The slope of the line can be calculated as [tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex].
Correct options are (A) and (D).
What is the slope of the line?
In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.
As the definition of the slope says that it is the ratio of rise by run.
so we can make the formula as
[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Hence, the slope of the line can be calculated as [tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex].
for example lets have two points (9,1) and (8,4) so the value of the slope can be calculated as
4-1 / 8-9
3/-1
= -3
Therefore, the slope of the line passing through the given points is -3
To learn more about the slope of a line, visit:
https://brainly.com/question/16949303
#SPJ1
A right triangle has side lengths of 15 in, 12 in, and 9 in. it is dilated by a scale factor and has new side lengths on 5 in, 4in, and 3 in. what was the scale factor?
Each side of the dilated triangle is 1/3 of the length of the corresponding side of the original triangle.
To find the scale factor of the dilation, we can divide the length of each side of the dilated triangle by the length of the corresponding side of the original triangle.
For example, for the side of length 5 inches in the dilated triangle, the scale factor is 5 inches / 15 inches = 1/3.
We can do the same for the other two sides and we will get the same scale factor for all three sides, since the dilation is uniform.
In this case, the scale factor is 1/3 for all three sides, so the scale factor for the dilation is 1/3.
This means that each side of the dilated triangle is 1/3 of the length of the corresponding side of the original triangle.
To learn more about dilated triangle
visit; brainly.com/question/29011026
#SPJ4
The side of length 5 inches in the dilated triangle, the scale factor is 5 inches / 15 inches = 1/3.
We can do the same for the other two sides and we will get the same scale factor for all three sides, since the dilation is uniform.
In this case, the scale factor is 1/3 for all three sides, so the scale factor for the dilation is 1/3.
This means that each side of the dilated triangle is 1/3 of the length of the corresponding side of the original triangle.
How do you write more than 50?
More than 50 in mathematical expression is written as >50.
Any two integers can be compared using the greater than and less than symbols. Greater than and less than symbols are used to indicate whether one number is greater than or less than another. The greater than sign (>) is used when the first number exceeds the second number. The less than sign (<) is used when the first number is less than the second number.
The quantity on the left of the > sign is the greater quantity. It could be a variable or expression [like 3x - 2 > 50].
To know more about mathematical symbols visit: brainly.com/question/29201092
#SPJ4
stephanie knows that a correlation between the number of bars and the number of churches in her city does not, in itself, mean that more bars will lead to a higher number of churches. which of the following would not be a lurking variable in the above scenario? a.) the city's budget b.) stephanie's proximity to the center of the city c.) the day of the week that stephanie attends service d.) population density
The option that would not be a lurking variable in the above scenario is c.) the day of the week that stephanie attends service
What is a lurking variable?a variable that has a connection (e.g., may be correlated) with the response and the explanatory variable but is neither the explanatory variable nor the response variable. Although it is not taken into account in the study, it might affect how the variables are related.
When researching the relationship between two or more variables, we occasionally neglect the influences on the relationship that exist outside of these two variables. These are also known as lurking variables or extraneous variables. These significantly impact the relationship. Lurking variables are those that were not taken into consideration for the study but have an impact on the two studied variables.
The day of the week will not be a lurking variable since we are talking about the number of churches and bars. Hence, Option c is correct.
Learn more about lurking variable on:
https://brainly.com/question/13285819
#SPJ1
Answer:
Step-by-step explanation:
a.) Correct.
A variable is a lurking variable if it can influence an explanatory/response relationship. So it must be related to both the explanatory and response variable. It is not likely street name length is related to the number of bars in a given area.
What is the range of this absolute value function? A line is graphed in an x y plane, where the x and the y axes range from negative 10 to 10 in increments of 2. The line rises through (negative 10, negative 3), (negative 7, 0) to (0, 7), and then it falls through (7, 0), and (10, negative 3). A. -∞ < y ≤ 0 B. 0 ≤ y < ∞ C. -∞ < y ≤ 7 D. -∞ < y < ∞
The range is an absolute value functions is
B. 0 ≤ y < ∞What are absolute value functions?A function that wraps an algebraic expression in absolute value symbols is known as an absolute value function.
Remember that a number's distance from 0 on the number line represents its absolute value.
A number can never have a negative absolute value. hence the negative values will never be in the range
This makes the range to start possibly from zero, from the graph explained 0 is among the values that are in the range
Considering that absolute values are non zero and option B is the only option that does not have a negative value. This is the best option
Learn more absolute values here:
https://brainly.com/question/29532815
#SPJ1
Answer:
The range is an absolute value functions is
B. 0 ≤ y < ∞
Step-by-step explanation:
Why is 2 root 2 equal to root 2?
Therefore , the given expression of this problem of square root
2√2 not equal to √2.
What is square root?The value that results from multiplying the square root of an integer by itself is the number.
Example: Since 5* 5 = 25, 5 is the square root of 25. Observe that (5) (5) also equals 25, proving that (5) is a square root of 25.
Here,
In this case, the mathematical symbol for Root 2 is 2.
Root 2 then multiplied by Root 2.
√2 + √2 = 2√2
If we take the estimated value of 2 = 1.4142
Then
=> 2√2 = 1.4142 x 2
=> 2.8284 (approximately)
Please take note that 2 is an irrational number.
Alternatively, root2* root 2
√2 * √2 = 2
Because 2 is just the square root of 2,
Therefore,
what happens when root 2 + root 2 and root2 root 2 are different
2√2 - 2 = 2.8284 - 2 = 0.8284 (approx)
Therefore , the given expression of this problem of square root
2√2 not equal to √2.'
To know more about square root , visit
brainly.com/question/29286039
#SPJ4
suppose x is 5 and y is 7. choose the value of the following expression: (x != 7) && (x <= y)
The value of the following expression is true.
Expressions include operators and can consist of any set of variables and constants that can be evaluated to produce a result. Relational expressions are used in decision-making to compare operands and evaluate to 1 (true) or 0. (false).
If a logical expression is true when it is evaluated by C++, it returns an integer value of 1; if it is false, it returns an integer value of 0. Any value other than zero is treated as true in C++, while a value of zero is considered false.
Correct Question :
Suppose x is 5 and y is 7. Choose the value of the following expression: (x ! = 7) & & (x <= y)
a. false
b. true
c. 0
d. null
To learn more about expression here:
https://brainly.com/question/28365581
#SPJ4
Consider a computer that uses 5 bits to represent positive and negative integers, using 1 bit for the sign and 4 bits for the actual value. Which of the following operations would result in integer overflow?
7+1
12 + 3
6 + 9
8×2
2×4
1+15
The operation 1+15 would result in integer overflow, because the result of this operation (16) cannot be represented with 4 bits.
What is integer overflow ?Integer overflow occurs when an arithmetic operation on two integers produces a result that is too large to be represented within the allocated number of bits. In the case of the computer described, integer overflow would occur if the result of an operation had a value that is too large to be represented with 4 bits.In this case, the operations 7+1, 12+3, 6+9, 82, and 24 would not result in integer overflow, because the results of these operations (8, 15, 15, 16, and 8, respectively) can be represented with 4 bits. However, the operation 1+15 would result in integer overflow, because the result of this operation (16) cannot be represented with 4 bits.To learn more about arithmetic operation refer :
https://brainly.com/question/13181427
#SPJ1
How do you write an equation in slope intercept form of the line that passes through the given point and is parallel to the graph of the given equation?
The equation of line in slope intercept form passing through (-5,-2) and parallel to y = -2x+1 is y = -2x -12 .
The Slope intercept form of the line is written as " y = mx + c " , where c is the y intercept and m is the slope of line .
the required line is parallel to the line with equation ⇒ y = -2x+1 ,
on comparing it with slope intercept form of line ,
we get the slope(m) as "-2" .
the required line is passing through (-5,-2).
substituting the values , we get ;
-2 = (-2)(-5) + c ,
-2 = 10 + c ,
c = -10 -2
c = -12 .
So , the equation is ⇒ y = -2x -12 .
Therefore , the slope intercept form of the required line is y = -2x -12 .
The given question is incomplete , the complete question is
How do you write an equation in slope intercept form of the line that passes through the given point and is parallel to the graph of the given equation ? the point is (-5,-2); and is parallel to y = -2x + 1 .
Learn more about Slope Intercept Form here
https://brainly.com/question/29114942
#SPJ4
What is the median of the following data sample 3 7 4 8 9 6 10 12 13 15?
The Median of the following sample 3 4 6 7 8 9 10 12 13 15 is 8.5.
One measure of central tendency is the median. The median of a set of numbers is its midway value. It splits a sample of given data into the upper and lower halves. A minimum of half of the observations are above the median and a minimum of half are below it.
When there are exactly even numbers of observations in a data collection, the median can be calculated as follows:
sort the data in ascending or descending order.
If there are an even number of observations (let's say n), identify the (n/2)nd and [(n/2) + 1] th observations.
The average of the top two observations is the same as the median of the data given (as determined in step 2).
Median = [tex]\frac{1}{2} [(\frac{n}{2} ) + (\frac{n}{2}+1 )][/tex].
Here n = 10, So [(10/2) + (10/2 + 1)]/2.
=> Median = 8.5.
Learn more about Median:
brainly.com/question/28060453
#SPJ4
can you guys help me with this plsss
Answer:
30 inches
Step-by-step explanation:
The longest piece (15 in) is represented as 5 in the ratio, so we can find what one unit is. We can do 15÷5=3, so one unit is 3 inches. We could multiply each of them by 3 and add them up, but there's a simpler way. We can find the total of the ratio, 2+3+5=10. So, we can do 3x10=30 inches. Therefore, the length of the stick is 30 inches.
Solve angle ABC by using the measurements angle ABC = 90°, angle BAC = 35°, and a = 10. Round measures of sides to the nearest tenth and measures of angles to the nearest degree.
The measure of the sides 'b' and 'c' will be 5.7 units and 8.2 and angle C will be 55°.
What is the sine law?The Law of Sines The law of trigonometric functions, sine law, sine formula, or sinusoidal rule is a trigonometric equation that relates the sizes of any triangle's edges to the sines of its orientations.
The sine law in the triangle ΔABC is given as,
AB / sin C = BC / sin A = CA / sin B
The measure of the third angle is given as,
∠A + ∠B + ∠C = 180°
35° + 90° + ∠C = 180°
∠C = 55°
Then the measure of the side c (AB) is calculated as,
AB / sin C = BC / sin A
c / sin 55° = 10 / sin 90°
c = 8.2
Then the measure of the side b (AB) is calculated as,
AC / sin B = BC / sin A
b / sin 35° = 10 / sin 90°
b = 5.7
More about the sine law link is given below.
https://brainly.com/question/17289163
#SPJ1
exercise 28 a sample of 20 joint specimens of a particular type gave a sample mean proportional limit stress of 8.52 mpa and a sample standard deviation of 0.78 mpa. (a) calculate and interpret a 95% lower confidence bound for the true average proportional limit stress of all such joints. (round your answer to two decimal places.)
95% confident that the true average proportional limit stress of all such joints is at least 8.19 mpa.
What is proportional limit?
The maximum stress at which stress and strain are directly proportional and the stress-strain graph is a straight line with a gradient equal to the elastic modulus of the material is known as the proportional limit.
To calculate the 95% lower confidence bound for the true average proportional limit stress of all such joints, we can use the following formula:
lower confidence bound = sample mean - (t-value * standard error)
The standard error of the mean is a measure of the variability of the sample mean, and is calculated as:
[tex]standard\ error = sample\ standard\ deviation / \sqrt{(sample \ size)}\\\\= 0.78 / \sqrt{(20)}\\\\= 0.19[/tex]
To find the t-value, we can consult a t-distribution table or use a t-distribution calculator. At a 95% confidence level with a sample size of 20, the t-value is approximately 1.725.
Substituting these values into the formula for the lower confidence bound, we get:
lower confidence bound = 8.52 - (1.725 * 0.19)
= 8.52 - 0.327
= 8.19
So the 95% lower confidence bound for the true average proportional limit stress of all such joints is approximately 8.19 mpa.
Hence, 95% confident that the true average proportional limit stress of all such joints is at least 8.19 mpa.
To know more about proportional limit visit,
https://brainly.com/question/22935390
#SPJ4
What is the difference between ≥ and ≤?
The notation a ≤ b denotes a value that is less than or equal to b (or, equivalently, at most b, or not larger than b), while the notation a ≥ b denotes a value that is greater than or equal to b (or, equivalently, at least b, or not less than b).
What is Inequality?An inequality in mathematics is a relationship that compares two numbers or other mathematical expressions in an unequal way. By comparing the sizes of two numbers on the number line, it is most frequently utilized. Different types of inequalities are represented by a variety of different notations, including:
The symbol a b indicates that an is less than b.
A bigger value for a than a lesser value for b is indicated by the notation a > b.
A is not equal to b in either situation. These relationships are referred to as stringent inequalities, which means that an is strictly less than or strictly bigger than b. Equivalence is not included.
There are two kinds of inequality relations that are not strict, in contrast to strict inequalities:
When something is written with an an or b, it signifies that.
A is smaller than or equal to b when a notation like a ≤ b is used (or, equivalently, at most b, or not greater than b).
A greater or equal value for a indicates that b is greater than it (or, equivalently, at least b, or not less than b).
The symbol for "greater than" that is divided in half by a slash, "not," can also be used to express the connection not greater than. The same applies to and not less than and a b.
Hence, The notation a ≤ b denotes a value that is less than or equal to b (or, equivalently, at most b, or not larger than b), while the notation a ≥ b denotes a value that is greater than or equal to b (or, equivalently, at least b, or not less than b).
To learn more about inequality refer to:
https://brainly.com/question/25944814
#SPJ4
It signifies that the supplied variable or number must have a value that is larger than or equal to the specified limit. It is the opposite of less than or equal to.
What is Greater and Lower than equal to function ?The phrase "more than or equal to" denotes that the variable is either greater than or equal to a specific value. When a quantity is bigger than another, the phrase "more than" is used to indicate this. Two quantities are said to be equal when the phrase "is equal to" is used. It is possible for the quantity or amount value limit to be equal to or larger than the stated limit when these phrases are combined to form the new term Greater Than Or Equal To.
The phrase "less than or equal to" denotes that a variable is either less than or equal to another quantity, number, or variable. Other ways to say "less than or equal to" include at most, no more than, a maximum of, and not surpassing.
Inequalities like less than or equal to and greater than or equal to are represented in a different way on a number line. To denote these, we use the closed circle to mark the limit value and point the arrow towards the given condition of inequality.
To learn more about ≥ and ≤ refer to :
https://brainly.com/question/28823603
#SPJ4
What is the coefficient of y² in the expression 3y²+ 4x?
The coefficient of y² in the expression 3y²+ 4x is 3.
A number multiplied by a variable is referred to as the coefficient of a number. For instance, the x2 coefficient in the formula 6x2+99 is 6.
Firstly,
The given equation is 3y²+ 4x
To find : The coefficient of y²
The coefficient is nothing but the number beside the variable.
In the equation 3y²+ 4x, the number beside the variable y² is 3 and it is termed as coefficient of y² which is 3.
As we can see that the term that is in multiplication with y² is 3. Similarly, the term that is coefficient of x is 4.
Hence, the coefficient of y² in the equation is 3.
To learn more about the coefficient click here:
brainly.com/question/28975079
#SPJ4
Mary want to buy a bookcae to hold all of her 138 book. Bookcae A ha 4 helve and can hold 35 book on each helf. Bookcae B ha 5 helve and can hold 26 book on each helf. Which bookcae hould he buy?Bookcae A or bookcae B?
Answer:
Bookcase A
Step-by-step explanation:
Bookcase A
1 half = 35 book
4 half = 140 books
So, bookcase A can hold 140 books
Bookcase B
1 half = 26 books
5 half = 130 books
So, bookcase B can hold 130 books
So, Mary should buy bookcase A
Answer:
Bookcase A is the answer
Step-by-step explanation:
Mary has 138 books
Bookcase A = 4 shelves holds 35 books per shelf
= 4 * 35=140
Bookcase B = 5 shelves holds 26 books per shelf
= 5 * 26=130
He should buy Bookcase A, it has enough space for his books
Hiro painted his room. After 3 33 hours of painting at a rate of 8 88 square meters per hour, he had 28 2828 square meters left to paint. Let y yy represent the area (in square meters) left to paint after x xx hours.
The function representing the area to paint as a function of time is A(t) = 52 - 8t, where A(t) represents the area left to paint after t hours.
The area to paint, A(t), can be represented as a linear function based on the given information. Initially, Hiro had the entire room to paint, which can be represented as A(0) = A₀, where A₀ is the total area of the room.
Given that Hiro painted at a rate of 8 square meters per hour, after t hours, he would have painted 8t square meters.
Therefore, the remaining area to paint after t hours can be expressed as A(t) = A₀ - 8t.
We are told that after 3 hours, Hiro had 28 square meters left to paint. Substituting t = 3 and A(t) = 28 into the equation, we can solve for A₀:
28 = A₀ - 8 x 3
28 = A₀ - 24
A₀ = 52
To learn more about the linear function;
brainly.com/question/20286983
#SPJ12
The complete question:
Hiro painted his room at a rate of 8 square meters per hour. After 3 hours of painting, he had 28 square meters left to paint. Let A(t) denote the area to paint A (measured in square meters) as a function of time t (measured in hours). What is the Functions formula? A(t)=?
what is simplify 4^-4
Answer:
1/256
Step-by-step explanation:
-4 times -4 times -4 times -4 = 256
A negative exponent means it's a fraction!
So, the answer is 1/256
answer :
1/256
steps:
negative exponent means it's a fraction
4^-4 =
1/4^4 :
4^4 =
4 * 4 * 4 * 4 =
256
again negative exponent means it's a fraction so
1/256
How many buses do you need for 500 people if each bus holds 40 people?
Answer:
13
Step-by-step explanation:
Divide 500 by 40 to find the amount of buses you need
500 ÷ 40 = 12.5
BUT, you cannot have .5 of a bus! So you need ONE extra bus to hold the remaining people
you'll need 13 buses
Answer:
13 buses
Step-by-step explanation:
12 buses but 20 people left so they need 12 buses, and the 13th bus will be half filed.
in the equation -2 - 6b = 32, the negative coefficient is ____??
Answer:
May be minus
Step-by-step explanation:
minus 2 and minus 6 means minus 8b than we have to find out the value of b so 8into 4 is equal to 32
Is i squared negative 1 or 1?
The value of "i" squared results in:
(-1) = i²
What are numeric sets?Numerical sets are groupings of numerical values that have a particularity in common, they can be integers, decimals, fractions, among others.
Among the numerical sets there is one that we call complex numbers, which include values that are not real, such as "i" a letter that denotes that it is an imaginary number.
In function to this type of numbers there is a particular value and it is the "i" which is the result of the square root of -1, then we have:
√(-1) = i[√(-1)]² = i²(-1) = i²Learn more about complex numbers at:
https://brainly.com/question/12241782
#SPJ4
How would you describe the end behavior of the graph of a polynomial function based on its equation?
The end behavior of a polynomial function can be determined by examining the leading coefficient and degree of the polynomial. If the leading coefficient is positive, the graph will increase without bound as the x-values increase. If the leading coefficient is negative, the graph will decrease without bound as the x-values increase.
The end behavior of a polynomial function depends on the equation of the function. The degree of a polynomial is the highest power of the variable, and the leading coefficient is the coefficient of the term with the highest degree. If the leading coefficient is positive, the graph will increase without bound as the x-values increase. This is because the terms in the equation with positive coefficients will become increasingly larger than the terms with negative coefficients as the x-values increase. On the other hand, if the leading coefficient is negative, the graph will decrease without bound as the x-values increase. This is because the terms in the equation with negative coefficients will become increasingly larger than the terms with positive coefficients as the x-values increase. In addition, the degree of the polynomial can also affect the end behavior of the graph. If the degree is even, the graph will not have an extreme point. However, if the degree is odd, the graph will have an extreme point. The extreme point will be a maximum or a minimum depending on the sign of the leading coefficient.
Learn more about function here
https://brainly.com/question/29633660
#SPJ4
What does it mean when numbers are closed?
Whole numbers are closed under addition and multiplication. If we add and multiply any two whole numbers, the result will be a whole number.
What are Whole numbers ?
The numbers that include natural numbers and zero. Not a fraction or decimal. {0, 2, 3, 4, 5 6, 7, 8, 9, 10, 11 …} Whereas Integer: A counting number, zero, or the negative.
If we add any two whole numbers, the result will be a whole number. For example, 2 + 4 = 6 and 6 is a whole number.
Therefore, whole numbers are closed under addition.
If we multiply any two whole numbers, the result will be a whole number. For example, 2 × 4 = 8 and 8 is a whole number.
Therefore, whole numbers are closed under multiplication.
Also , Whole numbers are not closed under Subtraction and division.
Learn more about Whole numbers at:
https://brainly.com/question/9879870
#SPJ4
What are the 4 methods of solving linear equations?
Systems of linear equations in two variables can be solved in one of four ways: by graphing; by the substitution approach; or by the elimination method and by matrix approach.
Define linear equation.A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables." Because a straight line emerges when we attempt to display the graph of the provided linear function, a linear equation is known as linear.
Given,
The four methods of solving linear equations are:
The Substitution Method
The Graphing Method.
The Addition Method, also known as the Linear Combination Method, and the Elimination Method.
The Matrix Approach
To learn more about linear equation, visit:
https://brainly.com/question/11897796
#SPJ1
What is the mean of 9 and 25?
Answer:
17
Step-by-step explanation:
(9+25)/2 = 34/2 = 17
when finding a mean, you have to add all the numbers and divide the sum by the number of values given.
In which triangle all the sides are equal and all the angles are also equal *?
Equiangular triangle or Equilateral triangle have all the sides equal and all the angles are also equal.
A triangle that has equal-length sides is known as an equilateral triangle in geometry. The three angles that lie across the three equal sides are also equal in size since the three sides are also equal.
With each angle measuring 60 degrees, it is also known as an equiangular triangle.
An equilateral triangle has three interior angles that are all equivalent to one another and each measure 60 degrees in the basic Euclidean geometry. The term "regular triangle" is also used to describe this polygon because it is a regular polygon. The exceptional case of an isosceles triangle with three equal sides and angles is an equilateral triangle.
For more such questions on Equilateral triangle:
brainly.com/question/3461022
#SPJ4
Giving 25 points!!!!!! PLEASE HELP
describe the correlation for this scatter plot
Answer: Strong Negative Correlation
Step-by-step explanation:
the w10×15 cantilevered beam is made of a-36 steel and is subjected to the loading shown
For a w10×15 cantilevered beam of A - 36 steel subjected to loading as in the attached image, slope at B is 0.0042rad and displacement at B is 0.034ft.
For w10×15, moment of inertia I = 68.9in⁴ and for A - 36 steel, Young's modulus E = 29e3 ksi
Slope at B
θB = P₂x³/ (2EI) + P₁l³/ (2EI)
θB = (5 × 6³ + 9 × 12³)/ (2 × 29 × 10³ × 68.9)
θB = 0.0042rad
Displacement at B
yB = P₂x³(3l - x)/ (6EI) + P₁l³(3l - l)/ (6EI)
yB = ( 5 × 6³ × (3 × 12 - 6) + 9 × 12³ × 2 × 12)/ (6 × 29 × 10³ × 68.9)
yB = 0.034ft
--The question is incomplete, answering to the question below--
"The W10×15 cantilevered beam is made of A - 36 steel and is subjected to the loading shown.
1. Determine the displacement at B, if P1 = 9kip and P2 = 5kip
2. Determine the slope at B, if P1 = 9kip and P2 = 5kip"
To know more on cantilever beam
https://brainly.com/question/17139148
#SPJ4
A population P is growing at the rate of 9% each year and the initial population is P0. Find, as a multiple of P0, the rate of change of population at time t=T when the population has doubled from its initial time?
(Explain why, thank you!
The solution is Option B.
The rate of change of population at time t = T when the population has doubled from its initial time is P' = 2P₀ ln ( 1.09 )
What is an 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.
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 data ,
Let the equation be represented as A
Now , the value of A is
The formula for the population at time t is
P ( t ) = P₀ ( 1 + 9/100 )^t
P ( t ) = P₀ ( 1 + 0.09 )^t
P ( t ) = P₀ ( 1.09 )^t
Now , when population is doubled from the initial population ,
P ( t ) = 2P₀
Substituting the values in the equation , we get
2P₀ = P₀ ( 1.09 )^t
Taking logarithm on both sides of the equation , we get
log ( 2 ) = t x log ( 1.09 )
Divide by log ( 1.09 ) on both sides of the equation , we get
t = log ( 2 ) / log ( 1.09 )
To find the rate of change , take the derivative
P'( t ) = P₀ ( 1.09 )^t ln ( 1.09 )
Now , we find P'(log(2)/log(1.09))
So , the equation will be
P′ ( log( 2 ) / log( 1.09 ) ) = 2P₀ln( 1.09 )
Hence , the equation will be A = 2P₀ln( 1.09 )
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ1
The length of a
rectangle is 5 ft more than twice its width. The
area of the rectangle
is 33 ft^2. Find the dimensions of the rectangle.
The dimensions of the rectangle is length = 5ft and width = 3ft
Define System of equation
A system of equations is a set of one or more equations involving a number of variables. The solutions to systems of equations are the variable mappings such that all component equations are satisfied—in other words, the locations at which all of these equations intersect.
Let,
x = length of rectangle
y = width of rectangle
Next, set up system of equation
We have given, the length of a rectangle is 5 ft more than twice its width.
x = 2y + 5 --------(a)
Next, The area of the rectangle is 33 ft²
xy = 33 ----------(b)
x = 33/y
substitute the value of x in eq(a)
x = 2y + 5
33/y = 2y + 5
33 = 2y² + 5y
2y² + 5y - 33 = 0
Factor it,
2y² + 11y - 6y - 33 = 0
y( 2y + 11) - 3( 2y + 11) = 0
(y - 3) (2y + 11) = 0
Split the values,
y - 3 = 0 and 2y + 11 = 0
y = 3 and y = -11/2 (ignore this as width cannot be -ve)
Substitute y = 3 in eq(b)
x * 3 = 33
x = 11
So, we get
length = 11 ft and width = 3 ft
Hence, the dimensions of the rectangle is length = 5ft and width = 3ft
To read more about System of equation.
https://brainly.com/question/25976025
#SPJ1
How do you read mean and SD?
The variability in your data collection is measured by the standard deviation. It reveals the average distance between each score and the mean.
How to interpret a standard deviation?
The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.
What are the mean, median, and example?
The most frequent number, or the one that happens the most frequently, is known as the mode.
Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.
Learn more about mean in mode
brainly.com/question/6813742
#SPJ4