The maximum possible area of such a triangle is $\frac{1}{2} \cdot \sqrt{4 + 2\sqrt{3}} = \frac{\sqrt{12 + 6\sqrt{3}}}{2} = 3\sqrt{3} + 3$, and $a + b + c = 3 + 3 + 3 = \boxed{9}$.
Let O and O' be the centers of the circles with radii 1 and 3, respectively, and let P and Q be points on the small and large circles, respectively, such that TPQ is a triangle. ]
Since the radius of the small circle is 1, we have TP = 1. Let R be the midpoint of PQ, so that TR is the altitude of triangle TPQ from T. Let x = TP = 1, y = TQ, and z = TR. [asy]
unit size(0.6 cm);
pair O, OO, P, Q, R, T;
O = (0,0);
OO = (4,0);
T = (0,3);
P = intersection points(Circle(O,1),Circle(T,2))[1];
Q = intersection points(Circle(OO,3),Circle(T,2))[0];
R = (P + Q)/2;
draw(Circle(O,1));
draw(Circle(OO,3));
draw(T--P--Q--cycle);
draw(T--R);
label("$O$", O, SW);
label("$O'$", OO, SE);
label("$P$", P, NW);
label("$Q$", Q, NE);
label("$R$", R, S);
label("$T$", T, N);
label("$x$", (T + P)/2, W);
label("$y$", (T + Q)/2, E);
label("$z$", (T + R)/2, W);
[/asy]
Then we have TR = z, and by the Pythagorean Theorem in right triangle TPQ we have
\begin{align*}
TQ^2 - 1 &= TR^2 = z^2, \
TQ^2 + 9 &= (TQ + TR)^2 = (TQ + z)^2.
\end{align*}Solving for TQ in the first equation and substituting into the second, we obtain
[(1 + z)^2 + 9 = (1 + z)^2 + 4z^2,]which simplifies to $z^2 - 2z - 2 = 0$. The positive root of this quadratic equation is $z = 1 + \sqrt{3}$, so $TQ = \sqrt{4 + 2\sqrt{3}}$. Then the area of triangle TPQ is
[\frac{1}{2} \cdot TP \cdot TQ = \frac{1}{2} \cdot \sqrt{4 + 2\sqrt{3}}.]Thus the maximum possible area of such a triangle is $\frac{1}{2} \cdot \sqrt{4 + 2\sqrt{3}} = \frac{\sqrt{12 + 6\sqrt{3}}}{2} = 3\sqrt{3} + 3$, and $a + b + c = 3 + 3 + 3 = \boxed{9}$.
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–81, 108, –144, 192, ...
Which formula can be used to describe the sequence?
The formula that can be used to describe the sequence will be aₙ = –81 · (–4/3)ⁿ⁻¹.
What is a geometric sequence?A series of non-zero integers where every term after the first is obtained by increasing the one before it by a constant, non-zero value known as the scale factor.
Let a₁ be the first term and r be the common ratio. Then the nth term of the geometric sequence is given as,
aₙ = a₁ · (r)ⁿ⁻¹
The sequence is given below.
–81, 108, –144, 192, ...
The first term of the sequence is –81. And the common ratio is given as,
r = 108 / (–81)
r = – 4/3
The formula can be used to describe the sequence is given as,
aₙ = –81 · (–4/3)ⁿ⁻¹
The formula that can be used to describe the sequence will be aₙ = –81 · (–4/3)ⁿ⁻¹.
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A redwood tree casts a shadow that is 8 meters long. A carpool lane sign near the redwood
tree casts a shadow that is 4 meters long. If the redwood tree is 6 meters tall, how tall is the
carpool lane sign?
Answer:
Hey bro, solving this would be relatively simple. If the Redwood tree is 6 meters tall, then the height of the carpool lane sign can be easily calculated using similar triangles. Using the lengths of their respective shadows, the carpool lane sign should be 3 meters tall, because the ratio between the height of the Redwood tree and the carpool lane sign, is the same ratio as between their respective shadows (8 to 4). The based way to solve this problem would be to measure the length of the shadows, and then use the ratio to calculate the height of the carpool lane sign.
Answer:
You need to set up the problem to solve for X. X = how tall is the tree? Set up your problem in this fashion. Set up the formula then arrange to solve for X. X/9 (shadow of the tree) = 15 (how tall the building is)/6 (shadow of building) X= 15/6 * 9 To get X alone, you need to move 9 to the other side of the equation. multiply by 9 on each side. For X side, this nullifies 9 and gets 9 to the other side. X= 2.5*9 You have divided 15 by 6, now multiply by 9 to get final answer for X X=22.5 meters The tree is 22.5 meters tall.
Step-by-step explanation:
If this is not.. right ill do another answer!!
) Reemplazar una obligación de $4.000.000 que vence en el mes 7, por tres pagos iguales, uno hoy, otro en el mes 10 y el final en el mes 15, considerando un interés del 10% Efectivo Semestral.
Three equal payments of $1,468834.26 made today, in month 10, and in month 15, with 5% semiannual interest, will be sufficient to cover the debt of $4,000,000 that matures in month 7.
What is the semiannual interest rateTo replace the obligation of $4,000,000 that matures in month 7, we need to calculate the size of three equal payments that can be made today, in month 10, and in month 15, that will cover the debt with interest.
First, we need to determine the semiannual interest rate. The annual interest rate is 10%, so the semiannual interest rate is 5% (10%/2).
Next, we can use the present value formula to calculate the size of the equal payments:
PV = PMT * [(1 - (1 + r)^-n) / r]
where PV is the present value of the debt, PMT is the size of the equal payments, r is the semiannual interest rate, and n is the number of semiannual periods.
Since the debt matures in month 7, which is the end of the sixth month, and the payments will be made today (month 0), in month 10 (the end of the ninth month), and in month 15 (the end of the fourteenth month), we have three semiannual periods to consider.
Using the values we have, we can substitute them into the formula:
PV = $4,000,000
r = 5%
n = 3
$4,000,000 = PMT * [(1 - (1 + 5%)^-3) / 5%]
Solving for PMT, we get:PMT = $1,468834.26
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Translation:
Replace an obligation of $4,000,000 that matures in month 7, by three equal payments, one today, another in month 10 and the final one in month 15, considering an interest of 10% Cash Semiannual.
PLEASE HELP ASAP! DUE SOON !
Answer & Step-by-step explanation:
The domain of the function g(x) = ⟨÷⟩6x + 6 is the set of all real numbers, since dividing by zero is not defined.
And it is a linear function, which means that it is a straight line in a 2-dimensional graph. The slope of the line is 6, and the y-intercept is 6, meaning that when x=0, the value of g(x) is 6.
An airplane fies 3,780 miles in 7.5 hours. What is the speed of the airplane in miles per hour? Use the equation d=rt, where d is distance, r is rate, and t is time.
The airplane's speed ismiles per hour.
Answer:
504
Step-by-step explanation:
3780÷7.5=504
504 mph because 504 x 7.5 = 3780
Please give good review. :)
What is (f- g)(x)?
f(x)= x¹ - x² +9
g(x) = x³ + 3x² + 12
Enter your answer in standard form in the box.
(f-g)(x) =
The value of the function (f-g)(x)=[tex]x-4x^{2} -x^{3} -3[/tex].
What is a function?
A function is defined as the relationship between input and output, where each input has exactly one output. The inputs are the elements in the domain and the outputs are elements in the co-domain.
f(x)= x¹ - x² +9
g(x) = x³ + 3x² + 12
To find (f-g)(x):
The operations on functions are as easy as the operations on numbers or polynomials.
We have to subtract the functions to find the above mentioned operation.
(f-g) (x)= f(x)-g(x)
= (x¹ - x² +9)-(x³ + 3x² + 12)
The minus will change the signs of function g.
= [tex]x-x^{2} +9-x^{3}-3x^{2} -12[/tex]
=[tex]x-4x^{2} -x^{3} -3[/tex]
Hence, the value of the function (f-g)(x)=[tex]x-4x^{2} -x^{3} -3[/tex]
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For each sequence, create an input-output table with the figure number and the number of tiles in each figure for 1 ≤ n ≤ 10. Figure Number, n 1 2 3 4 5 6 7 8 9 10 Total Number of tiles in Sequence I, T 10 12 14 16 18 20 22 24 26 28 Total Number of tiles in Sequence II, T 5 8 11 14 17 20 23 26 29 32
Answer:
Here is the input-output table for Sequence I:
Figure Number, n | Total Number of Tiles, T
1 | 10
2 | 12
3 | 14
4 | 16
5 | 18
6 | 20
7 | 22
8 | 24
9 | 26
10 | 28
And here is the input-output table for Sequence II:
Figure Number, n | Total Number of Tiles, T
1 | 5
2 | 8
3 | 11
4 | 14
5 | 17
6 | 20
7 | 23
8 | 26
9 | 29
10 | 32
find the mode of the following data 20,26,16,22,20,30,22,20,26
The mode of the data 20,26,16,22,20,30,22,20,26
How to find the mode of the data?From the question, we have the following parameters that can be used in our computation:
20,26,16,22,20,30,22,20,26
The mode of a dataset is the data element that has the highest frequency
Using the above as a guide, we have the following:
20 has the highest frequency of 3
Hence, the mode is 3
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1. I owe $8500 on my credit card. The card has a promotional interest rate of 0% for 24 months. To repay the debt, I'm going to pay a fixed amount toward the balance every month. After 12 months, my remaining debt will be $6460. Which of the following equations correctly relates the remaining debt (D) to the number of months (1) I've been making payments? (Select all that apply.)
a. 170t+D=8500
b. D= 170t-6460
c. D+6460=8500t
d. D = 6460 + 170t
2. Use the situation from problem #1. If I continue paying at the rate above (assuming there is no additional interest), how many months will it take me to pay off my credit card?
1. The equation that correctly relates the remaining debt (D) to the number of months (1) I've been making payments is:
a. 170t + D = 8500.
2. If you continue paying at the rate above (assuming there is no additional interest), it will take 38 months for you to pay off the credit card balance.
What is an equation?An equation is a mathematical statement showing the equality of two or more mathematical expressions using the equation symbol (=).
The total debt on the credit card = $8,500
The promotional interest rate for 24 months = 0%
Monthly repayment = $170
Total repayment after 12 months = $2,040 ($170 x 12)
Balance on the credit card after 12 months of repayment = $6,460 ($8,500 - $2,040)
The number of months to repay the balance without interest = 38 months ($6,460/$170).
Thus, D, the remaining debt can be determined using this equation, a. 170t + D = 8500 and it will take 38 months to repay without interest.
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If $16,000 is invested at 10% for 20 years, find the future value if the interest is compounded daily.
Lemon disinfectant is mixed 4 oz to one gallon. How many lemon disinfectant needs to be added to 6 gallons of water?
Answer:
If the ratio of lemon disinfectant to water is 4 oz to one gallon, then we can say that for each gallon of water, we need 4 oz of lemon disinfectant. To find how much lemon disinfectant is needed for 6 gallons of water, we can multiply the amount needed for one gallon by the number of gallons:
4 oz/gallon * 6 gallons = 24 oz
Therefore, we need 24 oz of lemon disinfectant to be added to 6 gallons of water.
Step-by-step explanation:
Answer:
Given: x * 4 oz = 6 gallons.
First, multiply 4 oz and x:
4x = 6 gallons.
Then convert 6 gallons to oz:
4x = 768 oz.
Then divide both sides by 4:
x = 192.
What is the center and radius of the circle with equation (x – 14)2 + (y – 2)2 = 9?
Choose one
(14, 2), r = 3
(14, 2), r = 9
(– 14, – 2), r = 3
(– 14, – 2), r = 9
none of these
The center and radius of the circle with equation (x – 14)2 + (y – 2)2 = 9 is (14, 2), r = 3, the correct option A.
What is an equation of a circle?
A circle can be characterized by its center's location and its radius's length.
Let the center of the considered circle be at (h,k) coordinate.
Let the radius of the circle be 'r' units.
Then, the equation of that circle would be:
(x-h)^2 + (y-k)^2 = r^2
We are given that;
The equation of circle= (x – 14)2 + (y – 2)2 = 9
Now,
We know the equation of a circle with center (h, k) and radius r is:
(x - h)^2 + (y - k)^2 = r^2
Comparing the given equation to this form, we can see that the center of the circle is (14, 2) and the radius is √9 = 3.
Therefore, by the given equation of circle answer will be (14, 2), r = 3.
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Avery had $25.83 in her wallet. If she bought lunch with 7 3/4 dollars from her wallet, how much money did she have in her wallet after lunch?
Answer: $ 18.08
Step-by-step explanation:
Given: Money in wallet = $25.83
Given: Money spent = $7.75
To find: Money left in the wallet after lunch = money in the wallet - money spent
= $(25.83-7.75)
= $ 18.08
Circle P is shown. Line segments P T, P U, P R, and P Q are radii. Line segments T S and S U are secants. Angle T S U is 120 degrees, angle U P R is 59 degrees, and angle Q P T is degrees. Use the drop-down menus to complete the statements. A central angle of circle P is angle . The measure of is degrees.
A central angle of circle P is angle TPQ.
The measure of RU is 59 degrees.
What is an arc?In Geometry, an arc can be defined as a trajectory that is generally formed when the distance from a given point has a fixed numerical value. Generally speaking, the degree measure of an arc in a circle is always equal to the central angle that is present in the included arc.
Based on the information provided about Circle P, we can logically deduce that m∠TPU and m∠UPR are supplementary angles:
m∠TPU + m∠UPR = 180°
m∠TPU = 180° - 59°
m∠TPU = 121°.
m∠TPQ + m∠QPR = 180°
m∠QPR = 180° - 107°
m∠QPR = 73°.
Therefore, the central angle of circle P is m∠TPQ and the measure of arc RU is equals to 59 degrees.
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Answer:
1. TPQ
2. 58
Step-by-step explanation:
Noah is making mini berry pies. For the filling, he mixes 1 pound each of raspberries, blueberries, and blackberries. Then, he scoops 6 ounces of the filling into each mini pie tin. If he wants to use up all of his filling, how many mini pies can he make?
Farid is able to produce 8 small pies.
What is addition?Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.
here, we have,
Given: For the filling, Farid blends 1 pound of each blackberries, blueberries, and raspberries. Following that, he spoons 6 ounces of the filling into each tiny pie pan.
We need to find How many tiny pies can be made if he wants to use all of the filling.
Raspberries, blueberries, and blackberries, each weighing 1 pound, are combined by Faris for the filling.
3 pounds of filler total from 1+1+1= 3*16 ounces.
1 pound equals 16 ounces. = 48 ounces
Each little pie tin is filled with 6 ounces of filling by Faris.
48 ounces divided by 6 ounces equals 8 mini pies.
Hence, the Farid made 8 mini pies with 6 ounces.
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An unused roll of paper towels is shown. What is the volume of the unused roll?
Volume of a Cylinder: V=Bh
USE THE PHOTO TO HELP ANSWER THE QUESTIONS
P.S. I WILL GIVE YOU BRAINLIEST IF RIGHT
The volume of the unused roll is approximately 10,316.97 cubic centimeters.
what is radius ?
A radius is a line segment that connects the center of a circle or a sphere to any point on its circumference or surface, respectively. It is half the length of the diameter, which is a line segment that passes through the center of the circle or sphere and has endpoints on its circumference or surface, respectively. The radius is an important measurement in geometry and is used to calculate other important properties of circles and spheres, such as their area, circumference, and volume.
Given by the question:
To find the area of the base of the cylinder, we need to know the radius. Since the paper towel roll has an inner radius of 4.2 cm and an outer radius of 12 cm, we can calculate the area of the base as follows:
[tex]Area of outer circle - Area of inner circle = πr_outer^2 - πr_inner^2[/tex]
[tex]= \pi (12 cm)^2 - \pi (4.2 cm)^2[/tex]
= [tex]452.16\pi cm^2 - 55.3896\pi cm^2[/tex]
= [tex]396.7704\pi cm^2[/tex]
Therefore, the volume of the unused roll can be calculated as:
V = Bh = [tex](396.7704\pi cm^2)(26 cm)[/tex]
[tex]= 10,316.97 cm^3[/tex]
Therefore, the volume of the unused roll is approximately 10,316.97 cubic centimeters.
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In ΔFCE, the ratio of ∠F to ∠C is 2:5. The measure of ∠E is one hundred ten degrees more than the sum of the measures of ∠F and ∠C. What is the measure of each angle in ΔFCE?
Answer:70
Step-by-step explanation:
Given: <f and <c ratio 2:5
To find: <f and <c
Solution: 2x+5n=180' minus 110'
7n=70'
x=10'
<f= 2x10=20'
<e= 5x10=50'
The sum of <F and <E
= 20'+50'=70'
How would a scale factor of 0.25 be used to determine the lengths of the original figure?
A) The scale factor is added to the scale figure’s lengths.
B)The scale factor is subtracted from the scale figure’s lengths.
C) The scale factor is multiplied by the scale figure’s lengths.
D) The scale factor is divided into the scale figure’s lengths.
Answer:
The correct answer is C) The scale factor is multiplied by the scale figure's lengths.
When using a scale factor, you are typically working with a "scale figure," which is a smaller or larger version of the original figure. To determine the lengths of the original figure using a scale factor of 0.25, you would multiply each length of the scale figure by 0.25.
For example, if the scale figure has a length of 8 units, you would multiply 8 by 0.25 to get 2, which would be the corresponding length of the original figure. So if the original figure was four times larger than the scale figure, it would have a length of 32 units (4 times 8).
Therefore, when using a scale factor to determine the lengths of an original figure, you need to multiply each length of the scale figure by the scale factor to get the corresponding length of the original figure.
Step-by-step explanation:
a triangle has side lengths 13, 14, and 15. find the area of the triangle whose vertices are the incenter, circumcenter, and centroid of the original triangle.
The Incircle, Circumcircle, and Centroid of a triangle are the three points which define a triangle, each with its own unique properties. In this case, we are looking for the area of a triangle whose vertices are the incenter, circumcenter, and centroid of our original triangle.
To find the area of this triangle, we will use Heron's Formula. This formula allows us to calculate the area of a triangle given its three side lengths. The three side lengths of our triangle are 13, 14, and 15. We can plug these values into Heron's Formula to find the area of our triangle.
The area of our triangle is approximately 54.47 units squared. This means that the area of our triangle, whose vertices are the incenter, circumcenter, and centroid of the original triangle, is 54.47 units squared. This can be verified by plugging in the side lengths into Heron's Formula and solving for the area.
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arrange the following fraction 5/6,8/9,2/3 in assending order
Answer: From Greatest to Least: 8/9, 5/6, 2/3
Step-by-step explanation:
Please answer both!! I’ll give brainlest to first!!!
Let's call the amount of water in the first pool "x" and the amount of water in the second pool "y". We know that:x = 582 + 20.25t (where t is the time in minutes)
y = 44.5tWe want to find the time "t" at which x = y, so we can set the two equations equal to each other:582 + 20.25t = 44.5t
Expanding the second equation and solving for t, we get:582 = 24.25t
t = 582 ÷ 24.25 = 24 minutes
So, after 24 minutes, the two pools will have the same amount of water.
To find out how much water will be in each pool, we can plug this value of t back into the first equation:x = 582 + 20.25t = 582 + 20.25(24) = 582 + 485 = 1067 liters
y = 44.5t = 44.5(24) = 1067 liters
So, both pools will contain 1067 liters of water.
Answer:
Below
Step-by-step explanation:
First pool starts with 582 and adds 20.25 * m m = minutes
Volume1 = 582 + 20.25 m
Volume 2 = 44.5 m
At what 'm' are they equal ?
582 + 20.25 m = 44.5 m subtract 20.25 m from both sides to get
582 = 24.25 m divide both sides of the equation by 24.25
m = 24 minutes <=====use this value in either equation to find the volume volume2 = 44.5 * 24 = 1060 gallons
The ration of female to male shoppers at a department store has been found to be 10 to 9. If 1,188 male shoppers were at the store one Saturday, how many shoppers were there in all that day?
Answer:
2,508 shoppers
Step-by-step explanation:
Ratio of female to male : 10:9
Let F be the number of female shoppers and M be the number of male shoppers
That can be expressed as
[tex]\dfrac{F}{M}= \dfrac{10}{9}[/tex]
Given M = 1188
[tex]\dfrac{F}{1188}= \dfrac{10}{9}[/tex]
Multiply both sides by 1188
[tex]\dfrac{F}{1188} \times 1188= \dfrac{10}{9} \times 1188\\\\F = 1,320[/tex]
Total number of shoppers = M + F
= 1188 + 1320
= 2,508 shoppers
There are 9 girls and 6 boys taking golf lessons. Write the ratio that compares the number of girls taking golf lessons to the total number of students taking golf lessons.
Answer:
2:5
Step-by-step explanation:
We know
There are 9 girls and 6 boys taking golf lessons.
So, there are a total of 15 taking a golf lesson.
Write the ratio that compares the number of girls taking golf lessons to the total number of students taking golf lessons.
The ratio is
6:15 = 2:5
So, the ratio is 2:5
Which letter
A
B
C
D
Answer:
Step-by-step explanation:
a
Answer:
ITS A
Step-by-step explanation:
The reason why is because that dude up there said the same thing so yeah..
I need help please this question makes no sence to me and I keep getting it wrong
In a parallelogram, the consecutive angles are supplementary (add up to 180 degrees). x can represent the first angle, and 4x can represent the second angle. With this information you can create the equation x + 4x = 180 and solve.
5x = 180
x = 36
So the measure of the first angle is 36 degrees, and the one that is 4 times larger is 144 degrees.
√6/√3 I’m struggling on this question this symbol / means divide
Answer:
√2
Step-by-step explanation:
√3 x√2/√3 =√2
Answer:
[tex]\sqrt{2}[/tex]
explanation:
[tex]\frac{\sqrt{6} }{\sqrt{3} }[/tex]
= [tex]\sqrt{2}[/tex]
(Decimal: 1.414214)
evaluate a - c ÷ 6 if a = 6 and c = 12
Answer:
-1
Step-by-step explanation:
1. Plug the numbers into the equation
6-12/6
2. Solve.
6-12=-6
-6/6=-1
Answer:
4
Step-by-step explanation:
A= 6
C= 12
6-12÷6
With BIDMAS the order becomes:
6-(12÷6) —> 6-2 = 4
Consider the following equation.
4−2y=8−2x
Step 1 of 2 : Find the x- and y-intercepts, if possible.
The x-intercept is (2, 0) and the y-intercept is (0, -2).
What is Intercept?An intercept in mathematics is a location on the y-axis through which the line's slope passes. It is a place on the y-axis where a straight line or a curve crosses. This is reflected in the equation for a line, which is written as y = mx+c, where m denotes slope and c denotes the y-intercept.
We have the Equation: 4−2y=8−2x
To find the x-intercept, we set y = 0
4 - 2(0) = 8- 2x
4 = 8 -2x
2x = 8-4
2x = 4
x = 2
and, For y-intercept we set x= 0
4 - 2y = 8- 2(0)
4- 2y = 8
-2y = 4
y= -2
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Find the probability of randomly selecting a number between 1 and 1000 (including both ends) which is divisible by:
a. 3.
b. 3 and 5.
c. 3 or 5.
The probability of randomly selecting a number between 1 and 1000 (including both ends) which is divisible by 3, 3 and 5, and 3 or 5 is 33.3%, 6.6%, and 46.7%, respectively.
To find the probability of randomly selecting a number between 1 and 1000 (including both ends), we can count the number of the desired outcomes and divide it by the total number of possible outcomes.
a. To find the probability of randomly selecting a number between 1 and 1000 (including both ends) which is divisible by 3, we can count the number of multiples of 3 between 1 and 1000, and divide by the total number of possible outcomes.
The first multiple of 3 is 3, and the last multiple of 3 that is less than or equal to 1000 is 999.
999/3 = 333
So there are 333 multiples of 3 between 1 and 1000.
probability = 333/1000 = 0.333 = 33.3%
b. To find the probability of randomly selecting a number between 1 and 1000 (including both ends) which is divisible by 3 and 5, we can count the number of multiples of 15 (the least common multiple of 3 and 5) between 1 and 1000, and divide by the total number of possible outcomes.
The first multiple of 15 is 15, and the last multiple of 15 that is less than or equal to 1000 is 990.
990/15 = 66
So there are 66 multiples of 15 between 1 and 1000.
probability = 66/1000 = 0.066 = 6.6%
c. To find the probability of randomly selecting a number between 1 and 1000 (including both ends) which is divisible by 3 or 5, we can count the number of multiples of 3 or 5 (or both) between 1 and 1000, and divide by the total number of possible outcomes.
To count the number of multiples of 3 or 5, we can add the number of multiples of 3 and the number of multiples of 5, and then subtract the number of multiples of 15 (to avoid double-counting).
The number of multiples of 3 between 1 and 1000 is 333, the number of multiples of 5 is 200, and the number of multiples of 15 is 66.
probability = (200 + 333 - 66)/1000 = 0.467 = 46.7%
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Which of the following correspond to a probability of an event occurring (i.e. when I get the value, I can determine how often the event(s) being described is likely to occur in a random sample)? Select any that apply. The integral of the density of the chi-squared distribution between chi-squared values of and 5 The
p
-value of a chi squared value of 4 The probability mass of observing 50 successes in 50 binomial trials The probability density of the chi squared distribution when the chi-squared value is 4
The statement that corresponds to a probability of an event occurring is the probability mass of observing 50 successes in 50 binomial trials.
Probability represents comprehensive analysis of the reasonable likelihood that a particular outcome shall typically occur. This occurrence is dependent on the ratio of favorable instances to probable instances. The integral of the chi-squared distribution's density among complex chi-squared values of zero and five and probability density of the chi-squared distribution at chi-squared value four are functionally related to the overall chi-squared distribution. However, neither of them directly reflects the likelihood that an event will actually take place.
The strength of evidence against null hypothesis in a chi-squared test is exhibited by p-value of a chi-squared value of numeral four, but it does not directly translate to likelihood that an event will take place. Therefore, the statement that the probability mass of observing 50 successes in 50 binomial trials corresponds with the given question.
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