The length of earthworm will be 4 cm after 4 hours. And the length is 14 cm after 49 hours.
What is meant by Proportion?Proportions are defined when two or more ratios are made to be equal to each other.
Two quantities are said to be directly proportional if a positive change in one quantity also lead to a positive change in the other quantity.
If a is proportional to b, we denote it as a ∝ b.
Given,
Length of an earthworm, l ∝ square root of the number of hours, n, which have elapsed since it's birth.
l ∝ √n
l = k √n, for some constant k.
If a worm is 2 cm long after 1 hour, we can write it as,
2 = k × √1
⇒ k = 2
So the proportionality constant is 2.
After 4 hours,
l = k √4
l = 2 × 2 = 4 cm
If the length is 14 cm,
14 = 2 √n
√n = 14 / 2
√n = 7
n = 7² = 49 hours
Hence the length of worm is 4 cm after 4 hours. It will take 49 hours to grow to a length of 14 cm.
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Let f(x) = x^2 − 2x + 1. Find the inverse function of f by identifying an appropriate restriction of its domain.
The inverse of f(x) is restricted to the domain x ≥ 1, since this is when[tex]x^2 − 2x + 1[/tex] is always greater than 0.
To find the inverse function of f(x), we must first determine the domain of f(x). We can do this by finding the values of x where f(x) is greater than or equal to 0.
We can start by setting f(x) to 0 and solving for x:
[tex]x^2 − 2x + 1 = 0[/tex]
[tex]x^2 − 2x + 1 − 1 = 0 − 1[/tex]
[tex]x^2 − 2x = -1[/tex]
(x − 1)(x − 1) = -1
x = 1
Therefore, the inverse of f(x) is restricted to the domain x ≥ 1, since this is when [tex]x^2[/tex] − 2x + 1 is always greater than 0.
The inverse of a function f(x) is a function that "undoes" f(x). In order to find the inverse of a function, the domain of the function must first be identified. This is done by solving f(x) = 0 and determining which values of x make the equation equal to 0.In the case of f(x) =[tex]x^2[/tex] − 2x + 1, the equation is equal to 0 when x = 1. This means that the inverse of f(x) is restricted to the domain x ≥ 1, since this is when [tex]x^2[/tex] − 2x + 1 is always greater than 0.Once the domain of the function is restricted, the inverse function can be found by switching the x and y values, and solving for the new equation. This process can be used to find the inverse of any function, as long as the domain is appropriately restricted.
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X-1
2x + 4
6
X
Determine the value of x in the
given diagram
The value of x in the diagram is given as follows:
x = 10.
What are similar triangles?Similar triangles share these two features:
Congruent angles, that is, angles that have the same measure.Proportional side lengths.Considering the similar triangles, the proportional relationship for the side lengths is given as follows:
6/(6 + x) = (x - 1)/(2x + 4).
Applying cross multiplication, the value of x is obtained as follows:
(x - 1)(x + 6) = 6(2x + 4)
x² + 5x - 6 = 12x + 24
x² - 7x - 30 = 0.
Factoring, we obtain the solutions are follows:
(x - 10)(x + 3) = 0.
x - 10 = 0 -> x = 10 -> value of x.x + 3 = 0 -> x = -3 -> extraneous, as a length cannot be negative.More can be learned about similar triangles at brainly.com/question/11920446
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g(n) = -1 +1 n f(n) = - 1 n-1
rectangle abcd is dilated by a scale factor of 1/4 to form a’b’c’d’. point t is the center of dilation and lies on segment ab as shown
The slope of A'B' is 0 and the length of A'B' is 1/4(5) = 1.25 units.
What is transformation?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
The line AB has the following coordinates.
A = (1, 4)
B = (6, 4)
The distance between AB is given as:
AB = √(6 - 1)² + (4 - 4)²
AB = √(5)²
AB = 5
The slope of AB = 0.
For the dilated rectangle the slope remains the same.
The slope of A'B' is 0 and the length of A'B' is 1/4(5) = 5/4 = 1.25 units.
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The correct question is:
a university is conducting research on ways to improve study habits and help students with lower grade point averages. it sends out a questionnaire to undergraduate students asking how they study and what they feel is the most productive way to study. what data collection method is the university using?
As the university is sending out questionnaires, the data collection method the university is using is a survey
The term "survey" describes the method of gathering data on a certain subject generally by employing questionnaires. In order to understand more about a certain topic, a survey is a method of data collection that involves asking a sample of respondents a number of questions. In the given case, the university is using a survey as a tool for gathering data.
Here, the institution is distributing a survey to undergraduate students to learn more about their study habits and what they believe to be the most effective method of studying. In order to efficiently gather data from a large number of participants quickly and effectively, surveys are frequently employed in research investigations.
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Find the approximate values of the five number summary for the data set represented by this box plot,
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
The Approximate values of the five number summary are ;
(i) the Minimum is 10 ,
(ii) the First quartile is 30 ,
(iii) the Third Quartile is 80 ,
(iv) the Median is 55 ,
(v) the Maximum is 100 .
The values of the data set are : {10 ,15 ,20 ,25 ,30 ,35 ,40 ,45 ,50 ,55 ,60 ,65 ,70 ,75 ,80 ,85 ,90 ,95 ,100 } ;
The Five number summary consists of the minimum , maximum , first quartile , third quartile and the median .
(i) the Minimum of the data set is = 10 ;
(ii) we split the data set into , 2 halves ;
that means ; {10 ,15 ,20 ,25 ,30 ,35 ,40 ,45 ,50 } and {60 ,65 ,70 ,75 ,80 ,85 ,90 ,95 ,100 } ;
the first quartile lies in the lower half : {10 ,15 ,20 ,25 ,30 ,35 ,40 ,45 ,50 } ;
So , first quartile (Q₁) = 30 ;
(iii) the third quartile (Q₃) lies in the upper half : {60 ,65 ,70 ,75 ,80 ,85 ,90 ,95 ,100 } ;
So , Q₃ = 80 ;
(iv) the total number of terms in the set is = 19 ;
So , the median is = tenth term = 55 ;
(v) the maximum of the data set is = 100 .
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Find −23−(−12). Write your answer as a fraction or mixed number in simplest form
The simplest fraction form of an expression, (- 2/3) - (-1/2) is equals to the -1/6.
A fraction is a number that represents a part of whole. It is expressed as quoitent, in which numerator is divided by denominator. For ex : 3/4 is a fraction, where 3 is numerator and 4 is denominator. We have an expression, (- 2/3) - (-1/2). This expression is substraction of two rational number and both are negative rational numbers. Using sign law of multiplication: - × - = + , i.e., multiplation of two negative numbers result positive number.
=> - 2/3 + 1/2
Both fraction has different denominators. Write as least common multiple of 2 and 3, i.e., LCM(2,3)= 6
=> ( -2 × 2 + 3 )/6
Simplify the expression as possible
=> (- 4 + 3 )/6
=> - 1/6
This is the needed simplified fraction. Hence, The solution in simplest fraction is -1/6.
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It is given that the volume of the cylinder and the cuboid are the same. Find the value of x and give your answer correct to two decimal places. Jawapan / Answer: 7 cm 8 cm [3 markah/ 3 marks] For Examine Use
who can help me pls
Step-by-step explanation:
the radius of the circular base is 7/2=3.5 cm
the surface of the base is πr^2=π*(3.5)^2=38.465
volume of the cylinder is surface of the base*high
38.465*30=1153.95
the cuboid volume=8^2*x=64x
64x=1153.95
x=1153.95/65=18.03 cm=18 cm
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The solution set of the system of equations is {(2,2), (4,-2)}
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
4x+2y =12------>(1)
Take some random values for x. Find the corresponding y values
Example: when x=0
(1) => 4(0)+2y = 12
=> 0+2y = 12
=> 2y =12
=> y= 12/2 = 6
The point obtained is (x,y) = (0,6)
This way, we get a line when we graph the equation 4x+2y =12.
Similarly, when we graph the equation y= -x² + 4x -2 , we get a parabola
Graph is attached:
In the graph, both graphs intersect at the points (2,2) and (4,-2)
Thus, the solution set of the system of equations is {(2,2), (4,-2)}
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please help
On a coordinate plane, the fountain is at (7, 5), the gardens are at (3, negative 5), the pond is at (negative 1, 7), and concessions are at (negative 7, 0). Your sister texted you, but the text cut off. Her text read, “Meet me at the trails located at (–2,”. Assuming that the trails are not located on the x-axis and given the content of her text, you can conclude that the trails must be located in either .
Answer: B quadrant 2 or quadrant 3
Step-by-step explanation:
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The solution to the given system of equation is (-2,7) and (2, -1).
What is system of equation?A system of equations are the set of equations where the solution for these equations are the intersecting point between the equations.
The graph denotes the two equations in which one is line and another one is parabola.
These system equation has two solutions.
That is, the point where the curve and line intersect is the solution for the system.
In this graph, the line and the curve intersects at two points,
i.e., (-2,7) and (2, -1).
Hence, the solution to the given system of equation is (-2,7) and (2, -1).
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The inn has ten rooms. One-half of the rooms are reserved for Friday. The rest are vacant. Of 12 more rooms are reserved for Friday, what will be the total number of occupied rooms on Friday?
Using, the mathematical inequalities, we can conclude that the total number of occupied rooms on Friday is 10.
Number of rooms in the inn = 10
It is given that One-half of the rooms are reserved for Friday which means 5 rooms were initially reserved on Friday.
Now, 12 more rooms are reserved for Friday.
So, the Initial reservation for Friday = 5
Final reservations for Friday = 5 + 12 = 17
Now, Final reservations for Friday(17) > Total number of rooms in the inn(10).
As the reservation exceeds the capacity of the hotel, 7 reservations will be cancelled and all 10 rooms will be occupied on Friday.
Hence, the total number of occupied rooms on Friday is 10.
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hello can anyone help me wiith this
Answer: Correct answer is -1
Step-by-step explanation:
In the linear equation y=2x+3, if x increases by 4 points, how much will y increase?
In the linear equation y=2x+3, if x increases by 4 points, the y will increase by 8 points.
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation's graph will always be a straight line. A linear equation is expressed using the linear equation formula. There are numerous ways to accomplish this. A linear equation, for instance, can be written in standard form, slope-intercept form, or point-slope form.
According to that,
y=2x+3 is the linear equation.
x will now rise by 4 points.
According to the data given, the calculation is as follows:
x = x + 4
So = 2(x)
= 2(x + 4) + 3
= (2x + 3) + 8
= y + 8
Eight points should be added to the y.
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3.37 examples of correlated variables. give an example of two variables in your field of study that are a. positively correlated b. negatively correlated
The length and width of a rectangle is Positively correlated variables and the base and height of a triangle is negativley correlated variables.
In mathematics, there are many examples of variables that can be positively or negatively correlated. Here are two examples:
a. Positively correlated variables: The length and width of a rectangle. If you increase the length of a rectangle, the width tends to increase as well. So, there is a positive correlation between the length and width of a rectangle.
b. Negatively correlated variables: The base and height of a triangle. If you increase the base of a triangle, you can keep the area the same by decreasing the height, and vice versa. So, there is a negative correlation between the base and height of a triangle.
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Can any one help with me please
For given geometrical shape, The angles which we need to find are ∠z=115° and y=21.
What are geometric shapes, exactly?
Geometric shapes are mathematical figures that reflect the shape of objects we see in our daily lives. Shapes are geometric shapes that have boundary lines, angles, and surfaces. There are several types of 2d and 3d shapes.
Shapes are also classified according to their regularity or homogeneity. A symmetrical regular form, such as a square or circle, is common. Asymmetry can take on irregular shapes. They're also referred to as organic forms or freeform shapes. A tree, for example, has an irregular or organic shape.
In plane geometry, two-dimensional forms are flat shapes and closed figures such as circles, squares, rectangles, rhombuses, and so on. In solid geometry, the three-dimensional shapes are the cube, cuboid, and sphere.
Now,
In given figure ∠z+65°=180° (Sum of two interior angles)
then ∠z=115°
and ∠z=∠6y-11 (vertically opposite angles)
6y-11=115
6y=126
y=21
Hence,
For given geometrical shape, ∠z=115° and y=21.
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Peter has a total of 22 nickels and dimes. There is a total of $1.80. Which of the following is a possible combination of coins that Peter has?
====================================================
Work Shown:
n = number of nickels
22-n = number of dimes
5n = value of the nickels in cents
10(22-n) = value of the dimes in cents
5n+10(22-n) = total value in cents
5n+10(22-n) = 180
5n+220-10n = 180
-5n+220 = 180
-5n = 180-220
-5n = -40
n = -40/(-5)
n = 8 is the number of nickels
22-n = 22-8 = 14 is the number of dimes
-----------------
Check:
8 nickels = 8*5 = 40 cents
14 dimes = 14*10 = 140 cents
8 nickels + 14 dimes = 40 cents + 140 cents = 180 cents = $1.80
8 nickels + 14 dimes = 22 coins total
The answers are confirmed.
Henry buys candy that costs $4 per pound. He will spend at most $20 on candy. What are the possible numbers of pounds he will buy?
Use p for the number of pounds Henry will buy
Write your answer as an inequality solved for p.
Answer:
5 pounds
Step-by-step explanation:
$20/$4 = 5 pounds
HOPE IT HELPS!
2. Order the following decimals from least to greatest.
0.439
0.394
0.441
0.531
0.342
Answer: 0.342 -> 0.394 -> 0.439 -> 0.441 -> 0.531
Step-by-step explanation:
0.342 -> 0.394 -> 0.439 -> 0.441 -> 0.531
If you convert the decimals into fractions out of a hundred, then it will be easily to keep going from least to greatest or greatest to least and soon you won't need help. Keep trying! :)
the density of zinc is 7.13 g/cm3. calculate the probability that a density measurement of the post-1982 pennies made using the caliper method is within 5% of the density of zinc. use the caliper data for the entire lab session to perform your calculation, and assume that the data fits a normal distribution.
As per the density the probability that a density measurement of the post-1982 pennies is 0.3565 g/cm3.
Density is an important physical property that can help identify materials. In this case, we are interested in the density of zinc and how it relates to the post-1982 pennies.
To calculate the probability of a density measurement within 5% of the density of zinc, we need to first determine the range of densities that fall within 5% of the zinc density.
The 5% range of the zinc density is calculated by multiplying the zinc density (7.13 g/cm3) by 5% (0.05), which gives us 0.3565 g/cm3.
The upper and lower limits of this range are then calculated by adding and subtracting this value from the zinc density, respectively.
The upper limit is 7.4865 g/cm3 (7.13 + 0.3565),
while the lower limit is 6.7735 g/cm3 (7.13 - 0.3565).
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The 3rd term of an arithmetic sequence is 1407 and the 10th term is 1183. Calculate the number of positive terms in the sequence.
Answer:
Let a be the first term and d be the common difference.
3rd term = 1407
a+2d = 1407 ------- 1
10th term = 1183
a+9d = 1183 ------- 2
By solving 1 and 2, a = 1471 and d = -32
so the general term T(n) = 1471 + (n-1)(-32)
= 1471 - 32n +32
= -32n + 1503
-32n + 1503 [tex]\geq[/tex] 0
-32n [tex]\geq[/tex] -1503
n [tex]\leq[/tex] 46.96875
The number of positive terms = 46
I need some help I'm confused
PLEASE GIVE BRAINLIEST!
thank you and have a good day :)
Answer:
b^5
Step-by-step explanation:
When you are multiplying exponents with the same letter base, you simply just add the exponents.
for example, x^2 * x^3 = x^5
another example, y^6 * y^8 = y^14
An expression equivalent to b^3 * b^2 would be b^5
I hope this helps!
Please read the photo
The average rate of change is 2.The rate of change of the function is its gradient or slope.
How is the average rate determined?To get the average rate of change, divide the change in y-values by the change in x-values.Knowing the average rate of change is necessary to detect changes in observable metrics like average speed or average velocity.
What is the average change rate?It displays the typical rate of change of the function for each unit during that time. It is determined using the slope of the line connecting the ends of the interval in the function graph.
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A.seqn T5 = 20, T₂² = T₁ T4 Find the order of the 1st term whose value is greater than 106.
The order of the first term whose value is greater than 106 is the smallest integer greater than 1 + [log(0.5)(T₁) - log(0.5)(212)].
How did we get the value?Using the given information, we can find the common ratio of the geometric sequence A.
First, we can use the equation T₂² = T₁ T4 to find T4. Substituting n = 4, we get:
T₂² = T₁ T4
20² = T₁ T4
T4 = 400/T₁
Next, we can use the equation T5 = 20 to find T₁r⁴:
T5 = T₁r⁴
20 = T₁r⁴
We can now substitute T4 in terms of T₁ in the equation above:
20 = T₁r⁴
20 = T₁(400/T₁)r⁴
20 = 400r⁴
r⁴ = 1/20
Therefore, the common ratio r = (1/20)^(1/4) = 0.5.
To find the order of the first term whose value is greater than 106, we can use the formula for the nth term of a geometric sequence:
Tn = T₁r^(n-1)
We want to find the smallest value of n such that Tn > 106. Substituting r = 0.5 and rearranging, we get:
T₁(0.5)^(n-1) > 106
T₁ > 212(0.5)^(1-n)
Since T₁ > 0, we can take the logarithm base 0.5 of both sides:
log(0.5)(T₁) < log(0.5)(212) + (n-1)
Solving for n, we get:
n > 1 + [log(0.5)(T₁) - log(0.5)(212)]
Therefore, the order of the first term whose value is greater than 106 is the smallest integer greater than 1 + [log(0.5)(T₁) - log(0.5)(212)].
Note that the exact value of this order depends on the value of T₁, which was not given in the original problem statement.
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There are 342 boys and girls at the canteen. After 51 boys and an equal number of girls as boys returned to their classroom, there were three times the number of boys than girls in the canteen. How many boys were there in the canteen at first?
Let b be the initial number of boys, and let g be the initial number of girls. We know that the total number of students at the canteen is 342, so:
b + g = 342
After 51 boys and an equal number of girls returned to their classroom, there were three times the number of boys than girls in the canteen. This means that the number of girls remaining in the canteen is:
g - 51
And the number of boys remaining in the canteen is:
b - 51
Since there were three times as many boys as girls, we can write:
b - 51 = 3(g - 51)
Now we have two equations and two unknowns. We can solve for one variable in terms of the other in the first equation, and substitute into the second equation:
b + g = 342
g = 342 - b
b - 51 = 3(g - 51)
b - 51 = 3(342 - b - 51)
b - 51 = 3(291 - b)
b - 51 = 873 - 3b
4b = 924
b = 231
So there were 231 boys in the canteen at first. To check our answer, we can substitute into the first equation:
b + g = 342
231 + g = 342
g = 111
Therefore, there were 231 boys and 111 girls in the canteen at first.
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how many pattern block triangles would create 2 hexagons
Answer:
Step-by-step explanation:
twelve triangles make 2 hexagons, which means there are 12 groups of in 2
100 is what percent less than 110?
Answer:
9.09%
(⬇Read my notes⬇)
Notes:
Hi there,
I know this answer is going to be incorrect on RSM, but it is the correct answer. Everyone has been saying that it's 9.09%, and I even found that as well. So I don't know why RSM is saying that it's wrong, because it should be correct.
- 201600823
A parabola can be drawn given a focus of (0, 4) and a directrix of y =
be said about the parabola?
Answer: A parabola can be defined as the set of all points that are equidistant from a focus and a directrix. Based on the information provided, the focus of the parabola is (0, 4) and the directrix is y =.
The parabola will open upwards or downwards depending on the location of the focus and the directrix. Since the focus is at (0, 4), and the directrix is at y =, the parabola must open upwards. The axis of symmetry of the parabola will pass through the focus and will be perpendicular to the directrix.
Without more information, it is not possible to fully determine the shape and equation of the parabola. The shape of the parabola and its equation can be found by using the focus and directrix and other information, such as the vertex or a point on the parabola.
Step-by-step explanation:
Which expression is equivalent to
O
13
√√2
√√√/2
8-3√11 is the expression which is equivalent to √11+√64-2√44.
What is Expression?The combination of variables, numbers and operators is called as expression.
The given expression is √11+√64-2√44
Square root of 11 plus square root of sixty four minus two square root of forty four.
Let us find the equivalent expression of √11+√64-2√44
The expressions in which the expressions look different but have save same value are Equivalent
√11+√64-2√44
√11+8-2√4×11
√11+8-4√11
Combine like terms
8-3√11
Hence, 8-3√11 is the expression which is equivalent to √11+√64-2√44.
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Which expression is equivalent to √11+√64-2√44
A. 8-4√44
B. 5√3-4√11
C. 8-3√11
Suppose that you plan on taking a summer job selling magazine subscriptions. The magazine company will pay you 1.50 for selling the first subscription. For each additional subscription sold, the magazine company will pay you 20 cent more than what was paid for the previous subscription. How much will you earn by selling magazine subscriptions?
As per unitary method, you'll earn $9.50 by selling five magazine subscriptions.
The unitary method is a method of finding a single value of a quantity or unit, given the value of a unit of the same quantity. In this case, we need to find out how much money you'll earn by selling magazine subscriptions.
We know that for selling the first subscription, the magazine company will pay you $1.50. For each additional subscription sold, the magazine company will pay 20 cents more than what was paid for the previous subscription.
Let's use the unitary method to find out how much you'll earn by selling the second subscription.
The magazine company pays 20 cents more than $1.50 for the second subscription. Therefore, the payment for the second subscription is
=> $1.50 + $0.20 = $1.70.
Using the same method, we can calculate the payment for the third subscription, which is
=> $1.70 + $0.20 = $1.90.
Similarly, we can use the unitary method to calculate the payment for the fourth, fifth, and so on, subscriptions.
By adding up the payments for each subscription, we can calculate your total earnings. Let's assume you sold five subscriptions.
The payment for the first subscription is $1.50, for the second subscription, it's $1.70, for the third subscription, it's $1.90, for the fourth subscription, it's $2.10, and for the fifth subscription, it's $2.30.
Total earnings = $1.50 + $1.70 + $1.90 + $2.10 + $2.30 = $9.50.
Therefore, you'll earn $9.50 by selling five magazine subscriptions.
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