The function representing the number of bacteria after t hours is N(t) = 5300 * (1 + 0.0592)^t, and the growth rate per hour is approximately 5.92%.
To represent the number of bacteria after t hours, we can use the exponential growth formula:
N(t) = N₀ * (1 + r)^t,
where N(t) is the number of bacteria after t hours, N₀ is the initial number of bacteria, r is the hourly growth rate, and t is the time in hours.
In this case, the initial number of bacteria is 5300, and the hourly growth rate can be determined from the doubling time of 12 hours. The growth rate can be calculated using the formula:
r = 2^(1/t_double) - 1,
where t_double is the doubling time in hours.
Substituting the given values, we have:
r = 2^(1/12) - 1 ≈ 0.0592.
Now we can write the function for the number of bacteria after t hours:
N(t) = 5300 * (1 + 0.0592)^t.
To determine the percentage of growth per hour, we can calculate the relative growth rate as a percentage:
percentage_growth = r * 100 ≈ 5.92%.
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a new social media sit is increasing its user base by approximately 4% per month. If the site currently has 35.930 users, what will the approximate user base be 10 months from now?
Answer:
The approximate user base of the social media site 10 months from now would be approximately 52,374.
Step-by-step explanation:
To calculate the approximate user base of the social media site 10 months from now, considering a 4% increase per month, we can use the following steps:
1. Calculate the monthly growth factor: 1 + (4% / 100) = 1 + 0.04 = 1.04
2. Apply the growth factor to the current user base for each month:
Month 1: 35,930 * 1.04 = 37,387.2 (approx.)
Month 2: 37,387.2 * 1.04 = 38,868.49 (approx.)
...
Month 10: Previous Month * 1.04
By repeating this calculation for each month, we can determine the approximate user base 10 months from now.
Month 1: 37,387.2
Month 2: 38,868.49
Month 3: 40,391.33
Month 4: 41,957.61
Month 5: 43,569.34
Month 6: 45,228.24
Month 7: 46,936.32
Month 8: 48,695.44
Month 9: 50,507.45
Month 10: 52,374.40 (approx.)
Therefore, the approximate user base of the social media site 10 months from now would be approximately 52,374.
Find the number that belongs
in the green box.
[?]
37°
64°
21.1
30
Round your answer to the nearest tenth.
The number that belongs in the green box is 32.8
How to find the number that belongs in the green boxFrom the question, we have the following parameters that can be used in our computation:
The triangle
The third angle in the triangle is calculated as
Third angle = 180 - 37 - 64
Evaluate
Third angle = 79
If the number that belongs in the green box is x, then we have
x/sin(79) = 30/sin(64)
This gives
x = sin(79) * 30/sin(64)
Evaluate
x = 32.8
Hence, the number that belongs in the green box is 32.8
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Type the correct answer in the box.
Fill in the missing term in the equation.
(1 + 2)(2+1) + blank
= 5(2+i)
11. Which one of the following is unique? b. mode a. Mean c. Median d. A and B
Among the mean, mode, and median, the unique one is the b. mode.
What is the mode?The mode is the data value that occurs many times more than other data values.
Unlike the mean that shows the average value of all the data values, the mode occurs more. While we compute the mean by dividing the total data value by the number of data items, the mode is not computed but found as the most frequent data value.
Similarly, the median can be computed when two values occur as the middle values.
Thus, among the three measures of central tendency, the mean, the median, and the mode, the mode is the most unique since it is not computed.
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Darren says that more students hands are 4 2/4 inches longer than 4 and 5 1/4 inches combined. is he right?Explain you're answer
In a case whereby Darren says that more students hands are 4 2/4 inches longer than 4 and 5 1/4 inches combined, he is wrong
What is the justification?
[tex]4\frac{2}{4}[/tex] that was given in the question can be seen as mixed fraction, we can expressed this as improper fraction so that it will be easier to handle.
[tex]4\frac{2}{4} = \frac{16+4}{2}[/tex]
=[tex]\frac{18}{4}[/tex]
Then [tex]4 + 5\frac{1}{4} = \frac{16}{4} +\frac{20+1}{4} \\\\=\frac{37}{4}[/tex]
Then after expressing the given fractions as improper fraction we can now compare them so that e will know may be Darren is right or wrong, then here we can see that [tex]\frac{18}{4}[/tex] is less than [tex]\frac{37}{4}[/tex] Hence, Darren is wrong.
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Stephen is combining all juice shown to make fruit punch. Does the expression (64+28+76)/6 make sense’s
Yes, the expression (64+28+76)/6 makes sense as it represents the average quantity of juice per unit when combining all the shown juices.
To determine whether the expression (64+28+76)/6 makes sense, we need to evaluate the components of the expression and consider whether the mathematical operations are valid.
The expression (64+28+76)/6 represents the sum of three numbers (64, 28, and 76), divided by 6. Let's break it down step by step:
Addition: We have three numbers being added together: 64, 28, and 76. The sum of these numbers is 168 (64 + 28 + 76 = 168).
Division: The sum of the three numbers, 168, is then divided by 6. Division is a valid mathematical operation.
Now, let's analyze whether the expression makes sense in the context of Stephen combining all the juice to make fruit punch. The numbers 64, 28, and 76 may represent quantities of juice (in some units) that Stephen is combining. However, without further information or context, we cannot determine if the expression accurately represents the combination of these juices.
If the numbers 64, 28, and 76 represent quantities of juice in the same units (such as milliliters or liters), then the expression (64+28+76)/6 would represent the average quantity of juice per unit. The result, 168/6, would be 28. This would imply that each unit (e.g., glass or serving) of the fruit punch contains an average of 28 units of juice.
In summary, mathematically, the expression (64+28+76)/6 is valid. However, without additional context regarding the units or quantities being represented, it is not possible to determine whether the expression accurately describes the process of combining the juices to make fruit punch.
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HELLLLPPPPP!!!!!!!!!!!! AHHHHHHHHHHH!!!!!!!
kenji is raising baby kittens. their weights after three weeks are 12 ounces, 14 ounces, 15 ounces, 15, ounces and 14 ounces, what is the mean weight of the kittens????
Answer: 14 ounces
Step-by-step explanation:
To find the mean, we add up all the values and divide by the number of values.
[tex]\displaystyle \frac{12+14+15+15+14}{5} =\frac{70}{5} =14\;ounces[/tex]
Factorize
8(p-q)^3-(p+q)^3
The factorization of[tex]8(p-q)^3-(p+q)^3 is 8(p-q)^3 - (p+q)^3 is [p - 3q][7p^2 - 8pq + 3q^2].[/tex]
The given expression is[tex]8(p-q)^{3}-(p-q)^{3}[/tex]
To factorize this expression, we can use the identity for the difference of cubes, which states that [tex]a^3 - b^3 = (a - b)(a^2 + ab + b^2).[/tex]
Let's apply this identity to the given expression:
[tex]8(p-q)^3 - (p+q)^3 = [2(p-q)]^3 - (p+q)^3.[/tex]
Now we can see that we have a difference of cubes:[tex](2(p-q))^3 - (p+q)^3.[/tex]
Using the identity, we can factorize this expression as follows:
[tex][(2(p-q)) - (p+q)][(2(p-q))^2 + (2(p-q))(p+q) + (p+q)^2].[/tex]
Simplifying further:
[tex][2p - 2q - p - q][(2(p-q))^2 + (2(p-q))(p+q) + (p+q)^2].[/tex]
Combining like terms:
[tex][p - 3q][(2(p-q))^2 + 2(p-q)(p+q) + (p+q)^2].[/tex]
Expanding the squared term:
[tex][p - 3q][4(p^2 - 2pq + q^2) + 2(p^2 - q^2) + (p^2 + 2pq + q^2)].[/tex]
Simplifying:
[tex][p - 3q][4p^2 - 8pq + 4q^2 + 2p^2 - 2q^2 + p^2 + 2pq + q^2].[/tex]
Combining like terms again:
[tex][p - 3q][7p^2 - 8pq + 3q^2].[/tex]
Therefore, the factorization of [tex]8(p-q)^3 - (p+q)^3 is [p - 3q][7p^2 - 8pq + 3q^2].[/tex]
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If 15% of the customers total is $98,880, then the sum total equals what
The sum total by the given data is equals to $658,880.
We are given that;
Percent=15%
Amount= $98,880
Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
To divide by a percentage, we can convert it to a decimal by moving the decimal point two places to the left. This gives us:
15% = 0.15
To divide by 0.15, we can multiply by its reciprocal, which is 1/0.15. This gives us:
$98,880 / 0.15 = $98,880 x 1/0.15
To multiply by 100, we can move the decimal point two places to the right. This gives us:
$98,880 x 1/0.15 x 100 = $658,880
Therefore, by the percentage the answer will be $658,880.
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What’s the answer please
Answer:
40
Step-by-step explanation:
plugging in a and b will get us:
[tex]2^{2} + 6^{2} = c^{2}[/tex]
4 + 36 = [tex]c^{2}[/tex]
40 = [tex]c^{2}[/tex]
c= [tex]\sqrt{40\\[/tex]
Simplify the rational expression
7x/14x^6
The simplified form of the rational expression is 1/(2[tex]x^5[/tex]).
To simplify the rational expression (7x)/(14[tex]x^6[/tex]), we can reduce the numerator and denominator by their greatest common factor.
In this case, the greatest common factor is 7x.
Dividing both the numerator and denominator by 7x, we get:
(7x)/(14[tex]x^6[/tex]) = (7x)/(7x × 2[tex]x^5[/tex])
Canceling out the common factor of 7x, we have:
= 1/(2[tex]x^5[/tex])
Therefore, the simplified form of the rational expression is 1/(2[tex]x^5[/tex]).
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Help pls i don't understand
ΔFSH ≅ ΔFSI by the rule of angle-angle-side theorem, or AAS.
What is Angle- Angle - Side theorem?The angle-angle-side theorem, or AAS, tells us that if two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another triangle, then the triangles are congruent.
If we consider triangle FSH and triangle FSI, we will observe the following;
angle HFS = angle IFSangle FSH = angle FSIlength HS = length SISo based on the angle-angle-side theorem, or AAS, we can see that triangle FSH is congruent to triangle FSI.
Thus, our answer will be; ΔFSH ≅ ΔFSI by the rule of angle-angle-side theorem, or AAS.
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Find the number that belongs
in the green box.
37⁰
64°
[?]
30
Round your answer to the nearest tenth.
Answer:
? ≈ 20.1
Step-by-step explanation:
using the Sine rule in the triangle
[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex]
with a = ? , b = 30 , ∠ A = 37° , ∠ B = 64° , then
[tex]\frac{?}{sin37}[/tex] = [tex]\frac{30}{sin64}[/tex] ( cross- multiply )
? × sin64° = 30 × sin37° ( divide both sides by sin64° )
? = [tex]\frac{30sin37}{sin64}[/tex] ≈ 20.1 ( to the nearest tenth )
Which data set could be represented by
the box plot shown below?
H
0 2 4 6 8
Choose 1 answer:
A
Creating box plots
B
C
D
10 12 14 16 18 20
3, 4, 8, 9, 9, 12, 12, 13, 13, 16, 18
3, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18
3, 4, 8, 9, 9, 10, 12, 13, 13, 16, 18
2, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18
The given box plot represented by the data sets in option A and B.
From the given box plot, we have
Minimum value = 3
Maximum value = 18
First quartile (Q1) = 7
Third quartile (Q3) = 13
Median = 10
Option A:
3, 4, 8, 9, 9, 12, 12, 13, 13, 16, 18
Median = 12
First quartile (Q1) = 8
Third quartile (Q3) = 13
Option B:
3, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18
Median = 10
First quartile (Q1) = 7
Third quartile (Q3) = 13
Option C:
3, 4, 8, 9, 9, 10, 12, 13, 13, 16, 18
Median = 10
First quartile (Q1) = 8
Third quartile (Q3) = 13
Option D:
2, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18
Median = 10
First quartile (Q1) = 7
Third quartile (Q3) = 13
Therefore, the correct options are B and D.
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Absolute value of 2.
Solve the following equations. Check the solutions. 8x^2 + 11 = 191 + 3x^2, 7x^2 - 15 = 49 + 3x^2, 14x^2 - 157 = 333 + 4x^2
The solutions to the equations are:
x = 6, x = 4, x = 7.
1. 8x² + 11 = 191 + 3x²
Rearranging the equation:
8x² - 3x² = 191 - 11
5x² = 180
Dividing both sides by 5:
x² = 36
Taking the square root of both sides:
x = ±6
Checking the solution:
8(6)² + 11 = 191 + 3(6)²
288 + 11 = 191 + 108
299 = 299
The solution x = 6 satisfies the equation.
2. 7x² - 15 = 49 + 3x²
Rearranging the equation:
7x² - 3x² = 49 + 15
4x = 64
Dividing both sides by 4:
x² = 16
Taking the square root of both sides:
x = ±4
Checking the solution:
7(4)² - 15 = 49 + 3(4)²
112 - 15 = 49 + 48
97 = 97
The solution x = 4 satisfies the equation.
3. 14x² - 157 = 333 + 4x²
Rearranging the equation:
14x² - 4x^2 = 333 + 157
10x² = 490
Dividing both sides by 10:
x² = 49
Taking the square root of both sides:
x = ±7
Checking the solution:
14(7)² - 157 = 333 + 4(7)²
686 - 157 = 333 + 196
529 = 529
The solution x = 7 satisfies the equation.
Therefore, the solutions to the equations are:
x = 6, x = 4, x = 7.
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factor completely using distributive law 25y-15z
Answer:
5(5y - 3z)
Step-by-step explanation:
25y - 15z ← factor out common factor of 5 from each term
= 5(5y - 3z)
The population of a small country is 2.457 million and its national debt is $5.99 billion. What is the amount of debt per person? Round to the nearest whole number.
The amount of debt per person in the small country is approximately $2,439. This means that, on average, each person in the country would be responsible for around $2,439 of the national debt.
To calculate the amount of debt per person in the small country, we divide the total national debt by the population and round the result to the nearest whole number. Let's perform the calculation.
The population of the small country is 2.457 million, which is equivalent to 2,457,000 people. The national debt is $5.99 billion.
To find the debt per person, we divide the national debt by the population:
$5.99 billion / 2,457,000 = $2,439.05 (rounded to two decimal places)
Since we want the answer in whole numbers, we round the result to the nearest whole number:
Debt per person = $2,439 (rounded to the nearest whole number)
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For the athletic banquet one adult ticket cost $15.00 and one student ticket cost $10.00. One hundred forty tickets were sold for a total of $1600. How many students tickets were sold
Answer:160 students
Step-by-step explanation:
did I do it
(your answer needs to be more than 20 characters long)
Twenty-five students were asked to rate—on a scale of 0 to 10—how important it is to reduce pollution. A rating of 0 means “not at all important” and a rating of 10 means “very important.” Here is a dot plot of their responses.
in the dot plot given, A rating of 6 is not a good description of the center of this data set because it does not accurately represent the most common or typical response.
How is this so?
To determine the center of data set, we typically look for the measure of central tendency, such as the mean, median, or mode.
From the dot plot, we can observe that the mode is at the rating of 10, with six students giving this highest rating. In contrast, the rating of 6 has only two students, making it less representative of the center.
Therefore, a rating of 6 does not accurately capture the overall sentiment or the central tendency of the data set.
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Full Question:
Please see the attached.
A segment with endpoints A (3, 4) and C (5, 11) is partitioned by a point B such that AB and BC form a 2:3 ratio. Find B.
The point B that partitions the segment AC into a 2:3 ratio is B (4.6, 9.6). To find the point B that partitions the segment AC into a 2:3 ratio, we can use the concept of section formulas or the concept of ratios of the coordinates.
Let's assume the coordinates of point B are (x, y). We can calculate the coordinates of point B using the following steps:
Step 1: Calculate the differences in the x and y coordinates between points A and C:
Δx = x-coordinate of C - x-coordinate of A = 5 - 3 = 2
Δy = y-coordinate of C - y-coordinate of A = 11 - 4 = 7
Step 2: Divide the differences by the sum of the ratios (2 + 3 = 5) to get the ratios of the segments AB and BC:
Ratio_AB = (2/5)[tex]\times[/tex] Δx = (2/5) [tex]\times[/tex]2 = 4/5
Ratio_BC = (3/5) [tex]\times[/tex] Δx = (3/5) [tex]\times[/tex] 2 = 6/5
Step 3: Apply the ratios to the coordinates of point A to find the coordinates of point B:
x-coordinate of B = x-coordinate of A + Ratio_AB [tex]\times[/tex] Δx = 3 + (4/5)[tex]\times[/tex]2 = 3 + 8/5 = 23/5
y-coordinate of B = y-coordinate of A + Ratio_AB [tex]\times[/tex]Δy = 4 + (4/5) [tex]\times[/tex] 7 = 4 + 28/5 = 48/5
Therefore, the coordinates of point B are (23/5, 48/5).
In decimal form, the coordinates of point B are approximately (4.6, 9.6).
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1. What is the solution of 2x+7|>27? Answer x < -17 orx> 10 x < -10 or x>10 x20 x>-17 or x < 10
The solution to the inequality 2x + 7 > 27 is x > 10
How to determine the solution to the inequalityFrom the question, we have the following parameters that can be used in our computation:
2x + 7 > 27
Subtract 7 from both sides of the inequality
So, we have
2x > 20
Divide both sides by 2
x > 10
Hence, the solution to the inequality 2x + 7 > 27 is x > 10
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The roof gable on Charlene's house has two
equal sides. One angle measures 110.4°. The
other two angles are equal to each other.
Estimate the measure of each of the other
two angles.
Each of the other two angles in the roof gable measures approximately 34.8°.
How to calculate the valueIf the roof gable on Charlene's house has two equal sides, and one angle measures 110.4°, we can determine the measure of each of the other two angles by using the fact that the sum of the angles in a triangle is always 180°.
Let's denote the measure of the other two angles as x.
Since the two equal sides of the gable form an isosceles triangle, the two angles opposite those sides are equal.
Therefore, we have:
x + x + 110.4° = 180°
Combining like terms:
2x + 110.4° = 180°
Now, let's solve for x:
2x = 180° - 110.4°
2x = 69.6°
x = 69.6° / 2
x = 34.8°
Therefore, each of the other two angles in the roof gable measures approximately 34.8°.
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Calculate the unshaded portion of the figure
Answer:
Approx 8.47 [tex]m^2[/tex]
Step-by-step explanation:
First, find the area of the entire figure. Which can be found by multiplying the two sides of the square by each other= [tex]6*6=36m^2[/tex]
Now, ignore the square and just focus on the pentagon and finding the area of that. The formula for the area of a pentagon is [tex]A=1/2Apothem*Perimeter[/tex]
In order to find the apothem, you can make a mini triangle and use trig (Tangent) to find the height (apothem) of the triangle. Then, you take the side length of the base of the pentagon which is 4 and then you multiply it by the number of sides (5) to get 20. Then, by plugging it into our formula, you use the apothem*10 (divided by 2) and you get the area, and then you just subtract that from 36.
a tip of $10 is typically suitable for which kind of service?
a mover delivering furniture
a valet who parks your car
a waiter at a fast food restaurant
5. If a triangular figure is in the shape of an
isosceles right triangle, what is the measure
of each base angle?
Answer: each base angle in an isosceles right triangle measures 45 degrees.
Step-by-step explanation:
In an isosceles right triangle, two sides have equal lengths, and one angle is a right angle (90 degrees).
Since it is an isosceles triangle, the two base angles (the angles opposite the equal sides) must be congruent, meaning they have the same measure.
To find the measure of each base angle, we can use the fact that the sum of the angles in a triangle is 180 degrees.
Let's denote the measure of each base angle as "x". Then, the sum of the three angles in the triangle can be expressed as:
x + x + 90 = 180
Simplifying the equation:
2x + 90 = 180
Subtracting 90 from both sides:
2x = 90
Dividing both sides by 2:
x = 45
Susan bought a 1 kilogram bag of grapes. On the way home, she ate 125 grams of the grapes. How many grams of grapes does Susan have left? use math language and symbols to explain how you used the correct measurement units to solve the problem.
Susan has 875 grams of grapes left.
1. Susan bought a 1 kilogram bag of grapes, which is equivalent to 1000 grams (since there are 1000 grams in a kilogram).
2. Susan ate 125 grams of the grapes on her way home.
3. To find out how many grams of grapes Susan has left, we need to subtract the amount she ate from the initial weight of the bag. Therefore, we subtract 125 grams from 1000 grams.
1000 grams - 125 grams = 875 grams
4. Thus, Susan has 875 grams of grapes left.
measurement units:
In this problem, we used grams as the measurement unit. Grams are commonly used to measure the weight of small objects like grapes. Since the problem stated that Susan bought a 1 kilogram bag of grapes, it was necessary to convert the kilogram measurement to grams.
This conversion was done by multiplying the kilogram value by 1000 (1 kilogram = 1000 grams). By using the correct measurement units, we were able to accurately calculate the amount of grapes Susan had left after eating a portion.
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Need help with this equation 8x²+10x-3
Answer:
Step-by-step explanation:
You have to use the quadratic formula
x = -b +/- [tex]\sqrt{(b^{2} -4ac)/2a[/tex]
and then you can simplify both answers so the first one would be -13/2 and the second would be -27/2
you usually have to reject an answer but since there is no equal sign in the question, you should be fine
A student takes a subway to a public library. The table shows the distance d (in miles) the student travels in t minutes. Determine whether the data can be modeled by a linear, exponential, or a quadratic function and then select a function rule to model the situation.
t
d
1
0.83
2
1.66
3
2.49
4
3.32
5
4.15
The linear function that models the situation is given as follows:
d = 0.85t.
What is a proportional relationship?A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.
The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:
y = kx.
The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.
The constant ratio for this problem is given as follows:
k = 0.83, as each division of d by t has a result of 0.83.
Hence the equation is given as follows:
d = 0.83t.
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What are the minimum and maximum values of the function?
