Answer:
The equation is [tex]A(t) = 0.52*(0.9885)^{(t)}[/tex].
0.4713 grams would remain in the tumor after 8.5 days.
Step-by-step explanation:
Exponential equation of decay:
The exponential equation for the amount of a substance that decays, after t days, is given by:
[tex]A(t) = A(0)*(1-r)^t[/tex]
In which A(0) is the initial amount and r is the decay rate, as a decimal.
A tumor is injected with 0.52 grams of Iodine-125.
This means that [tex]A(0) = 0.52[/tex]
After 1 day, the amount of Iodine-125 has decreased by 1.15%.
This means that [tex]r = 0.0115[/tex]
So
[tex]A(t) = A(0)*(1-r)^t[/tex]
[tex]A(t) = 0.52*(1-0.0115)^t[/tex]
[tex]A(t) = 0.52*(0.9885)^t[/tex]
Then use the formula for A(t) to find the amount of Iodine-125 that would remain in the tumor after 8.5 days.
This is A(8.5).
[tex]A(t) = 0.52*(0.9885)^t[/tex]
[tex]A(8.5) = 0.52*(0.9885)^{8.5} = 0.4713[/tex]
0.4713 grams would remain in the tumor after 8.5 days.
Clarissa wants to create more shade in her yard to block the hot sun, so she buys a sapling of an oak tree and plants it in the yard. To make sure the tree is growing at a healthy rate, she makes the following table to track its height over a period of weeks. What is the average rate of change in the tree's height from week 3 to week 9? Enter your solution into the box below.
Answer:
The answer is 7.
Step-by-step explanation:
Determine what values to use from the table to find the average rate of change.
The problem asks for the average rate of change (AROC) from week 3 to week 9. The points referring to these measurements would be (3, 41) and (9, 83), respectively.
Step 2
FInd the AROC from (3, 41) to (9, 83).
The formula for the slope of a line between two given points (which is the same as AROC from the first two the second point) is
AROC = y2−y1x2−x1
In your points, x1 is 3, x2 is 9, y1 is 41, and y2 is 83. Plug these values into the above formula and simplify.
AROC = 83−419−3=426=7
The AROC is 7.
Step 3
Enter your solution.
Enter the value 7 and move on to the next question.
n 1990, the mean height of women 20 years of age or older was 63.7 inches based on data obtained from theCDC. Suppose that a random sample of 45 women who are 20 years of age or older in 2015 results in a meanheight of 63.9 inches with a standard deviation of 0.5 inch. Does your sample provide sufficient evidencethat women today are taller than in 1990
Answer:
The sample does not provide sufficient evidence that women today are taller than women in 1990.
The difference in mean height is not significant to arrive at such a conclusion.
Step-by-step explanation:
Mean height of women 20 year of age or older in 1990 = 63.7 inches
Mean height of women 20 years of age or older in 2015 = 63.9 inches
The standard deviation of the mean height in 2015 = 0.5 inch
The difference between the two years' mean height is 0.2 (63.9 - 63.7) inch.
This difference is less than the standard deviation of the mean height in 2015.
Therefore, the difference does not provide sufficient evidence that women today are taller than women in 1990.
VERY EASY, WILL GIVE 50 POINTS FOR CORRECT ANSWER ASAP AND WILL GIVE BRAINLIEST.
Answer:
Is it multiple choice? If it is then it’s B and D
Step-by-step explanation:
find the value of x. round to the nearest tenth if needed.
[tex]6^{2}+8^{2}=x^{2} \\36+64=x^{2} \\100=x^{2} \\x=10[/tex]
Helppppppp plzzzzzzzzz
Ewan HH
Step-by-step explanation:
Ewanjajsbehudbeiisiejebejehehehheehhehehe
Answer:
???
Step-by-step explanation:
Pls help its urgent
Question 1:
In my backyard there are chickens and cows (no other animals). Among them there is a total of 366 eyes and 558 legs. How many chickens do I have in my backyard?
The total animals = 139, and we can substitute this value into equation (3) to obtain:x = 2(139) - 279 => x = -1This doesn't make sense since we can't have negative chickens.
Let the number of chickens be x and the number of cows be y in the backyard. We can create two equations based on the given information:The total number of animals is x + y = total animals ...
(1)The total number of eyes and legs can also be expressed as 2x + 2y = 366 (since each animal has two eyes) and 2x + 4y = 558 (since each chicken has 2 legs and each cow has 4 legs).
Simplifying the equations, we get:x + y = total animals ... (1)x + 2y = 279 ... (2)From equation (1),
we can substitute y = total animals - x in equation (2) to obtain:x + 2(total animals - x) = 279 => 2total animals - x = 279 => x = 2total animals - 279 ... (3)We also know that x + y = total animals, so y = total animals - x.
Substituting equation (3) into this expression, we get:y = total animals - (2total animals - 279) => y = 279 - total animals ... (4)
To find the value of x, we need to know the value of total animals. We can obtain this value by adding equations (1) and (4):x + y + (279 - total animals) = total animals => x + y = 279/2 => x + y = 139.5
Since x and y are both whole numbers, they must add up to an even number. The only possible value is 70 + 69 = 139. Therefore, there must be a mistake in the problem statement or calculations.
To learn more about : value
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A rectangle is 17 inches long and 7 inches wide find the area
Answer:
119
Step-by-step explanation:
A=w 1=7x17=119
x^2 =1 how many solutions are there
Answer:
Answer:
x=1 or x=−1
Step-by-step explanation:
I think just 2
Answer:
x=1, x=-1
Step-by-step explanation:
x^2=1
x=sqrt(1)=+-1
Thus, there are 2 solutions: 1 and -1
A student ties a string around a weight and swings the weight in a circle around her body. If the student
represents the Sun and the weight represents
Name the figure below in two different ways.
Answer:
LDM
MDL
Step-by-step explanation:
The names of a figure are gotten from the points on the figure. The names of the figure are LDM and MDL.
There are three points on the given figure, and these points are: point L, point D and point M, where Point D is between L and M.
This means that, when naming the figure, alphabet D must be at the middle while alphabets M and L can be at either sides of D.
So, the possible names of the figure are: LDM and MDL.
Read more about naming figures at:
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Pls help I’ll pay u 30$ if it’s right
Answer:
8 5 7 1 3 2 4 6
Step-by-step explanation:
my Cashsap kinqcollin
I need the area can someone help meeee pls?
Answer:
54ft
Step-by-step explanation:
9ft x 6ft
In a class of 23 students, 9 play an instrument and 7 play a sport. There are 3
students who play an instrument and also play a sport. What is the
probability that a student does not play an instrument given that they play a
sport?
Answer:
4/7
Step-by-step explanation:
The probability that a student does not play an instrument given that they play a sport is 4/23.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
Total number of students = 23
From the Venn diagram,
Number of students who play sport but not an instrument = 4
The probability that a student does not play an instrument given that they play a sport.
= 4/23
Thus,
The probability is 4/23.
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A machine that is programmed to package 1.20 pounds of cereal is being tested for its accuracy In a sample of 36 cereal boxes, the sample mean filling weight is calculated as 1.22 pounds. The population standard deviation is known to be 0.06 pound. Identify the relevant parameter of interest for these quantitative data. The parameter of interest is the proportion filling weight for all cereal packages. The parameter of interest is the average filling weight for all cereal packages.
A-1. Identify the relevant parameter of interest for these quantitative data.
A) The parameter of interest is the average filling weight of all cereal packages.
B) The parameter of interest is the proportion filling weight of all cereal packages.
A-2. Compute its point estimate as well as the margin of error with 95% confidence. (Round intermediate calculations to 4 decimal places.
B-1. Calculate the 95% confidence interval.
B-2. Can we conclude that the packaging machine is operating improperly?
A) Yes, since the confidence interval contains the target filling weight of 1.20.
B) Yes, since the confidence interval does not contain the target filling weight of 1.20.
C) No, since the confidence interval contains the target filling weight of 1.20.
D) No, since the confidence interval does not contain the target filling weight of 1.20.
C. How large a sample must we take if we want the margin of error to be at most 0.01 pound with 95% confidence?
Answer:
A) The parameter of interest is the average filling weight of all cereal packages. ;
Point estimate = 1.22
Margin of Error = 0.0196
Confidence interval = (1.2004, 1.2396)
C) No, since the confidence interval contains the target filling weight of 1.20.
Step-by-step explanation:
A) The parameter of interest is the average filling weight of all cereal packages.
The point estimate = sample mean = 1.22
The margin of error with 95% confidence :
Zcritical * σ/sqrt(n)
Zcritical at 95% confidence = 1.96
Margin of Error = 1.96 * 0.06/sqrt(36)
Margin of Error : 1.96 * 0.01
Margin of Error = 0.0196
Confidence interval :
xbar ± margin of error
1.22 ± 0.0196
Lower boundary = 1.22 - 0.0196 = 1.2004
Upper boundary = 1.22 + 0.0196 = 1.2396
(1.2004, 1.2396)
C) No, since the confidence interval contains the target filling weight of 1.20.
Since, the internal contains 1.20, then we can conclude that it is filling properly.
Please help and stop with the links!
Help 80 Points BRAINLIEST FOR CORRECT ANSWER!!!!
Answer:
3x+5-7
Step-by-step explanation:
Answer:
If im not mistaken it should be answer 3. Because you would have to divide amongst groups.
Which graph represents the function f(x)=|x−1|−3 ?
help plzzzz!!!!!!!!!
Answer:
28.27
Step-by-step explanation:
3.14 x 9
is how to do this problem
Identify the 3D shape shown below. Choose 1 answer: A Cone B Cylinder © Sphere
Answer:
Cylinder
Step-by-step explanation:
A cone is a 3D triangle with a circular base, and a sphere is a 3D circle
Answer:
CYLIDER
Step-by-step explanation:
Lawrence got a car loan from a bank, with the car as collateral. What kind of loan did he get?
Answer:
secured loan
Step-by-step explanation:
Answer: Here
Step-by-step explanation:
You Go
Find the distance between A(4, —2) and B(—1, 2).
Round to the nearest tenth.
Answer:
6.4 to nearest tenth.
Step-by-step explanation:
AB = √[(x2 - x1)^2 + (y2-y1)^2]
= √[(-1 - 4)^2 + (2 - (-2))^2]
= √(25 + 16)
= 6.403
A sample size 25 is picked up at random from a population which is normally
distributed with a mean of 100 and variance of 36. Calculate-
(a) P-{ X<99}
(b) P{98X
Answer:
a) P(X < 99) = 0.2033.
b) P(98 < X < 100) = 0.4525
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 100 and variance of 36.
This means that [tex]\mu = 100, \sigma = \sqrt{36} = 6[/tex]
Sample of 25:
This means that [tex]n = 25, s = \frac{6}{\sqrt{25}} = 1.2[/tex]
(a) P(X<99)
This is the pvalue of Z when X = 99. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{99 - 100}{1.2}[/tex]
[tex]Z = -0.83[/tex]
[tex]Z = -0.83[/tex] has a pvalue of 0.2033. So
P(X < 99) = 0.2033.
b) P(98 < X < 100)
This is the pvalue of Z when X = 100 subtracted by the pvalue of Z when X = 98. So
X = 100
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{100 - 100}{1.2}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a pvalue of 0.5
X = 98
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{98 - 100}{1.2}[/tex]
[tex]Z = -1.67[/tex]
[tex]Z = -1.67[/tex] has a pvalue of 0.0475
0.5 - 0.0475 = 0.4525
So
P(98 < X < 100) = 0.4525
Anyone can help me with questions
Answer:
3x+18+4x+15=180
7x+33=180
7x=147
x=21
This had me confused i need big help!!!!
Answer:
[tex]3\frac{7}{8}[/tex]
Step-by-step explanation:
Equation: 4 1/7 + 2 1/8 + x= 10 1/7
Convert into improper fractions:
29/7 + 17/8= 71/7
Add fractions
351/56+x= 71/7
Subtract on both sides
X= 31/8 or 3 7/8
Proving triangles similar
Answer: AA
Step-by-step explanation:
You can do vertical angles or alternate interior angles. Hope this helps :)
PLS ANSWER QUICK, HELP
Answer:
1014 in
Step-by-step explanation:
(13 x 13) x 6 = 1014 in^3
Answer:
The answer should be A (676)
Step-by-step explanation:
f(x)=x^2x+3;f(x)=-2x+12
Answer:
F
(
−
2
x
+
12
)
=
−
8
x
3
+
144
x
2
−
864
x
+
1731
Step-by-step explanation:
Teresa is a video game designer andher annual income is $134,723. Teresa must pay income tax of 6%. What is the amount of income tax in dollars and cents that Teresa pays
PLEASE HELP EASY 30 POINTS
Answer:
I want her mollah
Step-by-step explanation:
solve for x in the equation
Answer:
third option
Step-by-step explanation:
subtract 125/4 from each side to get:
x² + 11x -1
use quadratic formula to get:
-11 ± √121 - 4(-1)/2
= -11 ± ([tex]\sqrt{125}[/tex]) / 2
* [tex]\sqrt{125}[/tex] = [tex]\sqrt{25}[/tex] · [tex]\sqrt{5}[/tex] = 5[tex]\sqrt{5}[/tex]
= -11 ± (5[tex]\sqrt{5}[/tex]) / 2
1) Which of the following is a measurement of length? *
O the amount of water in a pool
O the height of a building
how many blocks of concrete cover a sidewalk
O the amount of writing space on a page