The radioactive decay of sm-151 (an isotope of samarium) can be modeled by the differential equation dy /dt = -0.0077y, DOthe half-life of Sm-151 is 90 years.
What is sm-151?Sm-151 is a radioactive isotope of the element Samarium. The symbol for Sm-151 is 151Sm, and the atomic number of Samarium is 62. This isotope has a half-life of 88 years.
Differential equations differential equation that model the radioactive decay of Sm-151 is given as
dy/dt = -0.0077y, where t is measured in years.
To find the half-life of Sm-151, we can use the formula for half-life, which is given as:
t1/2 = (ln 2) / k
Where k is the decay constant. To find k, we can use the given differential equation.
dy/dt = -0.0077y
Separating variables, we get
dy / y = -0.0077 dt
Integrating both sides,
we get ln y = -0.0077 t + C
Where C is the constant of integration.
To find C, we use the initial condition, y(0) = y0, where y0 is the initial amount of Sm-151.
Substituting this in the above equation, we get ln y0 = CSo,
the equation becomes y = -0.0077 t + ln y0
Taking the exponential of both sides, we get y = y0 e^(-0.0077t)
Using the formula for k, we get k = 0.0077
Substituting this in the formula for half-life,
we get: t1/2 = (ln 2) / k
= (ln 2) / 0.0077
= 90 years
Therefore, the half-life of Sm-151 is 90 years.
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I Really want this pleaseeeeeeeeeeeeeeeeeee
Answer:no
Step-by-step explanation:
using the Pythagorean theorem:
a^2+b^2=c^2
42^2+26^2=50^2
1764+676=2500
2440=2500
2440<2500
So the answer is no
Which of the following sets would have a graph with an open circle on 5 and a ray pointing left on the number line?
A. {x | x R, x < 5}
B.{x | x R, x > 5}
C.{x | x R, x ≤ 5}
{x | x ∈ R, x < 5} would have a graph with an open circle on 5 and a ray pointing left on the number line.
What is an interval notation?In interval notation, the set {x | x R, x < 5} can be written as (-∞, 5). The symbol (-∞) represents negative infinity, which means all numbers less than any finite number.
So, the interval (-∞, 5) includes all real numbers less than 5, but does not include 5 itself.
To graph this set on a number line, we would draw an open circle at the point 5, because 5 is not included in the set. Then, we would draw a ray pointing to the left, because the set includes all numbers less than 5.
The ray extends indefinitely to the left, because there is no greatest number that is less than 5.
Therefore, the graph of the set {x | x R, x < 5} on a number line would have an open circle at 5 and a ray pointing to the left.
What does an open circle on a number line indicate?
An open circle on a number line indicates that the number is not included in the set.
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The function g(x) is shown on the graph.
The graph shows an upward opening parabola with a vertex at negative 3 comma negative 2, a point at negative 5 comma 2, and a point at negative 1 comma 2.
What is the equation of g(x) in vertex form?
g(x) = (x − 3)2 − 2
g(x) = (x − 3)2 + 2
g(x) = (x + 3)2 − 2
g(x) = (x + 3)2 + 2
The equation of g(x) in vertex form include the following: C. g(x) = (x + 3)² - 2.
What is the vertex form of a quadratic equation?In this exercise, you are required to determine the vertex form of a quadratic function h(x) that is written in standard form. Mathematically, the vertex form of a quadratic equation is given by this formula:
y = a(x - h)² + k
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.Based on the information provided about the graph of this quadratic function, we can reasonably infer and logically deduce that a mathematical expression which quickly reveals the vertex of the quadratic function is given by:
y = a(x - h)² + k
y = (x - (-3))² + (-2)
y = g(x) = (x + 3)² - 2
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nug
4. Alex wants to go Go Karting. There are two options for pricing:
i. $30 for 25 laps
or ii. $75 for 2 hours.
a) Convert each to UNIT RATES.
The statements when converted to unit rates are $1.20 per lap and $37.50 per hour
How to calculate the unit ratesTo compare the pricing options, we can convert each to a unit rate, which is a rate with a denominator of 1.
This allows us to compare the cost of each option per lap or per hour.
i. $30 for 25 laps:
To find the unit rate, we can divide the total cost by the number of laps:
Unit rate = $30 ÷ 25 laps = $1.20 per lap.
ii. $75 for 2 hours:
To find the unit rate, we can divide the total cost by the number of hours:
Unit rate = $75 ÷ 2 hours = $37.50 per hour.
So, the unit rate for option i is $1.20 per lap and the unit rate for option ii is $37.50 per hour.
By comparing the unit rates, we can determine which pricing option is more cost-effective based on the number of laps or hours Alex wants to ride.
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on a control chart, what separates common from assignable causes of variation? a. specification limits b. mean divided by standard deviation c. control limits d. production limits e. x-bar lines
On a control chart, Control limits separates common from assignable causes of variation option C.
Shewhart charts, after Walter A. Shewhart, are another name for control charts. It is a statistical process control tool that aids in tracking process advancements over time. For instance, hospital management decides to utilise a solution technique in order to shorten the time required to admit a patient.
The process flow diagram for how patients are admitted to the hospital is first created. The average amount of time it takes to admit a patient each day is then measured. Lastly, plot the process variables across time on a control chart.
This control chart's goals are to identify any "special" reasons of variation as well as to document any process improvements.
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a vat with 900 gallons of beer contains 4% alcohol (by volume). beer with 6% alcohol is pumped into the vat at a rate of 9 gal/min and the mixture is pumped out at the same rate. what is the percentage of alcohol after an hour? (round your answer to one decimal place.)
The percentage of alcohol in the vat after an hour will be 4.8%.
Explanation:
Given that a vat with 900 gallons of beer contains 4% alcohol (by volume), beer with 6% alcohol is pumped into the vat at a rate of 9 gal/min and the mixture is pumped out at the same rate. We need to find the percentage of alcohol after an hour.
Let's consider V be the volume of the vat and x be the percentage of alcohol in the vat. Now, the total amount of alcohol in the vat will be Vx.
Let A be the volume of alcohol added in the vat per minute by the pump. Now the volume of alcohol in the vat after a minute will be Vx + A and the volume of the mixture will be V+ 9.
Now the volume of alcohol in the mixture will be (Vx + A)×(x%) and the total amount of alcohol in the mixture will be Vx(x%) + 9A×(6%).
So, the volume of alcohol in the mixture after a minute will be (Vx(x%) + 9A×(6%))/(V + 9).
The rate of change of x will be given by (Vx(x%) + 9A×(6%))/(V + 9) - x/(V + 9). On solving this we get the differential equation:
dx/dt = 0.06 - 0.000067x
On solving the differential equation we get:
x = 80 + 8200/(75e^(0.000067t))
At t = 60 minutes, x = 80 + 8200/(75e^(0.000067×60)) = 4.8%.
Therefore, the percentage of alcohol in the vat after an hour will be 4.8%.
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you need to have a password with 4 letters followed by 2 even digits between 0 and 9 , inclusive. if the characters and digits cannot be used more than once, how many choices do you have for your password?
There are 6,354,000 choices for the password.
To generate a password, you need to have 4 letters followed by 2 even digits between 0 and 9, inclusive.
If the characters and digits cannot be used more than once,
Solution: We have to find the number of choices of the password with given conditions.
To find the number of choices, let us follow the following steps:
Step 1: Choose the first letter in 26 ways
Step 2: Choose the second letter in 25 ways (excluding the letter that we have already chosen)
Step 3: Choose the third letter in 24 ways (excluding the 2 letters that we have already chosen)
Step 4: Choose the fourth letter in 23 ways (excluding the 3 letters that we have already chosen)
Step 5: Choose the first even digit in 5 ways (from 0, 2, 4, 6, and 8)
Step 6: Choose the second even digit in 4 ways (excluding the even digit that we have already chosen)
Therefore, the total number of choices for the password with the given conditions is given by:
Total number of choices = 26 × 25 × 24 × 23 × 5 × 4= 6,354,000.
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from the position of the bus on the street, the l'arc de triomphe is at an angle of 34 degrees. if the arc is 162 feet tall, how far away is the bus? round to the nearest tenth.
The bus is approximately 373.8 feet away from the base of the l'Arc de Triomphe
To solve this problem, we can use trigonometry. Let's assume that the bus is at point A on the street, and the top of the l'Arc de Triomphe is at point B. The height of the arc is 162 feet.
We want to find the distance AB, which is the horizontal distance from the bus to the base of the arc. We know that the angle of elevation from the bus to the top of the arc is 34 degrees. Let's call the height of the bus H, and the distance AB D.
From the perspective of the bus, we can see that the height of the arc and the height of the bus together form a right triangle with angle of elevation 34 degrees. Therefore, we have:
tan(34) = (162 + H)/D
We can solve this equation for D:
D = (162 + H)/tan(34)
We need to find H to solve for D. To do this, we can use similar triangles. The triangle formed by the bus, the base of the arc, and the top of the arc is similar to the triangle formed by the bus, the ground, and the point directly beneath the top of the arc. Let's call the distance from the base of the arc to the point directly beneath the top of the arc x.
From the perspective of the bus, we can see that the height of the arc and the distance from the base of the arc to the point directly beneath the top of the arc together form a right triangle with angle of elevation 34 degrees. Therefore, we have:
tan(34) = 162/x
Solving for x, we get:
x = 162/tan(34)
Now, the height of the bus is simply H = x*tan(34). Substituting this into the equation for D, we get:
D = (162 + x*tan(34))/tan(34)
Substituting the value of x, we get:
D = (162 + (162/tan(34))*tan(34))/tan(34) = 373.8 feet (rounded to the nearest tenth)
Therefore, the bus is approximately 373.8 feet away from the base of the l'Arc de Triomphe.
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PLEASE HELP ASAP!!!!!!!!!!!!!!
Rewrite each of the following expressions without using absolute value
1.|x-1| if x>1
2. |x-y| if x>y
3. |3-[tex]\sqrt{4}[/tex]
4. |4r -12| if r<3
5. |[tex]\sqrt{15} -5+1[/tex]
6. |4-[tex]\sqrt{7}[/tex]
7. |7m-56| if m<8
8. |z-7|-|z-9| if z<7
Answer:
1 4(3-r) or 12-4r
2. 7( 8-m) or 56-7m
3. -2
Step-by-step explanation:
1) |4r−12| , if r<3
|4r-12|
Factor out a 4
4|r-3|
|r-3| will be less than 0 since r is less than 3
So we can rewrite it as 3-r to remove the absolute value signs and make it positive
4 (3-r)
12 -4r
2. |7m–56| , if m<8
Factor out a 7
7| m-8|
|m-8| will be less than 0 since m is less than 8
So we can rewrite it as 8-m to remove the absolute value signs and make it positive
7( 8-m)
56-8m
3) |z−7|−|z−9| , if z<7
|z-7| will be less than 0 since z is less than 7 and |z-9| will be less than 0 since z is less than 7
So we can rewrite it as 7-z and 9-z to remove the absolute value signs and make it positive
7-z - (9-z)
Distribute the minus sign
7-z-9+z
-2
As shown below, Ghana makes a triangular decoration out of clay.
When she fires it in the kiln, it shrinks proportionally. If the base of the
finished decoration is only 9 inches after firing, what is the height, in inches,
of the finished decoration?
A
B
с
D
4
5
6
10 in.
8
15 in.
TIPS AND F
Check your answe
makes sense. Since
half of 15, the answ
more than half of 10
Answer:
Since the decoration is in the shape of a triangle, we can use the formula for the area of a triangle to solve for its height. The area of a triangle is given by:
Area = (1/2) x base x height
Let's call the height of the decoration h. We know that the base after firing is 9 inches, so we can plug in the given values and solve for h:
Area = (1/2) x 9 x h
Area = 4.5h
We don't know the exact area of the decoration, but we do know that the decoration maintains its shape after firing. This means that the ratio of the areas before and after firing is the same, and so is the ratio of the heights and bases. Since the height and base are proportional, we can write:
h / 15 = 9 / 10
Simplifying the equation, we get:
h = (9/10) x 15
h = 13.5
Therefore, the height of the finished decoration is 13.5 inches.
X-y=1/5 in slope-intercept form
The equation in slope- intercept form is y = x - 1/5
How to write the expressionIt is important to note that the expression representing the equation of a line in slope- intercept form is written as;
y = mx + c
Such that the parameters are;
y is a point on the y - axis of the graph.m is the slope of the line.x is a point on the x - axis.c is the intercept on the y -axis of the graph.From the information given, we have;X-y=1/5collect the variables and constants, we have;
- y = 1/5 - x
reconstruct the expression
- y = -x + 1/5
Divide both sides by the coefficient of y , we have;
y = x - 1/5
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Solve the system of equations. \begin{aligned} &-4y+11x - 67=0 \\\\ &2y+5x-19=0 \end{aligned}
−4y+11x−67=0
2y+5x−19=0
The solution to the system of equations is x = 5 and y = -3.
We can use the elimination method by multiplying the second equation by 2 and adding it to the first equation to eliminate y:
= -4y + 11x - 67 + 2(2y + 5x - 19) = 0
-4y + 11x - 67 + 4y + 10x - 38 = 0
21x - 105 = 0
Dividing both sides by 21, we get:
x - 5 = 0
So x = 5.
Now we can substitute x = 5 into either of the original equations:
2y + 5x - 19 = 0
2y + 5(5) - 19 = 0
y = -3
Thus, the solution to the system of equations is:
x = 5, and y = -3.
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0.
Ryan checked out 3 books from the library: one mystery (M), one history book (H), and one biography (B). Which tree diagram shows all the possible orders in which Ryan can read the 3 books?
...
This tree diagram shows all possible orders in which Ryan can read the 3 books, including reading the mystery book (M) first, the history book (H) second, and the biography (B) last, as well as reading the biography first, the mystery second, and the history last.
What is mystery?Mystery is an intriguing and often baffling phenomenon or situation. It is something that is not easily explained or understood and often involves a puzzle or secret that needs to be solved. It can be an event, an entity, or a situation that evokes curiosity, suspense, and a desire to uncover the truth. Mystery can be found in everyday life, literature, films, and other forms of entertainment. It is often used to create a sense of anticipation and wonder, and can be a powerful tool in storytelling. Mystery can also be used to explore deeper truths and to connect with our own inner mysteries.
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Complete Question is attached below:
inspect the furnsale7 data set. what structure do these data appear to take? panel data time series cross sectional
The furnsale7 data set appears to take the form of a panel data structure.
Panel data is a type of longitudinal data that combines observations over multiple time periods for the same individual or group.
This type of data contains multiple observations for the same unit over time and provides valuable insight into changes that occur over time.
Panel data can provide valuable insights into long-term trends and changes in behavior or trends in a population. Panel data can also be used to study economic growth and development, market trends, and consumer behavior.
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what will happen to the solution if the objective function coefficient for variable 1 decreases by 20?
If the objective function coefficient for variable 1 decreases by 20, the solution will shift in the direction of the decrease in the objective function coefficient. It means that the optimal solution that was obtained previously will no longer remain optimal, and the new optimal solution will be found with the new objective function coefficient.
In linear programming, the objective function determines the maximum or minimum value that can be attained in the solution, subject to the constraints. The constraints in the problem can be either equalities or inequalities, which limit the range of values that the decision variables can take on.
The change in the objective function coefficient will change the direction of the optimal solution, and it may affect the feasibility of the solution. It means that some constraints may no longer be satisfied, or some variables may become infeasible.
In such cases, it will be necessary to revise the constraints or the variables to ensure the feasibility of the solution.
The solution can also be affected if the constraints of the problem change. The new constraints may limit the range of values that the variables can take on, or they may add new variables to the problem. These changes can affect the feasibility of the solution, and it may require the problem to be solved again to obtain the new optimal solution.
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you have six bottles of paroxetine 10 mg in stock. the par level is four bottles, and the maximum quantity is ten bottles. how many bottles should be ordered?
The order quantity should be 4 bottles.
There are 6 bottles of paroxetine 10 mg in stock, and the par level is 4 bottles, while the maximum quantity is 10 bottles. The question is asking how many bottles should be ordered.
This can be found by calculating the difference between the current stock level and the par level and then adding this difference to the current stock level. If the result exceeds the maximum quantity, the order quantity is equal to the difference between the maximum quantity and the current stock level.
Otherwise, the order quantity is equal to the difference between the current stock level and the par level.In this case, the difference between the current stock level and the par level is 6 - 4 = 2 bottles. Adding this difference to the current stock level gives us a total of 6 + 2 = 8 bottles.
Since 8 is less than the maximum quantity of 10, the order quantity is 8 - 4 = 4 bottles. Therefore, 4 bottles should be ordered to maintain the par level of 4 bottles. Therefore, the order quantity should be 4 bottles.
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please help dude i have no clue what to do
Answer:94.2
Step-by-step explanation: here is a answer i think
Answer:
C= 94.2
Step-by-step explanation:
To find the circumference you would multiply 15 and 2 and then multiply that answer by pi, or 3.14.
Tom
Sean
Darryl
Anne
0825
$300
$750
$1,300
$145
Return
7%
10%
EF
After One Year
A
C
156
10.5
The number that goes to column D is the total equity of $825.
Explain about the total equity?The sum that investors put in a firm in return for stock, plus all future profits realized by the company, less all future dividends paid out, is referred to as total equity.Any investment made by the business's owner counts as equity, as do the total assets less the total liabilities. To give just a few examples, consider common stock, extra special capital, preferred stock, interest income, and total other comprehensive income.Using annual rate of return APR:
A = P *[tex](1 + r/n)^{nt}[/tex]
P = $750.
r = 10%
t = 1 year
n = 1
A = 750 * [tex](1 + 0.1/1)^{1*1}[/tex]
A = 750 * 1.1
A = 825
Thus, the number that goes to column D is the total equity of $825.
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Please help me find the Surface Area and Volume of this triangular prism
Surface area
2 triangles: Just do bh instead of 1/2bh, bh = 8 * 3 = 24
2 rectangles: 2bh but we first need to find h. The altitude pictured by dotted line, creates a right triangle where its hypotenuse is h. Since it also has side lengths 3 and 4, h = 5 (by pythag triplets). Then, 2bh = 2 * 12 * 5 = 120
base: bh = 12 * 8 = 96
Adding these areas we have 24 + 120 + 96 = 240
Volume: Bh (big b signifies area of the base)
B = area of the triangle = 1/2bh = 1/2 * 8 * 3 = 12
So Bh = 12 *12 = 144
Hope this helps you understand the process.
Will ran around a track that was 1/4 of a mile long. He ran around the track 12 times. How many miles did Will run?
When Will ran around the track 12 times, he ran a total distance of 12 x 0.25 = 3 miles. The answer is 3 miles.
What is a lap?The lap is the total distance a runner has to cover to complete one full circuit of the track. Depending on the size of the track, the lap distance can vary.
In the case of Will, he ran a total of 12 laps of a track that was 1/4 of a mile long.
This means that he ran a total distance of 12 x 0.25 = 3 miles.
This is because 1/4 of a mile is equal to 0.25 miles.
The equation used to calculate the total distance run by Will is: Distance = Number of laps x Length of each lap.
This equation can be used to calculate the total distance run by any runner on any track of any length.
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Ignore everything above look at bottom of pic for question
The surface area of the triangular prism Milo paints red is equal to 186 square centimeters.
How to evaluate for the surface area of the triangular prismThe triangular prism have two triangle and three rectangle faces, so we shall calculate for each area of the faces and add them to get the surface area of the triangular prism as follows:
area of triangle = 1/2(base × height)
area of one triangle face = 1/2(6 cm × 4 cm)
area of one triangle face = 12 cm²
area of two triangle faces = 2 × 12 cm² =24 cm²
area of one rectangle face = 10.8 cm × 5 cm
area of one rectangle face = 54 cm²
area of three rectangle faces = 162 cm²
area of the triangular prism = 24 cm² + 162 cm³
area of the triangular prism = 186 cm²
Therefore, the surface area of the triangular prism Milo paints red is equal to 186 square centimeters.
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5. Janice is creating a design that is part of a logo consisting of a small and a large circle.
The diameter of the small circle is of the diameter of the large circle. The diameter of
the large circle is 27 centimeters. To the nearest tenth of a centimeter, what is the area
of the smaller circle?
27 cm
Answer: The area of the smaller circle is [tex]65.6cm^{2}[/tex].
Step-by-step explanation:
A = [tex]\pi r^{2}[/tex], r is the radius.
1. Find out the diameter of the small circle.
[tex]\frac{1}{3}(27)= 9[/tex]
2) Find out the radius, r.
[tex]radius = \frac{diameter}{2} =\frac{9}{2} =4.5[/tex]
3) We plugin r = 4.5 into the formula to solve the area of the smaller circle.
[tex]A=\pi r^{2}=\pi (4.5)^{2} =65.6cm^{2}[/tex]
in a baseball league of 10 teams, how many games are needed to complete the schedule if each team plays 11 games with each other?
Which one of the following decisions most clearly reflects a lack of understanding of the concept of sunk costs? You pay to have your car towed back to the repair shop because it was not fixed properly the first time. You decide to get a master's degree because you cannot find a job in the field in which you majored. You decide to purchase a piece of machinery for your business that will eliminate three employees' positions. You study eight hours for a final exam even though there is no way now that you can pass the course.
The decision that most clearly reflects a lack of understanding of the concept of sunk costs is "You study eight hours for a final exam even though there is no way now that you can pass the course".
What are sunk costs?Sunk costs refer to any costs that have already been incurred and cannot be recovered. Sunk costs are irrelevant in decision-making because they are already gone and cannot be recovered. Decision-makers must only consider future costs and benefits when making decisions.
What does it mean to lack an understanding of sunk costs?A lack of understanding of sunk costs may result in individuals making decisions based on past costs rather than future costs and benefits. Decision-making that is influenced by sunk costs may result in inefficient resource allocation and lost opportunities.
Individuals must ignore sunk costs and instead focus on future costs and benefits to make effective decisions.
In the given options, "You study eight hours for a final exam even though there is no way now that you can pass the course" is the decision that most clearly reflects a lack of understanding of the concept of sunk costs.
Even though the student has already spent 8 hours studying, the sunk costs are irrelevant because the student cannot pass the course now. The student should focus on future costs and benefits and use the remaining time to study for other courses.
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the time it takes a person to wash the dishes is uniformly distributed between 8 minutes and 17 minutes. what is the probability that a randomly selected event of washing dishes will take a person between 12 and 15 minutes? round your answer accurate to two decimal places.
The probability that a randomly selected event of washing dishes will take a person between 12 and 15 minutes is 0.33 or 33%.
Uniform distribution is a probability distribution where all outcomes are equally likely. In this case, the time it takes to wash dishes is uniformly distributed between 8 and 17 minutes. This means that any time between 8 and 17 minutes is equally likely to occur.
To find the probability that a randomly selected event of washing dishes will take a person between 12 and 15 minutes, we need to find the area under the curve of the uniform distribution function between 12 and 15 minutes.
Since the distribution is uniform, the area under the curve between 12 and 15 minutes is simply the width of the interval divided by the total width of the distribution. Mathematically, we can express this as:
P(12 ≤ X ≤ 15) = (15 - 12) / (17 - 8)
P(12 ≤ X ≤ 15) = 3 / 9
P(12 ≤ X ≤ 15) = 0.33 or 33%.
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combined with a high tide on september 16, 2020 by how many feet did that storm surge submerge the lowest parts of pensacola beach? enter a number (no words) in the blank.
The steps to find the depth through which the storm submerges the lowest parts of the Pensacola Beach is given below.
How to solve for the feet that the storm submerges?As it has been given in the question, Pensacola beach is located 5-10 feet above sea level.
The ocean water rises upto 5.5 feet during a storm
Hence you need to add up the height of the highest tide on 16 September to 5.5 feet.
If the combined height of the highest tide and the storm tide is greater than 10 feet, then the whole Pensacola beach submerges.
You just subtract the combined height of the storm and the highest tide from the height of the beach.
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Portions of Pensacola Beach, a coastal community built on a barrier island, are located at 3 - 10 feet above sea level.
Hurricane Sally, which struck Pensacola on September 16, 2020 and brought a 5.5 foot storm.
Combined with a high tide on September 16,202, by how many feet did that storm surge submerge the lowest parts of Pensacola Beach? (Hint: use the information in question and change the date on the tidal chart to September 16, 2020) Now, compare your answers above, and think about how the type (pattern) and size of the tides differ for these two locations
At Rachel's 11th birthday party, 8 girls were timed to see how long (in seconds) they could hold their breath in a relaxed position. After a two-minute rest, they timed themselves while jumping. The girls thought that the jumping would not affect their times, on average. Test their hypothesis at the 5% level. Relaxed time (seconds) Jumping time (seconds) 27 20 49 43 31 28 22 21 23 25 45 43 37 35 29 32 NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) What is the p-value? (Round your answer to four decimal places.)
The p-value is (0.0297)
To test the hypothesis that jumping does not affect the girls' breath-holding times, we will conduct a paired t-test using the given data. Here's a step-by-step explanation:
Solution:
1. Calculate the difference between relaxed and jumping times for each girl:
(27-20), (49-43), (31-28), (22-21), (23-25), (45-43), (37-35), (29-32)
The differences are: 7, 6, 3, 1, -2, 2, 2, -3
2. Compute the mean and standard deviation of the differences:
Mean = (7+6+3+1-2+2+2-3)/8 = 16/8 = 2
Standard Deviation = sqrt[((7-2)^2+(6-2)^2+(3-2)^2+(1-2)^2+(-2-2)^2+(2-2)^2+(2-2)^2+(-3-2)^2)/7] = sqrt(42/7) = sqrt(6)
3. Calculate the t-statistic:
t = (Mean - Hypothesized Mean) / (Standard Deviation / sqrt(N))
t = (2 - 0) / (sqrt(6) / sqrt(8)) = 2 / (sqrt(6) / 2.828) ≈ 2 / 0.748 ≈ 2.675
4. Determine the p-value using the t-distribution table or calculator for a two-tailed test with 7 degrees of freedom (N-1) at the 5% level:
The p-value is 0.0297 (rounded to four decimal places).
Since the p-value (0.0297) is less than the significance level of 0.05, we reject the null hypothesis that jumping does not affect the girls' breath-holding times, on average.
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Please answer with explanation!
The extreme values of the function f(x, y, z) = x^2 + y^2 + z^2, x^2 + y^2 + z^2 + xy = 27 are minimum = 0 and maximum = 18
Calculating the extreme values of the functionGiven that
f(x, y, z) = x^2 + y^2 + z^2, x^2 + y^2 + z^2 + xy = 27
To find the extreme values of the function f(x, y, z) subject to the given constraint, we can use the method of Lagrange multipliers.
Defining the Lagrangian function L as follows:
L(x, y, z, λ) = f(x, y, z) - λ(g(x, y, z))
where g(x, y, z) is the constraint function and λ is the Lagrange multiplier.
In our case, we have:
f(x, y, z) = x^2 + y^2 + z^2
g(x, y, z) = x^2 + y^2 + z^2 + xy - 27
So, our Lagrangian function becomes:
L(x, y, z, λ) = x^2 + y^2 + z^2 - λ(x^2 + y^2 + z^2 + xy - 27)
To find the extreme values of f(x, y, z) subject to the constraint g(x, y, z) = 0, we need to solve the following system of equations:
∂L/∂x = 0
∂L/∂y = 0
∂L/∂z = 0
∂L/∂λ = 0
g(x, y, z) = 0
Taking the partial derivatives of L with respect to x, y, z, and λ, we get:
∂L/∂x = 2x - λ(2x + y) = 0
∂L/∂y = 2y - λ(2y + x) = 0
∂L/∂z = 2z - λz = 0
∂L/∂λ = x^2 + y^2 + z^2 + xy - 27 = 0
From the third equation, we get:
2z - λz = 0
z(2 - λ) = 0
So, either z = 0 or λ = 2.
If z = 0, then from the first two equations, we get:
2x - λy = 0
2y - λx = 0
Multiplying the first equation by y and the second equation by x, we get:
2xy - λy^2 = 0
2xy - λx^2 = 0
Subtracting the second equation from the first, we get:
λ(x^2 - y^2) = 0
Since λ cannot be zero, we have x^2 = y^2 and x = y
Similarly, if λ = 2, then from the first two equations, we get:
2x - 2y = 0
x = y
Substituting x = y into the constraint equation, we get:
2x^2 + x^2 = 27
x^2 = 9
x = ±3
So, the possible critical points are:
(3, 3, 0)
(-3, -3, 0)
(0, 0, 0)
Recall that
f(x, y, z) = x^2 + y^2 + z^2
So, we have
f(3, 3, 0) = 3^2 + 3^2 + 0^2 = 18
f(-3, -3, 0) = -3^2 + -3^2 + 0^2 = 18
f(0, 0, 0) = 0^2 + 0^2 + 0^2 = 0
Hence, the minimum is 0 and the maximum is 18
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a researcher wishes to test the hypothesis that the difference between two population means is zero. if the sample means are 106.4 and 99.2, the standard error of the difference is 6.1, and the critical value needed to reject the null hypothesis is 2.09, what should the researcher decide about the difference between the two populations means?
There is not enough evidence to suggest that the difference between the two population means is statistically significant at the 5% significance level.
To test the hypothesis that the difference between two population means is zero, the researcher can use a two-sample t-test. The test statistic is calculated as the difference between the sample means divided by the standard error of the difference.
In this case, the sample means are 106.4 and 99.2, and the standard error of the difference is 6.1. Therefore, the test statistic is (106.4 - 99.2) / 6.1 = 1.18.
To decide whether to reject the null hypothesis that the difference between the two population means is zero, the researcher needs to compare the test statistic to the critical value. The critical value needed to reject the null hypothesis at a 5% significance level with 2 degrees of freedom (n1 + n2 - 2 = 2) is 2.09.
Since the test statistic of 1.18 is less than the critical value of 2.09, the researcher fails to reject the null hypothesis.
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Solve for x (please help me with this I’m willing to give 20 points)
Answer:
75°
Step-by-step explanation:
The angle in the given figure is 90°.
x + 15 = 90
x = 90 - 15
x = 75°