Answers
The measure of angles 1, 2, and 3 in exercise 11. are 100°, 80°, and 100°.
The measure of angles 1, 2, and 3 in exercise 12. are 47°, 133°, and 47°.
The measure of angles 1, 2, and 3 in exercise 13. are 80°, 80°, and 100°.
The measure of angles 1, 2, and 3 in exercise 14. are 94°, 86°, and 94°.
For 11. part:
Considering a transversal p that cuts two parallel lines l and m,
Each pair of internal angles on the same side of a transversal that intersects two parallel lines are supplementary.
m∠1 + 80° = 180°
m∠1 = 180° - 80°
m∠1 = 100°
Similarly, m∠1 + m∠2 = 180°
⇒ 100° + m∠2 = 180°
⇒m∠2 = 180° - 100°
⇒m∠2 = 80°
and also, m∠2 + m∠3 = 180°
⇒ 80° + m∠3 = 180°
⇒m∠3 = 180° - 80°
⇒m∠3 = 100°
Therefore, m∠1 = 100°, m∠2 = 80° and m∠3 = 100°.
For 12. part:
m∠3 + 133° = 180°(interior angles are supplementary)
m∠3 = 180° - 133°
⇒m∠3 = 47°
m∠2 = 133°(alternate interior angles)
The angle vertically opposite to 133° would also be 133°.
So, 133° + m∠1 = 180°( interior angles are supplementary)
m∠1 = 47°
Therefore, m∠1 = 47°, m∠2 = 133° and m∠3 = 47°.
For 13. part:
m∠3 = 100° (vertically opposite angle)
Let's assume the angle adjacent to ∠3 is x.
m∠3 + m ∠x = 180° (Linear pair property)
100° + m ∠x = 180°
m ∠x = 180° - 100°
m ∠x = 80°
Therefore, m∠1 = m∠2 = m ∠x = 80°(Corresponding angles are equal.)
For 14. part:
m∠1 + 86° = 180°(co-interior angles are supplementary)
m∠1 = 180°- 86° = 94°
The angle vertically opposite to m∠1 is also equal to 94°.
94° + m∠1 = 180°(co-interior angles are supplementary)
m∠2 = 86°
Similarly, the angle vertically opposite to m∠2 is also equal to 86°.
86° + m∠3 = 180°(co-interior angles are supplementary)
m∠3 = 94°
Therefore, m∠1 = 94°, m∠2 = 86° and m∠3 = 94°.
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Related Questions
This semester Hung Lee took four 3-credit courses at Pikes Peak Community College. She received an A in accounting and C’s in history, psychology, and algebra. What is her cumulative grade point average (assume A = 4 and C = 2)
Answers
The cumulative grade point average of Hung Lee is 2.5.
It is given in the question that:-
A = 4
B = 3
C = 2
Grade received in Accounting = A
Grade received in History = C
Grade received in Psychology = C
Grade received in Algebra = C
We have to find her cumulative grade point average.
We know that:-
The cumulative grade point average of Hung Lee will be:-
Sum of grade point averages in the all the courses/Total number of courses
Hence, we can write,
The cumulative grade point average of Hung Lee is given by:-
(4+2+2+2)/4 = 2.5
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Which table dose not show as a function x ?
Answers
Table b. doesn't show y as a function of x as is has to two x values for a same y value '100'.
What is a function?A function, as used in mathematics, is an expression that depicts the relationship between an independent variable (input) and a dependent variable (output), where only one output is possible for each input. In daily life and many professions, functions are useful.
For instance, assuming a constant stride length, a person's distance traveled in an hour is dependent on the number of steps taken. The same individual can extend their walking distance by merely changing the number of steps taken.
Similar to this, the quantity of goods sold may affect the amount of profit a bakery makes. The bakery will generate more revenue by offering more items. The function form of both of these examples is writable. In mathematics, function notation is used to express functions. Such as, f(x) = 3x+ 2
The meaning of y as a function of x is x is y is directly varied with x that is y = ax + b, so for every different x there is a unique y too,
But in Table b. there are two y whose values are 100 but the x are different
which is not possible.
Therefore, Table b. doesn't show y as a function of x as is has to two x values for a same y value '100'.
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If the pattern below was tripled, what would be the ratio of black squares to gray squares
Answers
If the pattern (see attachment) below was tripled, the ratio of black squares to gray squares would be equal to 1:2.
What is a proportion?A proportion can be defined as an equation which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.
Mathematically, a direct proportion can be represented by the following equation:
y = kx
Where:
y and x are the variables.k represents the constant of proportionality.What is a ratio?A ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.
For this exercise, the ratio of black square to gray squares is given by:
B:G = 1:2
Tripling the pattern, we would multiply by three (3) as follows:
B:G = [1:2] × 3
B:G = 3:6
Dividing all through by 3, we have:
B:G = [3:6]/3
B:G = 3/3 : 6/3
B:G = 1:2.
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a path bounds a circular lawn at a park. if the inner edge of the path is 132 ft. around, approximate the amount of area of the lawn inside a circular path
Answers
A path bounds a circular lawn at a park. if the inner edge of the path is 132 ft. around, Approximate the amount of area of the lawn inside a circular path ?
CIRCULAR LAWN
Inner edge Perimeter = 132 feet
2 x pi x r = 132
2 x 22/ 7 x r = 132
r = 132 / ( 2 x 22/ 7 )
r = 132 x 7 / 44
r = 924 / 24
r
Use the number line to find the coordinate of P that represents the weighted average of the set of points such that Point C has a weight of 3, and point E has a weight of 5.
Answers
Using the number line to find the coordinate of P that represents the weighted average of the set of points we see that the value of 6 represents the weighted average of the coordinates.
How exactly does one determine the weighted average?The ordinary arithmetic mean is comparable to a weighted arithmetic mean. The primary difference between the two is that the weighted arithmetic mean takes into account the fact that not all of the data points contribute the same amount to the overall average; rather, some data points contribute more than others.
Generally, the equation for Average weight is mathematically given as
[tex]Av=\frac{ (3 * 2 + 8 * 3)}{(2 + 3)}[/tex]
Consider the quotient in question.
Average weight = 6
As a direct result of this, the value 6 was determined to be the weighted average of the coordinates.
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you randomly select an integer from 0 to 9 (inclusively) and then randomly select an integer from 0 to 4 (inclusively). What is the probability of selecting a three both times?
Answers
The probability of selecting a three both times is 0.2
Probability:
Probability is a measure of the likelihood of an event to occur.
Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.
The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes.
Probability of event to happen P(E) = Number of favorable outcomes / Total Number of outcomes
Given,
you randomly select an integer from 0 to 9 (inclusively) and then randomly select an integer from 0 to 4 (inclusively).
Here we need to find the probability of selecting a three both times.
Here we need to find the individual probabilities for both,
So, the probability of getting 3 in 0 - 9 is
=> 1/10
And the probability of getting 3 in 0 -4 is
=> 1/5
So, in both times
=> (1/10)/(1/5)
=> 1/10 x 5
=> 0.2
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I need help with this question
Answers
ANSWER:
C.
STEP-BY-STEP EXPLANATION:
We have that the population is the following:
A group of individuals under consideration is known as polulation.
The sample would be a subset of the population.
From the information provided, we have that the weights of the golden retrevier dogs are normally distributed. This means that the study population follows a normal distribution.
Therefore, if the original population has a normal distribution, the sample means will also be normally distributed regardless of the sample size.
Therefore, the correct option is C.
Find the measure of <1 and <2
Answers
Answer:
Below in bold.
Step-by-step explanation:
< 1 = 122 degrees (alternate angles)
< 2 = 180 - 122
= 58 degrees (adjacent angles)
(a) Grogg is ordering pizza from a local pizzeria, which offers ten different toppings: pepperoni, mushrooms, sausage, onion, olives, green peppers, pineapple, spinach, garlic, and hummus (an favorite). For any pizza, any combination of toppings is possible, including no toppings. How many different pizzas can Grogg order, if Grogg must order at least five toppings?
(b) Lizzie hears about Grogg's plans, and is also interested in ordering a pizza. For variety, they agree to order one pizza each so that they have no toppings in common. In how many different ways can Lizzie and Grogg order their pizzas, if each pizza must have at least three toppings?
(c) It turns out Winnie is also interested in ordering a pizza! Lizzie and Grogg still agree that their pizzas can't have any toppings in common, but Winnie will include a topping on her pizza only if it appears on Grogg's pizza or Lizzie's pizza (but she doesn't have to include it). In how many different ways can Grogg, Lizzie, and Winnie order their pizzas, if Lizzie's pizza must have at least four toppings, and Grogg's pizza must have at least one topping?
You may leave your answers in exponential form.
Answers
Using the combination formula, the number of ways to order the pizzas in each case is given as follows:
a) 638 ways if Grogg must order at least five toppings.
b) 937,024 ways if each pizza must have at least three toppings.
c) 1024 ways if Lizzie's pizza must have at least four toppings and Grogg's must have at least one topping.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula, involving factorials.
[tex]C(n,x) = \frac{n!}{x!(n-x)!}[/tex]
For this problem, the order of the toppings is not important, which is why the combination formula is used.
Hence the numbers of pizzas from 0 to 10 toppings are given as follows:
0 toppings: C(10,0) = 1.1 topping: C(10,1) = 10.2 toppings: C(10,2) = 45.3 toppings: C(10,3) = 120.4 toppings: C(10,4) = 210.5 toppings: C(10, 5) = 252.6 toppings: C(10, 6) = 210.7 toppings: C(10, 7) = 120.8 toppings: C(10, 8) = 45.9 toppings: C(10, 9) = 10.10 toppings: C(10,10) = 1.In item a, Greg must order at least five, hence the number of ways is:
252 + 210 + 120 + 45 + 10 + 1 = 638 ways.
In item b, each must have at least three toppings, hence the number of ways for each is:
120 + 210 + 252 + 210 + 120 + 45 + 10 + 1 = 968 ways.
968 ways for each, two people, hence, by the Fundamental Counting Theorem, the number of ways is:
968² = 937,024 ways.
In item c, the number of ways is the sum of all the possible toppings, except zero, from the conditions given, hence:
1 + 10 + 45 + 120 + 210 + 252 + 210 + 120 + 45 + 10 + 1 = 1024 ways.
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W
E
Find the slope of the line shown below
-2 -1
slope =
4
3
2
1
-1
-3
-4
-5+
ينا
1
2
a
Answers
Answer:
slope = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, - 2) and (x₂, y₂ ) = (2, - 1) ← 2 points on the line
m = [tex]\frac{-1-(-2)}{2-0}[/tex] = [tex]\frac{-1+2}{2}[/tex] = [tex]\frac{1}{2}[/tex]
Question 2
What are the rational roots of P(x) = x³ + 2x - 1?
O x = 1, x = -1
O x = 1, x = 0
O x = 1, x = 2
O This polynomial has no rational roots.
Answers
The rational roots of the equation is x=0, x=-1.
What is a rational number?
A rational number in mathematics is one that can be stated as the quotient or fraction p/q of two numbers, p and q, with p being the numerator and q being the denominator. For instance, every integer and 3/7 are rational numbers. Boldface Q is typically used to represent the set of all rational numbers, commonly known as "the rationals," the field of rationals, or the field of rational numbers.
The rational roots of the equation is x=0, x=-1.
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Hey can anyone pls answer this!
Answers
The graph of the linear function y = 2/3x + 1 is given at the end of the answer.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which:
m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).For this problem, the function is given as follows:
y = 2/3x + 1.
From this, we have that:
The slope is of m = 2/3, hence when x changes by 1, y changes by 2/3, ..., when x changes by 3, y changes by 2, and so on.The intercept is of b = 1, meaning that the graph of the line crosses the y-axis at point (0,1).From the slope, when x changes by 3, y changes by 2, hence:
x -> x + 3: 0 -> 0 + 3, x = 3.y -> y + 2: 1 -> 1 + 2, y = 3.Thus the linear function also passes through point (3,3), and it's graph is sketched at the end of the answer.
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A baseball player gets 7 hits every 8 times at bat. If this player comes up to bat 16 times in an entire series, find how many hits he would be expected to get.
Answers
The number of hits the baseball player should expect is 14 hits
What is proportion?A proportion an be defined as a mathematical comparison of two numbers.
The numbers mostly represent a comparison between events, people, elements or things.
It is also described as an equation having two ratios that are set equal to each other.
The arithmetic operations involved in proportion includes;
SubtractionAdditionBracketMultiplicationDivisionFrom the information given, we have that;
If 7 hits is equivalent = 8 times
Then x hits is equivalent = 16
cross multiply
8x = 112
Make 'x' the subject of formula by dividing both sides by 8
x = 112/8
x = 14 hits
Hence, the number is 14 hits
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please help i am struggling
Answers
By using the equations of sides and angles and congruence properties, the values of x and y are equal to 34 and 8, respectively. (Correct choice: A)
How to find the values of the variables associated with two congruent trianglesHerein we find two triangles that are congruent when the share the same sides and angles in magnitudes and distribution. As triangle CDE and triangle LMN are congruent, then we have following relationships:
DE = LN (1)
CE = MN (2)
m ∠ D = m ∠ L (3)
m ∠ C = m ∠ M (4)
By (1):
2 · y + 1 = 17
2 · y = 16
y = 8
By (2):
MN = 4 · 8 - 3
MN = 29
By (3):
x + 17 = 51
x = 34
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Use degree and the sign of the leading
coefficient determine end behavior of the
corresponding graph. State the number of
possible x-intercepts and the value of the y-
intercept.
f(x)=x²+2x² - 4x²
2
Answers
As x approach to +∞ function y approaches -∞
And as x approach to -∞ function y approaches -∞
What is coordinate plane ?A coordinate plane is a two-dimensional surface created when two number lines are combined. When a horizontal line crosses the origin, which is the location where the X and Y axes meet, it is generated. A coordinate grid's integers are used to locate points. A coordinate plane can be used to graph points, lines, and a variety of other objects. It functions as a map and offers straightforward directions between two sites.
F(x)=[tex]x^{2} +2x^{2} -4x^{2}[/tex]
F(x)=-[tex]x^{2}[/tex]
if x =0 then y = 0
if x = 1 then y = -1
End behavior
As x approach to +∞ function y approaches -∞
And as x approach to -∞ function y approaches -∞
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Colton mowed 3 lawns in 6 hours. Fill out a table of equivalent ratios and plot the points on the coordinate axes provided.
Answers
the equivalent ratios will be 1 : 2 and 4 : 8.
We are given that:
Colton mowed 3 lawns in 6 hours.
We are also given the table:
Lawns Hours
____ 2
3 6
4 ____
We need to fill the table with the equivalent ratios.
We get the ratio between lawns: hours as = 3 : 6
= 1 : 2
So, for 2 hours, it will be 1 lawn
and for 4 lawns, it will be:
= 4 : 8
So, we get the table as:
Lawns Hours
1 2
3 6
4 8
Therefore, we get that, the equivalent ratios will be 1 : 2 and 4 : 8.
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Olivia has 5 sundaes for her friends. She has 15
5
6
ounces of sprinkles to put equally on the sundaes. How many ounces of sprinkles will be on each sundae?
Answers
explanation: 5/15 = 3
can anyone help me with this its driving me nuts.
Answers
Given:
Surfacea area of cylinder is 82π square meter.
The objective is to find the new surfacea area if dimensions are tripled.
Consider the radius of cylinder as r, height of the cylinder as h.
The formula to find the surfacea area is,
[tex]SA=2\pi r(h+r)[/tex]It is given that the dimensions are tripled. Then, the formula will become.
[tex]\begin{gathered} SA=2\pi\cdot3r(3h+3r) \\ =2\pi\cdot3r\cdot3(h+r) \\ =9\lbrack2\pi r(h+r)\rbrack \end{gathered}[/tex]Now, substitute the given value of surface area in the above equation.
[tex]\begin{gathered} SA=9\lbrack82\pi\rbrack \\ =738\pi m^2 \end{gathered}[/tex]Thus, the new surfacea area is 738π square meter.
Hence, option (C) is the correct answer.
math 38 help please
Answers
8) I
8.2)
[tex]\begin{gathered} \sqrt[3]{x+4}=5 \\ \left(\sqrt[3]{x+4}\right)^3=5^3 \\ x+4=125 \\ x+4-4=125-4 \\ x=121 \\ Verify: \\ \sqrt[3]{121+4}=5 \\ \sqrt[3]{125}=5 \\ 5=5\:True! \end{gathered}[/tex]hus , the answer is x=121
I don’t really need a explanation just give answer
Answers
we know that
the coordinates of point A are (0,1) and point C(3,3)
Applying the formula to calculate the distance between two points
[tex]d=\sqrt{(3-1)^2+(3-0)^2}[/tex]therefore
The answer is option Cwhich equation are correct select each other answers
Answers
Answer:
second and fourth are correct
Step-by-step explanation:
remembering the rule of exponents
• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m +n)}[/tex]
then
- 7x²(4x³ + 2) = - 28[tex]x^{5}[/tex] - 14x² ≠ - 28[tex]x^{6}[/tex] - 14x²
- 2b³(6b² + 5) = - 12[tex]b^{5}[/tex] - 10b³ ← correct
- 3[tex]y^{4}[/tex] (5y² + 2) = - 15[tex]y^{6}[/tex] - 3[tex]y^{4}[/tex] ≠ - 15[tex]y^{8}[/tex] - 6[tex]y^{4}[/tex]
- 5d³ (3d² + 4) = - 15[tex]d^{5}[/tex] - 20d³ ← correct
Based on meteorological records, the probability that it will snow in a certain town on January 1st is 0.428. Find the probability that in a given year it will not snow on January 1st in that town.
Answers
The probability that in a given year it will not snow on January 1st in that town is 0.572.
How to calculate the probability?It should be noted that from the information, the meteorological records illustrates that the probability that it will snow in a certain town on January 1st is 0.428.
Therefore, the probability that in a given year it will not snow on January 1st in that town will be:
= 1 - 0.428
= 0.572
The probability is 0.572.
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plete the process of solving the equation. in the missing term and select the missing description. Simpli -2(c + 8) = -8 S Subtract 8 from both sides
Answers
Answer:
Divide both sides by -2
Step-by-step explanation:
-2(c+8) = -8
-2(c+8) / -2 = -8/-2
c + 8 = 4
c = -4
If 111 people attend a concert and tickets for adults cost $3.5 while tickets for children cost $2.25 and total receipts for the concert was $347.25, how many of each went to the concert?
adults
children
Answers
Using equation, the number of children and adult tickets sold are 33 and 78 respectively
How to find number of each tickets?111 people attend the concert and tickets for adults cost $3.5 while tickets for children cost $2.25 and total receipts for the concert was $347.25.
Therefore, the number of ticket sold for adult and children can be calculated as follows :
let
x = number of children ticket sold
y = number of adult tickets sold.
Therefore, the equation that represent the situation is as follows:
2.25x + 3.5y = 347.25
x + y = 111
multiply equation(ii) by 3.5
2.25x + 3.5y = 347.25
3.5x + 3.5y = 388.5
subtract equation(i) from equation(ii)
1.25x = 41.25
divide both sides by 1.25
x = 41.25 / 1.25
x = 33
Hence,
y = 111 - 33
y = 78
Therefore,
number of children ticket = 33
number of adult ticket = 78
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Simplify the expression.
(4²)6
6
(4³) 5 = 41
Answers
The simplified expression of (4²) x (4³) is 4⁵
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to evaluate the expression?The expression is given as
(4²) x (4³)
The base of the above expression are the same
i.e. Base = 4
This means that we can apply the law of indices
When the law of indices is applied, we have the following equation:
(4²) x (4³) = 4²+³
Evaluate the sum in the above equation
So, we have
(4²) x (4³) = 4⁵
Hence, the simplified expression of the expression given as (4²) x (4³) is 4⁵
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Possible question
Simplify the expression.
(4²) x (4³)
what is the maximal domain on the function x^2+8/x^2+4x-5?
Answers
Answer:
{x ∈ R: x ≠ -5 and x ≠ 1}.
Step-by-step explanation:
x^2+8/x^2+4x-5
= x^2+8 / (x - 1)(x + 5)
The denominator is zero when x = 1 or x = -5
So:
Domain is:
{x ∈ R : x ≠ -5 and x ≠ 1}.
Evalúe the limit. Show steps
Answers
After evaluating the limit we have came to find that the limit of [tex]\lim_{x\rightarrow \infty }-\frac{3x^4}{3x^2\ +4}[/tex] as x approaches ∞ is -∞
What is limit?A limit in mathematics is the value that a function, sequence, or index approaches as an input, or that an index approaches as an index. Limits are required in the definitions of continuity, derivatives, and integrals, which are basic to calculus and mathematical analysis.
The concept of a sequence limit is further generalised to encompass the concept of a topological network limit, as well as being strongly related to the concepts of limit and direct limit in category theory.
A limit of a function is typically expressed in formulas as
[tex]{\displaystyle \lim _{x\to c}f(x)=L,}[/tex]
To find the limit we will use L'Hôpital's Rule
Find the derivative
⇒ [tex]\lim_{x\rightarrow \infty }-\frac{3x^4}{3x^2\ +4}[/tex]
⇒ [tex]\lim_{x\rightarrow \infty }\frac{-12x^3}{6x + 0}[/tex]
⇒ [tex]\lim_{x\rightarrow -\infty }\frac{-12x^3}{6x }[/tex]
Evalúe ∞ as x
⇒ [tex]\frac{-12(\infty)^3}{6(\infty)} }[/tex]
⇒ -2 × ∞
⇒ -∞
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The sum of three numbers is 65. The first number is 5 more than the second. The third number is 2 times the second. What are the numbers
Answers
Let the three numbers be a, b, and c.
a+b+c=65
The second number is 3 times the first.
b=3a.
This makes the sum a+3a+c=65.
The third number is 3 times the second. Consequently this also means that the third number is 9 times the first.
c=9a
This makes the sum a+3a+9a=65
13a/13=65/13
a=5
b=3a
b=15
c=3b
c=45
5+15+45=65, so the numbers are 5, 15, and 45.
A researcher at the center of disease control and prevention is studying the growth of a certain bacteria he starts his experiment with 300 bacteria that grow at a rate of 20% per hour
Answers
After a certain time of n hours, the number of bacteria inside the lab will be, 300 ( 1 + 1/5n ) ^ n.
This is a problem with compound interest calculation. Here we have to calculate the number of bacteria present at the center of disease control and prevention after a certain time of n hours.
We can solve this using a few steps.
Let's assume that,
The time interval is n hoursThe growth rate is 20%.The period is 1 hour.So, the number of times this rate is applied is n/1 = n times.The principal number is 300 bacteriaAs we all know the formula for compound interest is,
A = P (1 + r/n) ^ nt
Where,
A = final amount
P = initial principal number = 300 bacteria
r = growth rate = 20% = 20/100
n = number of times growth applied per period
t = number of periods elapsed = 1 hour
So,
A = 300 ( 1 + 20/ 100n ) ^ n = 300 ( 1 + 1/5n ) ^ n
Hence we can conclude that after n hours the number of bacteria inside the lab will be, 300 ( 1 + 1/5n ) ^ n.
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Correct question :
A researcher at the center for disease control and prevention is studying the growth of a certain bacteria he starts his experiment with 300 bacteria that grow at a rate of 20% per hour. After n hours, what will be the number?
1000 yards is how many inches
Answers
Answer:
36000 inches
Step-by-step explanation: