The correct factor of both terms of the expression 2d - 10 is,
⇒ 2
Since, A mathematical expression is a group of numerical variables and functions that have been combined using operations like addition, subtraction, multiplication, and division.
We have to given that;
An expression is,
⇒ 2d - 10
Since, There are two terms in expression which are 2d and - 10.
And,
2d = 2 × d
- 10 = - 2 × 5
Therefore, The correct factor of both terms of the expression 2d - 10 is,
⇒ 2
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suppose the parity check matrix for an [n, k] code c has rows (1, 1, 1, 0, 0),(1, 0, 0, 1, 0) and (0, 1, 0, 0, 1). find n and k. find the generator matrix for c. list the codewords in c.
The codewords of C are {[0 0 0 0 0], [1 0 1 1 0], [0 1 1 0 1], [1 1 0 1 1]}.
What is the value of n and k for a code c?The given parity check matrix H has 3 rows and 5 columns, which implies that code C has length n = 5 and dimension k = n - rank(H). To find k, we need to row-reduce H and count the number of linearly independent rows:
[1 1 1 0 0]
[1 0 0 1 0]
[0 1 0 0 1]
R2 = R2 - R1: [1 1 1 0 0]
[0 -1 -1 1 0]
[0 1 0 0 1]
R3 = R3 + R2: [1 1 1 0 0]
[0 -1 -1 1 0]
[0 0 -1 1 1]
R2 = -R2: [1 1 1 0 0]
[0 1 1 -1 0]
[0 0 -1 1 1]
R1 = R1 - R2: [1 0 0 1 0]
[0 1 1 -1 0]
[0 0 -1 1 1]
R3 = -R3: [1 0 0 1 0]
[0 1 1 -1 0]
[0 0 1 -1 -1]
The row-reduced form of H has 3 linearly independent rows, so k = n - rank(H) = 5 - 3 = 2.
To find the generator matrix G, we can use the method of systematic encoding. We first construct a matrix A consisting of k linearly independent columns of the identity matrix of size k:
[1 0]
[0 1]
Next, we compute the matrix B as the row-reduced form of the transpose of H:
[1 0 1]
[0 1 1]
We can then form the generator matrix G as:
[ A | B^T ] = [1 0 | 1 0 1]
[0 1 | 0 1 1]
Therefore, the generator matrix of C is:
[1 0 1 1 0]
[0 1 1 0 1]
To list the codewords of C, we can use the generator matrix to encode all possible combinations of the message bits. Since k = 2, there are 2^2 = 4 possible message vectors:
[0 0]
[0 1]
[1 0]
[1 1]
Encoding each message vector with the generator matrix G, we obtain the corresponding codewords:
[0 0 0 0 0]
[1 0 1 1 0]
[0 1 1 0 1]
[1 1 0 1 1]
Therefore, the codewords of C are {[0 0 0 0 0], [1 0 1 1 0], [0 1 1 0 1], [1 1 0 1 1]}.
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(please help!!!) What is the area of a right triangle with a base of 8 feet and a height of 12 feet?
20 ft2
32 ft2
48 ft2
96 ft2
Answer:
48 ft2
Step-by-step explanation:
area- 1/2 b*h-
1/2*8*12-
4*12-
48
find a function f such that f = ∇f. f(x, y, z) = 6y2z3i 12xyz3j 18xy2z2k
To find a function f such that f = ∇f, we need to take the gradient of f and set it equal to f:
f(x, y, z) = 6y^2z^3i + 12xyz^3j + 18xy^2z^2k
∇f = (∂f/∂x)i + (∂f/∂y)j + (∂f/∂z)k
= 0i + (12xz^3)i + (36y^2z^2)i + (12xyz^3)j + (36xy^2z)j + (36xy^2z)k
Setting ∇f = f, we get the following system of equations:
6y^2z^3 = 0
12xyz^3 = 12xz^3
18xy^2z^2 = 36y^2z^2
12xyz^3 = 36xy^2z
18xy^2z^2 = 36xy^2z
The first equation tells us that y or z must be 0. If y = 0, then the fourth and fifth equations reduce to 0 = 0, which is true for any value of x and z.
If z = 0, then the second and third equations reduce to 0 = 0, which is also true for any value of x and y.
Therefore, let's assume y is not equal to 0 and z is not equal to 0. Then we can simplify the system of equations to:
6z = 0
12x = 12
18y = 36
12y = 36
The first equation tells us that z must be 0, which derivatives our assumption. Therefore, we must have y = 2 and x = 1.
Substituting these values into f, we get:
f(x, y, z) = 6(2)^2(0)^3i + 12(1)(2)(0)^3j + 18(1)(2)^2(0)^2k
= 0i + 0j + 0k
= 0
Therefore, the function f(x, y, z) = 0 satisfies the condition f = ∇f.
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∆ABC~∆DEF area of triangle abc is 64cm² and area of triangle DEF is 9cm². if AB is 16cm what is De?
The calculated value of the length DE is 6 units
How to calculate the length DEFrom the question, we have the following parameters that can be used in our computation:
∆ABC~∆DEF Area of ABC = 64cmArea of DEF = 9cm².AB = 16cmusing the above as a guide, we have the following:
AB/DE = √Ratio of the areas of the triangles
substitute the known values in the above equation, so, we have the following representation
16/DE = √64/9
So, we have
16/DE = 8/3
Inverse the equation
DE/16 = 3/8
So, we have
DE = 16 * 3/8
Evaluate
DE = 6
Hence, the length DE is 6 units
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Find the length of the arc of the curve y=lnx over the interval: [1,5]. Round the answer to four decimal places
The length of the arc of the curve y=lnx over the interval [1,5] is approximately 43.85 units long.
To find the length of the arc of the curve y=lnx over the interval [1,5], we need to use the arc length formula:
L = [tex]\int_1^5[/tex] √(1+(dy/dx)²) dx
We can find dy/dx by taking the derivative of y=lnx:
y' = 1/x
Then, we can substitute into the formula:
L = [tex]\int_1^5[/tex] √(1+(1/x)²) dx
Using substitution, let x = eⁿ, so dx = eⁿ dt:
L = [tex]\int_1^{ln5}[/tex] √(1+e²ⁿ) eⁿ dt
We can use u-substitution with u=1+e²ⁿ, so du/dt=2e²ⁿ:
L = (1/2) [tex]\int_1^{26}[/tex] √(u) du
L = (1/2) * (2/3) * ([tex]26^\frac{3}{2}[/tex] - 1)
L = 43.85
Therefore, the length of the arc of the curve y=lnx over the interval [1,5] is approximately 43.85 units long.
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Can someone answer check please
Answer:
you got them all correct! good job :)
Step-by-step explanation:
The ________ could be used to describe a data set by itself, while ___________ would almost never be used to describe a data set by itself.
A. interquartile range ; mean
B. range ; mean
C. mean ; range
D. mean ; interquartile range
The mean could be used to describe a data set by itself, while interquartile range would almost never be used to describe a data set by itself.
Descriptive statistics :-
These are operations which are used to summarize certain characteristics a set of data has.
Descriptive statistics can be defined as a field of statistics that is used to summarize the characteristics of a sample by utilizing certain quantitative techniques.
It helps to provide simple and precise summaries of the sample and the observations using measures like mean, median, variance, graphs, and charts.
Univariate descriptive statistics are used to describe data containing only one variable. On the other hand, bivariate and multivariate descriptive statistics are used to describe data with multiple variables.
Mean and range deals with the full set of data while interquartile range measures just the middle half of the data and is denoted as option A.
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The cost of tuition at a college is $12,000 in 2014. The tuition price is increasing at a rate of 7.5% per year. What will be the cost of tuition in 2023?
The calculated cost of tuition in 2023 is 23006.86
What will be the cost of tuition in 2023?From the question, we have the following parameters that can be used in our computation:
Inital tuition, a = 12000
Rate of increase, r = 7.5%
Using the above as a guide, we have the following:
The function of the situation is
f(x) = a * (1 + r)ˣ
Substitute the known values in the above equation, so, we have the following representation
f(x) = 12000 * (1 + 7.5%)ˣ
In 2023, we have
x = 2023 - 2014
x = 9
So, we have
f(9) = 12000 * (1 + 7.5%)⁹
Evaluate
f(9) = 23006.86
Hence, the cost of tuition in 2023 is 23006.86
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Suppose you want to test the claim that μ < 65.4. Given a sample size of n = 35 and a level of significance of α = 0.01, when should you reject H0?A) Reject H0 if the standardized test statistic is less than -2.33.B) Reject H0 if the standardized test is less than -2.575.C) Reject H0 if the standardized test statistic is less than -1.96.D) Reject H0 if the standardized test statistic is less than -1.28.
The correct answer is B) Reject H0 if the standardized test is less than -2.575.
To determine whether to reject or fail to reject the null hypothesis, we need to calculate the standardized test statistic, which is the number of standard errors away from the mean that our sample statistic falls. In this case, we are given a sample size of n = 35, and we are testing the claim that the population mean is less than 65.4. We can use a one-tailed t-test with a level of significance of α = 0.01.
Using the t-distribution table with degrees of freedom (df) = n - 1 = 34 and a one-tailed α level of 0.01, we find that the critical value is -2.575. If our calculated t-statistic is less than -2.575, we would reject the null hypothesis.
Therefore, the correct answer is B) Reject H0 if the standardized test is less than -2.575.
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In a two population proportions problem, why is the use of the individual proportions for X and Y (i.e, p_x,q_x and p_y,q_y ) used for confidence intervals instead of the "common p" used in hypothesis testing? 1. It's not. Unless the sample sizes are outside the 1/3 to 3/1 ratio, the two methods result in the same boundaries 2. Because it's a Cl on the difference". If you're going in assuming that the proportions are in fact different, it doesn't make sense to support using an average p and q 3. It doesn't make any difference.......this is not the answer, don't pick this 4. It's not, you use the common p in both instances 5. Because it's a Cl on the "difference", so it makes sense to use an averaged value for p.
In a two population proportions problem, the use of individual proportions for X and Y (i.e., p_x, q_x, and p_y, q_y) is used for confidence intervals instead of the "common p" used in hypothesis testing.
The reason for this is that in hypothesis testing, we are assuming that the two population proportions are equal (i.e., p_x = p_y = p), which means that we can estimate p using the combined sample proportion. However, in a confidence interval problem, we are interested in estimating the difference between the two population proportions, and using the combined sample proportion to estimate p would not be appropriate. Instead, we use the individual sample proportions for X and Y to construct separate confidence intervals for each population proportion, which we can then use to estimate the difference between them.
In other words, when constructing a confidence interval for the difference in proportions, we are interested in estimating the variability of each population proportion separately, and not the variability of the combined sample proportion. This is why we use the individual sample proportions for X and Y in constructing confidence intervals, rather than the common sample proportion used in hypothesis testing.
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old mcdonald evenly divided his goats between his two children, lilly and hawk. careless lilly lost 35 goats and reckless hawk lost 40 of his goats. both lilly and hawk sold their herds, lilly sold each goat for $80 while hawk sold each of his goats for $60. if lilly got $1100 more than hawk for her herd, how many goats did mcdonald have?
Let the total number of goats that McDonald had be x. After evenly dividing them between Lilly and Hawk, each of them would have received x/2 goats. However, Lilly lost 35 goats, so she was left with (x/2 - 35) goats. Similarly, Hawk lost 40 goats and was left with (x/2 - 40) goats.
When Lilly sold each goat for $80, she earned (x/2 - 35) * $80 = 80x/2 - 35*80 = 40x - 2800 dollars. When Hawk sold each goat for $60, he earned (x/2 - 40) * $60 = 60x/2 - 40*60 = 30x - 2400 dollars.
Given that Lilly earned $1100 more than Hawk, we can set up the equation:
40x - 2800 = 30x - 2400 + 1100
Solving for x, we get x = 400. Therefore, McDonald had a total of 400 goats.
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in multiple regression, which is indicative of an inverse relationship between any of the value of x and y?
The sign of the corresponding regression coefficient for that specific predictor variable (x) would be negative, indicating an inverse relationship between that predictor and the response variable (y).
In multiple regression, the relationship between the response variable and each predictor variable can be either positive or negative. A negative relationship means that as the value of the predictor variable increases, the response variable decreases. In order to determine whether there is a negative relationship between a specific predictor variable and the response variable, we look at the sign of the corresponding regression coefficient for that variable. If the coefficient is negative, then there is an inverse relationship. For example, if we have a multiple regression model with two predictor variables, x1 and x2, and we find that the coefficient for x1 is negative, this indicates that there is an inverse relationship between x1 and the response variable y.
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A triangular prism is 16 yards long and has a triangular face with a base of 12 yards and a height of 8 yards. The other two sides of the triangle are each 10 yards. What is the surface area of the triangular prism?
Answer:
576 (square yards)
Step-by-step explanation:
length of slanted height of triangle = √(6² + 8²)
= √100
= 10.
surface area = area of 2 triangle faces + area of 3 lengths
= 2 (1/2 X 12 X 8) + 3 (10 X 16)
= 576 (square yards)
Each bag of different colored jelly beans is supposed to have 30% blue jelly beans. Ramon believes there are actually a greater proportion of blue jelly beans. He randomly selects 25 bags of jelly beans and finds the proportion of blue jelly beans to be 36%. He uses a significance level of alpha equals 0.1 and calculates a p-value of 0.256. What null and alternative hypothesis did Ramon use for the test, and what conclusion can he make?
Answer:
Ramon's null hypothesis (H0) is that the proportion of blue jelly beans in each bag is 30%:H0: p = 0.30His alternative hypothesis (Ha) is that the proportion of blue jelly beans in each bag is greater than 30%:Ha: p > 0.30To test this hypothesis, Ramon uses a significance level of alpha equals 0.1, which means that he is willing to accept a 10% chance of making a Type I error (rejecting the null hypothesis when it is true).From the sample of 25 bags of jelly beans, Ramon calculates a sample proportion of blue jelly beans of 36%. He then uses this value to calculate a test statistic and a corresponding p-value of 0.256.Since the p-value (0.256) is greater than the significance level (0.1), Ramon fails to reject the null hypothesis. This means that he does not have enough evidence to conclude that the proportion of blue jelly beans in each bag is significantly greater than 30%. It is possible that the observed difference in the sample proportion is due to random sampling variability.In other words, Ramon's conclusion is that there is not enough evidence to support his belief that there are actually a greater proportion of blue jelly beans than the specified 30%. He should not make any changes to the production or distribution process based on this sample result
Step-by-step explanation:
Mark each of the following statements as either AT (for "always true"), or ST (for "some- times true"), or NT (for "never true"). You must justify your answers. a. [2] If A is a 8 x 9 matrix of maximum rank, the dimension of the orthogonal complement of the null space of A is 1.
ST. The statement is sometimes true. The dimension of the orthogonal complement of the null space of A is equal to the rank of A.
Since A is a 8 x 9 matrix of maximum rank, its rank is 8. Therefore, the dimension of the orthogonal complement of the null space of A is 1, if and only if the null space of A has dimension 7. This means that there are 7 linearly independent vectors that satisfy Ax = 0. It is possible for this to happen, but it is not always true. For example, if A is the identity matrix, then the null space of A is the zero vector, and the dimension of the orthogonal complement of the null space of A is 9, not 1. Therefore, the statement is not always true, but it is sometimes true, depending on the specific matrix A.
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Work out the size of angle x and the size of angle y. Give each of your answers in degrees to 1 d.p. 14.8 cm X Y 11.4 cm Not drawn accurately
The value of angle X can be obtain as shown below:
Opposite = 13.1 cmHypotenuse = 16.7 cmAngle X =?Sine θ = Opposite / Hypotenuse
Sine X = 13.1 / 16.7
Sine X = 0.7844
Take the inverse of Sine
X = Sine⁻¹ 0.7844
X = 51.7 degrees
Thus, the value of angle X is 51.7 degrees
2. How do i determine the size of angle Y?The value of angle Y can be obtain as shown below:
Adjacent = 13.1 cmHypotenuse = 16.7 cmAngle Y =?Cos θ = Adjacent / Hypotenuse
Cos Y = 13.1 / 16.7
Sine Y = 0.7844
Take the inverse of Cos
Y = Cos⁻¹ 0.7844
Y = 38.3 degrees
Thus, the value of angle Y is 38.3 degrees
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Complete question:
See attached photo
The teacher's crayon has a mass of 20 grams her bottle of glue is 65 grams more than the crayon what is the mass of the glue
If the teacher's crayon has a mass of 20 grams her bottle of glue is 65 grams more than the crayon the mass of the glue is 85 grams.
What is arithmetic sequence?
An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term. For example, the sequence 2, 5, 8, 11, 14, ... is an arithmetic sequence with a common difference of 3, since each term after the first is found by adding 3 to the preceding term.
The nth term of an arithmetic sequence can be found using the formula:
an = a1 + (n-1)d
The mass of the glue is the sum of the mass of the crayon and the additional 65 grams.
So, the mass of the glue would be:
20 grams (mass of the crayon) + 65 grams (additional mass of the glue) = 85 grams.
Therefore, the mass of the glue is 85 grams.
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Suppose that X is the number of successes in an experiment with 9 independent trials where the probability of success is 2/5 . Find each of the following probabilities. Round answers to the nearest ten-thousandth.P (X < 2)P(X ≥ 2)
P(X < 2) ≈ 0.1338 and P(X ≥ 2) ≈ 0.8662.
Determine the probability?To find the probability P(X < 2), we need to calculate the probability of having fewer than 2 successes in 9 independent trials. This includes the cases where X is 0 or 1.
To find the probabilities P(X < 2) and P(X ≥ 2) in this scenario, we'll use the binomial distribution formula.
The binomial distribution formula is given by:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
Where:
P(X = k) is the probability of getting exactly k successes,
n is the number of trials,
k is the number of successes,
p is the probability of success in a single trial, and
C(n, k) is the number of combinations of n items taken k at a time.
Given that n = 9 and p = 2/5, we can calculate the probabilities as follows:
P(X < 2):
P(X < 2) = P(X = 0) + P(X = 1)
P(X = 0):
P(X = 0) = C(9, 0) * (2/5)^0 * (1 - 2/5)^(9 - 0)
Using the combination formula C(9, 0) = 1:
P(X = 0) = 1 * 1 * (3/5)^9
P(X = 1):
P(X = 1) = C(9, 1) * (2/5)^1 * (1 - 2/5)^(9 - 1)
Using the combination formula C(9, 1) = 9:
P(X = 1) = 9 * (2/5) * (3/5)^8
Now we can calculate P(X < 2) by adding P(X = 0) and P(X = 1).
P(X ≥ 2):
P(X ≥ 2) = 1 - P(X < 2)
After calculating P(X < 2), we can subtract it from 1 to find P(X ≥ 2).
Let's perform the calculations:
P(X = 0) = 1 * 1 * (3/5)^9 = 0.01917808 (rounded to 8 decimal places)
P(X = 1) = 9 * (2/5) * (3/5)^8 = 0.11462304 (rounded to 8 decimal places)
P(X < 2) = 0.01917808 + 0.11462304 = 0.13380112 (rounded to 8 decimal places)
P(X ≥ 2) = 1 - P(X < 2) = 1 - 0.13380112 = 0.86619888 (rounded to 8 decimal places)
Therefore, P(X < 2) ≈ 0.1338 and P(X ≥ 2) ≈ 0.8662.
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iqs revisited based on the normal model n(100,15) describing iq scores what percent of peoples iqs would you expect to be over 80 under 90 between 112 and 123
Based on the normal model N(100,15) describing IQ scores, we can use the standard normal distribution to answer these questions. To find the percentage of people with IQs over 80, we need to calculate the Z-score for 80: Z = (80-100)/15 = -1.33. Using a standard normal distribution table, we find that the area to the right of Z = -1.33 is 0.0918, which means about 9.18% of people have IQs over 80.
To find the percentage of people with IQs under 90, we calculate the Z-score for 90: Z = (90-100)/15 = -0.67. Using the same table, we find that the area to the left of Z = -0.67 is 0.2514, which means about 25.14% of people have IQs under 90.
To find the percentage of people with IQs between 112 and 123, we need to calculate the Z-scores for 112 and 123: Z1 = (112-100)/15 = 0.80 and Z2 = (123-100)/15 = 1.53. Using the table, we find the area to the left of Z1 is 0.7881 and the area to the left of Z2 is 0.9370. Therefore, the percentage of people with IQs between 112 and 123 is approximately 14.89%.
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A bag contains 8 green marbles, 5 yellow marbles, and 12 black marbles. If a green marble is drawn, you win $10. If a yellow marble is drawn, you win $15. If a black marble is drawn, you lose $10. It costs $1 to play. Should you play the game? Justify your answer
Answer:
Hey hopes this helps
Step-by-step explanation:
o determine whether you should play the game or not, we can calculate the expected value (EV) of playing the game. The EV represents the average outcome you can expect over the long run if you play the game many times.
The EV can be calculated as follows:
EV = (probability of winning green * amount won from green) + (probability of winning yellow * amount won from yellow) + (probability of winning black * amount lost from black) - cost to play
Probability of winning green = 8/25
Amount won from green = $10
Probability of winning yellow = 5/25
Amount won from yellow = $15
Probability of winning black = 12/25
Amount lost from black = -$10
Cost to play = -$1
Substituting the values:
EV = (8/25 * $10) + (5/25 * $15) + (12/25 * -$10) - $1
EV = $3.20 - $1
EV = $2.20
Since the EV is positive ($2.20), this means that on average, you can expect to win $2.20 per game
by how many times does the sample size have to be increased to decrease the margin of error by a factor of 1/7
To decrease the margin of error by a factor of 1/7, the sample size needs to be increased by a factor of 49.
To understand why this is the case, recall that the margin of error is a function of the sample size, the standard deviation of the population, and the confidence level. The margin of error is proportional to the inverse square root of the sample size, which means that if we want to decrease the margin of error by a factor of 1/7, we need to increase the sample size by a factor of 7.
However, increasing the sample size by a factor of 7 only decreases the margin of error by a factor of the square root of 7 (approximately 2.65). To decrease the margin of error by a factor of 1/7, we need to increase the sample size by a factor of 7 times the square of 2.65, which is approximately 49.
In other words, to decrease the margin of error by a factor of 1/7, we need to increase the sample size by a factor of 49. This means that we need to collect almost 50 times more data than we currently have in order to achieve the desired level of precision.
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1. Austin is participating in a 30K race. He runs at an average speed of
10 kilometers per hour and walks at an average speed of 6 kilometers
per hour. He wants to complete the race in 4 hours. Let x represent the
number of hours he runs. Let y represent the number of hours he walks.
a. What equation relates x and y to the goal of covering 30 kilometers?
b. What equation relates x and y to the goal of completing the course in
exactly 4 hours?
2. For each equation in Exercise 1, find three ordered-pair solutions (x, y).
Then, plot the points with those coordinates and use the pattern to
draw a graph of each equation. Graph both equations on the same
coordinate grid.
Walking Hours
5
N
1
0
0
y
1 2 3 4 5
Running Hours
X
O
Using the relation between velocity, distance and time, the equation that relates x and y is given by x + y - 3 = 0.
What's the connection between velocity, distance, and time?Velocity is distance divided by time, so
v = d/t
In this case , Austin wants to run 30 km at a rate of 10 km per hour, this can be represented as
10t = 30
t = 3.
The total time is 3 hours.
Looking at x as the number of hours he runs and y the number of hours he walks, along with the total time, the equation is given by
x + y = 3.
In standard form
x + y - 3 = 0.
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i need help with this
Answer:
(x - 3) (x + 12)
Step-by-step explanation:
2x² + 18x - 72
divide the equation by 2
x² + 9x - 36 -36
(x - 3) (x + 12) 12 -3 = 9
find r'(t), r(t0), and r'(t0) for the given value of t0. r(t) = (1 t)i t3j, t0 = 1
Here, Derevative: r'(t) = i + 3t^2j, r(t0) = i + j, and r'(t0) = i + 3j.
For the given function r(t) = (1 t)i + t^3j and t0 = 1, we can find r'(t), r(t0), and r'(t0) as follows:
r'(t) = i + 3t^2j
r(t0) = (1 1)i + 1^3j = i + j
r'(t0) = i + 3(1)^2j = i + 3j
We are given a vector-valued function r(t) = (1 t)i + t^3j, and a value of t0 = 1. To find r'(t), we need to take the derivative of each component of the function separately.
Taking the derivative of the first component, we get:
d/dt (1 t) = 0 1 = i
Taking the derivative of the second component, we get:
d/dt (t^3) = 3t^2 = 3t^2j
Therefore, r'(t) = i + 3t^2j.
To find r(t0), we substitute t0 = 1 into the function. This gives us:
r(1) = (1 1)i + 1^3j = i + j
Finally, to find r'(t0), we substitute t0 = 1 into r'(t) that we found earlier:
r'(1) = i + 3(1)^2j = i + 3j
Therefore, r'(t) = i + 3t^2j, r(t0) = i + j, and r'(t0) = i + 3j.
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A 3-phase, 6-pole induction motor runs on no-load at 1160 rpm. Determine the slip and frequency of rotor currents on no-load.
The frequency of the rotor currents on no-load is fr = 0.033 * 60 = 1.98 Hz.
The synchronous speed of the motor is given by
Ns = (120f) / P,
where Ns is the synchronous speed in revolutions per minute (RPM), f is the supply frequency in hertz (Hz), and P is the number of poles.
For the given motor, the synchronous speed is
Ns = (120 * 60) / (6 * 2) = 1200 RPM
On no-load, the rotor speed is equal to the synchronous speed, i.e., N = Ns = 1200 RPM.
The slip of the motor is given by
s = (Ns - N) / Ns,
where N is the rotor speed in RPM.
Thus, the slip of the motor is
s = (1200 - 1160) / 1200 = 0.033 or 3.3%
The frequency of the rotor currents on no-load is given by
fr = s * f,
where f is the supply frequency.
Thus, the frequency of the rotor currents on no-load is
fr = 0.033 * 60 = 1.98 Hz
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A soda company wants a cylindrical can that is 6 inches in height with a volume of 18.8 cubic inches.
a) What needs to be the radius of the can to the nearest inch?
Answer:
1 inch
Step-by-step explanation:
Volume of cylinder = π r ² h
18.8 = π r ² (6)
r² = (18.8) / (6π)
r = 1 inch to nearest inch
order the rational numbers -10,2,-0.5, and 5/16 from least to greatest
Answer: -10 < -0.5 < 0.3125 < 2
a radial saw has a blade with a 12-in. radius. suppose that the blade spins at 1500 rpm. (b) find the linear speed of the sawteeth in ft/s.
In this problem, we are given the radius and rotational speed of a radial saw blade and are asked to find the linear speed of the saw teeth in feet per second.
To approach this problem, we can use the formula for linear speed, which relates the linear speed v to the radius r and angular speed ω (in radians per second) as:
v = rω
We are given the radius r = 12 inches and the rotational speed of the blade in revolutions per minute (rpm). To convert this to radians per second, we can use the conversion factor:
1 revolution/minute = 2π radians/60 seconds
which gives us:
ω = (1500 rpm) * (2π/60) = 157.08 radians/second
Substituting these values into the formula for linear speed, we get:
v = (12 inches) * (157.08 radians/second) = 1884.96 inches/second
To convert this to feet per second, we can divide by 12 inches/foot, which gives us:
v = 1884.96 inches/second / 12 inches/foot = 157.08 feet/second
Therefore, the linear speed of the saw teeth is approximately 157.08 feet per second.
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When examining group difference where the direction of the difference is specified, which of the following is used? Select one: a. two-tailed test b. one-tailed test C. directional hypothesis o d. critical value
When examining group differences with a specified direction, a one-tailed test is used i.e., option b is correct.
In statistical hypothesis testing, researchers often have a specific direction in mind when comparing two groups.
For example, they may hypothesize that Group A performs better than Group B or that Group A has a higher mean than Group B. In such cases, a one-tailed test is appropriate.
A one-tailed test is designed to detect differences in a specific direction. It focuses on evaluating whether the observed data significantly deviates from the null hypothesis in the specified direction.
The null hypothesis assumes no difference or no relationship between the groups being compared.
In a one-tailed test, the critical region is defined on only one side of the distribution, corresponding to the specified direction of the difference.
The critical value, which determines whether the observed difference is statistically significant, is chosen based on the desired level of significance (e.g., alpha = 0.05).
On the other hand, a two-tailed test is used when the direction of the difference is not specified, and the researchers are interested in determining whether there is a significant difference between the groups in either direction.
In this case, the critical region is divided equally between the two tails of the distribution.
A directional hypothesis (option C) is a statement that specifies the expected direction of the difference, but it is not the statistical test itself. The critical value (option D) is the value used to determine the cutoff for rejecting or accepting the null hypothesis.
Therefore, when examining group differences with a specified direction, a one-tailed test is used to assess the statistical significance of the observed difference in that particular direction.
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please help i need this answer fast
A dietitian was interested in the heights of 13-year-olds in the state. He gathered data from a random sample of 400 pediatricians in the state and wanted to create an appropriate graphical representation for the data. Which graphical representation would be best for the data?
Bar graph
Circle graph
Histogram
Line plot
The ideal graphical depiction for the state's 13-year-old population's heights would be a histogram.
What is histogram ?A histogram is a sort of bar graph that shows how continuous or discrete data are distributed. It is made up of bars that stand in for various data ranges or intervals, with the height of each bar indicating the frequency or relative frequency of the data included inside that range.
It is possible that the data acquired contains a variety of different heights because the nutritionist received information from a random sample of 400 pediatricians. The dietitian can see the height distribution and spot any trends, clusters, or gaps in the data by utilizing a histogram. This graphical representation makes it possible to see how all the state's 13-year-old population is distributed.
Therefore, the best graphical representation would be a histogram.
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