Using an exponential function, it would take 824 minutes before the amount of medication in Aldi's bloodstream is effectively 0.
How to determine the timeA decaying exponential function is given as;
[tex]A(t) = A(0)e^-kt[/tex]
Where A = initial value
k = decay constant
We have the half-life of amoxicillin as 62minutes, to determine k, we get
[tex]A(62) = 0. 5(0)[/tex]
[tex]A(62) = 0.5A(0)[/tex]
[tex]0. 5A(0) = A(0) e^{-62k}[/tex]
Solve the exponential function thus
[tex]e^{-62k} = 0. 5[/tex]
㏑ [tex]e^{-62k}[/tex] = ㏑ 0. 5
- 62k = ㏑ 0.5
Make k subject of formula
k = -㏑[tex]\frac{0. 5}{62}[/tex]
k = 0. 011179
The equation is given by
[tex]A(t) = A(0)e^-0.011179[/tex]
We have
[tex]0. 0001A(0) = A(0)e^-0.01179[/tex]
[tex]e^-0.011179t = 0. 0001[/tex]
㏑ [tex]e^-0.011179[/tex] = ㏑ 0.0001
[tex]-0.011179t = In 0.0001[/tex]
t = [tex]-\frac{In 0. 0001}{0. 011179}[/tex]
t = [tex]824[/tex]
Therefore, it would take 824 minutes before the amount of medication in Aldi's bloodstream is effectively 0.
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Murder Rates The data represent the murder rate per 100,000 individuals in a sample of selected cities in the United States. Find the variance and standard deviation. Round your answers to at least one decimal place. Class limits Frequency 5-11 10 12-18 9 19-25 10 26-32 5 33-39 2 40-46 6
The Sample mean,Sample Variance, Standard deviation is mathematically given as
x=21.66[tex]\sigma=138.52[/tex][tex]\mu=11.769[/tex]What is the Sample mean,Sample Variance, Standard deviation.?Generally, the equation for Sample mean is mathematically given as
[tex]x = \frac{1}{N}(\sum xifi )[/tex]
Where
[tex]\sum xifi=80+135+220+145+72+258[/tex]
[tex]\sum xifi=910[/tex]
Therefore
x=1/42 (910)
x=21.66
Sample Variance
[tex]\sigma = \frac{1}{N-1}(\sum xi^2fi-(\frac{1}{N}(\sum xifi^2 )) )[/tex]
Where
[tex]\sum xi^2fi=640+2025+4840+4205+2592+11094[/tex]
[tex]\sum xi^2fi=25396[/tex]
Therefore
[tex]\sigma = \frac{1}{41}(25396-(\frac{1}{42}(910^2 )) )[/tex]
[tex]\sigma=138.52[/tex]
Standard deviation.
[tex]\mu=\sqrt{\sigma^2}\\\\\mu=\sqrt{138.52}[/tex]
[tex]\mu=11.769[/tex]
In conclusion,
x=21.66
[tex]\sigma=138.52[/tex]
[tex]\mu=11.769[/tex]
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Shota invests $2000 in a certificate of deposit that earns 2%, percent in interest each year.
Write a function that gives the total value V(t) in dollars, of the investment t years from now.
Answer:
[tex]2 * 10^3 * 1,02^t[/tex]
Step-by-step explanation:
Let [tex]S = 2000 = 2 * 10^3[/tex] dollars be our investment, [tex]r = 2\%[/tex] - our interest rate. In order to simplify things, I suggest bringing the variable [tex]p[/tex] into play: [tex]p = 1 + \frac{r}{100}[/tex]. So, after year [tex]1[/tex] we will have [tex]S_{1} = S + \frac{r}{100}S = S(1 + \frac{r}{100} ) = Sp[/tex]. After year [tex]2[/tex]: [tex]S_{2} = S_{1}p = Sp * p = Sp^2[/tex]. After year [tex]t[/tex]: [tex]S_{t} = S_{t - 1}p = Sp^t[/tex]. Besides, we can count [tex]p[/tex]. Indeed, [tex]p = 1 + \frac{r}{100} = 1 + \frac{2}{100} = \frac{100}{100} + \frac{2}{100} = \frac{102}{100} = 1,02[/tex]. Therefore, [tex]V(t) = Sp^t = 2 * 10^3 * 1,02^t[/tex].
How do I even do this...
Answer:
x = 2 ± [tex]\sqrt{15}[/tex]
Step-by-step explanation:
x² - 4x - 11 = 0 ( add 11 to both sides )
x² - 4x = 11
to complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 2)x + 4 = 11 + 4
(x - 2)² = 15 ( take square root of both sides )
x - 2 = ± [tex]\sqrt{15}[/tex] ( add 2 to both sides )
x = 2 ± [tex]\sqrt{15}[/tex]
which of the following are equivalent to 55%? (Check all that apply.)
5.5
13/25
0.55
11/20
Answer:
The answer is 0.55
Step-by-step explanation:
Because 55% = [tex]\frac{55}{100}[/tex] = 0.55
The line graph on the y-axis is parallel to the x-axis, 3rd quadrant point, and an open downward parabola.
can anyone help?
Answer:
[tex](x + 5) {}^{2} = - 12(y - 1)[/tex]
=Which composition of transformations will create a pair of similar, not congruent triangles?
a rotation, then a reflection
a translation, then a rotation
a reflection, then a translation
a rotation, then a dilation
Option d) is correct, i.e. a rotation, then a dilation. Transformation will create a pair of similar but not congruent triangles.
Which composition of transformations will create a pair of similar, not congruent triangles?
In congruent geometry, the shapes that are so identical. can be superimposed to themselves.
When triangle is rotated, than position of angles will change. Aftermath the dilation of the triangle would increase the proportion of the sides, but angles remains equal, by which the triangle remain similar but not congruent.
Thus, a rotation, then a dilation transformation will create a pair of siilar but not congruent triangles.
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Answer:
D. a rotation, then a dilation
Step-by-step explanation:
got it right on edge 23
Which of the following is equivalent to the complex number i^36?
1
i
-1
-i
Answer:
1
Step-by-step explanation:
[tex]i^4=1\\\\i^{36}=(i^{4})^9=(1)^9=1[/tex]
Colin found 22 more mushrooms that sophie did while they were out picking them in the forest. On the way home Sophie asked Colin to give her mushrooms so they have equal amounts. How many mushrooms did Colin give to Sophie?
Answer:
11 mushrooms
Step-by-step explanation:
Let's take two sets of numbers that fulfill the requirements (2 and 24 | 5 and 27)
In the first case, there are 26 mushrooms, and to have an equal amount they each need 13. Collin had to give 11 mushrooms to Sophie.
In the second case, there are 32 mushrooms, and they both need 16 each. So in this case, Collin also had to give 11 to Sophie.
The answer is 11 mushrooms.
When using BINOM.DIST to calculate a probability mass function, which argument should be set to FALSE?
The question is incomplete. Please read below to find the missing content.
D) cumulative is an argument that should be set to FALSE.
If we use cumulative =fake then we are able to get a precise probability
If we use cumulative= genuine, we will get less than or equal to possibility.
A sequence of actions wherein the effects are always unsure. I was tossing a coin, deciding on a card from a deck of playing cards, and throwing a cube. occasion. It is a single final result of a test. Getting a Head at the same time as tossing a coin is an occasion.
When using BINOM.DIST to calculate a probability mass function, which argument should be set to FALSE? Select an answer
A) number_s
B) probability_s
C) trials
D) cumulative
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PLEASE ANSWER I'LL GIVE BRAINLIEST. Mrs. Nestler enjoys listening to classical music. She has the following audio CDs by her favorite composers in her collection: 4 by Bach, 6 by Beethoven, 3 by Brahms, and 2 by Handel. If she selects 4 CDs randomly from her collection without replacing them, what is the probability that she will choose one by each composer?
16/455
2/455
16/5625
2/5625
The probability that she will choose one by each composer is 2/455.
What is the probability?
Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
Probability = (number of bach cds / total number of cds) x (number of beethoven cds / total number of cds - 1) x (number of Brahms cds / total number of cds-2) x (number of Handel's cds / total number of cds-3)
= 4/15 x 6/14 x 3/13 x 2/12 = 2/455
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A simple random sample of 81 8th graders at a large suburban middle school indicated that 87% of them are involved with some type of after school activity. Find the 90% confidence interval that estimates the proportion of them that are involved in an after school activity.
The 90% confidence interval that estimates the proportion of 8th graders that are involved in an after-school activity is (0.80853,0.93147).
The confidence interval for a population proportion for a given sample is given by the formula:
[tex](p-Z\sqrt{\frac{p(1-p}{n} } , p+Z\sqrt{\frac{p(1-p}{n} })[/tex],
where p is the population proportion, Z is the Z-score value for the confidence interval, and n is the sample size.
In the question, we are given a random sample of 81 8th graders at a large suburban middle school. This implies that the sample size, n = 81. Also, we are told that they indicated 87% of them were involved with some type of after-school activity. This implies that the population proportion, p = 87% = 0.87.
We are asked to find the 90% confidence interval that estimates the proportion of them that are involved in an after-school activity.
Z-score (Z) corresponding to a 90% confidence interval is 1.645.
Thus, we can find the confidence interval as follows:
(0.87 - 1.645√{(0.87(1 - 0.87))/81},0.87 + 1.645√{(0.87(1 - 0.87))/81})
= (0.87 - 0.061469,0.87 + 0.061469)
= (0.80853,0.93147).
Thus, the 90% confidence interval that estimates the proportion of 8th graders that are involved in an after-school activity is (0.80853,0.93147).
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Which of the following is correct equation for the trend line in the scatter plot? A. Y= 2/5 x -2 B. Y= 5x-1 C. Y= 5x +5 D. Y= -x+5
Answer: C. Y = 5x + 5
Step-by-step explanation:
We need to write, or decide on, the equation for the blue line as this line represents the trend line for this scatter plot. We will write this in slope-intercept form. See attached for a visual.
First, we will find our slope. We will use [tex]\frac{rise}{run}[/tex] for this since we have a graph with clear points. See attached, we count up [5] and then count to the right [1] for a slope of 5.
-> Slope = 5
Now, we will find our y-intercept. This is where the line intersects the y-axis. The line hits the y-axis at point (0, 5) giving us a y-intercept of 5.
-> Y-intercept = 5
Lastly, we will write our equation and decide on an answer.
y = mx + b
y = (5)x + (5)
Y = 5x + 5
C. Y = 5x + 5
Match the average rates of change of f(x) to the corresponding intervals.
The intervals [-5,-1], [-4,-1], [-3,1],[-2,1] match with -8,-7,4,-3.
Given the value of function at x=-5 is 35, at x=-4 is 24, at x=-3 is 15,at x=-2 is 8,at x=-2 is 8,at x=-1 is 3, at x=0 is 0, at x=1 is -1.
Average rate of change of values refers to the average of differences in the values divided by the difference of values of x.
First finding the average rate of change of interval [-5,-1]
Average rate of change={f(-1)-f(-5)}/(-1+5)
=(3-35)/4
=-32/4
=-8
Finding the average rate of change of interval [-4,-1]
Average rate of change={f(-1)-f(-4)}/(-1+4)
=(3-24)/3
=-21/3
=-7
Finding the average rate of change of interval [-3,1]
Average rate of change={f(1)-f(-3)}/(-3-1)
=(-1-15)/-3-1
=-16/-4
=4
Finding the average rate of change of interval [-2,1]
Average rate of change={f(1)-f(-2)}/(1+2)
=(-1-8)/3
=-9/3
=-3
Hence the values which are to be filled in the boxes are -8,-7,4,-3.
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The equation 9(u – 2) + 1.5u = 8.25 models the total miles Michael traveled one afternoon while sledding, where u equals the number of hours walking up a hill and (u – 2) equals the number of hours sledding down the hill. Which is the value of u?
u = 0.25
u = 0.75
u = 1.1
u = 2.5
The value of u, number of hours walking up a hill based on the equation is 2.5
Equation9(u – 2) + 1.5u = 8.25
where,
u = number of hours walking up a hill (u - 2) = number of hours sledding down the hill9(u – 2) + 1.5u = 8.25
9u - 18 + 1.5u = 8.25
9u + 1.5u = 8.25 + 18
10.5u = 26.25
u = 26.25/10.5
u = 2.5
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A grocery store sells 1 gallon containers of milk for 3.99. The store also sells orange juice in a 6 pack of 5.5 fluid ounce bottles for $1.79. Suppose the store wants to sell its orange juice in gallon containers instead. To the nearest dollar, how much more would a gallon of orange juice cost than a gallon of milk?
The a gallon of orange juice will cost $ 3.0 more than a gallon of milk.
Size of the orange juiceThe size of the orange juice in gallon is calculated as follows;
1 ounce = 0.0078125 gal
5.5 ounce = ?
= 0.043 gallon
Total volume of 6 pack = 6 x 0.043 gal = 0.258 gal
0.258 gal = $1.79
1 gal = ?
= $ 6.94
Difference between cost of gallon of milk and orange juice= $ 6.94 - $ 3.99
= $2.95
≈ $ 3.0
Thus, the a gallon of orange juice will cost $ 3.0 more than a gallon of milk.
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Fill in the digit on the right side of each equation so that each equation has an integer solution.
A) 35x−11=107....
B)9m+34=68....
C)7965−4m=19....
20 pts
The digit on the right side of each equation so that each equation has an integer solution are 2.74, 3.78 and 1986.5 respectively.
Equation35x - 11 = 107
35x = 107 - 11
35x = 96
x = 96/35
x = 2.74
9m + 34 = 68
9m = 68 - 34
9m = 34
m = 34/9
m = 3.78
7965 - 4m = 19
-4m = 19 - 7965
-4m = -7946
m = -7946/-4
m = 1986.5
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To prove part of the triangle midsegment theorem using the diagram, which statement must be shown?
The length of JK equals the length of JL.
The length of GH is half the length of KL.
The slope of JK equals the slope of JL.
The slope of GH is half the slope of KL.
The statement which the diagram shows is that the length of GH is half of the length of KL . Option B
What is the midsegment theorem?
The midsegment theorem holds that any segment that forms the joining midpoints of two sides of a triangle is parallel to half the length of the third side.
It can be seen that the length of GH is half of the length of KL as deduced from the diagram
Therefore, the statement which the diagram shows is that the length of GH is half of the length of KL . Option B
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CAN YALL PLEASE WORK IT OUTTT
$18.79 + $2.11 + ‐$1.92 + $17.28
Answer:
40.1
Step-by-step explanation:
Because the order of operations (Bodmas or Pedmas) tells you to add from left to right. So you would do 18.79 + 2.11 = 20.9, then you would do 20.90 + 1.92 (Add 0 at the end of 20.9) = 22.81. Then you will add 22.81 + 17.28 = 40.1. So your answer is 40.1. Hope this helps!
if a cake was sold GH 200 cedis. However, there is a reduction sale of 10% on each cake if you buy 4. Amanda decides to buy 8 cakes, how much would she pay
Amanda needs to pay 1440 cedis for purchasing 8 cakes on discounted price.
What is Cost Price?
Cost price is the amount we pay to buy an item at which it is available.
Here,
Selling price of a cake = 200 cedis
Discount because of sale = 10% on each unit.
(Only if 4 cakes purchased at a time)
Amanda purchased 8 cakes
So, Amanda need to pay only 90 percent of the total amount.
Total cost price of 8 cakes for Amanda = (200 X 90%) X 8
= 180 X 8
= 1440
Thus, Amanda needs to pay 1440 cedis for purchasing 8 cakes on discounted price.
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Please help me out :P
cos θ = [tex]\frac{-4\sqrt{65} }{65}[/tex], sin θ = [tex]\frac{-7\sqrt{65} }{65}[/tex], cot θ = 4/7, sec θ = [tex]\frac{-\sqrt{65} }{4}[/tex], cosec θ = [tex]\frac{-\sqrt{65} }{7}[/tex]
What are trigonometric ratios?Trigonometric Ratios are values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
Sin θ: Opposite Side to θ/Hypotenuse
Tan θ: Opposite Side/Adjacent Side & Sin θ/Cos
Cos θ: Adjacent Side to θ/Hypotenuse
Sec θ: Hypotenuse/Adjacent Side & 1/cos θ
Analysis:
tan θ = opposite/adjacent = 7/4
opposite = 7, adjacent = 4.
we now look for the hypotenuse of the right angled triangle
hypotenuse = [tex]\sqrt{7^{2} + 4^{2} }[/tex] = [tex]\sqrt{49+16}[/tex] = [tex]\sqrt{65}[/tex]
sin θ = opposite/ hyp = [tex]\frac{7}{\sqrt{65} }[/tex]
Rationalize, [tex]\frac{7}{\sqrt{65} }[/tex] x [tex]\frac{\sqrt{65} }{\sqrt{65} }[/tex] = [tex]\frac{7\sqrt{65} }{65}[/tex]
But θ is in the third quadrant(180 - 270) and in the third quadrant only tan and cot are positive others are negative.
Therefore, sin θ = - [tex]\frac{7\sqrt{65} }{65}[/tex]
cos θ = adj/hyp = [tex]\frac{4}{\sqrt{65} }[/tex]
By rationalizing and knowing that cos θ is negative, cos θ = -[tex]\frac{-4\sqrt{65} }{65}[/tex]
cot θ = 1/tan θ = 1/7/4 = 4/7
sec θ = 1/cos θ = 1/[tex]\frac{4}{\sqrt{65} }[/tex] = -[tex]\frac{-\sqrt{65} }{4}[/tex]
cosec θ = 1/sin θ = 1/[tex]\frac{\sqrt{65} }{7}[/tex] = [tex]\frac{-\sqrt{65} }{7}[/tex]
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help me please 20 points
Answer:
28 square meters.
Step-by-step explanation:
The total area - the grass area = the cement area.
36 - 8 = 28.
28 square meters.
Calculate: 1/1x3+1/3x5+…+1/47x49
Answer:
24/49
Step-by-step explanation:
Find the length of JH help pls
Answer:
19 units
Step-by-step explanation:
JM is 40 units, and it is composed of JH and HM. HM is 21 units, and so JH must be the remaining units.
40 - 21 = 19
Brainliest, please :)
HELP QUICKLY PLEASE!!!!!!!!
Answer: 20
Step-by-step explanation:
We will set up a proportion to solve.
[tex]\displaystyle \frac{?}{16}=\frac{15}{12}[/tex]
Now, we will cross-multiply.
12 * ? = 16 * 15
12? = 240
? = 20
what is the gradient?
please help
The gradient of line A is -2. 67
How to determine the gradient
Gradient = slope = Δy/ Δx
We have,
y2 = 3
y1 = -5
x2 = -3
x1 = 0
Substitute the values
Gradient = [tex]\frac{3 - (-5)}{-3 -0}[/tex]
Gradient = [tex]\frac{3 + 5}{-3}[/tex]
Gradient = [tex]\frac{8}{-3}[/tex]
Gradient = -2. 67
Thus, the gradient of line A is -2. 67
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help trigonometry
cccccc
Answer:
D
Step-by-step explanation:
Trigonometry ratios:[tex]\sf Sin \ \theta =\dfrac{opposite \ side }{hypotenuse} =\dfrac{12}{37}[/tex]
To find the adjacent side use Pythagorean theorem.
Opposite side² + adjacent side² = hypotenuse²
adjacent side² = hypotenuse² - opposite side²
= 37² - 12²
= 1369 - 144
= 1225
adjacent side = √1225
= 35
[tex]\sf tan \ \theta =\dfrac{Opposite \ side }{adjacent \ side}\\\\tan \ \theta = \dfrac{12}{35}[/tex]
Giving 15 points for the answer.
Answer:
4p-3
Explaination
when we subtract
4p-3 -3p-6
it will give us p _9
Provide the next step to derive the quadratic formula.
Step 1 : ax2+box+c=0
Step 2 : ax2+box=-c
Step 3 : x2 + b/ax=-c/a
Step 4 : ??
The next step to derive the quadratic formula is x² + (b/a)x + (b²/2a²)= -c/a + (b²/2a²)
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Step 1:
ax² + bx + c = 0
Step 2:
ax² + bx = -c
Step 3:
x² + (b/a)x = -c/a
Step 4:
x² + (b/a)x + (b²/2a²)= -c/a + (b²/2a²)
The next step to derive the quadratic formula is x² + (b/a)x + (b²/2a²)= -c/a + (b²/2a²)
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Which of the following equations have no solutions?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
A
33x+25=33x+2533x+25=33x+2533, x, plus, 25, equals, 33, x, plus, 25
(Choice B)
B
33x-33=33x+2533x−33=33x+2533, x, minus, 33, equals, 33, x, plus, 25
(Choice C)
C
33x-25=33x+2533x−25=33x+2533, x, minus, 25, equals, 33, x, plus, 25
(Choice D)
D
33x+33=33x+2533x+33=33x+25
Answer:
A. 33x-25=33x+25
C. 33x-33=33x+25
D.33x+33=33x+25
A. 33x-25=33x+25
33x-33x=25+25
0 = 50
This is incorrect equality, as it is not equal on both sides.
Therefore this equation has no solutions.
B. 33x+25=33x+25
33x−33x=25−25
0=0
This is correct equality, as it is equal to zero on both sides.
Therefore the equation has an infinite number of solutions.
C. 33x-33=33x+25
33x-33x=33+25
0=58
This is incorrect equality, as it is not equal on both sides.
Therefore this equation has no solution.
D. 33x+33=33x+25
33x−33x=25−33
0=−8
This is incorrect equality, as it is not equal on both sides.
Therefore this equation has no solution.
Hence, the equations which has no solution are;
A. 33x-25=33x+25
C. 33x-33=33x+25
D.33x+33=33x+25
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8. In February 2018, a newspaper reported that the total land area of Singapore is expected to reach 76 600 hectares by 2030. This is an increase of about 6.4% from the total land area in 2017. Find the total land area in 2017, giving your answer correct to 4 significant figures.
Answer:
The answer is 7.199 x 10^4 hectares
Step-by-step explanation:
Let's set x as the total land area in 2017.
x * (1 + 6.4%) = 76,600
x * (1 + 0.064) = 76,600
x * 1.064 = 76,600
x = 76,600 / 1.064
x = 71,992.48
x = 7.199 * 10^4 hectares