Is 60 a rational number
Answers
Answer:
I think yes I. not sure I am pretty tired
The number 60 is real and is a rational number since it can be written in the form \(\dfrac{p}{q}\).
Given the number 60.
It is required to find whether the number 60 is rational or not.
Rational numbers can be defined as numbers that can be written in the form of fractions, that is \(\dfrac{p}{q}\), where p and q must be integers.
If a number is not rational, then it is an irrational number.
Here, the number is 60.
60 can be written in the form \(\frac{60}{1}\), \(\frac{120}{2}\), \(\frac{180}{3}\), ...
That is 60 can be written as the fraction of the integers.
Hence, the number 60 is a rational number.
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Related Questions
Which of the following sets contain only rational numbers that are integers?
F
(6, -3, 1.25}
G
(8, 4, 0.5)
H
(-8, 4/3,✔️16, 25)
J
(16/4,-8, 7, √5)
Answers
The set that contains only rational numbers that are integers is:
H: (-8, 4/3, 16, 25)
The number -8 is an integer, 16 and 25 are also integers, and 4/3 is a rational number, but not an integer.
The other sets contain numbers that are not integers or are not rational:
F: contains the rational number 1.25, which is not an integer.
G: contains the rational number 0.5, which is not an integer.
J: contains the irrational number √5, which is not rational and not an integer.
at a school pep rally, a group of sophomore students organized a free raffle for prizes. they claim that they put the names of all of the students in the school in the basket and that they randomly drew 36 names out of this basket. of the prize winners, 6 were freshmen, 14 were sophomores, 9 were juniors, and 7 were seniors. the results do not seem that random to you. you think it is a little fishy that sophomores organized the raffle and also won the most prizes. your school is composed of 30% freshmen, 25% sophomores, 25% juniors, and 20% seniors. a. what are the expected frequencies of winners from each class? b. conduct a significance test to determine whether the winners of the prizes were distributed throughout the classes as would be expected based on the percentage of students in each group. report your chi square and p values.
Answers
The winners of the prizes are distributed throughout the classes as per the percentage of students in the respective group.
The total number of surveyed students is 36.
We calculate the expected number of students for each class is:
Class
Expected Frequency
Freshman
30% of 36 = 10.8
Sophomore
25% of 36 = 9
Junior
25% of 36 = 9
Senior
20% of 36 = 7.2
(b)
We set up:
H0: The number of observed winners is indifferent to the number of expected winners.
H1: The number of observed winners is not indifferent to the number of expected winners.
The Test Statistic Calculation Table:
Class Observed Frequency (fi) Expected Frequency (ei) (fi -ei )² /ei
Freshman 6 10.8 2.1333
Sophomore 14 9 2.7778
Junior 9 9 0
Senior 7 7.2 0.0056
Total = 36 36 4.9167
The calculated
\(x^{2}\) = 4.9167
The p-value for 4 - 1=3 degree of freedom for the above test score is 0.177999.
(c)
Since p-value (=0.177999) > α0..05 (standard level of significance),
H0 is failed to be rejected.
The number of observed winners is concluded to be indifferent to the number of expected winners, i.e., the winners of the prizes are distributed throughout the classes as per the percentage of students in the respective group.
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we are worried that is measured with error in our survey. let tvhours denote the reported hours of television viewing per week. what do the classical errors-in-variables (cev) assumptions require in this application? do you think the cev assumptions are likely to hold? explain.
Answers
The classical errors-in-variables (CEV) assumptions require that the measurement error in tv hours is not related to the true value of television viewing.In other words, the error should be random and not correlated with the actual amount of time spent watching TV.
Additionally, the CEV assumptions require that the measurement error has a mean of zero and a constant variance. Whether or not the CEV assumptions are likely to hold in this application depends on several factors. One important consideration is the accuracy of the survey instrument used to collect data on tv hours.
If the survey is poorly designed or administered, it may introduce systematic measurement error that is correlated with the true value of television viewing.
Another important factor is the population being surveyed. If the population is highly diverse with respect to television viewing habits, it may be difficult to ensure that the CEV assumptions hold for all subgroups.
Overall, while it is possible that the CEV assumptions hold in this application, it is also possible that they do not. Researchers should carefully consider the potential sources of measurement error and take steps to minimize them if possible.
Additionally, sensitivity analyses can be conducted to explore the robustness of study results to violations of the CEV assumptions.
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The value of x in the given proportion is:
x/9= 9/3
(those are fractions)
A 12
B 15
C 45
D None of these choices are correct.
can someone please help me??
Answers
Answer:
D None of these choices are correct.
Step-by-step explanation:
The value of x is 27.
\(\frac{x}{9} = \frac{9}{3}\), x = 9 x \(\frac{9}{3}\) = 27
PLS HELP QUICKKK its almost due
Answers
I think its the second one. I hope it is
Solve, be sure to show each step under the original problem for any credit.
1 =k/12 +5
Answers
1. subtract 5 from both sides
-4 = k/12
2. multiply 12 from both sides to get k alone
-48 = k
someone please help me with this question, I've been sitting here for a while trying to figure it out.
Answers
Answer:
B) h=10
Step-by-step explanation:
5sq rt 2=sq rt 50
Pythagorean theorem
(sq rt 50)^2=50
h^2=50^2+50^2=100^2
h=10
There were 53 competitors in a downhill skiing event. Their times in seconds) are shown below. Complete parts a through d below 98.06 98.09 98.46 9847 99.09 98.96 98 99 99.12 99.35 99.57 99.98 100.08 100.11 100.28 100.64 101.32 101.06 101.25 101.34 101.39 102.48 101.99 103.01 103.87 104.11 103.64 104.15 104.27 104.37 104.33 104.52 105.47 105.48 105.69 105.61 113.02 105.73 109.65 106.92 116.11 117.43 117.59 99.09 100 67 103.12 105.02 114.55 99.11 100.77 103.18 105.39 115.97 a) The mean time was 103 59 seconds, with a standard deviation of 5 16 seconds if the Normal model is appropriate what percent of times will be less than 98 43 secon (Round to the nearest integer os needed) b) What is the actual percent of times less than 98.43 seconds? (Round to one decimal place as needed) c) Do the two percentages agree? Why or why not? OA. Yes, because a Normal probability plot shows that the Normal model is appropriate OB. No, because a Normal probability plot shows that the Normal model is appropriate O C Yes, because a Normal probability plot shows that the Normal model is not appropriate O D. No, because a Normal probability plot shows that the Normal model is not appropriate
Answers
The two percentages do not agree. Hence, option D is correct.
a) The mean time was 103.59 seconds, with a standard deviation of 5.16 seconds. If the Normal model is appropriate, the percentage of times that will be less than 98.43 seconds can be calculated as follows:
z = (x - μ) / σz = (98.43 - 103.59) / 5.16z = -1.00Using z-score table, we can determine that the percentage of times that will be less than 98.43 seconds is approximately 15%.
Therefore, the percentage of times that will be less than 98.43 seconds is 15%.
(Round to the nearest integer as needed)Hence, option A is correct.b) The actual percentage of times less than 98.43 seconds can be calculated by finding the number of competitors that finished with a time less than 98.43 seconds and dividing that number by the total number of competitors.
98.06, 98.09, 98.46, 98.47, 98.96, 98, 99, 99.12, 99.35, 99.57, 99.98, 100.08, 100.11, 100.28, 100.64, 101.32, 101.06, 101.25, 101.34, 101.39, 102.48,
101.99, 103.01, 103.87, 104.11, 103.64, 104.15, 104.27, 104.37, 104.33, 104.52, 105.47, 105.48, 105.69, 105.61, 113.02, 105.73, 109.65, 106.92, 116.11, 117.43, 117.59, 99.09, 100.67, 103.12, 105.02, 114.55, 99.11, 100.77, 103.18, 105.39, 115.97
There are no competitors who finished with a time less than 98.43 seconds. Therefore, the actual percentage of times less than 98.43 seconds is 0%. (Round to one decimal place as needed)Thus, option D is correct.c) The two percentages do agree.
This is because the Normal probability plot shows that the Normal model is not appropriate.
Therefore, the actual percentage of times less than 98.43 seconds is 0%, which is different from the percentage that was calculated using the Normal model. Since the Normal model is not appropriate, the actual percentage of times is more accurate.
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in how many ways can a committee of two democrats and three republicans be formed from a froup of eight democrats and eleven republicans
Answers
the total way the committee formed is 3080.
What is combination?
A combination is a choice made in mathematics from a group of different elements when the order of the choices is irrelevant (unlike permutations). For instance, if three fruits, such as an apple, an orange, and a pear, are supplied, there are three possible pairings of the two: an apple and a pear. Formally speaking, a k-combination of a set S is a subset of S's k unique components. In other words, two combinations are the same if and only if they have the same members. (It is not important how the individuals in each set are arranged.) The quantity of k-combinations for a set with n components
The available candidates from a group are 8 Democrats and 11 Republicans.
Three Democrats and two Republicans must be included on the committee that we choose.
Thus, from a pool of 11 Republicans and 8 Democrats, we must select 3 each.
Both 8C3 and 11C2 approaches are viable for achieving this.
8C3 * 11C2 = 3080 are the total ways to form this committee.
Hence the total way the committee formed is 3080.
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Consider the arithmetic sequence.
16, 14, 12, 10, ...
Given that the sequence is represented by the function f(n), what are the values of f(1) and the common difference?
Answers
Answer:
Work shown below!
Step-by-step explanation:
f(n) = 16 - 2(n - 1)
f(1) = 16 - 2(1 - 1)
f(1) = 16 - 2(0)
f(1) = 16
Common difference is -2
Ms. Reiger’s students found a total of 16 bird feathers. The line plot shows the lengths, in inches, of the bird feathers found by the students
Look at the line plot, and then select the two correct statements about the bird feathers.
The difference between the lengths of the shortest feather and the longest feather is 318 inches.
A. The difference between the lengths of the shortest feather and the longest feather is 238 inches.
B. The combined length of the two longest feathers is 828 inches.
C. The combined length of the shortest feather and the longest feather is 738 inches.
D. The combined length of the shortest feather and the longest feather is 618 inches.
Answers
Answer:
B
Step-by-step explanation:
Ashton carried out a survey asking people about the pets they own. 70% of the people who responded own a pet and 30% do not own a pet. 10% of the people who own a pet own a rabbit. What percentage of the people who responded own a rabbit?
Answers
Answer:
my answer is 60
Step-by-step explanation:
when the people who respond 70-30 =40
40-10=30 the ans is 30
test the hypothesis that the mean weight of the two sheets is equal (μ1−μ2)against the alternative that it is not (and assume equal variances). find the t-stat to 3 decimal places.
Answers
To test the hypothesis that the mean weight of two sheets is equal (μ1 - μ2) against the alternative that it is not, and assuming equal variances, we can use a two-sample t-test. The t-statistic can be calculated using the following formula:
t = (x1 - x2) / (s_p * sqrt(1/n1 + 1/n2))
where:
x1 and x2 are the sample means of the two sheets,
s_p is the pooled standard deviation,
n1 and n2 are the sample sizes.
The pooled standard deviation (s_p) can be calculated using the following formula:
s_p = sqrt(((n1 - 1) * s1^2 + (n2 - 1) * s2^2) / (n1 + n2 - 2))
where:
s1 and s2 are the sample standard deviations.
To calculate the t-statistic, we need the sample means, sample standard deviations, and sample sizes.
Once you provide the specific values for these variables, I can assist you in calculating the t-statistic to 3 decimal places.
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To test the hypothesis that the mean weight of the two sheets is equal (μ1 - μ2) against the alternative that it is not, we can use a paired t-test assuming equal variances. The paired t-test is used when we have paired data or measurements on the same subjects or objects.
The t-statistic for a paired t-test is calculated as follows:
t = (X1 - X2) / (s / √n)
where X1 and X2 are the sample means of the two samples, s is the pooled standard deviation, and n is the number of pairs.
Please provide the sample means, standard deviation, and sample size for each sheet so that we can calculate the t-statistic to 3 decimal places.
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Select the correct answer from each drop-down menu. Consider the following sequence of numbers 3, -9, 27, -81
Answers
Answer:
-243
Step-by-step explanation:
Each value is multiplied by -3. 3 x -3 = -9, -9 x -3 = 27, and the rest goes the same
Answer:
The common ratio of the sequence is -3
The sum of the first five terms of the sequence is 183
Step-by-step explanation:
I got it right, but -3*3= -9 and you just keep multiplying by -3 to get 183
Which rational number is the additive inverse of -0.75?
Negative three-fourths
StartFraction 7 over 5 EndFraction
Three-fourths
Negative four-thirds
Answers
Answer:
Three-fourths.
Step-by-step explanation:
The additive inverse produces a zero result:
-0.75 + 0.75 = 0
so it is 0.75 or 3/4.
Answer:
three- fourths
Step-by-step explanation:
The opposite, or additive inverse, of a number is the same distance from 0 on a number line as the original number, but on the other side of 0. Zero is its own additive inverse. In other words, the additive inverse of a rational number is the same number with opposite sign.
Suppose $m$ is a two-digit positive integer such that $6^{-1}\pmod m$ exists and $6^{-1}\equiv 6^2\pmod m$. What is $m$
Answers
The value of $m$ is $43$.
The equation $6^{-1}\equiv 6^2\pmod m$ implies that $6^{-1}$ is a valid inverse of $6$ modulo $m$. This means that multiplying $6^{-1}$ by $6$ must result in the remainder $1$ when divided by $m$.
To find the value of $m$, we can then set up the equation:
$0\equiv 215\pmod m$
and find all possible values of $m$ that make this equation true.
Multiplying $6^{-1}\equiv 6^2\pmod m$ by $6$, we get $1\equiv 6^3\pmod m$, so $0\equiv 215\pmod m$. So, $m$ must be a divisor of $215$. The only 2-digit divisor of $215$ is $43$.
Therefore, $m$ is a two-digit number, the only possible value of $m$ is $43$.
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In testing for differences between the means of 2 independent populations the null hypothesis is?
Answers
In testing for differences between the means of 2 independent populations the null hypothesis is zero.
What is Null hypothesis?This is defined as a statistical hypothesis which has no statistical significance in a set of given observations.
In testing for differences between the means of 2 independent populations the null hypothesis is the difference between the two population means and is not significantly different from zero which is denoted below:
H₀: µ₁ - µ₂ = 0
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Given that the primitive basis vectors of a lattice are a = (a/2)(i + j), b = (a/2) + k), and c = (a/2)(k + i), where i, j, and k are the usual three unit vectors along cartesian coordinates, what is the Bravais lattice?
Answers
The Bravais lattice for the given primitive basis vectors is a centered rectangular lattice.
The primitive basis vectors are a = (a/2)(i + j), b = (a/2)(1 + k), and c = (a/2)(k + i). These vectors represent the translations in three orthogonal directions of a unit cell in the lattice.
By comparing the basis vectors, we can determine the shape of the unit cell.
The vector a is parallel to i + j, which means it spans the x-y plane.
The vector b is parallel to 1 + k, which spans the y-z plane.
The vector c is parallel to k + i, which spans the z-x plane.
Based on the above calculations, we find that the unit cell has sides along the x, y, and z directions. Furthermore, the lattice is centered rectangular because the lengths of the sides are different, indicating a non-cubic structure.
In summary, the Bravais lattice for the given primitive basis vectors is a centered rectangular lattice, as determined by the arrangement and orientations of the basis vectors.
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Solve the equation.
- 5x - 3 = 2x + 11
.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Answers
Answer:
= 14/3
Step-by-step explanation:
add 3 to both sides of the equation
A dressmaker needs to cut 4-inch pieces of ribbon from rolls of ribbon that are 12 feet in length. How many 4-inch pieces can the dressmaker cut from 5 of these rolls of ribbon?
Before you try that problem, answer the question below.
How many inches of ribbon does the dressmaker have, in total?
Answers
Answer:
15 pieces
Step-by-step explanation:
First, 4 goes into twelve 3 times. since it goes in three times, and you have 5 rolls, you would just multiply the two together.
3*5 = 15 pieces
Question #1
First we have to convert feet to inches.
Knowing that 1 foot is 12 inches we just need to multiply our values by 12.
Meaning that 12 feet of a roll of ribbon is basically 144 inches.
That isn't our final answer because he has 5 rolls so we multiply our answer by 5.
12×12 = 144 ← how many inches are in a single roll
144×5 = 720 So in total there are 720 inches in total.
Question #2
Now that we answered one of the questions we can use this information to answer the other question asking us how many 4 inch pieces can he make from the 5 rolls.
As mentioned above we know the 5 rolls are equivalent to 720 inches..
So we will take that number and divide it by 4.
720÷4 = 180
Meaning that 180 4-inch pieces can be made.
Statement
Therefore the dressmaker has 720 inches of ribbon and with that is able to make 180 4 inch pieces from it.
As a certain object falls, its position s (in meters) above ground after t seconds is given by s(t) = 40 - 5t². (a) What is the average velocity of the object on the interval from t = 1 to the time 0.5 seconds later? m/s (b) What is the average velocity of the object on the interval from t = 1 to the time 0.1 seconds later? m/s (c) Use algebra to find a simplified expression for the average velocity from t = 1 to the time h seconds later (h+ 0). m/s (d) (e) What does this average velocity tend toward for h closer and closer to 0 (smaller and smaller time interval)? m/s Using the results of part (d), find the instantaneous velocity of the object at 1 second? m/s
Answers
a) The average velocity will be -5 m/s. (b) The average velocity is -9.5 m/s. (c) The average velocity is -10h m/s. (d) The average velocity -10 m/s,(e) The instantaneous velocity -10 m/s.
(a) To find the average velocity on the interval from t = 1 to 0.5 seconds later, we calculate the change in position and divide it by the change in time. The change in position is s(0.5) - s(1) = (40 - 5(0.5)²) - (40 - 5(1)²) = -2.5 meters. The change in time is 0.5 - 1 = -0.5 seconds. Therefore, the average velocity is -2.5 / -0.5 = -5 m/s.
(b) Following the same method, we find the change in position to be s(1.1) - s(1) = (40 - 5(1.1)²) - (40 - 5(1)²) = -0.5 meters. The change in time is 1.1 - 1 = 0.1 seconds. Hence, the average velocity is -0.5 / 0.1 = -9.5 m/s.
(c) The average velocity from t = 1 to h seconds later can be found by calculating the change in position as s(1 + h) - s(1) and dividing it by the change in time h. Simplifying the expression, we get (-5h - 5h²) / h = -10h m/s.
(d) As h approaches 0, the average velocity expression becomes -10h. Since h is getting smaller and smaller, the average velocity tends toward -10 m/s.
(e) The instantaneous velocity at 1 second can be found by taking the derivative of the position function with respect to time and evaluating it at t = 1. The derivative of s(t) = 40 - 5t² is ds/dt = -10t. Substituting t = 1, we get ds/dt = -10(1) = -10 m/s. Therefore, the instantaneous velocity of the object at 1 second is -10 m/s.
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HELP PRETTY PLEASEE !!!!!!!!!!!!
Answers
Answer:
Im 99% sure its the first one
Step-by-step explanation:
Answer:
Algebraic terms are separated by x, +, -, / except =
A complex number of the form z = a + bi has an absolute value of 4.00. What could the values of a and b be?
a = 1.6, b = 2.3
a = 1.6, b = 2.5
a = 1.9, b = 2.1
a = 2.1, b = 3.4
Answers
Answer:
According to the question z must be equal to 4. So value of a+b=z or a+b=4
Lets try each of the options
A) a+b
1.6+2.3=3.9 which is not equal to 4
So option a is not the asnwer.
B) a+b = 1.6+2.5= 4.1 which is not equal to 4
C) a+b= 1.9+2.1= 4.00 which is equal to 4
D) a+b= 2.1+3.4= 5.5 which is not eqaul to 4
Thus, we have OPTION C AS THE CORRECT ANSWER
Answer:
It's NOT C, it's D!
Step-by-step explanation:
E=5s^2. If s is doubled, what happens to E?
Answers
I assume it stays the same
Suppose triangle TIP and triangle TOP are isosceles triangles. Also suppose that TI=5, PI=7, and PO=11. What are all the possible lengths TP? Enter the possible values, separated by commas.
Answers
Answer:
5, 7.
Step-by-step explanation:
If both triangles are isosceles, then, for each triangle, two of their sides must be equal. Since TI and PI are different, then TP is either equal to TI or PI.
That being said, TO will necessarily be equal to PO, which is 11, and the possible values for TP are:
If TP = TI, then TP = 5
If TP = PI. then TP = 7.
Determine the TAYLOR’S EXPANSION of the following function:
2
(1 + z)3 on the region |z| < 1.
Please show all work and circle diagrams.
Answers
The coefficients of the function (1 + z)^3 can be esxpressed as an infinite series:
(1 + z)^3 = 1 + 3z + 3z² + z³ + ...
The Taylor expansion of the function (1 + z)^3 on the region |z| < 1 can be obtained by applying the binomial theorem. The binomial theorem states that for any real number n and complex number z within the specified region, we can expand (1 + z)^n as a series of terms:
(1 + z)^n = C₀ + C₁z + C₂z² + C₃z³ + ...
To find the coefficients C₀, C₁, C₂, C₃, and so on, we use the formula for the binomial coefficients:
Cₖ = n! / (k!(n - k)!)
In this case, n = 3, and the region of interest is |z| < 1. To obtain the coefficients, we substitute the values of n and k into the binomial coefficient formula. After calculating the coefficients, we can express the function (1 + z)^3 as an infinite series:
(1 + z)^3 = 1 + 3z + 3z² + z³ + ...
By expanding the function using the binomial theorem and calculating the coefficients, we have obtained the Taylor expansion of (1 + z)^3 on the region |z| < 1.
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Han is multiplying 10x^4 by 0.5x^3 and gets 5x^7. He says that 0.5^3 is not a polynomial because 0.5 is not an integer. What is the error in Han’a thinking? Explain your reasoning
Answers
The error in Han’s thinking is that he takes 0.5 as the power of x instead of coefficient
What are polynomial expressions?Polynomial expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine what is the error in Han’s thinking?The polynomial expression is given as
The product of 10x^4 and 0.5x^3 to get 5x^7
The above implies that
10x^4 x 0.5x^3 = 5x^7
From the question, we have
Han says that 0.5^3 is not a polynomial because 0.5 is not an integer.
The above statement is false, because 0.5 is not a power of x; but instead it is a coefficient
So, the error in Han’s thinking is that he takes 0.5 as the power of x instead of coefficient
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Find the value of x in the equation: -2x-6=12−2x−6=12
Answers
Answer:
- 2 x - 6 = 12 x = -9
Step-by-step explanation:
If the frequency of a fm wave is 8.85 × 107 hertz, what is the period of the fm wave? a. 2.58 × 10–8 seconds b. 1.13 × 10–8 seconds c. 1.25 × 10–7 seconds d. 5.82 × 10–7 seconds
Answers
The time period of fm wave is found to be 1.13 x 10⁻⁸ sec.
Define the term frequency of the wave?The quantity of waves that pass a fixed point in a unit of time is referred to as frequency in physics.
A body in periodic motion undergoes how many cycles or vibrations in one unit of time, according to this definition.The rate at which current changes direction each second is known as frequency. It is expressed in hertz (Hz), a unit of measurement that is used internationally. One hertz is equal to one cycle per second. One hertz (Hz) is equivalent to one cycle per second. A complete alternating current or voltage wave is referred to as a "cycle.".For the given frequency of a fm wave = 8.85 × 10⁷ hertz.
Time period = 1 / frequency
T = 1 / 8.85 × 10⁷
T = 0.112 x 10⁻⁷ sec
T = 1.13 x 10⁻⁸ sec
Thus, the period of the fm wave is found to be 1.13 x 10⁻⁸ sec.
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Write the Standard Form of the line with x-intercept of 3 and y-intercept of 4.
Answers
Answer:
Use a model to find the sum of two fractions with the same denominator
Add fractions with a common denominator without a model
Add fractions with a common denominator that contain a variable h
Step-by-step explanation:
h