The period of the given degree-4 LFSR with the polynomial p(x) = x^4 + x^2 + 1 and the seed (s3, s2, s1, s0) = 0110 is 15.
A Linear Feedback Shift Register (LFSR) is a deterministic algorithm that generates a pseudo-random sequence of numbers based on a polynomial function and an initial seed. The period of an LFSR is the length of the generated sequence before it repeats itself. In this case, the polynomial is p(x) = x^4 + x^2 + 1, and the seed is (s3, s2, s1, s0) = 0110. To find the period, we iterate through the LFSR sequence and count the steps until the seed is repeated. In this specific case, after iterating 15 times, the seed (0110) is repeated.
Thus, given the degree-4 LFSR with polynomial p(x) = x^4 + x^2 + 1 and seed (s3, s2, s1, s0) = 0110, the period of the generated sequence is 15.
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(1 point) a car factory produces a variable number of cars to keep up with the demand. the following measurements, made at the start of each month, show the rate at which cars are produced (in hundred cars/month): time (months) 0 1 2 3 4 5 6 rate (hunderd cars/month) 4 7 10 13 12 10 8 A. Make an overestimate and an underestimate of the total number of cars produced in the first month overestimate = underestimate = B. Make an overestimate and an underestimate of the total number of cars produced for the whole six months for which we have data. overestimate = underestimate =
A. The rate at which cars are produced in the first month is 4 hundred cars/month. To make an overestimate of the total number of cars produced in the first month, we can assume that the rate remains the same for the entire month. Therefore, the overestimate would be 4 hundred cars.
To make an underestimate of the total number of cars produced in the first month, we can assume that the rate increases linearly throughout the month. Therefore, we can take the average rate between 0 and 7 (the rate at the end of the first month) and multiply it by the number of days in the first month (assuming a 30-day month). This gives us an underestimate of 3.5 hundred cars.
B. To make an overestimate of the total number of cars produced for the whole six months, we can assume that the rate remains the same as the highest rate (13 hundred cars/month) for all six months. Therefore, the overestimate would be 78 hundred cars.
To make an underestimate of the total number of cars produced for the whole six months, we can assume that the rate decreases linearly from 13 to 8 hundred cars/month. Therefore, we can take the average rate between 13 and 8 and multiply it by the number of months (6). This gives us an underestimate of 9 hundred cars.
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HELPP PLEASEE WITH 6!!!! WILL GIVE BRAINLYIST!!!
Answer:
C
Step-by-step explanation:
you just count from where A is to where A' is. easy.
An 81° angle is decomposed into two angles, one of which is 57°. What is the measure of the unknown angle?
13°
14°
23°
24°
Answer:24
Step-by-step explanation: 81-57=24
pls hurry. 12. Given that a, b, and c are the side lengths of a right triangle, which set of numbers does NOT necessarily represent side lengths of a right triangle?
Out of the given options, Option D (a+5, b+5, c+5) does not necessarily represent side lengths of a right triangle.
How to explain the triangleFor a set of three numbers to represent the side lengths of a right triangle, they must satisfy the Pythagorean theorem, which states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In mathematical terms, for side lengths a, b, and c (where c is the hypotenuse), the Pythagorean theorem can be represented as a² + b² = c²
In this case, the correct option is D.
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The length, width and height of a rectangular box are 12m, 8m and 6m respectively. How many small boxes can it hold if each box occupies 1.5 m³ space?
14. Rahab shared oranges among her three children John, Sarah and Peter, John got 1/3 of the fruit, Sarah got % of the fruit and Peter got / of the remainder. If she was left with 60 fruits, how many oranges had she before? B. 398 D. 336 A. 1680 C. 276
Rahab originally had 165 oranges.
How many oranges did Rahab have before sharing?Let total number of oranges Rahab had be x.
John got 1/3 of x, which is (1/3)x.
Sarah got 5% of x, which is (5/100)x = (1/20)x.
The remaining fruit after John and Sarah got their share is:
= (1 - 1/3 - 1/20)x
= (16/60)x
= (4/15)x.
Peter got 2/3 of this remainder, which is:
(2/3)*(4/15)x
= (8/45)x.
The total number of oranges Rahab originally had is:
x = (1/3)x + (1/20)x + (8/45)x + 60
Multiplying through with 135 gives:
135x = 45x + 9x + 32x + 8100
We will simplify it
135x - 45x - 9x - 32x = 8100
49x = 8100
x = 8100/49
x = 165.306122449
x = 165.
Note we assumed some figures that were missing:
Rahab shared oranges among her three children John, Sarah and Peter, John got 1/3 of the fruit, Sarah got 5% of the fruit and Peter got 2/3 of the remainder. If she was left with 60 fruits, how many oranges had she before?
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What is the value of 2x when 4x - 4 = 18?
By solving the equation 4x - 4 = 18, we find x = 5.5. Substituting this value into 2x, we get 2(5.5) = 11. Hence, the value of 2x when 4x - 4 = 18 is 11.
To find the value of 2x when 4x - 4 = 18, we need to solve the equation for x. Let's solve it step by step:
1. Add 4 to both sides of the equation to isolate the term with x:
4x - 4 + 4 = 18 + 4
4x = 22
2. Divide both sides of the equation by 4 to solve for x:
4x/4 = 22/4
x = 5.5
Now that we have found the value of x as 5.5, we can substitute it into the expression 2x to find the value of 2x:
2x = 2 * 5.5 = 11
Therefore, the value of 2x when 4x - 4 = 18 is 11.
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80% of a number is 30. What is 100% of the number?
Answer:
37.5
Step-by-step explanation:
If 80% of a number is 30, then we can use the proportion method to find 100% of the number. Let x be the number we are looking for. Then we have:
80/100 = 30/x
Multiplying both sides by x, we get:
80x/100 = 30
Simplifying, we get:
4x/5 = 30
Multiplying both sides by 5/4, we get:
x = (5/4) × 30 = 37.5
Therefore, 100% of the number is 37.5
yw;)
43. which numbers for x would make [tex]\sqrt{x}[/tex] irrational
multiple choice
A. 1
B. 2
C. 3
D. 4
E. 5
The numbers for x would make the √x irrational are 2, 3 and 5
How to determine the numbers for x would make the expression irrationalFrom the question, we have the following parameters that can be used in our computation:
√x
By definition, irrational numbers are numbers that cannot be represented as a fraction of integers
Next, we test the options
A. √1 = 1
B. √2 = 1.414...
C. √3 = 1.732...
D. √4 = 2
E. √5 = 2.236
Hence, the numbers for x would make the expression irrational are 2, 3 and 5
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Select Function 1 to investigate the average rate of change between two points for the function RCx) =3/4 x - 1. (a) What is the average rate of change between a = 0 and b - 1? a (1) Lock the difference between a and bar 1.00 and move point a around on the graph. What happens to the average rate of change? The average rate of change decreases from left to right The average rate of change is always the same. The average rate of change increases from left to right: () What is the average rate of change for a straight line? The average rate of change for a straight line is always greater than the slope, The average rate of change for a straight line equals the slope. The average rate of change for a straight line equals the y-coordinate of the y-intercept. The average rate of change for a straight line is always less than the slope
(a) The average rate of change between a = 0 and b = 1 for RC(x) = 3/4x - 1 is:
RC(1) - RC(0)
= (3/4(1) - 1) - (3/4(0) - 1)
= 3/4 - 1 + 1
= -1/4
So, the average rate of change between a = 0 and b = 1 is -1/4.
(2) As we move point a around on the graph, the average rate of change between a and b = 1 changes.
Specifically, if we move point a to the right, the average rate of change increases, and if we move point a to the left, the average rate of change decreases.
(3) The average rate of change for a straight line equals the slope.
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2. At age 46, Jasper invested $34,000 in an annuity at an APR of 5.4%, compounded monthly, and
agreed to start receiving payments at age 60. However, after exactly 8 years, Jasper withdrew
$9200. His insurance company has a surrender charge of 2.2% of the withdrawal for taking money
out of the annuity early, and the IRS also charges a 10% fee if you withdraw money before you are
59.5 years of age. Jasper is wondering what effect this early withdrawal had on his finances. Work
with him to figure it out. (5 points: Part 1-1 point; Part II - 1 point; Part III - 1 point; Part IV-1 point;
Part V- 1 point)
Jasper's early withdrawal reduced his future annuity payments by $16,906.31.
How to compute Jasper's future annuity payments?To help Jasper compute his future annuity payment,
First, we have to calculate the future value (FV) of his investment at age 60 if he had not made any early withdrawals using the formula:
FV = [tex]PV (1 + r/n)^{(n*t)}[/tex]
where:
PV = present value (amount invested)
r = annual interest rate,
n = number of compounding periods per year
t = number of years.
Given:
PV = $34,000
r = 5.4% per year
n = 12 (monthly compounding)
t = 14 years (from age 46 to age 60)
Logging the values, we get:
FV = [tex]$34,000 (1 + 0.054/12)^{(12*14)}[/tex]
= [tex]$34,000 (12.0045/12)^{168}[/tex]
= [tex]$34,000 (1.000375)^{168}[/tex]
FV = $68,786.56
This is the amount he would have received at age 60 if he had not withdrawn early.
Next, we shall now estimate the surrender charge and IRS fee that Jasper has to pay for his early withdrawal of $9,200.
Surrender charge = 2.2% x $9,200 = $202.40
IRS fee = 10% x $9,200 = $920
So, the total amount that Jasper receives from his early withdrawal is:
Amount received = $9,200 - $202.40 - $920 = $8,077.60
To calculate the new FV Jasper's investment by adjusting the present value (PV).
Subtract the withdrawn amount and add back the surrender charge:
New PV = $34,000 - $8,077.60 + $202.40 = $26,125.80
So, the new future value can then be calculated using the same formula:
New FV = $[tex]$26,125.80 (1 + 0.054/12)^{(12*12)}[/tex]
New FV = $[tex]$26,125.80 (1.0045)^{144}[/tex]
New FV = $26,125.80 x 2.2424
New FV = $58,651.29
Thus, Jasper's early withdrawal reduced his future annuity payments by $68,786.56 - $51,880.25 which is $16,906.31.
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persevere fifteen boys and fifteen girls entered a drawing for four free movie tickets. what is the probability that all four tickets were won by girls? express your answer as a fraction in simplest form.
We are given that fifteen boys and fifteen girls entered a drawing for four free movie tickets. We want to find the probability that all four tickets were won by girls.
To solve this problem, we need to consider the total number of possible outcomes and the number of favorable outcomes.
Total number of outcomes:
The total number of outcomes represents all the possible ways to choose four winners from the thirty participants (boys and girls). We can calculate this using the combination formula:
C(30, 4) = 30! / (4!(30 - 4)!) = 27,405
Here, C(n, r) represents the combination of choosing r objects from a set of n objects.
Favorable outcomes:
We want to determine the number of ways to select all four winners from the group of fifteen girls. This can also be calculated using the combination formula:
C(15, 4) = 15! / (4!(15 - 4)!) = 1365
Probability calculation:
The probability is the ratio of the favorable outcomes to the total number of outcomes. So, we divide the number of favorable outcomes by the total number of outcomes:
P(Girls winning all four tickets) = 1365 / 27,405
Simplifying the fraction, we find:
P(Girls winning all four tickets) = 1 / 20
Therefore, the probability that all four tickets were won by girls is 1/20.
In summary, out of all the possible combinations of selecting four winners from the thirty participants, only one out of every twenty combinations will result in all four tickets being won by girls.
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a model uses the decision variables x, y and z. the objective function formula for this model is x 2y -z2. which of the following statements is true?
The objective function represents the mathematical expression that the model seeks to optimize. In this case, the expression is x 2y -z2. This means that the model is trying to find the combination of values for x, y, and z that maximize this expression.
To determine which of the following statements is true, we need to analyze the given objective function formula x 2y -z2 in relation to the decision variables x, y, and z.
The objective function represents the mathematical expression that the model seeks to optimize. In this case, the expression is x 2y -z2. This means that the model is trying to find the combination of values for x, y, and z that maximize this expression.
To do this, the model may have certain constraints or limitations that need to be taken into account. These constraints can be represented as inequalities or equations involving the decision variables.
Without any additional information about the model's constraints, it is difficult to determine which of the following statements is true. The statements could be related to the feasibility of the model's solutions, the optimal values of the decision variables, or the sensitivity of the objective function to changes in the decision variables.
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T/F
A statistical test to determine whether some observed pattern of frequencies corresponds to an expected pattern is called a chi-square goodness-of-fit test.
A statistical test to determine whether some observed pattern of frequencies corresponds to an expected pattern is called a chi-square goodness-of-fit test is True.
The chi-square goodness-of-fit test is a statistical test used to determine whether an observed set of categorical data frequencies is consistent with some expected set of frequencies. It compares the observed frequencies to the expected frequencies using the chi-square test statistic. If the test statistic is large enough, indicating a significant difference between the observed and expected frequencies, then the null hypothesis that the observed frequencies are consistent with the expected frequencies is rejected.
This test is commonly used in various fields of study, including biology, psychology, and social sciences, to evaluate whether an observed data set follows a particular theoretical or expected distribution.
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The quadratic functions f(x) and g(x) are described in the table.
x f(x) g(x)
−2 4 64
−1 1 49
0 0 36
1 1 25
2 4 16
3 9 9
4 16 4
5 25 1
6 36 0
In which direction and by how many units should f(x) be shifted to match g(x)?
A. Left by 18 units
B. Right by 18 units
C. Left by 6 units
D. Right by 6 units
The direction and by how many units should f(x) be shifted to match g(x) is Left by 6 units. Option C
How to determine the direction and by how many units should f(x) be shifted to match g(x)To determine the direction and magnitude of the shift needed for f(x) to match g(x), we can compare the corresponding values of f(x) and g(x) in the table.
For x = -2, f(x) = 4 and g(x) = 64.
For x = -1, f(x) = 1 and g(x) = 49.
For x = 0, f(x) = 0 and g(x) = 36.
For x = 1, f(x) = 2 and g(x) = 25.
For x = 2, f(x) = 4 and g(x) = 16.
By comparing the values, we can observe that the graph of f(x) is shifted to the right compared to g(x). To match the graph of g(x), we need to shift f(x) to the left.
The magnitude of the shift can be determined by the difference in x-values between the corresponding points of f(x) and g(x).
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suppose a simple random sample of size n=36 is obtained from a population that is skewed right with μ=75 and σ=12. (a) describe the sampling distribution of x.
The sampling distribution of the x-bar is approximately normally distributed with a mean of 75 and a standard deviation of 2.
Describe the sampling distribution of x:
The sampling distribution of the sample mean (x-bar) can be described based on the given information.
Given that the population is skewed right with a mean (μ) of 75 and a standard deviation (σ) of 12, the sampling distribution of the x-bar will approach a normal distribution as the sample size (n) increases.
This is known as the Central Limit Theorem.
According to the Central Limit Theorem, regardless of the shape of the population distribution, the sampling distribution of the x-bar will be approximately normal if the sample size is large enough.
In this case, with a sample size of n = 36, the sampling distribution of the x-bar can be considered approximately normal.
The mean of the sampling distribution of the x-bar will be equal to the population mean (μ), which is 75 in this case.
The standard deviation of the sampling distribution of the x-bar, also known as the standard error of the mean (SE), can be calculated by dividing the population standard deviation (σ) by the square root of the sample size (n).
Hence, the standard error of the mean (SE) is calculated as σ/√n = 12/√36 = 12/6 = 2.
Therefore,
The sampling distribution of the x-bar is approximately normally distributed with a mean of 75 and a standard deviation of 2.
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find a power series representation for the function. f(x) = x2 (1 − 2x)2 f(x) = [infinity] n = 0 determine the radius of convergence, r. r =
The power series representation for f(x) is x²(1 - 2x)² = x² × Σ[n = 0 to ∞] [tex]C(2, n) (-2x)^{n}[/tex] and the radius of convergence, r, is equal to 1/2.
To find a power series representation for the function f(x) = x²(1 - 2x)², we will first find a power series for the function (1 - 2x)² and then multiply it by x².
The power series representation for (1 - 2x)² can be found using the binomial series formula:
[tex](1 - 2x)^{k}[/tex] = Σ[n = 0 to ∞] [tex](C(k, n)[/tex] × [tex](-2x)^{n})[/tex], where C(k, n) represents the binomial coefficient.
For k = 2, the series becomes:
(1 - 2x)² = Σ[n = 0 to ∞] [tex](C(2, n)[/tex] × [tex](-2x)^{n})[/tex]
Now, we will multiply this series by x² to get the power series representation for f(x):
f(x) = x²(1 - 2x)² = x² × Σ[n = 0 to ∞] [tex](C(2, n)[/tex] × [tex](-2x)^{n})[/tex]
Now, we will determine the radius of convergence, r, using the Ratio Test:
[tex]\lim_{n \to \infty} |(a_{n+1}/(a_{n})| = |((-2)^{n+1} x^{n+1})/(2^n x^n)| = |(-2x)|[/tex]
For convergence, the limit must be less than 1:
|-2x| < 1
Divide both sides by 2:
|-x| < 1/2
The radius of convergence, r, is equal to 1/2.
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5. (04.02 MC)
Ophelia owns a home, has a weekly gross income of $1,219.00, and has total minimum monthly debt payments of $4,7
monthly debt payments by to have a debt-to-income ratio of 35%. (4 points)
Ox≤ $2,343.18
Ox> $1,848.82
Ox>$2,343.18
x≤ $1,848.82
Ophelia's maximum allowable monthly debt payments to maintain a debt-to-income ratio of 35% would be $1,848.82. The correct option is (D).
Understanding Debt-to-Income RatioTo calculate the maximum allowable monthly debt payments to maintain a debt-to-income ratio of 35%, we first need to determine Ophelia's maximum monthly gross income.
We can do this by multiplying her weekly gross income by the number of weeks in a month.
Given that:
Weekly gross income = $1,219.00
Number of weeks in a month (approximated) = 4.33 (52 weeks / 12 months)
Monthly gross income: $1,219.00 * 4.33 = $5,282.33
Next, we calculate the maximum allowable monthly debt payments by multiplying the monthly gross income by the debt-to-income ratio of 35%:
Maximum allowable monthly debt payments: $5,282.33 * 0.35 = $1,848.82
Therefore, Ophelia's maximum allowable monthly debt payments to maintain a debt-to-income ratio of 35% would be $1,848.82.
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A pentagonal pyramid is intersected by plane parallel to the base
Answer:
if the answer is true or false is true
Serena is trying to find out the radius of a large circular fountain. She measures the distance from a point on a tangent and a line passing through the centar of the fountain. What is the radius of the fountain? Round your answer to the nearest tenth meter.
Circle B has tangent line AC with lenght 5.6 m. BC length is r+3.8 m.
The Radius of the fountain is approximately 9.4 meters plus the value of r.
In circle B with a tangent line AC of length 5.6 m.A represents the point of tangency and C represents the point where the tangent line intersects the circle. Additionally, BC represents the length of the line segment from point B to point C, and it is given as r + 3.8 m.
The radius of the fountain,the length of BC and subtract the known value of 3.8 m.
From the given information, we can set up the following equation:
AC + BC = AB
Substituting the known values, we have
5.6 m + (r + 3.8 m) = AB
Simplifying the equation, we get:
9.4 m + r = AB
Since point B lies on the circle, AB represents the radius of the fountain. Thus, the radius of the fountain is given by:
AB = 9.4 m + r
Therefore, the radius of the fountain is approximately 9.4 meters plus the value of r.
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develop the estimated regression equation to predict the repair time given the number of months since the last maintenance service, the type of repair, and the repairperson who performed the service. assume that if the type of repair is electrical and if dave newton performed the service. enter negative value as negative number.
To develop the estimated regression equation to predict the repair time given the number of months since the last maintenance service, the type of repair, and the repairperson who performed the service, we need to perform a multiple linear regression analysis.
The estimated regression equation can be represented as: Repair time = β0 + β1(Months since last maintenance) + β2(Type of repair) + β3(Repairperson)
where β0 is the intercept, β1 is the coefficient of months since last maintenance, β2 is the coefficient of type of repair, and β3 is the coefficient of repairperson.
To incorporate the assumption that if the type of repair is electrical and if Dave Newton performed the service, the repair time is lower, we can introduce an interaction term between the type of repair and the repairperson. The equation will then be:
Repair time = β0 + β1(Months since last maintenance) + β2(Type of repair) + β3(Repairperson) + β4(Type of repair × Repairperson)
The coefficients can be estimated using regression analysis techniques, and the resulting equation can be used to predict the repair time for a given set of values for the independent variables.
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Find the greatest number from to which when 7 is added, the sum divides 90,105,224 without leaving a reminder.
The greatest number from to which when 7 is added, the sum divides 90,105,224 without leaving a reminder is 8.
How can the number be known?We can represent the greatest number as x, which implies that the greatest number that when 7 is added it will divide the givn numbers without remainder, hence x +7 = hcf.
Then we can test for the factors of the given numbers on after the other as;
90 = (2 * 5 * 3 * 3)
105 = (5 * 3 * 7)
120 = (5 * 2 * 3 * 2 * 2)
Hence the hcf here can be expressed as 5 and 3 which is equivalent to 15
Then (x + 7) = 15
x = (15 - 7)
x = 8
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It’s time to grade papers! Mr Putnam can grade this test in 4 minutes. Mrs persons can grade this test in 6 minutes. But poor Mr Orwell is not nearly as fast at grading. It takes him 12 minutes to grade this test. If they all work together how fast can they grade this test?
If all three of them work together, they can finish work in 2 minutes.
Given that, Mr Putnam can grade this test in 4 minutes.
Work done by Mr Putnam is 1/4
Mrs persons can grade this test in 6 minutes.
Work done by Mrs persons is 1/6
Mr Orwell can grade this test in 12 minutes.
Work done by Mr Orwell is 1/12
Total time taken by all three be x.
Here, 1/4 +1/6 +1/12 = 1/x
Now, LCM of 4, 6 and 12 is 12
3/12 + 2/12+1/12 = 1/x
(3+2+1)/12 = 1/x
6/12 = 1/x
x=12/6
x=2 minutes
Therefore, if all three of them work together, they can finish work in 2 minutes.
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If an isotope has a cycle (half-life) of 2,000 years, approximately what percent of an original amount will remain after 6,000 years?
a. 50%
b. 25%
c. 12.5%
d. 6.25%
The correct answer is c. 12.5% of the original amount of the isotope will remain after 6,000 years.
In the first cycle (2,000 years), half of the original amount would remain. In the second cycle (another 2,000 years), half of that remaining amount would remain, which is one quarter of the original amount. In the third cycle (another 2,000 years), half of that remaining amount would remain, which is one eighth of the original amount. Therefore, after three cycles (6,000 years), only one eighth or 12.5% of the original amount would remain.
Your answer is based on the half-life of the isotope, which is 2,000 years. After each half-life period, the remaining amount of the isotope will be reduced by 50%.
In this scenario, 6,000 years have passed, which is equal to three half-life cycles (6,000 / 2,000 = 3). To find the percentage of the original amount that remains after these three cycles, you can simply apply the half-life reduction for each cycle. After the first half-life (2,000 years), 50% remains. After the second half-life (4,000 years), 50% of the remaining 50% remains, which is 25%. Finally, after the third half-life (6,000 years), 50% of the remaining 25% remains, which is 12.5%.
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need help quickly (screenshot added)
Answer:
3 1/2
3 whole trapezoids and half trapezoid
a randomized controlled trial is run to evaluate the effectiveness of a new drug for asthma in children. a total of 250 children are randomized to either the new drug or a placebo (125 per group). the mean age of children assigned to the new drug is 12.4 with a standard deviation of 3.6 years. the mean age of children assigned to the placebo is 13.0 with a standard deviation of 4.0 years. is there a statistically significant difference in ages of children assigned to the treatments? run the appropriate test at a 5% level of significance.
Therefore, based on the given data, there is not enough evidence to suggest a statistically significant difference in ages between children assigned to the new drug and the placebo.
To determine if there is a statistically significant difference in ages between children assigned to the new drug and the placebo, we can perform a two-sample t-test.
Given:
Sample size of children assigned to the new drug (n1) = 125
Sample size of children assigned to the placebo (n2) = 125
Mean age of children assigned to the new drug (X1) = 12.4 years
Mean age of children assigned to the placebo (X2) = 13.0 years
Standard deviation of ages in the new drug group (s1) = 3.6 years
Standard deviation of ages in the placebo group (s2) = 4.0 years
Level of significance (α) = 0.05
The null hypothesis (H0) is that there is no difference in the mean ages between the two groups, and the alternative hypothesis (Ha) is that there is a difference.
We can calculate the test statistic using the formula:
t = (X1 - X2) / √((s1^2/n1) + (s2^2/n2))
Substituting the given values, we get:
t = (12.4 - 13.0) / √((3.6^2/125) + (4.0^2/125))
Calculating this, we find t ≈ -0.571.
The degrees of freedom (df) for the t-test is (n1 + n2 - 2) = (125 + 125 - 2) = 248.
Using the t-distribution table or a statistical calculator, at a significance level of 0.05 with df = 248, the critical t-value is approximately ±1.97 (two-tailed test).
Since the calculated t-value (-0.571) is not greater than the critical t-value (-1.97 or 1.97), we fail to reject the null hypothesis.
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Last semester there were 35 students in Ms. Janicki's homeroom. This semester the class decreased by 20% due to students going virtual. How many students are currently in Ms. Janicki's homeroom?
Decrease in number of students by 20% will result in reduction of 7 students from the total of 35 students. Therefore, the remaining students that are currently in Ms. Janicki's homeroom are 28 students.
We must calculate 20% of the total number of students from the previous semester (35) in order to determine the number of students now enrolled in Ms. Janicki's homeroom.
20% of 35 is [tex](\frac{20}{100} ) \times 35[/tex] = 7.
7 students therefore took the virtual course this semester. We deduct 7 from the starting student count to get the current student count.
35 - 7 = 28.
Hence, there are 28 students are currently in Ms. Janicki's homeroom.
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What is the volume of this prism? All angles are right angles.
Answer:
528 cubic inches
Step-by-step explanation:
You want to know the volume of the L-shaped prism shown.
Base areaThe area of the L-shaped face can be found a couple of ways. Drawing a diagonal line from the inside corner to the outside corner divides it into two congruent trapezoids with bases 12 in and 10 in, and height 2 in. The area of one such trapezoid is ...
A = 1/2(b1 +b2)h
A = (1/2)(12 in + 10 in)(2 in) = 22 in²
The area of the L-shaped face is then ...
base area = 2(22 in²) = 44 in²
Prism volumeAs with all prisms, the volume is given by ...
V = Bh
where B is the area of the base, and h is the distance between bases.
V = (44 in²)(12 in) = 528 in³
The volume of the prism is 528 cubic inches.
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Additional comment
Another way to find the area of the L shape is to subtract the 10 in × 10 in cutout area from the 12 in × 12 in square that bounds that face.
12² - 10² = 144 -100 = 44 in²
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Given the following data calculate the correlation coefficient. Then describe the correlation based on the correlation coefficient.
x y
2 3
5 1
7 6
9 5
8 4
Find the unit rate miles per hour.