Answer: 0.0972
Step-by-step explanation:
To find the probability that the first roll is a total of at least 7 and the second roll is a total of at least 10, we need to find the probabilities of each event separately and then multiply them together.
First, let's find the probability of the first roll being a total of at least 7. There are a total of 36 possible outcomes when rolling a pair of dice (6 sides on each die, so 6 x 6 = 36). To get a total of at least 7, the following outcomes are possible:
7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)
8: (2, 6), (3, 5), (4, 4), (5, 3), (6, 2)
9: (3, 6), (4, 5), (5, 4), (6, 3)
10: (4, 6), (5, 5), (6, 4)
11: (5, 6), (6, 5)
12: (6, 6)
There are 21 successful outcomes out of the total 36 possibilities. So, the probability of getting a total of at least 7 in the first roll is:
P(at least 7) = 21/36
Next, let's find the probability of the second roll being a total of at least 10. The following outcomes are possible:
10: (4, 6), (5, 5), (6, 4)
11: (5, 6), (6, 5)
12: (6, 6)
There are 6 successful outcomes out of the total 36 possibilities. So, the probability of getting a total of at least 10 in the second roll is:
P(at least 10) = 6/36
Now, to find the probability that both events happen, we multiply the probabilities of each event:
P(first roll at least 7 and second roll at least 10) = P(at least 7) * P(at least 10) = (21/36) * (6/36)
P(first roll at least 7 and second roll at least 10) = 126/1296
So, the probability that the first roll is a total of at least 7 and the second roll is a total of at least 10 is 126/1296, or approximately 0.0972 (rounded to four decimal places).
An economy is operating with output $400 billion above its natural level, and fiscal policymakers want to close this expansionary gap. The central bank agrees to adjust the money supply to hold the interest rate constant, so there is no crowding out. The marginal propensity to consume is 3/4, and the price level is completely fixed in the short run.
to close the expansionary gap, the government would need to increase or decrease spending by $ billion.
Hence, to close the expansionary gap, the government would need to decrease spending by $100 billion.
To close the expansionary gap, the government would need to decrease spending by $100 billion.
The formula to calculate the change in equilibrium output due to a change in government spending is:
∆Y = (∆G / (1 - MPC))
Where:
∆Y = change in equilibrium output
∆G = change in government spending
MPC = marginal propensity to consume
Here, the output is $400 billion above its natural level, and the central bank agrees to adjust the money supply to hold the interest rate constant, so there is no crowding out. Therefore, we can assume that the change in government spending (∆G) would have a one-to-one effect on the equilibrium output (∆Y).
Given that MPC = 3/4, we can plug in the values into the formula:
400 = (∆G / (1 - 3/4))
∆G = (1 - 3/4) * 400
∆G = (1/4) * 400
∆G = 100
Hence, to close the expansionary gap, the government would need to decrease spending by $100 billion.
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Find the area of a rectangle with length 4.3 cm and breadth 3.9 cm
Answer:
16.77 cm²
Step-by-step explanation:
Area of rectangle = L x W
L = 4.3 cm
Width = 3.9 cm
Let' solve
4.3 x 3.9 = 16.77 cm²
So, the area of the rectangle is 16.77 cm²
So I tried solving this problem with the population growth formula,
· Population Growth: =^; a=initial amount, r=growth rate as a decimal; t=time in years; y=resulting population
My equation looked like this but I got this question wrong so any help will be appreciated
9667=11211e^(.418)(t)
The number of years it would take is approximately equal to 53 years.
How to determine the population after a number of year?In Mathematics, a population that increases at a specific period of time represent an exponential growth. This ultimately implies that, a mathematical model for any population that increases by r percent per unit of time is an exponential function of this form:
P(t) = I(1 + r)^t
Where:
P(t ) represent the population.t represent the time or number of years.I represent the initial number of persons.r represent the exponential growth rate.By substituting given parameters, we have the following:
96627 = 11211(1 + 0.0418)^t
8.61894567835 = (1.0418)^t
By taking the ln of both sides, we have:
Time, t = ln(8.61894567835)/ln(1.0418)
Time, t = 52.60 ≈ 53 years.
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simplify the expression ^5√-32x^5y^30
Alberto gets a fish tank
Jackson is on point. Of all fish, catfish make up one-third of the total.
How much gravel does Alberto add to the tank in pounds?The United States of America, Great Britain, and other English-speaking countries predominately utilise the pound as a unit of weight.
Any quantity associated with something is assumed to contain one pound if it does. The pound is the most widely used weight unit in the English-speaking world, including Britain, America, and other nations.
Zebra danios make up half of all the fish.
More fancy guppies than catfish, by a factor of two.
x = guppies
2x = catfish
x + 2x = 1/2 of the fish population
3x = 1/2 of the fish population
3x * 2 = 6x
x = 1/6 number of fancy guppies
catfish:
2x = 2(1/6) = 2/6 = 1/3 catfish.
Jackson is on point. Of all fish, catfish make up one-third of the total.
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The complete question is,
Alberto puts 3 kinds of fish in his fish tank: zebra danios, fancy guppies, and cat fish. Half of Alberto's fish are zebra danios. He has 2 times as many catfish as he has fancy guppies. Alberto's friend Jackson says 1/3 of Alberto's fish are catfish. Is Jackson correct?
On a given planet, the weight of an object varies directly with the mass of the object. Suppose that an object whose mass is 2 kg weighs 4 N. Calculate the mass of another object that weights 18 N.
Answer:
Let m be the mass of the object and w be the weight of the object. According to the problem, weight varies directly with mass, so we can write:
w = k * m
where k is the constant of proportionality.
To find k, we can use the information given in the problem. We know that when m = 2 kg, w = 4 N. Substituting these values into the equation above, we get:
4 N = k * 2 kg
Solving for k, we get:
k = 4 N / 2 kg = 2 N/kg
Now we can use this value of k to find the mass of an object that weighs 18 N. We can rearrange the equation above to solve for m:
m = w / k
Substituting w = 18 N and k = 2 N/kg, we get:
m = 18 N / 2 N/kg = 9 kg
Therefore, the mass of the object that weighs 18 N is 9 kg.
Elliot read a report from a previous year saying that 6 % 6%6, percent of adults in his city biked to work. He wanted to test whether this had changed, so he took a random sample of 240 240240 adults in his city to test H 0 : p = 0.06 H 0 :p=0.06H, start subscript, 0, end subscript, colon, p, equals, 0, point, 06 versus H a : p ≠ 0.06 H a :p =0.06H, start subscript, start text, a, end text, end subscript, colon, p, does not equal, 0, point, 06, where p pp is the proportion of adults in Elliot's city that bike to work. The sample results showed 21 2121 adults who biked to work, and the corresponding test statistic was z ≈ 1.79 z≈1.79z, approximately equals, 1, point, 79. Assuming that the necessary conditions are met, what is the approximate P-value for Elliot's significance test?
Answer: To find the P-value, we first need to determine the direction of the alternative hypothesis. Since the alternative hypothesis is two-tailed, we need to divide the significance level (α) by 2 before finding the critical values and the rejection region. Therefore, we have:
H0: p = 0.06
Ha: p ≠ 0.06
α = 0.05/2 = 0.025
The test statistic is z = 1.79, which represents the number of standard errors that the sample proportion is from the hypothesized population proportion under the null hypothesis. We can find the P-value by looking up the area in the standard normal distribution table beyond the test statistic in both tails:
P-value = P(Z ≤ -1.79 or Z ≥ 1.79)
= P(Z ≤ -1.79) + P(Z ≥ 1.79)
= 0.0364 + 0.0364
= 0.0728
Therefore, the approximate P-value for Elliot's significance test is 0.0728. Since the P-value is greater than the significance level of 0.05, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the proportion of adults who bike to work in Elliot's city has changed significantly from the previous year.
Step-by-step explanation:
At a train station in the morning rush hour, the Westbound train arrives every 9 minutes, and the Eastbound train arrives every 15 minutes. If both trains were just in the station, after how many minutes will both trains again be in the station at the same time?
Step-by-step explanation:
Find the LCM of 9 and 15
West 9 18 27 36 45
East 15 30 45 In 45 minutes
HELLO PLEASE HELP!
i only need help with the second problem which is:
5. For 0≤x≤ 6, express g(x) in terms of x. Do not include +C in your final answer.
please and thanks!
From the calculation, g increases on the interval [-3, 6) and for 0 ≤ x ≤ 6, g(x) = 6 - 1/2(x-2)²
What is a mathematical expression?
A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. This mathematical operation may be addition, subtraction, multiplication, or division. An expression's basic components are as follows: The formula is (Number/Variable, Math Operator, Number/Variable).
Since f(x) is a piecewise-defined function, we need to consider each interval separately.
For -3 ≤ x < 0, f(x) = 3, so g'(x) = 3, which is positive.
For 0 ≤ x ≤ 6, f(x) = -x + 3, which is a decreasing function, so g'(x) is also decreasing. However, since f(x) is always non-negative on this interval, g'(x) is non-negative as well.
For 6 < x ≤ 9, f(x) = -3, so g'(x) = -3, which is negative.
Therefore, g is increasing on the interval [-3, 6).
To justify this, note that g'(x) = 0 at x = 0 and x = 6, where g has local maxima. This means that g is increasing on the intervals (-3, 0) and (0, 6) and decreasing on (6, 9]. Since g is continuous, it cannot have any jumps, so it must be increasing or decreasing on each of these intervals. Since g(-3) = 0 and g(6) = 9, we know that g is increasing on the interval [-3, 6).
We can evaluate g(x) on the interval [0, 6] by integrating f(x) with respect to t from -2 to x:
g(x) = ∫_{-2}^{x} f(t) dt
On the interval [-3, 0), f(t) = 3, so we have
g(x) = ∫_{-2}^{0} 3 dt + ∫_{0}^{x} (-t + 3) dt
Simplifying the integrals, we get:
g(x) = 6 - 1/2(x-2)^2, for 0 ≤ x ≤ 6
Therefore, for 0 ≤ x ≤ 6, g(x) = 6 - 1/2(x-2)²
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The expression of g in terms of x is increases on the interval [-3, 6) and for 0 ≤ x ≤ 6 is g(x) = [tex]6 - \frac{1}{2(x-2)^2}[/tex].
What is a mathematical expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.
Since f(x) is a piecewise-defined function, we need to consider each interval separately.
For -3 ≤ x < 0, f(x) = 3, so g'(x) = 3, which is positive.
For 0 ≤ x ≤ 6, f(x) = -x + 3, which is a decreasing function, so g'(x) is also decreasing.
However, since f(x) is always non-negative on this interval, g'(x) is non-negative as well.
For 6 < x ≤ 9, f(x) = -3, so g'(x) = -3, which is negative.
Therefore, g is increasing on the interval [-3, 6).
We can evaluate g(x) on the interval [0, 6] by integrating f(x) with respect to t from -2 to x:
[tex]g(x) = \int{-2}^{x} f(t) dt[/tex]
On the interval [-3, 0), f(t) = 3, so we have
[tex]g(x) = \int_{-2}^{0} 3 dt + \int_{0}^{x} (-t + 3) dt[/tex]
Simplifying the integrals, we get:
[tex]g(x) = 6 - \frac{1}{2(x-2)^2}[/tex], for 0 ≤ x ≤ 6
Therefore, for 0 ≤ x ≤ 6, g(x) = 6 - 1/2(x-2)².
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James recorded the prices of 10 brands of cereal. The prices are: $3.50, $2.30, $2.50, $3.90, $2.90, $2.40, $1.90, $2.50, $3.20, $2.70. What is the median cost of these boxes of cereal?
Answer:
To find the median cost of these boxes of cereal, we need to order the prices from least to greatest:
$1.90, $2.30, $2.40, $2.50, $2.50, $2.70, $2.90, $3.20, $3.50, $3.90
There are 10 numbers, so the median is the average of the 5th and 6th numbers:
Median = ($2.50 + $2.70) / 2 = $2.60
Therefore, the median cost of these boxes of cereal is $2.60.
Answer:
What is the median cost of these boxes of cereal?
$3.50, $2.30, $2.50, $3.90, $2.90, $2.40, $1.90, $2.50, $3.20, $2.70
Let's put it in order first:
$1.90, $2.30, $2.40, $2.50, $2.50, $2.70, $2.90, $3.20, $3.50, $3.90
Now find the middle number (s):
$1.90, $2.30, $2.40, $2.50, $2.50, $2.70, $2.90, $3.20, $3.50, $3.90
In this case, there are 2 middle numbers so do this:
$2.50 + $2.70
= $5.20
5.20 ÷ 2
= $2.60So the median cost of those cereal boxes would be $2.60.
Step-by-step explanation:
You're welcome.
A local department store can sell 100 gaming systems at a price of $180 each. Research
shows that for each $18 price increase, the store will sell 4 fewer systems, and vice versa.
a. Find a linear price equation for the gaming system. That is, express the price, p, as a
function of the quantity, q. (2 points)
b. Use your answer from (a) to find the revenue equation.
c. Use your knowledge of quadratic functions to find the price and quantity sold that will maximize revenue.
Therefore, the price that maximizes revenue is $135, and the quantity sold at that price is q0/2.
What is the unit price?
In order to find the unit price of a certain item, we just need to divide the total price paid (or total cost) by the number of items bought.
According to given information
a. Let x be the number of $18 price increases from the original price of $180, and let y be the corresponding decrease in the number of gaming systems sold. Then we have the data point (x, y) = (0, 0) and the slope of the line is -4/18 = -2/9. Using the point-slope form of a linear equation, we have:
y - 0 = (-2/9)x
y = (-2/9)x
Substituting x = 18n, where n is the number of $18 price increases, we have:
y = (-2/9)(18n) = -4n
Let q be the quantity of gaming systems sold at a price of $180. Then the equation for the price of the gaming system as a function of the quantity sold is:
p(q) = 180 + 18n = 180 + 18(q - q0)/4 = 180 + (9/2)(q - q0),
where q0 is the quantity of gaming systems sold at the original price of $180.
b. The revenue equation is given by R(q) = q*p(q). Substituting the expression for p(q) found in part (a), we have:
R(q) = q*(180 + (9/2)(q - q0)) = (9/2)q^2 + (180 - 9q0/2)q
c. To find the price and quantity sold that will maximize revenue, we can differentiate the revenue equation with respect to q, set the derivative equal to zero, and solve for q:
R'(q) = 9q - 9q0/2 = 0
q = q0/2
Substituting q = q0/2 into the revenue equation, we have:
R(q0/2) = (9/2)(q0/2)^2 + (180 - 9q0/2)(q0/2)
R(q0/2) = (9/8)*q0^2 + (45/2)*q0
To find the corresponding price, we can use the expression for p(q) found in part (a):
p(q0/2) = 180 + (9/2)(q0/2 - q0)
p(q0/2) = 135
Therefore, the price that maximizes revenue is $135, and the quantity sold at that price is q0/2.
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The table contains some points on the graph
of an exponential function. Based on the
table, which function represents the same
relationship?
Answer: 1st one
Step-by-step explanation:
The width of the set of the shelves needs to be 5 times the height of the set of shelves and the set of shelves must have three shelves If there are 80 feet of wood to use to build the set of shelves what should the dimensions the set of shelves be?
The dimensions of the set of shelves should be approximately 4.21 feet in height and 21.05 feet in width.
What is a linear equation?When plotted on a coordinate plane, an algebraic equation known as a linear equation looks like a straight line. The variable (or variables) in this equation always have a greatest power of 1, making it a constant. In other words, a linear equation simply makes use of the fundamental operations of addition, subtraction, and multiplication of variables to the first power, as well as constants.
Given:
Width of the set of shelves = 5 times the height of the set of shelves
Number of shelves = 3
Total amount of wood available = 80 feet
Let's denote the height of the set of shelves as "h" and the width of the set of shelves as "w".
Using the first given information, we can write the equation:
Width (w) = 5 times the height (h) ==> w = 5h
Next, we know that the set of shelves has 3 shelves, so the number of shelves is fixed at 3.
Finally, we are given that we have 80 feet of wood available to build the shelves.
Using these equations, we can substitute w = 5h into the equation for the total amount of wood:
3w + 4h = 80
Substituting w = 5h, we get:
3(5h) + 4h = 80
15h + 4h = 80
19h = 80
h = 80/19
So, the height of the set of shelves is approximately 4.21 feet.
Now, substituting this value of h back into w = 5h, we get:
w = 5(4.21)
w = 21.05
So, the width of the set of shelves is approximately 21.05 feet.
Therefore, the dimensions of the set of shelves should be approximately 4.21 feet in height and 21.05 feet in width.
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4. Tamara claims that Sweet Grove apple juice tastes better than Bushels apple juice. Isaac claims that there is no difference between the 2 types of apple juice. Tamara and Isaac would like to find the answer to the following question: Do more 6th graders prefer Sweet Grove apple juice or Bushels apple juice? a. Is this a statistical question? Explain your reasoning. 5. Explain how this question can be answered with an experiment
Answer: a. Yes, this is a statistical question since it includes collecting information from a test of 6th graders and utilizing factual strategies to analyze the comes about and draw a conclusion approximately the inclinations for Sweet Grove and Bushels apple juice.
b. Draw a conclusion based on the results of the experiment, and report any limitations or assumptions made during the experiment.
Step-by-step explanation:
What is the range of the relation whose graph is shown?
The range of the relation whose graph is shown include the following: C. -1 ≤ y ≤ 1.
What is a domain?In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.
Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = {-4, 4} or -4 ≤ x ≤ 4.
Range = {-1, 1} or -1 ≤ y ≤ 1.
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Jeff surveyed all the students at his school and reported the fraction of students who liked each flavor of sherbet.
Six-sevenths liked cherry.
One-ninth liked grape.
Three-fifths liked orange.
Four-elevenths liked strawberry.
Which list has the flavors in order from least liked to most liked?
A. grape, strawberry, orange, cherry
B. grape, orange, strawberry, cherry
C. orange, cherry, grape, strawberry
D. cherry, grape, orange. strawberry
Write a fraction that has a value greater than 3/8 using 3 as the numerator
Answer: 3/4
Step-by-step explanation:
Any number as the denominator of the fraction that is less than 8 (the denominator) will give you a fraction greater than 3/8.
Another different answer could be 3/5 or 3/6.
A fraction that has a value greater than 3/8 using 3 as the numerator is 3/6, 3/4, 3/2 and so on.
What is the fraction?In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.
The given fraction is 3/8.
Here, 3/8 = 0.375
We need write the fraction which is greater than 3/8 using 3 as the numerator is 3/6 = 0.5
Therefore, a fraction that has a value greater than 3/8 using 3 as the numerator is 3/6, 3/4, 3/2 and so on.
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Explain what went wrong.
Please solve both.
75 points
7. Can the following be the lengths of the sides of a triangle?
a. 20 cm, 40 cm, 50 cm
b. 20 cm, 40 cm, 60 cm
c. 41 cm, 250 mm, 12 cm
Answer:
B
Step-by-step explanation:
THE TWO SMALLER SIDES = THE LARGER SIDE HENCE ITS A TRIANGLE
Use the slip and y-intercept to identify the equation of this line
Answer:
y=2x
Step-by-step explanation:
equation formula is y=mx+b
m is slope
b is y-intercept
you know that slope is 2
y intercept is 0
so plug it into the equation
y=2x+0 or just y=2x
Choose scales for the coordinate plane shown so that you can graph the points J (5, 50), K(3, 50), L (4, -40), M (-2, 40), and N (-5, -10). on the x-axis use a scale of ____ units for each grid square. on the y-axis use a scale of ____ units of each grid square. complete the explanation for using these scales for each axis. the x-coordinates range from ____ to ____, and the y-coordinates range from ____ to ____.
On the x-axis use a scale of 2 units for each grid square. on the y-axis use a scale of 10 units of each grid square. The x-coordinates range from -5 to 5. y-coordinates range from -40 to 50.
What is coordinate plane?In mathematics, points and functions are represented and graphed on the coordinate plane, commonly known as the Cartesian plane. The x-axis and y-axis are two perpendicular number lines that meet at the origin to form the plane (0,0).
On the coordinate plane, points are denoted by ordered pairs (x, y), where x denotes the point's separation from the y-axis and y denotes its separation from the x-axis.
For the given coordinates the range of x and y coordinates are:
x-coordinates range from -5 to 5
y-coordinates range from -40 to 50.
Thus, we use a scale of 2 on the x-axis and 10 units on the y axis.
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How to find the circumference of a circle
Answer: To find the circumference of a circle, there are 2 formulas.
Step-by-step explanation:
The first formula is 2πr and the second formula is πd when solving any math problem. You can use either one but you would use which one is the most helpful to answer your question. Hope this helps!
Calculate the value for each determinant:
Answer:
step by step explanation:
1. 9 4. -12
2. -48 5. 0
3. 17 6. 1
Which is the closest to the area of the shaded region in the given square containing a circle? (Use ≈ 3.14.)
10 m
21.5 square meters
50 square meters
O 78.5 square meters
O 100 square meters
5m
The area of the shaded region in the specified figure of the square containing a circle is 21.5 m², which is the first option
21.5 square metersWhat is a square?A square is a quadrilateral with all sides of the same length and four interior angles which are right angles.
The figure is a composite figure comprising of a square and a circle
The radius of the circle, r = 5 meters
The side length of the square = 10 meters
The value of π = 3.14
The area of the square = 10 m × 10 m = 100 m²
The area of the circle = π × (5 m)² = 25·π m²
The area of the shaded region is the difference between the area of the square and the area of the circle, therefore;
The area of the shaded region = (100 - 25·π) m²
The area of the shaded region is therefore; (100 - 25 × 3.14) m² = 21.5 m²
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A machine in a factory makes chairs at rate of two chairs every 10 minutes how much time does the machine take to make five chairs how many minutes would it take for the factory to fulfill an order for 32 chairs show your work or explain how you determine your answers
Luisa has great news, she communicates it to 3 people. Each of them tells 3 more. This is how a chain is set up, since each new person who learns the news communicates it to three others. It takes one person approximately 10 minutes to communicate the news to three others. If an hour has passed, how many people have heard the news?
Answer:
The amount of persons who have heard in 30mins would be:
45 persons
Help pleasee
The half-life of Palladium-100 is 4 days. After 16 days a sample of Palladium-100 has been reduced to a mass of 2 mg.
What was the initial mass (in mg) of the sample? --------------
What is the mass 7 weeks after the start?-------------
The initial mass (in mg) of the sample is 32 mg
The mass 7 weeks after the start is 0.198 mg
What is exponential decay:Exponential decay is a process in which a quantity decreases at a rate proportional to its value. This means that the larger the quantity, the faster it will decrease.
Exponential decay is modeled by the following formula:
[tex]A = A_{0} \times (1/2)^{\frac{t}{T} }[/tex]
where A is the amount after time t, A₀ is the initial amount,
T is the half-life, and t is the time elapsed
Here we have
The half-life of Palladium-100 is 4 days. After 16 days a sample of Palladium-100 has been reduced to a mass of 2 mg.
For the first question, we know that after 16 days, the amount is 2 mg, and the half-life is 4 days. We can plug these values into the formula:
[tex]2 = A_{0} \times (1/2)^{\frac{16}{4}}[/tex]
Simplifying, we get:
2 = A₀ × (1/2)⁴
2 = A₀ × (1/16)
A₀ = 2 × 16
A₀ = 32 mg
So the initial mass of the sample was 32 mg.
For the second question, we need to find the mass after 7 weeks, or 49 days. We can use the same formula, but with t = 49:
[tex]A = 32 \times (1/2)^{\frac{49}{4} }[/tex]
A ≈ 0.198 mg
Therefore,
The initial mass (in mg) of the sample is 32 mg
The mass 7 weeks after the start is 0.198 mg
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The owner of a sports complex wants to carpet a hallway connecting to buildings. The carpet costs $1.50 per square foot. How much does it cost to carpet the hallway?
Answer:
$526.75 i believe
Step-by-step explanation:
if you dilate triangle ABC by a scale factor of 3 and (0,0) is the center, what will be the length of AB?
the new length of AB after a dilation by a scale factor of 3 with (0,0) as the center would be 3 times the original length of AB.
How to solve the question?
To find the new length of AB after a dilation by a scale factor of 3 with (0,0) as the center, we can use the following formula:
AB' = AB x 3
where AB' is the length of AB after the dilation, and AB is the original length of AB.
However, we need to first determine the length of AB in the original right triangle ABC. To do this, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
Let's assume that AB is the hypotenuse of the right triangle ABC, and that AC and BC are the other two sides. Then we have:
AB²= AC²+ BC²
Without more information about the lengths of AC and BC, we cannot determine the value of AB. However, once we have determined the length of AB, we can use the formula above to find the new length of AB after dilation.
Assuming we know the length of AB in the original right triangle ABC, we can now use the formula for dilation to find the new length of AB:
AB' = AB x 3
For example, if AB is 5 units long in the original triangle, then after dilation, AB' would be:
AB' = 5 x 3 = 15 units
Therefore, the new length of AB after a dilation by a scale factor of 3 with (0,0) as the center would be 3 times the original length of AB.
To know more about Pythagoras theorem visit,:-
https://brainly.com/question/343682
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a right triangle has a hypotenuse of length 7 inches. If one angle is 38 degrees, find the length of each leg.
Check the picture below.
[tex]\sin(38^o )=\cfrac{\stackrel{opposite}{x}}{\underset{hypotenuse}{7}}\implies 7\sin(38^o)=x\implies 4.31\approx x \\\\[-0.35em] ~\dotfill\\\\ \cos(38^o )=\cfrac{\stackrel{adjacent}{y}}{\underset{hypotenuse}{7}}\implies 7\cos(38^o)=y\implies 5.52\approx y[/tex]
Make sure your calculator is in Degree mode.
Answer:
4.31 in5.52 inStep-by-step explanation:
You want the leg measures in a right triangle with a hypotenuse of 7 inches and an angle of 38°.
Trig functionsThe mnemonic SOH CAH TOA reminds you of the relations between side lengths and trig functions:
Sin = Opposite/Hypotenuse ⇒ Opposite = Hypotenuse×Sin
Cos = Adjacent/Hypotenuse ⇒ Adjacent = Hypotenuse×Cos
ApplicationThe given triangle will have opposite and adjacent sides of ...
opposite = (7 in)sin(38°) ≈ 4.31 in
adjacent = (7 in)cos(38°) = 5.52 in
The leg lengths of the triangle are 4.31 inches and 5.52 inches.