The probability of both free throws is 0.7921, at least one free throw is 0.9889, missing both free throws is 0.0121. 58% of his free throws is a better strategy as it results in a higher probability of missing at least one free throw.
The probability of making one free throw is 0.89. Therefore, the probability of making both free throws is: 0.89 * 0.89 = 0.7921 (rounded to 2 decimals).
The probability of missing one free throw is 1 - 0.89 = 0.11. Therefore, the probability of making at least one free throw is: 1 - 0.11 * 0.11 = 0.9889 (rounded to 2 decimals).
The probability of missing one free throw is 0.11. Therefore, the probability of missing both free throws is: 0.11 * 0.11 = 0.0121 (rounded to 2 decimals).
For the worst free-throw shooter who makes 58% of his free throws:
The probability of making both free throws is: 0.58 * 0.58 = 0.3364 (rounded to 4 decimals).
The probability of making at least one free throw is: 1 - 0.42 * 0.42 = 0.8236 (rounded to 2 decimals).
The probability of missing both free throws is: 0.42 * 0.42 = 0.1764 (rounded to 4 decimals).
For the player who makes 89% of his free throws:
The probability of making both free throws is: 0.89 * 0.89 = 0.7921 (rounded to 4 decimals).
The probability of making at least one free throw is: 1 - 0.11 * 0.11 = 0.9889 (rounded to 2 decimals).
The probability of missing both free throws is: 0.11 * 0.11 = 0.0121 (rounded to 4 decimals).
Therefore, intentionally fouling the player who makes 58% of his free throws is a better strategy as it results in a higher probability of missing at least one free throw.
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Please Help Me!!!!!!!
Answer: the answer is sos not please help me dude
Step-by-step explanation:
but you use kami and go to files and download the pdf use kami
Jana needs to rent a moving van for one day. Reliable Rentals charges $20 for the day and $0.50
for each mile. Dependable Rentals charges $10 for the day and $0.80 for each mile. Jana wrote
and solved the equation below to find the number of miles for which the costs of renting from the
companies will be the same. She used m to represent the number of miles.
20-0.5m= 10+ 0.8m
20= 10 + 1.3m
10 = 1.3m
= 13 = 100 = 77/3
The costs will be equal if the van is driven about 8 miles.
m=
Answer:
20 + .50M = 10 + .80M subtract .50M, 10 from both sides
10 = .30M divide both sides by .30
10 / .30 = M = about 33 + 1/3 miles driven equalize the cost
[Jana used " -.50M" in the original set up instead of " +.50M" ]
Step-by-step explanation:
In a class of 60 students, the number of students who passed Ga is 6 more than the number that passed fante. Every student passed at least one of the two subjects and 8 students passed both subjects. How many students passed only one subject?
52 students passed only one subject
How to find the number of students who passed each subject
Let's use the following variables to represent the number of students who passed each subject:
P(Ga): the number of students who passed Ga
P(Fante): the number of students who passed Fante
From the problem statement, we know that:
P(Ga) = P(Fante) + 6, since the number of students who passed Ga is 6 more than the number who passed Fante
P(Ga ∩ Fante) = 8, since 8 students passed both subjects
P(Ga ∪ Fante) = 60, since every student passed at least one subject
We want to find the number of students who passed only one subject, which is equal to the total number of students who passed Ga minus the number of students who passed both subjects, plus the number of students who passed Fante but not Ga. In symbols:
P(Ga) - P(Ga ∩ Fante) + (P(Fante) - P(Ga ∩ Fante))
Substituting the values we know:
(P(Fante) + 6) - 8 + (P(Fante) - 8)
Simplifying:
2P(Fante) - 10
We also know that P(Ga) + P(Fante) - P(Ga ∩ Fante) = P(Ga ∪ Fante) = 60.
Substituting the values we know:
P(Ga) + P(Fante) - 8 = 60
P(Ga) + P(Fante) = 68
Substituting P(Ga) = P(Fante) + 6:
2P(Fante) + 6 = 68
2P(Fante) = 62
P(Fante) = 31
Therefore, the number of students who passed only one subject is:
2P(Fante) - 10 = 2(31) - 10 = 52
Therefore, 52 students passed only one subject.
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Someone please help with this question
Tony and his cousin are playing a game where they pick up colored sticks. Tony currently has 12 points and likes to pick up the yellow sticks, earning 10 points every turn. His cousin just lost all his points on the previous turn, and has a strategy to catch up by getting all the blue ones, earning 14 points per turn. In a certain number of turns, the score will be tied. How many points will they each have? How long will that take?
Tony and his cousin will each have __ points in __ turns.
Answer:
Tony and his cousin will each have 42 points in 3 turns.
Step-by-step explanation:
10 x 3 = 30
30 + 12 = 42
14 x 3 = 42
A standard deck of 52 playing cards contains 13 cards in each of four suits: diamonds, hearts, clubs, and spades. Two cards are chosen from the deck at random. What is the approximate probability of choosing one club and one heart?
0. 0588
0. 0637
0. 1176
0. 1275
The probability of getting one club and one heart is 0.127.
p= [tex]\frac{13*13*2*1}{52*51}[/tex]=0.1275
One of the areas of probability theory is the estimation of the chance of experiments occurring. Using a probability, we can calculate everything from the likelihood of getting heads or tails when flipping a coin to the likelihood of making a research error, for example. It is essential to appreciate the most basic definitions of this branch, such as the formula for computing probabilities in equiprobable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc., in order to properly understand it .Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. Mathematics has incorporated probability to forecast the likelihood of various events.
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A construction crew needs to pave a road that is 205 miles long. The crew paves 9 miles of the road each day. The length, L (in miles), that is left to be paved after d days is given by the following function
The length, L (in miles), that is left to be paved after d days is given by the following function L = 205 - 9d.
In this function, 205 represents the total length of the road that needs to be paved, and 9 represents the number of miles that the crew paves each day. The variable d represents the number of days that the crew has been working on the road.
To find the length of the road that is left to be paved after a certain number of days, we can substitute the value of d into the function and solve for L. For example, if the crew has been working on the road for 10 days, we can find the length of the road that is left to be paved as follows:
L = 205 - 9d
L = 205 - 9(10)
L = 205 - 90
L = 115
Therefore, after 10 days, the crew still has 115 miles of road left to pave.
This function can be useful for the construction crew to keep track of their progress and plan their work accordingly. It can also be used by project managers and other stakeholders to monitor the project and ensure that it is on track to be completed within the desired timeframe.
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for a given value of x, the function f will output a value y that satisifies the following equation. 4x-5y=20 write the formula for f(x) in terms of x
According to the given information the formula for f(x) in term of x is f(x) = (4/5)x - 4.
What is a function, exactly?A function is a relationship between a number of inputs and outcomes. Simply described, a function is an association between inputs where each input is linked to exactly one output. There is a range, codomain, as well as domain for every function. A function is commonly referred to as f(x), where x is in fact the input.
How can a math function be identified?When looking at a graph, we use a procedure known as the Vertical Line Test to determine whether a function is indeed a function. Simply drawing a vertical line will reveal if the graph is a function if it touches it once.
4x - 5y = 20
Subtracting 4x from both sides
-5y = -4x + 20
Dividing 5 from the both sides
y = (4/5)x - 4
The formula for f(x) in terms of x is:
f(x) = (4/5)x - 4
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help plssssssssssssssssssss
Answer: look at the image for the answer and solution
Step-by-step explanation:
Which value of x makes the expression equivalent to 24√47?
O A. 8
OB. 64
O C. 192
OD. 576
3√47x
Answer: A
Step-by-step explanation:
To solve for x, we can set the expression equal to 24√47 and solve for x.
24√47 = x√47
24 = x
Therefore, the value of x that makes the expression equivalent to 24√47 is x = 24, which corresponds to the answer choice A.
a wireless garage door opener has a code determined by the up or down setting of 16 switches. how many outcomes are in the sample space of possible codes?
The number of possible outcomes in the sample space of a wireless garage door opener with 16 switches can be determined using the concept of combination is 1.
Combination is a mathematical concept that refers to the number of ways that a set of objects can be selected from a larger set without regard to their order.
To determine the number of possible outcomes in the sample space, we can use the concept of combination. In this case, the objects are the 16 switches, and the larger set is the set of all possible settings for these switches (up or down).
To calculate the number of possible combinations, we can use the formula for combination, which is:
ⁿCₓ = n! / (x! * (n - x)!)
where n is the total number of objects (16 switches), and x is the number of objects selected (in this case, also 16 switches). The exclamation mark (!) represents the factorial function, which is the product of all positive integers up to and including the given integer.
Using this formula, we can calculate the number of possible combinations as follows:
=> 16! / (16! x (16 - 16)!)
=> 16! / (16! x 0!)
=> 1
Therefore, the sample space of possible codes for a wireless garage door opener with 16 switches is 1.
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Scientists rope off two excavation sites. Site A is rectangular with a length of 60 meters and a width of 40 meters. Site B is similar in shape to Site A but has a length of 45 meters. How much rope is needed for both sites?
Answer:
First, we need to find the area of Site A and Site B. The area of a rectangle is found by multiplying its length and width, so:
Site A: 60 m x 40 m = 2400 m^2
Site B: 45 m x 40 m = 1800 m^2
Next, we need to find the perimeter of each site, which is the distance around the edges of the rectangle. The perimeter is found by adding up the lengths of all four sides, so:
Site A: 2 x (60 m + 40 m) = 2 x 100 m = 200 m
Site B: 2 x (45 m + 40 m) = 2 x 85 m = 170 m
Finally, to find the total amount of rope needed, we add up the perimeters of both sites:
200 m + 170 m = 370 m
So, we need a total of 370 meters of rope to rope off both sites.
Answer:350
ITS NOT 370
A triangle has side lengths 35cm, 46cm, and 68cm. What true of triangle is this
The triangle is scalene triangle as none of the sides of a triangle are equal to each other.
Triangles are classified into three types on the basis of its sides.
Equilateral triangle = If all sides of a triangle are equal then it is known as equilateral triangle.
Isosceles triangle = If any two sides of a triangle are equal then it is known as isosceles triangle.
Scalene triangle = If none of the sides of a triangle are equal then it is known as scalene triangle.
The question states that a triangle has side lengths 35cm, 46cm, and 68cm
so, none of the side are equal so the given triangle is scalene triangle
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lily's car has a fuel efficiency of 8 88 liters per 100 100100 kilometers. what is the fuel efficiency of lily's car in kilometers per liter?
The fuel consumption per liter of Lilly's car is 12.5 kilometers per liter .
Average mileage The average mileage of a vehicle is the ratio of the distance traveled by the vehicle and the total amount of fuel used for that distance.
You can specify:
where (d) is the distance traveled and (n) is the fuel consumption.
Lily's car consumes 8 liters per 100km. This is your car's mileage or efficiency.
average mileage = 100/8 = 12.5 kilometers per liter
Therefore, the fuel efficiency in kilometers per liter of a Lily car with a fuel efficiency of 8 liters per 100 kilometers is 12.5 kilometers per liter.
Complete Question - Lily’s car has a fuel efficiency of 8 liters per 100 kilometers. What is the fuel efficiency of Lily’s car in kilometers per liter ?
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customers arrive according to a poisson process, stay for a time g and then leave. what is the joint distribution of customers remaining and having left
The joint distribution of X(t) and Y(t) is P(X(t) = k, Y(t) = n) = ((μt)^k / k!) * (μt)^(n+1) * e^(-μt)
The joint distribution of customers remaining and having left can be expressed using the Poisson process as follows:
Let N(t) be the number of customers that arrive in the time interval [0, t], and let S₁, S₂, S₃, ... be the sequence of service times for each customer, where S_i is the time the i-th customer spends in the system (i.e., waiting and being served). Let Y(t) be the number of customers who have left the system by time t, and let X(t) be the number of customers who are still in the system at time t.
The joint distribution of X(t) and Y(t) can be written as:
P(X(t) = k, Y(t) = n) = P(N(t) = k + n) * P(sum of S_i for i = 1 to k + n > t) * P(sum of S_i for i = 1 to k + n - 1 <= t)
where the first term on the right-hand side represents the probability that k + n customers arrive in the time interval [0, t], the second term represents the probability that the sum of service times for the first k + n customers exceeds t (i.e., there are still k + n customers in the system at time t), and the third term represents the probability that the sum of service times for the first k + n - 1 customers is less than or equal to t (i.e., the first k + n - 1 customers have left the system by time t).
The distribution of X(t) and Y(t) can be quite complex, depending on the distribution of service times and the arrival rate of customers. However, in some special cases, closed-form expressions for the joint distribution can be derived. For example, if the service times have an exponential distribution and the arrival rate of customers is constant, then the joint distribution of X(t) and Y(t) is given by the following formula:
P(X(t) = k, Y(t) = n) = ((μt)^k / k!) * (μt)^(n+1) * e^(-μt)
where μ is the rate parameter for the exponential distribution of service times.
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HELP you will get brainlie
Answer:
A. 112 units^2
Step-by-step explanation:
64 + 32 + 12 + 4 = 112
when taping a television commercial, the probability that a certain actor will get his lines straight on any one take is 0.40. what is the probability that this actor will get his lines straight for the first time on the fourth attempt? assume attempts are independent. round your answer to three decimal places.
The probability that the actor will get his lines straight for the first time on the fourth attempt is 0.0864, rounded to three decimal places.
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
The probability that the actor will get his lines straight on any one take is 0.40. This means that the probability of him not getting his lines straight on any one take is 1 - 0.40 = 0.60.
P(getting lines straight on 4th attempt)
= P(not getting lines straight on 1st, 2nd, or 3rd attempt) x P(getting lines straight on 4th attempt)
P(not getting lines straight on any one attempt) = 0.60
P(not getting lines straight on 1st, 2nd, or 3rd attempt) = 0.60 x 0.60 x 0.60 = 0.216
P(getting lines straight on 4th attempt) = 0.40
P(getting lines straight for the first time on the fourth attempt) = P(not getting lines straight on 1st, 2nd, or 3rd attempt) x P(getting lines straight on 4th attempt)
= 0.216 x 0.40 = 0.0864
Therefore, the probability that the actor will get his lines straight for the first time on the fourth attempt is 0.0864, rounded to three decimal places.
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4. Round each fraction to help you estimate the solution for the following equation:
one-sixth plus five-sixths equals
1. 0
2. one half
3. 1
4. 2
5. Round each fraction to help you estimate the solution for the following equation:
seven twelfths plus two-twelfths equals
1. one half
2. 1
3. one and one half
4. 2
6. Round each fraction to help you estimate the solution for the following equation:
nine-tenths minus four-tenths equals
1. 0
2. one half
3. 1
4. one and one half
The fractions have values -
4. one-sixth plus five-sixths equals - Option 3 : 1
5. seven twelfths plus two-twelfths equals - Option 1 : 0
6. nine-tenths minus four-tenths equals - Option 4 : 2
What is fraction?
In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.
The first fractional statement is -
one-sixth plus five-sixths
The mathematical expression is -
1/6 + 5/6
Since the denominator is same just add the numerator.
(1 + 5) / 6
6/6
1
Therefore, the value is obtained as 1.
The second fractional statement is -
seven twelfths plus two-twelfths
The mathematical expression is -
7/12 + 2/12
Since the denominator is same just add the numerator.
(7 + 2) / 12
9/12
3/4
0.75 ≈ 0
Therefore, the value is obtained as 3/4.
The third fractional statement is -
nine-tenths minus four-tenths
The mathematical expression is -
9/10 - 4/10
Since the denominator is same just subtract the numerator.
(9 - 4) / 10
5/10
2
Therefore, the value is obtained as 2.
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4. Round each fraction to help you estimate the solution for the following equation:
one-sixth plus five-sixths equals
1. 0
2. one half
3. 1
4. 2
5. Round each fraction to help you estimate the solution for the following equation:
seven twelfths plus two-twelfths equals
1. 0
2. one half
3. 1
4. one and one half
6. Round each fraction to help you estimate the solution for the following equation:
nine-tenths minus four-tenths equals
1. one half
2. 1
3. one and one half
4. 2
Amy says “to find 50x20,I multiply 5x2 and then place the total number of zeros in both factors at the end.Do you agree?Explain
Answer:
Yes, because 50x20= 5x10x2x10= (5x2)x(10x10)
So you can multiply 5x2 first and than add the zeros
Lamonte is going to invest in an account paying an interest rate of 4% compounded
continuously. How much would Lamonte need to invest, to the nearest cent, for the
value of the account to reach $12,300 in 8 years?
The amount that needs to be invested at the interest rate of 4% compounded continuously is P = $8932.461.
What is compound interest?Compound interest, also known as interest on principal and interest, is the practise of adding interest to the principal amount of a loan or deposit. It occurs when interest is reinvested, or added to the loaned capital rather than paid out, or when the borrower is required to pay it, so that interest is generated the next period on the principal amount plus any accumulated interest. In finance and economics, compound interest is common.
Given that the interest is compounded continuously.
For the given situation the formula of compound interest is:
[tex]A = Pe^{rt}[/tex]
where, A is the amount = $12300
P is the principal amount
r is the rate = 4% = 0.04
t is the time = 8 years
Substituting the values we have:
[tex]12300 = Pe^{(0.04)(8)}\\\\P = \frac{12300}{e^{(0.04)(8)}} \\\\P =8932.461[/tex]
Hence, the amount that needs to be invested at the interest rate of 4% compounded continuously is P = $8932.461.
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11. Suppose that the volume of four stars in the Milky Way are: 1.3 × 1024 km3, 6.9 x
1015 km3, 3.4 x 1015 km3, and 2.7 x 1024 km3. What is the order of the stars from least to greatest volume? (Im giving 30 points so pls show work)
13 4 73 efine a variable for the quantity that changes. Then, write an algebraic expression for the amount of etergent remaining in the container. ▸Math symbols Relations ▸ Geometry Groups ▸Trigonometry Statistics
The algebraic expression for the amount of etergent remaining in the container isy = x - 13 - 4 - 73
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
We are given that;
13 4 73
Let's define the variable 'x' to represent the amount of detergent initially present in the container.
Then, if 'y' represents the amount of detergent remaining in the container, we can write an algebraic expression for it as:
y = x - 13 - 4 - 73
where:
13 represents the amount of detergent used on the first day
4 represents the amount of detergent used on the second day
73 represents the amount of detergent used on the third day
By subtracting the total amount of detergent used from the initial amount 'x', we get the remaining amount 'y'.
Therefore, the expression will be y = x - 13 - 4 - 73.
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g knowing the value of p tells one: select one: a. the size of the difference between two groups or means. b. whether there is statistical significance. c. the correlation between two groups or means. d. the t value.
Knowing the value of p tells one that option b. whether there is statistical significance.
The concept of probability, which is a measure of the likelihood of an event occurring. It is an essential tool in statistics, and it helps us make informed decisions based on data.
Now, let's dive into the answer to the question. Knowing the value of p tells us about the statistical significance of our results. In statistical analysis, we often conduct hypothesis tests to determine whether a particular effect is significant or just occurred by chance.
The p-value is the probability of observing the results we obtained under the null hypothesis, assuming that the null hypothesis is true. The null hypothesis is the default assumption that there is no significant difference between groups or means.
If the p-value is low, say less than 0.05, we reject the null hypothesis and conclude that there is a significant difference between groups or means. On the other hand, if the p-value is high, we fail to reject the null hypothesis, and we cannot claim that there is a significant difference between groups or means.
To give an example, suppose we conducted an experiment to test whether a new drug reduces blood pressure. We would have a control group that receives a placebo and a treatment group that receives the drug. We measure the blood pressure of both groups and compute the p-value. If the p-value is less than 0.05, we would conclude that the drug is effective in reducing blood pressure.
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the measure of one interior angle of a parallelogram is 0.25 times the measure of another angle.
The interior angle of a parallelogram is proportional to the measure of another angle with a ratio of 0.25:1.
A parallelogram is a four-sided flat shape that has opposite sides that are parallel and equal in length. The sum of the interior angles of a parallelogram is equal to 360 degrees. If the measure of one interior angle is 0.25 times the measure of another angle, this means that there is a proportionate relationship between the two angles. To find the measure of the second angle, we can use the formula:
Angle 2 = (Angle 1) / 0.25
For example, if Angle 1 is 100 degrees, then Angle 2 is 100 / 0.25 = 400 degrees. This means that if one angle measures 100 degrees, the other angle measures 400 degrees. The sum of the two angles is 500 degrees, which is still less than the total sum of interior angles in a parallelogram, which is 360 degrees.
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Felipe wants to go to all 19 home games at a football club.
For each game, a ticket costs £32
A season ticket costs £389 and gives entry to all 19 home games.
In total, how much does Felipe save by buying a season ticket?
Answer: 219
Step-by-step explanation:
32 times 19= 608
608 minus 389=219
A, B & C form the vertices of a triangle. ∠ CAB = 90°, ∠ ABC = 36° and AB = 8.6. Calculate the length of AC rounded to 3 SF.
Answer:
AC ≈ 6.25
Step-by-step explanation:
using the tangent ratio in the right triangle
tan36° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{AC}{8.6}[/tex] ( multiply both sides by 8.6 )
8.6 × tan36° = AC , then
AC ≈ 6.25 ( to 3 SF )
Which inequality is represented by the number line?
A. |2x + 1| > 7
B. 2|x + 1| < 8
C. |2x - 1| > 9
D.2 |x - 1| < 10
The number line is represented by the inequality -
Option C - |2x - 1| ≥ 9
What is an inequality?
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.
The number line indicates two filled circles which suggests the inequality contains (≤,≥) symbols and is inclusive of range.
The first inequality will be x ≤ -4 since the value is starting from -4 and moving towards negative infinity.
Similarly, the second inequality will be x ≥ 5 since the value is starting from 5 and moving towards positive infinity.
The compound inequality that results in same is -
|2x - 1| ≥ 9
Apply the absolute rule -
2x - 1 ≥ 9 or 2x - 1 ≤ -9
Solve the inequality -
2x - 1 ≥ 9 or 2x - 1 ≤ -9
2x - 1 + 1 ≥ 9 + 1 or 2x - 1 + 1 ≤ -9 + 1
2x ≥ 10 or 2x ≤ -8
x ≥ 5 or x ≤ -4
Therefore, the inequality is |2x - 1| ≥ 9.
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7. consider four values for the predictor. in which instance(s) would you have a trustworthy prediction when using the simple linear regression equation?
The trustworthiness of the prediction depends on the specific data and relationship between the predictor and response variable, and must be evaluated on a case-by-case basis.
To determine the trustworthiness of a prediction using a simple linear regression equation, we need to assess the degree of linearity and the strength of the relationship between the predictor and the response variable.
If the relationship between the predictor and response is linear, the simple linear regression model is appropriate, and if the relationship is strong, the predictions will be more trustworthy.
So, if we have four values for the predictor, we would need to evaluate the scatterplot of the predictor and response variable to determine the linearity and strength of the relationship.
If the scatterplot shows a clear and strong linear relationship between the predictor and the response variable, with a relatively small amount of scatter around the line of best fit, then we can be more confident that our predictions using the simple linear regression equation will be trustworthy.
On the other hand, if the scatterplot shows a weak or non-linear relationship, or a high amount of scatter around the line of best fit, then the predictions using the simple linear regression equation may not be as trustworthy.
Therefore, the trustworthiness of the prediction depends on the specific data and relationship between the predictor and response variable, and must be evaluated on a case-by-case basis.
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the radius of a circle is 14 yards. what is the circles circumference
Answer:
roughly 88 but 87.9645943005...
Step-by-step explanation:
First, the formula for the circumference of a circle is 2pi(r), so plugging in 14 yards, you get 28pi roughly 88 but for an actual answer 87.9645943005
buses from dallas to houston leave every hour on the hour. buses from houston to dallas leave every hour on the half hour. the trip from one city to the other takes 5 hours. assuming the buses travel on the same highway, how many dallas-bound buses does a houston-bound bus pass in the highway (not in the station)? buses from dallas to houston leave every hour on the hour. buses from houston to dallas leave every hour on the half hour. the trip from one city to the other takes 5 hours. assuming the buses travel on the same highway, how many dallas-bound buses does a houston-bound bus pass in the highway (not in the station)?
In the 5-hour trip from Dallas to Houston, a Houston-bound bus passes 10 Dallas-bound buses on the highway
The first step to solving this problem is to understand the time it takes for each bus to travel from one city to another. We know that the trip from Dallas to Houston takes 5 hours.
Now, let's use the concept of time to determine how many Dallas-bound buses a Houston-bound bus passes on the highway. We know that buses from Dallas to Houston leave every hour on the hour and buses from Houston to Dallas leave every hour on the half hour. This means that a Houston-bound bus leaves at 1:30 pm, 2:30 pm, 3:30 pm, and so on.
If a Houston-bound bus leaves at 1:30 pm, it will pass the first Dallas-bound bus that left at 1:00 pm after 2.5 hours. This is because the distance between the two cities is the same, and both buses are traveling at the same speed. Therefore, the Houston-bound bus will have traveled half of the distance in 2.5 hours, and it will pass the Dallas-bound bus on the highway.
Similarly, if a Houston-bound bus leaves at 2:30 pm, it will pass the second Dallas-bound bus that left at 2:00 pm after 2.5 hours. This process continues for every Houston-bound bus that leaves on the half hour.
In other words, for every hour that passes, a Houston-bound bus passes two Dallas-bound buses on the highway. Therefore,
=> (5 hours x 2 buses per hour) = 10 hours
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Two urns contain white balls and yellow balls. The first urn contains 5 white balls and 4 yellow balls and the second urn contains 3 white balls and 2 yellow balls. A ball is drawn at random from each urn. What is the probability that both balls are white?
The probability that the both balls would be white when drawn at random from each urn would be = 1 7/45
How to calculate the probability that both balls are white?The number of colour that is found in two urns = 2( white and yellow).
The first urn contains the following:
5 white balls
4 yellow balls
The total number of balls = 9 balls.
The probability of getting a white ball = 5/9
The second urn contains the following:
3 white balls
2 yellow balls
The total number of balls = 5 balls
The probability of getting a white ball = 3/5
Therefore the probability that both balls are white;
= 5/9 + 3/5
= 25+27/45
= 52/45
= 1 7/45
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