4) The half-life of a medication is the amount of time for half of the drug to be eliminated from the body. The half-life of Advil or ibuprofen is represented by the equation 2 ) 5 . 0 ( t M R = , where R is the amount of Advil remaining in the body, M is the initial dosage, and t is time in hours.
Answers
Based on the half-life, 35.36 mg will remain at 6:00P PM in the body
The amount of the medication that will remain at 6:00P PM?The details that complete the question are added as an attachment
From the question, we have
Initial dosage = 200 mg
This means that
M = 200
Also, we have
Initial time =1 : 00 pm
This means that the number of hours, is
n = 6pm - 1pm
n = 5
Recall that the function is given as
R = M(0.5)ⁿ/²
So, we have the following equation
R = 200 x (0.5)⁵/²
Evaluate the quotient of the exponents
So, we have the following equation
R = 200 x (0.5)².⁵
Evaluate the products
R = 35.36 mg
Using the above computation as a guide, we have the remaining amount to be 35.36 mg
Hence, the amount of the medication that will remain at 6:00P PM is 35.36 mg
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Related Questions
What is the equation in slope-intercept form of the line that passes through the points (-4,8) and (12,4)?
Answers
ANSWER
y = -0.25 + 7
EXPLANATION
The line passes through the points (-4, 8) and (12, 4).
The slope-intercept form of a linear equation is written as:
y = mx + c
where m = slope
c = y intercept
First, we have to find the slope of the line.
We do that with formula:
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \text{where (x}_1,y_1)\text{ = (-4, 8) } \\ (x_2,y_2)\text{ = (12, 4)} \end{gathered}[/tex]Therefore, the slope is:
[tex]\begin{gathered} m\text{ = }\frac{4\text{ - 8}}{12\text{ - (-4)}}\text{ = }\frac{-4}{12\text{ + 4}}\text{ = }\frac{-4}{16}\text{ = }\frac{-1}{4} \\ m\text{ = -0.25} \end{gathered}[/tex]Now, we use the point-slope method to find the equation:
[tex]\begin{gathered} y-y_{1\text{ }}=m(x-x_1) \\ \Rightarrow\text{ y - 8 = -0.25(x - (-4))} \\ y\text{ - 8 = -0.25(x + 4)} \\ y\text{ - 8 = -0.25x - 1} \\ y\text{ = -0.25x - 1 + 8} \\ y\text{ = -0.25x + 7} \end{gathered}[/tex]That is the equation of the line. It is not among the options.
helpppppppppp!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
A. y = -250x + 3750
B. $2125
Step-by-step explanation:
A.
(5, 2500), (7, 2000)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 2000 - 2500 -500
m = ----------------- = ---------------------- = ---------- = -250
x₂ - x₁ 7 - 5 2
y - y₁ = m(x - x₁)
y - 2500 = -250(x - 5)
y - 2500 = -250x + 1250
+2500 +2500
-------------------------------------
y = -250x + 3750
B.
y = -250x + 3750
y = -250(6.50) + 3750
y = -1625 + 3750
y = 2125
(6.50, 2125)
I hope this helps!
I need help with a math problem. I linked it below
Answers
According to the distributive property of multiplication:
[tex]a\cdot(b+c)=a\cdot b+a\cdot c[/tex]Then,
[tex]\begin{gathered} -6(x+5)=12 \\ -6x-6\cdot5=12 \\ -6x-30=12 \end{gathered}[/tex]To find x, add 30 to both sides:
[tex]\begin{gathered} -6x-30+30=12+30 \\ -6x=42 \end{gathered}[/tex]And divide both sides by -6:
[tex]\begin{gathered} \frac{-6}{-6}x=\frac{42}{-6} \\ x=-7 \end{gathered}[/tex]Answer:
- 6x - 30 = 12
x = -7
For each ordered pair, determine whether it is a solution.
Answers
To determine which ordered pair is a solution to the equation we shall substitute the values of x and y in the ordered pair.
Taking the first ordered pair;
[tex]\begin{gathered} \text{For;} \\ 3x-5y=-13 \\ \text{Where;} \\ (x,y)\Rightarrow(9,8) \\ 3(9)-5(8)=-13 \\ 27-40=-13 \\ -13=-13 \end{gathered}[/tex]This means the ordered pair (9, 8) is a solution.
We can also solve this graphically a follows;
Observe from the graph attached that the solution to the equation shown above is indicated at the point where x = 9 and y = 8.
The other ordered pairs in the answer options cannot be found on the line which simply mean they are not solutions to the equation given.
ANSWER:
The ordered pair (9, 8) is a solution to the equation 3x - 5y = -13
A quality control expert at glow tech computers wants to test their new monitors . The production manager claims that have a mean life of 93 months with the standard deviation of nine months. If the claim is true what is the probability that the mean monitor life will be greater than 91.4 months and a sample of 66 monitors? Round your answers to four decimal places
Answers
Given the following parameter:
[tex]\begin{gathered} \mu=93 \\ \sigma=9 \\ \bar{x}=91.4 \\ n=66 \end{gathered}[/tex]Using z-score formula
[tex]z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]Substitute the parameter provided in the formula above
[tex]z=\frac{91.4-93}{\frac{9}{\sqrt{66}}}[/tex][tex]z=-1.4443[/tex]The probability that the mean monitor life will be greater than 91.4 is given as
[tex]\begin{gathered} P(z>-1.4443)=P(0\leq z)+P(0-1.4443)=0.5+0.4257 \\ P(z>-1.4443)=0.9257 \end{gathered}[/tex]Hence, the probability that the mean monitor life will be greater than 91.4 months is 0.9257
Graph the reflection of the polygon in the given line
Answers
Let:
[tex]\begin{gathered} A=(-3,2) \\ B=(1,-1) \\ C=(-2,-2) \\ D=(-4,-1) \end{gathered}[/tex]After the reflection over y = -x:
[tex]\begin{gathered} A->(-y,-x)->A^{\prime}=(-2,3) \\ B->(-y,-x)->B^{\prime}=(1,-1) \\ C->(-y,-x)->C^{\prime}=(2,2) \\ D->(-y,-x)->D^{\prime}=(1,4) \end{gathered}[/tex]Rewrite the polynomial in standard form: 2x + 7x^2 - 3+ x^3
Answers
The given polynomial is
[tex]2x+7x^2-3+x^3[/tex]The standard form refers to organizing the terms where the exponents are placed in decreasing order.
[tex]x^3+7x^2+2x-3[/tex]D. What is the change in temperature when the thermometer readingmoves from the first temperature to the second temperature? Write anequation for each part.1. 20°F to +10°F2. 20°F to 10°F3. 20°F to 10°F4. 10°F to +20°F
Answers
Given
What is the change in temperature when the thermometer reading
moves from the first temperature to the second temperature? Write an
equation for each part.
Solutiion
need help finding the exact value of sec pi/3
Answers
Solution:
Given:
[tex]sec(\frac{\pi}{3})[/tex]To find the exact value,
Step 1: Apply the trigonometri identieties.
From the trigonometric identities,
[tex]sec\text{ }\theta\text{ =}\frac{1}{cos\theta}[/tex]This implies that
[tex]sec(\frac{\pi}{3})=\frac{1}{\cos(\frac{\pi}{3})}[/tex]Step 2: Evaluate the exact value.
[tex]\begin{gathered} since \\ \cos(\frac{\pi}{3})=\frac{1}{2}, \\ we\text{ have} \\ sec(\frac{\pi}{3})=\frac{1}{\cos(\pi\/3)}=\frac{1}{\frac{1}{2}}=2 \end{gathered}[/tex]Hence, te exact value of
[tex]sec(\frac{\pi}{3})[/tex]is evaluated to be 2
Find the maximum value:13, 18, 27, 12, 38, 41, 32, 15, 32
Answers
We can find the maximum value by creating a list of the provided numbers from the smallest to the largest.
[tex]12,13,15,18,27,32,32,38,41[/tex]As we see on the list, the last number and the largest is 41. Some tools are used to solve this kind of problem like the diagram of leaves and stems, a table os fre
Find the volume of each prism. Round your answers to the nearest tenth, if necessary. Do not include units (i.e. ft, in, cm, etc.). (FR)
Answers
EXPLANATION:
Given;
We are given the picture of an isosceles trapezoidal prism.
The dimensions are as follows;
[tex]\begin{gathered} Top\text{ }base=4 \\ Bottom\text{ }base=9 \\ Vertical\text{ }height=4.3 \\ Height\text{ }between\text{ }bases=6 \end{gathered}[/tex]Required;
We are required to find the volume of this trapezoidal prism.
Step-by-step solution;
The area of the base of a trapezium is given as;
[tex]Area=\frac{1}{2}(a+b)\times h[/tex]For the trapezium given and the values provided, we now have;
[tex]\begin{gathered} a=top\text{ }base \\ b=bottom\text{ }base \\ h=height \\ Therefore: \\ Area=\frac{1}{2}(4+9)\times4.3 \\ Area=\frac{1}{2}(13)\times4.3 \\ Area=6.5\times4.3 \\ Area=27.95 \end{gathered}[/tex]The volume is now given as the base area multiplied by the length between both bases and we now have;
[tex]\begin{gathered} Volume=Area\times height\text{ }between\text{ }trapezoid\text{ }ends \\ Volume=27.95\times6 \\ Volume=167.7 \end{gathered}[/tex]ANSWER:
The volume of the prism is 167.7
Seventh gradeK.2 Write equations for proportional relationships from tables 66UTutorialVer en español1) Over the summer, Oak Grove Science Academy renovates its building. The academy'sprincipal hires Jack to lay new tile in the main hallway.3) There is a proportional relationship between the length (in feet) of hallway Jack coverswith tiles, x, and the number of tiles he needs, y.0)) (feet)y (tiles)3276547631199Write an equation for the relationship between x and y. Simplify any fractions.y =
Answers
Proportional Relationship
Two variables x and y have a proportional relationship it the following equation stands:
y = kx
Where k is the constant of proportionality.
The number of tiles needed by Jack (y) has a proportional relationship with the length in feet of the hallway (x).
The table gives us some values. We'll summarize them as ordered pairs (x,y) as follows:
(3,27) (6,54) (7,63) (11,99)
We can use any of those ordered pairs to find the value of k. For example, (3,27). Substituting into the equation:
27 = k.3
Solving for k:
k= 27/3 = 9
Thus the equation is:
y = 9x
Note: We could have used any other ordered pair and we would have obtained the very same value of k.
a. Draw any obtuse angle and label it angle AXB. Then draw ray XY so that it bisects < AXB.b. if m AXB = 140°, then what is m ZYXB?
Answers
The obtuse angle is shown in the diagram below:
The word, "bisect" means to divide an angle into 2 equal parts. Given that ray XY bisects angle AXB, it mean that it divides it into two equal halves. Theregfore, angle YXB is 140/2 = 70 degrees
Solve the equation for w.
4w + 2 + 0.6w = −3.4w − 6
No solution
w = 0
w = 1
w = −1
Answers
Answer:
w = -1
Step-by-step explanation:
Given equation:
[tex]4w + 2 + 0.6w=-3.4w-6[/tex]
Add 3.4w to both sides:
[tex]\implies 4w + 2 + 0.6w+3.4w=-3.4w-6+3.4w[/tex]
[tex]\implies 4w + 2 + 0.6w+3.4w=-6[/tex]
Subtract 2 from both sides:
[tex]\implies 4w + 2 + 0.6w+3.4w-2=-6-2[/tex]
[tex]\implies 4w +0.6w+3.4w=-6-2[/tex]
Combine the terms in w on the left side of the equation and subtract the numbers on the right side of the equation:
[tex]\implies 8w=-8[/tex]
Divide both sides by 8:
[tex]\implies \dfrac{8w}{8}=\dfrac{-8}{8}[/tex]
[tex]\implies w=-1[/tex]
Therefore, the solution to the given equation is:
[tex]\boxed{w=-1}[/tex]
Given that,
→ 4w + 2 + 0.6w = -3.4w - 6
Now the value of w will be,
→ 4w + 2 + 0.6w = -3.4w - 6
→ 4.6w + 2 = -3.4w - 6
→ 4.6w + 3.4w = -6 - 2
→ 8w = -8
→ w = -8/8
→ [ w = -1 ]
Hence, the value of w is -1.
i need help with this question... it's about special right triangles. The answer should not be a decimal.
Answers
4) The given triangle is a right angle triangle. Taking 30 degrees as the reference angle,
hypotenuse = 34
adjacent side = x
opposite side = y
We would find x by applying the Cosine trigonometric ratio which is expressed as
Cos# = adjacent side/hypotenuse
Cos 30 = x/34
Recall,
[tex]\begin{gathered} \cos 30\text{ = }\frac{\sqrt[]{3}}{2} \\ \text{Thus, } \\ \frac{\sqrt[]{3}}{2}\text{ =}\frac{x}{34} \\ 2x=34\sqrt[]{3} \\ x\text{ = }\frac{34\sqrt[]{3}}{2} \\ x\text{ = 17}\sqrt[]{3} \end{gathered}[/tex]To find y, we would apply the Sine trigonometric ratio. It is expressed as
Sin# = opposite side/hypotenuse
Sin30 y/34
Recall, Sin30 = 0.5. Thus
0.5 = y/34
y = 0.5 * 34
y = 17
Use the distance formula to find the distance between the points given.(3,4), (4,5)
Answers
Solution:
To find the distance between two points, the formula is
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Where
[tex]\begin{gathered} (x_1,y_1)=(3,4) \\ (x_2,y_2)=(4,5) \end{gathered}[/tex]Substitute the values of the variables into the formula above
[tex]d=\sqrt{(4-3)^2+(5-4)^2}=\sqrt{1^2+1^2}=\sqrt{1+1}=\sqrt{2}\text{ units}[/tex]Hence, the answer is
[tex]\sqrt{2}\text{ units}[/tex]What is the slope of a line parallel to the line whose equation is 12x – 15y = 315.Fully simplify your answer.
Answers
Answer:
4/5
Explanation:
Definition: Two lines are parallel if they have the same slope.
Given the line:
[tex]12x-15y=315[/tex]Determine the slope of the given line by expressing it in the slope-intercept form (y=mx+b), where m is the slope:
[tex]\begin{gathered} 12x-15y=315 \\ \text{ Add 15y to both sides of the equation} \\ 12x-15y+15y=315+15y \\ 12x=315+15y \\ \text{ Subtract 315 from both sides:} \\ 12x-315=315-315+15y \\ 12x-315=15y \\ \text{ Divide all through by 15} \\ \frac{15y}{15}=\frac{12}{15}x-\frac{315}{15} \\ y=\frac{4}{5}x-21 \end{gathered}[/tex]• The slope of the line, m = 4/5.
Since the lines are parallel, they have the same slope.
Hence, the slope of a line parallel to the line whose equation is 12x – 15y = 315 is 4/5.
When you purchase a T.V., the size refers to the diagonal measurement of the screen. If
the 46 inch TV has a square screen, what is the approximate length and width? Round
your answer to the nearest tenth.
Answers
TV Dimensions (Diagonal) Screen Width
46 inch TV 40.1 inches + Bezel
A TV's screen size is determined by measuring the panel diagonally from one corner to the other. The TV's bezels and other exterior surfaces are not included in this. There are numerous models in a certain size group.
What does diagonal screen size mean?A screen's size is often determined by the diagonal, or the distance between its opposite corners, which is typically measured in inches. To distinguish it from the "logical image size," which characterizes a screen's display resolution and is measured in pixels, it is also often referred to as the physical image size.
Start at the top-left corner and measure diagonally down to the bottom-right corner using a measuring tape. Do not include the bezel (the plastic, metal, or glass edge), if any, when measuring the screen alone.
because the units are too large to be offered by furlongs and fathoms. Since the United States does not use the metric system, while television was being invented, American engineers used the units they were most accustomed to.
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Dante is arranging 11 cans of food in a row on a shelf. He has 7 cans of beans, 3 cans of peas, and 1 can of carrots. In how many distinct orders can the cans be arranged if two cans of the same food are considered identical (not distinct)?
Answers
Given:
The number of cans of food =11
The number of cans of beans=7
the number of cans of peas=3
the number of cans of carrots=1
Condition : two cans of the same food are considered identical.
To arrange the n objects in order,
[tex]\begin{gathered} \text{Number of ways= }\frac{n!}{r_1!r_2!r_3!} \\ =\frac{11!}{7!3!1!} \\ =\frac{39916800}{30240} \\ =1320 \end{gathered}[/tex]Answer: the number of ways are 1320.
Yoonie is a personnel manager in a large corporation. Each month she must review 16 of the employees. From past experience, she has found that the reviews take her approximately four hours each to do with a population standard deviation of 1.2 hours. Let X be the random variable representing the time it takes her to complete one review. Assume X is normally distributed. Let X be the random variable representing the mean time to complete the 16 reviews. Assume that the 16 reviews represent a random set of reviews.
Find the probability that the mean of a month's reviews will take Yoonie from 3.5 to 4.25 hrs.
a. Give the probability statement and the probability. (Enter exact numbers as integers, fractions, or decimals for the probability statement. Round the probability to four decimal places.
Answers
Using the normal distribution and the central limit theorem, the probability that the mean of a month's reviews will take Yoonie from 3.5 to 4.25 hrs is:
[tex]P(3.5 \leq \bar{X} \leq 4.25) = 0.7482[/tex]
Normal Probability DistributionThe z-score of a measure X of a variable that has mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above or below the mean of the distribution, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The mean and the standard deviation of each review are given as follows:
[tex]\mu = 4, \sigma = 1.2[/tex]
For the sampling distribution of sample means of size 16, the standard error is given as follows:
[tex]s = \frac{1.2}{\sqrt{16}} = 0.3[/tex]
The probability that the mean of a month's reviews will take Yoonie from 3.5 to 4.25 hrs is the p-value of Z when X = 4.25 subtracted by the p-value of Z when X = 3.5, hence:
X = 4.25:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (4.25 - 4)/0.3
Z = 0.83.
Z = 0.83 has a p-value of 0.7967.
X = 3.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (3.5 - 4)/0.3
Z = -1.67.
Z = -1.67 has a p-value of 0.0475.
Hence the probability is:
0.7967 - 0.0485 = 0.7482.
The statement is:
[tex]P(3.5 \leq \bar{X} \leq 4.25)[/tex]
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Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.a=47ftb=59ftc=65ft
Answers
Okay, here we have this:
Considering the provided measures, we are going to calculate the area of the triangle, so we obtain the following:
So to calculate the area of the triangle we are going to use Heron's formula. so, we have:
[tex]A_=\sqrt{S(S-a)(S-b)(S-c)}[/tex]And S is equal to (a+b+c)/2, let's first calculate S and replace with the values in the formula:
S=(47+59+65)/2=171/2=85.5
Replacing:
[tex]\begin{gathered} A=\sqrt{85.5(85.5-47)(85.5-59)(85.5-65)} \\ A=\sqrt{85.5(38.5)(26.5)(20.5)} \\ A=\sqrt{1788243.1875} \\ A\approx1337.3ft^2 \end{gathered}[/tex]Finally we obtain that the area of the triangle is approximately equal to 1337.3 ft^2
while eating your yummy pizza, you observe that the number of customers arriving to the pizza station follows a poisson distribution with a rate of 18 customers per hour. on average, how many customers arrive in each 10 minutes interval?
Answers
In every 10 minutes an average of 3 customers will arrive to the pizza station
Given,
The number of customers arriving to the pizza station follows a poisson distribution with a rate of 18 customers per hour.
We have to find the average number of customers arrives in each 10 minutes.
Here,
The chance that X represents the number of successes of a random variable in a Poisson distribution is provided by the following formula:
P (X = x) = (e^-μ × μ^x) / x!
Where,
The number of successes is x.
The Euler number is e = 2.71828.
μ is the average over the specified range.
Now,
Rate of 18 customers per hour;
μ = 18 n
n is the number of hours.
Number of customers arrive in each 10 minutes
10 minutes = 10/60 = 1/6
Then,
μ = 18 x 1/6 = 3
That is,
In every 10 minutes an average of 3 customers will arrive to the pizza station.
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7n + 2 - 7n How can I simplify the expression by combining like terms
Answers
In order to simplify this expression, we can combine the terms with the variable n, like this:
[tex]\begin{gathered} 7n+2-7n \\ =(7n-7n)+2 \end{gathered}[/tex]Since the terms with the variable n have opposite coefficients (+7 and -7), the sum will be equal to zero:
[tex]\begin{gathered} (7n-7n)+2 \\ =(0)+2 \\ =2 \end{gathered}[/tex]Therefore the simplified result is 2.
8. (03.07 MO)Solve x2 - 10x = -21. O x = 7 and x = 3O x = -7 and x = 3O x = -7 andx = -3O x = 7 and x = -3
Answers
Given:
Quadratic equation
[tex]x^2-10x+21=0[/tex]To find:
Values of x satisfying given equation.
Explanation:
Roots of equation of type
[tex]ax^2-bx+c=0[/tex]roots will be (x-a)(x-b) and x = a,b.
Solution:
We will factorize equation as:
[tex]\begin{gathered} x^2-10x+21=0 \\ x^2-7x-3x+21=0 \\ (x-3)(x-7)=0 \\ x=3,\text{ 7} \end{gathered}[/tex]Hence, 3 and 7 are values of x.
Northeast Hospital’s Radiology Department is considering replacing an old inefficient X-ray machine with a state-of-the-art digital X-ray machine. The new machine would provide higher quality X-rays in less time and at a lower cost per X-ray. It would also require less power and would use a color laser printer to produce easily readable X-ray images. Instead of investing the funds in the new X-ray machine, the Laboratory Department is lobbying the hospital’s management to buy a new DNA analyzer.
Answers
The classification of each cost item as a differential cost, a sunk cost, an opportunity cost, or None, is as follows:
Cost Classification1. Cost of the old X-ray machine Sunk cost
2. The salary of the head of the Radiology Dept. None
3. The salary of the head of the Laboratory Dept. None
4. Cost of the new color laser printer Differential cost
5. Rent on the space occupied by Radiology None
6. The cost of maintaining the old machine Differential cost
7. Benefits from a new DNA analyzer Opportunity cost
8. Cost of electricity to run the X-ray machines Differential cost
9. Cost of X-ray film used in the old machine Sunk cost
What are differential cost, sunk cost, and opportunity cost?A differential cost is a cost that arises as the cost difference between two alternatives.
A sunk cost is an irrelevant cost in managerial decisions because it has been incurred already and future decisions cannot overturn it.
An opportunity cost is a benefit that is lost when an alternative is not chosen.
Thus, the above cost classifications depend on the decision to replace the old X-ray machine with a new machine (new X-ray or new DNA analyzer).
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Question Completion:Required Classify each item as a differential cost, a sunk cost, or an opportunity cost in the decision to replace the old X-ray machine with a new machine. If none of the categories apply for a particular item, select "None".
1. Cost of the old X-ray machine
2. The salary of the head of the Radiology Department
3. The salary of the head of the Laboratory Department
4. Cost of the new color laser printer
5. Rent on the space occupied by Radiology
6. The cost of maintaining the old machine
7. Benefits from a new DNA analyzer
8. Cost of electricity to run the X-ray machines
9. Cost of X-ray film used in the old machine
The number of bacteria in a culture increased from 27,000 to 105,000 in five hours. When is the number of bacteria one million if:a) Does the number increase linearly with time?b) The number increases exponentially with time?
Answers
We have the following situation regarding the growth of bacteria in a culture:
• The given initial population of bacteria is 27,000
,• After 5 hours, the population increases to 105,000.
Now, we need to find the moment when that population is one million if:
• The population increases linearly with time
,• The population increases exponentially with time
To find the time in both situations, we can proceed as follows:
Finding the moment when the population is one million if it increases linearly with time1. We need to find the equation of the line that passes the following two points:
• t = 0, population = 27,000
,• t = 5, population = 105,000
2. Then the points are:
[tex]\begin{gathered} (0,27000)\rightarrow x_1=0,y_1=27000 \\ (5,105000)\rightarrow x_2=5,y_2=105000 \\ \end{gathered}[/tex]3. Now, we can use the two-point form of the line equation:
[tex]\begin{gathered} y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ \\ y-27000=\frac{105000-27000}{5-0}(x-0) \\ \\ y-27000=\frac{78000}{5}x=15600x \\ \\ y=15600x+27000\rightarrow\text{ This is the line equation we were finding.} \end{gathered}[/tex]4. We can see that the population is given by y. Then if y = 1,000,000, then we need to solve the equation for x as follows:
[tex]\begin{gathered} 1000000=15600x+27000 \\ \\ 1000000-27000=15600x \\ \\ \frac{(1000000-27000)}{15600}=x \\ \\ x=62.3717948718\text{ hours} \\ \\ x\approx62.3718\text{ hours} \end{gathered}[/tex]Therefore, if the population increases linearly with time, the number of bacteria will be one million around 62.3718 hours.
Finding the moment when the population is one million if it increases exponentially with time1. In this case, we also need to find the equation that will give us the time when the number of bacteria is one million. However, since the equation will be exponential, we have:
[tex]\begin{gathered} y=a(1+r)^x \\ \\ a\rightarrow\text{ initial value} \\ \\ x\rightarrow\text{ number of time intervals that have passed.} \\ \\ (1+r)=b\text{ }\rightarrow\text{the growth ratio, and }r\rightarrow\text{ the growth rate.} \end{gathered}[/tex]2. Now, we can write it as follows:
[tex]\begin{gathered} a=27000 \\ \\ x=5\rightarrow y=105000 \\ \\ \text{ Then we have:} \\ \\ 105000=27000(b)^5 \\ \end{gathered}[/tex]3. We can find b as follows (the growth factor):
[tex]\begin{gathered} \frac{105000}{27000}=b^5 \\ \\ \text{ We can use the 5th root to obtain the growth factor. Then we have:} \\ \\ \sqrt[5]{\frac{105000}{27000}}=\sqrt[5]{b^5} \\ \\ b=1.31209447568 \end{gathered}[/tex]4. Then the exponential equation will be of the form:
[tex]\begin{gathered} y=27000(1.31209447568)^x \\ \\ \text{ To check the equation, we have that when x = 5, then we have:} \\ \\ y=27000(1.31209447568)^5=105000 \end{gathered}[/tex]5. Now, to find the time when the number of bacteria is one million, we can proceed as follows:
[tex]\begin{gathered} 1000000=27000(1.31209447568)^x \\ \\ \frac{1000000}{27000}=1.31209447568^x \end{gathered}[/tex]6. Finally, we need to apply the logarithm to both sides of the equation as follows:
[tex]\begin{gathered} ln(\frac{1000000}{27000})=ln(1.31209447568)^x=xln(1.31209447568) \\ \\ \frac{ln(\frac{1000000}{27000})}{ln(1.31209447568)}=x \\ \\ x=13.2974595282\text{ hours} \end{gathered}[/tex]Therefore, if the population increases exponentially with time, the number of bacteria will be one million around 13.2975 hours.
Therefore, in summary, we have:
When is the number of bacteria one million if:
a) Does the number increase linearly with time?
It will be 62.3718 hours
b) The number increases exponentially with time?
It will be around 13.2975 hours
Lulu the Lucky puts chests of gems into her treasure vault.
Each chest holds the same number of gems. The table
below shows the number of gems Lulu received from
three different adventures and the number of chests she
needed to hold the gems.
Number of gems
Number of chests
Adventure A
600
2
Adventure B
1500
5
Adventure C
4800
16
Write an equation to describe the relationship between
g, the number of gems, and c, the number of chests.
Answers
The equation that represents the relationship of gems 'g' and chest 'c' is 300c = g.
What are equations?A mathematical statement that uses the word "equal to" between two expressions with the same value is called an equation. Like 3x + 5 = 15, for instance. Equations come in a wide variety of forms, including linear, quadratic, cubic, and others. Point-slope, standard, and slope-intercept equations are the three main types of linear equations.So, the equation representing the relation of 'g' and 'c':
We can observe that:
600/2 = 3001500/5 = 3004800/16 = 300So, we can conclude that:
g/c = 300300c = gTherefore, the equation that represents the relationship of gems 'g' and chest 'c' is 300c = g.
Know more about equations here:
https://brainly.com/question/28937794
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Use the graph to answer the question.Find the interval(s) over which the function is decreasing.A. (-infinity,-2)U(5,infinity)B. (-infinity,-2)U(-2,1)U(5,infinity)C.infinity,-2)U(-2,-1)U(-1,1)U(5,infinity )D. (1,5)
Answers
Okay, here we have this:
Considering the provided graph, and that a function is decreasing when as x increases, "y" decreases, we obtain the following:
The intervals over which the function is decreasing are:
(infinity,-2)U(-2,-1)U(-1,1)U(5,infinity )
Finally we obtain that the correct answer is the option C.
Identity the triangle congruence postulate (SSS,SAS,ASA,AAS, or HL) that proves the triangles are congruent. I will mark brainliest!!!
Answers
SSS, or Side Side Side
SAS, or Side Angle Side
ASA, or Angle Side Side
AAS, or Angle Angle Side
HL, or Hypotenuse Leg, for right triangles only
Side Side Side Postulate
A postulate is a statement taken to be true without proof. The SSS Postulate tells us,
If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.
Congruence of sides is shown with little hatch marks, like this: ∥. For two triangles, sides may be marked with one, two, and three hatch marks.
If △ACE has sides identical in measure to the three sides of △HUM, then the two triangles are congruent by SSS:
Side Angle Side Postulate
The SAS Postulate tells us,
If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
△HUG and △LAB each have one angle measuring exactly 63°. Corresponding sides g and b are congruent. Sides h and l are congruent.
A side, an included angle, and a side on △HUG and on △LAB are congruent. So, by SAS, the two triangles are congruent.
Angle Side Angle Postulate
This postulate says,
If two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
We have △MAC and △CHZ, with side m congruent to side c. ∠A is congruent to ∠H, while ∠C is congruent to ∠Z. By the ASA Postulate these two triangles are congruent.
Angle Angle Side Theorem
We are given two angles and the non-included side, the side opposite one of the angles. The Angle Angle Side Theorem says,
If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.
Here are congruent △POT and △LID, with two measured angles of 56° and 52°, and a non-included side of 13 centimeters:
[construct as described]
By the AAS Theorem, these two triangles are congruent.
HL Postulate
Exclusively for right triangles, the HL Postulate tells us,
Two right triangles that have a congruent hypotenuse and a corresponding congruent leg are congruent.
The hypotenuse of a right triangle is the longest side. The other two sides are legs. Either leg can be congruent between the two triangles.
Here are right triangles △COW and △PIG, with hypotenuses of sides w and i congruent. Legs o and g are also congruent:
[insert congruent right triangles left-facing △COW and right facing △PIG]
So, by the HL Postulate, these two triangles are congruent, even if they are facing in different directions.
Proof Using Congruence
Proving Congruent Triangles 5
Given: △MAG and △ICG
MC ≅ AI
AG ≅ GI
Prove: △MAG ≅ △ICG
Statement Reason
MC ≅ AI Given
AG ≅ GI
∠MGA ≅ ∠ IGC Vertical Angles are Congruent
△MAG ≅ △ICG Side Angle Side
If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
Solve the inequality
And how do I graph Graph the solution below:
Answers
Answer:
Step-by-step explanation:
to solve, divide both sides by -3/2 to isolate x
you'll get x>1.5
to graph, make a ray pointing right from 1.5 with an open dot