = 15.3
What is the sine and cosine rulesThe sine rule is a relationship between the size of an angle in a triangle and the opposing side. While the cosine rule relates the lengths of the sides of a triangle to the cosine of one of its angles.
1). Using the sine rule:
19/sin85 = 13/sunQ
Q = sin⁻¹[(13 × sin85)/19] {cross multiplication}
Q = 43
m∠P = 180° - (85 + 43) = 52°
QR = sin⁻¹[(19 × sin52)/sin85]
QR = 15.
2). m∠C = 180 + (19 + 139) = 22°
Using the sine rule:
BC = (12 × sin139)/sin22
BC = 21.
DC = (12 × sin19)/sin22
DC = 10.4
3). m∠V = 180 - (41 + 100) = 39°
Using the sine rule:
VX = (16 × sin41)/sin100
VX = 10.7
WX = (16 × sin39)/sin100
WX = 10.2
4). Using the cosine rule:
HF² = 7² + 13² - 2(7)(13)cos136°
HF = √338.8491
HF = 18.4
applying sine rule;
F = sin⁻¹[(7 × sin136)/18.4]
F = 15.3
m∠H = 180 - (15.3 + 136) = 28.7
Therefore, the measures of angles and sides using the sine and cosine rules are:
1). QR = 15, m∠P = 52°, m∠Q = 43°
2). BC = 21, DC = 10.4, m∠C = 22°
3). VX = 10.7, WX = 10.2, m∠V = 39°
4). HF = 18.4, m∠H = 28.7, m∠F = 15.3
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Michael thought he could only run five laps around the track but he was actually able to run eight laps what was his percent error
Answer:
Rounded percent error = 38% So, Michael's percent error was 38%.
Step-by-step explanation:
Rounded percent error = 38% So, Michael's percent error was 38%.
Modeling London's
Population
Task
The table below shows historical estimates for the
population of London.
Year
1801
1821 1841 1861 1881
1901 1921 1939
1961
London
population 1,100,000 1,600,000 2,200,000 3,200,000 4,700,000 6,500,000 7,400,000 8,600,000 8,000,000
No data was available in 1941 because of the war.
a. Can the London population data be accurately
modeled by a linear, quadratic, or exponential function?
Explain.
b. A logistic growth equation can be written in the form
a
P(1) = 1 + e-b(t-c)
where a, b, and care positive numbers and t represents
time measured in years. Using the application supplied,
determine if the London population data can be
accurately modeled by a logistic equation.
a
c. Explain the shape of the graph of P in terms of the
structure of the equation P(t) = 1). What impact do
the values of a, b, and c have on the graph of P?
a. Models featuring a linear function are not appropriate for representing London's population data due to its steadily growing exponent over time, as opposed to a fixed rate.
b. Computing the parameters a, b, and c of the logistic growth equation necessitates employing an application, however the language of this model does not offer this capability.
How to explain the modelThe logistic growth equation P(t) = 1 / [1 + e^(-b(t-c))] has an S-shaped curve, indicative of a population commencing with a slow growth, then rapidly propagating towards its carrying capacity (represented by parameter a), before ultimately hitting an equilibrium near the maximum size.
Parameters a, b, and c in the equation respectively symbolize the highest sustainable populous, rate of growth, and peak point at which the increase is most pronounced. Variations of value among these three determine the graph of P; higher figures of a result in more spacious upper limit, larger values of b indicate a higher rise pace, whilst bigger results of c cause the inflection juncture to appear later.
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Help me! Match the angle inscribed in a circle to the measure of its intercepted arc.
(Best answer gets brainliest)
Angle ∠B = 35 degrees then Intercepted arc AC is 70 degrees
∠B = 31 degrees then Intercepted arc AC is 62 degrees
∠B = 28 degrees then Intercepted arc AC is 56 degrees
∠B = 17 degrees then Intercepted arc AC is 34 degrees
∠B = 42 degrees then Intercepted arc AC is 84 degrees
Using the inscribed angle theorem, we have
∠B=1/2AC
When ∠B is 35 degrees
Intercepted arc AC = 2×35 =70 degrees
When ∠B is 31 degrees
Intercepted arc AC = 2×31 =62 degrees
When ∠B is 28 degrees
Intercepted arc AC = 2×28 =56 degrees
When ∠B is 17 degrees
Intercepted arc AC = 2×17 =34 degrees
When ∠B is 42 degrees
Intercepted arc AC = 2×42 =84 degrees
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What is the equation of the blue line
Answer:
y = 3x + 1
Step-by-step explanation:
The equation is y = mx + b
m = the slope
b = y-intercept
Slope = rise/run or (y2 - y1) / (x2 - x1)
Pick points (0,1) (1,4)
We see the y increase by 3 and the x increase by 1, so the slope is
m = 3
Y-intercept is located at (0,1)
So, the equation of the line is y = 3x + 1
A right triangle has side lengths of 8 inches and 6 inches. What is the length of the hypotenuse, in inches?
The length of the hypotenuse is 10 inches.
What is a right triangle?
A given triangle is said to be a right triangle if the measure of only one of its internal angles is equal to 90^o. So that the sum of the internal angles of the triangle is 180^o.
Applying the Pythagorean theorem to the given right triangle, we have;
/Hyp/^2 = /Adj/^2 + /Opp/^2
= 8^2 + 6^2
= 64 + 36
= 100
Hyp = (100)^1/2
= 10
Therefore, the length of the hypotenuse of the right triangle is 10 inches.
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Find the area of a triangle with a height of 11 inches and a base of 23 inches
Answer:
Area of a triangle = 126.5 cm²
Step-by-step explanation:
Area of a triangle = (base * height) / 2
Area of a triangle = (23 in * 11 in) / 2
Area of a triangle = 253 in² / 2
Area of a triangle = 126.5 in²
Celia's house is located at point A on the image shown.
Celia drives 6 miles along a straight road to reach her friend's house at point B. Later, she makes a right turn and drives 8 miles to reach a store located at point C. Rhonda starts from Celia's house at point A and reaches the same store at point C driving along a straight road. How much more did Celia drive than Rhonda?
A. 10 miles
B. 14 miles
C. 4 miles
D. 2 miles
The number of miles Celia drove than Rhonda is 4 miles. The correct option is C. 4 miles
Pythagorean theorem: Calculating how much more Celia drove than RhondaFrom the question, we are to determine how much more Celia drove that Rhonda.
From the given information,
The total distance covered by Celia is
6 miles + 8 miles
= 14 miles
In the given diagram, we have right triangle
We can calculate the distance Rhonda covered using the Pythagorean theorem.
Let the distance Rhonda covered be R
Then,
R² = 6² + 8²
R² = 36 + 64
R² = 100
R = √100
R = 10 miles
Thus,
The distance Rhonda covered is 10 miles
Now,
The number of miles Celia drove more than Rhonda is
14 miles - 10 miles
= 4 miles
Hence, Celia drove 4 miles more than Rhonda
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pls help me
Leon is making a cake for the first time. His recipe calls for 280 grams of sugar, but he accidentally pours 295 grams on his first try. He uses a small spoon to remove the extra sugar. If he needs to remove 12 spoonfuls, how many milligrams of sugar does his spoon hold?
Answer:
1250 milligrams
Step-by-step explanation:
He adds an extra 15 grams, or 15000 milligrams, of sugar. The small spoon can scoop up 15000 milligrams in 12 spoonfuls. So it scoops up (15000/12) or 1250 milligrams per scoop.
A football is kicked into the air. It's height in meters after t seconds is given by h= -4.9(t-2.4)^2+29.
a. What was the height of the football when it was kicked?
b. What was the maximum height of the ball? At what time was the maximum height reached?
c. How high was the ball after 2 seconds?
d. Was the ball still in the air after 5 seconds?
The height of the football when it was kicked is 0.776 meter.
The maximum height of the ball is 29 meters, at a time of 2.4 seconds.
The height of the football after 2 seconds is 28.87 meter.
No, the ball was not in the air after 5 seconds.
What is the vertex form of a quadratic equation?In Mathematics and Geometry, the vertex form of a quadratic equation is modeled by this formula:
f(x) = a(x - h)² + k
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.The football was kicked when t = 0, so the height is given by;
h(0) = -4.9(0 - 2.4)² + 29
h(0) = 0.776 meter.
For the maximum height of the ball, we have:
Vertex (h, k) = (2.4, 29).
Maximum height, k = 29 meters.
After 2 seconds, the height of the ball is given by;
h(2) = -4.9(2 - 2.4)² + 29
h(2) = 28.87 meter.
After 5 seconds, the height of the ball is given by;
h(5) = -4.9(5 - 2.4)² + 29
h(5) = -4.124 meter.
In conclusion, the ball would not be in the air after 5 seconds because because it would land after 4.124 seconds.
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Which statement regarding the diagram is true?
m∠WXY = m∠YXZ
m∠WXY < m∠YZX
m∠WXY + m∠YXZ = 180°
m∠WXY + m∠XYZ = 180°
The true statement regarding the diagram is this: m∠WXY = m∠YXZ.
What is the true statement?In the diagram, we find that angles WXY and angle YXZ are supplementary. The meaning of this is that the two angles add up to give 180 degrees. First, we have the angle that is at 90 degrees while the second angle is also at 90 degrees.
When we add these two together, we arrive at 180 degrees. So, the two angles are supplementary and equal thus, we can arrive at the conclusion that m∠WXY = m∠YXZ.
Complete Question:
The image is a straight line with points W, X, Z, and an angle with axis Y, appended at 45°.
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Please answer
P(A) = 0.04 and P(A ∩ B) = 0.028. A and B are independent events. Find P(B).
The probability of the independent events are solved and P ( B ) = 0.7
Given data ,
Let the probability of the independent events be
P ( A ) = 0.04
P ( A ∩ B ) = 0.028
Now , If events A and B are independent, then we know that:
P(A ∩ B) = P(A) × P(B)
We are given that P(A) = 0.04 and P(A ∩ B) = 0.028
P(A ∩ B) = P(A) × P(B)
0.028 = 0.04 × P(B)
P(B) = 0.028 / 0.04
P(B) = 0.7
Hence , the probability of event B, P(B), is 0.7
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Use the graph to answer the question.
The graph shows the number of meals served each day at two different restaurants.
Meals Served in January
Restaurant A
Restaurant B
30 32 34 36 38 40 42
Restaurant
Based on this data, which restaurant is more likely to serve the greater number of meals on a given day?
Move a letter to the box and a word to the blank to answer the question.
46 48 50 52 54 56 58 60
Number of Meals Served
is more likely to serve a greater number of meals because it has the greater
median
A
range
62 64
interquartile range
Answer: median of a: 40
b: 54
Restaurant B is more likely to serve a grater number of meals it it has the grater median
[use median to compare two lets]
Step-by-step explanation:
how many numbers consisting of 1,2, or 3 digits(without repitions)can be formed using the digits 1,2,3,4,5,6?
Therefore, there are 156 numbers consisting of 1, 2, or 3 digits that can be formed using the digits 1, 2, 3, 4, 5, 6 without repetitions.
We need to find the number of numbers consisting of 1, 2, or 3 digits that can be formed using the digits 1, 2, 3, 4, 5, 6 without repetitions.
1-digit numbers: There are 6 choices for the first digit.
2-digit numbers: There are 6 choices for the first digit, and 5 choices for the second digit (since we cannot repeat the first digit).
3-digit numbers: There are 6 choices for the first digit, 5 choices for the second digit (since we cannot repeat the first digit), and 4 choices for the third digit (since we cannot repeat the first or second digit).
Therefore, the total number of numbers that can be formed is:
1-digit numbers: 6
2-digit numbers: 6 x 5 = 30
3-digit numbers: 6 x 5 x 4 = 120
The total number of numbers is the sum of these:
6 + 30 + 120 = 156
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What is -2/9 expressed as a decimal number?
Answer:
Step-by-step explanation:
-.222 repeated
Plot the point (-10,2π), given in polar coordinates, and find other polar coordinates (r,θ) of this same point for which the following are true.
(a) For the same point on the graph, find new values of (r,θ) for which r>0, -2π≤θ<0
(Type an ordered pair. Type an exact answer, using π as needed.)
The polar coordinates of this same point is (-8, -2π).
The point (-10, 2π) can be plotted on a graph with polar coordinates by beginning at the origin (0,0) and moving -10 units along the θ axis and then 2π units along the r axis.
To find other polar coordinates (r, θ) of this same point for which r > 0 and -2π ≤ θ < 0, we can move the point along the θ axis and then along the r axis in the opposite direction. This will result in a new point (r, θ) where r > 0 and -2π ≤ θ < 0.
For example, we can move the point along the θ axis to (-10, -2π), and then move it along the r axis to (-8, -2π).
This would result in the new point (r = -8, θ = -2π), which satisfies the given conditions.
Therefore, the polar coordinates of this same point is (-8, -2π).
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