f(x) = 3x+2
f(5) = 3(5) +2 = 15 +2 =17
Answer is D. 17
If you have 256 data points, how many classes (bins) would sturges' rule suggest
Final answer:
Sturges' rule suggests using 9 classes or bins for 256 data points.
Explanation:
Sturges' rule is a method for determining the number of classes or bins required for a histogram. According to Sturges' rule, the formula to calculate the number of classes is:
K = 1 + log2(n)
Where K is the number of classes and n is the number of data points. In this case, since you have 256 data points, the number of classes suggested by Sturges' rule would be:
K = 1 + log2(256)
K = 1 + log2(28)
K = 1 + 8
K = 9
Therefore, Sturges' rule would suggest using 9 classes or bins for the histogram.
The random variable x is the number of shots it takes before you make the first free throw in basketball. assuming the probability of success (making a free throw) is constant from trial to trial, what type of distribution does x follow?
Ralphie has 23 more toys than his little brother Joey. If they were to get all of their toys out and lay them on the floor, there would be 384 toys on the floor.
The volume of a cube depends on the length of its sides. This can be written in function notation as v(s). What is the best interpretation of v(2) = 8?
Simplify the function f(x)=1/3(81)^3x/4 . Then determine the key aspects of the function. The initial value is . The simplified base is . The domain is . The range is .
1.1 Factoring: x3-81
Theory : A difference of two perfect cubes, a3 - b3 can be factored into
(a-b) • (a2 +ab +b2)
Proof : (a-b)•(a2+ab+b2) =
a3+a2b+ab2-ba2-b2a-b3 =
a3+(a2b-ba2)+(ab2-b2a)-b3 =
a3+0+0+b3 =
a3+b3
Check : 81 is not a cube !!
Ruling : Binomial can not be factored as the difference of two perfect cubes
1.2 Find roots (zeroes) of : F(x) = x3-81
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 1 and the Trailing Constant is -81.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,3 ,9 ,27 ,81
Let us test ....
Polynomial Roots Calculator found no rational roots
2.1 Solve : x3-81 = 0
Add 81 to both sides of the equation :
x3 = 81
When two things are equal, their cube roots are equal. Taking the cube root of the two sides of the equation we get:
x = ∛ 81
Can ∛ 81 be simplified ?
Yes! The prime factorization of 81 is
3•3•3•3
To be able to remove something from under the radical, there have to be 3 instances of it (because we are taking a cube i.e. cube root).
∛ 81 = ∛ 3•3•3•3 =
3 • ∛ 3
The equation has one real solution
This solution is x = 3 • ∛3 = 4.3267
Answer:
The initial value is
✔ 1/3
The simplified base is
✔ 27
The domain is
✔ all real numbers
The range is
✔ y > 0
Step-by-step explanation:
Jenna hikes 1/2mile every 1/4 hour. how far does she hike in 1 hour?
Jenna hikes 2 miles in 1 hour, as she covers 1/2 mile in each 1/4 hour and there are four 1/4 hours in a full hour.
Jenna hikes 1/2 mile every 1/4 hour. To determine how far she hikes in 1 hour, we need to calculate the distance she can cover in four such intervals since 1 hour is composed of four 1/4 hours.
So, the calculation would be:
1/2 mile in 1/4 hour
1/2 mile x 4 (since there are 4 quarters in a full hour) = 2 miles
Therefore, Jenna hikes 2 miles in 1 hour.
12 packs of juice cost $3.00 after a 40% discount. Which equation would allow you to find the original price of a 12-pack
10 and two tens, and then double the amount, and 5, 3, and 2. How much now?
select the proper order from least to greatest 2/3 , 7/6 , 1/8 , 9/10
There are 3 brothers Adam Ben and Callum Callum is 3/8 of adams age Ben is 4/5 of Adams age given that Callum is 2 years younger than Ben find Adams age
What is the solution to the proportion? Round the answer to the nearest tenth if necessary.
52/x = 9.5/3.25
A: x=14.6
B: x=17.8
C: x=157.8
D:x=169
Yeah it's B:17.8 I agree with you
what is the greatest perfect square that,s a factor of 244 ?
Greatest perfect square that is a factor of 244 is 4 which is the perfect square of 2 .
Given, number 244 .
Firstly the factors of 244 :
244 = 2 × 2 × 61
244 = 4 × 61
Therefore the greatest perfect square that is the factor of 244 will be 4 .
4 is the perfect square of 2.
2² = 4.
Know more about factors,
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Angles opposite to one another at the intersection of two lines are called _ _ _ _ _ _ _ _ _ _ _ _ _ _ angles.
Answer:
Step-by-step explanation: vertical angel
A cube has a volume of 729 cubic centimeters. What can be concluded about the cube? Check all that apply. Recall the formula mr021-1.jpg. The side length, s, can be found using the equation mr021-2.jpg This is a perfect cube. The side length is 243 centimeters. The side length is 9 centimeters. Taking the cube root of the volume will determine the side length. If you multiply the volume by three, you can determine the side length.
Answer:
This is a perfect cube
The side length is [tex]9[/tex] centimeters
Taking the cube root of the volume will determine the side length
Step-by-step explanation:
we know that
The volume of a cube is equal to
[tex]V=s^{3}[/tex]
where
s is the length side of the cube
In this problem we have
[tex]V=729\ cm^{3}[/tex]
Solve for s-------> that means isolate the variable s
Find the length side of the cube s
[tex]s=\sqrt[3]{V}[/tex]
substitute the value of V
[tex]s=\sqrt[3]{729}=9\ cm[/tex] --------> a perfect cube
therefore
Statements
This is a perfect cube--------> Is true
The side length is [tex]9[/tex] centimeters -------> Is true
Taking the cube root of the volume will determine the side length ------> Is true
The side length of the cube is 9cm³ showing that the cube is a perfect cube
Volume of the cubeThe formula for calculating the volume of a cube is expressed as:
V = s³
where:
s is the side length of the cube
Given the following
V = 729cm³
Substitute the given parameters into the formula
729 = s³
s³ = 729
s = 9cm
Hence the side length of the cube is 9cm³ showing that the cube is a perfect cube
Learn more on volume of a cube here: https://brainly.com/question/1972490
Your bowl contains 8 red balls, and 9 blue balls, and you draw 4 balls. in how many ways can the selection be made so that at least one of each color is drawn?
In 2156 ways the selection be made so that at least one of each color is drawn?
The question is asking for the number of ways to select balls from a bowl containing 8 red balls and 9 blue balls if 4 balls are drawn and at least one of each color is drawn.
To solve this, we must consider the different combinations of red and blue balls that meet the requirement.
Calculate the total possible outcomes: 17C4 = 2380
Calculate the outcomes where all balls of one color are drawn: 9C4 + 8C4 = 224
Subtract the outcomes where only one color is drawn from the total: 2380 - 224 = 2156 ways
Which answer represents a speed, not a velocity?
A. 35m/s east
B. -35 m/s down
C. 35 m/s
D. 35 m/s south
The expression that represents the speed will be 35 m/s. Then the correct option is C.
What is a vector?The quantity which has magnitude, and direction, and follows the law of vector addition is called a vector.
The velocity is the rate of change of the displacement. And it is a vector quantity.
The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
In options A, B, and D, then speed depend on the direction which means they are velocity.
The expression that represents the speed will be 35 m/s. Then the correct option is C.
More about the vector link is given below.
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a smoothie recipe calls for 2 1/4 cups of frozen mango. if the recipe serves two, how many cups of frozen mango is needed to serve one?
Answer: The required number of cups of frozen mango is 1.125.
Step-by-step explanation: Given that a smoothie recipe calls for [tex]2\dfrac{1}{4}[/tex] cups of frozen mango and the recipe serves two.
We are to find the number of cups of frozen mango that is needed to serve one.
We will be using the UNITARY method to solve the problem.
We have
The number of cups of frozen mango that needs to serve two is
[tex]2\dfrac{1}{4}=\dfrac{9}{4}=2.25.[/tex]
Therefore, the number of frozen mango that needs to serve one is given by
[tex]\dfrac{2.25}{2}=1.125.[/tex]
Thus, the required number of cups of frozen mango is 1.125.
A house costs $600 more than 12 times the lot on which it was built. If the lot cost x dollars, what did the house cost?
Which expression represents this?
$600 + 12x
$600x + 12
$720x
The expression that represents the situation is:
$ 600+12x
Step-by-step explanation:cost of lot is: $ x
This means that 12 times the lot on which it was built is: $ 12x
Also, it is given that:
A house costs $600 more than 12 times the lot on which it was built.
This means that the total cost of the house is:
600 plus the total cost of the lot on which it was built.
i.e. The expression that represents the total cost of the house is:
$ 600+12x
what's the equation of this line.
8 1/2% of 4000
I hope u understood that.
What is math compass used for ?
A sampling distribution is constructed based on a sample size of 9. if the sampling distribution has a mean of 500 and a standard error of 15, what is the standard deviation of the original comparison population
The standard deviation of the original comparison population is 45.
Explanation:The standard deviation of the original comparison population can be calculated using the formula:
Standard deviation of the sampling distribution = standard error * sqrt(sample size)
Given that the standard error of the sampling distribution is 15 and the sample size is 9, we can substitute these values into the formula:
The standard deviation of the original comparison population can be determined by using the relationship between the standard deviation, standard error, and sample size in a sampling distribution. The formula is:
[tex]\[ \text{Standard deviation of the original comparison population} = \text{Standard error} \times \sqrt{\text{Sample size}} \][/tex]
Given a standard error of 15 and a sample size of 9, substitute these values into the formula:
\[ \text{Standard deviation of the original comparison population} =[tex]15 \times \sqrt{9} = 15 \times 3 = 45 \][/tex]
Therefore, the standard deviation of the original comparison population is 45.
Standard deviation of the original comparison population = 15 * sqrt(9) = 15 * 3 = 45
Therefore, the standard deviation of the original comparison population is 45.
Farmer Fred has 200 sheep on his farm.He sells 40 of them.What percentage of his sheep does he have left?
78·112=7278·112=72 . how can you tell that her answer is wrong?
In the formula l=prt, what does the p stand for
How to find mean and standard deviation for binomial distribution?
To calculate mean and standard deviation for a binomial distribution, use the formulas μ = np and σ = √npq. Ensure both np and nq are greater than five to use the normal approximation.
Explanation:To find the mean (μ) and standard deviation (σ) for a binomial distribution, you use the formulas μ = np and σ = √npq respectively. Here, 'n' represents the number of trials, 'p' is the probability of success on a single trial, and 'q' is the probability of failure on a single trial, which is calculated as q=1-p.
If you want to determine whether you can use the normal approximation to the binomial, it is essential to ensure that both np and nq are greater than five. This is because the normal approximation is most accurate when the binomial distribution is symmetrical, which typically occurs when both np and nq exceed five.
please help! Algebra 1 math.
Find the ordered pairs for the x- and y-intercepts of the equation 3x − 2y = 18 and select the appropriate option below.
A. The x-intercept is (0, 6); the y-intercept is (–9, 0).
B.The x-intercept is (6, 0); the y-intercept is (0, –9).
C. The x-intercept is (3, 0); the y-intercept is (0, –2).
D.The x-intercept is (0, 3); the y-intercept is (–2, 0).
What is the median of this set of data: 10, 11, 12, 12, 15, 19, 20, 21, and 22? Express your answer as an integer.
Question 7 options:
12
15
16
19
Los angles is about 385 miles from san francisco. how far apart should the city's be on a map with a scale of 1in=1515mil
which action illustrates rational behavior