Answers
As a result, we are unable to determine the age of a child who is 133 cm tall using the regression equation.
what is linear regression?A statistical technique called linear regression is used to represent the connection between two variables, where one of the variables is the dependent variable and the other is the independent variable. Finding the best-fit line that depicts the connection between the two variables is the objective of linear regression. This enables us to make predictions or estimate values based on the known data.
given
These numbers allow us to determine a and b:
a = 0.997 (9.285 / 1.547) ≈ 5.977
b = 128.2 - 5.977 (8.02) ≈ 81.704
The regression equation is therefore y = 5.977 x + 81.704.
(ii) Based on the calculations made above, the Pearson's product-moment correlation coefficient, or r, has a value of roughly 0.997.
(b) We enter x = 9 into the regression equation to calculate an approximation of the height of a 9-year-old child:
As a result, we calculate that a 9-year-old kid will be roughly 134.6 cm tall.
We must resolve the regression equation for x in order to determine the age of a kid who measures 133 cm in height.
x = (y - b) / a
This calculation, though, would result in an illogically negative age. As a result, we are unable to determine the age of a child who is 133 cm tall using the regression equation.
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The complete question is:-
The following table shows the mean height, y cm, of primary school children who are age x years old.
Age, x years Mean Height, y cm
6.25 7.35 8.5 9.25 10.75
115 121 129 136 140
The relationship between x and y can be modelled by the regression line of y on x with equation y = ax + b.
(a) (i) Find the value of a and the value of b.
(ii) Write down the value of Pearson's product-moment correlation coefficient, r.
(b) Use your regression equation from part (a)(i) to estimate the height of a child aged 9 years old.
(c) Explain why it is not appropriate to use the regression equation to estimate the age of a child who is 133 cm tall.
Related Questions
if a fair die is rolled 5 times, what is the probability, rounded to the nearest thousandth, of getting at least 2 fours?
Answers
So the probability, rounded to the nearest thousandth, of getting at least 2 fours in 5 rolls of a fair die is 0.194.
What is the simple definition of probability?A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
According to the given information:The probability of getting at least 2 fours is the sum of the probabilities of getting exactly 2, 3, 4, or 5 fours:
P(X ≥ 2) = P(X=2) + P(X=3) + P(X=4) + P(X=5)
Using the binomial formula, we can calculate each of these probabilities:
P(X=k) = (n choose k) p^k (1-p)^(n-k)
where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from n distinct items.
P(X=2) = (5 choose 2) (1/6)² (5/6)³ = 0.1608
P(X=3) = (5 choose 3) (1/6)³ (5/6)² = 0.0322
P(X=4) = (5 choose 4) (1/6)⁴ (5/6)¹ = 0.0013
P(X=5) = (5 choose 5) (1/6)⁵ (5/6)⁰ = 0.00003
Therefore,
P(X ≥ 2) = 0.1608 + 0.0322 + 0.0013 + 0.00003 = 0.1943
So the probability, rounded to the nearest thousandth, of getting at least 2 fours in 5 rolls of a fair die is 0.194.
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Providing free access to a variety of stimuli for the purposes of identifying potential reinforcers is best described by which of the following?
Free Operant Preference Assessment
Answers
Providing free access to a variety of stimuli for the purposes of identifying potential reinforcers is best described by Free Operant Preference Assessment.
What is a free operant preference assessment? Free operant preference assessment refers to a behavior analysis process used to determine the preferred stimulus of an individual in a naturalistic environment. This method measures the potential and meaningful reinforcers through the observation of a child's free time. A reinforcement is a consequence that strengthens a behavior.The free operant preference assessment is frequently utilized in the autism field to identify reinforcing stimuli. It is a process of assessing a child's preferred items and actions in a naturalistic setting.The free operant preference assessment is conducted in three different stages: Stage 1: involves observation of preferred items and items that are likely to become potential reinforcers, Stage 2: involves assessing for a hierarchy of items and stage 3 involves using the data gathered to plan the student’s schedule, including reinforcement and non-contingent time periods.
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FREE OPERANT PREFERENCE ASSESSMENT. Providing free access to a variety of stimuli for the purposes of identifying potential reinforcers is best described by Free Operant Preference Assessment.
A free operant preference assessment is a measure of the attractiveness or preference for various stimuli by measuring an individual's time spent with them.
Free access to different stimuli is given to the individual to determine their preferences, which are subsequently used to reinforce the desired behavior or work on behavior modification through behavior analysis.
The steps to conducting a Free Operant Preference Assessment: Prepare the list of stimuli: Initially, you have to prepare a list of stimuli that you believe may act as a reinforcer for the individual, which may include toys, foods, or other things that the person likes.
Prepare the environment: Arrange the stimuli in a room, and let the individual enter it.
Make sure that there is sufficient space to move around and that the person has free access to all of the stimuli.
Record the time the individual spends with each stimulus. You can observe the person, either directly or through video recording.
Based on the data obtained, the most preferred and least preferred stimuli can be identified. Then, these preferred stimuli can be used as potential reinforcers.
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in a large population, 71% of the people have been vaccinated. if 5 people are randomly selected, what is the probability that at least one of them has been vaccinated? round your answer to three decimal places.
Answers
In a large population, 71% of the people have been vaccinated. if 5 people are randomly selected, 0.997 is the probability that at least one of them has been vaccinated.
To compute the probability that at least one of five people selected at random from a large population has been vaccinated if 71% of the population has been vaccinated.
We need to use the Complement Rule.
This rule tells us that the probability of event A not happening is equal to one minus the probability of event A happening.
P (A) + P (A') = 1
where P(A) is the probability of A happening and P(A') is the probability of A not happening.
We need to compute the probability that none of the five people selected at random have been vaccinated.
Then, we will use the Complement Rule to compute the probability that at least one of them has been vaccinated.
The probability that the first person selected has not been vaccinated is:
P(first person not vaccinated) = 1 - 0.71 = 0.29
The probability that the second person selected has not been vaccinated is:
P(second person not vaccinated) = 1 - 0.71 = 0.29
The probability that the third person selected has not been vaccinated is:
P(third person not vaccinated) = 1 - 0.71 = 0.29
The probability that the fourth person selected has not been vaccinated is:
P(fourth person not vaccinated) = 1 - 0.71 = 0.29
The probability that the fifth person selected has not been vaccinated is:
P(fifth person not vaccinated) = 1 - 0.71 = 0.29
We assume that the selections are made randomly and independently of one another.
Thus, we can multiply the probabilities to get the probability that none of the five people selected have been vaccinated:
P(none vaccinated) = 0.29 × 0.29 × 0.29 × 0.29 × 0.29 = 0.0028
We can use the Complement Rule to compute the probability that at least one of the five people selected has been vaccinated:
P(at least one vaccinated) = 1 - P(none vaccinated)P(at least one vaccinated)
= 1 - 0.0028P(at least one vaccinated)
= 0.9972
Thus, the probability that at least one of five people selected at random from a large population has been vaccinated is approximately 0.997 when rounded to three decimal places.
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how many five-card hands from a normal deck of cards contain exactly two aces and have exactly two red cards.
Answers
There are 816 possible five-card hands from a normal deck of cards containing exactly two aces and having exactly two red cards.
There are 80 possible five-card hands from a standard deck of 52 cards that contain exactly two aces and have exactly two red cards.
To calculate this, first count the total number of combinations of two aces from the four aces in the deck. This can be done using the combination formula C(n, r) where n is the number of items (4 aces) and r is the number of items to choose (2 aces). Therefore, the number of combinations of two aces is C(4,2) = 6.
Next, count the number of combinations of two red cards. There are 26 red cards in a deck, which can be divided into the two suits of spades and hearts. For each of these suits, calculate the number of combinations of two cards using the same formula as before, C(n, r). Therefore, the number of combinations of two red cards is C(13,2) * 2 = 156.
Finally, multiply the two values together to get the total number of possible five-card hands with exactly two aces and two red cards. This equals 6 * 156 = 960. This value must be reduced by the number of hands that contain more than two aces and/or more than two red cards. This value can be calculated using the same formula. For instance, the number of hands with three aces is C(4,3) * C(13,2) * 2 = 144. This value must be subtracted from 960, leaving a total of 960 - 144 = 816.
Therefore, there are 816 possible five-card hands from a normal deck of cards containing exactly two aces and having exactly two red cards.
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a population has a mean of 50 and a standard deviation of 10. if a random sample of 64 is taken, what is the probability that the sample mean is greater than 52?
Answers
The probability that the sample mean is greater than 52 is 5.5%.
Given population mean (μ) = 50 and standard deviation (σ) = 10Sample size (n) = 64 Sample mean (X-bar) = 52The formula for finding the probability of a sample mean is greater than a given value is:
P ( X-bar > 52 ) = P ( z > (52-50) / (10/√64) ) = P ( z > 1.6 )The formula for finding the probability of z-score is:
P ( z > 1.6 ) = 1 - P ( z < 1.6 )Now, we need to find the value of P ( z < 1.6 ) from the standard normal distribution table.P ( z < 1.6 ) = 0.9452 (approx)Now, substitute this value in the above equation, we get:
P ( z > 1.6 ) = 1 - 0.9452 = 0.0548 .Therefore, the probability that the sample mean is greater than 52 is 0.0548 or approximately 5.5%.
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true or false: if event a is tina is the first woman to finish the 2020 boston marathon and event b is tina is the first woman to finish the 2021 new york marathon, event a and event b are independent.
Answers
It is true that the events a and b, relating to Tina being the first woman to finish the 2020 Boston Marathon and the 2021 New York Marathon, are independent.
What are independent events?Independent events are events where the occurrence or non-occurrence of one event does not affect the probability of the occurrence or non-occurrence of the other event. In other words, the outcome of one event has no impact on the outcome of the other event.
In the context of this problem, the outcome of one marathon has no bearing on the outcome of another marathon, hence it is true that the events a and b are independent.
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Order the angles from greatest to least.
Answers
Answer:
∠D, ∠C, ∠E
Step-by-step explanation:
"The angle opposite to the shortest side is the smallest angle and the side opposite to the longest side is the largest angle."
Really appreciated :)))) (25 points) Reupload
Answers
find the vertex and x-intercept(s) for the quadratic function f(x)=4.9x^2-28x+40
Answers
Answer:
To find the vertex and x-intercepts for the quadratic function f(x)=4.9x^2-28x+40:
First, we can find the x-coordinate of the vertex using the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic function.
In this case, a = 4.9 and b = -28, so:
x = -(-28)/2(4.9) = 2.86
Next, we can find the y-coordinate of the vertex by plugging in this x value into the original function:
f(2.86) = 4.9(2.86)^2 - 28(2.86) + 40 = 6.65
So the vertex is at (2.86, 6.65).
To find the x-intercepts, we can set the function equal to zero and solve for x:
4.9x^2 - 28x + 40 = 0
We can use the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
Plugging in the coefficients, we get:
x = (28 ± sqrt(28^2 - 4(4.9)(40))) / 2(4.9)
Simplifying:
x = (28 ± sqrt(144.4)) / 9.8
x = 5.36 or 1.43
So the x-intercepts are (5.36, 0) and (1.43, 0).
suppose you are on the sandy river 20 river miles from mount hood. if a lahar originates on mount hood at 3 pm and travels down the sandy river at a 40 miles an hour when should you expect it to arrive at your location?
Answers
We should expect the lahar to arrive at your location at 3:30 pm if we travel down the sandy river at 40 miles an hour.
The given data is as follows:
Length of river = 20 miles
Time = 3 pm
Speed = 40 miles an hour
To calculate the time, we need to use the formula,
Time required = (distance/speed)
It is given that the distance between Mount Hood and your location is 20 river miles, and the speed of the lahar is 40 miles per hour. Therefore, the time it will take for the lahar to arrive is calculated as:
Time required = distance/speed
Time required = 20 miles / 40 miles per hour
Time required = 0.5 hours = 30 min
to determine the expected arrival time at your location,
Total time required = 3.00 + 0.30 = 3.30 pm.
Therefore we can conclude that we should expect the lahar to arrive at your location at 3:30 pm.
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assuming that the population from which you select your sample is not normal, which of the statements about m are true? check all that apply.
Answers
1. m may be higher or lower than the population mean.
2. The value of m is not necessarily representative of the population mean.
3. The sampling distribution of m is not necessarily normal.
4. The mean, median, and mode of the sample may all be different.
Assuming that the population from which you select your sample is not normal, the following statements about m (the mean of the sample) are true:
1. m may be higher or lower than the population mean.
2. The value of m is not necessarily representative of the population mean.
3. The sampling distribution of m is not necessarily normal.
4. The mean, median, and mode of the sample may all be different.
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When a population is not normal, it means that the distribution of the data is not symmetric and has non-uniform spread.
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i thought of a number. 4 times my number increased by 30 equals 70 decreased by the number. what is my number
Answers
The 4 is the number the student thought about.
To solve this problem, we will use algebraic expressions. First, let us define the unknown number, x. The problem states that "4 times my number increased by 30 equals 70 decreased by the number." This can be translated into the following equation:
4x + 30 = 70 - x
To solve for x, we need to isolate it on one side of the equation. Let's start by moving all the terms with x to the left side and all the constant terms to the right side.
4x + x = 70 - 30x + 4x + x = 40
Simplifying, we get:
10x = 40
Dividing both sides by 10:
x = 4
Therefore, the number that the student thought of is 4.
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Mai's water bottle had 24 ounces in it. After she drank x ounces of water, there were 10 ounces left. Select ALL the equations that represent this situation. * (a) 24 ÷ 10 = x (b) 24 + 10 = x (c) 24 − 10 = x (d) x + 10 = 24 (e) 10x = 24
Answers
Answer:
1 4/5
Step-by-step explanation:
the defect levels, as reported by motorola in their six sigma program, were higher than they expected from using a standard normal table for their capability calculations. why was this true? motorola found their processes followed the exponential distribution motorola allowed for failure in one tail only motorola had not allowed for a 1.5 sigma shift in the mean motorola found that six sigma efforts increased process variation
Answers
The defect levels reported by Motorola in their Six Sigma program were higher than expected because of the nature of their processes following an exponential distribution.
This means that Motorola only allowed for failure in one tail of the distribution, which increases the likelihood of failure and causes the defect levels to be higher than the standard normal table's capability calculations. Additionally, Motorola had not accounted for a 1.5 sigma shift in the mean, which also contributed to the higher defect levels. Through their Six Sigma efforts, Motorola found that their process variation had increased, which explains why their defect levels were higher than expected.
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caden is 208 miles away from rahquez. they are traveling towards each other. if rahquez travels 6 mph faster than caden and they meet after 8 hours, how fast was each traveling?
Answers
Caden's speed is 10 mph and Rahquez's speed is 16 mph faster, which is 16+6 = 32 mph
Let's use the formula: distance = rate x time
Since Caden and Rahquez are traveling towards each other, their combined distance will be 208 miles. Let's call Caden's speed "x" and Rahquez's speed "x+6", since Rahquez is traveling 6 mph faster than Caden.
Using the formula above, we can set up the equation:
208 = (x + x + 6) * 8
Simplifying, we get:
208 = (2x + 6) * 8
208 = 16x + 48
160 = 16x
x = 10
Therefore, Caden's speed is 10 mph and Rahquez's speed is 32 mph.
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Which formula would you use to calculate the total enclosed space of firm’s 3 structure?
Answers
To calculate the total enclosed space of a firm's 3 structures, you would need to measure the interior space of each structure and then add the three values together.
Why it is?
Assuming that each structure is a simple rectangular prism, the formula to calculate the volume (enclosed space) of a rectangular prism is:
Volume = Length x Width x Height
Therefore, to calculate the total enclosed space of the three structures, you would use the following formula:
Total Enclosed Space = Volume of Structure 1 + Volume of Structure 2 + Volume of Structure 3
where the volume of each structure would be calculated using the formula:
Volume of Structure = Length x Width x Height
Make sure to use the same unit of measurement for all three dimensions (length, width, and height) for each structure to ensure accurate calculations.
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Complete Question:
What formula would you use to calculate the total enclosed space of a firm's three structures? Please provide the necessary information such as the dimensions or measurements of each structure and the units used, if available, to accurately calculate the total enclosed space.
. If your savings account has a %4.50 APR and you have $100 saved, what is the How
much money will earn by the end of the year? What is the equation you will use to figure
this out?
Answers
The required amount of money earned on the savings account by the end of the year is $4.50.
How to find the interest amount?To calculate the amount of money earned on a savings account with a given Annual Percentage Rate (APR), we can use the formula:
Interest = Principal x Rate x Time
where:
Principal is the initial amount of money in the account
Rate is the annual interest rate (as a decimal)
Time is the length of time the money is invested (in years)
In this case, the principal is $100, the rate is 4.50% per year (or 0.045 as a decimal), and the time is one year. Therefore, the interest earned can be calculated as:
Interest = $100 x 0.045 x 1
Interest = $4.50
So, the amount of money earned on the savings account by the end of the year is $4.50.
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8 x 10^6 is how many times as large as 4 x 10^4
Answers
Answer:
200 times as large.
Step-by-step explanation:
To find out how many times 8 x 10^6 is as large as 4 x 10^4, we need to divide 8 x 10^6 by 4 x 10^4:
(8 x 10^6)/(4 x 10^4) = (8/4) x (10^6/10^4) = 2 x 10^2
Therefore, 8 x 10^6 is 200 times as large as 4 x 10^4.
Answer:
3x as large
Step-by-step explanation:
8 x 10^6 = 4800
4 x 10^4 = 1600
4800/3 = 1600
What is 7x2 – 4 + 6x3 – 4x – x4 in standard form?
A. –4 – 4x + 7x2 + 6x3 – x4
B. 4(–4 – x) + x2(7 + 6x – x2)
C. x4 + 6x3 + 7x2 – 4x – 4
D. –x4 + 6x3 + 7x2 – 4x – 4
Answers
The polynomial 7x² - 4 + 6x³ - 4x - x⁴ in standard form is - x⁴ + 6x³ + 7x² - 4x - 4
Expressing the polynomial in standard formGiven that
7x² - 4 + 6x³ - 4x - x⁴
The standard form of a polynomial is when the terms are arranged in decreasing order of degree
To rewrite 7x² - 4 + 6x³ - 4x - x⁴ in standard form, we need to rearrange the terms accordingly:
- x⁴ + 6x³ + 7x² - 4x - 4
Now the terms are in decreasing order of degree, with the highest degree term first
This is the standard form of the polynomial.
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Which of the following are prime factorizations of the number 100? Check all
that apply.
A. 5, 2, 2,5
B. 2, 5, 10
C. 5, 10, 2
D. 5, 2, 5, 2
Answers
Answer:
Step-by-step explanation:
A. 5, 2, 2, 5 is a prime factorization of 100 since 5 and 2 are prime factors of 100 and multiplying them gives 100.
B. 2, 5, 10 is not a prime factorization of 100 since 10 is not a prime factor of 100.
C. 5, 10, 2 is not a prime factorization of 100 since 10 is not a prime factor of 100.
D. 5, 2, 5, 2 is not a prime factorization of 100 since it can be simplified as 5x2x5x2 = 100, but it is not a unique prime factorization.
Therefore, the correct answer is A. 5, 2, 2, 5.
GIVING BRAINLIEST FOR RIGHT ANSWER (provide proof please i need to know how you got the answer)
Answers
Answer:
x > 3
Step-by-step explanation:
This is an open circle, meaning there will be no equal sign.
The line is going to the right of 3, meaning x > 3
So, our inequality is x > 3
true/false. the null hypothesis predicts there is a relationship between the variable and a significant difference between the groups.
Answers
The given statement " the null hypothesis predicts there is a relationship between the variable and a significant difference between the groups." is False because the null hypothesis predicts that there is no relationship between the variables and no significant difference between the groups.
A null hypothesis is a statement that suggests that no relationship exists between two variables. It serves as the baseline assumption and a starting point for researchers to test their alternative hypothesis.
Null hypothesis testing is a statistical method used to compare two mutually exclusive propositions: the null hypothesis and the alternative hypothesis.
In hypothesis testing, the null hypothesis states that there is no significant difference between two groups, while the alternative hypothesis suggests that there is a significant difference between the two groups.
If the observed data deviates significantly from what we would expect under the null hypothesis, we reject it in favor of the alternative hypothesis.
If the observed data does not significantly deviate from what we would expect under the null hypothesis, we fail to reject it.
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a jar contains 21 brown and 19 blue marbles. a marble is drawn at random. what is the theoretical probability of drawing a blue marble?
Answers
The theoretical probability of drawing a blue marble from a jar containing 21 brown and 19 blue marbles is 19/40, or 0.475.
To calculate this, divide the number of blue marbles by the total number of marbles in the jar. 19 divided by 40 equals 0.475, or 19/40. This means that there is a 47.5% chance of drawing a blue marble from the jar.
The probability of drawing a specific marble from the jar can be expressed using the formula P(A) = n(A)/n(T).
In this example, the probability P(A) is the chance of drawing a blue marble, n(A) is the number of blue marbles (19) and n(T) is the total number of marbles in the jar (40). Therefore, P(A) = 19/40 = 0.475.
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The present shown below is a cube.
Find the surface area of the present.
cm
20
cm
20
Answers
Answer:
2400 cm^2
Step-by-step explanation:
we first find the area of a face of the cube, which is a square, with the formula A=L^2, we multiply the result by the number of faces (6) and we have the surface area of the cube
everything is resolved with the expression:
20^2 x 6 = 2400 cm^2
4) There are 14 screws in a packet. Justin buys 5 packets of screws. He needs 68 screws. Has Justin bought enough screws?
Answers
Answer:
Yes, Justin bought enough
Step-by-step explanation:
if there are 14 screws in a packet and Justin buys 5, all we have to do is multiply 14 x 5
14 x 5 = 70
So Justin bought 2 extra
"A box contains 8 crayons: 3 red, 2 blue, 1 black, 1 green, and 1 yellow. Remove one crayon from the box at random and set it apart, then remove a second crayon from the box. Use the conditional probability equation to find P (the second crayon is blue and the first crayon is blue)
Answers
The probability that the second crayon drawn is blue and the first crayon drawn is blue is 1/28.
To solve this problem, we can use the conditional probability formula:
P(A and B) = P(B|A) * P(A)
where:
P(A and B) is the probability that both events A and B occur
P(B|A) is the probability of event B given that event A has already occurred
P(A) is the probability of event A occurring
In this case, we want to find the probability of selecting a blue crayon on the second draw given that the first crayon selected was blue. So we have:
P(the second crayon is blue and the first crayon is blue) = P(blue on the second draw | blue on the first draw) * P(blue on the first draw)
To find each of these probabilities, we can start by calculating the total number of possible outcomes:
Total number of outcomes = 8 crayons in the box
Next, we need to find the probability of selecting a blue crayon on the first draw:
P(blue on the first draw) = 2/8 = 1/4
After the first blue crayon has been set aside, there are only 7 crayons left in the box, so the probability of selecting a blue crayon on the second draw given that the first crayon was blue is:
P(blue on the second draw | blue on the first draw) = 1/7
Putting it all together:
P(the second crayon is blue and the first crayon is blue) = P(blue on the second draw | blue on the first draw) * P(blue on the first draw)
= (1/7) * (1/4)
= 1/28
Therefore, the probability that the second crayon drawn is blue and the first crayon drawn is blue is 1/28.
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PLEASE HELP ME!!
A beach ball has a volume of approximately 10,332 in³. Find the approximate radius of the beachball. Use 3.14 for π. Round your answer to the nearest tenth
Answers
Answer:
Step-by-step explanation:
Given diameter of a beach ball is d=10 inches.Let us find the radius of the beach ball:d=2 r10=2×rr=102∴r=5Therefore, the radius of a beach is 5 inches.Let us find the volume of air contained inside the beach ball:V=43 π×r3=43 π×53=43 π×125=500π3∴V=523.59877Therefore, the volume of air contained inside the beach ball is approximately 523.6 in3.
Answer:
The formula for the volume of a sphere is:
V = (4/3)πr³
We can rearrange this formula to solve for the radius (r):
r = [(3V) / (4π)]^(1/3)
where V is the volume of the sphere.
Substituting the given volume of the beach ball, we get:
r = [(3 × 10,332 in³) / (4 × 3.14)]^(1/3)
r = 10.27 in
Rounding to the nearest tenth, the approximate radius of the beach ball is 10.3 inches.
How does the value of a in the function affect its graph when compared to the graph of the quadratic parent function? g(x)=6x^2
Answers
Changing the value of "a" in the quadratic function affects the vertical stretch or compression and the direction of the opening of the parabola, compared to the graph of the quadratic parent function.
What is function?
A relationship or expression involving one or more variables
The function g(x) = 6x^2 is a quadratic parent function, which means it is the simplest form of a quadratic function.
When we change the value of "a" in the general form of a quadratic function:
f(x) = ax^2 + bx + c
we change the shape of the graph of the function. Specifically, changing the value of "a" stretches or compresses the graph vertically, and changes the direction of the opening of the parabola.
If "a" is positive, the parabola opens upwards, and if "a" is negative, the parabola opens downwards. The larger the absolute value of "a", the more stretched or compressed the parabola becomes.
In the case of g(x) = 6x^2, "a" is positive and equal to 6, which means the graph is stretched vertically by a factor of 6 compared to the parent function. The parabola opens upwards and is narrower than the parent function.
If we were to change the value of "a" to a different positive value, for example "a" = 3, the graph would still open upwards but would be less stretched than g(x) = 6x^2. On the other hand, if we were to make "a" negative, for example "a" = -6, the graph would open downwards, and be a reflection of the graph of g(x) = 6x^2 about the x-axis.
In summary, changing the value of "a" in the quadratic function affects the vertical stretch or compression and the direction of the opening of the parabola, compared to the graph of the quadratic parent function.
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2e - 1 ≤ 18
I need to solve the inequality and I need the work and the answer
Answers
Answer:
To solve the inequality 2e - 1 ≤ 18, we can add 1 to both sides of the inequality to isolate the term with e:
2e - 1 + 1 ≤ 18 + 1
Simplifying:
2e ≤ 19
Finally, we can divide both sides of the inequality by 2 to isolate e:
2e/2 ≤ 19/2
Simplifying:
e ≤ 19/2
Therefore, the solution to the inequality is e ≤ 9.5.
there are 204 students at lliswerry high
the teacher put 15 chairs on each roll in the school
how many complete rows of chairs must a teacher put so that all the student can sit and how many empty chairs will remain