A specific bacteria is given a favorable growth medium, the bacteria has a growth rate of 30.5% every hour. In the beginning there are 100 bacteria, how many bacteria will there be in 36 hours? Round your answer to the nearest tenth.
a. 1550236.7 bacteria
b. 1452039.5 bacteria
c. 152.3 bacteria
d. 149.1 bacteria
Answers
Answer:
36hrs is 36/6.5=5.538 doubling periods. Initial population x0=100
Step-by-step explanation:
The rate of exponential growth of a bacterial culture is expressed as generation time, also the doubling time of the bacterial population. Generation time (G) is defined as the time (t) per generation (n = number of generations). Hence, G=t/n is the equation from which calculations of generation time (below) derive.
Related Questions
Ronnie made a scale drawing of a shopping center. A bakery in the shopping center is 7 inches wide in the drawing. The actual bakery is 42 feet wide. What is the scale of the drawing?
Answers
Answer:
1:72
Step-by-step explanation:
The scale of a drawing is the ratio of the length in the drawing to the real length.
Drawing length: 7 inches
Real length: 42 ft × 12 in. / ft = 504 in.
Scale:
7 in. to 504 in.
Divide both numbers by 7:
1 in. to 72 in.
Scale: 1:72
Find the value of x, 6,4, 3x, 4x+1
Answers
Answer:
If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.
6(3x) = 4(4x + 1)
18x = 16x + 4
2x = 4
x = 2
Find the polar coordinates of rectangular coordinates (-√2,1). Limit θ to the interval [0,2pi) and round 2 dceimal places if needed
Answers
The point (-√2,1) can also be represented as (√3, 5.18) in polar coordinates.
To find the polar coordinates of the rectangular coordinates (-√2,1), we can use the following formulas:
r = √(x² + y²)
θ = tan^⁻1(y/x)
Plugging in the given values of (-√2,1), we get:
r = √((-√2)² + 1²) = √(2 + 1) = √3
θ = tan^⁻1(1/(-√2)) ≈ 2.0344 radians
Note that since the point (-√2,1) is in the second quadrant, we need to add π to the value of θ obtained from the inverse tangent in order to obtain an angle in the interval [0,2π). Thus, we have:
θ ≈ 2.0344 + π ≈ 5.1779 radians
Rounding to 2 decimal places as needed, we get the polar coordinates of (-√2,1) as (r,θ) ≈ (√3, 5.18).
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what is the distance between points F(2,9) and G(4,14)? Round to the nearest whole number. Distance=[ ]
Answers
Answer:
The distance between the two points to the nearest whole number is;
\(\text{ Distance = 5}\)Explanation:
Given the points;
\(\begin{gathered} (x_1,y_1)=(2,9) \\ (x_2,y_2)=(4,14) \end{gathered}\)We want to find distance between the two points.
Using the formula;
\(d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}\)Substituting the given coordinates;
\(\begin{gathered} d=\sqrt[]{(4-2)^2+(14-9)^2} \\ d=\sqrt[]{(2)^2+(5)^2} \\ d=\sqrt[]{4+25} \\ d=\sqrt[]{29} \\ d=5.385 \\ d\approx5\text{ units} \end{gathered}\)Therefore, the distance between the two points to the nearest whole number is;
\(\text{ Distance = 5}\)Danny’s home cost $350,000. If the federal government program for flood damage insurance covers only $150,000, what percent of the total value does this represent?
Answers
Amount of $150,000 represents 42.86% of $350,000.
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have Danny’s home cost $350,000. The federal government program for flood damage insurance covers only $150,000.
Assume that it represents [x%] percent of the total value. Then, we can write -
x = (150000/350000) x 100
x = 42.86%
Therefore, $150,000 represents 42.86% of $350,000.
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Help plssssssss thanks 15 points
Answers
Step-by-step explanation:
before buying any songs (0 number of songs) she has $50.
after buying 5 songs she has $37.50 left.
after buying 10 songs she has $25 left.
so, we see, each song costs $2.50 (5×2.5 = 12.5, 50-12.5 = 37.5, 10×2.5 = 25, 50 - 25 = 25).
that ratio continues also for 15 and 20 songs.
so, yes, the problem definition is right, it is a linear function.
the function is
m(x) = y = 50 - 2.5x
"m" standing for "money left".
x = number of songs bought.
the y-intercept is the y-value, when x = 0.
that is in our case 50. or $50.
that stands in this case (as the first sentence in this explanation shows) for the initial amount of money she had before buying any songs.
Find an equation for the graphed function below by using transformations of the grade h of a toolkit function.
Answers
Explanation
Step 1
the original function is
\(y=\sqrt[\square]{x}\)we can see that the original function was shifted
a) one unit to the rigth
b) 2 units up
so
Step 2
A) shifted one unit to the right:
To shift, move, or translate horizontally, replace y = f(x) with y = f(x + c) (left by c) or y = f(x - c) (right by c).so
C=1, to the rigth, so f(x-1)
replace
\(\begin{gathered} y=\sqrt[]{x} \\ y^{\prime}=\sqrt[]{x-1} \end{gathered}\)Step 3
B)now, shifted 2 units up.
To move a function up, you add outside the function: f (x) + b is f (x) moved up b units. Moving the function down works the same way; f (x) – b is f (x) moved down b units.
hence,
\(\begin{gathered} y^{\prime}=\sqrt[]{x-1} \\ b=2,so \\ y^{\prime}^{\prime}=\sqrt[]{x-1}\text{ +2} \end{gathered}\)therefore, the answer is
\(y^{}=\sqrt[]{x-1}\text{ +2}\)I hope this helps you
I will mark you brainiest!
Given an equilateral triangle with two vertices located at (-8, -5) and (3, 7), what is its perimeter?
A) 16.2 units
B) 32.4 units
C) 48.9 units
D) 63.2 units
Answers
The correct option is C) 48.9 units. To find the perimeter of the equilateral triangle, we first need to determine the length of one side of the triangle. Since the triangle is equilateral, all three sides are of equal length.
We can use the distance formula to find the length of one side of the triangle. Let's choose the two vertices located at (-8, -5) and (3, 7) to find the distance between them.
Distance between (-8, -5) and (3, 7) = √[(3 - (-8))² + (7 - (-5))²]
= √[11² + 12²]
= √(121 + 144)
= √265
Since the triangle is equilateral, all three sides are of the same length, so the length of one side of the triangle is also √265.
Therefore, the perimeter of the triangle is 3 times the length of one side:
Perimeter = 3 × √265
= 48.91 (rounded to two decimal places)
Therefore, the correct option is C) 48.9 units.
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20p-8p-6p=12 please make sure it's right
Answers
Answer: step by step
Step-by-step explanation:
not totally sure what you're asking but in this equation p=2
Use the function f(x) to answer the questions:
f(x) = 2x2 − 5x + 3
Part A: What are the x-intercepts of the graph of f(x)? Show your work.
Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work.
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph.
Answers
The x-intercepts of the graph of f(x) are x = 3/2 and x = 1,the Vertex of the graph of f(x) is (5/4, 3/8), and it is a minimum point, The vertex is at (5/4, 3/8). This is the minimum point of the graph.
Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x.
2x^2 - 5x + 3 = 0
To factor this quadratic equation, we look for two numbers that multiply to give 3 (the coefficient of the constant term) and add up to -5 (the coefficient of the linear term). These numbers are -3 and -1.
2x^2 - 3x - 2x + 3 = 0
x(2x - 3) - 1(2x - 3) = 0
(2x - 3)(x - 1) = 0
Setting each factor equal to zero, we get:
2x - 3 = 0 --> x = 3/2
x - 1 = 0 --> x = 1
Therefore, the x-intercepts of the graph of f(x) are x = 3/2 and x = 1.
Part B: To determine whether the vertex of the graph of f(x) is a maximum or a minimum, we look at the coefficient of the x^2 term, which is positive (2 in this case). A positive coefficient indicates that the parabola opens upwards, so the vertex will be a minimum.
To find the coordinates of the vertex, we can use the formula x = -b/2a. In the equation f(x) = 2x^2 - 5x + 3, the coefficient of the x term is -5, and the coefficient of the x^2 term is 2.
x = -(-5) / (2*2) = 5/4
Substituting this value of x back into the equation, we can find the y-coordinate:
f(5/4) = 2(5/4)^2 - 5(5/4) + 3 = 25/8 - 25/4 + 3 = 3/8
Therefore, the vertex of the graph of f(x) is (5/4, 3/8), and it is a minimum point.
Part C: To graph f(x), we can use the information obtained in Part A and Part B.
- The x-intercepts are x = 3/2 and x = 1. These are the points where the graph intersects the x-axis.
- The vertex is at (5/4, 3/8). This is the minimum point of the graph.
We can plot these points on a coordinate plane and draw a smooth curve passing through the x-intercepts and the vertex. Since the coefficient of the x^2 term is positive, the parabola opens upwards, and the graph will be concave up.
Additionally, we can consider the symmetry of the graph. Since the coefficient of the linear term is -5, the line of symmetry is given by x = -(-5) / (2*2) = 5/4, which is the x-coordinate of the vertex. The graph will be symmetric with respect to this line.
By connecting the plotted points and sketching the curve smoothly, we can accurately graph the function f(x).
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In Mr. Romeo's class, a student must work on i-Ready for at least 4 hours per month to receive a grade of 100. Last month Sophia received a math grade of 100. Which inequality represents the number of hours Sophia spent working on i-Ready last month, where h represents the number of hours? (PLEASE HELP MEE!! GIVING 10 POINTS!)
A. h≥4
B. h>100
C. h≤100
D. h<4
Answers
The inequality that represents the number of hours Sophia spent working on i-Ready last month is h ≥ 4.
Option A is the correct answer.
We have,
The problem states that a student must work on i-Ready for at least 4 hours per month to receive a grade of 100.
Since Sophia received a math grade of 100, it means that she has met the requirement of working on i-Ready for at least 4 hours in the last month.
And,
The symbol "≥" means "greater than or equal to," indicating that Sophia worked for at least 4 hours.
Therefore,
The inequality that represents the number of hours Sophia spent working on i-Ready last month is h ≥ 4.
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Halla el menor de tres enteros impares consecutivos tales que 7 veces el entero del medio sea 15 más que la suma del primero y tercer enteros.
Answers
Using an algebraic equation to represent the word problem, the smallest integer is 1
Word ProblemThis is a way of representing mathematical problems with words. To solve this, we have to use algebraic equations or expressions.
Let the integers be represented as
xx + 2x + 4We can write an equation from the word problem given as
7 × (x + 2) = 15 + [x + (x + 4)]
7x + 14 = 15 + x + x + 4
7x + 14 = 15 + 2x + 4
collect like terms
7x - 2x = 15 - 14 + 4
5x = 5
Divide both sides by coefficient of x
5x / 5 = 5 / 5
x = 1
The smallest integer is 1
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Translation:
Find the smallest of three consecutive odd integers such that 7 times the middle integer is 15 more than the sum of the first and third integers
we want to factor the following expression: (x - 3)^2 - 64y^4 which pattern can we use to factor the expression? u and v are either constant integers or single variable expression.
Answers
The factored expression of (x - 3)^2 - 64y^4 is given as follows:
(x - 3)^2 - 64y^4 = (x - 3 + 8y²)(x - 3 - 8y²).
What is the subtraction of perfect squares?The subtraction of perfect squares is a notable product that gives the simplification of an expression containing the subtraction of perfect squares as follows:
a² - b² = (a - b)(a + b).
In this problem, the expression is presented as follows:
(x - 3)^2 - 64y^4
This expression is a subtraction of perfect squares, as the terms are given as follows:
Term a: square root of (x - 3)² = x - 3.Term b: square root of 64y^4 = 8y².Then the expressions are given as follows:
a - b = x - 3 - 8y².a + b = x - 3 + 8y².Then the factored expression is presented as follows:
a² - b² = (a - b)(a + b).
(x - 3)² - 64y^4 = (x - 3 + 8y²)(x - 3 - 8y²).
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Create a factorable polynomial with a GCF of 6. Rewrite that polynomial in two
other equivalent forms. Explain how each form was created. (10 points)
Answers
Polynomial: 6x^3 + 12x^2 - 18x
Form 1: 6(x^3 + 2x^2 - 3x)
Explanation: This form was created by factoring out the GCF of 6 from each term in the polynomial.
Form 2: 6x(x^2 + 2x - 3)
Explanation: This form was created by factoring out the GCF of 6x from each term in the polynomial.
In both forms, the GCF of 6 allows us to factor out common factors and simplify the polynomial expression while preserving its original meaning.
To create a factorable polynomial with a greatest common factor (GCF) of 6, we can start by considering the common factors of the terms. Let's construct a polynomial:
Polynomial: 6x^3 + 12x^2 - 18x
To rewrite this polynomial in two other equivalent forms, we can factor out the GCF from each term and simplify.
Form 1: 6(x^3 + 2x^2 - 3x)
In this form, we factored out the GCF of 6 from each term: 6x^3/6 = x^3, 12x^2/6 = 2x^2, and -18x/6 = -3x.
Form 2: 6x(x^2 + 2x - 3)
In this form, we factored out the GCF of 6x from each term: 6x^3/6x = x^2, 12x^2/6x = 2x, and -18x/6x = -3.
We created each form by identifying the common factors in the polynomial and factoring them out. This process allows us to rewrite the polynomial in equivalent forms that emphasize different aspects.
In Form 1, we factored out the GCF of 6, leaving the remaining polynomial inside the parentheses. This form highlights the fact that the polynomial can be written as the product of the GCF and the remaining terms.
In Form 2, we factored out the GCF of 6x, again leaving the remaining polynomial inside the parentheses. This form emphasizes the fact that the polynomial can be written as the product of the GCF and another factor, in this case, x.
By rewriting the polynomial in these two forms, we have created equivalent expressions that emphasize the presence of the GCF and demonstrate the polynomial's factorability.
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Algebra 2
K.14
Write a quadratic function with zeroes 2 and 8.
Answers
Answer:
\(x^{2}\) - 10x + 16
Step-by-step explanation:
If the 0s are 2 and 8, then the factors are (x - 2) and (x - 8)
Multiply them together to get \(x^{2}\) - 10x + 16
There are 380 students at school. 25% are on the honor roll. How many students are on the honor roll?
Answers
Answer:95
Step-by-step explanation:380/.25=95
Answer:
95 students
Step-by-step explanation:
380 x 25%
how many fourths in 1/4
Answers
Answer:
1
Step-by-step explanation:
a fourth is 1/4 meaning Fourth = 1/4
write as a rate
4 shirts for every 3 pairs of pants
A:3/4
b:4 shirts/3 pairs of pants
c:3 pairs of pants/4 shirts
d:4/3
Answers
What is:
2 x 4 + 3 - 8 ÷ 1 x 6 + 4 - 11
Answers
Answer:
-44
Step-by-step explanation:
2 x 4 + 3 - 8 ÷ 1 x 6 + 4 - 11=-44
Hope this helps!
Answer:
-44
Step-by-step explanation:
Hi can any one teach me this constant difference
Answers
The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).
How do you find the constant difference in a sequence of numbers?In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.
Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.
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Is the following number rational or irrational?
7.11
Choose 1 answer:
Rational
Irrational
Answers
Answer: Rational
Step-by-step explanation: Only numbers that go on infinitely like pi or the square root of 7 are irrational
What is the power of A if 5a=1/125
Answers
Answer:
5^a= 1/5^3
5^a= 5^-3
a=-3
Step-by-step explanation:
Work out the missing numbers:
a) 1.6÷ nothing = 0.04
b) 10.2÷ nothing = 0.8
Answers
Answer:
A is 40
B is 12
Step-by-step explanation:
A- because 1.6 divided by 40 is 0.04
B- because 12 or 12.6 for an exact answer
an equation is show. 30/100 +b= 7/10
Answers
Answer:
b = 4/10
Step-by-step explanation:
30/100 = 3/10 [ 0 will get cancelled]
3/10 + b = 7/10
b = 7/10 - 3/10
b = 4/10
I hope it helps u dear
3
0
1
0
0
+
=
7
1
0
30
100
+
b
=
7
10
10030+b=107
3
1
0
+
=
7
1
0
3
10
+
b
=
7
10
103+b=107
2
Rearrange terms
3
1
0
+
=
7
1
0
3
10
+
b
=
7
10
103+b=107
+
3
1
0
=
7
1
0
b
+
3
10
=
7
10
b+103=107
3
Subtract
3
1
0
3
10
103
from both sides of the equation
+
3
1
0
=
7
1
0
b
+
3
10
=
7
10
b+103=107
+
3
1
0
−
3
1
0
=
7
1
0
−
3
1
0
b
+
3
10
−
3
10
=
7
10
−
3
10
b+103−103=107−103
4
Simplify
Subtract the numbers
Subtract the numbers
again
=
2
5
b
=
2
5
b=52
Solution
=
2
5
b
results of the questionaire were obtained for 39 of the 40 workers at the plant. six ill employees who ate at the cafeteria on september 27
Answers
From the given data, 6 employees are ill and 7 are not ill after ate in cafeteria. and 1 employee is ill and 25 are not ill after did not ate in cafeteria.
In the given question,
Results of the questionnaire were obtained for 39 of the 40 workers at the plant.
Six of the seven ill employees ate at the factory cafeteria on September 26 and 27.
7 of 32 non-stricken workers who ate at the factory cafeteria in both days.
We have to construct a 2x2 table using these data.
6 employees are ill and 7 are not ill after ate in cafeteria.
1 employee is ill and 25 are not ill after did not ate in cafeteria.
So the table should be
ILL Not ILL Total
Ate in Cafeteria 6 7 13
Did not ate in cafeteria 1 25 26
TOTAL 7 32 39
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The right question is
Results of the questionnaire were obtained for 39 of the 40 workers at the plant. Six of the seven ill employees ate at the factory cafeteria on September 26 and 27, compared to 7 of 32 non-stricken workers who ate at the factory cafeteria in both days. You also learn that the factory cook died from respiratory complication 3 weeks after hospital admissions.
In the preliminary analysis of results that you will provide to the Health Commissioner, you set up a 2 x 2 table, relating exposure and disease. You calculate the attack rate, case-fatality rate, and the relative risk of getting botulism after eating at the factory cafeteria on September 26 and 27.
1) Construct a 2x2 table using these data.
ILL Not ILL Total
Ate in Cafeteria
Did not ate in cafeteria
TOTAL 39
Find the porportion 3/12 = 2/x
Answers
Answer:
x = 8
Step-by-step explanation:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. First, multiply 12 and x to both sides of the equation:
(3/12)(12)(x) = (2/x)(12)(x)
3 * x = 2 * 12
3x = 24
Isolate the variable, x. Divide 3 from both sides of the equation:
(3x)/3 = (24)/3
x = 24/3
x = 8
x = 8 is your answer.
~
Step-by-step explanation:
the answer to this question is 2/8, x is 8
in order to do this proportion, you have to
1.Cross multiply:
3 * x = 12 * 2
2.
Simplifying
3 * x = 12 * 2
3.
Multiply 12 * 2
3x = 24
4.
Solving
3x = 24
5.
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
6.
Divide each side by '3'.
x = 8
7.
Simplifying
x = 8
meaning that 3/12 = 2/8
Using the present value approach, solve the following:
Tom has $100 in a bank account that pays a guaranteed 5% interest rate each year. How much would Tom have at the end of Year 3?
Answers
Answer:
Step-by-step explanation:
$100x0.5x1=$5
on the first day of school bethanys family donated $60 to the field trip fundraiser. what percent of their goal did bethanys family donate the goal is 8,000
Answers
Answer:
B
Step-by-step explanation:
Got it right on edge, plz mark brainliest
Answer: 0.25
Step-by-step explanation:
What is the difference?
-3 2/3 - (-2 1/4)
Answers
let's firstly convert the mixed fractions to improper fractions.
\(\stackrel{mixed}{3\frac{2}{3}}\implies \cfrac{3\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{11}{3}}~\hfill \stackrel{mixed}{2\frac{1}{4}} \implies \cfrac{2\cdot 4+1}{4} \implies \stackrel{improper}{\cfrac{9}{4}} \\\\[-0.35em] ~\dotfill\\\\ -\cfrac{11}{3}-\left( \cfrac{9}{4} \right)\implies -\cfrac{11}{3}+\cfrac{9}{4}\implies \cfrac{-(4)11~~ + ~~(3)9}{\underset{\textit{using this LCD}}{12}} \\\\\\ \cfrac{-44+27}{12}\implies \cfrac{-17}{12}\implies {\Large \begin{array}{llll} -1\frac{5}{12} \end{array}}\)
Which equation is the inverse of y = 100-x²?
Answers
Answer:
To find the inverse equation, switch the x and y variables then solve for y.
Original equation: .
y = 100 - x²
Inverse:
x = 100 - y²
y² = 100 - x
y = + √(100 - x) or the first option
Step-by-step explanation: