if 12g of a radioactive substance are present initially and 4 year later only 6 g remain, how much of the substance will be present after 11 year?
Answers
The radioactive substance has a half-life of 4 years, and initially, there were 12 grams of it. After 4 years, half of it would have decayed, leaving 6 grams. Therefore, after 11 years, another 4 half-lives have passed, and the remaining 6 grams would have halved four more times, leaving only 0.375 grams of the substance.
The given problem involves the calculation of the amount of a radioactive substance remaining after a certain period. The problem states that initially, there were 12 grams of the substance, and after four years, only 6 grams remained. This implies that half of the substance had decayed in four years, which indicates a half-life of 4 years for the substance.
To find the amount of substance remaining after 11 years, we need to calculate how many half-lives have passed. Since each half-life is 4 years, 11 years represent 2.75 half-lives. Therefore, the remaining 6 grams would have halved 2.75 times, which gives 0.375 grams. Hence, the amount of the radioactive substance that would be present after 11 years is 0.375 grams.
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Related Questions
Jenny is a software salesperson. Her base salary is $ 1500 and she makes $50 more for every copy of English is Fun she sells. Her total pay, P (in dollars), after
selling c copies is given by the following.
P = 50c+1500
oo
Answer the following questions.
B
(a) What is Jenny's total pay if she sells 21 copies?
si
(b) If Jenny's total pay is $3150, how many copies did she sell?
copies
Answers
an exam is given to students in an introductory statistics course. what is likely to be true of the shape of the histogram of scores if the exam is quite easy?
Answers
If the exam is quite easy then the shape of the histogram would be negatively skewed.
What is a histogram?
A histogram is a statistical information display that uses rectangles to show the frequency of data items in equal-sized numerical intervals. The independent variable is plotted along the horizontal axis and the dependent variable is plotted along the vertical axis in the most common form of a histogram.
a) If the exam is quite easy, it is expected that the majority of the students score well on the test, and since most of the data is closer to the maximum value rather than the minimum, the histogram has a negatively skewed shape.
Hence, if the exam is quite easy then the shape of the histogram would be negatively skewed.
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Pinocchio's nose (-2,-4) grows when he tells a lie. It can grow as much as (25,40) when he tells a whopper! If Pinocchio tells Geppetto a small fib, it only grows of 1/4 the way out. At what coordinate is Pinocchio's nose when he tells a small fib?
Answers
25+-2=23/4=5.75
40+-4=36/4=9
HELP ME PLEASE
In square PQRS the measure of <PRQ is 45°. What is the measure of <PRS in degrees?
Answers
Answer:
<PRS = 45
Step-by-step explanation:
In a square, all 4 angles are complementary so:
<PRS + <PRQ = 90
<PRS + 45 = 90
<PRS = 45
hi how to solve this question n(n+1)2
; where n=9
Answers
Answer:180
Step-by-step explanation:
.
Answer:
2×9(9+1)
18(10)
.180.
Topic: Representations of arithmetic sequences
Use the given information to complete the other representations for each arithmetic
sequence.
PLEASE JUST USE THE PHOTOS
Answers
Answer: For context, create a scenario where the numbers in the table might apply. for example:
It costs $8 per day to rent a parking place. Write an equation that will output the total cost depending on the number of days the space is rented.
The equation would be
y = 8x where y is the total cost and x is the number of days.
The graph is attached
Let C be the event that a student received a grade of B or better in Calculus I and let S be event that a student received a grade of A in Statistics I. Which of the following denotes the probability that a student received an A in statistics given that the student received les: than a B grade in Calculus I. P(S∣C) P(S′∣C′) P(C∣S)
Answers
The probability that a student received an A in Statistics given that the student received less than a B grade in Calculus I is denoted as P(S|C'). Here's the explanation for each option:
P(S∣C): This denotes the probability of receiving an A in Statistics given that the student received a B or better grade in Calculus I. However, this is not the probability asked in the question.
P(S'∣C'): This denotes the probability of not receiving an A in Statistics given that the student did not receive a B or better grade in Calculus I. Again, this is not the probability asked in the question.
P(C∣S): This denotes the probability of receiving a B or better grade in Calculus I given that the student received an A in Statistics. This is also not the probability asked in the question.
Therefore, the correct notation for the probability that a student received an A in Statistics given that the student received less than a B grade in Calculus I is P(S|C').
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fill in the blank. In a 4x3x2x2 factorial experiment, you have ___ independent variables and potentially ___ main effect hypotheses.
4; 4
Answers
In a 4x3x2x2 factorial experiment, you have 4 independent variables and potentially 4 main effect hypotheses.
The 4 independent variables are represented by the four numbers in the experimental design
(i.e., 4 levels of variable A, 3 levels of variable B, 2 levels of variable C, and 2 levels of variable D).
The potentially 4 main effect hypotheses are one for each independent variable, which states that there is a significant effect of that independent variable on the outcome variable.
Factorial experiment:A factorial experiment includes multiple factors simultaneously, each consisting of two or more
levels. Many factors simultaneously influence what is studied in a factorial experiment, and
experimenters consider the main effects and interactions between factors.
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A certain right triangle with integer side lengths has perimeter $150$. What is its area?
Answers
Note that the right triangle's area is 750 units². Here is how to get this.
What is a right triangle?A right triangle or right-angled triangle, or more technically an orthogonal triangle, formerly known as a rectangle triangle, is a triangle with one right angle, i.e. two perpendicular sides.
Trigonometry is founded on the relationship between the sides and other angles of a right triangle.
So since this triangle is a multiple of a 5-12-13 triangle
Its sides are 25 - 60 - 65( summing this will give 150.)
Its area is (1/2) * product of the legs = (1/2)(25)(60) = 750 units²
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On Friday, 375 people attended the school concert. On Saturday, 250 people attended the concert. On Sunday, 300 people attended the school concert . What is the percent change in attendance from Saturday to Sunday? Show your work
Answers
Answer: \(20\%\)
Step-by-step explanation:
Given
375 people attended the concert on Friday
250 people attended the concert on Saturday
300 people attended the concert on Sunday
Percentage change in attendance from Saturday to Sunday
\(\Rightarrow \dfrac{300-250}{250}\times 100\\\\\Rightarrow \dfrac{50}{250}\times 100\\\\\Rightarrow 20\%\)
slope=?
please help
Answers
Answer: It's 4
Step-by-step explanation: 12-8 is 4, 4-3 is 1
Which expression is equivalent to -9x^-1y^-9/-15x3y-3? Assume x & y ≠ 0
Answers
Step-by-step explanation:
when we have multiplications of fractions, we can simply "break" the multiplications apart, simplify every fraction, and then combine the results again.
-9/-15 = 3/5
x^-1/x⁵ = 1/x¹x⁵ = 1/x⁶
y^-9/y^-3 = y³/y⁹ = 1/y⁶
so, when we multiply the 3 fractions again, we get
3/(5x⁶y⁶)
which is the second answer option.
The following table shows the monthly flow through a dam from October through April.
Answers
Solution:
Given the data below:
A) Mean monthly flow:
The mean monthly flow is evaluated as
\(\begin{gathered} \frac{total\text{ volume}}{total\text{ number of months}}=\frac{92+133+239+727+345+495}{6} \\ =\frac{2031}{6} \\ =338.5 \end{gathered}\)Thus, the mean monthly flow is 338.5 KAF
B) Median monthly flow:
The median is evaluated as
\(undefined\)
Tiys earns $7 an hour owing her neighbors lawn.
Part A: create two variables and determine which is dependent and which is independent for this situation.
Part B list three order pairs to show the values of the two variables.
Part C write and equation to represent the relationship between the two variables.
Answers
Answer:
Part A) The independent variable is the hours that Tiya mows her neighbor's lawn, and we can denote that with x. It's the variable that isn't affected by other factors. The dependent variable is the amount of money Tiya earns, which we can denote with y. The dependent variable is the variable that is affected by other factors. The amount of money Tiya makes depends on how many hours she works.
Part B) As stated in part A, x is the hours and y is the money earned. The ordered pairs are in (x, y) form, with x being the hours and y being the money earned. For example, if Tiya worked one hour, x would be 1. As she earns 7 dollars per hour, she would earn 7 dollars (1*7), which is y. Therefore, one ordered pair could be (1, 7). Two hours would give Tiya 14 dollars, so we have another pair of (2, 14). Three hours would give Tiya 21 dollars, so we have (3, 21). We can do that for any numbers.
Part C) With every hour, Tiya earns 7 dollars. In order to find y, which is the amount of money totally earned, we multiply x by 7 (7 dollars per hour). Therefore, y = 7x.
Will mark brainiest if right Is this function linear or nonlinear?
y=3x−5
Answers
Answer: This function is linear because it forms a straight line when graphed.
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You wish to test the following claim (H_{a}) at a significance level of alpha = 0.01 .
H : mu = 89.5 H_{a} / mu > 89.5
You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 300 with mean M = 91.6 and a standard deviation of SD = 10.6
What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic-
What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value-
The p-value is...
Oless than (or equal to) a
Ogreater than a
This test statistic leads to a decision to...
O reject the null
O accept the null
O fail to reject the null
Answers
The test statistic for the sample is approximately 3.295. The p-value for this sample is approximately 0.0006. The p-value is less than the significance level of 0.01. Therefore, based on the test statistic and p-value, the decision is to reject the null hypothesis.
To test the claim that the population mean (μ) is greater than 89.5 at a significance level of α = 0.01, we can perform a one-sample t-test. Since the population standard deviation (σ) is unknown, we will use the sample standard deviation (SD = 10.6) as an estimate.
The test statistic for this sample is calculated using the formula:
t = (M - μ) / (SD / √n)
Plugging in the values from the problem, we have:
t = (91.6 - 89.5) / (10.6 / √300) ≈ 3.295
The p-value for this sample can be found by comparing the test statistic to the t-distribution with n - 1 degrees of freedom. Since the alternative hypothesis is μ > 89.5, we are interested in the right-tail area.
Using statistical software or a t-table, we find that the p-value associated with a t-statistic of 3.295 and 299 degrees of freedom is approximately 0.0006.
Comparing the p-value to the significance level (α = 0.01), we can see that the p-value (0.0006) is less than α. Therefore, the p-value is less than or equal to α.
This test statistic leads to a decision to reject the null hypothesis. In other words, there is sufficient evidence to support the claim that the population mean is greater than 89.5 at a significance level of 0.01.
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What is included in capital invested?
Answers
The capital includes :
Any financial contribution made to a business to assist in achieving and advancing its commercial goal is referred to as a capital investment. The phrase may also refer to a long-term purchase made by a company, such as one for land, equipment, businesses, etc.
When a corporation issues securities to equity investors and debt to bondholders, the total amount of debt and capital lease obligations are added to the amount of stock given to investors to determine the overall amount of money raised. This amount is referred to as invested capital. The balance sheet of the business does not include an item for invested capital because debt, capital leases, and stockholders' equity are all stated separately.
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Find the area of the region between the curve x^3+2x^2-3x and the x-axis over the interval [-3,1]
Answers
Answer:
\(\displaystyle A = \frac{32}{3}\)
General Formulas and Concepts:
Calculus
Integrals
Definite IntegralsArea under the curveIntegration Rule [Reverse Power Rule]: \(\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C\)
Integration Rule [Fundamental Theorem of Calculus 1]: \(\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)\)
Integration Property [Multiplied Constant]: \(\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx\)
Integration Property [Addition/Subtraction]: \(\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx\)
Area of a Region Formula: \(\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx\)
Step-by-step explanation:
Step 1: Define
Identify
Curve: x³ + 2x² - 3x
Interval: [-3, 1]
Step 2: Find Area
Set up: \(\displaystyle A = \int\limits^1_{-3} {(x^3 + 2x^2 - 3x)} \, dx\)[Integral] Rewrite [Integration Property - Addition/Subtraction]: \(\displaystyle A = \int\limits^1_{-3} {x^3} \, dx + \int\limits^1_{-3} {2x^2} \, dx - \int\limits^1_{-3} {3x} \, dx\)[Integrals] Rewrite [Integration Property - Multiplied Constant]: \(\displaystyle A = \int\limits^1_{-3} {x^3} \, dx + 2\int\limits^1_{-3} {x^2} \, dx - 3\int\limits^1_{-3} {x} \, dx\)[Integrals] Integrate [Integration Rule - Reverse Power Rule]: \(\displaystyle A = (\frac{x^4}{4}) \bigg| \limits^1_{-3} + 2(\frac{x^3}{3}) \bigg| \limits^1_{-3} - 3(\frac{x^2}{2}) \bigg| \limits^1_{-3}\)Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: \(\displaystyle A = -20 + 2(\frac{28}{3}) - 3(-4)\)Evaluate: \(\displaystyle A = \frac{32}{3}\)Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Book: College Calculus 10e
write a polynomial that represents the total area of the six sides of the cube having edges with length x-4
Answers
To find the total area of the six sides of a cube, we can calculate the sum of the areas of each side. Since the cube has equal sides, we only need to find the area of one side and multiply it by 6.
The area of one side of a cube is given by the formula A = s^2, where s represents the length of each side. In this case, the length of each side is x-4. Therefore, the area of one side is (x-4)^2.
To find the total area of the six sides, we multiply the area of one side by 6:
Total area = 6 * (x-4)^2
So, the polynomial that represents the total area of the six sides of the cube with edges of length x-4 is 6 * (x-4)^2.
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can you please help me find X in this problem it is so confusing
Answers
Answer:
x = 25°
Step-by-step explanation:
There are different ways to get there.
1.The unmarked angle at bottom left is an alternate interior angle with the one at the top marked 50°. So, it is congruent to 50°.
That makes the angles along the line at the bottom be ...
50° +x° +105° = 180° . . . . . the measure of a linear angle
x° = 180° -155° = 25°
__
2.The unmarked angle at top right is a same-side interior angle relative to the one at bottom marked 105°. As such it is supplementary to 105°, and has measure ...
180° -105° = 75°
This angle (upper right) is an exterior angle to the triangle. As such, it is equal to the sum of the two "remote" interior angles of the triangle—the ones marked 50° and x°.
75° = 50° +x°
25° = x° . . . . . . . subtract 50°
__
3.The unmarked interior angle of the triangle is an alternate interior angle with the one marked 105°. So, it is congruent to 105°. The sum of the triangle interior angles is 180°, so you have ...
x° +50° +105° = 180°
x = 180° -155° = 25° . . . . as we had with our first approach
what answer below best addresses the following statistical problem? a new advertisement for ben and jerry's ice cream introduced in late may of last year resulted in a 30% increase in ice cream sales for the following three months. does this mean that the advertisement was effective? a. yes, because an increase in sales means the advertisement worked. b. no, because the increase in sales was all caused by another variable (specifically a change in weather) c. uncertain, because there are other variables at play and correlation does not equal causation d. uncertain, because it's impossible to measure the effectiveness of advertising.
Answers
The correct answer to this statistical problem is (c) uncertain, because there are other variables at play and correlation does not equal causation.
In this scenario, we're looking at the sales of Ben and Jerry's ice cream before and after the advertisement was introduced. The sales increased by 30% for the following three months after the advertisement. So, does this mean that the advertisement was effective? The answer is not as straightforward as a simple "yes" or "no."
Option (c) acknowledges that there are other variables at play and that correlation does not equal causation.
This is the most accurate answer because it recognizes that while the increase in sales may be related to the advertisement, it's impossible to say for sure whether the advertisement was the cause of the increase in sales.
There could be other factors, such as the weather or a change in consumer preferences, that also contributed to the increase in sales.
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What is the equation of the line with a slope of 3 and passing through the point (1, -3)?
Answers
Step-by-step explanation:
The equation of the line is y = 3x - 6 (D).
Answer:
y = 3x - 6 or D
Step-by-step explanation:
Each morning, Jon rides 1. 5 miles to school and then rides to his aunt’s house after school. Later in the evening, he takes the same route to get back to his house. Over 5 days, he rides 44 miles. Which equation can be used to find x, the distance from school to his aunt’s house? 5 left-bracket 2 (1. 5 x) right-bracket = 44 2 (1. 5 x) = 44 5 (1. 5 x) = 44 5 times left-bracket 2 (1. 5 x) right-bracket = 44.
Answers
Answer:
d
Step-by-step explanation:
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which of the following affect the width of a confidence interval? (select all that apply) group of answer choices mean standard deviation confidence level sample size
Answers
b) Decreasing the sample size
c) Increasing the standard deviation
a) Decreasing the confidence level will decrease the width of the confidence interval. A lower confidence level means we are less certain about capturing the true population mean, so we allow for a smaller margin of error, resulting in a narrower interval.
b) Decreasing the sample size will increase the width of the confidence interval. With a smaller sample size, there is less information available to estimate the population mean. This increased uncertainty leads to a wider confidence interval to accommodate a potentially larger margin of error.
c) Increasing the standard deviation will increase the width of the confidence interval. A larger standard deviation indicates more variability in the data. With greater variability, the estimated population mean could be further away from the true mean, requiring a wider interval to capture the potential range.
d) Decreasing the mean does not affect the width of the confidence interval. The width of the interval is primarily determined by factors such as confidence level, sample size, and standard deviation. The value of the population mean itself does not impact the width of the interval since it is the target value being estimated.
In summary, decreasing the confidence level and sample size, as well as increasing the standard deviation, will all increase the width of the confidence interval for a population mean, reflecting increased uncertainty and potential variability in the estimation. However, decreasing the mean does not directly impact the width of the interval.
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Paul took a 140 mile trip on his motorcycle. If he drove 60% of his trip on the first day, how many miles did Paul drive on day one? Answer value
Answers
Answer:
84 miles
Step-by-step explanation: 140/100 x 60 which gives you 84 miles
IN NEED OF HELP!!
15 POINTS!!!
Answers
Answer:
what do you need help with?
Step-by-step explanation:
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Which statement is true of the snowfall data in the box plots? Check all that apply. The median snowfall for Resort A is greater than the median for Resort B. The median snowfall for Resort B is greater than the median for Resort A. The interquartile range has higher values for Resort A than for Resort B. The data have more variation for Resort A than for Resort B. Resort B has more snowfall overall than Resort A does.
Answers
True statement for the snowfall data in the box plots comparing Resort A and Resort B are,
The median snowfall for Resort B is greater than the median for Resort A.Resort B has more snowfall overall than Resort A does.What is box plot representation of data?
Box plot is the way of representation of data which gives the graphical image of the data set to understand better.
The minimum and the maximum values in the box plot is plotted at the end points.
The median snowfall for Resort A is greater than the median for Resort B- As shown in the box plot, the average of the snowfall for Resort B is greater than the Resort A. Thus, the median snowfall for Resort A is not greater than the median for Resort B. This option is not correct.The median snowfall for Resort B is greater than the median for Resort A- As shown in the box plot, the average of the snowfall for Resort B is greater than the Resort A. Thus, the median snowfall for Resort B is greater than the median for Resort A. This option is correct.The interquartile range has higher values for Resort A than for Resort B- The interqurtile range of Resort A is 275 inches and the interqurtile range of Resort B is 325 inches. Thus the interquartile range has lower values for Resort A than for Resort B. This is incorrect option.The data have more variation for Resort A than for Resort B-No, the data have less variation for Resort A than for Resort B. Thus this is incorrect option.Resort B has more snowfall overall than Resort A does-As the resort B snowfall box plot has more value, than resort A. Thus resort B has more snowfall overall than Resort A does. This option is correct.The true statement for the snowfall data in the box plots comparing Resort A and Resort B are,
The median snowfall for Resort B is greater than the median for Resort A.Resort B has more snowfall overall than Resort A does.Learn more about the box plot here;
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Answer:
The answer is B and E
Step-by-step explanation:
I just took the assignment, the other guy is correct.
jackson and ginger are both learning to ride a bike. Jackon can travel y = 4x miles. and ginger travels y = 3x + 15
Answers
We can say that the distance travelled and minutes spent biking will be equal for both of them if they bike for 15 minutes.
What is the general equation of a straight line?The general equation of a straight line is of the form -
y = mx + c
where -
[m] is slope of line
[c] is y - intercept
Given are Jackson and Ginger who are learning to ride a bike. Jackson can travel (y = 4x) miles and ginger can travel (y = 3x + 15) miles.
Both the equations represent a straight line, plot the graph for both the lines. The point of intersection of these two lines will represent the point when the distance between and minutes spent biking are same for both Jackson and Ginger.
Refer to the graph attached. Both of these graphs intersect at (15, 60).
Therefore, we can say that the distance travelled and minutes spent biking will be equal for both of them if they bike for 15 minutes.
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[ The complete question is attached with the answer ]
Which expression has the greatest value?
Answers
Answer:
6 DIVIDED BY 1/8
Step-by-step explanation:
Answer: 6 divided by 1/8
Which graph matches the equation y+3=2(x+3)?
What is the slope of the line whose equation is y−4= StartFraction 5 Over 2 EndFraction.(x−2)?
A coordinate plane with a line passing through the points (0, negative 1) and (2, 4).
–negative StartFraction 5 Over 2 EndFraction.
–negative StartFraction 2 Over 5 EndFraction.
StartFraction 2 Over 5 EndFraction.
StartFraction 5 Over 2 EndFraction.
Answers
The graph with a line y+3=2(x+3) is
A coordinate plane with a line passing through the points (0, 3) and (-2, -1) with a slope of 2.
The answer is the fourth option: the slope of the line y - 4 = 5/2(x - 2), is
StartFraction 5 Over 2 End raction.How to find the graphTo find the graph that matches the equation y+3=2(x+3), we need to rewrite the equation in slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
y + 3 = 2(x + 3)
y + 3 = 2x + 6
y = 2x + 6 - 3
y = 2x + 3 slope-intercept form
The equation is now in slope-intercept form, y = 2x + 3,
where
the slope is 2 and the y-intercept is 3.The graph of this equation should be a line that passes through the y-axis at 3 and has a slope of 2. From the attached graph we can see point (-2, -1)
To find the slope of the line whose equation is y - 4 = 5/2(x - 2), we can rewrite the equation in slope-intercept form.
y - 4 = 5/2(x - 2)
y - 4 = 5/2x - 5
y = 5/2x - 5 + 4
y = 5/2x - 1 slope-intercept form
The equation is now in slope-intercept form, y = 5/2x - 1,
where the slope is 5/2.
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