Both events A and B have probabilities of 1/12, and they are independent events since the outcome on one die does not affect the outcome on the other die.
The event A consists of all outcomes in which the number of spots showing on the red die is three or less.
Since the red die has six equally likely outcomes (1, 2, 3, 4, 5, and 6), the probability of A is:
P(A) = the number of outcomes in A / the total number of possible outcomes.
Out of the six possible outcomes on the red die, three of them are three or less: 1, 2, and 3.
Therefore, the number of outcomes in A is three.
Since there are six equally likely outcomes for the green die as well, the total number of possible outcomes is 6 x 6 = 36.
Therefore, we have:
P(A) = 3/36 = 1/12.
The event B consists of all outcomes in which the number of spots showing on the green die is more than three.
There are also three outcomes on the green die that satisfy this condition: 4, 5, and 6.
Thus, we have:
P(B) = 3/36 = 1/12.
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Question 8(Multiple Choice Worth 2 points)
(Creating Graphical Representations MC)
The number of milligrams of Vitamin C from 100 different gummy vitamins sold in the world was collected.
Which graphical representation would be most appropriate for the data, and why?
Box plot, because the median can easily be determined from the large set of data
Stem-and-leaf plot, because you can see the shape of the data
Histogram, because it shows each individual data point
Bar chart, because the data is categorical
The box plot, as the median can be easily estimated from the big set of data, is the graphical representation that's most suitable for the data for gummy vitamins sold globally.
Explain about the box plot:The distribution of data is shown using a boxplot, which is a standardised method based on a five-number summary ("minimum," first quartile ("Q1"), median ("Q3"), and "maximum").
It can reveal information about your outliers' values. Boxplots can also show you how tightly that data is grouped, whether or not your data is skewed, and whether or not your data is symmetrical.The lower and upper quartiles are shown on the left and right sides of a box and whisker plot, respectively. The interquartile range, which contains 50% of the data, is covered by the box. The median is the vertical line which it divided the box in half.For the case of -
A total of 100 distinct gummy vitamins that are offered worldwide were counted for their milligrammes of vitamin C content.
The box plot, as the median can be easily estimated from the big set of data, is the graphical representation that's most suitable for the data for gummy vitamins sold globally.
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The formula v=0. 83B^3/2 represent the wind speed, v, in relation to b, the Beaufort scale number Determine the Beaufort scale number when the wind speed is 9. 4 meter per second
Answer:
5.0
Step-by-step explanation:
You want the Beaufort scale number corresponding to 9.4 m/s, given the formula ...
v = 0.83B^(3/2)
SolutionPut the given speed in the formula and solve for B.
9.4 = 0.83B^(3/2)
9.4/0.83 = B^(3/2)
B = (9.4/0.83)^(2/3) ≈ 5.043
The wind speed is about 5.0 on the Beaufort scale.
Three softball players discussed their batting averages after a game.
................Probability
Player 1: four sevenths
Player 2: five eighths
Player 3: three sixths
By comparing the probabilities and interpreting the likelihood, which statement is true?
A. Player 1 is more likely to hit the ball than Player 2 because P(Player 1) > P(Player 2)
B. Player 2 is more likely to hit the ball than Player 1 because P(Player 2) > P(Player 1)
C. Player 3 is more likely to hit the ball than Player 1 because P(Player 3) > P(Player 1)
D. Player 3 is more likely to hit the ball than Player 2 because P(Player 3) > P(Player 2)
The true statement is B. Player 2 is more likely to hit the ball than Player 1 because P(Player 2) > P(Player 1), by comparing the probabilities and interpreting the likelihood.
From the given information,
Probability of the batting average of player 1 = 4/7
Probability of the batting average of player 2 = 5/8
Probability of the batting average of player 3 = 3/6 = 1/2
We have to find the likelihood of each player.
LCM (7, 8, 6) = 56
Probability of player 1 = (4 × 8) / (7 × 8) = 32/56
Probability of player 2 = (5 × 7) / (8 × 7) = 35/56
Probability of player 1 = (1 × 28 ) / (2 × 28) = 28/56
Here the likelihood is greatest for player 2, then player 1 and the least likelihood is for player 3.
Hence the correct option is B.
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Question 1-2
The relationship between two variables a and b is proportional. When a is 4, b is 49, What is a when b is 147?
12
16
4
8
Therefore , the solution of the given problem of equation comes out to be the value of an is 12 when b is 147. Therefore, 12 is the right response.
Define equation.In intricate algorithms, variable words are typically employed to demonstrate consistency between two opposing arguments. Equations are academic phrases that are used to demonstrate the equality of different academic figures. Consider the specifics of the above x + 7 suggestions. improving in this case provides b + 7 while constructing y + 7 before integrating.
Here,
The following values can be used to put up a proportion if the relationship between variables a and b is proportional:
=> a / b = 4 / 49
The value of a when b is 147 can therefore be calculated using this ratio:
=> a / 147 = 4 / 49
By cross-multiplying, we can isolate a:
=> a = (4 / 49) * 147
Now that we know the value of a, we can:
=> a = 12
Therefore, the value of an is 12 when b is 147. Therefore, 12 is the right response.
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Which type of government structure would be threatened by debate over public policy?
A government structure that is authoritarian or dictatorial in nature would be threatened by debate over public policy.
In such a system, the government exercises complete control over decision-making and any opposition or dissent is not tolerated.
Open debate and discussion over public policy would challenge the authority of the government and its ability to maintain control over the population.
Democracies, on the other hand, thrive on healthy debate and discussion over public policy, as it allows for diverse perspectives and ideas to be heard and considered.
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How does sample variance influence the estimated standard error and measures of effect size such as r2 and Cohen's d?
A) Larger variance increases both the standard error and measures of effect size.
B) Larger variance increases the standard error but decreases measures of effect size.
C) Larger variance decreases the standard error but increases measures of effect size.
D) Larger variance decreases both the standard error and measures of effect size.
The estimated standard error and measures of effect size such as r2 and Cohen's d larger variance increases the standard error but decreases measures of effect size. B.
Larger variance increases the standard error but decreases measures of effect size.
The standard error is a measure of how much the sample mean is likely to vary from the true population mean.
It is calculated as the standard deviation of the sample divided by the square root of the sample size.
If the sample variance is large, the standard deviation of the sample will also be large, resulting in a larger standard error.
Measures of effect size, such as r2 and Cohen's d, indicate the strength of the relationship between variables or the size of the difference between groups, respectively.
Larger sample variances indicate greater variability in the data, which can make it more difficult to detect significant effects.
This can result in smaller effect sizes, as the magnitude of the effect is reduced relative to the variability in the data.
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EFGH is a square. If FG= 9, what is FJ? Round your answer to the nearest tenth, if necessary.
~a.) 4.5
~b.) 6.4
~c.) 9
~d.) 12.7
Answer:
6.4
Step-by-step explanation:
The energy for a rigid rotator constrained to rotate in the x-y plane is given by 21 where the moment of inertia I is a constant. (a) What is the Hamiltonian? Show that the Hamiltonian and L commute. What are the allowed energies and normalized energy eigenfunctions of the rigid rotator?
a. The Hamiltonian is given by:
H = T + V = (p² / 2I) + 0 = p² / 2I
b. Since the commutator is zero, we can conclude that the Hamiltonian and L commute.
c. The energy eigenfunctions are given by:
ψ[tex]_{n}[/tex](θ, φ) = √((2n + 1) / (4π)) × [tex]e^{(inφ)[/tex] × P[tex]_{n}[/tex](cosθ)
What is Hamiltonian?When time is not explicitly included in the function, it is used to characterize a dynamic system (such as the motion of a particle) in terms of momentum components and coordinates of space and time, and it is equal to the total energy of the system.
(a) The Hamiltonian is given by:
H = T + V = (p² / 2I) + 0 = p² / 2I
where T is the kinetic energy and V is the potential energy. Since the rotator is constrained to rotate in the x-y plane, there is no potential energy.
b. To show that the Hamiltonian and L commute, we need to calculate their commutator:
[H, L] = HL - LH
where L is the angular momentum operator given by L = r x p, where r is the position vector and p is the momentum operator.
HL = (p² / 2I) × (r × p) - (r × p) × (p² / 2I)
= (1/2I) × (p² × r × p - r × p × p²)
= (1/2I) × [p², r x p]
LH = (r x p) × (p² / 2I) - (p² / 2I) × (r x p)
= (1/2I) × (r × p × p² - p² × r x p)
= -(1/2I) × [p², r x p]
Therefore, [H, L] = [p², r x p] / 2I - [p², r x p] / 2I = 0.
Since the commutator is zero, we can conclude that the Hamiltonian and L commute.
c. The allowed energies of the rigid rotator are given by:
E[tex]_{n}[/tex]= (n² × h²) / (8I)
where n is a positive integer and h is Planck's constant. The energy levels are quantized and spaced equally apart, with the energy increasing as n increases.
The energy eigenfunctions are given by:
ψ[tex]_{n}[/tex](θ, φ) = √((2n + 1) / (4π)) * [tex]e^{(inφ)[/tex] * P[tex]_{n}[/tex](cosθ)
where θ is the polar angle and φ is the azimuthal angle, and P_n(x) is the n-th order Legendre polynomial. The eigenfunctions are normalized and orthogonal, with each energy level having a unique set of eigenfunctions.
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The simplified slope of item number 2 is:
a. 1/6
b. 6
c. -6
d. -1/6
The simplified slope of item number 3 is:
a. 4/7
b. 3/4
c. 7/4
d. -4/3
The simplified slope of item number 4 is:
a. 3/5
b. -3/5
c. -5/12
d. -12/5
Answer:
c and a
Step-by-step explanation:
find the sum of the first 6 terms of the finite geometric series 18, -54, 162
The sum of the first 6 terms of the given sequence is -1350.
What is sum?
In mathematics, the term "sum" refers to the result of adding two or more numbers or quantities together. The sum of two numbers a and b is denoted by a + b. Similarly, the sum of three numbers a, b, and c is denoted by a + b + c.
The given sequence is a finite geometric sequence with a common ratio of -3. To find the sum of the first 6 terms of this sequence, we can use the formula for the sum of a finite geometric series:
[tex]S_n = a(1 - r^n) / (1 - r)[/tex]
where S_n is the sum of the first n terms of the sequence, a is the first term of the sequence, r is the common ratio, and n is the number of terms in the sequence.
Substituting the given values, we get:
[tex]S_6 = 18(1 - (-3)^6) / (1 - (-3))\\\\S_6 = 18(1 - 729) / 4\\\\S_6 = -1350[/tex]
Therefore, the sum of the first 6 terms of the given sequence is -1350.
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Answer:
Step-by-step explanation:
-1,092
Suppose a continuous random variable X is uniformly distributed on the interval [4,9]. able Y distributed? That is, determine the probability density function fy(y) 1. None of these. 2. for 4-y-9 = 10, 0 otherwise
For a continuous random variable X, which is uniformly distributed on an interval [4,9], the probability density function of [tex]f_Y( y)[/tex] is equals to
[tex]f_Y( y) =\begin{cases} \frac{2y}{5},\quad 2≤ x ≤ 3 \\ 0, \quad \: otherwise\ \ \end{cases}[/tex]. So, option(5) is correct.
We have a continuous random variable X is uniformly distributed on the interval [4,9]. The PDF is a probability that a random variable acquire a value exactly same or equal to the random variable but in case of CDF, this probability values is less than or equal to the random variable. The probability density function for X is defined as [tex]f_X(x) = \frac{1}{b - a} [/tex] so, we can write it as [tex]f_X ( x) =\begin{cases} \frac{1}{5},\quad 4≤ x ≤ 9 \\ 0, \quad otherwise \\ \end{cases}[/tex].
We have to determine the probability density function [tex]f_Y(y)[/tex]. For this first we have to calculate the cumulative distribution function for f(x) is written as [tex]F_X(x) = \int_{4}^{x} f(x) dx [/tex]
[tex]= \int_{4}^{x} \frac{1}{5} dx [/tex]
[tex]= \frac{1}{5} [ x]_{4}^{x} [/tex]
[tex]F_X(x) = \frac{x - 4}{5}[/tex]
Now, we have, [tex] Y = \sqrt{X}[/tex]
when X = 4 => Y = 2 and X = 9 => Y = 3
Also, X = Y²
Differentiating X = Y² with respect to Y
=> dX = 2Y dY
=> dX/dY = 2Y
Now, pdf of Y is written as [tex]f_Y(y) = f_X(x)|\frac{dX}{dY}| [/tex]
[tex] = \frac{ 1}{5} × 2y[/tex]
[tex]= \frac{ 2y}{5}[/tex]
So, [tex]f_Y( y) =\begin{cases} \frac{2y}{5},\quad 2≤ x ≤ 3 \\ 0, \quad \: otherwise \ \ \end{cases}[/tex]. Hence, required value is [tex]f_Y( y) =\begin{cases} \frac{2y}{5},\quad 2≤ x ≤ 3 \\ 0, \quad \: otherwise \ \ \end{cases}[/tex].
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Complete question:
The above figure complete the question.
URGENT - Will also give brainliest to simple answer
Find the length of the arc that outlines the sector
Answer:
arc length ≈ 37.7
Step-by-step explanation:
the arc length is calculated as
arc = circumference of circle × fraction of circle
= 2πr × [tex]\frac{135}{360}[/tex] ( r is the radius )
= 2π × 16 × [tex]\frac{3}{8}[/tex]
= 32π × [tex]\frac{3}{8}[/tex]
= 4π × 3
= 12π
≈ 37.7 ( to the nearest tenth )
Help I don't understand.
Using the given percentage we can see that the minimum and maximum numbers are:
N- = 967
N+ = 1,150
How to get the minimum and maximum amounts?The total number of students is 3,650, and we know that the average percentage is 29% ± 2.5%
The minimum value is what we get when we use the minus sign:
29% - 2.5% = 26.5%
The 26.5% of 3,650 is:
N- = (0.265)* 3,650 = 967
The maximum value is what we get when we use the plus sign:
29% + 2.5% = 31.5%
The 31.5% of 3,650 is:
N+ = (0.315)*3,650 = 1,150
These are the two values.
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I need help on this question
Answer:
Step-by-step explanation:
I think it’s b
Tangent ratios can be greater than or equal to 1 because...
Tangent ratios can be greater than or equal to 1 because acute angle is between 45 degrees and 90 degrees.
If the opposite side is longer than the adjacent side, then the tangent ratio will be greater than 1.
Similarly, if the opposite side is equal in length to the adjacent side, then the tangent ratio will be equal to 1.
In general, the tangent ratio can be greater than or equal to 1 when the opposite side is longer or equal in length to the adjacent side. This occurs when the acute angle is between 45 degrees and 90 degrees.
It is important to note that when the acute angle is less than 45 degrees, the tangent ratio will always be less than 1. Conversely, when the acute angle is greater than 90 degrees, the tangent ratio will be negative and less than 1.
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Suppose that Leni and Thom are lawyers and each has a taxable income of $230,000. They can't decide if they should be married in December or in January. If they marry in December, then they are considered married for the entire tax year and could file a joint return. If they get married in January of the next year, they would file a separate return each as a single taxpayer. Examine Schedules X and Y-1. Which filing status would yield the lower tax? If so, by how much? is there really a marriage penalty?
Answer:
1. Neither would yield the lower tax.
2. (not sure yet about how much)
3. and there is not really a marriage penalty.
What is the definition LCD
Answer:
The definition of LCD is Least Common Denominator.
Step-by-step explanation:
Question 2:
LCD of 7/8 and 3/4 is 8
Question 3 :
7/8 - 3/4
7/8 - 6/8
1/8
Hope this helps :) !!
Answer:
Step-by-step explanation: First of all, the full form of LCD is "Lowest Common Denominator"
LCD is the least common denominator that can be used for all types of fractions.
For example, if we have the fractions 1/2 and 2/3, we can write:
1/2 as 2/4,3/6 or 4/8
and
2/3 as 4/6,6/9 or 8/12
Hence, the least common denominator of 1/2 and 2/3 is 6, since it is present in the denominators of all the fractions.
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A random sample of 100 middle schoolers were asked about their favorite sport. The following data was collected from the students.
Sport Basketball Baseball Soccer Tennis
Number of Students 17 12 27 44
Which of the following graphs correctly displays the data?
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
The graph that correctly displays the data is this: C. bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44.
How to obtain the correct graphA graph plots values to show the relationship between two variables often depicted by the x and y axes. The correct graph to display this data is a bar graph with the title "Favorite Sport" and the x-axis labeled "Sport" and the y-axis labeled "Number of Students."
The first bar should be labeled "Basketball" and go to a value of 17, the second bar should be labeled "Baseball" and go to a value of 12, the third bar should be labeled "Soccer" and go to a value of 27, and the fourth bar should be labeled "Tennis" and go to a value of 44.
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Amazon's "Smile" logo is a parabola and is modeled by h(x) =-0.03x + 0.4x, where h(x) is the height of
the Smile (in feet) at a distance of x (in feet) from one side. Find the Axis of Symmetry. How high is the Smile
at the Axis of Symmetry?
The axis of symmetry is located at a distance of 6.67 feet from one side of the smile and the height of the smile at the axis of symmetry is 0.891 feet.
The equation of the Amazon Smile logo is given by:
h(x) = -0.03x² + 0.4x
To find the axis of symmetry, we need to use the formula:
x = -b / 2a
where a and b are the coefficients of the quadratic equation ax² + bx + c = 0.
a = -0.03 and b = 0.4.
x = -0.4 / 2(-0.03) = 6.67 feet
Therefore, the axis of symmetry is located at a distance of 6.67 feet from one side of the smile.
To find the height of the smile at the axis of symmetry, we need to substitute x = 6.67 into the given equation:
h(6.67) = -0.03(6.67)² + 0.4(6.67) = 0.891 feet
Therefore, the axis of symmetry is located at a distance of 6.67 feet from one side of the smile and the height of the smile at the axis of symmetry is 0.891 feet.
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help help help urgenttt.. i need this done today by 11:59 pmm
The one less likely to be picked is the one with less & (Vice Versa).
To find the probability: (#of paper clips/total amount of items)
Ima be giving brainliest plus help!!!!!!!
Answer:
32 degrees
Step-by-step explanation:
Recall the three main trig functions: sine, cosine, and tangent.
When using sine, we divide the opposite side from the angle by the hypothenuse.
When using cosine, we divide the adjacent side of the angle by the hypothenuse.
When using tangent, we divide the opposite side from the angle by the adjacent side to the angle.
Since we are given the opposite and adjacent sides, we'll use tangent.
We set up the equation like normal:
tan x [tex]= \frac{13}{21}[/tex]
Now, when finding the angle measurement using trig, we must use the opposing trig function, arcsine, arccosine, and arctangent. The opposing trig function is arctangent. We have to move arctangent to the other side, so that it can be used with the fraction, so:
[tex]x = arctan(\frac{13}{21} )[/tex]
(You would also write arctan, as tan with an exponent of -1) Now, just punch the right side of the equation into a calculator. The nearest degree is 32.
Therefore, the answer is 32 degrees. If you got something different, make sure your calculator is in degrees, not radians! (They are usually abbreviated as DEG and RAD.)
Please help!!!!!!!!
The following data shows the grades that an 8th grade mathematics class received on a recent exam.
{99, 94, 91, 79, 88, 94, 92, 93, 90, 89, 77, 75, 65, 90, 87, 93, 92, 82, 65, 60, 78}
Part A: Determine the best graphical representation to display the data. Explain why the type of graph you chose is an appropriate display for the data. (6 points)
Part B: Explain, in words, how to create the graphical display you chose in Part A. Be sure to include a title, axis label(s), scale for axis if needed, and a clear process of how to graph the data. (6 points)
The line plot of the data points is added as an attachment
The best representation and whyPart A:
A line plot or dot plot would be an appropriate graphical representation for this data set. A line plot would show each data point on a number line with an X above the value,
This graph would be appropriate for displaying this data because the data set is relatively small and the values are discrete (whole numbers), making it easy to see the frequency and distribution of the data points.
Part B:
To create a line plot or dot plot for this data set, you would first need to create a number line that spans the range of values in the data set.
In this case, the range of values is from 91 to 125, so the number line would include all values between these two numbers.
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PLEASE HELP!!!
A principal of $4200 is invested at %8 interest, compounded annually. How much will the investment be worth after 12 years?
Answer:
$10,244.14 after 12 years
Step-by-step explanation:
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
A = the final amount of the investment
P = the principal amount ($4200 in this case)
r = the annual interest rate (8% or 0.08 as a decimal)
n = the number of times the interest is compounded per year (once annually in this case)
t = the number of years the money is invested (12 years in this case)
Substituting the given values into the formula, we get:
A = 4200(1 + 0.08/1)^(1*12)
A = 4200(1.08)^12
A = 4200(2.44140625)
A = $10,244.14 (rounded to the nearest cent)
What is ¨the surface area of a tissue box¨ unit of measurement
A - Square meters
B - Yards
C - Cubic inches
D - Cubic feet
E - Square centimeters
The surface area of a tissue box is a measure of the total area that the surface of the box occupies. Out of the options given, A - Square meters and E - Square centimetres are both square units and could be used to measure the surface area of a tissue box.
Explain surface area
The surface area is the total area that covers the outer surface of a three-dimensional object. It is calculated by adding the areas of all the faces or surfaces of the object.
Explain area
The area is the measure of the size of a two-dimensional surface or region. It is expressed in units of square units (e.g., square meters, square inches).
According to the given information
The surface area of a tissue box is a measure of the total area that the surface of the box occupies. Since area is measured in square units, the correct unit of measurement for the surface area of a tissue box would be a square unit. Out of the options given, A - Square meters and E - Square centimeters are both square units and could be used to measure the surface area of a tissue box.
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kelly has 3 bags whith 8 pieces of candy in each bag.lori has 8 bags whith 6 pieces candy in each . how much more candy does lori have then kelly
If Kelly has 3 bags containing 8 pieces each, and Lori has 8 bags containing 6 pieces each, then Lori have 24 candies more than Kelly.
If Kelly has 3 bags which contains 8 pieces of candy in each bag,
then Total number of candies with Kelly is = 3×8 = 24 candies,
If Lori has 8 bags which contains 6 pieces of candy in each bag,
then Total number of candies with Lori is = 8×6 = 48 candies,
So, to find how much more candy Lori has than Kelly, we need to subtract the number of pieces of candy Kelly has from the number Lori has;
The equation to find the difference in candies is written;
⇒ Difference = (total candies with Lori) - (total candies with Kelly),
⇒ Difference = 48 - 24 = 24 candies;
Therefore, Lori has 24 more pieces of candy than Kelly.
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Function f is a logarithmic function with a vertical asymptote at x=0 and an x-intercept at (4,0). The function is decreasing over the interval (0, ∞)
The interval over which both functions are positive is (4, ∞).
How to write an equation for the transformed logarithm?In Mathematics and Geometry, the general form of a logarithm function is represented by the following mathematical equation:
f(x) = alog(±x + h) + k
Where:
a represent the scale factor of the logarithmic graphh represent a horizontal translation.k represent a vertical translation.x represent the base.Based on the given logarithm function g(z) = log₂(z + 3) - 2, we can reasonably infer and logically deduce that it is a vertical translation of this logarithmic function f(z) = log₂(z + 3).
Additionally, the logarithm function g(z) has a vertical asymptote at z = -3 and would be positive on the interval (-3, ∞). This ultimately implies that, an intersection of the intervals over which each function is positive is given by;
Intersection of intervals = (4, ∞) ∪ (-3, ∞).
Positive interval = (4, ∞).
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Which of the following are examples of rational numbers? Select all that apply.
√4+√16
√5 +√36
√9+√24
2* √4
√49 • √81
3√12
The rational numbers in the list of options are √4+√16, 2* √4 and √49 • √81
The examples of rational numbers among the given options are:
2√4: √4 is equal to 2, so 2√4 = 2*2 = 4, which is a rational number.√49 • √81: √49 is equal to 7 and √81 is equal to 9, so √49 • √81 = 7 • 9 = 63, which is a rational number.√4+√16: √4 is equal to 2 and √16 is equal to 4, so √4+√16 = 2 + 4 = 6, which is a rational number.The other options are not rational numbers:
√5+√36: √5 is an irrational number, so √5+√36 is not a rational number.√9+√24: √24 is an irrational number, so √9+√24 is not a rational number.3√12: √12 is equal to 2√3, so 3√12 = 3 • 2√3 = 6√3, which is not a rational number.Read more about rational numbers at
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The length of a rectangle is three feet less than two times the width. The perimeter is 27 feet. Find the dimensions.
Answer:
l = 2w - 3
2(2w - 3) + 2w = 27
4w - 6 + 2w = 27
6w - 6 = 27
6w = 33, so w = 5.5 feet and l = 8 feet
Answer:
Width: 5.5 feet
Length: 8 feet
Step-by-step explanation:
Let's begin by assigning variables to stand in for the rectangle's width and length.
Let x represent the rectangle's width.
The length is three feet shorter than double the width, according to the problem. As a result, the length may be written as:
2x - 3
The lengths of all the sides make up a rectangle's perimeter, which in this instance is:
2w + 2l
By substituting the width and length measurements we discovered:
2x + 2(2x - 3)
Simplifying:
2x + 4x - 6 = 27
6x = 33
x = 5.5
The rectangle is 5.5 feet wide as a result.
We may change x into the expression we discovered earlier to figure out the length:
2(5.5) - 3 = 8
The rectangle is 8 feet long as a result.
As a result, the rectangle's measurements are:
Width: 5.5 feet
Length: 8 feet
research conducted a few years ago showed that 12% of uw-platteville students had traveled outside the us. uw-platteville has recently implemented a new study abroad program and results of a new survey show that out of the 100 randomly sampled students 35 have traveled abroad. to know if the proportion of students at uw-platteville who have traveled abroad has increased after the implementation of the study abroad program, what is the appropriate null and alternative hypothesis?
The null hypothesis is that the proportion of students who have traveled abroad is still 12%, while the alternative hypothesis is that the proportion has increased and is now greater than 12%.
The appropriate null hypothesis is that the proportion of students at UW-Platteville who have traveled abroad remains the same as before the implementation of the study abroad program. The alternative hypothesis is that the proportion of students who have traveled abroad has increased after the implementation of the program.
Mathematically:
H0: p = 0.12
Ha: p > 0.12
where p is the true proportion of students at UW-Platteville who have traveled abroad.
To test this hypothesis, we can use a one-tailed z-test for proportions. Using the given sample information, we can calculate the test statistic as:
z = (0.35 - 0.12) / sqrt((0.12 * 0.88) / 100) = 3.87
where 0.88 is the complement of 0.12, and sqrt denotes the square root. The critical value for a one-tailed test at the 0.05 level of significance is 1.645.
Since the test statistic (3.87) is greater than the critical value (1.645), we reject the null hypothesis and conclude that there is sufficient evidence at the 0.05 level to support the claim that the proportion of students who have traveled abroad has increased after the implementation of the study abroad program.
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what are the points that are contained in the graph of the equation?
Answer:
(0, [tex]\frac{1}{2}[/tex] ) , (1, [tex]\frac{5}{4}[/tex] ) , (2, 2 )
Step-by-step explanation:
to determine which points are contained in the graph.
substitute the x- coordinate of each point into the equation and if the value obtained is equal to the y- coordinate of the point then it is contained in the graph.
(0, [tex]\frac{1}{2}[/tex] )
y = [tex]\frac{3}{4}[/tex] (0) + [tex]\frac{1}{2}[/tex] = 0 + [tex]\frac{1}{2}[/tex] = [tex]\frac{1}{2}[/tex] = y- coordinate ← contained in graph
(1, [tex]\frac{5}{4}[/tex] )
y = [tex]\frac{3}{4}[/tex] ( 1) + [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{4}[/tex] + [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{4}[/tex] + [tex]\frac{2}{4}[/tex] = [tex]\frac{5}{4}[/tex] = y- coordinate ← contained in graph
([tex]\frac{1}{2}[/tex], 0 )
y = [tex]\frac{3}{4}[/tex] ([tex]\frac{1}{2}[/tex] ) + [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{8}[/tex] + [tex]\frac{4}{8}[/tex] = [tex]\frac{7}{8}[/tex] ≠ y- coordinate ← not contained in graph
(2, 2 )
y = [tex]\frac{3}{4}[/tex] (2) + [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{2}[/tex] + [tex]\frac{1}{2}[/tex] = [tex]\frac{4}{2}[/tex] = 2 = y- coordinate ← contained in graph