The probability that Burt allowed a total of 2 or more walks and hits in one inning is approximately 0.363 or 36.3%.
To solve this problem, we can use the Poisson distribution, which is commonly used to model the number of events occurring in a fixed amount of time or space. In this case, we can use it to model the number of hits and walks allowed by Burt in a randomly selected inning.
Let λ be the expected number of hits and walks allowed by Burt in one inning. We can find λ using the given whip:
whip = (walks + hits) / innings pitched
1.271 = (walks + hits) / 1
walks + hits = 1.271
So, λ = 1.271.
Now, we want to find the probability that Burt allowed a total of 2 or more walks and hits in one inning. Let X be the number of hits and walks allowed by Burt in one inning. Then, we want to find P(X ≥ 2).
Using the Poisson distribution, we have:
P(X ≥ 2) = 1 - P(X < 2) = 1 - P(X = 0) - P(X = 1)
where
P(X = k) = (e^(-λ) × λ^k) / k!
So, we need to calculate P(X = 0) and P(X = 1):
P(X = 0) = (e^(-λ) × λ⁰) / 0! = e⁽⁻¹.²⁷¹⁾ = 0.280
P(X = 1) = (e^(-λ) × λ¹) / 1! = e⁽⁻¹.²⁷¹⁾ 1.271 = 0.357
Therefore,
P(X ≥ 2) = 1 - P(X < 2) = 1 - (P(X = 0) + P(X = 1)) = 0.363
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9. You and two friends went to the store. You each bought
a bag of chips and drink for $5.75. How much will you pay
total with 6% tax?
A. $6.10
B. $12.19
C. $18.29
D. $24.40
Answer:
The answer rounded is 6.10, but the actual answer would be 6.095
Step-by-step explanation:
5.75 X 0.06 = 0.345 || 0.345+5.75 = 6.095
A 6.10
According to the laws of stuff a calculate of 5.75 to the percentage of 6 is 6.10
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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Help, I need help please
Answer:
Step-by-step explanation:
2534 i think
Solve the inequality x+2<5. Then graph the solutions. Question content area bottom Part 1 What are the solutions? Select the correct choice below and fill in the answer box to complete your choice.
The solution to the inequality expression given as x + 2 < 5 is x < 3
How to determine the solution to the inequalityInequality expressions refer to statements in mathematics that use symbols like <, >, ≤, or ≥ to compare two values.
From the question, we have the following parameters that can be used in our computation:
x + 2 < 5
Subtract 2 from both sides of the inequality expression
So, we have the expression below
x + 2 < 5 - 2
Evalaute the like terms
x < 3
This means that, the solution is x < 3
The graph of the inequality is added as an attachment
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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%.
The area of the parallelogram below is
2m
8m
6m
square meters.
Answer:
Below
Step-by-step explanation:
Area of a parallelogram is given by: base * height
base = 6 m height = 8 m
area = 6* 8 = 48 m^2
kate is remodeling her kitchen. she goes shopping for a refrigerator. the model price is $405, and the estimated energy cost per year is $36. if the model has an estimated lifetime of 10 years, what is the lifetime cost of the model? answer to integer without a unit.
The lifetime cost of the model is $765.
Kate is re-modelling her kitchen.
She is going shopping for a refrigerator.
The model price is $405, and the estimated energy cost per year is $36.
If the model has an estimated lifetime of 10 years,
Lifetime cost of the model:
The lifetime cost of the model is $765
Explanation: Given, The model price is $405
Estimated energy cost per year is $36.
The model has an estimated lifetime of 10 years.
Lifetime cost of the model can be calculated as follows:
Total lifetime cost = Initial cost + (Estimated energy cost per year × Estimated lifetime)
Initial cost = $405
Estimated energy cost per year = $36
Estimated lifetime = 10 years
Total lifetime cost = $405 + ($36 × 10)
Total lifetime cost = $405 + $360
Total lifetime cost = $765
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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.
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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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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A water bottle that holds 24 1/4 ounces of water is 3/5 full. Is there enough water in the bottle to fill three glasses with 5 ounces each? Explain your answer.
Therefore , the solution of the given problem of unitary method comes out to be the quantity of water in the bottle (14 11/20 ounces) is less than the amount required to fill three glasses (15 ounces).
Define unitary method.By applying what was acquired and bringing this variable tactic into practise, along with all supporting information from two people who used a particular tactic, the work can be finished. In other words, if the wanted expression result occurs, either the entity specified in the formula will also be discovered, or both crucial processes will actually ignore the colour. A refundable fee of Rupees ($1.01) may be necessary for forty pencils.
Here,
The water bottle is currently 3/5 full and contains 24 1/4 ounces of water.
By dividing the bottle's capacity by the percentage that indicates how filled it is, we can determine how much water is inside:
=> 24 1/4 × 3/5 = (97/4) × (3/5)
=> 291/20 = 14 11/20
Therefore, there are 14 11/20 ounces of water in the water container.
We want to fill three cups, each of which needs five ounces of water, so we will need:
=> 5 x 3 = 15 ounces
There isn't enough water in the bottle to fill three glasses with 5 ounces each because the quantity of water in the bottle (14 11/20 ounces) is less than the amount required to fill three glasses (15 ounces).
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what is the simplest form of this radical expression? 3√2a−6√2a please show ur work
The simplest form of the given radical expression as required to be determined is; -3³√2a.
What is the simplified form of the expression?As evident form the task content; the given expression whose simplified form is to be determined is;
3 ³√2a - 6 ³√2a
Since; 3³√2a is common to both terms of the expression; Hence, by factorisation; we have;
3³√2a (1 - 2)
= 3³√2a • -1
= -3³√2a
Ultimately, the simplified form of the radical expression is; -3³√2a.
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Mishka is on a long road trip, and she averages 75 mph for 3 hours while she's driving on the highway. While she's driving on side roads for 1 hour, she only averages 40 mph. What is the total distance that she covers on her road trip?
The total distance that Mishka covers on the trip is 265 miles.
What is the total distance covered?Speed measures how fast an object is moving with respect to time. Speed is the ratio of total distance to total time.
Speed = distance / time
Distance = speed x time
Distance covered while driving on the highway = 75 x 3 = 225 miles
Distance covered while driving on the side road = 40 x 1 = 40 miles
Total distance covered = 225 miles + 40 miles = 265 miles
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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
A piling for a high-rise building is pushed by two bulldozers at exactly the same time. One bulldozer exerts a force of 1850 pounds in a westerly direction. The other bulldozer pushes the piling with a force of 3250 pounds in a northerly direction. What is the direction of the resulting force upon the piling, to the nearest degree?
I need some help with this yall
The direction of the resulting force upon the piling is approximately 298.85 degrees
We can use vector addition to find the direction of the resulting force. Let's call the force exerted by the first bulldozer F1, and the force exerted by the second bulldozer F2. We can represent each force as a vector with a magnitude and direction.
F1 has a magnitude of 1850 pounds and points in a westerly direction. We can represent it as a vector (-1850, 0).
F2 has a magnitude of 3250 pounds and points in a northerly direction. We can represent it as a vector (0, 3250).
To find the resulting force, we need to add these two vectors. We can do this by adding the x-components and the y-components separately.
The x-component of the resulting force is -1850 (from F1) plus 0 (from F2), which is -1850.
The y-component of the resulting force is 0 (from F1) plus 3250 (from F2), which is 3250.
So the resulting force is a vector with components (-1850, 3250). We can find the direction of this vector by taking the inverse tangent of the ratio of the y-component to the x-component.
tan(theta) = (3250) / (-1850)
theta = -61.15 degrees
The negative sign indicates that the resulting force points to the southwest. To get the angle in the range of 0 to 360 degrees, we can add 360 degrees to the angle if it is negative.
theta = 360 - 61.15
theta = 298.85 degrees
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Please answer these questions and show working
Case 1: The value of the vector B is equal to [tex]\overrightarrow {B} = (7, - 20)[/tex].
Case 2: The values of variables m and n from vector operations are - 5 and - 4, respectively.
How to deal operation between vectors
In this problem we find two cases of operations between two vectors. According to linear algebra, there are two fundamental operations:
Vectorial additionVectorial scalar multiplication.Case 1:
The value if vector B can be found by following operation:
[tex]\overrightarrow{B} - \overrightarrow {A} = (5, - 5)[/tex]
[tex]\overrightarrow {B} = \overrightarrow {A} + (5, - 5)[/tex]
[tex]\overrightarrow{B} = (2, - 4) + (5, - 5)[/tex]
[tex]\overrightarrow{B} = (2 + 5, - 4 - 5)[/tex]
[tex]\overrightarrow {B} = (7, - 20)[/tex]
Case 2:
First, determine the expression for the given operator:
2 · a - 2 · b = 2 · (- 3, m) - 2 · (n, - 4)
2 · a - 2 · b = (- 6, 2 · m) + (- 2 · n, 8)
2 · a - 2 · b = (- 6 - 2 · n, 2 · m + 8)
Second, find the values of m and n:
(- 6 - 2 · n, 2 · m + 8) = (2, - 2)
- 6 - 2 · n = 2
- 3 - n = 1
n = - 4
2 · m + 8 = - 2
- m - 4 = 1
m = - 5
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a. Select the probability density function. b. What is the probability of generating a random number between 0.25 and 0.85 (to 1 decimal place)? c. What is the probability of generating a random number with a value less than or equal to 0.4 (to 1 decimal place)? d. What is the probability of generating a random number with a value greater than 0.6 (to 1 decimal place)? e. Using 50 random numbers given below, compute the mean and standard deviation. Mean = (to 6 decimals) Standard deviation = (to 6 decimals)
The probability density function (PDF) is a mathematical function that describes the probability of a random variable taking a certain value. It is a measure of the probability of a given outcome within a given range.
What is Probability?Probability is a branch of mathematics used to quantify the likelihood of an event occurring. It is used to calculate the chances of a certain outcome or a combination of outcomes in a given situation. Probability is expressed as a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. Probability is used to make predictions, analyze data, and understand the complexity of the world around us.
b. The probability of generating a random number between 0.25 and 0.85 (to 1 decimal place) is 0.6.
c. The probability of generating a random number with a value less than or equal to 0.4 (to 1 decimal place) is 0.4.
d. The probability of generating a random number with a value greater than 0.6 (to 1 decimal place) is 0.4.
e. The mean of the given set of 50 random numbers is 0.527084 and the standard deviation is 0.307766.
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A mathematical function known as the probability density function (PDF) calculates the likelihood that a random variable will have a particular value. It is a measurement of the likelihood of a specific outcome within a specific range.
What is probability?
Mathematics' branch of probability is used to determine how likely an event is to occur. It is employed to determine the probabilities of a specific outcome or a mixture of outcomes in a particular circumstance. A number between 0 and 1 is used to represent probability, with 1 denoting a certain event and 0 denoting an impossibility. To generate predictions, examine data, and comprehend how complicated the world is around us, probability is used.
b. The probability of generating a random number between 0.25 and 0.85 (to 1 decimal place) is 0.6.
c. The probability of generating a random number with a value less than or equal to 0.4 (to 1 decimal place) is 0.4.
d. The probability of generating a random number with a value greater than 0.6 (to 1 decimal place) is 0.4.
e. The mean of the given set of 50 random numbers is 0.527084 and the standard deviation is 0.307766.
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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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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?
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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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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Can someone please help me with this ASAP? Show work!
The experimental probability of not selecting a peppermint candy is 77.78%, so the correct option is the third one.
How to find the probability?We want to find the experimental probability of selecting a candy that is not peppermint.
To get this, we need to get the difference between 1 and the probability of getting a peppermint candy, then we will get:
p = 1 - 2/9
p = 7/9
Now we want to express this as a percentage, so we need to multiply this by 100%
p = (7/9)*100%
p = 77.78%
We can see that the experimental probability is the one in the third option.
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Janella's basis in her partnership interest was $120,000, including her $150,000 share of partnership debt. At
the end of the current year, the partnership pays off its debts and liquidates. Janella receives a proportionate
liquidating distribution consisting of $42,000 cash and inventory valued at $24,000 (adjusted basis to the
partnership = $20,000). How much gain or loss does Janella recognize, and what is her basis in the distributed
property?
Janella recognizes a gain of $36,000 and her basis in the distributed property is $54,000.
Janella's basis in her partnership interest is $120,000, which includes her share of partnership debt. When the partnership pays off its debts and liquidates, Janella receives a proportionate liquidating distribution consisting of $42,000 cash and inventory valued at $24,000 (adjusted basis to the partnership = $20,000).
To calculate Janella's recognized gain or loss, we need to compare her basis in the partnership interest to the fair market value of the distributed assets.
The fair market value of the distributed assets is $42,000 (cash) + $24,000 (inventory) = $66,000.
The amount of the loss is the excess of her basis over the fair market value of the distributed assets, which is $120,000 - $66,000 = $54,000.
To determine Janella's basis in the distributed property, we need to adjust her basis in the partnership interest by the amount of the liquidating distribution she received.
Janella received a total liquidating distribution of $42,000 cash + $24,000 inventory = $66,000. Her share of partnership debt was $150,000, and the partnership paid off all its debts, so she no longer has any debt basis.
Janella's distribution of $66,000 exceeds her adjusted basis of $30,000 by $36,000. She recognizes a gain of $36,000. Therefore, Janella's new basis in the distributed property is $120,000 - $66,000 (liquidating distribution) = $54,000.
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The ability to determine the age of some individuals can be difficult if there are not quality government records of birth.
Bone growth takes place at the growth plates at the end of long bones. Once all growth plates fuse, growth stops, and
an individual is considered a biological adult. The age at which growth plates fuse for males is approximately normally
distributed with a mean of 19.1 years and a standard deviation of 16.1 months. Complete parts (a) through (d).
The probability a male's growth plate will fuse before age 17 is 0.1112, for this we have to learn probability.
What is Probability?Probability of an event is a number that shows what is the possibility of an event occur.
we have to take entire area under the standardized curve from and including the left tail up to the z-score for 17.
[tex]= \frac{(17 - 18.6 years)}{1.308333 years}[/tex]
[tex]= \frac{(-1.6) }{1.308333}[/tex]
[tex]= -1.22293[/tex]
[tex]= approx. 1.22.[/tex]
The area from the mean to +ve or -ve 1.22 is .3888
We have to subtract .3888 from area from the tail to the mean (.5000) to get area from the tail to 1.22.
So, the growth plates will fuse before age 17 [tex]= .5000-.3888 = 0.1112[/tex]
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I NEED HELP ON THIS ASAP!!
The constraints as a system of linear inequalities include the following;
x + y ≤ 180
x ≥ 40
y ≥ 40
3x + 4y ≤ 640
75x + 60y ≤ 12,900
The solution set for the system of linear inequalities is shown in the coordinate plane below.
How to write the required system of linear inequalities?In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of SOS Smartcall produced in one day and number of SOS Basic produced in one day respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the SOS Smartcall produced in one day.Let the variable y represent the number of SOS Basic produced in one day.Based on the information provided about this cell phone company, the constraints can be written as a system of linear inequalities as follows;
x + y ≤ 180
x ≥ 40
y ≥ 40
3x + 4y ≤ 640.
75x + 60y ≤ 12,900
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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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Draw a number line to show that 2/8 and 1/4 are equivalent fraction and make sure to DRAW it!
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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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? 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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