This compound inequality is the range of numbers that Penelope might be thinking of;
Compound inequalities are inequalities that have been joined by the words “and” or “or.” For example: − 2 < x ≤ 5 Read, “ is greater than -2 and less than or equal to 5.” x ≥ 3 or Read, “ is greater than or equal to 3 or less than -4.” Notice that both of these inequalities have two inequality signs.
3x + 5 > -1 and 3x + 5 < 35
This compound inequality is the range of numbers that Penelope might be thinking of; the first inequality shows that the number must be greater than -1, and the second inequality shows that the number must be less than 35.
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If F and f are differentiable function such that F(x) = integral^x_0 f(t) dt and if F(a) = -2 and F(b) = -2 where a < b which must be true? a. f(x) = 0 for some x such that a < X < b b. f(x) < 0 for all X such that a < X < b c. f(x) = 0 for some X such that a < X < b d. f(x) > 0 for all X such that a < X < b e. f(x) less than or equal to 0 for all X such that a < X < b
By differentiable polynomial f(x) = 0 for some x such that a < X < b , A is correct
What is an example of a differentiable function?
If a function's derivative is present at every location inside its domain, the function is said to be differentiable. If a function f(x) is differentiable at x = a, in particular, then f′(a) exists in the domain.
Let's examine a few instances of differentiable polynomial and transcendental functions, such as f(x) = x4 - 3x + 5.
A is correct
F receives two equal values in different places .
consider the line between them .
it cannot be in a coustant ascent nor descent, since it must return to the minimal value .
therefore, A, either coutant or has an surprising and descending area ,
thus from Fermat's rule the derivate must be equal to zero .
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f the current population size is x individuals, what fraction of the resources are they using collectively?
The fraction of resources used collectively by X individuals can be represented as X/R, where R represents the total resources available. The fraction of resources not being used is represented as (R-X)/R. The per-capita growth rate can be represented as dX/dt = kX, where k is the proportionality constant. The differential equation for the population's size is dX/dt = kX.
A detailed explanation:
a) If the current population size is X individuals, then the fraction of resources they are using collectively can be calculated as X/R, where R represents the total resources available. This calculation gives us the proportion of resources used by X individuals relative to the total resources available.
b) To calculate the fraction of resources not being used, we subtract the fraction of resources used by X individuals from 1. So, the fraction of resources not being used is (R-X)/R.
c) The per-capita rate of change of X can be represented as dX/dt = kX, where k is the proportionality constant. This equation states that the rate of change of X (dX/dt) is proportional to X and the constant of proportionality is k.
d) To convert the equation into a differential equation for the population's size, we simply make X' stand alone on the left-hand side of the equation. So, the differential equation for the population's size becomes dX/dt = kX.
e) This differential equation states that the rate of change of X (dX/dt) is proportional to X and the constant of proportionality is k. This equation can be used to model the growth of a population over time and to understand the relationship between the population size and the rate of change of the population.
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Complete questin:
If the current population size is X individuals, what fraction of the resources are they using collectively? c) In the same situation, what fraction of the resources are not being used? d) The per-capita rate of change of X can be written as 7%. The key assumption mentioned above says that this quantity is pro- portional to the expression you wrote down in part (c). Call the proportionality constant 1', and write an equation for the per-capita growth rate. e) Convert this equation into a differential equation (change equa- tion) for the population's size. (Just make X' stand alone on the left-hand side of the equation.)
What is the name of the relationship when a function of the form y = abx is
used to fit the data?
The formula for an exponential function is y = abx, where an is the value of y at x = 0 and b is the growth factor over each unit of time.
What relation also serves as a function?Consider the connection to be a function if each input value results in just one output value. Do not classify the relationship as a function if any input value results in two or more outputs.
When a function of the type y = a bX is used to fit the data, what is the name of the relationship?Simple linear regression uses the equation Y = a + bX to connect X and Y. Both quantify the link between two numerical variables, including its intensity and direction.
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Y = abx is the equation for an exponential function, where b is the growth factor per unit of time and an is the value of y at x = 0.
What is mathematical function?A mathematical function is a rule that assigns a dependent variable a value based on one or more independent variables having the specified values. Several formats, including a table, a formula, or a graph, can be used to express a function. An association between members of two sets that is made specifically by a relation is called a function. Formally, an object that has every being uniquely associated with an object is said to be a function from to. A function, then, is a many-to-one (or occasionally, a one-to-one) relation. A function is analogous to a machine. With that machine, you put something in, and it produces something. If f(2)=4, we can infer that the machine (f) will produce 4 if we enter 2 into it.To learn more about mathematical function, refer to:
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In isosceles ABC, AC is the base, Points D. Band
Fare the midpoints of AB. A and BC
respectively. The length of BD is 13 inches and
ZBFD 65. Find each measure
a. A
b. DE
G. AD
d. M EDF
According to the question
Given an isosceles triangle, ABC with AC as its base, points D and F are the midpoints of AB and BC, respectively. Let's refer to the length of BD as x.
a. In a triangle sum of all the sides is equals to 180 degrees.
So the following formula may be used to get the value of angle A:
∴ A = 180 - (2 * ZBFD)
⇒ A = 180 - (2 * 65/2)
⇒ A = 115 degrees.
b. The Pythagorean theorem,i.e.,
Perpendicular^2 + base^2 = Hypoteneuse^2
can be used to get the length of DE:
∴ (AD)^2 = x^2 + (x/2)^2
⇒ DE = AD/2
⇒ DE = √(x^2 + (x/2)^2) / 2
⇒ DE = √((13^2) + (13/2)^2) / 2
⇒ DE = √338 / 4
c. The Pythagorean theorem,i.e.,
Perpendicular^2 + base^2 = Hypoteneuse^2
can be used to determine the length of AD:
∴ (AD)^2 = x^2 + (x/2)^2
⇒ AD= √(13^2 + (13/2)^2)
⇒ AD = √338 / 2
d. We utilize the fact that the angles at a triangle's midpoints are half its angle measurements to get the measure of angle EDF.
EDF = A/2
⇒ EDF = 115/2
⇒ EDF = 57.5 degrees
The measure of each of the following are as follows :
the measure of A = 115 degree.
the measure of DE = √338/4.
the measure of AD = √338/2.
the measure of DEF = 57.5 degrees.
According to the question
Given an isosceles triangle, ABC with AC as its base, points D and F are the midpoints of AB and BC, respectively. Let's refer to the length of BD as x.
a. In a triangle sum of all the sides is equals to 180 degrees.
So the following formula may be used to get the value of angle A:
∴ A = 180 - (2 * ZBFD)
⇒ A = 180 - (2 * 65/2)
⇒ A = 115 degrees.
b. The Pythagorean theorem,i.e.,
Perpendicular^2 + base^2 = Hypoteneuse^2
can be used to get the length of DE:
∴ (AD)^2 = x^2 + (x/2)^2
⇒ DE = AD/2
⇒ DE = √(x^2 + (x/2)^2) / 2
⇒ DE = √((13^2) + (13/2)^2) / 2
⇒ DE = √338 / 4
c. The Pythagorean theorem,i.e.,
Perpendicular^2 + base^2 = Hypoteneuse^2
can be used to determine the length of AD:
∴ (AD)^2 = x^2 + (x/2)^2
⇒ AD= √(13^2 + (13/2)^2)
⇒ AD = √338 / 2
d. We utilize the fact that the angles at a triangle's midpoints are half its angle measurements to get the measure of angle EDF.
EDF = A/2
⇒ EDF = 115/2
⇒ EDF = 57.5 degrees
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Work out:
2 x 2.2 x 10^12 × 1.5 × 10^12/
2.2 x 10^12 - 1.5 x 1012
Give your answer in standard form correct to 3 significant figures.
The index forms is expressed as 9. 40 × 10¹²
What are index forms?Index forms are simply described as representation of a number in the form of an exponential expression or a single number that is raised to a number or variable.
Other names for index forms are standard form and scientific notation.
It also explains how many times a number contains itself.
From the information given, we have that;
2 x 2.2 x 10^12 × 1.5 × 10^12/2.2 x 10^12 - 1.5 x 1012
Represented as;
2(2.2) × 10¹² × 1.5 × 10¹²/ 2.2 × 10¹² - 1. 5 × 10¹²
We can add or subtract the index forms because they have the same exponential value, we have;
4.4(1.5)× 10²⁴/0.7 × 10¹²
Find the quotient
9. 4 × 10¹²
Hence, the value is 9. 4 × 10¹²
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the multiplication rule is used to calculate what type of probability?
The multiplication rule is used to calculate joint probability.
Joint probability is the probability of two events happening simultaneously. The multiplication rule states that the probability of two independent events happening together is equal to the product of their individual probabilities.
The formula can be expressed as: P(A and B) = P(A) x P(B). For example, if the probability of event A is 0.3 and the probability of event B is 0.4, then the joint probability of both events happening together is 0.3 x 0.4 = 0.12. The multiplication rule is only applicable for independent events, meaning that the occurrence of one event does not affect the probability of the other event.
When events are dependent, the calculation of joint probability is more complicated and may involve conditional probability.
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(2n^4)^-2 simplify (positive exponents)
Step-by-step explanation:
The expression (2n^4)^-2 can be simplified as follows:
(2n^4)^-2 = 1 / (2n^4)^2
Using the rule that (a^b)^c = a^(bc), we can simplify further:
= 1 / (2^2 * n^4 * 2)
= 1 / (4 * n^4 * 2)
= 1 / (8 * n^4)
So (2n^4)^-2 = 1 / (8 * n^4) in simplified form using positive exponents.
This question has two parts. First, answer Part A. Then, answer Part B.
Part A
Below are two dot plots containing sample means from the same population
How many samples are represented in each plot?
There are __ samples in both plot A and plot B. Each dot represents one sample.
The number of samples for each dot plot is given as follows:
32.
What is shown by the dot plot?The dot plot shows the number of times that each measure appears in the data-set.
Hence the dot plot in this problem shows the number of samples that had means of 10, 20, 30, 40, 50, 60, 70, 80 and 90.
Hence, the total number of samples is obtained by the number of dots in each of the dot plots, which is of 32, hence the sentence is completed as follows:
There are 32 samples in both plot A and plot B. Each dot represents one sample.
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given the function f ( x ) = x − 4 x 2 − 7 x 12 . find the value(s) of x where the function is not continuous. if there is more than one answer, then list them separated by a comma.
There is point i.e., value of x where the function f(x) = x³ - 4x² - 7x +12 is not continuous.
Consider the polynomial function f(x) = x³ - 4x² - 7x +12
As we know if a function f be a function defined on an open interval containing point a where t a ∈ R be a constant, a function f is continuous at a if lim_(x→a) f(x) = f(a).
Here, the domain of polynomial function f(x) = x³ - 4x² - 7x +12 is set of all real numbers, as the function is well defined for all real values of x.
We know that every polynomial function is continuous in their domain.
This means, the polyomial function f(x) = x³ - 4x² - 7x +12 is continuous on set of all real numbers.
Therefore, there is no value of x where the polynomial function f(x) = x³ - 4x² - 7x +12 is not continuous.
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What is the interquartile range of the set of data this box-and-whisker plot represents
The interquartile range of the data represented in the box-and-whisker plot is given as follows:
IQR = 3.
How to obtain the interquartile range?The measures represented in the box-and-whisker plot are given as follows:
Minimum value of 12.First quartile of 15.Median of 16.Third quartile of 18.Maximum value of 20.The interquartile range is calculated as the difference between the third quartile and the first quartile.
Hence the correct value is given as follows:
IQR = 18 - 15
IQR = 3.
Meaning that the last option is the correct option.
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10 ≤ 2x ≤ x+9
I need an explanation in how to solve this step by step?
The solution to the given inequality, 10 ≤ 2x ≤ x+9, is 5 ≤ x ≤ 9
Solving Linear inequalitiesFrom the question, we are to solve the given inequality
The given inequality is
10 ≤ 2x ≤ x+9
Then,
We can write that
10 ≤ 2x and 2x ≤ x+9
First, solve the inequality 10 ≤ 2x
10 ≤ 2x
Divide both sides by 2
5 ≤ x
Now, solve
2x ≤ x + 9
2x - x ≤ 9
x ≤ 9
Thus,
5 ≤ x and x ≤ 9
5 ≤ x ≤ 9
Hence, the solution is 5 ≤ x ≤ 9
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Let b ≠1 and consider the integral ∫(6x-9)dx where b is some real number.
a) What value of b will make this integral equal to 0?
If b ≠1 and integral [tex]\int\limits^b_1[/tex](6x-9)dx where b is some real number , then value of b that make this integral equal to 0 is b = 2 .
The integral is given as [tex]\int\limits^b_1[/tex](6x-9)dx ;
Since , at the value of (b) the given integral is 0.
So , evaluate the integral as :
⇒ [tex]\int\limits^b_1[/tex](6x-9)dx = 0 ;
⇒ [3x² - 9x]₁ᵇ = 0 ;
Simplifying further ,
we get ;
⇒ 3b² - 9b -3(1²) +9(1) = 0 ;
⇒ 3b² -9b +6 = 0 ;
⇒ b² - 3b +2 = 0 ;
On writing the above quadratic equation in factor form ,
we get ;
⇒ (b - 1)(b - 2) = 0 ;
that means b = 1 or b = 2 , but it given that b ≠ 1 ,
So , b = 2 .
Therefore , value of b = 2 , to make the integral 0 .
The given question is incomplete , the complete question is
Let b ≠1 and consider the integral [tex]\int\limits^b_1[/tex](6x-9)dx where b is some real number.
What value of b will make this integral equal to 0 ?
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. STATE YOUR ASSUMPTION Breelyn is making cookies using a cookie cutter in the shape of a parallelogram. What are the perimeter and area of each cookie? Explain any assumptions that you make. Round your answers to the nearest hundredth, if necessary. order of get
The perimeter and area of a parallelogram can be determined if the length and width are known.
How to explain the perimeterThe perimeter of a shape is simply the total length of the boundary that the shape has. It should be noted that in this case, it's gotten by adding all the length that the shape has.
Without additional information, it is not possible to determine the exact perimeter and area of each cookie. Assuming the length and width are given, we can use the formula for the perimeter of a parallelogram (2 times the sum of the length and width) and the formula for the area of a parallelogram (length times width) to find the desired quantities.
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Help and write out the steps pls!???
f(x) = x + 4. q(x) = 12x1
F(g(x))
The composite result function of (f( g(x) ) in the given functions f(x) = x+4 and g(x) = 12x + 1 is 12x + 5.
What is the composite result function of f(g(x)) in the given function?A function is simply a relationship that maps one input to one output.
Given that;
f(x) = x + 4g(x) = 12x + 1f(g(x)) = ?First, we set up the composite result function f(g(x))
f(x) = x + 4
f( g(x) ) = g(x) + 4
f( 12x + 1 ) = ( 12x + 1 ) + 4
Simplify
f( 12x + 1 ) = 12x + 1 + 4
Add 1 and 4
f( 12x + 1 ) = 12x + 5
Therefore, the composite function f( 12x + 1 ) is 12x + 5.
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Which of the following equations have infinitely many solutions? Choose all answers that apply: Choose all answers that apply: (Choice A) A 76 � + 76 = 76 � + 76 76x+76=76x+7676, x, plus, 76, equals, 76, x, plus, 76 (Choice B) B 76 � + 76 = − 76 � + 76 76x+76=−76x+7676, x, plus, 76, equals, minus, 76, x, plus, 76 (Choice C) C − 76 � + 76 = 76 � + 76 −76x+76=76x+76minus, 76, x, plus, 76, equals, 76, x, plus, 76 (Choice D) D − 76 � + 76 = − 76 � + 76 −76x+76=−76x+76
The equations have infinitely many solutions
-76x+76=-76x+76
76x + 76 = 76x +76
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
When certain requirements are met, an equation can have an unlimited number of solutions.
We have the equation
76x+ 76 = -76x+76
So, 152x = 0
x = 0
and, -76x+76=-76x+76
0= 0
and, 76x + 76 = 76x +76
0 = 0
and, -76x + 76x = 76x - 76
-152x = -152
x= 1
So, the equation with 0=0 shows infinite many solution which are
-76x+76=-76x+76
76x + 76 = 76x +76
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There are 2 red, 5 green, 3 blue and 4 white point on a circle. Find the number of line egment which have endpoint of different color at the given point
The number of those line segments which have endpoints of different colors is 40.5.
What is permutation?A permutation of a set in mathematics is, broadly speaking, the rearrangement of its elements if the set already has an ordered structure into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are arranged in a linear or sequential order. For instance, the set A=1,6 has a permutation of 2, which is 1,6,1. There is no other way to organise the components of set A, as you can see.Given data :
There are 2 red, 5 green, and 3 blue points on a circle.
There are different colored endpoints on each line segment that starts at a red point and travels to either a green point or a blue point.
There are 2 red points and 7 segments from each of them, making a total of 14 segments.
There are different colored endpoints on each line segment that leaves at a green point and travels to either a red or blue point.
There are 5 green points and 8 segments from each, for a total of 40 segments.
There are different colored endpoints on each line segment that leaves at a blue point and travels to either a green point or a red point.
Each blue point has 9 segments, and there are a total of 3 blue points.
Add all the ways = 14 + 40 + 27
= 81 segments.
Number of segment = 81/2 = 40.5 Segments
Thus, the number of those line segments which have endpoints of different colors is 40.5.
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which two parent trigonometric functions have a period of π and a range that consists of the set of all real numbers? (select all that apply.)
a. sine
b. cosine
c. tangent
d. cosecant
e. secant
f. cotangent
The cosecant, secant, and cotangent functions are defined as the reciprocals of the sine, cosine, and tangent functions, respectively which have two parent trigonometric functions have a period of π and a range that consists of the set of all real numbers.
These functions also have a period of 2π and their ranges depend on the range of the corresponding parent function.
Therefore, correct answer will be a. sine, b. cosine and c. tangent.
The trigonometric functions are mathematical functions used to describe relationships involving lengths and angles of triangles. These functions include sine, cosine, tangent, cosecant, secant, and cotangent. Each of these functions has its own unique properties, including period and range.
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What does it mean if the graph is skewed to the right?
If the histogram is skewed to the right, the graph's peak will be to the left of the center.
What happens when the distribution is skewed to the right?The peak of the graph is located to the left of the center if the histogram is skewed to the right. The frequency of observations is less frequent on the right side of the graph than it is on the left.
The mean is typically higher than the median when the distribution is right-skewn. We anticipate that the mean and median will be roughly identical in value in symmetric distributions. There is a significant link between the distribution's form and how the mean and median are related.
A positively skewed distribution, sometimes referred to as a right-skewed distribution, is a type of distribution where the majority of values are concentrated around the left tail and the right tail is longer. The distribution that leans positively is the exact opposite of one that leans negatively.
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A rectangular flag i 40 centimeter by 72 centimeter. What are the dimenion of a cale drawing of the flag uing the cale 1:8?
320 cm by 576 cm
5 cm by 9 cm
4 cm by 7. 2 cm
1. 8 cm by 11. 11 cm
The dimensions of a scale drawing of a rectangular flag that is 40 centimeters by 72 centimeters using the scale 1:8 is 4 cm by 7.2 cm. Option C.
This is because a 1:8 scale means that for every actual unit of length, the corresponding length on the scale drawing is 8 times smaller.
Therefore, in order to find the dimensions of the scaled drawing of the flag, we must divide the actual dimensions (40 cm by 72 cm) by 8. The result is 4 cm by 7.2 cm.
It is important to make sure that you use the correct scale when attempting to determine the dimensions of a scaled drawing. If you use a different scale than the one intended, your result will be incorrect.
For example, if you use a 1:4 scale instead of a 1:8 scale, you will end up with a scaled drawing that has dimensions of 20 cm by 36 cm, which is double the correct answer.
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Select all of the situations that could be represented by two numbers whose product is equal to
−
20
.
A.
The change in the balance of a checking account after a man spends
$
4
a day for five days.
B.
The miles traveled after a sailor makes two trips of
10
miles each.
C.
The total number of pages read if
8
students each read two and a half pages.
D.
The difference in altitude after a kite loses altitude four times by
5
feet each time.
E.
The amount of sugar in a recipe if it calls for
2
cups per pitcher and Martha is making
10
pitchers.
F.
The total charge created from twenty electrons each with a
(
−
1
)
charge.
The situations that could be represented by two numbers whose product is equal to 20 are options A, B, D, E and F
How to find the situation?Recall that the product of two numbers is the result you get when you multiply them together/
The Factors of 20 are: 1,2,4,5,10,20
From the analysis,
Option A: The change in the balance of a checking account after a man spends $4 a day for five days. = $4*5 = 20
Option B: The miles traveled after a sailor makes two trips of 10 miles each. = 2*10 = 20
Option D: The difference in altitude after a kite loses altitude four times by 5 feet each time.
⇒4*5 = 20
Option E: The amount of sugar in a recipe if it calls for 2 cups per pitcher and Martha is making 10 pitchers.
⇒2*10 = 20
Option F: The total charge created from twenty electrons each with a 1 charge
⇒1*20 = 20
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Is or Is Not? what is the correct answer?
The ordered pair (-2, 1) is not a solution
How to determine if the ordered pair is a solution or notFrom the question, we have the following parameters that can be used in our computation:
6x + 5y = -7
2x - 4y = -8
The ordered pair is given as
(-2, 1)
Substitute the known values in the above equation, so, we have the following representation
6(2) + 5(-1) = -7 == false
The above equation is false
Hence, the ordered pair is not a solution
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help please.........
The required quotient of the given expression -1/8 × 2/3 is given as -1/12.
What is simplification?The procedure in mathematics to work and crack the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Given expression,
= -1/8 × 2/3
= -1/ [4×3]
= -1/12
Thus, the needed quotient of the given expression -1/8 × 2/3] is given as -1/12.
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How do you convert 140 Kilogram (kg) to Pound (lb)?
180 lb to 140 kg conversion. The base unit of weight in the metric system is the kilograms, sometimes known as the kilograms.
How do you convert 1b to kg?Convert 140 Kilograms to Pounds.
kg lb
140.00 308.65
140.01 308.67
140.02 308.69
140.03 308.71
Basically, to convert cost per kg to cost per lb, take the price for the kilogramme and divide it by 2.2046 to get the price for the pound. Fundamentally, 1 kilogramme equals 2.2046 pounds (there is a longer decimal position, but I shorten it to 2.2046).
Mathematical and technical fields frequently need to convert between kilogrammes and pounds; fortunately, this is a simple process. The majority of the time, all you have to do to convert is multiply the number of kilograms by 2.2 to get the number of pounds. Generally speaking, there are 2.2046 pounds in every kilograms.
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S. The table below shows the relationship between the number of hours a student studied and their
grade on a certain test.
100
80
Test Grade
888
60
20
0246 8
Hours Studying
a) Find the line of best fit
b) Estimate the grade for a student that did not study at all:
a) The line of best fit is y = 10x + 60
b) the grade for a student that did not study at all is 0.
What is the slope?
The slope of a line represents the change in the dependent variable (y) for a unit change in the independent variable (x). In this case, the slope of the line of best fit represents the average change in the test grade for a one hour increase in studying. To find the slope, you can use the formula:
m = (Σxy - (Σx)(Σy)/n) / (Σx² - (Σx)²/n)
a) The line of best fit is a line that best approximates the relationship between two variables. To find the line of best fit for this data, we can use the least squares method to minimize the sum of the squares of the differences between the observed data points and the line. The equation of the line of best fit is y = mx + b, where m is the slope and b is the y-intercept. The slope can be calculated as (Σxy - (Σx)(Σy)/n) / (Σx² - (Σx)²/n), and the y-intercept as (Σy - m(Σx)) / n, where n is the number of data points.
(2, 60) and (5, 90)
The slope is
y2 - y1 = m(x2 - x1)
90 - 60 = m(5-2)
30 = 3m
m = 10
Slope line is
y - 60 = m(x - 2)
y = 10x - 20 + 80
y = 10x + 60
b) To estimate the grade for a student that did not study at all, we can use the line of best fit and plug in x=0 for the number of hours studying. The estimated grade for a student that did not study at all would be the y-intercept of the line,
which represents the expected test grade when
x = 0
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Complete question:
Can anyone solve 21x>5y+49x>2y>2-28x>2y for me?
A point in the solution of the system of inequalities is (2, 0.5)
How to determine the solution to the inequalityFrom the question, we have the following parameters that can be used in our computation:
21x>5y+49x>2y>2-28x>2y
Express properly
So, we have the following representation
21x > 5y+49
x > 2y
2 - 28x > 2y
Next, we plot the graphs of the inequality expressions on a plane
(See attachment for the graph)
The shaded region represent the solution
And a point in this region is (2, 0.5)
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The distribution of ph levels for all community swimming pools in a large county is approximately normal with mean 7. 5 and standard deviation 0. 2. According to swimming pool studies, the safest ph levels for water in swimming pools are between 7. 2 and 7. 8. (a) one community swimming pool in the county will be selected at random. What is the probability that the selected pool has a ph level that is not considered safe?.
The probability that the selected pool has a ph level not considered safe is approximately 0.22 (or 22%). This can be calculated using the cumulative probability of a normal distribution with a mean of 7.5 and a standard deviation of 0.2.
1. Calculate the z-score for the lower limit of 7.2: (7.2 - 7.5) / 0.2 = -1.5
2. Calculate the z-score for the upper limit of 7.8: (7.8 - 7.5) / 0.2 = 1.5
3. Calculate the cumulative probability of the lower limit: P(-1.5) = 0.0668
4. Calculate the cumulative probability of the upper limit: P(1.5) = 0.9332
5. Calculate the probability that the selected pool has a ph level not considered safe: P(not safe) = 1 - (P(1.5) - P(-1.5)) = 0.22
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You have a total of 200 Coins, Consisting of nickels and dimes. The total value of the 200 Coins is $16.85. How many of each do you have?
Answer:
Below
Step-by-step explanation:
n = # nickels value = 5n
(200-n) = # dimes value = 10(200-n)
summed, these equal 1685
5n + 10(200-n) = 1685
5n + 2000 -10 n = 1685
-5n = -315
n = 63 then dimes = 137
evaluate the following. give your answers as exact fractions. 2 x2−4 dx −2 = 2 x2−4 dx −2 =
After evaluating the given equation ∫(x²-4)dx, we get -32/3.
Integration is the process of finding the area of the region under the curve. This is done by drawing as many small rectangles covering up the area and summing up their areas. The sum approaches a limit that is equal to the region under the curve of a function. Integration is the process of finding the antiderivative of a function. If a function is integrable and if its integral over the domain is finite, with the limits specified, then it is the definite integration. If F(x) is a particular anti-derivative of f(x) on an interval I, then every anti-derivative of f(x) on I is given by ∫ f(x) dx = F(x) + C.
Here, ∫ f(x) dx represents the whole class of integral.
C is the arbitrary constant, and all the antiderivatives of f(x) on I can be obtained by assigning a particular value to C.
Here f(x) is the integrand,
The variable x in dx is called the integrator and the whole process of finding the integral is called the integration. The ∫ sign stands for the sum.
The given equation is:
∫(x²-4)dx for interval (-2,2).
Integrate the above equation, we get
∫(x²-4)dx = x³/3 -4x +c
Now, solving this for the interval (-2,2), we get
= (2³/3 - 4×2) - ((-2)³/3 - 4×-2)
= (8/3)-8 + 8/3 - 8 = -32/3
Thus, after evaluating the given equation ∫(x²-4)dx, we get -32/3.
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when commercial aircraft are inspected, wing cracks are reported as nonexistent, detectable, or critical. the history of a particular fleet indicates that 69% of the planes inspected have no wing cracks, 21% have detectable wing cracks, and 10% have critical wing cracks. five planes are randomly selected. (round your answers to three decimal places.) (a) find the probability that one has a critical crack, two have detectable cracks, and two have no cracks. 0.063 correct: your answer is correct. (b) find the probability that at least one plane has critical cracks.
The probability of two planes having no cracks is 0.063 and The probability of no plane having critical cracks is 0.405.
(a) The probability of one plane having a critical crack is 10% or 0.10. The probability of two planes having detectable cracks is (0.21)^2 = 0.0441. The probability of two planes having no cracks is (0.69)^2 = 0.4761. So, the desired probability is 0.10 * 0.0441 * 0.4761 = 0.063.
(b) To find the probability that at least one plane has critical cracks, we can use the complementary probability approach, i.e., finding the probability that no plane has critical cracks and then subtracting it from 1. The probability of no plane having critical cracks is (0.90)^5 = 0.595. So, the desired probability is 1 - 0.595 = 0.405.
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Describe all solutions of Ax = 0 in parametric vector form, where A is row equivalent to the given matrix. [2 -1 -4 2 6 -3] x = x_2 + X_3 (Type an integer or fraction for each matrix element.)
The solutions of Ax = 0 in parametric vector form, where A is a row equivalent to the given matrix are : x_1 = 2x_3 + 2x_2,x_2 = x_2 + x_3,x_3 = x_3,x_4 = 2x_3 + 6x_2,x_5 = -3x_3 - 6x_2,x_6 = -4x_3 - 2x_2
The given matrix is row equivalent, which means that it can be reduced to row echelon form using elementary row operations. To solve for the parametric vector, we start by performing the same operations to the identity matrix. First, we divide the first row by 2 to get the leading coefficient of 1 on the leftmost column. Then, we add the first row to the second row, and the third row to the fourth row to eliminate the elements below the leading coefficients.
Finally, we multiply the first row by -4 and add it to the third row to get the leading coefficient of 1 on the third column. After performing the same operations on the identity matrix, we get the parametric vector x_2 + x_3. This means that x_1 = 2x_3 + 2x_2, x_2 = x_2 + x_3, x_3 = x_3, x_4 = 2x_3 + 6x_2, x_5 = -3x_3 - 6x_2, and x_6 = -4x_3 - 2x_2. Essentially, the parametric vector is the sum of the two columns of the identity matrix that correspond to the two leading coefficients in the row echelon form of the original matrix.
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