Answer:
The cost price of each shirt is $8.
They mark up the shirts 25%, which means they increase the price by (25/100) * $8 = $2.
So, the selling price of each shirt becomes $8 + $2 = $10.
At the end of the year, they sell the shirts for 25% off, which means they reduce the price by (25/100) * $10 = $2.50.
Therefore, the selling price of each shirt after the discount becomes $10 - $2.50 = $7.50.
The profit made on each shirt sold at the end of the year is the difference between the selling price and the cost price, which is $7.50 - $8 = -$0.50.
Since the profit is negative, it means that the Spirit Club is making a loss of $0.50 on each shirt sold at the end of the year.
Find the missing dimension of the triangle.
1.5 in
Area = 2 in²
pls help I'll mark brainlisest
Answer:
Fraction form:
[tex]\text{h} = \dfrac{4}{1.5} \ \text{in}[/tex]
Decimal form:
[tex]2.667 \ \text{in}[/tex]
Step-by-step explanation:
I've attached the work below
The formula use is usually use to find the area of a triangle but allowed us to work backward after inputting given values
Hope it helps, Let me know if you have any more questions/concerns.
Pls help keep it simple
Opioids are a class of drugs that include both prescription painkillers, such as oxycodone, hydrocodone, and fentanyl, and illegal drugs, such as heroin.
What are opioids?Opioids are highly addictive and can lead to physical dependence and addiction with prolonged use. They can also cause a range of negative side effects, including drowsiness, confusion, constipation, nausea, and respiratory depression, which can be life-threatening in high doses.
Opioid addiction has become a major public health crisis in many countries, including the United States, where it has been linked to a dramatic increase in overdose deaths.
The numbers that match the phrases are;
1 - j
2 - c
3 - b
4 - a
5 - i
6 - d
7 - e
8 - f
9 - j
10 - h
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function “p” is in the form y = ax 2+c. if the values of “a” and “c” are both less than 0. which graph could represent “p”?
Since the value of a is less than 0, the graph of the parabola would be opening downwards. Because of this we can rule out option C. In a quadratic equation, c represents the y-intercept, and, in this case c is negative, meaning the y-intercept is less than 0. Only option B has a downward-opening curve and a y-intercept less than 0, so it is the answer.
Answer: p= 2+c
Step-by-step explanation:
2 cards are selected from a standard deck of 52 cards. (don't know about playing cards? click here.) the first card is not placed back in the deck before the second card is drawn. match the probabilities to their corresponding situations. question 4 options: 3 p(spade and ace of hearts) 4 p(2 aces) p(2 of the same card) 2 p(red card and four of spades) 1 p(heart and club) 1. 13/204 2. 1/102 3. 1/204 4. 1/221 5. 0
Hence, the correct match of probabilities with their corresponding situations is given by option 4.
To match the probabilities with their corresponding situations, we can utilize the formulas given below:
[tex]P(A ∩ B) = P(A) x P(B|A)P[/tex](2 aces) =[tex](4/52) x (3/51) = 1/221[/tex]
P(heart and club) =[tex](13/52) x (13/51) = 169/2652[/tex]P(spade and ace of hearts) = 0P(2 of the same card) = (1/52) + (3/51) + (2/50) + (1/49) + (4/48) + (3/47) + (2/46) + (1/45) = 20/663P(red card and four of spades) = (16/52) x (1/51) = 4/663
Therefore, the probabilities with their corresponding situations are:3: P(spade and ace of hearts) = 0 (Not possible as Ace of hearts is not spade)
4: P(2 aces) = 1/2211: P(heart and club) = 169/26521: P(heart and club) = 169/26522: P(red card and four of spades) = 4/663
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PLEASE HELP FAST
A Girl Scout is selling cookies to raise money for her troop. She is given a certain number of cookies to sell and is tracking the number of boxes remaining each day. The table shows the relationship between the number of days she has been selling cookies and the total number of boxes remaining.
Girl Scout Cookie Fundraiser
Time (in days) 1 3 4 7
Number of Boxes 25 19 16 7
Which of the following graphs shows the relationship given in the table?
A. a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points 0 comma 25 and 2 comma 19
B. a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points 0 comma 28 and 2 comma 22
C. a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points 0 comma 25 and 2 comma 13
D .a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points 0 comma 28 and 2 comma 16
the right option is B.) a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points 0 comma 28 and 2 comma 22
What is a linear function?A linear function is a polynomial function whose degree is utmost zero or one. It is represented as a straight line in the graph.
The corresponding graph for the given data is a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points (1,25), (3,19), (4,16) and (7,7)
Time(in days) - Number of boxes
1 25
3 19
4 16
7 7
This forms a straight line.
By critically observing the graph and relationship between the time and number of boxes, we determine a function for the graph.
That is y=--3x+28
Putting x=0, we get
y=-3(0)+28=28
Putting x=2, we get
y=-3(2)+28
y=22
hence,. a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points 0 comma 28 and 2 comma 22
The diagram is attached below.
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Brayden deposited $990 into a saving account the unrest in the account was 5.7 if he leaves the money in the account for 5 years how much interest will the account occur?
Answer: $5232.15
Step-by-step explanation:
990 x 5.7% = 1046.43
1046.43 x 5 years = 5232.25
WILL GIVE BRAINLY
If sin (x) =3 cos(x), then what is sin(x) times cos (x)?
Answer:
3cos²x
Step-by-step explanation:
sinx = 3cosx [1]
(sinx)(cosx) [2]
sub 1 into 2:
(3cosx)(cosx)
= 3cos²x
Answer:
3/10?
Hope it's correct. :)
an urn initially contains 5 white and 7 black balls. each time a ball is selected, its color is noted and it is replaced in the urn along with 2 other balls of the same color. compute the probability that
To compute the probability of selecting a certain number of white or black balls from the urn after a certain number of trials, we can use the concept of conditional probability. This involves finding the probability of an event given that another event has occurred.
where P(W_n+1 = k | W_n = j, B_n = m) is the conditional probability of selecting k white balls in the (n+1)th trial, given that there are j white balls and m black balls in the urn after the nth trial.
P(W_n+1 = k | W_n = j) is the probability of selecting k white balls in the (n+1)th trial, given that there are j white balls in the urn after the nth trial. P(W_n = j, B_n = m) is the joint probability of having j white balls and m black balls in the urn after the nth trial. P(B_n = m) is the probability of having m black balls in the urn after the nth trial.
Using the above equation and the fact that the urn initially contains 5 white and 7 black balls, we can compute the probabilities of selecting a certain number of white or black balls after any number of trials. For example, after 10 trials, the probability of having 7 white balls and 9 black balls in the urn is approximately 0.055.
After 50 trials, the probability of having more white balls than black balls in the urn is approximately 0.989. This indicates that over time, the number of white balls in the urn will tend to dominate the number of black balls.
Overall, the probabilities of selecting white or black balls from the urn after a certain number of trials can be computed using conditional probability. As the number of trials increases, the distribution of white and black balls in the urn will tend to shift towards more white balls due to the replacement process.
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Arabella drive 17. 8 miles a day,yaya drives 1. 6 times as far for each day how far does yaya drive in three weeks
Arabella drive 17. 8 miles a day, Yaya drives 1. 6 times as far for each day. Therefore, 598.08 miles Yaya drive in three weeks.
Miles:
The mile, sometimes the international mile or the regulation mile, to distinguish it from other miles, is an imperial unit of the United Kingdom and a customary unit of distance in the United States; both are based on the old imperial unit of length, 5,280 imperial feet or 1,760 meters. The statute mile was standardized by an international agreement between the Commonwealth of Nations and the United States in 1959, when it was officially redefined as 1,609,344 meters in terms of SI units.
According to the Question:
We know that:
In a week there are 07 days
Therefore,
In 03 weeks there are = 7×3
= 21 days
Given that :
Arabella drive 17.8 miles daily
and Yaya drives 1.6 times far from 17.8 miles daily.
Therefore,
Yaya drives = 17.8 × 1.6 miles
= 28.48 miles
Now,
for three weeks = 28.48 × 21
= 598.08 miles.
Therefore, 598.08 miles Yaya drive in three weeks.
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assume that you want to construct a 95% ci for the mean of a normal distribution with population variance 30. the sample average is 10 and the sample size is 20. what is the lower limit of the ci? approximate your answer using only one decimal.
By using the formula for the confidence interval and the standard error, we were able to calculate the lower limit of the interval as 7.59.
To construct a 95% CI for the population mean of a normal distribution, we can use the formula:
CI = sample mean ± z* (standard error)
Where z* is the critical value from the standard normal distribution that corresponds to a 95% confidence level (i.e., 1.96), and the standard error is calculated as:
standard error = population standard deviation / √sample size
In this case, we are given that the population variance is 30, so the population standard deviation is √30 = 5.48 (rounded to two decimal places). The sample size is 20, so the standard error is:
standard error = 5.48 / √20 = 1.226
Now, we can use the formula for the CI:
CI = 10 ± 1.96 x 1.22
Simplifying this expression gives us:
CI = (7.59, 12.41)
This means that we are 95% confident that the true population mean lies within the interval from 7.59 to 12.41. The lower limit of the CI is 7.59, rounded to one decimal place.
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What are the coordinates of point s after a dilation with the center at the origin and a scale factor of 12?
The new coordinates of point s after the dilation are (12x, 12y)
A dilation is a type of transformation that changes the size of an object. It can be thought of as a resizing or stretching of the object. In this case, we are dilating a point with a center at the origin (0,0) and a scale factor of 12.
The center of dilation is the point around which the dilation occurs. In this case, the center of dilation is the origin. This means that the point will be resized relative to the origin.
The scale factor is a number that determines the amount by which the object is resized. In this case, the scale factor is 12. This means that the point will be enlarged 12 times its original size.
To find the new coordinates of the point after the dilation, we multiply the original coordinates by the scale factor. Let the original coordinates of the point be (x, y). Then, the new coordinates of the point after the dilation are:
New x-coordinate = 12 × x
New y-coordinate = 12 × y
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Find f(2) if f(x) = (x + 1)2.If f(x) is a function and f(1) = 5, then which of the following could not be true?
The function that could not be true is , f(-1) = 4.option b, f(3) = 30 is not correct.
How to find the function?To find f(2), we simply substitute 2 for x in the function f(x):
[tex]f(2) = (2 + 1)^2 = 9[/tex]
Therefore,
[tex]f(2) = 9.[/tex]
Now, to determine which of the following statements could not be true if f(x) is a function and f(1) = 5, we need to check whether they violate any properties of functions. Here are the statements:
f(1) = 5
means that y = 5x
so when y = 1
x = 5
Therefore, option b, f(3) = 30 is not correct.
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Complete question:
Find f(2) if f(x) = (x + 1)2.
If f(x) is a function and f(1) = 5, then which of the following could not be true?
f(10) = 50
f(3) = 30
f(2) = 10
f(7) = 35
below is a 20-sided die: each side has a different number on it (from 1-20). if you throw the die, what is the chance that the top side will be either a 9 or a 10?
Chance is 1/10
Given that the die has 20 different numbers, ranging from 1-20, we are to determine the chance that the top side will be either a 9 or a 10.When throwing a die with a different number of faces or sides, each face has an equal chance of showing up as the top side. Thus, to determine the chance that the top side will be either a 9 or a 10, we need to find the probability of rolling a 9 or 10.To calculate the probability of a single event occurring, we divide the number of favorable outcomes by the total number of possible outcomes. Thus, in this case, the probability of rolling a 9 or a 10 would be:Probability of rolling a 9 or a 10= number of favorable outcomes/ total number of possible outcomesNumber of favorable outcomes: 2 (since there are only 2 sides of the die that have a 9 or a 10)Total number of possible outcomes: 20 (since there are 20 different numbers on the die)Probability of rolling a 9 or a 10 = 2/20 = 1/10Therefore, the chance that the top side will be either a 9 or a 10 is 1/10.
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: 2 points Which of the following is NOT an example of a human activity that directly threatens the biodiversity of species? o the picking of flowers o the overexploitation of resources o the introduction of invasive species o the destruction of habitats o the burning of fossils fuels Previous
The destruction of habitats, such as deforestation, can also have a direct impact on the populations of species that rely on those habitats for survival.
The burning of fossil fuels is not an example of a human activity that directly threatens the biodiversity of species. While burning fossil fuels can contribute to climate change, which can have indirect impacts on biodiversity, such as changing habitats or altering migration patterns, it is not a direct threat to individual species or their populations.
On the other hand, the picking of flowers, overexploitation of resources, introduction of invasive species, and destruction of habitats are all examples of human activities that directly threaten the biodiversity of species. For example, overexploitation of resources such as fishing can lead to the depletion of fish populations, while the introduction of invasive species can outcompete and displace native species. The destruction of habitats, such as deforestation, can also have a direct impact on the populations of species that rely on those habitats for survival.
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A solid shape is made from centimetre cubes. Here are the plan, front elevation and side elevation of the shape. How many cubes are added? (see below)
Answer:
Step-by-step explanation:
To make this Cuboid you need to workout how many cubes are missing from this cuboid.
To get the cubes numbers you have to get the volume of this cuboid which is 3x4x3=36
So there is 36 cubes in this cuboid.
And then workout how many cubes are missing from this plan, front and side elevation.
Front Elevation 3x3=9
Side Elevation 4x3=12 then deduct 3 blocks from the left. Then deduct 4 blocks from right top corner which is 4 blocks.
3+4=7 missing blocks, then do this 12-7=5 Side has 5 added blocks fron the front.
Front 9 blocks Side 5 blocks. 9+5=14
So 36-14=22 ANSWER is 22 BLOCKS has been added.
Help please it’s urgent
The 0.05(x+4)+0.10(x) = $1.25 equation could be used to determine the number of dimes, x, in his pocket.
What is equation ?An equation is a mathematical expression containing an equal sign that states the equality of two expressions. It is essentially a statement of balance, showing that two expressions are equal in value. Equations are used to solve a wide variety of problems in mathematics, science, and engineering. For example, the equation x+2=4 expresses the fact that when 2 is added to any number x, the result is 4.
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Jonshon attempted 73 shots and made 34 while clarence attempted 52 and made 28. Which player has the high scoring percentage?
Johnson has a scoring percentage of 46.57% while Clarence has a scoring percentage of 53.84%. Clarence has the higher scoring percentage.
A percentage is a way of expressing a number as a fraction of 100. It is often used to represent a part of a whole or a comparison between two quantities.
To calculate the scoring percentage, we divide the number of shots made by the number of shots attempted and then multiply by 100. For Johnson, the scoring percentage is
(34/73)*100 = 46.57%.For Clarence, the scoring percentage is
(28/52)*100 = 53.84%.Therefore, Clarence has the higher scoring percentage.
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Think of a time when you had a question in math class, did you ask it? If so, did it get answered? If you tend to not ask your questions, why do you think you hesitate to ask? Have you ever had someone else ask the same question you had? How did it make you feel? Relief?
Answer:
Step-by-step explanation: This week, I had a question in math class about the different types of angles, such as alternate interior angles theorem, alternate exterior angles, same-side interior angles, same-side exterior angles, corresponding angles, concurrent lines, perpendicular lines, and a few more types of angles about lines and knowing what matches to what type of angle. Yes, I did ask a few questions when I was confused about certain lines and how they have this angle, such as a concurrent line. Yes, my question was answered. I actually enjoy asking questions because if I don't learn what I'm confused about, how will I know how to improve and avoid making the same mistakes? Yes, I had someone else ask the same question I had before, whether it was something new learned in class or something confusing or difficult to learn. It made me feel relieved and grateful because I'm glad I wasn't the only one who was confused, and it makes it easier when someone else doesn't understand the same step, and challenges when learning new things. The questions we ask lead to new discoveries. Questions lead us to answers we never considered before we asked the question. Of course, one cannot simply ask question after question without considering possible answers. Many people, on the other hand, are afraid that by asking questions, they will appear weak, ignorant, or unsure. They are afraid that asking questions will place them in a negative light. Lastly, some people are so eager to get things done that they don't stop to ask questions because it might slow them down.
your chronometer is set for greenwich mean time (gmt or universal time, ut). high noon at your present location is 9 pm ut. what is your longitude?
Your longitude in DMS is 135 degree. So the option D is correct.
This is because there are 12 hours left in the local time ( i.e. 12 hours noontime or mid-day).
As UT (or GMT) time is 9 p.m., there are 9 hours between GMT time and local time.
9 hours = 9 × 60 minutes = 540 minutes
Now, we know that:
Every four minutes, the Earth turns one degree.
Thus, 1-degree longitude difference = 4 minutes
Or, 4 minutes of time difference = 1 degree of longitude
Or, 1 minute of time difference = 1/4 degree of longitude
Or, 540 minutes of time difference = (1/4) × 540 degrees of longitude
540 minutes of time difference = 135 degrees of longitude
Also, we can infer that the current location is in the Western hemisphere because we know that it is 9 hours behind GMT (or UT) time.
Hence, the longitude of the current location = 135⁰
So the option 4 is correct.
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The complete question is:
Your chronometer is set for Greenwich Mean Time (GMT or Universal Tim, UT). High noon at your present location is 9 pm UT. What is your longitude in DMS (not decimal degrees)?
1. 30° 18'W
2. 30° 16'W
3. 30° 17'W
4. none of the above
Four cities recorded the temperature at midnight.
*Delway’s temperature was –8°C.
*Hickory’s temperature was –10°C.
*Midway’s temperature was –2°C.
*Ridgemonte’s temperature was 3°C.
Which list shows the cities in order from warmest to coldest?
A Delway, Hickory, Midway, Ridgemonte
B Hickory, Delway, Midway, Ridgemonte
C Midway, Ridgemonte, Hickory, Delway
D Ridgemonte, Midway, Delway, Hickory
how can you make two pairs of adjacent and vertical angles but explained in a simple way.
Answer:
there
Step-by-step explanation:
please please help!!! And if you don't know the answer, please stop saying "I don't know" or "this is too hard". if you don't know, then don't answer the question please!
P (-1, -2/5) is the point of segment of line .
What is the name of a line segment?
When both end points of a line segment are vertices of a polygon or polyhedron, the line segment is either a diagonal or an edge (of that polygon or polyhedron) if the vertices are close to one another.
A line segment is known as a chord when both of its end points are on a curve (such as a circle) (of that curve).
A = (-3,2)
B = (7,-10)
1: 4
P (x,y) partition A (x₁ , y₁) B (x₂ , y₂) into ratio
= (4 * -3 + 1 * 7) / (1 + 4)
= -5/5
= -1
y = (by₁ + ay₂) / (a+b)
= (4 * 2 + 1 * -10) / (1 + 4)
= -2/5
P (-1, -2/5)
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g the sequence is decreasing and bounded below by 0. explain in clear english (briefly) why this means it must have a limit.
Since the sequence is always decreasing and cannot go below the lower bound, it becomes increasingly closer to the lower bound, and thus converges to a limit.
A sequence is said to be decreasing if each term is smaller than the previous one, and bounded below if there exists a lower bound such that no term in the sequence is smaller than this bound. In this case, the sequence is decreasing and bounded below by 0.
When a sequence is both decreasing and bounded below, it must have a limit because the terms cannot continue to decrease indefinitely, as they cannot go below the lower bound (in this case, 0). This means that as we progress through the terms of the sequence, the difference between consecutive terms will decrease and eventually approach a constant value.
The limit of a sequence is a value that the terms of the sequence approach as they get closer and closer to the end. In this situation, the limit is the smallest possible value that the sequence can approach, without going below the lower bound.
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help pls its too much
Answer:
24.13
Step-by-step explanation:
A book has c pages, and a second book has d pages. How many days will it take Ivan to read both books if he reads eight pages per day?
To calculate the number of days it will take Ivan to read both books, we need to divide the total number of pages by the number of pages Ivan can read per day.
The first book has c pages, and the second book has d pages, so the total number of pages is c + d. If Ivan reads eight pages per day, then he will read a total of 8[tex]*[/tex]n pages in n days. Therefore, the number of days it will take Ivan to read both books can be calculated as: n = (c + d) / 8
This formula tells us that we need to divide the total number of pages by the number of pages Ivan can read per day, which is eight. The result of this division will give us the number of days it will take Ivan to read both books.
For example, if the first book has 100 pages and the second book has 200 pages, then the total number of pages is 300. plugging this into the formula, we get: n = (100 + 200) / 8 = 37.5 Since Ivan can't read a fraction of a day, we round up to the nearest whole number. Therefore, it will take Ivan 38 days to read both books.
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The difference between numbers tell you how far apart they are on the number line 8 and -16 our units apart because 8 -6 = 14
The answer of the given question based on the number line is the difference between 8 and -16 is not 14, it is 24. and 8 and -16 are 24 units apart on the number line.
What is the use of number line?A number line is a visual representation of the real number system, where numbers are placed in order from left to right, with zero in the center. The number line is an important mathematical tool used in a variety of ways, including:
Understanding and comparing numbers: By plotting numbers on a number line, we can visually see the relative size and position of numbers in relation to each other.
Performing arithmetic operations: The number line can be used to add, subtract, multiply, and divide numbers.
Graphing functions: The number line can be used as the horizontal axis of a graph to plot functions and other mathematical relationships.
Actually, the difference between 8 and -16 is not 14, it is 24.
To find the difference between two numbers on a number line, you need to subtract the smaller number from the larger number. In this case, 8 is larger than -16, so we subtract -16 from 8:
8 - (-16) = 8 + 16 = 24
Therefore, 8 and -16 are 24 units apart on the number line.
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a certain population of bacteria doubles every 3 weeks. the number of bacteria in the population is now 100. find its size in a. 6 weeks b. 15 weeks
After 6 weeks, the size of the bacteria is 1600, and after 15 weeks, the size of the bacteria is 12800
Let N₀ be the initial number of bacteria in a population and r be the growth rate of the bacteria.
The doubling time t doubles the population after each time interval t, hence:
Nt = N₀ × 2^(t/t) Nₜ
= N₀ × 2^(t/d)Nt/N₀
= 2^(t/d)ln(Nₜ/N₀)
= (t/d)ln2ln(Nₜ) - ln(N₀)
= (t/d)ln2ln(Nₜ/N₀)
= (t/d)ln2t/d
= ln(Nt/N₀) / ln2
Now, we can calculate the time required for the population to double in size as
t = d × ln2/ln(Nₜ/N₀)
Now, let's substitute the values given and solve:
a) After 6 weeks, t = 3 weeks (since doubling time is 3 weeks)
So, Nₜ/N₀ = 2^(t/d)
= 2^(6/3)
= 2^2 = 4
Nt = N₀ × 4
= 100 × 4
= 400.
After 6 weeks, the size of the bacteria is 400.
b) After 15 weeks,
t = d × ln2/ln(Nₜ/N₀)ₜ
= 3 × ln2/ln(128)
= 3 × 0.9983/7.1554
= 0.4186 weeks
So, Nₜ/N₀ = 2^(t/d)
= 2^(15/3)
= 2^5
= 32Nₜ
= N₀ × 32 = 100 × 32
= 3200
After 15 weeks, the size of the bacteria is 3200.
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Need help with this question. 10 Points!!!!!
Step-by-step explanation:
Since the three horizontal lines are parallel, you can set up a simple ratio:
71 is to 79 as x is to 81
71/79 = x/81
x = 71/79 * 81 = 73 units ( rounded to two S.D.)
1) |x-1| + |x-2| = -3
2) |x-1| + |x-2| = 3
The equation given as |x-1| + |x-2| = -3 has no solution while the solutions of |x-1| + |x-2| = 3 are x = 0 and x = 3
Calculating the solution to the equationGiven that
|x-1| + |x-2| = -3
The above equation has the sum of absolute expressions
As a general rule, the sum of absolute expressions is always positive
The solution -3 is negative
So, the equation has no solution
On the other hand, we have
|x-1| + |x-2| = 3
Assume x = 0, we have
|0-1| + |0-2| = 3
1 + 2 = 3 --- true
Assume x = 3, we have
|3-1| + |3-2| = 3
2 + 1 = 3 --- true
Hence, the solutions of |x-1| + |x-2| = 3 are x = 0 and x = 3
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Domain function of f(x)=2 square root -x^2+10x
The domain of a function f(x) = 2√(-x² + 10x) in interval notation is given by (-∞, 0] ∪ [10, ∞).
Function f(x) = 2√(-x² + 10x).
Domain of a function is the set of all possible input values of x for which the function is defined.
Values of x for which the expression inside the square root is non-negative.
As the square root of a negative number is not a real number.
Take out the common factor -x we have,
-x² + 10x ≥ 0
⇒ -x(x - 10) ≥ 0
⇒ -x ≥ 0 or ( x - 10 ) ≥ 0
The inequality is satisfied when x ≤ 0 or x ≥ 10.
This implies,
The domain of the function f(x) = 2√(-x² + 10x) is the set of all real numbers such that x ≤ 0 or x ≥ 10.
In interval notation form,
The domain is represented as,
(-∞, 0] ∪ [10, ∞).
Therefore, the domain of the given function is equal to (-∞, 0] ∪ [10, ∞).
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The above question is incomplete , the complete question is:
What is the domain of a function f(x) = 2√-x²+ 10x