The probability that a randomly selected bicycle from a bicycle shop will have either a water bottle holder or a kickstand is 95%, calculated by adding the probabilities of each component being present and subtracting the probability of both being present.
The probability that a randomly selected bicycle from a bicycle shop will have either a water bottle holder or a kickstand is 95%. To calculate this, we first need to consider the probability that a bicycle has a water bottle holder, which is 60%. The probability that the bicycle has a kickstand is 55%. Then, the probability of a bicycle having both a kickstand and a water bottle holder together is the product of the individual probabilities, which is 34%. Thus, the probability that a randomly selected bicycle will have either a water bottle holder or a kickstand is 60% + 55% - 34% = 95%.
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Suki took $20 to the carnival she spent one half of her money on rides 1/4 of her money on food and 1/10 of her money on parking how much did Suki spend on rides on food and on parking
Suki spent a total of $17 on rides, food, and parking at the carnival.
The problem states that Suki took $20 to the carnival and spent some portion of it on rides, food, and parking. The first step is to figure out what fractions of her money she spent on each of these things.
The problem tells us that she spent one half of her money on rides, 1/4 of her money on food, and 1/10 of her money on parking. We can write this mathematically and use the multiplication :
Suki spent 1/2 x $20 = $10 on rides
Suki spent 1/4 x $20 = $5 on food
Suki spent 1/10 x $20 = $2 on parking
To find the total amount that Suki spent on rides, food, and parking combined, we simply add up these three amounts:
Total spent = $10 + $5 + $2 = $17
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The new Iphone was reduced from $320 to $224. By what percentage was the price of the Iphone reduced? 7.4D A. 33% B. 96% C. 70% D. 30%
Answer:
D
Step-by-step explanation:
To calculate the percentage decrease in price, we need to find the difference between the original price and the reduced price, divide that difference by the original price, and then multiply by 100 to express it as a percentage.
The original price of the iPhone was $320, and it was reduced to $224. Therefore, the difference between the two prices is:
$320 - $224 = $96
To find the percentage decrease, we divide this difference by the original price:
$96 ÷ $320 = 0.3
Finally, we multiply this result by 100 to express it as a percentage:
0.3 × 100 = 30%
Therefore, the answer is D. The price of the iPhone was reduced by 30%.
Sadie needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 5 hours and charged her $70 for parts. The total was $395. Which equation or tape diagram could be used to represent the context if
�
x represents the cost of labor per hour?
We get the equation as : 5y + 70 = 395 if the computer for 5 hours and charged her $70 for parts. The total was $395.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
Let's use the variable "y" to represent the cost of labor per hour.
The technician worked on the computer for 5 hours, so the cost of labor would be 5y. Additionally, the technician charged $70 for parts. The total cost was $395. We can set up the following equation to represent the context:
5y + 70 = 395
This equation represents the total cost Sadie paid for the repair, which includes the cost of labor and parts.
Alternatively, we can use a tape diagram to represent the context. We can draw a rectangle and divide it into two parts, one representing the cost of labor and the other representing the cost of parts. The length of the labor part would be Five times the cost per hour (5y), and the length of the parts part would be $70.
]The length of the whole rectangle would represent the total cost ($395). We can label the unknown cost per hour as "y".
Therefore, we get the equation as : 5y + 70 = 395 if the computer for 5 hours and charged her $70 for parts. The total was $395.
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A long wire is wound to a circular coil of radius 1m and consists of 70 loops of wire around it
The resistance of the coil is given by R = N x ρL = 70 x ρ x 0.0897 = 617.9 x ρ ohms.
The length of the wire is equal to the circumference of the circular coil. The circumference C of a circle of radius r is C = 2πr, so for the circular coil of radius 1m, the length of the wire is 2π x 1m = 6.28m.
The number of loops around the coil (N) is 70. Therefore, the length of one loop is L = 6.28/70 = 0.0897 m.
The resistance of the coil (R) is equal to the resistance of the single loop multiplied by the number of loops (N). Therefore, R = N x R', where R' is the resistance of a single loop.
The resistance of a single loop is equal to the resistance of the wire per unit length multiplied by its length. Therefore, R' = ρL, where ρ is the resistivity of the wire and L is the length of one loop of the wire.
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Complete question:
What is the resistance of a circular coil of radius 1m that consists of 70 loops of wire?
(12 points ) Find the area of an equilateral triangle with side length 2cm. Show all necessary calculations. Round your answer to the nearest hundredth.
The area of the equilateral triangle with side length 2cm is approximately 1.73 cm².
What is the area of the equilateral triangle?An equilateral triangle with side length 2cm can be divided into two right triangles with hypotenuse equal to 2cm and the other two sides of length 1cm each.
We can then use the Pythagorean theorem to find the length of the height of the equilateral triangle, which is also the height of the right triangles.
Let h be the height of the equilateral triangle, then:
h² = 2² - 1²
h² = 3
h = √3
The area of the equilateral triangle can be found using the formula:
Area = (base × height) / 2
Since the equilateral triangle has three equal sides, the base is also equal to 2cm. Therefore, we have:
Area = ( 2 × √3 ) / 2
Area = √3
Rounding to the nearest hundredth, we get:
Area = 1.73 cm²
Therefore, the area of the equilateral triangle is 1.73 cm².
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If you toss one dime and roll one die. Predict how many time you would flip heads and roll an odd number In 120 tries.
We can predict that in 120 tries, we would expect to get heads and an odd number around 30 times. However, it is important to note that this is just a prediction and the actual number of times this occurs may vary due to chance.
When flipping a dime, there are two possible outcomes: heads or tails. Similarly, when rolling a die, there are six possible outcomes: 1, 2, 3, 4, 5, or 6. An odd number is any number that is not divisible by 2, so the odd numbers on a die are 1, 3, and 5.
The probability of flipping heads on a dime is 1/2, and the probability of rolling an odd number on a die is 3/6 or 1/2. To predict how many times you would flip heads and roll an odd number in 120 tries, we can use the multiplication rule of probability.
The multiplication rule of probability states that the probability of two independent events occurring together is the product of their individual probabilities. Since flipping a dime and rolling a die are independent events, we can multiply the probability of flipping heads and the probability of rolling an odd number to get the probability of both events occurring together.
So, the probability of flipping heads and rolling an odd number is:
P(heads and odd) = P(heads) x P(odd)
P(heads and odd) = (1/2) x (1/2)
P(heads and odd) = 1/4
We can estimate that in 120 trials, we should get heads about 30 times and an odd amount about the same. It is crucial to keep in mind that this is only a prediction and that there is a possibility that the actual frequency of occurrence will differ.
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Jacob conducts another survey of students in the school in the Example. This time,
he surveys a random sample of 30 students.
a. In Jacob's sample, 24 students say they will vote for Garrett. Based on this
sample, about how many students in the school should Garrett expect to vote
for him? Show your work.
SOLUTION
Jacob's sample suggests that Garrett should expect approximately 80 percentage of the students in the school to vote for him.
Jacob's sample of 30 students suggests that 24 of them will vote for Garrett, which is an 80% ratio. Applying this ratio to the entire school population, Garrett can reasonably expect that 80% of the students in the school will vote for him. This means that out of the total student population, Garrett can expect approximately 24/30, or 80%, of them to vote for him. This is a useful estimate for how many votes Garrett can expect to receive from the student body. It is important to note, however, that this is only an estimate and may not accurately reflect the actual number of students who will vote for Garrett. Factors such as student opinion or external influences may affect the actual voting results.
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Solve using the Zero Product Property. Give your answer as a decimal, if necessary. A group of friends tries to keep a small bean bag from touching the ground by kicking it. On one kick, the beanbags height can be modeled by the equation h = −(2t − 3) − 8t(2t − 3), where h is the height of the beanbag in feet and t is the time in seconds. Find the time it takes the beanbag to reach the ground. The time it takes for the beanbag to reach the ground is ___ second(s)
As per the given equation, the beanbag will reach the ground after 1.5 seconds.
To find the time it takes for the beanbag to reach the ground, we need to set h equal to zero, since the beanbag will be on the ground when its height is zero. So we have the equation:
0 = −(2t − 3) − 8t(2t − 3)
We can simplify this equation by factoring out the common factor of (2t − 3):
0 = (2t − 3)(−1 − 8t)
Now we can use the Zero Product Property, which states that if the product of two factors is equal to zero, then at least one of the factors must be zero. So we can set each factor equal to zero and solve for t:
2t − 3 = 0 or −1 − 8t = 0
Solving the first equation for t, we get:
2t = 3
t = 3/2
Solving the second equation for t, we get:
−1 − 8t = 0
8t = −1
t = −1/8
However, we need to discard the negative value of t, because time cannot be negative. So the time it takes for the beanbag to reach the ground is t = 3/2 seconds or 1.5 seconds
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Which numbers are factors of 42? Check all that apply.
• 1
• 2
• 3
• 4
• 6
• 8
Answer:
1, 2, 3, 6
Step-by-step explanation:
Buffy and Addy launch their rockets at the same time. The height of Buffy’s rocket, in meters, is given by the function f(x) = -4. 9x^2 +50x ,where x is the number of seconds after the launch. The height of Addy’s rocket, in meters, is given by the function g(x) = -4. 9x^2 +25x +34 ,where x is the number of seconds after the launch. Algebraically find the moment when the rockets are at the same height, and then use that to calculate the height? Round to the nearest hundred.
PLEASE SHOW ALL WORK!!
The rockets are at a height of 83.15 meters after 1.36 seconds. Rounded to the nearest hundred, this is 83 meters.
To find the moment when the rockets are at the same height, set f(x) = g(x) and solve for x:
-4.9x2 +50x = -4.9x2 +25x + 34
50x = 25x + 34
25x = 34
x = 1.36
Therefore, the rockets are at the same height after 1.36 seconds. To calculate the height, plug x = 1.36 into either function:
f(1.36) = -4.9(1.36)2 +50(1.36)
f(1.36) = -4.9(1.85) + 68
f(1.36) = 83.15 meters
Therefore, the rockets are at a height of 83.15 meters after 1.36 seconds. Rounded to the nearest hundred, this is 83 meters.
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Me podrían ayudar no entiendo cómo hacerlo
A bisector in math is a line or a line segment that divides an angle or a line segment into two equal parts.
What is bisector?The bisector, also known as the perpendicular bisector, is a geometric concept in mathematics that is used to construct a line that is perpendicular to a given segment and passes through its midpoint. The bisector is an important tool in geometry and is used in a variety of applications, including constructing triangles, circles, and finding the circumcenter.
To construct the bisector of a segment, one must first locate the midpoint of the segment. This is done by dividing the length of the segment in half, using a straightedge to connect the two endpoints, and then drawing a perpendicular line through the midpoint. The resulting line is the bisector of the segment.
The bisector has several important properties. First, it is always perpendicular to the segment it bisects. This means that the angle between the bisector and the segment is always 90 degrees. Second, the bisector always passes through the midpoint of the segment. Finally, any point on the bisector is equidistant from the two endpoints of the segment. This means that the bisector can be used to construct other geometric objects that are equidistant from the endpoints of the segment, such as circles.
In summary, the bisector is a line that is perpendicular to a given segment and passes through its midpoint. It is an important tool in geometry and is used in a variety of applications, including constructing triangles, circles, and finding the circumcenter.
Note: This question is in Spanish. Here is the translation to English.
Bisector: the line by which a segment is divided into two parts perpendicularly.
Please explain this.
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Work out the value of 4 cubed - 6 squared.
help if can for 10+ points
Answer:
28
Step-by-step explanation:
4 cubed means 4 x 4 x 4, which is 64.
6 squared means 6 x 6, which is 36.
So,
4 cubed - 6 squared = 64 - 36 = 28.
suppose you have a set of data with a mean of 50 and a standard deviation of 10. if you add 5 to each data point, what will happen to the mean and the standard deviation of the new set of data?
If you add 5 to each data point in a set of data with a mean of 50 and a standard deviation of 10, the mean of the new set of data will become 55. The standard deviation of the new set of data will remain the same at 10.
What is the standard deviation?The term standard deviation is frequently used in statistics to quantify the dispersion or spread of a set of data. The standard deviation is a measure of the amount of variation or dispersion of a set of data values from the mean. Standard deviation is denoted by the symbol s or σ (sigma).
What is the mean of a set of data?The term mean or arithmetic mean is used in statistics to refer to the value that represents the central tendency of a data set. It is computed by dividing the sum of all data values into a data set by the total number of data points. The formula for computing the mean is given as:
mean = (sum of data values) / (total number of data points)
When you add 5 to each data point in a data set with a mean of 50, the sum of all data values in the data set will increase by (5 * n), where n is the total number of data points. Consequently, the new mean will be given as:
new mean = (sum of new data values) / (total number of data points)
⇒ [(sum of old data values) + (5 * n)] / n ⇒ (50n + 5n) / n ⇒ 55
What is the effect of adding a constant to every data point in a data set?When you add a constant value to each data point in a data set, the measure of central tendency, i.e., mean, median, and mode will also be shifted by the same constant value. This is because the sum of all data values in the data set increases by the product of the constant value and the total number of data points, n.
The measure of variability or spread, i.e., range, interquartile range, variance, and standard deviation, however, remains the same because it is independent of the location of the data values in the data set. Therefore, adding a constant value to every data point in a data set does not change the spread of the data set but shifts the measure of central tendency to a new value.
Hence, the mean of the new dataset will increase by 5, from 50 to 55, and the standard deviation of the new dataset will remain the same at 10.
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what is the value of x, given that PQ||BC??
After answering the presented question, we can conclude that As a equation result, the value of x is 34.
What is equation?An equation is a mathematical statement that validates the equivalent of two expressions joined by the equal symbol '='. For instance, 2x - 5 = 13. 2x-5 and 13 are two examples of expressions. The character '=' connects the two expressions. An equation is a mathematical formula that has two algebras on each side of an assignment operator (=). It demonstrates the equivalency link between the left and middle formulas. L.H.S. = R.H.S. (left side = right side) in any formula.
We can see from the diagram that PQ is parallel to BC and that the line segments PQ and BC overlap at point O.
As a result, we have:
angle QPO stands for angle. 70° angle = ABC QOP stands for angle. ACB = 110°
angle AOB = angle - 180 ACB - ABC angle = 180 - 70 - 110 = 0
This indicates that points A, O, and B are collinear and that angle AOB is a straight angle, implying that angles AOP and POB are supplementary angles.
We may use this data to calculate the value of x:
AOP angle + POB angle = 180
(3x - 10) + (2x + 20) = 180
5x + 10 = 180
5x = 170
x = 34
As a result, the value of x is 34.
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5/5 = 3/3 because they both equal 1. Leopold takes one part away from each.
If Leopold takes one part away from each of the fractions, they will not be equal anymore.
What makes fractions to be equal?Two or more fractions are said to be equal or equivalent if we simplify them and obtain the same result for both. Let's analyze the fractions given:
5/5 = 1
3/3 = 1
What happens if we remove one part away?Even when some fractions are equivalent if you modify them this will change the equivalence property, let's prove it with the fractions given:
4/5 = 0.8
2/3 = 0.66
Note: This question is incomplete; here is the missing section:
Leopold takes one part away from each. Will the fraction still be equal?
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Refer to exercise 3. 67. What is the expected number of applicants who need to be interviewed in order to find the first one with advanced training?
The expected number of applicants who need to be interviewed in order to find the first one with advanced training is 8.
We can calculate this by using the formula for the geometric series. The formula for the geometric series is given by S = a1(1-rn)/1-r, where a1 is the first term in the series, r is the common ratio, and n is the number of terms. In this problem, a1 = 1 (since the probability of finding the first applicant with advanced training is 1/8), and r = 1/8 (since the probability of finding the next applicant with advanced training is 1/8). Thus, plugging these values into the formula yields S = 1(1-(1/8)^n)/1-(1/8) = 8. Therefore, the expected number of applicants who need to be interviewed in order to find the first one with advanced training is 8.
S = a1(1-rn)/1-r
S =[tex]1(1-(1/8)^n)/1-(1/8)[/tex]
S = 8
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Use Excel to find the critical value of z for each hypothesis test. (Round your answers to 3 decimal places. Negative values should be indicated by a minus sign.) (a) 10 percent level of significance, two-tailed test. Critical value of z ± (b) 1 percent level of significance, right-tailed test. Critical value of z (c) 5 percent level of significance, left-tailed test. Critical value of z
Using hypothesis testing, the critical value of z for a 5 percent level of significance, left-tailed test is -1.645.
(a) For a 10 percent level of significance, two-tailed test, the critical value of z is:
z_critical = ± invNorm(1 - (0.10/2))
where invNorm is the inverse normal cumulative distribution function. Evaluating this expression gives:
z_critical = ± 1.645
Therefore, the critical value of z for a 10 percent level of significance, two-tailed test is ±1.645.
(b) For a 1 percent level of significance, right-tailed test, the critical value of z is:
z_critical = invNorm(1 - 0.01)
Evaluating this expression gives:
z_critical = 2.326
Therefore, the critical value of z for a 1 percent level of significance, the right-tailed test is 2.326.
(c) For a 5 percent level of significance, left-tailed test, the critical value of z is:
z_critical = invNorm(0.05)
Evaluating this expression gives:
z_critical = -1.645
Therefore, the critical value of z for a 5 percent level of significance, left-tailed test is -1.645.
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? Work out the total surface area of this solid cone. Give your answer rounded to 1 DP. 10m 7m
The total surface area of the solid cone, given the slant height and the radius, would be 374 m².
How to find the surface area of the cone ?To find the surface area of a solid cone, we need to consider both the curved lateral surface and the circular base.
Lateral Surface Area = π x 7 m x 10 m = 70π m²
The base of a cone is a circle with radius r. The area of the base can be calculated using the formula:
Base Area = π x (7 m)² = 49π m²
Total Surface Area = Lateral Surface Area + Base Area = 70π m² + 49π m² = 374 m².
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Clty Line What is the measure of the angle formed by the intersection of the River Line and the Northeast Line?
The measure of the angle formed by the intersection of the River Line and the Northeast Line is equal to: C. 42°.
What is a supplementary angle?In Mathematics, a supplementary angle simply refers to two (2) angles or arc whose sum is equal to 180 degrees.
Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can logically deduce that the sum of the given angles are supplementary angles:
60° + (8x - 18)° + (3x + 6)° = 180°
60° + 8x - 18° + 3x + 6° = 180°
11x = 180° - (18° - 6° - 60°)
11x = 180° - 48°
11x = 132°
x = 132/11
x = 12
For the intersection of the River Line and the Northeast Line, we have:
R = (3x + 6)°
R = 3(12) + 6
R = 36 + 6
R = 42°.
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Complete Question:
What is the measure of the angle formed by the intersection of the River Line and the Northeast Line?
40
41
42
43
Find the value of x.
Answer:
x = -10
Step-by-step explanation:
Note that it is a isosceles triangle. This means that the base angles (the angles that are not forged by the congruent sides) are congruent.
It is given that one of the angle measurements are 67°, meaning that ∠A would also be equal to 67. Set the equation:
m∠A = x + 77
67 = x + 77
Isolate the variable, x. Subtract 77 from both sides of the equation:
67 (-77) = x + 77 (-77)
x = 67 - 77
x = -10
x = -10 is your answer.
~
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Check to see if the given number is a solution to the given equation. -5(x-5)+1=4(x-1)+75;x=-5
Answer: not sure
Step-by-step explanation: it would help me if you had a pic of the worksheet to help you with the problem
What is the arc length of an arc with radius 18 inches and central angle 22°? Round to nearest hundredth or leave in terms of π. Show your work.
We calculate the arc length to be 6.86 inches by rounding to the closest hundredth.
What is a Circle's Arc Length?The distance between two places in a curve's section is known as the arc length of a circle. Any portion of a circle's circumference is an arc. The angle formed by the two line segments joining a point to an arc's endpoints at any given position is known as the arc's angle.
An arc with a radius of 18 inches and a centre angle of 22° can be calculated using the formula below:
Arc length = (central angle / 360°) × (2πr)
where r denotes the circle's radius.
Substituting the given values, we get:
Arc length = (22° / 360°) × (2π × 18 inches)
Arc length = (0.0611) × (2π × 18 inches)
Arc length ≈ 6.86 inches
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Help, I need help please
Answer:
Step-by-step explanation:
2534 i think
Why is a data point with an x-coordinate of 0 a good point to use when creating a trend line for a data set? Select all that apply.
A. It is easy to compute the slope using this point.
B. The y-coordinate of this point is the y-intercept.
C. The y-coordinate of this point is always positive.
D. The coordinates of this point are both 0
This point does not always have a positive y-coordinate, it is still a useful point in creating a trend line.
A. It is easy to compute the slope using this point.
B. The y-coordinate of this point is the y-intercept.
A data point with an x-coordinate of 0 is a good point to use when creating a trend line for a data set because it is easy to compute the slope using this point. The y-coordinate of this point is also the y-intercept, which is the point at which the line crosses the y-axis. Additionally, the coordinates of this point are both 0, making it easy to locate on a graph. While this point does not always have a positive y-coordinate, it is still a useful point in creating a trend line.
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what is the answer to this
Answer:
[tex]\huge\boxed{\sf 10(9n + 8m)}[/tex]
Step-by-step explanation:
Given expression:= 90n + 80 m
Common factor = 10
So, the expression becomes:
= 10(9n + 8m)[tex]\rule[225]{225}{2}[/tex]
Answer: C
Step-by-step explanation: If you factor 10 out of 90n and 80m then you get 9n and 8m for each. to make the equation you get: 10(9n+8n)
Reasoning The measure of ∠1 is 39°. Find the measure of the angle adjacent to ∠1. The figure is not drawn to scale. Use pencil and paper. Explain how you know your answer is reasonable
Assuming that ∠1 and its adjacent angle form a straight line, we know that the sum of the angles on a straight line is 180°. Therefore, the measure of the adjacent angle is 180° - 39° = 141°.
we can also look at the other angles in the figure. From the diagram, we can see that ∠2 and ∠3 are acute angles, which means they are less than 90°. Additionally, we know that the sum of the angles in a triangle is 180°, so ∠2 + ∠3 + ∠4 = 180°.
Since ∠2 and ∠3 are acute, their sum must be less than 180°. Therefore, ∠4 must be an obtuse angle (greater than 90°) in order for the sum to be 180°. This makes sense, as an obtuse angle is required to form a triangle with two acute angles.
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Remember that the sine of an angle is the opposite over the hypotenuse.
Answer:
1.)
[tex]R = 8/17\\S = 15/17[/tex]
2.)
[tex]R = 5/13[/tex]
[tex]S=12/13[/tex]
Step-by-step explanation: sin represents the ratio between a side opposite to an angle and the hypotenuse. It is important to learn these ratios as they allow for you to solve for side lengths in a triangle and angles. We were in this case finding the ratios. A lowercase letter represents a side length opposite to the angle. So to find R we would just need to divide r by t. In the first example, it would just be 16/34 which simplifies to 8/17. Do the same thing for s, and it would be for 30/34 which simplifies to 15/17. Repeat the same steps and you should get 5/13 for R and 12/13 for S.
Lin needs to mix a specific shade of orange paint for the set of the school play. The color uses 3 parts yellow for every 2 parts red.
Complete the table to show different combinations of red and yellow paint that will make the shade of orange Lin needs
Combination of red and yellow paint that follows the ratio of 3 parts yellow for every 2 parts red will make the shade of orange Lin needs.
Red Yellow
2 3
4 6
6 9
8 12
The formula for this specific shade of orange paint is 3 parts yellow for every 2 parts red. To calculate the amounts of red and yellow paint that can be used for different combinations we can use the following equation:
Yellow = 2 x Red/3
For the first combination of 2 parts red and 3 parts yellow, the equation can be written as:
Yellow = (2 x 2)/3
Simplified, that is 2/3, or 3 parts yellow.
For the second combination of 4 parts red and 6 parts yellow, the equation can be written as:
Yellow = (2 x 4)/3
Simplified, that is 4/3, or 6 parts yellow.
For the third combination of 6 parts red and 9 parts yellow, the equation can be written as:
Yellow = (2 x 6)/3
Simplified, that is 8/3, or 9 parts yellow.
For the fourth combination of 8 parts red and 12 parts yellow, the equation can be written as:
Yellow = (2 x 8)/3
Simplified, that is 16/3, or 12 parts yellow.
Therefore, any combination of red and yellow paint that follows the ratio of 3 parts yellow for every 2 parts red will make the shade of orange Lin needs.
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Two balanced and fair dice are rolled. One is six-sided and the other is eight-sided. What is the probability of rolling a sum greater than 12 or a sum that is an odd number? Submit the answer as a simplified fraction. Use the forward slash (/) to separate the numerator from the denominator without spaces before or after. For example, three-fourths should be submitted as
5/6
The probability of rolling a sum greater than 12 or a sum that is an odd number after rolling two balanced and fair dice is 47/96.What is the probability of rolling a sum greater than 12 or a sum that is an odd number?The given information says that there are two balanced and fair dice. One is a six-sided die, and the other is an eight-sided die. We need to find the probability of rolling a sum greater than 12 or a sum that is an odd number after rolling the two dice.It's necessary to know the possible outcomes of the dice game when two dice are rolled. The 6-sided die has possible outcomes {1,2,3,4,5,6}, and the 8-sided die has possible outcomes {1,2,3,4,5,6,7,8}.The possible outcomes for each sum from 2 to 14 are shown below in the following table:The sum of the faces is odd if only one of the dice has an even number. In contrast, the sum of the faces is even if both dice have an even number. The red color represents the sum of the faces, which is an odd number, while the blue color represents the sum of the faces, which is an even number. Now we can easily calculate the total number of sums that are either greater than 12 or an odd number. It is important to note that the sum of 2 and 4 is even, and the sum of 13 and 14 is greater than 12. So the total number of sums that are either greater than 12 or an odd number is: 1 + 4 + 1 + 6 + 8 + 8 + 6 + 1 + 4 + 1 = 40It's also necessary to calculate the total number of possible outcomes when rolling two dice. The number of possible outcomes when rolling two dice is 6 x 8 = 48.We now have everything we need to find the probability of rolling a sum greater than 12 or a sum that is an odd number:Probability = Number of favorable outcomes / Total number of possible outcomes= 40/48 = 5/6Therefore, the probability of rolling a sum greater than 12 or a sum that is an odd number is 5/6.
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A ball is dropped from a height of 10 ft. Assuming that on each bounce, the ball rebounds to one-fifth of its previous height, find the total distance traveled by the ball.
Answer: The ball is dropped from a height of 10 ft, so it first travels down 10 ft until it hits the ground. The distance traveled in this first part is 10 ft.
On the first bounce, the ball rebounds to one-fifth of its previous height, which is 2 ft (since 10/5 = 2). The ball then travels up 2 ft and back down 2 ft to the ground, for a total distance traveled of 10 + 2 + 2 = 14 ft.
On the second bounce, the ball rebounds to one-fifth of its previous height, which is 2/5 ft (since 2/5 x 2 = 4/5). The ball then travels up 4/5 ft and back down 4/5 ft to the ground, for a total distance traveled of 2/5 + 4/5 + 4/5 = 2 ft.
On the third bounce, the ball rebounds to one-fifth of its previous height, which is 4/25 ft (since 4/25 x 2/5 = 8/125). The ball then travels up 8/125 ft and back down 8/125 ft to the ground, for a total distance traveled of 4/25 + 8/125 + 8/125 = 0.32 ft (rounded to two decimal places).
The ball will continue to bounce, getting closer and closer to the ground with each bounce. We can calculate the total distance traveled by summing the distances traveled on each bounce:
10 + 14 + 2 + 0.32 + ...
To calculate the sum of this infinite series, we can use the formula for the sum of an infinite geometric series:
S = a / (1 - r)
where S is the sum, a is the first term, and r is the common ratio.
In this case, a = 10 (the distance traveled on the first drop), and r = 1/5 (the fraction by which the height decreases on each bounce). Plugging in these values, we get:
S = 10 / (1 - 1/5)
= 12.5
So the total distance traveled by the ball is 12.5 ft.
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