For a certain species of virulent bacteria with the rate of growth of the bacterial population as proportional to the number the bacteria present after 3 hours is 256000.
What is exponential function?A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth.
When there is exponential growth, the quantity grows initially extremely slowly and subsequently quickly. Over time, the rate of change quickens. As time goes on, the rate of increase accelerates. It is intended for the quick growth to be a "exponential increase".
The species of bacteria follow an exponential growth pattern.
The exponential growth is given as:
[tex]A(t) = A_0e^{kt}[/tex]
Where, A₀ is the initial population = 4000
k = constant
t = time = 30 minutes = 1/2 hour.
The bacteria doubles in 30 minutes, thus A(t) = 2(4000) = 8000.
Substituting the values in the equation:
[tex]8000 = 4000e^{k(\frac{1}{2} )}\\\\2 = e^{k(\frac{1}{2} )}[/tex]
Takin ln on both sides of the equation:
ln(2) = 1/2 k
2(ln(2)) = k
k = 1.38
The number of bacteria present after 3 hours:
[tex]A(t) = 4000e^{(1.38)(3)}\\\\[/tex]
A(t) = 256000
Hence, for a certain species of virulent bacteria with the rate of growth of the bacterial population as proportional to the number the bacteria present after 3 hours is 256000.
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Combine the like terms to simplify this expression: ( the 2 to the right of the x, is an exponent)
2x² + 3x-4-x² + x + 9
Answer:
x^2 +4x +5
Step-by-step explanation:
2x^2 -x^2 will be x^2
3x+x is 4x
-4+9 is 5
convert the following measurements into centimeters
A. 15m
B. 1.6km
C. 467mm
Answers:
A. 150 cmB. 160,000 cmC. 46.7 cm===========================================
Work Shown:
[tex]15 \text{ m} = (15 \text{ m})*\frac{100 \text{ cm}}{1 \text{ m}} = 1500 \text{ cm}\\\\\\1.6 \text{ km} = (1.6 \text{ km})*\frac{1000 \text{ m}}{1 \text{ km}}*\frac{100 \text{ cm}}{1 \text{ m}} = 160,000 \text{ cm}\\\\\\467 \text{ mm} = (467 \text{ mm})*\frac{1 \text{ cm}}{10 \text{ mm}} = 46.7 \text{ cm}[/tex]
Each conversion fraction is set up to cancel out any unit that isn't "centimeters".
Side notes:
1 m = 100 cm1 km = 1000 m1 cm = 10 mmA person is measuring for new carpet in an auditorium. the angle of elevation from the front to back is 12 degrees and the last row is 15 feet higher than the front row. what is the straight line distance from the front seat to the back? round to the nearest tenth
The straight line distance from the front seat to the back is approximately 69.7 feet.
What is a straight line distance?Straight line distance refers to the shortest distance between two points in a straight line, as opposed to the distance that would be traveled along a curved path or following the contours of the terrain.
Let the distance from the front row to the back row be x.
Then, we can use the tangent function to find the height difference between the front and back rows:
tan(12°) = (height difference) / x
Solving for the height difference:
height difference = x * tan(12°)
The problem tells us that the height difference is 15 feet, so we can set up an equation:
15 = x * tan(12°)
Solving for x:
x = 15 / tan(12°) ≈ 69.7 feet
Therefore, the straight line distance from the front seat to the back is approximately 69.7 feet.
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Alan and betty collected cans for recycling. Alan collected 154 cans. Betty collected 215 cans. How many cans did they collect?
Answer:
369 cans
Step-by-step explanation:
Add the two numbers of cans collected by each:
Alan: 154 cans
Betty: 215 cans
Total: 369 cans
convert 1hour 38 min 14 second to seconds
Answer:
5894 seconds
Step-by-step explanation:
Convert 1 hour 38 min 14 seconds to seconds
1 hour = 3600 seconds
1 min = 60 seconds
38 mins = 60 x 38 = 2280 seconds
Now add all numbers together
3600 + 2280 + 14 = 5894 seconds
So, 1 hour 38 minutes 14 seconds is 5894 seconds.
Mia invests $7500 at a rate of 3.5% per year simple interest
Calculate the total amount she has after 5 years.
Answer:
$8812.50
Step-by-step explanation:
To calculate the simple interest earned on Mia's investment, we can use the formula:
I = Prt
where I is the interest earned, P is the principal amount invested, r is the interest rate as a decimal, and t is the time in years.
Plugging in the values, we have:
I = $7500 * 0.035 * 5
I = $1312.50
The total amount Mia has after 5 years is the sum of her original investment and the interest earned:
$7500 + $1312.50 = $8812.50
A STORY OF RATIOS
A positive, finite decimal s is said to be written in scientific notation if it is expressed as a product d x 10", where d
is a finite decimal so that 1 ≤ d < 10, and n is an integer.
The integer n is called the order of magnitude of the decimal d x 10".
Are the following numbers written in scientific notation? If not, state the reason.
Exercise 1
1.908 x 1017
Exercise 2
0.325 x 10-2
Exercise 3
7.99 x 10³2
EUREKA
MATH
Lesson 9:
Scientific Notation
© 2019 Great Mindeurekamath.org
Exercise 4
4.0701 +10
Exercise 5
18.432 x 5
Lesson 9 Classwork 8.1
Exercise 6
8x 10-¹1
85
Exercise 1: Yes, 1.908 x 10^17 is written in scientific notation.
Exercise 2: Yes, 0.325 x 10^-2 is written in scientific notation.
Exercise 3: No, 7.99 x 10^32 is not written in scientific notation. The decimal d must be between 1 and 10, not between 10 and 100.
Exercise 4: No, 4.0701 + 10 is not written in scientific notation. The correct format is d x 10^n.
Exercise 5: No, 18.432 x 5 is not written in scientific notation. The correct format is d x 10^n.
Exercise 6: No, 8x 10^-11 is not written in scientific notation. The correct format is d x 10^n.
The number of each type of ticket sold in the following situation: Tickets to a football game cost $5.oo if purchased before the day of the game. They cost $7.50 if purchased at the game. For a particular game, 600 tickets were sold and the receipts were $3500.
The number of each type of ticket sold in the following situation:
1. The tickets of $5.00 = 400
2. The tickets of $7.50 = 200
What is linear equation ?A linear equation is an algebraic equation in which the highest power of the variable is 1. In simple words, a linear equation is an equation in which the variables appear only in the first degree.
Linear equations can be written in the form:
y = mx + b
where y and x are variables, m is the slope (or rate of change), and b is the y-intercept (the point where the line crosses the y-axis).
Let x be the number of tickets sold before the day of the game and y be the number of tickets sold at the game.
Then we have:
x + y = 600 (the total number of tickets sold)
and
5x + 7.5y = 3500 (the total receipts from ticket sales)
To solve for x and y, we can use substitution.
Simplify and solve for y:
3000 - 5y + 7.5y = 3500,
2.5y = 500
y = 200
Substitute y = 200 back into the equation x + y = 600 to find x:
x + 200 = 600,
x = 400.
Therefore, 400 tickets were sold before the day of the game and 200 tickets were sold at the game.
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The complete question:
The number of each type of ticket sold in the following situation: Tickets to a football game cost $5.oo if purchased before the day of the game. They cost $7.50 if purchased at the game. For a particular game, 600 tickets were sold and the receipts were $3500. Find the number of tickets sold before the day of the game and the number of tickets sold at the day of the game?
please help me quikly
A video rental company offers a plan that includes a membership fee of $10 and charges $4 for every DVD borrowed. They also offer a second plan, that costs $50 per month for unlimited DVD rentals. If a customer borrows enough DVDs in a month, the two plans cost the same amount. How many DVDs is that?
Write a system of equations, graph them, and type the solution.
The solution to this system of equations is (10, 50).
A graph of this system of equations is shown in the image attached below.
How to determine the number of DVDs when the two companies cost the same amount?Based on the information provided above, one of the plan includes a membership fee of $10 and charges $4 for every DVD borrowed. Therefore, the total cost, y, can be represented by this equation:
y = 4x + 10 .......equation 1.
where:
x represents the number of DVDs borrowed in a month.
For the second plan, it costs $50 per month for unlimited DVD rentals. Therefore, the total cost, y, can be represented by this equation:
y = 50 ....equation 1.
By equating equation 1 and equation 2, we have the following:
4x + 10 = 50
4x = 50 - 10
4x = 40
x = 40/4
x = 10 DVDs.
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If you get paid $13 per hours and work 8 hours and 45 minutes how much money did you earn? round your answer to the nearest hundred?
Answer:
113.75
Step-by-step explanation:
13$ x 8.75 h (45 minutes is 3/4 of an hour) = $113.75
keeping in mind that an hour has 60 minutes, so you're really getting paid $13 per 60 minutes, so now, 8 hours and 45 minutes is just 8*60 + 45 = 525 minutes.
[tex]\begin{array}{ccll} \$&minutes\\ \cline{1-2} 13 & 60\\ x& 525 \end{array} \implies \cfrac{13}{x}~~=~~\cfrac{60}{525} \\\\\\ \cfrac{ 13 }{ x } ~~=~~ \cfrac{ 4 }{ 35 }\implies 455=4x\implies \cfrac{455}{4}=x\implies 113.75=x[/tex]
Write the equation of the ellipse and find the foci with the given vertices (2,3),(2,13),(0,8),(4,8)
Step-by-step explanation:
Equation of ellipse depends on the points
The points that lie on the horizontal axis is (0,8) and (4,8). They have a distance of 4, therefore a radius of 2
The points that lie on the vertical axis is (2,3) and (2,13)
They have a distance of 10, therefore a radius of 5
Since the vertical axis is bigger, we have a vertical ellipse which is the equation of,
[tex] \frac{(y - k) {}^{2} }{ {a}^{2} } + \frac{(x - h) {}^{2} }{ {b}^{2} } = 1[/tex]
Where a is the major radius
b is the minor radius
(h,k) is the center
Step 1: Finding the center
The center should be the midpoint of the horizontal vertices or vertical vertices
Let's use the horizontal vertices
[tex] (\frac{(0 + 4}{2} ) = 2[/tex]
[tex]( \frac{8 + 8}{2} ) = 8[/tex]
So the center is (2,8)
Step 2: Finding the major and minor radius
We already know it , a is 5
b is 2, so we as of now, have this equation
[tex] \frac{(y -8) {}^{2} }{25} + \frac{(x - 2) {}^{2} }{4} = 1[/tex]
This is the equation of the ellisoe
Step 3: Find the foci
The foci for a vertical ellipse should lie on the same line as the same line as the major vertices and center.
The equation for an ellipse foci that is vertical are
(x,y+c) and (x,y-c)
Where C is
[tex]c = \sqrt{ {a}^{2} - {b}^{2} } [/tex]
[tex]c = \sqrt{25 - 4} [/tex]
[tex]c = \sqrt{21} [/tex]
So our foci are
,,,
[tex](2,8 + \sqrt{21} )[/tex]
and
[tex](2,8 - \sqrt{21} )[/tex]
,
3= g/-4 -5
tysm for helping me
For the equation 3 = (g/-4) - 5, the value of g is g = -32.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
The given equation is -
3 = (g/-4) - 5
The equation contains a fractional component.
Simplify the equation to get the value of g.
First collect all the like terms -
g/-4 = 3 + 5
Then use arithmetic operation of addition -
g/-4 = 8
Then move the denominator of the fraction to right hand side of the equation -
g = 8 × -4
Then use arithmetic operation of multiplication -
g = -32
Therefore, the value of g is -32.
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x + 1/2y when x= -5/6 and y= -2/5 in simplest form
Answer:
Improper fraction: -31/30
Mixed number: -1 1/30
Step-by-step explanation:
If x = -5/6 and y = -2/5, we can start by replacing x and y in the equation x + 1/2y.
x+1/2y -> -5/6+1/2(-2/5)
Now we can start solving the equation:
According to the Order of Operations, we have to start with multiplication before addition. So, let's multiply 1/2 and -2/5. We get -2/10, which simplifies to -1/5.
Now we have to do the addition: -5/6+(-1/5)
To add fractions together, we have to find a common denominator. We can do this by finding the LCM of the two denominators(Least common multiple).
6: 6, 12, 18, 24, 30, 36...
5: 5, 10, 15, 20, 25, 30, 35...
The LCM is 30.
-5/6 x 5/5 = -25/30 <-- the equivalent fraction of -5/6
-1/5 x 6/6 = -6/30 <-- the equivalent fraction of -1/5
-25/30 + (-6/30) = -31/30
The answer is -31/30 in improper fraction form, and -1 1/30 in mixed number form.
__ % of 90 is 90?
O 90%
O 100%
O 10%
O 50%
Answer:
100
Step-by-step explanation:
I hate that I have to use 20 characterz
If
D=1−s^2 −s and C=3+3s, find an expression that equals 2D−3C in standard form.
The expression that equals 2D−3C in standard form is -2s² - 11s - 7
What are algebraic expressions?Algebraic expressions are defined as expressions that are composed of coefficients, variables, terms, factors and constants.
From the information given, we have that;
D=1−s^2 −s and C=3+3s,
To determine the expression for 2D - 3C
substitute the values of the expressions, we get;
2(1-s² - s) - 3(3 + 3s)
expand the bracket
2 - 2s² - 2s - 9 -9s
collect the like terms or factors, we get;
-2s² - 2x - 9s - 9 + 2
Add or subtract the values
-2s² - 11s - 7
Hence, the expression is -2s² - 11s - 7
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In parallelogram ABCD, AB = 5x * 3 and CD = 15 * x. FInd the value of x
In a parallelogram, opposite sides are equal. Therefore, AB = CD.
5x * 3 = 15 * x
15x = 15
x = 1
Therefore, the value of x is 1.
If the height of parallelogram ABCD is 6, what is the area of the parallelogram?To find the area of parallelogram ABCD, we can use the formula A = base x height, where the base is the length of side AB and the height is the perpendicular distance between side AB and the opposite side CD. Since the height of parallelogram ABCD is given as 6, we need to find the length of side AB.
From the given information, we know that AB = 5x * 3, where x = 1. Therefore, AB = 15. Now we can calculate the area of parallelogram ABCD as:
A = base x height
A = 15 x 6
A = 90 square units
Therefore, the area of parallelogram ABCD is 90 square units.
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A dust particle weighs around 7.53 x 10-16 grams.
grams
O 7,530,000,000,000,000,000
0.0000000000000753 grams
75, 300,000,000,000,000 grams
O 0.0000000000000000753 grams
O'0.0
0.000000000000000753 grams
Answer:
It would be 3.765 pounds. You have to do 7.53 x 10 to the -10= 0.000000000753. Then do 0.000000000753 x 5 billion to get 3.765.
Step-by-step explanation:
Find the lower bound for the following weights
b) 21. 58 g correct to 2 decimal place
The lower bound for the weight 21.58 g correct to 2 decimal places is 21.57 g. This is because the next smallest value based on the rounding is obtained rounding down the number in second decimal place, which is 5.
To find the lower bound for the weight 21.58 g correct to 2 decimal places, we need to consider the next smallest number that can be represented to 2 decimal places.
Since the second decimal place is 8, the next smallest number is obtained by rounding down the number in the second decimal place, which is 5. Therefore, the lower bound for 21.58 g correct to 2 decimal places is: 21.57g
Note that the weight could be more precise than what we are given, but to represent it to 2 decimal places we have to make an assumption about the last digit.
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Question in picture! Thanks
Answer:
~ generally is substituted by negation
Hence, option D (Even numbers are not divisible by 2) would be the correct answer.
1. Polygon ABCDE is congruent to polygon TVSRK.
The angle that VSR would correspond to, given that polygon ABCDE is congruent to polygon TVSRK, is 2. Angle C.
How to find the angle ?When polygons are said to be congruent, then it means that their sides are the same lengths, and they have the same angles which means that they are corresponding.
This therefore means that the angle at A in polygon ABCDE would be congruent to the angle at T in TVSRK.
This therefore means that the angle VSR would correspond to the angle C in ABCDE because S is the third letter in TVSRK and C is the third letter in ABCDE.
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The full question is:
Polygon ABCDE is congruent to polygon TVSRK. what do angle VSR correspond to _____?
1. Angle B
2. Angle C
3. Angle D
4. Angle A
every time these two wheels are spun, two numbers are selected by the pointers. what is the probability that the sum of the two selected numbers is even?
The probability that the sum of the two selected numbers is even is 1/2.
The parity of the two chosen numbers must match for the sum to be even.
Given this information, we can divide the larger problem into smaller ones. First, we may determine the likelihood that the first spinner will land on an even number.
Exists a [tex]$\frac{1}{2}$[/tex] chance that this happens, and a [tex]$\frac{1}{3}[/tex] there is a chance that the second spinner will also land on an even number, hence
[tex]$\frac{1}{2} \cdot \frac{1}{3} = \frac{1}{6}$[/tex]
There is a win if both the first and second spinners land on an odd number.
[tex]$\frac{1}{2} \cdot \frac{2}{3} = \frac{2}{6}$[/tex]
chance of this happening. Adding these two probabilities together, we get
[tex]\frac{1}{6} +\frac{2}{6} =\frac{3}{6} =\frac{1}{2}[/tex]
Therefore, The probability that the sum of the two selected numbers is even is 1/2.
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a) Hassan deposits $325 into an account that pays 4.7% annual interest compounded monthly. Write an equation to represent Hassanʼs account balance A after t years.
b) Use a system of equations to determine how many years it will take for the account reach $200. Round to the nearest year.
The equation will be written as [tex]A = 325[1.004]^{12t}[/tex]. The time taken to reach $200 will be 10 years.
What is compound interest?Compound interest is defined as the interest levied upon the interest. The formula to calculate the compound interest will be written as:-
[tex]A = P[1+\dfrac{r}{m}]^{rt}[/tex]
Given that Hassan places $325 into a savings account that offers a monthly compound interest rate of 4.7%.
The equation for the compounding on monthly basis,
[tex]A = 325[1+\dfrac{0.047}{12}]^{12t}[/tex]
[tex]A = 325[1.004]^{12t}[/tex]
The time will be calculated as:-
[tex]A = 325[1.004]^{12t}[/tex]
[tex]200 = 325[ 1.004]^{12t}[/tex]
log(0.615) = 12 x t x log(1.004)
12t = 121.77
t = 10 years
Therefore, the equation will appear as [tex]A = 325[1.004]^{12t}[/tex]. It will take 10 years for the price to reach $200.
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On a number line, where would 5. 2 be located?
A. To the left of 5. 1
OB. To the right of 5. 3
OC. Between 1. 5 and 5. 1
O D. Between 5. 1 and 5. 3
5. 2
Option (D) Between 5.1 and 5.3 is the correct answer fore the question where 5.2 on the number line would be located.
On a number line, each number is represented by a point. The location of a number on a number line depends on whether it is greater than or less than other numbers.
In the case of 5.2, it is located between 5.1 and 5.3, as option D states. This is because 5.2 is greater than 5.1 but less than 5.3. Therefore, its location on the number line would be between the points representing 5.1 and 5.3.
A number line is a useful visual tool for understanding the relative position of numbers to each other, as well as for performing basic arithmetic operations. Option (D) Between 5.1 and 5.3 is the correct answer fore the question where 5.2 on the number line would be located.
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what is f(-3) given that f(x)=-x+2
Answer:
f(-3) = 5
Step-by-step explanation:
f(-3) → x = -3
f(x) = -x+2
f(-3) = -(-3)+2
f(-3) = 3+2
f(-3) = 5
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers.
The Pythagorean theorem describes the relationship between the lengths of legs a and b and the hypotenuse c of any
right triangle.
a² + b² = c²
Complete the equation below by writing an expression equivalent to the length of a, the leg of a right triangle.
Completing the equation below by writing an expression equivalent to the length of a, the leg of a right triangle is given below
a^2 + b^2 = c^2a^2 = c^2 - b^2a = square root of (c^2 - b^2)What is Pythagoras' Theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.
According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Hence, the complete equation according to this theorem is given above.
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nonononononononnnono
Can you please answer the question???
The volume of given triangular prism is 24,000 cubic yards.
What is the volume?Volume is the measure of the capacity that an object holds.
Formula to find the volume of the object is Volume = Area of a base × Height.
Here, the dimensions of base are 30 yards and 20 yards.
Here, area = 1/2×30×20
= 300 yd²
Volume of a triangular prism = Area of base triangle × Length of the prism.
= 300×80
= 24,000 yd³
Therefore, the volume is 24,000 yd³.
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texting and driving does providing additional information affect responses to a survey question? two statistics students decided to investigate this issue by asking different versions of a question about texting and driving. fifty mall shoppers were divided into two groups of 25 at random. the first group was asked version a and the other half were asked version b.
Yes, providing additional information affect responses to a survey question. The difference in the proportion of shoppers who admitted to texting and driving in the two groups is 0.2.
To calculate the difference in the proportion of shoppers who admitted to texting and driving in the two groups, we need to first determine the number of shoppers in each group who admitted to texting and driving.
Let's assume that in Group A, 10 shoppers admitted to texting and driving, while in Group B, 5 shoppers admitted to texting and driving.
Then, we can calculate the proportion of shoppers who admitted to texting and driving in each group by dividing the number of shoppers who admitted to texting and driving by the total number of shoppers in each group:
Proportion in Group A = 10/25 = 0.4
Proportion in Group B = 5/25 = 0.2
The difference in proportions is then:
Difference = Proportion in Group A - Proportion in Group B
Difference = 0.4 - 0.2
Difference = 0.2
Therefore, the difference in the proportion of shoppers who admitted to texting and driving in the two groups (A-B) is 0.2 or 20%.
This suggests that providing additional information about the potential consequences of texting and driving may reduce the proportion of people who admit to engaging in this behavior. However, it's important to note that this study has a small sample size and there may be other factors that influence people's responses to survey questions about texting and driving.
Correct Question :
Does providing additional information affect responses to a survey question? Two statistics students decided to investigate by asking different versions of a question about texting and driving. Fifty mall shoppers were divided into two groups of 25 at random. The first group was asked Version A and the other half were asked Version B. Version A: A lot of people text and drive. Are you one of them? Version B: About 6000 deaths occur per year due to texting and driving. Knowing the potential consequences, do you text and drive? Calculate the difference in the proportion of shoppers who admitted to texting and driving in the two groups (A-B).
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1 Colour three parts green. Colour five parts yello a What fraction of the circle is green?
Answer:
3/8
Step-by-step explanation:
1. If there are three parts green and 5 parts yellow, you can add them to find the total parts
2. 5+3 is 8
3. Then to find the green, which is three, we can divide it
4. 3 green parts/ total which is 8
5. 3/8
17
What is the slope of the line that contains the points (-1, 9) and (5, 21)?
slope found by rise over run or m = (y2 - y1) / (x2 - x1)
orientation is important to not mix either values order.
( 9 - 21) / ( -1 - 5) => ( -12 ) / ( - 6 )
negatives cancel and simplify to find
m = 2
The altitude of an airplane is represented by the equation shown below, where Y represents the altitude, in feet, of the airplane and x represents the number of minutes the airplane has been descending:
Y = 1025x + 24,600
Part A: Create a table for the values when x = 0, 5, 8, 10, 30.
Include worked-out equations used to identify the values within the table.
Part B: Identify the altitude after 5 minutes and after 30 minutes. Use 1-2 sentences to explain the altitude at these two times and describe what is happening to the airplane at these time intervals.
The way the altitude changes is 24,600 (0 minutes), 19,475 (5 minutes), 16,400 (8 minutes), 14,350(10 minutes), and 6,150 (30 minutes).
How does the altitude change over time?To calculate the change in the altitude, let's use the formula given:
0 minutes:
Y = - 1025 x 0+ 24,600
Y = 24,600
5 minutes:
Y = - 1025 x 5+ 24,600
Y = -5125 + 24, 600
Y = 19,475
8 minutes:
Y = - 1025 x 8+ 24,600
Y = -8200 + 24, 600
Y = 16,400
10 minutes:
Y = - 1025 x 10+ 24,600
Y = -10250 + 24, 600
Y = 14,350
30 minutes:
Y = - 1025 x 30+ 24,600
Y = -30,750 + 24, 600
Y = 6,150
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