The function rule for the line is f(x) = [tex]\frac{2}{3}x[/tex] - 2
What is a linear function?A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.
The line cuts the x and y axis at (3,0) and (0, -2)
standard form of equation of line: y = mx + c
when x =3, y = 0
substitute these values into the equation
0 = 3m + c
c = -3m----------------1
when x = 0, y = -2
substitute these values into the equation, we have
-2 = 0(m) + c
c = -2
substitute the value of c in equation 1 to find m
-2 = -3m
m = 2/3
Substitute the values of m and c into the standard equation,
y = [tex]\frac{2}{3}x[/tex] - 2
In conclusion, the function rule for the given line is y = [tex]\frac{2}{3}x[/tex] - 2
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When using a counterexample to prove a conditional statement false, which must be true about the counterexample?
The true statement is that the counterexample must satisfy the conclusion of the conditional statement.
What is a counterexample?A counterexample is a situation in which the hypothesis and conclusion are both accurate. We employ a counter example to show that a conditional assertion is untrue.
The true statement regarding the counterexample can be written as a conditional assertion.
This is shown to be untrue by a counterexample,
Therefore, only one counter-example is enough to demonstrate the falsity of a proposition. In this case where a counterexample is used to refute a conditional statement.
The counter-example should be supported the conditional statement's hypothesis.
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Simplify.
−81--√ pls help
Answer:
9i
Step-by-step explanation:
Complex numbers:i² = -1
[tex]\sqrt{-81}=\sqrt{81i^2}\\[/tex]
[tex]\sf \bf = \sqrt{9*9*i * i}\\\\ = 9i[/tex]
IXL Please Help Fast !
Answer:
y = 8/9 x - 4
Step-by-step explanation:
y-4 = 8/9(x-9)
y-4 = 8/9 x -8
y = 8/9 x +4 -8
y = 8/9 x -4
Answer:
y=8/9x-4
Step-by-step explanation:
4=8/9(9)+2
4=72/9+2
4=8+2
4=10
10-4=6
2-6=-4
4=8/9(9)-4
4=8-4
4=4
Hopes this helps please mark brainliest
What change of state occurs when fog forms? O Water vapor cools and changes to liquid water. O Liquid water cools and changes to water vapor. Water vapor warms and changes to liquid water. O Liquid water warms and changes to water vapor.
Answer:
O Liquid water warms and changes to water vapor.
Step-by-step explanation:
Kristine bought a car for $23,000. It's
d=-3,000.
Write the equation for this sequence
Y=21,000(1.20)*. D=anan1 d = a n a n 1 is the formula for figuring out the common difference of an arithmetic series, where d is the common difference and an a n is the nth term. A common difference in an arithmetic series is one between any term and its predecessor, and it is typically denoted by the letter "d".
A Commen difference is defined.A common difference in an arithmetic series is one between any term and its predecessor, and it is typically denoted by the letter "d". So, subtract the first term from the second term, the second term from the third term, etc. to find the common difference of an arithmetic sequence.Every two numbers in an arithmetic sequence that differ from one another constitute the common difference.Take any two consecutive terms as your first step.Step 2: Determine their difference, d = a(n) - a(n-1); a(n-1) is the phrase that comes before a(n) (n).The formula to determine an arithmetic sequence's common difference is: d = a(n) - a(n - 1), where a(n) is a term its succeeding phrase in the series is a(n - 1), and vice versa.To learn more about Commen difference refer to:
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helpp me out thank u
The equations that are true include the following:
(8 × 7)/2 - 12 = 22 - (2 × 3)
48 ÷ 8 + 2³ = 5 + 3²
How to determine the true equations?In order to determine the equations that have a true and valid solution, we would simplify and evaluate each of the equations as follows:
(8 × 7)/2 - 12 = 22 - (2 × 3)
Opening the bracket on both sides of the equation, we have:
56/2 - 12 = 22 - 6
28 - 12 = 16
16 = 16 (True).
48 ÷ 8 + 2³ = 5 + 3²
Evaluating the exponents, we have:
48 ÷ 8 + 8 = 5 + 9
6 + 8 = 14
14 = 14 (True).
150/5² = 30 - 4² - 12
Evaluating the exponents, we have:
150/25 = 30 - 16 - 12
6 = 2 (False and incorrect).
9² - 7² = 20 ÷ (7 - 2)
Opening the bracket, we have:
9² - 7² = 20 ÷ 5
Evaluating the exponents, we have:
81 - 49 = 4
32 = 4 (False and incorrect).
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Determine whether the following quadratic function has a maximum or a minimum value. Then find the maximum or minimum value and where it occur:
F(x)=-3x²+18x+3
Select the correct choice below and fill in the answer boxes to complete your choice.
(Simplify your answers.)
The function has a maximum value of ___ at x=____.
The function has a minimum value of ____ at x=____.
The maximum value of the quadratic function F(x) = -3x² + 18x + 3 is 30 when x = 3
How to determine the maximum or minimum value?The quadratic equation is given as
F(x) = -3x² + 18x + 3
The above function is a quadratic function
As a general rule, a quadratic function has the following representation:
F(x) = ax² + bx + 3
This means that: a = -3
The value of a for a quadratic function must be less than 0 for the function to have a maximum
This means that the function has a maximum value because -3 is less than 0
Solving further, we have
F(x) = -3x² + 18x + 3
Differentiate and set to 0
-6x + 18 = 0
So, we have
x = 3
Substitute x = 3 in F(x)
F(3) = -3(3)² + 18(3) + 3
Evaluate
F(3) = 30
This represents the maximum value
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There are 100 apples. 35 are red apples and 65 are green apples. What percentage is a green apple?
NEED HELP RIGHT NOW THIS IS DUE TOMORROW
Answer:
35%
Step-by-step explanation:
35 divided by 100 = 0.35 = 35%
Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean = 67.0 kg and standard deviation = 7.9 kg. Suppose a doe that weighs less than 58 kg is considered undernourished.
What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.)
In the national park, the probability that a single doe captured (weighed and released) at random in December is undernourished is 25.5%
How to determine the probabilityData is symmetrically distributed and skew-free in a normal distribution. When the data is shown on a graph, it has the shape of a bell, with the majority of values congregating in the center and diminishing as they move outward.
Due to their structure, normal distributions are sometimes known as bell curves or Gaussian distributions.
Assuming normal distribution we calculate the probability as follows
Definition of variables
mean adult female deer, μ = 67.0 kg
Standard deviation, σ = 7.9 kg
sample, X = 58
Z score, z is given by the formula
= (X - μ) / σ
= (58 - 67) / 7.9
= -1.139 has a p value of 0.2546
P = 25.5%
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(0, -7) (2, 1) (5,-2)
Find a quadratic equation from three points, Alg 2
Step-by-step explanation:
A quadratic equation is in the form of
[tex]ax {}^{2} + bx + c[/tex]
C is the y intercept a.k.a the value of c is when x=0,
when x is 0, c is -7 so
c=-7
[tex] {ax}^{2} + bx - 7 [/tex]
Next we know when x is 2, y is 1 so
[tex]a(2) {}^{2} + 2b - 7 = 1[/tex]
[tex]4a + 2b = 8[/tex]
When x is 5, y is -2
[tex]a(5) {}^{2} + b(5) - 7 = - 2[/tex]
[tex]25a + 5b = 5[/tex]
So we have a system of equations, using elimination.
[tex]5a + b = 1[/tex]
[tex] - 6a = 6[/tex]
[tex]a = - 1[/tex]
So
[tex]5( - 1) + b = 1[/tex]
[tex]b = 6[/tex]
Our quadratic is
[tex] - {x}^{2} + 6x - 7[/tex]
1. A hive of bees contains 20 bees when it is first discovered. After 5 days, there are 29 bees. It is determined that the population of bees increases exponentially. How many bees are will there be after 100 days? Express your answer as an exact value and rounded to the nearest whole number.
2.Can you find the inverse of the function y=4x^2+12+9? Why or why not?
What domain restrictions are necessary to allow the function to have an inverse?
Find the inverse of the domain restricted function.
1. ≈ 33759 bees
The parent function for exponential functions is y = a(b^x), where "a" is the initial value and "b" is the growth rate. In this case, "x" is the number of days, and "y" is the number of bees after "x" days. We already know that the initial value is 20, so we can set "a = 20". Next, we know that after 5 days, there are 29 bees, which we can also plug into our equation: "x = 5" and "y = 29". Then, we end up with the equation 29=20(b^5) and solve for the growth rate, "b". To solve for "b", first divide both sides by 20, and then take the 5th root of both sides:
29 = 20(b^5)
29/20 = b^5
^5√(29/20) = ^5√(b^5)
^5√(29/20) = b
Now, we know the equation to this problem is y = 20((^5√(29/20))^x). We can plug in "x = 100" to find the number of bees after 100 days.
y = 20((^5√(29/20))^100)
y ≈ 33759 bees
2. No, you can't find the inverse of the function y=4x^2 + 12x + 9, because, for an inverse to be possible, it must pass the horizontal line test, which this function does not pass. The domain restriction necessary would have to make it so the function passes the horizontal line test, which would mean restricting half of the function from its vertex in this case. The x-value of the vertex (refer to the vertex formula) of this function is -12/8, so we can restrict the domain by only letting the domain be [-12/8, +infinity). Finding the inverse (switch "x" and "y", and solve for "y"):
x = 4y^2 + 12y + 9 x: [-12/8, +infinity)
x - 9 = 4y^2 + 12y
x - 9 = 4y^2 + 12y
(x - 9)/4 = y^2 + 3y
(x - 9)/4 + 2.25 = y^2 + 3y + 2.25
(x - 9)/4 + 2.25 = (y + 1.5)^2
√((x - 9)/4 + 2.25) = y + 1.5
√((x - 9 + 9)/4) = y + 1.5
(√(x) / 2) - 1.5 = y
(-3 + √(x))/2 = y
3a. To solve this problem, we have to find a way to use "log base5 of 3" and "log base5 of 8" to get "log base5 of 2".
First, we can exclude the logbase5 so the problem is easier to look at. We need to find a way to get "2" using "3" and/or "8" (cannot use subtraction/addition in this step, and using "3" and/or "8" is required with multiplication/division). Keep in mind the rules of logs with the same base.
8^1/3 = 2
Now, we put the logbase5 back in:
logbase5 of (8^1/3) = logbase5 of 2
From log rules, we can move the exponent "1/3" down:
1/3 * logbase5 of 8
We know that logbase5 of 8 = 1.2920
1/3 * 1.2920
approximately 0.4307
3b. As previously explained, we need to use "3" and "8" to get to "75/8" while keeping in mind the rules of logs.
First, we can simplify "logbase5 of (75/8)":
logbase5 of (75/8) = (logbase5 of 75) - (logbase5 of 8)
Now, ignore the "logbase5" and use provided values of "3" and "8" to get to 75. Note that we can use the number 5: logbasex of x= 1 [x^1 = x]
(5^2) * 3 = 75
Next, place the "logbase5" back in, and simplify
logbase5 of ((5^2) * 3) - logbase5 of 8
logbase5 of (5^2) + logbase5 of 3 - logbase5 of 8
2logbase5 of 5 + logbase5 of 3 - logbase5 of 8
2(1) + 0.6826 - 1.2920
approximately 1.3906
How to solve this problem?
The answer of the problem by the SAS similarity theorem sides is [tex]\frac{AC}{GI} = \frac{HI}{BC}[/tex].
What is the SAS similarity theorem of triangle?
According to the SAS similarity theorem, two triangles are considered similar if their included angles are congruent and their two sides are proportionate to one other.
It is also known as Side-Angle-Side similarity of two triangles.
There is a common ratio of sides in the given problem figure, which is,
[tex]\frac{AC}{GI} = \frac{HI}{BC}[/tex]
Additionally, these similar sides produce equal relative angles,
∠[tex]ACB =[/tex] ∠[tex]GIH[/tex]
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is the
following statement true or false? If false,
provide a counterexample.
The difference between a positive mixed
number and negative mixed number is
never positive.
The difference between a positive mixed number and negative mixed number is never positive is false.
Depending on how the phrases might be ordered
If we think that the first term is the positive mixed number, the second term is the negative mixed number, and we consider that "difference" is equal to subtraction, then the outcome is positive.For illustration, (3 + 1/2) - [-(1 + 1/2)] = (3 +1/2) + (1 + 1/2) = 5 because removing a negative produces a positiveHowever, if we performed the same procedure in reverse, we would get -(1 + 1/2) - (3 + 1/2), and the outcome is - 5.I To start, arrange the numbers vertically so that the ones' and tens' place digits are aligned, which simply implies that one number should be written above the other number. Under the bottom number, draw a line.(ii) Remove the numbers from the ones location. Addition (6 – 2) equals 4.Hence the given statement, the difference between a positive mixed number and negative mixed number is never positive is false.
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In a marching band maneuver, the marcher at the left spins 180° in place with arms spread, and hands the horn to the marcher at the right, who spins 180° with arms spread, and stops.
a. How far from the initial position is the horn?
The initial position is the hor from inch b.
What composition maps the horn from the initial position to the final position?
A. 136 in.
When spinning 180, you face backwards. When the initial spins, you can just think of it as moving the horn from the left hand to the right. That happens a second time. Two arms is equal to 68 in., so double of that is 136 in.
I don’t believe I can solve the 2nd question
rearrange the formula to make x the subject in y=1/2x+5
The rearranged formula with the x as subject is x = 2y - 10
Formula
Formula refers a fact or a rule written with mathematical symbols. It usually connects two or more quantities with an equal sign.
Given,
Here we have the formula y = 1/2x + 5
Now, we have to rearrange the given formula in order to make x as the subject.
Here we we need to find the formula, as x the subject,
So, the given formula,
y = 1/2 x+ 5
We have to move the number 5 to the left hand side, then the sign of the number changes into negative,
So, it can be written as,
=> y - 5 = 1/2x
Here we need the value of x alone, so move the number that is in division to the LHS, then it will be changed as multiplication, then we get,
=> 2 (y - 5) =x
When we expand it, then we get,
=> 2y - 10 = x
Therefore, the formula that has x as subject is 2y - 10.
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Please list all of the corresponding parts (segments and angles).
Using the angle sum property and the definition of congruency, the measure of angle G is determined to be 118°.
What makes two triangles congruent?If the following requirements are met, two triangles are congruent.One triangle's three sides line up perfectly with the three sides of another triangle (SSS)One triangle's two sides and included angle are identical to the other triangle's two sides and included angle (SAS)One triangle's two angles and included side are identical to the other triangle's two angles and included side (ASA)One triangle's two angles and excluded side are congruent with the other triangle's two angles and excluded side.Right triangle hypotenuse and one of its legs are similar to the hypotenuse and one of its other triangles.Therefore,
ΔCAT ≅ ΔDOG
m∠C = 25°
m∠O = 37°
The following formula is used to determine angle ∠G:
According to the definition of congruency, the arrangement of the letters in the congruency statement shows that angle ∠C is congruent to angle ∠D, angle ∠A is congruent to angle ∠O, and angle T is congruent to angle ∠G, indicating that we have;
m∠C = m∠D = 25°
m∠A = m∠O = 37°
m∠T = m∠G
The measure of angle ∠G and angle ∠T can therefore, be found from the angle sum property of the interior angles of a triangle.
m∠C + m∠A + m∠T= 180° (angle sum property of a triangle)
m∠D + m∠O + m∠G= 180° (angle sum property of a triangle)
m∠G = 180° - (m∠D + m∠O) (subtraction property of equality)
m∠G = 180° - (25° + 37°) = 118°
The measure of angle ∠G, m∠G is 118°
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Pleasee Help Mee! Alot of Pointss 40!!! Look at the pictures attached:) People keep on answering it wrong or leaving some of it incomplete I really need help
The measurement of Angle ∠5=52°
What is interor angle property?when two parallel lines are cut by a transversal line, then the resultant alternate interior angles are equal.
In the given figure, lines AB║CD.
And ∠3=52, ∠5=?
By using alternate interior angle property ,
Angle ∠3 and ∠5 are cut by a transversal line, so this both angle will be equal
⇒∠3=∠5=52°
Here, the value of ∠5=52°
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The rule for dilation of a quadrilaterial is D O,0.16 (x, y) (0.16x, 0.16y). What is the Y coordinate of a new point if the new coordinate is (0,-8)? Round
hundredth if necessary.
The Y coordinate of the new point is -1.28 y.
What are coordinates?A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. Typically expressed by the x-value and y-value pair (x,y).You do the reverse to determine a point's coordinates in a coordinate system. Start at the point, then move up or down a vertical line until you reach the x-axis. Your x-coordinate is shown there. To get the y-coordinate, repeat the previous step while adhering to a horizontal line.So, the new Y coordinate is:
The rule of dilation for the quadrilateral D is:
0.16 (x, y) (0.16x, 0.16y)The new coordinate plan is:
(0, -8)Then, calculate the Y coordinate as follows:
(0.16x, 0.16y)(0.16x, 0.16(-8))(0.16x, -1.28y)
Therefore, the Y coordinate of the new point is -1.28 y.
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The equipment cost to the contractor (you) is $4200 and 16 man-hours are required to install the
equipment. The cost of labor for your company is $32 per man-hour. Overhead for your company is
45 percent. How much do you need to sell this job for in order to make 15% net margin?
The amount you need to sell the job if you want to make 15% net margin, based on the costs, is $7, 857.26
How to find the amount to sell?First, find the total cost for the project:
= Equipment + cost of labor + overhead
Cost of labor and equipment:
= 4, 200 + ( 16 x 32 per man- hour)
= $ 4, 712
The total cost is then:
= 4, 712 x ( 1 + 45%)
= $6, 832.40
The amount to sell for is:
= Total cost x ( 1 + net margin)
= 6, 832.40 x ( 1 + 15%)
= $7, 857.26
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The materials for one headband cost $0.95. Each headband is sold for $3.80.
What percentage of $0.95 is $3.80?
250%
4%
25%
400%
The percentage of $0.95 to $3.80: 25%
What is Percentage?
A percentage, often known as percent, is a division by 100. Percentage, which meaning "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance. Finding the percentage of a whole in terms of 100 is what percentage calculation is. Both manual calculation and the use of internet calculators are options.
The terms "out of 100" and "for every 100" can also be used to refer to percentages. For instance, you may say "it snowed 20% of the time" or "it snowed 20 days out of every 100 days."
A decimal can also be used to represent a percentage. For instance, 24 percent, 0.24, 24/100, or 24 hundredths could also be used to represent the percentage. By dividing the percentage by 10, you can obtain the percent in decimal form.
Given,
The material cost for one headband = $0.95
The cost of one headband sold = $3.80
Now to take the percentage of the cost of material of the headband to the selling price of the headband will be:
= (0.95/3.80) x 100
it can be also written as
= (0.95 x 100)/3.80
= 95 / 3.80
= 25%
Hence, The percentage of $0.95 to $3.80 is 25%
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How do you find the standard error of two samples?
In order to find the standard error of two samples, the following are needed:
1: Find the mean. .
2: Find each score's deviation from the mean. ...
3: Square each deviation from the mean.
4: Find the sum of squares.
5: Find the variance.
6: Find the square root of the variance.
What is a standard error?The standard error is a statistical term that refers to the degree to which a sample distribution accurately represents a population using standard deviation.
A statistic's standard error is the standard deviation of its sampling distribution or an estimate of that standard deviation. The standard error of the mean is used when the statistic is the sample mean.
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To determine the standard error of two samples the following procedure are followed
First, determine the mean.
second: Calculate the variation between each score and the mean
third: Square each variation from the mean
4th: Determine the sum of the variance
5th: Determine the variance by dividing the sum in 3 by 1 less the number of sample
6th: Calculate the standard deviation by variance's square root
7th: find the square toot of the number of samples
lastly: divide the standard deviation by result of step 7
What is standard error?
The population mean's likelihood to differ from a sample mean is indicated by the standard error of the mean, or simply standard error.
It reveals how much the sample mean would change if you conducted the same study again with fresh samples drawn from a single population.
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So I have to rearrange this formula:
a=2b+c (to make b the subject)
Kindly help!
Formula a = 2b + c in subject to b is b = a-c / 2
Changing the subject of formula is a way of rearranging formula to determine missing variable in terms of other variable
Changing the subject of formula is also known as rearranging formula or changing the subject of an equation.
Given ,
Formula : a = 2b + c
Subtracting by c on both sides,
=> a - c = 2b + c - c
=> a - c = 2b
Dividing by 2 on both sides,
=> [tex]\frac{a-c}{2} = b[/tex]
Formula in subject to b is
b = a-c / 2
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please help me with these questions
ALL experts please help
Answer: The correct answers are:
4^4 (same answer for the equation shown) = 256 (option# B) for the first one
((2^2)^4)*2^-5= 8 (option# B) for the first one
Step-by-step explanation: Confirmed correct
Answer:
First one:
[tex]2^{2} (3+1) *[2(7-5)]^{2}[/tex]
= [tex]2^2(4)* [2(2)]^2[/tex]
= [tex]2^2(4)(4)^2[/tex]
= [tex]2^2(4)(16)[/tex]
= [tex]2^2*2^2*2^4[/tex]
= [tex]4*4*4^2[/tex]
= [tex]4^4[/tex]
The answer is four
and for the second one:
[tex]2^8*\frac{1}{2^5}[/tex]
[tex]2^3 = 8[/tex]
the answer is 8
Which values complete the table for the function ƒ(x) = 3x – 1?
HELP
Answer:
5 and 11
Step-by-step explanation:
x =2
fx=3x-1
3(2)-1
6-1
= 5
when x= 4
fx=3x-1
3(4)-1
12-1
11
f(x) =5 and 11
Answer:
5 and 11
Step-by-step explanation:
Input the values of x in the function and solve using basic mathematical operations.
[tex]f(2)=3(2)-1=6-1=5\\\\\\f(4)=3(4)-1=12-1=11[/tex]
If −5x+10y=1 and −x−6y=−10 are true equations, what would be the value of 4x−16y?
The value of 4x - 16y is -11.
4x - 16y = -11.
Given, two equations
−5x + 10y = 1 and −x − 6y = −10
Now, On subtracting both the equations, we get
−5x + 10y + x + 6y = 1 + 10
- 4x + 16y = 11
On multiplying both the sides by -1, we get
4x - 16y = -11
Hence, the value of 4x - 16y is -11
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The graph below is a polynomial function in the form f(x)=(x−a)(x−b). Find suitable real numbers a and b that describe the graph.
Brianna found an orange caterpillar and a green caterpillar in her backyard. The green caterpillar was 4 inches long and the orange caterpillar was 1 1/12 inches long. How much longer was the green caterpillar than the orange caterpillar?
Simplify your answer and write it as a fraction or as a whole or mixed number.
The length longer of the green caterpillar than the orange caterpillar is 2 1/2 inches.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this case, the green caterpillar was 4 inches long and the orange caterpillar was 1 1/12 inches long.
The difference in length will be:
= 4 - 1 1/2
= 2 1/2 inches.
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On average a certain battery used in smartphones has a lifespan of 3 years. What is the probability that a brand new battery lasts for at least 2 years? Give your answer to 3 significant figures. P=
The probability that a brand new battery lasts for atleast 2 years is 0.801
How to determine the probability?From the question, we have the following parameters that can be used in our computation:
Mean, λ = 3 years
The probability of a Poisson distribution is represented as
P(x) = λˣe⁻λ/x!
In this case,
x = At least 2
This means that
x = 2, 3....
So, we have
P(x ≥ 2) = 1 - P(0) - P(1)
This gives
P(x ≥ 2) = 1 - 3⁰ * e⁻³/0! - 3¹ * e⁻³/1!
Evaluate
P(x ≥ 2) = 1 - 0.0497 - 0.1494
Evaluate the difference
P(x ≥ 2) = 0.801
Hence, the probability is 0.801
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If 4x + 9 = 16, what is the value of 12x + 21 ?
Differentiate the function with respect to x. Shot steps
The differentiation or rate of change of the given function y = ln x² will be 2/x.
What is the rate of change?The rate of change is the change of a quantity over 1 unit of another quantity.
Most of the time the rate of change is the change with respect to time.
For example the speed 3meter/second.
As per the given,
y = ln x²
By log property
y = 2ln x
Take the first derivative,
dy/dx = 2/x
Hence "The differentiation or rate of change of the given function y = ln x² will be 2/x".
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