(Sum of the two dice is not 10 and not 7) = 1 - P(3, 4) - P(4, 3) - P(5, 2) - P(2, 5)= 1 - (2/36) - (2/36) - (4/36) - (4/36)= 20/36.
In the rolling of two fair dice, the following probabilities are calculated: P(Sum of the two dice is 8) = 5/36P(Sum of the two dice is 6) = 5/36P(Sum of the two dice is not 4) = 33/36P(Sum of the two dice is 5 or 9) = 10/36P(Sum of the two dice is not 10 and not 7) = 20/36
Note: We can earn partial credit on this problem. We have attempted this problem 0 times. We have unlimited attempts remaining.The step-by-step explanation of how these probabilities are calculated is given below:P(Sum of the two dice is 8) = P(2, 6) + P(3, 5) + P(4, 4) + P(5, 3) + P(6, 2)= (1/36) + (2/36) + (1/36) + (2/36) + (1/36)= 5/36P(Sum of the two dice is 6) = P(1, 5) + P(2, 4) + P(3, 3) + P(4, 2) + P(5, 1)= (1/36) + (1/36) + (1/36) + (1/36) + (1/36)= 5/36P(Sum of the two dice is not 4) = 1 - P(1, 3) - P(2, 2) - P(3, 1)= 1 - (1/36) - (1/36) - (1/36)= 33/36P(Sum of the two dice is 5 or 9) = P(1, 4) + P(2, 3) + P(3, 2) + P(4, 1) + P(3, 6) + P(4, 5) + P(5, 4) + P(6, 3)= (1/36) + (2/36) + (2/36) + (1/36) + (2/36) + (1/36) + (1/36) + (2/36)= 10/36P(Sum of the two dice is not 10 and not 7) = 1 - P(3, 4) - P(4, 3) - P(5, 2) - P(2, 5)= 1 - (2/36) - (2/36) - (4/36) - (4/36)= 20/36.
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Simplify (5+1)^2-(11+3^2) divided by 4
Answer:
(5+1)^2 = 6^2 = 36
3^2 = 9
Next, we can substitute these values into the expression:
(5+1)^2 - (11+3^2) = 36 - (11+9) = 16
Finally, we can divide by 4:
16/4 = 4
Therefore, the simplified expression is 4.
Step-by-step explanation:
I heed a lot of help Guys
Answer: The graph is translated to the left 9 units
Step-by-step explanation:
When the thing is negative it will move to the right it will be positive. When it's negative it will move to the left than it will be negative.
Find an equation of the line with gradient 4 and that passes through the point
(-5, -5)
Answer:
y = 4x + 15
Step-by-step explanation:
Using 'y=mx+c' form,
Since m = 4,
y = 4x + c
Substituting (-5, -5) into the above equation:
-5 = -20 + c
c = 15
Hence,
y = 4x + 15
Feel free to mark this as brainliest! :)
PLS HELP ASAP
!!!!!!!!!
Answer:
3x³- 8x² + 2x +3
Step-by-step explanation:
All you need to do is multiply everything in the second bracket with the first bracket like you would normally do with double brackets.
3x³-3x²-5x²+5x-3x+3=
3x³-8x²+2x+3
Jason wants to walk the shortest distance to get from the parking lot to the beach. How far is the spot on the beach from the parking lot?
How far will his place on the beach be from the refreshment stand?
A: 24 m; 32 m
B: 38 m; 12 m
C: 24 m; 18 m
D: 34 m; 16 m
the shortest distance from the parking lot to the beach is 24 m and the distance between the beach and the refreshment stand is 18 m.
The answer is C: 24 m; 18 m. To find the shortest distance from the parking lot to the beach, one should measure the distance between the two locations. The distance between the parking lot and the beach is 24 m. To find the distance between the beach and the refreshment stand, one should measure the distance between the two locations. The distance between the beach and the refreshment stand is 18 m. Therefore, the shortest distance from the parking lot to the beach is 24 m and the distance between the beach and the refreshment stand is 18 m.
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A car moving at a constant speed passed a timing device at t= 0. After 7 seconds, the car has traveled 812 ft. er of seconds t after passing the timing device.
Answer: y= 116x
Step-by-step explanation:
A baseball team played 154 regular season games. The ratio of the number of games they won to the number of games they lost was 2/5. How many games did they lose?
(Type a whole number)
Answer:
Ratio of 2/5 can be added like 2+5=7
And then
154÷7=22
22×2=44
22×5=110
They lost 110 games
problem i need help now
Answer:
Step-by-step explanation: 55 i think
Answer:
2%?
Step-by-step explanation:
Roy, Sydney, Mila, Taniya invested money on a project. Roy invested twice as Sydney. Mila invested twice as Roy. Taniya invested half as Mila. If the total profit of the project is $27,000. What percentage of profit Mila should receive?
Mila should receive 44.44% of the profit.
What is equations?An equation is a statement that asserts the equality of two expressions, typically with one or more variables. Equations are used to represent relationships between different quantities, such as the relationship between the length and width of a rectangle or the relationship between the time and distance traveled by an object.
What is profit?Profit is the financial gain that is earned by a business or an individual after all expenses and costs have been subtracted from revenue or income. It is the difference between the amount earned from sales or services and the costs incurred to produce or provide those goods or services.
In the given question,
Let's begin by determining the amount of money each person invested in the project.
Let Sydney's investment be x.
Roy's investment is twice Sydney's, so Roy invested 2x.
Mila's investment is twice Roy's, so Mila invested 2(2x) = 4x.
Taniya's investment is half of Mila's, so Taniya invested 0.5(4x) = 2x.
The total amount invested is x + 2x + 4x + 2x = 9x.
Now, we need to find the percentage of profit Mila should receive. Since the profit is shared in proportion to the amount invested, Mila should receive a fraction of the profit equal to her investment divided by the total investment.
Mila's share = (Mila's investment) / (Total investment) x (Total profit)
Mila's share = (4x / 9x) x 27000
Mila's share = 12000
So Mila should receive $12,000 of the profit. To find the percentage of profit Mila should receive, we can divide her share by the total profit and multiply by 100:
Percentage of profit Mila should receive = (Mila's share / Total profit) x 100%
Percentage of profit Mila should receive = (12,000 / 27,000) x 100%
Percentage of profit Mila should receive = 44.44%
Therefore, Mila should receive 44.44% of the profit.
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At a coffee shop, the first 100 customers'
orders were as follows.
Hot
Cold
Small Medium Large
5
48
22
8
12
5
Find the probability a customer ordered a hot
drink, given that they ordered a small.
P(B|A) =
P(AnB)
P(A)
Round to the nearest hundredth.
P(hot | small) = [?]
Enter
The probability that a customer ordered a hot drink, given that they ordered a small, is approximately 0.045.
The Bayes theorem is what?A mathematical technique called the Bayes theorem enables us to revise our views or probability regarding an occurrence in light of fresh data or evidence. It has the name of the reverend Thomas Bayes, a statistician and philosopher active in the 18th century. According to the Bayes theorem, the likelihood of an event A given that an event B has already happened is equal to the likelihood of an event B given that an event A has already occurred, multiplied by the prior likelihood of an event A, divided by the previous likelihood of an event B.
The Baye's Theorem is given as:
P(B|A) = P(A|B) × P(B) / P(A)
Here,
P(A) is the probability that a customer ordered a small drink = 0.22.
P(B) is the probability that a customer ordered a hot drink, regardless of whether it was small or medium or large = 0.05.
P(A|B) is the probability that a customer ordered a small drink, given that they ordered a hot drink = 0.2.
Substitute the value we have:
P(B|A) = P(A|B) × P(B) / P(A) = (0.2 × 0.05) / 0.22 ≈ 0.045
Therefore, the probability that a customer ordered a hot drink, given that they ordered a small, is approximately 0.045.
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Find the slope of a line with the cordnates of (6,1) and (-3,5)
Answer:
Answer:
Slopem=−49
As a decimal:
m = -0.444444
Step-by-step explanation:
Slope m with two points
Graph of the line for y = mx + b
Point Slope Form y - y1 = m(x - x1)
Slope Intercept Form y = mx + b
Standard Form Ax + By = C
y-intercept, when x = 0
x-intercept, when y = 0
If two points on a line are A(4, 6) and B(8, −8), the rise is __________, and the run is __________, so the slope of the line is __________.
Find the discriminant of $3x^2 + \left(3 + \frac 13\right)x + \frac 13$.
The discriminant, D of the quadratic equation [tex]3x\² + 3 \frac 13x + \frac 13[/tex] when calculated is 64/9
How to determine the discriminant of the equationThe quadratic equation is given as
[tex]3x\² + 3 \frac 13x + \frac 13[/tex]
The discriminant of a quadratic equation of the form ax² + bx +c = 0 is given by the expression b² - 4ac
In this case, we have the quadratic equation [tex]3x\² + 3 \frac 13x + \frac 13[/tex], which can be written in the standard form as
[tex]3x\² + \frac {10}3x + \frac 13[/tex]
Comparing with the standard form ax² + bx + c = 0,
we have a = 3, b = 10/3 and c = 1/3
The discriminant of this quadratic equation is therefore:
D = b² - 4ac
[tex]D = (\frac{10}{3})\² - 4 \cdot 3 \cdot \frac{1}{3}[/tex]
D = 64/9
Hence, the discriminant of [tex]3x\² + 3 \frac 13x + \frac 13[/tex] is 64/9
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The path of a firecracker is modeled by the equation h(t) = -t^2 + 19t + 14, where h(t) is the hight, in feet, of the firecracker at any given time, t. What is the hight of the firecracker after 4 seconds from launch.
A. 63 feet
B. 68 feet
C. 70 feet
D. 74 feet
the height of the firecracker after 4 seconds from launch is 68 feet.
To find the height of the firecracker after 4 seconds from launch, we need to plug in t = 4 into the equation h(t) =[tex]-t^2[/tex] + 19t + 14. This gives us h(4) =[tex]-4^2[/tex] + 19(4) + 14 = -16 + 76 + 14 = 68 feet. Therefore, the height of the firecracker after 4 seconds from launch is 68 feet.
To find the height of the firecracker after 4 seconds from launch, we need to use the equation h(t) =[tex]-t^2[/tex] + 19t + 14. This equation models the path of the firecracker, with h(t) being the height in feet of the firecracker at any given time, t. When we plug in t = 4, we get h(4) = [tex]-4^2[/tex] + 19(4) + 14 = -16 + 76 + 14 = 68 feet. So, the height of the firecracker 4 seconds after launch is 68 feet. This equation allows us to calculate the height of the firecracker at any given time, making it a useful tool for predicting the trajectory of the firecracker.
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A family is traveling a total distance of 532 miles. If the family travels at an average speed of 57 miles per hour, which equation represents the number of miles remaining, m, after h hours?
m = 532 - (57 * h) represents the number of miles remaining after h hours of traveling at an average speed of 57 miles per hour.
The equation m = 532 - (57 * h) is used to represent the number of miles remaining, m, after h hours of traveling at an average speed of 57 miles per hour. The equation works by taking the total distance, 532 miles, and subtracting the product of the average speed, 57 miles per hour, and the amount of hours traveled, h. The result of the equation is the number of miles remaining, m. For example, if the family has been traveling for four hours, the equation would be m = 532 - (57 * 4). Solving the equation, m = 344, meaning the family has 344 miles left to travel. This equation allows the family to easily determine how many miles they have left to travel, given the average speed and amount of time traveled.
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a particle of mass 0.58 kg is subject to a force that is always pointed towards east or west but whose magnitude changes sinusoidally with time. with the positive x-axis pointed towards the east, the x-component of the force is given as follows: fx
The work done by the force as the particle moves from x = 0 m to x = 2.2 m is approximately -0.53 J.
A particle of mass 0.58 kg is subject to a force that is always pointed towards east or west but whose magnitude changes sinusoidally with time. With the positive x-axis pointed towards the east, the x-component of the force is given as follows: fx(t) = (2.6 N) sin(2.2t)where t is in seconds.
The work done by the force as the particle moves from x = 0 m to x = 2.2 m: For a sinusoidal force that changes with time, the work done is given by W = ∫F dx where F is the force, and dx is the displacement. For this problem, the force is given by fx(t) = (2.6 N) sin(2.2t)dx is the displacement, which is given by dx = x2 – x1 where x2 = 2.2 m, and x1 = 0 m.
Substituting for F and dx, we get W = ∫02.2(2.6 sin(2.2t)) dx= 2.6 ∫02.2 sin(2.2t) dx= 2.6 [(-1/2.2) cos(2.2t)]02.2= 1.18 (cos(4.84) – 1)≈ -0.53 J. So, the work done by the force as the particle moves from x = 0 m to x = 2.2 m is approximately -0.53 J.
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Find the unit rate for each, then tell which is the least expensive brand.
Bugsy-B: $9.99 for 64 ounces, How many dollars per ounce?
Tazi-D: $2.25 for 16 ounces, how many dollars per ounce?
Answer: Tazi-D
Bugsy-B: 0.16 per ounce
Tazi-D: 0.14 per ounce
Step-by-step explanation:
divide the $ by the ounce for both.
name the property the equation illustrates-4x-1/4=1
The prοperty the equatiοn illustrates-4x-1/4=1 is multiplicatiοn inverse.
What is an equatiοn?The definitiοn οf an equatiοn in algebra is a mathematical statement that demοnstrates the equality οf twο mathematical expressiοns.
οr,
A mathematical expressiοn cοmpοsed οf twο expressiοns jοined tοgether by the equal sign.
Given equatiοn is (-4)×(-1/4) = 1.
The name οf prοperties are
Distributive Prοperty: a(b+c) = ab + bc
Cοmmutative Prοperty: ab =ba
Assοciative Prοperty :a(bc) = (ab)c
Identity Prοperty a×b=1
Inverse Prοperty: a×b=1
These characteristics hοld true in mathematical and algebraic expressiοns just as they dο in prοpοsitiοnal language.
In the Inverse Prοperty, the prοduct οf a number and its inverse is equal tο 1.
The given equatiοn represents Inverse Prοperty.
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Q9) Rashmi obtains 480 marks out of 600. Rajan obtains 560 marks out of 700. Whose performance is better?
Answer:
Step-by-step explanation:
Let us first make the denominators equal, so
600 x 700 = 420000
[tex]\frac{480}{600} * \frac{700}{700} \\\\= \frac{336000}{420000}[/tex]
Similarly,
[tex]\frac{560}{700} * \frac{600}{600} = \frac{336000}{420000}[/tex]
By comparison, both of them are equal.
Hope It Helps!
Write the ratio in its simplest form: 2m: 8cm : 40mm
The simplest form of the ratio 2m : 8cm : 40mm is
50mm : 2mm : 1mm
What is ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.
For we to simplify the ratio , we have to convert the unit to the least form. The least form of the unit is millimeter
2m = 2× 1000mm = 2000mm
8cm = 8 × 10 = 80mm
40mm = 40mm
therefore the ratio will be in form of
2000mm : 80mm ; 40mm
divide through by 10
200mm : 8mm : 4mm
divide through by 4
50mm : 2mm : 1mm
therefore the simplest form of the ratio 2m: 8cm : 40mm is 50mm : 2mm : 1mm
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Work out the value of 4 squared + 3 cubed
help if can for 10+ points
Answer:
43
Step-by-step explanation:
We can simplify the expression:
[tex]4^2 + 3^3[/tex]
by rewriting exponents as multiplication of their base.
[tex]4^2 + 3^3[/tex]
[tex]= (4\cdot 4) + (3\cdot 3 \cdot 3)[/tex]
Then, we can simplify using the order of operations (PEMDAS).
[tex](4\cdot 4) + (3\cdot 3 \cdot 3)[/tex]
[tex]= 16 + (9 \cdot 3)[/tex]
[tex]= 16 + 27[/tex]
[tex]\boxed{= 43}[/tex]
Randy claims that he can purchase 3. 5 pounds of chicken salad for $23. 50. Is he correct? Explain.
Randy's claim is not correct Therefore, he cannot purchase 3.5 pounds of chicken salad for $23.50
To determine if Randy's claim is correct, we can use the given linear graph and points to find the equation of the line that represents the relationship between the amount of chicken salad purchased and the cost.
We can use the two points (1, 7.5) and (3, 22.5) to find the slope of the line:
slope = (change in y) / (change in x)
slope = (22.5 - 7.5) / (3 - 1)
slope = 15 / 2
slope = 7.5
Now we can use the slope-intercept form of the equation of a line, y = mx + b, where m is the slope and b is the y-intercept, to find the equation of the line:
y = 7.5x + b
To find b, we can use one of the points on the line, such as (1, 7.5):
7.5 = 7.5(1) + b
b = 0
So the equation of the line is:
y = 7.5x
Now we can use this equation to check if Randy's claim is correct. If he can purchase 3.5 pounds of chicken salad for $23.50, we can plug in x = 3.5 and see if y = 23.5:
y = 7.5x
y = 7.5(3.5)
y = 26.25
Since y = 26.25 is not equal to $23.50
Therefore, Randy's claim is not correct
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The given question is incomplete, the complete question is:
Randy claims that he can purchase 3. 5 pounds of chicken salad for $23. 50. Is he correct? Explain.
A pair of parallel lines is cut by a transversal.
A pair of parallel lines is shown cut by a transversal. Angle A is located in the upper left exterior next to the transversal, and angle B is located in the bottom right exterior corner of the transversal.
If m∠A = (5x − 4)° and m∠B = (8x − 28)°, what is the value of x?
Answer:
8 degrees
Step-by-step explanation:
Given in the picture, hope it helps.
What is the area of this trapezoid? Enter your answer in the box.
Answer:153
Step-by-step explanation
we can see height is equal to 9. if we consider height and 10sm as sides of rectangle, we can say top of trapezoid is equal to 10 as well.
Area of trapezoid is A=(a+b)/2*h
h-height=9
a-top=10
b-bottom=10+7+7=24
A=(10+24)/2*h=34/2*9=17*9=153
Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following.
0 , x<0
f(x) = ((x^2)/4) , 0 <= x <= 2
1 , 2<= x
Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.)
(a) P(X %u2264 1)
(b) P(0.5 %u2264 X %u2264 1)
(c) P(X > 1.5)(d) The median checkout duration [solve 0.5 = F(mew)](e) Use F'(x) to obtain the density function f(x)
(f) Calculate E(X)
(g) Calculate V(X) and %u03C3x
(h) If the borrower is charged an amount h(X) = X2 when checkout duration is X, compute the expected charge E[h(X)].
Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following. For [tex]0 ≤ x ≤ 2, F(1) = (1^3/12) = 0.0833.So, P(X ≤ 1) = 0.0833.[/tex] Hence, the correct option is (a) P(X ≤ 1).
Given that X denotes the amount of time a book on two-hour reserve is actually checked out, and the cdf is the following:
[tex]cdf: 0 , x<0f(x) = ((x^2)/4) , 0 <= x <= 21 , 2<= x[/tex]
To use the cdf to obtain the following.P(X ≤ 1)
So, the probability distribution function is the derivative of the cumulative distribution function.
∴ f(x) = d/dx(F(x))
Also, from the cdf, we know that:
[tex]f(x) = 0 when x < 0.f(x) = ((x^2)/4) when 0 ≤ x ≤ 2.[/tex]
f(x) = 1 when x ≥ 2.
Using the above conditions, we have to calculate the following:
(a) P(X ≤ 1)
Here, P(X ≤ 1) = F(1).
When[tex]0 ≤ x ≤ 2, F(x) = ∫[0,x] f(t)dt=∫[0,x] (t^2/4)dt=[t^3/12]0x=(x^3/12)[/tex]
Thus, for[tex]0 ≤ x ≤ 2, F(x) = (x^3/12).[/tex]
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What is the coordinate for G(3,-2) after it is reflected across the x-axis?
(2,3)
(-2,3)
(3,2)
(-3,-3)
Answer:The coordinates of the resulting point after the reflection across the y - axis will be P'(3, 2).
What do you mean by reflection of coordinates?
A reflection on the coordinate plane is a type of transformation. It takes a geometric figure such as a point, line segment, or shape and transforms it into a congruent geometric figure called the image.
Given is a point (-3, 2) reflected across the y - axis.
Now, when any given coordinate is reflected across the y - axis then, the sign of the x - coordinate is inverted and the y - coordinate remains same.
As given, the coordinates of the point are - P(-3, 2)
Now, after reflection across the y - axis, the new coordinates of the image of this point will be -
x' = - (- 3) = 3
y' = y = 2
P'(3, 2)
Therefore, the coordinates of the resulting point after the reflection across the y - axis will be P'(3, 2)
Answer:
3,2
Step-by-step explanation: Just took the test
Arthur can paint a wall in 45 minutes alone. Cheyenne can paint a wall in 1 hour alone. One
room has 4 walls. How many minutes will it take them to paint 3 rooms together?
The time needed to paint 3 rooms together is given as follows:
308.4 minutes.
How to obtain the time needed?The time needed is obtained applying the proportions in the context of the problem.
First we use the together rate, which is the sum of each separate rate, for the time needed to paint a single wall, hence:
1/x = 1/45 + 1/60
1/x = 7/180
7x = 180
x = 180/7
x = 25.7 minutes per wall.
The number of walls in 3 rooms is given as follows:
3 x 4 = 12 walls.
Thus the time needed to paint the 3 rooms is given as follows:
25.7 x 12 = 308.4 minutes.
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PLEASE HELP!!!! DUE TOMORROW AND GRADED!!!! I WILL GIVE BRAINLIEST
Answer:
f(-3) = 6
Step-by-step explanation:
You want the value of f(-3) given a graph of f(x).
Reading a graphTo find the value of f(-3), locate -3 on the x-axis. Follow the vertical grid line to where it intersects the graph of f(x). Follow the horizontal grid line from there to the axis marked f(x), and read the value on the vertical scale.
The attachment shows this process, and that the value of f(-3) is 6.
__
Additional comment
Unless there is information to the contrary, the usual assumption is that each grid line represents one unit. Positive is to the right of the vertical axis, and up from the horizontal axis. Then x=-3 is 3 grid lines left of the vertical axis.
The notation f(x) means the value of function f depends on the value x. The expression f(-3) is the function value when x=-3. Here, it is found by reading the graph. In other situations, it might be found from a table or by evaluating an algebraic expression.
Alex picked 15 ⅘ kilograms of red apples and 9 ⅗ kilograms of green apples. What is the total mass of the apples Alex picked?
The total mass of the apples Alex picked is 25 2/5 kilograms.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants
To find the total mass of the apples Alex picked, we need to add the mass of the red apples and the mass of the green apples.
First, let's convert the mixed numbers to improper fractions to make the addition easier:
15 ⅘ = 15 + 8/10 = 15 + 4/5 = 75/5 + 4/5 = 79/5
9 ⅗ = 9 + 6/10 = 9 + 3/5 = 45/5 + 3/5 = 48/5
Now we can add the fractions:
79/5 + 48/5 = (79 + 48)/5 = 127/5
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 1 in this case:
127/5 = 25 2/5
Therefore, the total mass of the apples Alex picked is 25 2/5 kilograms.
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Unit 10: circles
Homework 8
#2, 4, 6, and & 8
The measures in the circles are calculated as:
2. FD = 22; 4. US = 58
6. MN = 11; 8. YZ = 34
What is the Intersecting Chords Theorem?The Intersecting Chords Theorem states that when two chords intersect inside a circle, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.
2. 12(3x - 5) = 15(8) [based on the Intersecting Chords Theorem]
36x - 60 = 120
36x = 120 + 60
36x = 180
x = 5
FD = 3x - 5 + 12 = 3(5) - 5 + 12
FD = 22
4. 30(3x + 1) = 42(x + 11) [based on the Intersecting Chords Theorem]
90x + 30 = 42x + 462
90x - 42x = -30 + 462
48x = 432
x = 9
US = 3x + 1 + 30 = 3(9) + 1 + 30 = 58
6. (2x - 7 + 9)(9) = (8 + 10)(10) [based on the intersecting secants theorem]
18x + 18 = 180
18x = 180 - 18
18x = 162
x = 9
MN = 2x - 7 = 2(9) - 7
MN = 11
8. (2x + 12 + 6)(6) = (x + 3 + 10)(10) [based on the intersecting secants theorem]
12x + 108 = 10x + 130
12x - 10x = -108 + 130
2x = 22
x = 11
YZ = 2x + 12 = 2(11) + 12
YZ = 34
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