Stephanie is collecting data on the reaction of bacteria to different antibodies. She did not measure the area of the bacteria in the dish when she began the experiment but measured 20 cm2 of bacteria after 1 hour. She continued to measure the bacteria each hour and entered the data in the table. show the explicit function. How much area would you predict the bacteria to have when measured during the 5th hour?
Answers
We take a look at the reduction in the area of the bacteria.
In the first hour, its arae is 20cm2. Following that, it reduces 1.25x, to 16. Then another 1.25x, from 16 to 12.8. And another 1.25x, from 12.8 to 10.24.
So, every hour, the bacteria's area reduces by 1.25x
Therefore, in the 5th hour (prediction probably if this is all a coincidence), the bacteria's area will be : 10.24 : 1.25 = 8.192 cm2.
Related Questions
Find the number that should be added to the equations to make it a complete squares.
1. x^2 + 22x
2. x^2 - 2x
3. x^2 + 7x
Answers
The number that must be added to complete the squares is 121 .
Since x² represents the area of a square with a side of length x and bˣ represents the area of a rectangle with sides b and x, the process of completing the square can be seen as a visual manipulation of rectangles.
When the x² and bˣ rectangles are simply joined into a larger square, a corner is lost. The expression (b/2)² can be added to each side of the equation above to calculate the area of the remaining corner, thereby giving rise to the idiom "completing the square".the given expressions are x² + 22x
This can be written in the form of a square polynomial as :
x² + 2×x×11 + 11² = (x+11)²
Therefore we have to add 11² = 121 to the polynomial to complete the square.
Similarly for x² - 2x we have to add 1 to get the form (x-1)²
And we have to add x²+ 7x + (7/2)²
Hence the number to be added is 49/4 .
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Identify the vertical angle to angle ADX.
Answers
Answer:bdf
Step-by-step explanation:
yes
Two airplanes are flying in the air at the same height. Airplane A is flying east at 200 mph and airplane B is flying north at 250 mph. If they are both heading to the same airport, located 30 miles east of airplane A and 40 miles north of airplane B, at what rate (in mph) is the distance between the airplanes changing?
Answers
The rate at which the distance between the airplanes is changing is;
dC/dt = 320 mi/h
We are given;
The Speed of Airplane A; dA/dt = 200 mi/h
The Speed of Airplane B; dB/dt = 250 mi/h
Aircraft A and B will form a right-angled triangle because Aircraft A is flying east and Aircraft B is flying north, and we can use Pythagoras' theorem to calculate their distance from one another.
Let C be the distance.
Therefore;
C² = A² + B²
Differentiating the above equation with respect to t,
2C(dC/dt) = 2A(dA/dt) + 2B(dB/dt)
Dividing each side of the equation by 2,
C( dC/dt ) = A( dA/dt ) + B( dB/dt )
Where dC/dt is the rate of change in distance between the two aircraft.
Now,
C² = A² + B²
C = √(A² + B²)
Substituting, A = 30 miles and B = 40 miles;
C = √(30² + 40²)
C = √( 900 + 1600 )
C = √2500
C = 50 miles
Substituting the value in the equation C( dC/dt ) = A( dA/dt ) + B( dB/dt ),
50(dC/dt) = (30 × 200) + (40 × 250)
50(dC/dt) = 6000 + 10000
50 × dC/dt = 16000
dC/dt = 16000/50
dC/dt = 320 mi/h
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i need help cuz im poopy dooky at math
Answers
Answer:
Reduction is correct
Scale factor is 0.5
Step-by-step explanation:
The distance from the point L to every point on the pink figure is 1/2 (0.5) times the distance from L to each of the corresponding points on the original figure
If scale factor < 1, it is a reduction
How to write 1.09 in a fraction
Answers
Answer:
1.09 = [tex]1\frac{9}{100} [/tex]
5) If a || b and b | c, can you conclude that a || c? Explain
your reasoning and include a drawing to support your
answer.
Answers
Parallel lines are any two line pairs that do not overlap or come together at any point. Despite being on the same plane, these lines do not intersect. Lines or rays that share a plane but do not intersect are also considered to be parallel.
a || b and b || c then a || c.
ie. a || b || c
What are parallel lines?Lines in a plane that are consistently spaced apart are known as parallel lines. Parallel lines don't cross each other. Perpendicular lines are those that cross at a straight angle of 90 degrees.Parallel Lines' Slope Parallel lines have an equal slope. The slope of parallel lines is equal because they are all equally inclined with respect to the positive x-axis. If m1, m2 are the slopes of two parallel lines, then m1 = m2 is the result.Parallel lines are any two line pairs that do not overlap or come together at any point. Despite being on the same plane, these lines do not intersect. Lines or rays that share a plane but do not intersect are also considered to be parallel.
a || b and b || c then a || c.
ie. a || b || c
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cuanto es 3416 dividido 23
Answers
Answer: 148.52173913
Step-by-step explanation:
Buenos Noches:)
espero que esto ayude
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answers
Answer:
90 degree counter-clockwise
Step-by-step explanation:
Write an expression that would represent the number of bags of Reese’s( three more than the number of bags of lollipops)
Answers
Answer:
1
Step-by-step explanation:
i don;t know
1.7x10*4 x 8.5x10*-2
Answers
Answer: 1.7×10*4×8.5×10*-2= 1445
Step-by-step explanation:
The question must be written as follows:
1.7×10∧4×8.5×10∧-2=
(1.7×10000×8.5)÷100
=144500÷100=1445
Which fractions have the same value as -1/4A) -1/-4B) - -1/-4C) -1/4D) - -1/4E) 1/-4
Answers
Then, options C and E are correct
[tex]\frac{-1}{-4}=\frac{1}{4}[/tex]Then, option A isn't correct
[tex]-\frac{-1}{4}=\frac{1}{4}[/tex]Then, option D isn't correct
[tex]-\frac{-1}{-4}=-\frac{1}{4}[/tex]I need to know the answer asp
Answers
In the given figure, BC is the Adjacent side. This is because the side is the closest side to the angle θ.
Using Trigonometry, we can also find out the measure of the ∠θ.
tan θ = opposite side / adjacent side
⇒ tan θ = 2/8 = 1/4
⇒ θ = tan^-1 (1/4)
⇒ θ = 0.245°
What is Trigonometry?The area of mathematics known as trigonometry studies how triangles' sides and angles relate to one another as well as how various angles might be used in useful ways. For determining the positions of the sun, moon, and stars, forecasting eclipses, and defining planet orbits, spherical trigonometry has been utilized for ages. To determine the distance to neighboring stars in the modern era, astronomers utilize the triangulation method. Satellite navigation systems also employ this method.By combining the laws of sines and cosines with these functions, it is possible to practically any queries concerning arbitrary triangles. When a triangle has two sides and an included angle or two angles and a side, these principles can be applied to determine the remaining angles and sides.As soon as two sides, their included angle, two angles, a side, or three sides are known, these principles can be used to calculate the remaining angles and sides of any triangle.
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(q027) a recent study by pew (purcell 2011) found gendered differences in applications (apps) downloaded by men and women. men are more likely to download and use , whereas women tend to use more than men.
Answers
Men are more likely to download and use , but women use both sides of the brain while men only use the left for visual or spatial expression. So, There is a relationship between gender and intended major.
Based on the given conditions,
Differences in applications (apps) downloaded by men and women.
Men are more likely to download and use , whereas women tend to use more than men.
So,
We can write,
According to studies comparing the brain activity of men and women,
When performing language-related tasks, women's brains are more likely than men's to be engaged in the right hemisphere.Men express their emotions using the right side of the brain, whereas women use both sides.Women use both sides of the brain while men only use the left for visual or spatial expression.Although men tend to be more emotional than women, women often express and display their feelings the most, giving the impression that they are more emotionally sensitive than men.From the above question, we can see that most women in research positions want to use, while most men want to study download and use. From this we can conclude that there is a greater correlation between female gender and use (according to this study) than male gender and download and use . Therefore, the results of this study indicate that there is a relationship between gender and primary intentions.Therefore,
Men are more likely to download and use , but women use both sides of the brain while men only use the left for visual or spatial expression. So, There is a relationship between gender and intended major.
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nits 5 and 6: Modeling Mania: Think 1 Question number 1 A scalene triangle has equal sides. I don't know
Answers
Explanation:
Scalene triangle has no side equal. Its angles are also not equal.
The three sides of scalene triangle are all differenet from one another.
Mandy created 2 patterns. She used the corresponding values in each pattern to make the coordinate pairs shown.
(1,0)
(3,2)
(11,10)
(14, 13)
What is the relationship between each x- and y-coordinate? Move numbers and symbols to the lines to make an equation.
y = x
2
3
8
11
Answers
The equation that represents the linear relationship between each x- and y-coordinate is: y = x - 2.
How to Create an Equation for a Relationship?For a linear relationship between x and y coordinate, an equation in slope-intercept form that can be created is expressed as y = mx + b.
"m" is the slope = change in y / change in x."b" is the y-intercept.Find the slope (m) using any two pairs of values, (1, 0) and (3, 2):
Slope (m) = (2 - 0)/(3 - 1)
Slope (m) = 2/2
Slope (m) = 1
Find the y-intercept by substituting m = 1 and (x, y) = (1, 0) into y = mx + b:
0 = 1(1) + b
0 = 2 + b
-2 = b
b = -2
Write the equation of the relation by substituting m = 1 and b = -2 into y = mx + b:
y = x - 2
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The relationship Mandy made with coordinate points is y = x - 1.
What is the x-y coordinate?an x-y coordinate is a 2D plane in which we can plot points of x and y together to make a coordinate. We can graph lines or any 2D figure using x-y coordinates.
We determine the relationship between x and y we'll go with the
hit-and-trial method.
At x = 1, y = 0.
At x = 11 , y = 10.
We can observe that y is one less than x, this can be represented as,
y = x - 1.
To cross-check out the equation can put given values of x and y and check whether it satisfies our equation or not.
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0. Complete the statement: 0.6L mL
Answers
Answer:
600mL
Step-by-step explanation:
1 Milliliter = 0.001 L
Find all the factors of the given polynomial using synthetic division.
[tex]{x}^{2} + {6x}^{5} - {2x}^{4} - {60x}^{3} - {71x}^{2} + 54x + 72[/tex]
Solution:
Answers
Factor of 6x⁵ – 2x⁴ – 60x³ – 70x²+54x+72: are 2(x−1) (3x+2x³ – 28x² – 63x – 63)
What are the factors of polynomial?A polynomial with coefficients in a specific field or in integers is expressed as the result of irreducible components with coefficients in the same domain using polynomial factorization. The polynomials that are multiplied to create the original polynomial are the factors in the case of polynomials. For instance, (x + 2) (x + 3) are the elements of x2 + 5x + 6. The original polynomial is produced when we multiply both x +2 and x +3.
615 - 2x-60x³- 70x² +54 +72
Factor out common term 2:
2(3x⁵-x⁴-30x³ - 35x² +63)
Factor 3x⁵ - x⁴ - 30x³ – 35x²+63:
(x-1) (3x² + 2x³ — 28x² – 63x – 63) -
=2(x − 1 ) (3x⁴ + 2x³ – 28t² – 63x – 63)
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Tell whether 18 is a solution of -13<5-x
Answers
x < 18 is the solution to the inequality -13 < 5 - x.
What is the solution to the given inequality?Given the inequality in the question;
-13 < 5 - xx = ?To solve the inequality, move all terms containing variable to the left side and the constant to the right side of inequality.
-13 < 5 - x
Add 13 to both sides
-13 + 13 < 5 + 13 - x
0 < 5 + 13 - x
Add 5 and 13
0 < 18 - x
Now, add x to both sides
0 + x < 18 - x + x
-x and x cancel out
0 + x < 18
x < 18
Therefore, the solution is x < 18.
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Original Price: $20
Discount: 40%
Answers
Answer:
$12
Step-by-step explanation:
C0-starting price
C1-price after discount
P- precentage
C1=C0-P/100*C0
C1=20-40/100*20
C1=20-8
C1=12
I need help with this one
Answers
It is because parallel line have same gradient/slope
Find the area of quadrilateral CHIL as pictured above.
Answers
Check the picture below.
so we really have two twin triangles pretty much
[tex]\stackrel{\textit{area of both triangles}}{2\left[ \cfrac{1}{2}(\underset{b}{9})(\underset{h}{4}) \right]\implies \text{\LARGE 36}}[/tex]
<1 is a complement of <2, and m<1=23. find m<2
Answers
The value of the angle m∠2 = 67°.
Angle may be defined as the space between two lines. An angle consists of a vertex with which the angle is extended. When sum of two angles is exactly 90°, they are called complementary angles. For example, if we have two angles a and b then, ∠a + ∠b = 90°. When sum of two angles is exactly 180°, they are called supplementary angles. For example, if we have two angles a and b then, ∠a +∠b =180°. According to the given question ∠1 is a complement of ∠2 and we know when two angles are complementary to each other sum of their angles is 90°. So,
m∠1 + m∠2 = 90°
Now, m∠1 = 23°
23° + m∠2 = 90°
m∠2 = 90° - 23°
m∠2 = 67° which is required angle.
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The cost of petrol rises by 2 cents a liter. last week dora the explorer bought 20 liters at the old price. This week she bought 10 liters at the new price. Altogether, the petrol costs $9.20. What was the old price for 1 liter?
Answers
The old price at which dora bought 20 liters of petrol is $0.30 per liter.
Given, dora bought 20 liters of petrol at old price.
The cost of petrol rises by 2 cents later.
Then she bought 10 liters at the new price.
Altogether the petrol costs = $9.20
old price for 1 liter = ?
let the old price for 1 liter of petrol be x.
Based on the conditions , we formulate:
20x+10(x+2)=920
20x+10x+20=920
30x+20=920
30x=920-20
30x=900
x=900/30
x=30
x=$0.30
hence the old price of the petrol is $0.30 per liter.
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whats the midpoint of (2,2) and (10,10)
Answers
Answer:
Midpoint=(6,−354)
Step-by-step explanation:
I solved this using the MidPoint Calculator:) Im a 7th grader.
A school club is raising money for a trip, and needs to reach $5,000. their fundraising progress is modeled by the equation: t = 350 + 750x, where x is measured in weeks. what is the meaning of the coefficient 750? question 13 options: it is the amount still to be raised. it is the amount they started with. it is the amount they raise each week. it is the amount left over.
Answers
Answer: It is the amount they raise each week
350 is the amount they started with
A straight line has the equation y=5x-1
a. what is the equation of a parallel line with a y intercept of 4
b. what is the equation of a parallel line with a y intercept of -2
c. why will your answers to part a and b also be parallel
Answers
a. The equation of a parallel line with a y intercept of 4 is:
y=5x+4
b. The equation of a line parallel line with a y intercept of -2 is:
y=5x-2
c. Since they have same slope and different intercepts, so the answers to part a and b are also parallel.
a. Given, the given straight line equation is: y=5x-1 eq(1)
hence the slope of the line is m=5
The required line is parallel to (1) so its slope is also same.
m = 5 and the y intercept is 4.
By using y = mx + c form the equation of the required line is:
y = 5x+4
b. The given straight line equation is: y=5x-1 eq(1)
hence the slope of the line is m=5
The required line is parallel to (1) so its slope is also same.
m = 5 and the y intercept is -2.
By using y = mx + c form the equation of the required line is:
y = 5x-2
c. If two lines have different y-intercepts and equal slopes, then they are said to be parallel. Hence answers to part a and part b are said to be parallel.
Hence we get the desired equations.
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Evaluate the expression when m=16 and n=6. M+36/n
Answers
explanation: first, replace m with its value, which is 16. then replace n with its value, which is 6. you will have this equation:
16+36/6. start with 36/6, which equals 6. then add 16. your answer will be 22. hope this helped!
1,072 ÷ 16 = 67
Write a situation for this number model and draw a picture that goes with it.
Answers
the sum of -15 /37 and 7/32 is? ANSWER ASAP WILL GIVE BRAINLIEST
Answers
Find the area of a regular hexagon with an apothem 11.4 yards long and a side 13 yards pong. Round your answer to the nearest tenth.
Answers
Answer:
444.6 square yards.
Explanation:
• A regular hexagon is divided into 6 equilateral triangles.
,• The apothem is the height of each equilateral triangle.
,• The side length is the base of each triangle.
Thus, the area of the hexagon will be:
[tex]\begin{gathered} A=6\times\text{Area of one equilateral triangle} \\ =6\times\frac{1}{2}bh \\ =6\times\frac{1}{2}\times13\times11.4 \\ =444.6\text{ square yards} \end{gathered}[/tex]The area of a regular hexagon with an apothem 11.4 yards long and a side 13 yards is 444.6 square yards.
