Answer:
x ≤ 14
Step-by-step explanation:
x = age of Sis
x - 6 = Martin's age
x + (x-6) ≤ 22
2x - 6 ≤ 22
2x ≤ 28
x ≤ 28/2
x ≤ 14
The map of a walking trail is drawn on a coordinate grid with three points of interest. The trail starts at R(−3, 2) and goes to S(2, 2) and continues to T(2, −5). The total length of the walking trail is
units. (Input whole numbers only.) (3 points)
Answer:
12
Step-by-step explanation:
the mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of per day. a sample of this radioactive substance was taken six days ago. if the sample has a mass of today, find the initial mass of the sample. round your answer to two decimal places.
As per the concept of exponential decay, the initial mass of the sample is 5,254.87 kg
What is meant by Exponential decay:
In math, the term exponential decay is a very common process especially when we are talking about radioactive materials.
The standard formula for this type of behavior which is written below:
A = Pe^-rt
where
A refers the amount left after time t
P refers the initial amount at t=0
r refers the rate
Here we have given that the mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of per day. a sample of this radioactive substance was taken six days ago.
And we need to find if the sample has a mass of today, then the initial mass of the sample.
Now, we have to substituting the values,
Then we get the equation as,
=> A = (9575 kg)(e^-0.12*5)
When we simplify this one, then we get,
=> A = 5,254.87 kg
Therefore, the initial mass of the sample is 5,254.87 kg
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Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 27x^3, y = 0, x = 1; about x = 2
The volume V of the solid is obtained by rotating the region bounded by the given curves about the specified line. y = 27x^3, y = 0, x = 1; about x = 2 is 81π/5
Shell method:
The shell method is an integration for calculating the volume of a solid of revolution when integrating along an axis perpendicular to the axis of revolution. This is in contrast to disc integration which integrates along the axis parallel to the axis of revolution.
V=2π∫01(2-x). 27x³dx
= 2π.27([tex]x^{4}[/tex]/2 - [tex]x^{5}[/tex]/5)01
=54π(1/2-1/5)
= 81π/5
Therefore The volume V of the solid is obtained by rotating the region bounded by the given curves about the specified line. y = 27x^3, y = 0, x = 1; about x = 2 is 81π/5
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A sampling distribution of the sample means of many large samples of a probability distribution is normally distributed. Which statement is true according to the Central Limit Theorem?
A the original PD can have any shape
B the original PD must also be normal
C the original PD must be uniform
D the original PD must be symmetric
The statement that is true according to the Central Limit Theorem is B. the original PD must also be normal.
Which is the Central Limit Theorem?According to the central limit theorem, if you take sufficiently large samples from a population, the means of the samples will be normally distributed even if the population is not normally distributed. The central limit theorem (CLT) states that as sample size increases, the distribution of sample means approaches a normal distribution, regardless of the distribution of the population.
The central limit theorem says that the sampling distribution of the mean will always be normally distributed, as long as the sample size is large enough.
In conclusion, the correct option is B.
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You can use induction. Here's a very very rusty sketch of the proof.
Given -
Union of two regular languages is regular.
Let f(n) be a function representing the union of n regular languages.
Question Is f(n) a regular language?
Lk+1 is the k+1th regular language, for example. The presented hypothesis states that f(n) = f(k+1) is regular since f(k) and Lk+1 are both regular.
What is the purpose of the inductive hypothesis?The induction hypothesis's function The assumption made at the beginning of the induction phase is known as the induction hypothesis, and it is the situation where n = k for the proposition we are trying to prove ("P(k)"). If you don't bring this hypothesis into play at any point throughout the proof of the induction phase, something is amiss.
Given:
It is normal for two regular languages to be combined.
Give the function f(n) the name "union of n regular languages."
Question Is the language f(n) regular?
The union of a single regular language is regular
if n = 1. Base Case
The provided hypothesis tells us that f(2) is regular
if n = 2.
Assume that f(n) is regular for every n = k.
This is the inductive hypothesis.
Let n equal k+1 in the inductive step. The inductive premise tells us that f(k) is a regular language.
Consequently, f(n) = f(k+1) = Lk+1 U f(k) (k)
Lk+1 is the k+1th regular language,
for example. The presented hypothesis states that f(n) = f(k+1) is regular since f(k) and Lk+1 are both regular.
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Which of the following is true about the t-distribution? Assume a reference (random) sample of size 100 with sample mean 10 and sample standard deviation of 1 with unknown population mean and variance.
a. The t-distribution will look similar to the standard normal distribution as the sample size increases which results in the degrees of freedom increasing.
b. The t-distribution will look similar to the standard normal distribution as the sample size increases which results in the degrees of freedom decreasing.
c. The t-distribution will look similar to the normal distribution with mean 10 and standard deviation 1 as the sample size increases which results in the degrees of freedom decreasing.
d. The t-distribution will look similar to the normal distribution with mean 10 and standard deviation 1 as the sample size increases which results in the degrees of freedom increasing.
e. None of these
1000 times were added to the n=30 sample. Even with n=30, the sample variance distribution is still very biased.
What is probability ?Probability refers to possibility.
A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.
Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
According to our question-
The sample variance's variance (SD) is still very large. The range is from 20 to 30%.
Because we are utilizing estimated population variance rather than the genuine population variance, which has some degree of uncertainty, the e t distribution has a longer tail when degrees of freedom are limited. Given that the estimated population variance is nearer to the actual population variance when sample size = 30, the t distribution will be closer to the z distribution.
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A food company distributes its tomato soup in two cans of different sizes. For the larger can, both the diameter and the height have been increased by 10%.
By what percentage does the volume of the can increase from the smaller can to the larger can? Round your answer to the nearest percent.
Answer:
Step-by-step explanation:
If the diameter increases by 10%,
new diameter = d+⅒ = 1.1d
also new radius = 0.55r
Height also increasesby 10%,
New height = h+⅒h = 1.1h
hence diameter of larger can =
π*(0.55)²*1.1= 1.0453
hence percentage change in volume
is 4.53% which can be rounded off to
-1/2h(2h+3)=0 answer
Step-by-step explanation:
-1/2h(2h+3) = 0
Seperate the equation:
-1/2 = 0
h = 0
(2h+3) = 0
Subtract 3 from both sides:
2h+3 = 0
2h+3-3 = 0
Simply:
2h = -3
Final Answer:
h = 0
h = -3/2
Graph the system of inequalities.
y>4 x-3
3 y-x≤9
Use the graphing tool on the right to graph the system of inequalities.
The graph of the inequality y > 4x - 3 , 3y - x ≤ 9 . is shown below.
In the question ,
the inequalities are given ,
we have to graph given inequalities ,
the inequalities are y > 4x - 3
3y - x ≤ 9 .
in the first inequality , y > 4x - 3
we put x = 0 , y is = -3 .
we put y = 0 , x is = 3/4 .
So ,the points for the line will be (0,-3) and (3/4,0) .
since the inequality does not have equal to sign , the line will be a dotted line .
in the second inequality ,3y - x ≤ 9 .
we put x = 0 , y is = 3 .
we put y = 0 , x is = -9 .
the points for the line will be (0,3) and (-9,0).
Since the inequality has equal to sign . Thus, line will be solid line .
Therefore , the for the given inequality is shown below.
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A piece of cardboard is 5 centimeters longer than it is tall. The area of the piece of cardboard is 66 square centimeters. How many centimeters long is the piece of cardboard?
Answer:
12.244 cm long
Step-by-step explanation:
The area of a rectangle is equal to its height times its width, so if the piece of cardboard has an area of 66 square centimeters and is 5 centimeters longer than it is tall, we can write the following equation to represent the dimensions of the piece of cardboard:
height * (height + 5) = 66
To solve this equation, we can first divide both sides of the equation by the height of the piece of cardboard to get:
height + 5 = 66 / height
We can then subtract 5 from both sides of the equation to get:
height = 66 / height - 5
We can then multiply both sides of the equation by the height to get:
height^2 = 66 - 5 * height
We can then use the quadratic formula to solve for the height of the piece of cardboard:
height = (-5 +/- sqrt(5^2 - 4 * 1 * -66)) / (2 * 1)
The value of the square root in the quadratic formula must be positive, so we take the positive value for the height:
height = (-5 + sqrt(5^2 + 4 * 1 * 66)) / (2 * 1)
This simplifies to:
height = (5 + sqrt(61)) / 2
The height of the piece of cardboard is approximately 7.244 centimeters. Since the piece of cardboard is 5 centimeters longer than it is tall, it must be 5 + 7.244 = 12.244 centimeters long.
Therefore, the piece of cardboard is approximately 12.244 centimeters long.
the data below are the final exam scores of 10 randomly selected statistics students and the number of hours they studied for the exam. find the equation of the regression line for the given data. (points : 4) hours x, 3 5 2 8 2 4 4 5 6 3 scores y, 65 80 60 88 66 78 85 90 90 71
Dependent variable: A dependent variable is a variable that changes or is impacted by other factors. independent variable: An independent variable is a variable that does not change or are impacted by other factors.
What is Regression?Regression is a method for figuring out the relationship between two or more variables. In other words, it is determined by how the predictor variable changes and how the dependent variable changes. Additionally, when more than one independent variable is included in a regression analysis, the change in the dependent is examined while maintaining the same values for the other independent variables.
The best fit for the data is linear regression if the data set is bivariate. The data with two variables are best represented by the straight line known as the least squares regression line.
When the explanatory variable has a value of zero, the response variable's projected value is shown by the regression line's y-intercept (though be wary of extrapolation in interpreting the intercept or other values outside the original data range).
The best fit for the data is linear regression if the data set is bivariate. The data with two variables are best represented by the straight line known as the least squares regression line. The line's equation is provided by,
y = a+bx
where,
a—Intercept
b—Regression coefficient
y—Predicted value of the dependent variable
x —Independent or predictor variable
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What is 1 1/2 + 5/7?
Find the cosecant. Someone help me asap pls!
Answer:
sqrt2
Step-by-step explanation:
csc (x)= 1/sin(x)
sin(x)= (sqrt22)/(sqrt22*sqrt2)= 1/sqrt2
1/(1/sqrt2)=sqrt2/1=sqrt2
Compute Shannon's %NMC. Round your answer to the nearest percent. For example, if your
computed answer is 99.4% your answer rounds down to 99%. If your computed answer is
99.5% you should round up to 100%.
The Shannon's %Net market contribution = 40%
What is NMC (Net market contribution)?
Net market contribution (NMC) is equal to total sales revenue less total costs (except market costs) minus market costs.
Cost overall (not including market expenses):
150000 packaged (in cans and bottles).
Kegs =80000
WIP Loss/Reduction = 42000
Labor Contracts = 9000
Total Direct Labor: 240000
18000 inbound pounds
180000 in compensation
Total= 719000
Consumer advertising costs 26850 on the market.
Marketing for trade = 31761
Promotional Sales = 18000
Total=76611 Net market contribution=1320271-719000-76611=$ 524660 %NMC=524660/1320271=0.3974=39.74%=40%
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What properties of equality do you need to use to solve the equation 2.1x−1.6=6.8? Solve the equation. Question content area bottom Part 1 What properties of equality do you need to use to solve the equation? Select all that apply. A. The Division Property of Equality B. The Multiplication Property of Equality C. The Subtraction Property of Equality D. The Addition Property of Equality Part 2 The solution is enter your response here. (Type the value of x.)
it is 6.1
Step-by-step explanation:
No matter what I've tried, nothing works. Hopefully you can help me
Answer:
see explanation
Step-by-step explanation:
given Δ ABD is isosceles with AB = AD then base angles are congruent, so
∠ ADB = ∠ ABD = 72°
then
∠ BAD = 180° - (72 + 72)° = 180° - 144° = 36° ( sum of angles in a triangle )
given Δ ABC is isosceles , then
∠ BCD = ∠ BAD = 36°
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ ADB is an exterior angle of Δ BCD , then
∠ BCD + ∠ DBC = ∠ ADB
36° + ∠ DBC = 72° ( subtract 36° from both sides )
∠ DBC = 36°
So ∠ BCD = ∠ DBC = 36°
Thus the base angles of Δ BCD are congruent , then
Δ BCD is isosceles with BD = CD
Which is the equation of line b
The equation of line b that passes through the point (-3,2) is y=-1/4x+5/4
How do you find a line equation?to get the equation of a line given a point and its slope.
Recognize the slope.
Decide on the point.
In the point-slope form, y y 1 = m (x x 1), substitute the values. y − y 1 = m (x − x 1) .
Slope-intercept form should be used to write the equation.
What are the 3 different equations of lines?There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form.
In the above question we see that,
The line b passes through the point (-3,2)
the equation of line should satisfy this point
In the given option the only line that satisfy the point is
option C
y=-1/4x+5/4
hence option C ,y=-1/4x+5/4 is the answer
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Please answer the two following questions.
The transformed graph is attached
The domain is (-∝, ∝) and the range is (-3, ∝)
How to transform the graph?From the question, we have the following parameters that can be used in our computation:
y = eˣ
To transform the graph to y = e⁻ˣ - 3, we make use of the following rules:
Reflect across the y-axisShift down by 3 unitsSee attachment for the graph of y = e⁻ˣ - 3
The domain and the rangeFrom the attached graph, we have:
The graph extends across the x-axis i.e. domain = (-∝, ∝)
The graph opens upward from y > -3 i.e. range = (-3, ∝)
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In the Two Period Consumer model, the Net Effect from a decrease in the interest rate for a net borrower is:
Group of answer choices
C1↓; C2?; Savings ↑
C1↑; C2?; Savings ↓
C1↑; C2↓; Savings ↓
C1?; C2↓; Savings ?
C1?; C2↑; Savings ?
In the two period consumer model , the net effect from a decrease in the interest rate for a net borrower is increase in present consumption (C1 increases) , future consumption decreases (C2 decreases) and savings decreases.
What is two period consumer model?
The consumer lives for two cycles before passing away. Therefore, there is no use in saving during the second time period. Rearranging, our present disposable income minus our current consumption is what we call savings.By deciding not to spend their entire income during the present period, consumers conserve money. They borrow money from the credit market to cover the difference between their income and current expenditure, boosting their future period income by the amount they saved plus interest.A useful simplification, in fact. Maximum current expenditure exceeds maximum current income.Hence, the net effect from a decrease in the interest rate for a net borrower is increase in present consumption (C1 increases) , future consumption decreases (C2 decreases) and savings decreases.
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a box contains ten sealed envelopes numbered 1, . . . , 10. the first six contain no money, the next two each contains $5, and there is a $10 bill in each of the last two. a sample of size 3 is selected with replacement (so we have a random sample), and you get the largest amount in any of the envelopes selected. if x1, x2, and x3 denote the amounts in the selected envelopes, the statistic of interest is m
The probability distribution for the statistic is ; for m = 0 , P(0) = 0.216 , for m = 5 ,P(5) = 0.296 and for m = 10 , P(10) = 0.488 .
In the question ,
it is given that ,
the box has 10 sealed envelopes , that contains number from 1,2,...,10 .
the first six envelopes has no money .
next two envelopes has $5
and the last two contains $10 bill .
if x₁, x₂, and x₃ denote the amounts in the selected envelopes,
the statistic of interest is m = maximum of X₁ , X₂ and X₃ .
we need to find probability distribution for the statistic m,
So , P(m = 0) = P( all three envelope contains no money) = (6/10)³ = 0.216
and P(m = 5) = P( all from 8 envelope which contains at most $5) - P(all three envelope with 0 money)
= (8/10)³ - 0.216
= 0.296
and P(m = 10) = 1 - (8/10)³ = 0.488
Therefore , the required probability is P(0) = 0.216 , P(5) = 0.296 and P(10) = 0.488 .
The given question is incomplete , the complete question is
A box contains ten sealed envelopes numbered 1, . . . , 10. the first six contain no money, the next two each contains $5, and there is a $10 bill in each of the last two. a sample of size 3 is selected with replacement (so we have a random sample), and you get the largest amount in any of the envelopes selected. if x₁, x₂, and x₃ denote the amounts in the selected envelopes, the statistic of interest is M = the maximum of X₁ ; X₂ , and X₃ . Obtain the probability distribution of this statistic ?
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Use the given data to find the minimum sample size required to estimate the population proportion. Margin of error: 0.04; confidence level: 99%; from a prior study, p is estimated by 0.12.
The value of the minimum sample size required to estimate the population proportion is 438.
What is the margin of error?Your results will vary from the actual population value by how many percentage points, as indicated by the margin of error. A 95% confidence interval with a 4% margin of error, for instance, indicates that your statistic will, 95% of the time, be within 4% of the true population figure.
Given:
The margin of error, ME = 0.04,
The value of p = 0.12,
The confidence level = 99%,
Calculate the minimum sample size as shown below,
ME = z √[p(1 - p) / n]
Calculate the value of z from the table attached below considering the confidence level, z = 2.576,
0.04 = 2.576 √[0.12(1 - 0.12) / n]
Squaring both sides,
0.0016 = 6.636 × 0.12 × 0.88 / n
n = 0.7 / 0.0016
n = 437.9 or 438
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can anyone please help me with this math question?
Answer:
a) (7-2x) +3 = 10 - 2X
b) x = y + 3 <=> y = x-3
c) (x-3).-2 +7 = -2x +6 +7 => -10 + 13 = 3
As part of her science project , Shay is making a model of a wind farm.She wants to put 24 turbines in her model.What arrays can Shay make using 24 turbines
Answer: In Shay's wind farm their can be 4 arrays
Search up the meaning of a Array if you are confused
Step-by-step explanation:
24 has 4 pairs of factors.
1,242,123,84,6
Overtime Hours Worked A random sample of 15 registered nurses in a large hospital showed that they worked on average 44.6
hours per week. The standard deviation of the sample was 2.3. Estimate the mean of the population with 99% confidence.
Assume the variable is normally distributed. Round intermediate answers to at least three decimal places. Round your final
answers to one decimal place.
Answer:
With 99% confidence we can say that the mean of the population is between 43.1 and 46.1
Step-by-step explanation:
Determine how many times the innermost loop will be iterated when the algorithm segment is implemented and run. (Assume that m and n are positive integers.)
for j := 1 to m
for k := 1 to n
[Statements in body of inner loop.
None contain branching statements that
lead outside the loop.]
next k
next j
Discrete mathematics
The inner loop iterates 'n' times, outer loop iterates 'm' times and total loop iterates (m×n) times.
Given program,
for j = 1 to m
k = 1 to n
statement in the body of innerloop. None contain branching statements that lead outside the loop.
next j
next k
Here, in the inner loop k iterates from 1 to n that is n times and j iterates from 1 to m that is m times.
Finally, the whole loop iterates m×n times because for every value of j from 1 to m, k value increases from 1 to n.
So, the inner loop iterates 'n' times, outer loop iterates 'm' times and total loop iterates (m×n) times.
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e. 2|x-4|-3y³ when x=3 and y=-2
Answer:
26
Step-by-step explanation:
To find the value of the expression 2|x-4|-3y³ when x=3 and y=-2, we need to substitute the values of x and y into the expression and then simplify. The absolute value part of the expression, |x-4|, is the distance between the number x and 4 on the number line. When x=3, this distance is |3-4|=1. So the expression becomes 2*1-3(-2)³ = 2-3(-8) = 2+24 = 26. Therefore, when x=3 and y=-2, the value of the expression 2|x-4|-3y³ is 26.
Ben and Bob made a snowman been spent two hours more than double the time Bob spent
Solve for x.
3/7x +1/4x =38
Answer:
x = 56
Step-by-step explanation:
[tex]\frac{3}{7}[/tex] x + [tex]\frac{1}{4}[/tex] x = 38 The common denominator would be 28
[tex]\frac{12}{28}[/tex] x + [tex]\frac{7}{28}[/tex] x =38
[tex]\frac{19}{28}[/tex] x = 38 Multiply both sides by [tex]\frac{28}{19}[/tex]
[tex](\frac{28}{19})[/tex][tex]\frac{19}{28}[/tex] x = [tex](\frac{28}{19})[/tex][tex]\frac{38}{1}[/tex] Cross cancel the 19 and 38.
x = [tex](\frac{28}{1})[/tex][tex]\frac{2}{1}[/tex]
x = 56
test for an association between handeness and career for these 5 professions. state the null and alternative hypothesis
Null Hypothesis: There is no association between handedness and career for Accountants. And Alternative Hypothesis: There is an association between handedness and career for Accountants.
Profession 1: Lawyer
Null Hypothesis: There is no association between handedness and career for Lawyers.
Alternative Hypothesis: There is an association between handedness and career for Lawyers.
Profession 2: Pilot
Null Hypothesis: There is no association between handedness and career for Pilots.
Alternative Hypothesis: There is an association between handedness and career for Pilots.
Profession 3: Accountant
Null Hypothesis: There is no association between handedness and career for Accountants.
Alternative Hypothesis: There is an association between handedness and career for Accountants.
Profession 4: Nurse
Null Hypothesis: There is no association between handedness and career for Nurses.
Alternative Hypothesis: There is an association between handedness and career for Nurses.
Profession 5: Teacher
Null Hypothesis: There is no association between handedness and career for Teachers.
Alternative Hypothesis: There is an association between handedness and career for Teachers.
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the sugar sweet company delivers sugar to its customers. let be the total cost to transport the sugar (in dollars). let be the amount of sugar transported (in tons). the company can transport up to tons of sugar. suppose that gives as a function of . identify the correct description of the values in both the domain and range of the function. then, for each, choose the most appropriate set of values.
The domain of the function is: [0,∞), the range of the function is: [3500,∞)
What does domain and range mean?Domain and Range: The set which contains all the first elements of all the ordered pairs of relation R is known as the domain of the relation. The set which contains all the second elements, on the other hand, is known as the range of the relation.
The potential input and output values of a function are its domain and range, respectively.
The formula for the function is C=130S+3500.
the region
This is a list of the function's potential S values.
Due to the fact that S refers to a physical quantity, it cannot be less than 0. (i.e. tons of sugar)
The domain of the function is [0,∞)
Since S can have any value larger than 0.
The variety
This represents the function's potential C values.
The formula for the function is C=130S+3500.
Assuming S = 0, the following is true: C=130*0+3500=3500.
C must be more than 3500.
Any number higher than 3500 can be used as the value of C.
Consequently, the function's range is [3500,∞)
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