Answers
The length of side x in simplest radical form with a rational denominator is: \(x =(2\sqrt{3})/3\)
What is radical form ?
Radical form is a mathematical expression that includes a square root or other root symbol. It is a way of representing numbers that cannot be simplified to a whole number or fraction. For example, the square root of 16 is 4, so the radical form of 16 is √16.
Radical form is often used to simplify and manipulate algebraic expressions. For example, the expression \(\sqrt{(a^2 + b^2)}\) represents the length of the hypotenuse of a right triangle with legs of lengths a and b, according to the Pythagorean theorem. Similarly, the expression ∛27 represents the cube root of 27, which is 3.
In general, a radical expression can be simplified by finding factors of the radicand (the number inside the radical symbol) that are perfect powers of the root.
According to the question:
We know that angle A is 30 degrees and angle B is 60 degrees, so angle C must be 90 degrees since the angles of a triangle add up to 180 degrees.
To find the length of side x, we can use the trigonometric ratios sine, cosine, or tangent. Since we have the opposite (x) and adjacent (\(\sqrt{12}\)) sides of angle A, we can use the tangent ratio:
tan(A) = opposite / adjacent
\(tan(30) = x / \sqrt{12}\)
We can solve for x by multiplying both sides by sqrt(12):
sqrt(12) * tan(30) = x
Using a calculator, we can simplify
\(\sqrt{12} * tan(30)\) as follows:
\(\sqrt{12} * tan(30) = \sqrt{4*3} * (1/\sqrt{3})\)
\(= 2 * (\sqrt{3})(1/\sqrt{3})\)
\(= (2/\sqrt{3}) * (\sqrt{3}/\sqrt{3})\)
\(= (2\sqrt{3})/3\)
Therefore, the length of side x in simplest radical form with a rational denominator is:
\(x = (2\sqrt{3})/3\)
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Answer:
x = 6
Step-by-step explanation:
We can use the tangent trigonometric ratio to find the length of side x.
\(\boxed{\begin{minipage}{7 cm}\underline{Tangent trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\end{minipage}}\)
Taking the angle, θ, to be 30°, from inspection of the given right triangle:
θ = 30°O = √{12}A = xSubstitute the values into the formula and solve for x:
\(\implies \tan 30^{\circ}=\dfrac{\sqrt{12}}{x}\)
\(\implies \dfrac{\sqrt{3}}{3}=\dfrac{\sqrt{12}}{x}\)
\(\implies x\sqrt{3}=3\sqrt{12}\)
\(\implies x=\dfrac{3\sqrt{12}}{\sqrt{3}}\)
To rationalise the denominator, multiply the numerator and denominator by √3:
\(\implies x=\dfrac{3\sqrt{12}}{\sqrt{3}}\cdot\dfrac{\sqrt{3}}{\sqrt{3}}\)
\(\implies x=\dfrac{3\sqrt{12}\sqrt{3}}{3}\)
Simplify:
\(\implies x=\sqrt{12}\sqrt{3}\)
\(\implies x=\sqrt{12 \cdot3}\)
\(\implies x=\sqrt{36}\)
\(\implies x=6\)
Therefore, the length of side x is 6 units.
Related Questions
The line segment joining the points P(-3,2) and Q(5,7) is divided by the y-axis in the ratio:
Answers
Answer:
Step-by-step explanation:
The line segment joining two points P and Q can be represented by the equation of a straight line in the form y = mx + b, where m is the slope and b is the y-intercept.
To find the equation of the line, we need to find the slope, which can be calculated using the formula:
m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the points P and Q, respectively.
In this case, the coordinates are:
P = (-3, 2) and Q = (5, 7)
So, the slope is:
m = (7 - 2) / (5 - (-3)) = 5 / 8
Next, we can use either of the points to find the y-intercept. Let's use point P:
b = y - mx, where y and x are the y and x coordinate of the point, respectively.
In this case,
b = 2 - m * (-3) = 2 - (5/8) * (-3) = 2 + 15/8 = 89/8
So, the equation of the line joining the points P and Q is:
y = (5/8)x + 89/8
Now, to find the point where the line crosses the y-axis, we need to find the x-coordinate of the point where y = 0.
So, we have:
0 = (5/8)x + 89/8
Solving for x, we get:
x = -(89/8) / (5/8) = -89 / 5
This means that the line crosses the y-axis at the point (-89/5, 0). To find the ratio in which the line segment is divided by the y-axis, we need to find the ratio of the distance from the y-axis to point P to the distance from the y-axis to point Q.
Let's call the point of intersection with the y-axis R. The distances are then:
PR = (3, 2) and QR = (5 - (-89/5), 7)
The ratio of the distances is then:
PR / QR = (3, 2) / (5 - (-89/5), 7) = 3 / (5 + 89/5) = 3 / (94/5) = 15/47
So, the line segment joining the points P and Q is divided by the y-axis in the ratio 15:47.
a bacteria culture begins with 8 bacteria which triples in size every week. How many bacteria exists in the culture after 4 weeks ?
Answers
Answer:
648
Step-by-step explanation:
8x3=24
24x3=72
72x3=216
216x3=648
Solve a triangle with b =7, c =10, and A= 51. round to the nearest tenth
Answers
The sides of the triangle are a ≈ 8.3, b = 7, and c = 10, and the angles are A = 51°, B ≈ 51.5°, and C ≈ 77.5°.
What is a triangle?A triangle is a closed, double-symmetrical shape composed of three line segments known as sides that intersect at three places known as vertices. Triangles are distinguished by their sides and angles.
To solve the triangle, we need to find the values of the remaining sides and angles. We can start by using the Law of Sines, which states that:
a / sin A = b / sin B = c / sin C
where a, b, and c are the sides of the triangle, and A, B, and C are the angles opposite to those sides.
Using the given values, we can write:
a / sin 51 = 7 / sin B
a / sin 51 = 10 / sin C
To solve for a, we can use either of the two equations above. Let's use the first one and solve for sin B:
sin B = (7 / sin 51) * sin B
sin B = 7 / (sin 51 / sin B)
sin B = 7 / sin(180 - 51 - B)
sin B = 7 / sin(129 - B)
Using the sine rule, we can determine the angle B:
sin B / 7 = sin(129 - B) / 10
sin B = (7/10) * sin(129 - B)
sin B = (7/10) * (sin 129 * cos B - cos 129 * sin B)
sin B = (7/10) * sin 129 * cos B - (7/10) * cos 129 * sin B
(7/10 + (7/10) * cos 129) * sin B = (7/10) * sin 129 * cos B
sin B = (7/10) * sin 129 * cos B / (7/10 + (7/10) * cos 129)
sin B = sin 51.5
B = sin(sin B)
B = sin(sin 51.5)
B ≈ 51.5°
We can now find the remaining angle, C:
C = 180 - A - B
C = 180 - 51 - 51.5
C ≈ 77.5°
Finally, we can use the Law of Sines again to find the remaining side, a:
a / sin A = c / sin C
a / sin 51 = 10 / sin 77.5
a = (10 * sin 51) / sin 77.5
a ≈ 8.3
Therefore, the sides of the triangle are a ≈ 8.3, b = 7, and c = 10, and the angles are A = 51°, B ≈ 51.5°, and C ≈ 77.5°.
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2x-1=y
3x-1=y
Consider the system of equations above. Which of the following statements about this system is true?
Answers
Answer:
B; There is only one (x,y) solution and y is negative
Step-by-step explanation:
First, I graphed the two equations. Attached is an image of the equations graphed. Next, I looked for overlapping points. Wherever the two points overlap, there is a solution. When looking at the graph, we can see the lines overlap at only one point, (0,-1). Since y is negative, the answer must be B; there is only one (x,y) solution and y is negative.
If this answer helped you, please leave a thanks!
Have a GREAT day!!!
What is the answer to this
Answers
Answer:
-23
Step-by-step explanation:
h(-5) = 4 * -5 - 3 = -20 - 3 = - 23 .... x ≥ -5
Sally has 2 cats and each cat eats of a tin of cat food each day.
Sally buys 7 tins of cat food.
For how many days will the cat food feed her 2 cats?
You must show your working.
days=?
Answers
Answer:
Step-by-step explanation:
9 tins of cat food feed her 2 cats for 18 days
Step-by-step explanation:
Sally has 2 cats
food eaten by 1 cat each day =
food eaten by 2 cat each day= tins
sally buys 9 tins of cat food
then
tins required in = 1 day
1 tin required in
i.e 1 tin required in 2 days
9 tin required for = 9×2 = 18 days
hence , 9 tins of cat food feed her 2 cats for 18 days
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Sue has 2 cats. Each cat eats 1/4 tin of food each day. Sue buys 8 tine of cat food. Has sue got enough cat food to feed her 2 cats for 14 days?
7 tins of cat food = 3 1/2 days
How many solutions does the following equation has
Answers
Answer:
I think only 1 but not 100% sure
Step-by-step explanation:
Answer:
One solution
Step-by-step explanation:
Combine like terms and simplify.
20z - 5 - 12z = 10z + 8
⇒ z(20 - 12) - 5 = 10z + 8
⇒ z(8) - 5 = 10z + 8
⇒ 8z - 5 = 10z + 8
Subtract 8z both sides.
⇒ 8z - 8z - 5 = 10z + 8 - 8z
⇒ -5 = 2z + 8
Subtract 8 both sides.
⇒ -5 - 8 = 2z + 8 - 8
⇒ -13 = 2z
⇒ -13/2 = 2z/2
⇒ -6.5 = z
Thus, there is 1 solution.
the school lisa goes to is selling tickets to the annual talent show. on the first day of ticket sales the school sold 4 senior citizen tickets and 5 student tickets for a total of $102. the school took in $126 on the second day by selling 7 senior citizen tickets and 5 student tickets. what is the price of on senior citizen ticket and one student ticket?
Answers
Answer: one senior ticket is $8 and one student ticket is $14
Hope this helps a little
Solve the inequality c+2/5≥11/5, and write the solution in interval notation
Answers
Answer:
[9/5,∞)
Step-by-step explanation:
Rearrange variables to the left side of the equation: c ≥ 11/5-2/5
Calculate: c ≥ 9/5
Express solution set in interval notation: [9/5,∞)
For what values of x is the inequality below true?
6x-2 ≥ 10
Answers
Answer:
x\(\geq\)2
Step-by-step explanation:
You add 2 to both sides. Then you divide everything by 6. Hope this helps!
Here is a frequency distribution table (FDT) for a small data set: data value frequency 14 14 15 11 16 23 17 10 18 13 Find the following measures of central tendency: mean (I (Please show your answer to one decimal place.) median (Please enter an exact answer:) mode (Please enter an exact answer: )
Answers
The mean is 14.7, the median is 16, and the mode is 16.
To find the mean, we need to calculate the sum of all the data values and divide it by the total number of observations.
The sum of the data values is:
14 x 14 + 15 x 11 + 16 x 23 + 17 x 10 + 18 x 13 = 196 + 165 + 368 + 170 + 234 = 1043
The number of observations is:
14 + 11 + 23 + 10 + 13 = 71
The mean is calculated as follows,
1043 / 71 = 14.7 (rounded to one decimal place)
The median is the central value in the data collection. To find the median, we need to arrange the data values in ascending order and find the middle value. In this case, we have an odd number of observations, so the median is simply the middle value.
14, 14, 15, 15, 16, 16, 16, 16, 16, 16, 16, 17, 17, 18, 18, 18
The median is 16.
The mode is the value that appears most repeatedly in the data set. In this case, the mode is 16 since it occurs the most (23 times).
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A diagram of a rectangular pool with a diagonal of 50 meters is shown below. Connected to the pool is a square shaped kid’s pool.What is the area of the kid’s pool in the diagram? Ulysses says the area of the kid’s pool is 900 square meters.Ursula says the area of the kid’s pool is 120 square meters. Which student is correct?
Answers
Let's find the length of the side of the pool.
Let it be x, so the diagram is:
Using the pythagorean theorem, we can figure out x. Shown below:
\(\begin{gathered} x^2+40^2=50^2 \\ x^2=50^2-40^2 \\ x^2=900 \\ x=\sqrt[]{900} \\ x=30 \end{gathered}\)So, 30 meters is the side length of the square (pool).
The area of a square is:
\(A=s^2\)Where "s" is the side length
We found s to be 30, thus the area of the pool is:
\(\begin{gathered} A=s^2 \\ A=(30)^2 \\ A=900 \end{gathered}\)Thus,
Ulysses is correct.
Felipe, Jill, and Cindy are neighbors. Jill is 7 years older than Cindy and Felipe is two-
thirds the age of Jill. The sum of their three ages is 137.
a. If a represents Jill's age, write an equation in terms of that can be used to
determine each person's age.
b. How old is Felipe?
Answers
On solving the provided question, we can say that vertex form of the equation is in the form of y = a(x-h)^2 + k.
In mathematics, what is the vertex?A vertex, or particular point, is a place where two or more lines or edges meet in a mathematical object. Angles, polygons, polyhedral, and graphs are where vertices are most frequently seen. Nodes and vertices in a graph are the same thing.
Recall that a parabola's General Form is y = ax2 + bx + c. The x-coordinate of the vertices, which is x = - b/2a, must first be discovered in order to find the vertex from this form. You will use this number to replace x in the parabola equation once you have determined the x-coordinate of the vertex.
a = -1/4 * (4 - 12) = -1
h = -b/(2a) = 12/(2(-1)) = -6
k = f(h) = -(-6)^2 + 12(-6) - 4 = 36
Therefore, the vertex form of the equation is y = -(x+6)^2 + 36.
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Rae leaves a party and heads north
walking at 2 km/hr. Dana leaves the same
party one hour later and heads south at
pace of 3 km/hr. How many hours will it
take the friends to put 7 km between
them?
Answers
The required it will take 2 hours for the friends to put 7 km between them.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Let's call the number of hours it takes the friends to be "x". During that time, Rae will have traveled 2x km. And Dana will have traveled 3(x-1) km (since she left an hour later).
We can now set up an equation:
2x + 3(x-1) = 7
Expanding the second term:
2x + 3x - 3 = 7
Combining like terms:
5x - 3 = 7
Adding 3 to both sides:
5x = 10
Finally, dividing both sides by 5:
x = 2
So it will take 2 hours for the friends to put 7 km between them.
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Which statement correctly explains the association of the scatter plot? Since the Y values increase as the X values increase the Scatter plot shows a positive association. Sense to Weibo use decrease as the X values increase the scatter plot shows a positive association.
Answers
The correct statement regarding the association in the scatter plot is given as follows:
Since the y-values decrease as the x-values increase, the scatter plot shows a negative association.
How to classify the association between variables?There can either be a positive association between variables or a negative association between variables, as follows:
Positive association happens when both variables have the same behavior, that is, as one increases the other increases, and as one decreases the other also decreases.Negative association happens when the variables have opposite behavior, as one variable is increasing the other is decreasing, or as one variable is decreasing, the other is increasing.In this problem, we have a decreasing scatter plot, hence there is a negative association between the variables.
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Find the mean, median, and mode(s) of the data. Choose the measure that best represents the data. Explain your reasoning. Find the mean, median, and mode(s) of the data with and without the outlier. Which measure did the outlier affect the most? 8, 10, 10, 11, 16, 17, 19, 21, 41
Answers
Answer:
Mean: 17
Median: 16
Mode: 10
Step-by-step explanation:
8, 10, 10, 11, 16, 17, 19, 21, 41
Median: (the middle number in the number list/data set) 16
Mode: 10
Mean: 8 + 10 + 10 + 11 + 16 + 17 + 19 + 21 + 41 = 153/9 = 17
The mean is equal to 17. The value of the median is 16 and the value of the mode is 10.
What are mean, mode and median?The mean of the numbers is defined as the ratio of the sum of the total numbers to the total count of the numbers.
The given numbers are,
8, 10, 10, 11, 16, 17, 19, 21, 41
Mean = ( 8 + 10 + 10 + 11 + 16 + 17 + 19 + 21 + 41 ) / 9
Mean = 153/9
Mean = 17
The median is calculated by arranging the numbers in ascending order and the middle term of the data.
8, 10, 10, 11, 16, 17, 19, 21, 41
The median is 16.
The mode is calculated as the highest repetition in the data,
8, 10, 10, 11, 16, 17, 19, 21, 41
Mode: 10
Therefore, the mean is equal to 17. The value of the median is 16 and the value of the mode is 10.
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Noah assigns a number to each of the 150 athletes at his school and puts the numbers in a box. He randomly chooses 30 numbers and finds that 18 of the
athletes watched television last night. Use this sample to make an inference about how many athletes watched television last night.
Answers
Answer:
90
Step-by-step explanation:
18 out of 30 watched tv
150/30 = 5
18/30 = (18 * 5)/(30 * 5) = 90/150
Answer: 90
From the tower of 32meter of heights,a car is observed at angle of the depression of 55 degrees. Find how far the a car from the tower
Answers
the car is approximately \(23.9\) Meters away from the tower.
The angle of depression is the angle formed when an object is observed from a horizontal line and the horizontal line.
What is observed at the angle of the depression of 55 degrees?We can solve this problem using trigonometry. Let's start by drawing a diagram:
C
|\
| \
| \ 32m
| \
| \
| \
| \
|-------T
x
In the diagram, T represents the top of the tower, C represents the car, and x represents the distance from the tower to the car that we want to find. The angle of depression from the top of the tower to the car is 55 degrees.
We can use the tangent function to solve for x:
\(tan(55) = 32 / x\)
To solve for x, we can rearrange this equation as follows:
\(x = 32 / tan(55)\)
We can calculate this expression's value by using a calculator to obtain:
\(x =23.9\) meters
Therefore, the car is approximately \(23.9\) Meters away from the tower.
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Real-life Problems Question 10
Answers
Answer :
a) It is given that
Everyday a machine makes 500000 staples and puts them into the boxes.
The machine need 170 staples to fill a box
One box contans = 170 staples.
Total number of staples = 500000
Number of box required to fill 500000 staples = Total number of staples/No. of staples 1 box contains.
\( \: :\implies \) 500000 /170
\( :\implies \: \) 2941 (approx)
Therefore, 2941 boxes are required to fill with 500000 staples.
b) It is given that,
Each staple is made of 0.21 g of metal .
Total weight of metal = 1 kg = 1000 g
1 staple = 0.21 g
Number of staples = weight of metal/ Weight of 1 staple.
\( \: :\implies \) 1000/0.21
\( \: :\implies \) 4761 (approximately)
Therefore, 4761 staples can be made from 1 kg of the metal.
The RLX Company just paid a dividend of $2.85 per share on its stock. The dividends are expected to grow at a constant rate of 4.5 percent per year, indefinitely. Assume investors require a return of 10 percent on this stock. What is the current price?
Answers
The current stock price is $54.15.
Given that RLX Company just paid a dividend of $2.85 per share on its stock and dividends are expected to grow at a constant rate of 4.5 percent per year, indefinitely.
Stock valuation alludes to the valuation of the natural worth per portion of an organization's stock which can help the organization in deciding its reasonable worth in case of twisting up or consolidation. One of the models used to esteem the stock cost is the profit development model. It expects the cost of the stock to be the current worth representing things to come profits of the stock accepted to develop at a consistent rate.
Dividend (D0) = $2.85
Growth rate (g) = 4.5%
Required return (r) = 10%
Firstly, we have to calculate the value of the current stock price.
The current stock price can be calculated by using the dividend growing model.
\(\begin{aligned}\text{Current stock price}&=\frac{D_{0}\times(1+g)}{r-g}\\ &=\frac{2.85\times (1+0.045)}{0.10-0.045}\\ &=\frac{2.85\times 1.045}{0.055}\\ &=\frac{2.97825}{0.055}\\ &=54.15\end\)
Hence, the current stock price when dividend of $2.85 are expected to grow at a constant rate of 4.5 percent per year, indefinitely is $54.15.
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Part B: Explain what the inequality means in relation to the positions of these numbers on the number line. (4 points) milldle school
Answers
Answer:
I guess I would say if the sign points to the number its higher and you start from left to right
Find the sum of the first 27 terms
of the arithmetic sequence.
First, fill in the equation.
a₁
= 5 and a27
Sn = 2/(a₁ + an)
Sn
=
[?]
2
+
=
83
Answers
Answer:
S₂₇ = 1188
Step-by-step explanation:
using the given formula for \(S_{n}\) , that is
\(S_{n}\) = \(\frac{n}{2}\) (a₁ + \(a_{n}\) )
with a₁ = 5 and \(a_{n}\) = a₂₇ = 83 , then
S₂₇ = \(\frac{27}{2}\) (5 + 83) = 13.5 × 88 = 1188
Pls help offering 20 points D:
Answers
Answer:
ok,soo I found out that when you add one of the y values to positive 9 it gives you the exact x value which is correct
b. Express log2 24 in terms of prime factors and leave answer in the most simplified form using properties of logarithms. (2 Marks)
Answers
log₂ 24 can be expressed as 3 + log₂ 3 in terms of prime factors, using the properties of logarithms.
To express log₂ 24 in terms of prime factors, we can use the properties of logarithms and the fact that any positive integer can be expressed as a product of prime factors.
First, let's find the prime factorization of 24.
24 can be divided by 2, so we have 24 = 2 × 12.
12 can be divided by 2, so we have 12 = 2 × 6.
6 can be divided by 2, so we have 6 = 2 × 3.
Therefore, the prime factorization of 24 is 2 × 2 × 2 × 3, or 2³ × 3.
Now, using the properties of logarithms, we can express log₂ 24 as the sum of logarithms of its prime factors.
log₂ 24 = log₂ (2³ × 3)
According to the properties of logarithms, we can separate the factors inside the logarithm as individual terms:
log₂ (2³ × 3) = log₂ 2³ + log₂ 3
Since log₂ 2³ is equal to 3, we can simplify the expression further:
log₂ (2³ × 3) = 3 + log₂ 3
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3x+20=5x how many Solutions does it have
Answers
Answer:
one
Step-by-step explanation:
3x + 20 = 5x
20 = 5x - 3x
20 = 2x
x = 10
one solution
Applying the General Multiplication Rule A box contains four red balls and eight black balls. Two balls are randomly chosen from the box, and are not replaced. Let event B be choosing a black ball first and event R be choosing a red ball second. What are the following probabilities? P(B) = P(R | B) = P(B ∩ R) = The probability that the first ball chosen is black and the second ball chosen is red is about percent.
Answers
The probability that the first ball chosen is black and the second ball chosen is red is 24.24%
How do i determine the probability?First, we shall obtain the total balls present in the box. Details below:
Red ball (R) = 4Black ball (B) = 8Total ball =?Total ball = 4 + 8
Total ball = 12 balls
Next, we shall obtain the probability of chosen a black ball first. Details below:
Black ball (B) = 8Total ball = 12 ballsProbability of chosen a black ball first, P(B) =?P(B) = n(B) / n(T)
P(B) = 8 / 12
Next, we shall obtain the probability of chosen red as the 2nd ball. Details below:
Red ball (R) = 4Total pen = 11Probability of chosen red as the 2nd ball, P(R | B) =?P(R | B)= n(R) / n(T)
P(R | B) = 4 / 11
Finally, we shall obtain the probability that the first ball chosen is black and the second ball chosen is red. Details below:
Probability of chosen a black ball first, P(B) = 8 / 12Probability of chosen red as the 2nd ball, P(R | B) = 3 / 11Probability that the 1st ball is black and the 2nd is red, P(B ∩ R) =?P(B ∩ R) = [P(B) × P(R | B)] × 100
P(B ∩ R) = [(8 / 12) × (3 / 11)] × 100
P(B ∩ R) = 0.2424 × 100
P(B ∩ R) = 24.24%
Thus, the probability that the first ball chosen is black and the second ball chosen is red is 24.24%
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-635 simplest radical form
Answers
Answer:
I believe it is (Square root) And then make it positive. Therefore, 634 should be the correct answer.
Step-by-step explanation:
3/5 + 1/4 = what is it
Answers
12+5/20=
17/20
Explanation:
you find the common denominator: 20.
So 3/5 turns into 12/20
And 1/4 turns into 5/20
Then add the new (but technically the same) fractions:
12/20 + 5/20 = 17/20
Since you can’t simplify, that’s your answer.
A piece of rope that is 10
feet long is cut into two pieces. One piece is used to form a circle and the other used to form a square. Write a function f
representing the area of the circle as a function of the length of one side of the square s.
Hint: If C
is the circumference of the circle and P
is the perimeter of the square, then C+P=10.
Enter the expression in simplest form.
f(s)=
Answers
The area of the circle as a function of the length of one side of the square s is given as \(A = \frac{(20 - 4s)^2}{4\pi}\).
What is area?An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The square unit, which is frequently expressed as square inches, square feet, etc., is the accepted unit of area.
The length of the rope is 10ft.
Let the length of the side of the square = s.
The perimeter of the square is 4s.
After making a square the length of rope remaining to form a circle is 20 - 4s.
The circumference of the circle is given as:
C = 2(pi)(r)
20 - s = 2(pi)(r)
r = 20 - 4s / 2(pi)
The area of the circle is:
\(A = \pi (\frac{20 - 4s}{2\pi} )^2\\\\A = \pi (\frac{(20 - 4s)^2}{4\pi^2} )\\\\A = \frac{(20 - 4s)^2}{4\pi}\)
Hence, the area of the circle as a function of the length of one side of the square s is given as \(A = \frac{(20 - 4s)^2}{4\pi}\).
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The numbers of beads on 500 handcrafted bead necklaces follow a normal distribution whose mean is 24 beads and standard deviation is 4 beads. Which sentence most closely summarizes the data?
Answers
About 80 necklaces have more than 28 beads. Then the correct option is C.
What is a normal distribution?The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.
The numbers of beads on 500 handcrafted bead necklaces follow a normal distribution whose mean is 24 beads and the standard deviation is 4 beads.
P(x > 28) = P(x - 24 / 4 > 28 - 24 / 4)
P(x > 28) = P(x - 24 / 4 > 1)
P(x > 28) = 1 - ∅1
P(x > 28) = 1 - 0.8413
P(x > 28) = 0.1587
Multiply both sides by 500, then we have
500 P(x > 28) = 0.1587 × 500
500 P(x > 28) = 79.35
500 P(x > 28) ≈ 80
About 80 necklaces have more than 28 beads. Then the correct option is C.
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The missing options are given below.
A. About 24 devices have more than 28 beads.
B. About 48 necklaces have more than 28 beads.
C. About 80 necklaces have more than 28 beads.
D. About 96 necklaces have more than 28 beads.