The inequality of the statement is x ≤ 30
How to determine the inequalityFrom the question, we have the following parameters that can be used in our computation:
The bus has a maximum capacity of 30 passengers
Represent the bus capacity with x
This means that the value of x cannot exceed 30
The term cannot exceed implies less than or equal to
So, we have
x ≤ 30
Hence, the inequality is x ≤ 30
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If 7i is a root of a polynomial equation, which of the following is also a root?
7+i
-7i
7-i
none
By polynomial equation, 7i , −7i this we get 1, y = x² + 49 .
What is polynomial equation?The x-axis and the graph's intersection points, or the places where y = 0, are known as the roots.
The roots of y equal 0
By figuring out what x is when x ( 7 I ) = y and y = 0 we can find the root at x = 7 i.
x 7 I is the factor.
By determining the value of x at the point where x ( 7 I ) = y and y = 0, the root at x = 7 I was discovered.
x + 7 I is the factor.
One equation can be created by combining all the variables.
y = ( x − 7 i ) ( x + 7 i)
To make the equation y = (x 7 I (x + 7 I easier to understand, multiply all the elements.
Use the FOIL Method to extend (x 7 I ) (x + 7 I
Put the distributive property to use.
y = x ( x + 7 i ) − 7 i ( x + 7 i )
Put the distributive property to use.
y = x ⋅ x + x ( 7 i ) − 7 i ( x + 7 i )
Put the distributive property to use.
y = x ⋅ x + x ( 7 i ) − 7 i x − 7 i ( 7 i )
Clarify terminology.
x x + x ( 7 I ) x 7 I x ( 7 I ) is the result of combining the opposing terms.
y = x x + 7 I x + 7 I x 7 I ( 7 I ) Rearrange the elements in the terms x ( 7 I ) and 7 I x.
To get y = x x + 0 7 I ( 7 I ), subtract 7 I x from 7 I x.
y = x x 7 I ( 7 I ) is the result of adding x x and 0.
Condense each phrase.
Divide x by x to get y: x 2 7 I (7 I
7 I ( 7 I times itself..
Calculate y = x 2 49 I I by multiplying 7 by 7.
Raising I to the power of 1, y = x²- 49 ( I I
I must be raised to the strength of
1 . y = x 2 − 49 ( i i )
Raise I to the power of 1 and then find y as y = x 2 49 ( I I )
When combining exponents, use the power rule a m a n = a m + n.
y = x ² − 49 i1 + 1
To get y = x ²- 49 I ² ,add 1 and 1.
I ² should be rewritten as 1; y = x ² - 49. - 1
y = x ² + 49 multiplied by 49 by 1.
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The current population of a small town is
4709
people. It is believed that town's population is tripling every
9
years. Approximate the population of the town
4
years from now.
The number of people in the town in the next four years is 7610.
What is the population growth rate?We know that the population growth rate can be obtained when we apply the exponential growth formula. In this case we would have;
P= Poe^rt
P = Population at time t
Po = Initial population
r = Population growth rate
t = time taken
3(4709) =4709e^9r
3 = e^9r
ln3 = 9r
r = ln3/9
r = 0.12 or 12%
In the next four years;
P =4709e^4 * 0.12
P = 7610
The population can be obtained as 7610.
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a rancher who wishes to fence off a rectangular area finds that the fencing in the east-west direction will require extra reinforcement due to strong prevailing winds. fencing in the east-west direction will therefore cost per (linear) yard, as opposed to a cost of per yard for fencing in the north-south direction. given that the rancher wants to spend on fencing, express the area of the rectangle as a function of its width .
The dimension of the largest possible rectangular area that can be fenced for $4800 is 300 yard × 150 yard. The area, A of the rectangle as a function of its width, w is A = 300w - 1.5w².
Let the width of the rectangular area be "w" and its length be "l".
The cost of the east-west direction fencing is
2w * 12 = 24w
and the cost of the north-south direction fencing is
2l * 8 = 16l
Since the rancher wants to spend exactly $4800 on fencing, we can write an equation to represent the cost:
24w + 16l = 4800
Divide by 8
3w + 2l = 600
Therefore, l = 300 - 1.5w
The area of the rectangle is given by "lw", so
A = lw
Substituting the value of "l" from the first equation into this second equation:
A = (300 - 1.5w)w
A = 300w - 1.5w²
Thus, the area of the rectangle is a function of its width and can be expressed as Area = 300w - 1.5w².
To find value of w with maximum area, dA/ dw = 0
300 - 3w = 0
w = 100
Therefore, l = 300 - 1.5*100
l = 150
--The question is incomplete, answering to the question below--
"A rancher who wishes to fence off a rectangular area finds that the fencing in the east-west direction will require extra reinforcement due to strong prevailing winds. Because of this, the cost of fencing in the east-west direction will be $12 per (linear) yard, as opposed to a cost of $8 per yard for fencing in the north-south direction. Find the dimensions of the largest possible rectangular area that can be fenced for $4800, express the area of the rectangle as a function of its width."
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hash ___ are mathematical functions that create a hash value, also known as a message digest, by converting variable-length messages into a single fixed-length value.
hash functions are mathematical functions that create a hash value, also known as a message digest, by converting variable-length messages into a single fixed-length value.
A hash function converts a given numeric or alphanumeric key into a practical and controllable integer value. The mapped integer value acts as an index in the hash table.
A hash function, in its simplest form, converts a significant number or string into a tiny integer that can be used as the index in the hash table. The pair has the form (key, value), and one can find a value for a given key by using a "function" that converts keys to values.
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find m
please and thank you
The measure of angle K and L in the first figure is ∠L = 23 degrees and ∠K = 157. Second figure, the measure of ∠K = ∠L = 70 degrees.
What is sum of interior angles?A polygon's interior angle is the angle created between its two adjacent sides. Alternately, we may state that the internal angle of a polygon refers to the angle measured at the interior portion of a polygon.
For figure 2 the two lines are parallel to each other, and the line that meets the parallel line at points at M and L are from two equal lines.
Hence, the angle suspended by both are equal, that is:
∠L = ∠M
∠L = 23 degrees.
Now, the ∠K and ∠J are created by two parallel lines; hence they are equal:
∠K = ∠J = x
The sum of interior angles of a quadrilateral is 360, so:
∠L + ∠M + ∠J + ∠K = 360
23 + 23 + x + x = 360
46 + 2x = 360
2x = 360 - 46
x = 157
Hence, the measure of angle K and L is 157 and 23 respectively.
For the second figure, the angle K and L are created by equal length of segments.
∠K = ∠L = x
The sum of interior angles of a quadrilateral is 360, so:
∠L + ∠M + ∠J + ∠K = 360
x + 90 + 130 + x = 360
2x + 220 = 360
2x= 360 - 220
x = 70
Hence, the angle of K and L is 70 degrees.
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which of the following are correct ways ofg determining of two compound propositions p and q are equailivanet
Two compound propositions p and q are logically equivalent if p↔q is a tautology. Alternatively, p and q are equivalent if and only if the columns in a truth table giving their truth values agree.
Two compound propositions p and q are logically equivalent if and only if p logically implies q and q logically implies p. In other words: two compound propositions are logically equivalent if and only if they have the same truth table.
let us consider,
T be the truth and F be the false of a problem statement.
Then the compound propositions p and q are logically equivalent if :
P q P→q
T T T
F F T
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The complete question is :
What is the correct way of determining of two compound propositions p and q are equivalent.
construct a truth table for p→q if the proposition is tautology.
HELPPPpppppppppppppppppppppppppppppp
Answer:
9 cm
Step-by-step explanation:
cos B = adj/hyp
cos B = BC/AB
cos 25° = 8 m / AB
AB = 8 m / cos 25°
AB = 9 cm
one week,Alonso earned $204.40 at his job when he worked for 14 hours.if he is paid the same hourly wage,how many hours would he have to work the next week to earn $554.40
The number of hours that Alonso would have to work to earn $ 554. 40, given the same hourly wage, is 37.9 hours
How to find the number of hours ?To find the number of hours that Alonso needs to work in the week to make $ 554. 40, you first need to find the hourly wage :
= Amount earned / Hours worked
= 204. 40 / 14
= $ 14. 60 per hour
If Alonso wants to earn $ 554 .40 then the number of hours he would need to work is:
= Amount to be earned / Hourly wage
= 554. 40 / 14. 60
= 37.9 hours
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You are tasked with helping plan a school dance. You expect 110 people to attend the dance and need to provide seating for each person. The tables come in two different sizes. The smaller tables can fit 2 people, the larger tables can seat 4 people. Write an equation that describes the relationship between the quantity of small tables and the quantity of large tables, assuming exactly 110 people need seats.
A possible equation to express the situation described is 2x + 4y = 110.
What is an equation?The word equation can be defined as a mathematical expression that uses numbers, symbols, and even letters to mathematically represent a situation.
How to write an expression in this case?Consider the variables:
Tables: There are two types, tables that can fit 2 or 4 peopleTotal of people: 110Now relate these variables using letters and symbols
2x (number of tables that can fit two people) + 4y (number of tables that can fit four people) = 110
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Consider this equation.cos(0)= -2â5/5If 0 is an angle in quadrant II, what is the value of sin(0)?
The value of sin(0) should be considered as the [tex]\frac{\sqrt5}{5}[/tex] in second quadrant.
The values of all trigonometric functions' dependent on the value of the ratio of sides of a right-angled triangle are known as trigonometric ratios. The trigonometric ratios of a right-angled triangle's sides about any of its acute angles are known as that angle's trigonometric ratios.
Calculation of the value of sin(0):
Since the equation is [tex]cos(o)=\frac{-2\sqrt{5}}{5}[/tex]
by the Pythagorean theorem -
[tex]h^2=p^2+b^2[/tex]
value of perpendicular is = [tex]\sqrt5[/tex].
The trigonometry ratios for a specific angle ‘θ’ is given below:
Trigonometric Ratios:
Sin θ = Perpendicular/Hypotenuse
Cos θ = Base/Hypotenuse
Also in the case when 0 is an angle in quadrant II
So based on this, we can say that value of sin(0) should be considered
as the [tex]\frac{\sqrt5}{5}[/tex].
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determine if (x-3) is a factor of (x^4-13x^2+36) using synthetic division
Answer: x^3+3x^2+22x+66+234/x-3
Step-by-step explanation: I used synthetic division and this is what I got hope this helps
One number is 11 less than another. If their sum is increased by eight, the result is 81. Find the numbers. (Enter your answers as a comma-separated list.)
In a case whereby One number is 11 less than another ,If their sum is increased by eight, the result is 81 the numbers will be 42.
How can the number be determined?The concept that will be used here is summation. A summation, also known as a sum, is the outcome of adding two or more numbers or quantities. There are always an even number of terms in a summation. There could be only two terms, or there could be one hundred, thousand, or a million. There are summations with an infinite number of terms.
Let the first number be wriiten as = x
second number = x-11
The we can add up as :
(x + x -11 + 8) =81
2x -3 =81
2x =84
x = 42
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What was the closing price for the last trading day?
Answer:
how would i know the closing price ...
i need an answer fast and correct and ill mark for brainiest
The correct orientation and location of triangle DEF is option B (as shown in the attachment to this answer).
Rotation of an object.Rotation is one of the types of solid transformation which involves turning a given object about a reference point or line at a certain required measure of angle. Other types of transformation are: dilation, translation and reflection.
Dilation: This is a process in which the dimensions of an object is either increased or decreased to produce its image.
Translation: This is a procedure that requires moving a given object a number of units in a specified direction.
Reflection: This requires flipping an object over a line to produce an image.
In the question, after rotating triangle ABC 90^o clockwise; the correct orientation and location of triangle DEF is option B.
A sketch of this is attached to this answer for clarity.
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use the definition of the riemann integral in terms of riemann sums to prove property (3) of definite integrals. that is, if f(x) is continuous on [a, b] and k is any constant, then: Integral from b ( k f(x) dx) = k integral fromb ( f(x) dx)
The integral of k*f(x) equals the integral of f(x) multiplied by k because the total of k*f(x) equals the sum of f(x) multiplied by k.
K*F(x) Integral = K*Fintegral (x). This is inferred from the description of a definite integral as the upper limit of a term sum. The area under the curve can be divided into a number of rectangles and their areas added if we are taking the integral of a function from a to b. The integral then equals the maximum value of this total. The result is identical to the original sum increased by k if we multiply each term of the sum by a constant called k. as a result, the maximum allowed f(x) multiplied by k because the total of k*f(x) equals the sum of f(x) multiplied by k.
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Are the ratios 1:5 and 18:20 equivalent?
Answer:
No, these ratios are not equivalent.
Step-by-step explanation:
Find the value of x.then  round to the nearest 10th
The value of x is 10.79
What is trigonometry ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
sin (tetha) = opp/ hyp
cos ( tetha) = adj/ hyp
tan ( tetha) = opp/ adj
tetha = 26
hyp = 12
adj = x
cos 26 = x/12
cos 26 × 12 = x
x = 0.899 × 12
x= 10.79
Therefore the value if x is 10.79
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Construct segment so that it is perpendicular to segment and segment so that it is perpendicular to segment .
Complete the proof.
The completed proof for the two triangles is as follows -
ST bisects ∠UTV - Given
∠UTS ≅ ∠VTS - Angle Bisection Theorem
∠TUS and ∠TVS are right angles - Given
∠TUS ≅ ∠TVS - All right angles are congruent
ST ≅ ST - Reflexive property of congruence
ΔUTS ≅ ΔVTS - Angle Angle Side (AAS) Theorem
SU ≅ SV - CPCTC Rule
SU = SV - Congruence Theorem
What are triangles?
Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.
Two right angle triangles ΔSUT and ΔSVT are given with line segment ST being the common.
It is given that line segment ST bisects ∠UTV as ST is the common line between the two triangles.
∠UTS ≅ ∠VTS as it is bisected by the line segment ST and it follows the rule of angle bisection theorem.
∠TUS and ∠TVS similar as they both are right-angles which is denoted by the small square symbol in the diagram.
∠TUS ≅ ∠TVS as they both are right-angles and all the right angles are equal and congruent having a measure of 90°.
ST ≅ ST since it is mid line segment of both the triangles and it follows the rule of reflexive property of congruency.
ΔUTS ≅ ΔVTS as they satisfy the AAS theorem, where two angles of a triangle and side between them are equal. Here, ∠UTS ≅ ∠VTS, ∠UTS ≅ ∠VTS and ST ≅ ST.
SU ≅ SV as corresponding parts of the congruent triangles are congruent. So, the CPCTC rule is applied.
SU = SV as they are part of the congruent triangles, so the line segments must be equal.
Therefore, ΔUTS is equal and congruent to ΔVTS.
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Answer: Hope this helps sorry for answering late ^ ^
Step-by-step explanation: i got it right
Find three consecutive odd
three times the
integers such that the sum of one times the first,
two times the second, and
third is 334. List the numbers in order from smallest to in largest.
The numbers in order from smallest to in largest are 65.6, 66.6. and 67.6 respectively
What are algebraic expression?Algebraic expression are expressions comprising of terms, variables, coefficients, constants and factors.
These algebraic expressions are also composed of arithmetic operation, such as;
DivisionSubtractionAdditionMultiplicationFloor divisionBracketParenthesesFrom the information given as;
x+1 + 2x + 4 + 2x + 6 = 334
collect like terms
x + 2x + 2x = 334 - 11
add or subtract like terms
5x = 323
Make 'x' the subject of formula
x = 64. 6
The numbers are;
x + 1 = 65.6
x+ 2 = 66. 6
x + 3 = 67. 6
Hence, the numbers are 65.6, 66.6. and 67.6
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Please see attached math problem.
a) The table is given below..
b) x + y = 45
c) 5.20x + 9y = 291
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 8 is an equation.
We have,
Cost of small box x = $5.20
Cost of large box y = $9
Now,
Number of boxes sold in one hour = 45
Total amount earned = $291
We can make two equations.
x + y = 45
x = 45 - y
Substituting
5.20x + 9y = 291
5.20 (45 - y) + 9y = 291
234 - 5.20y + 9y = 291
234 + 3.8y = 291
3.8y = 291 - 234
3.8y = 57
y = 15
Now,
x = 45 - y
x = 45 - 15
x = 30
Table:
Categories Value Number Amount
Small box 5.20 30 30 x 5.20 = 156
Large box 9 15 15 x 9 = 135
Thus,
The table is given above.
The equation is x + y = 45
The equation is 5.20x + 9y = 291
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If RS = x + 5, ST = 14x − 15, and RT = 20, what is RS?
please help as fast as you can.
The Length of RS = 7 units.
Collinear points:The set of points that lie on a straight line is known as Collinear points. In other words, two or more points that lie on the same straight line are said to be Collinear points.
Here we have
RS = x + 5, ST = 14x − 15, and RT = 20
When R, S, and T are considered as 3 collinear points
=> RT = RS + ST
From the given data,
=> 20 = x + 5 + 14x − 15
=> 15x − 10 = 20
=> 15x = 30
=> x = 2
Length of RS = x + 5 = 2 + 5 = 7
Therefore,
The Length of RS = 7 units
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which equation can be used to find the scale price, s,of an oil change?
If an oil change at city auto is regularly $30 Mr. Allen has a coupon for 15% off. The equation that can be used to find the sale price, S, of an oil change is: 3. s=0.85(30).
How to find the sales price?First step is to find the percentage left if he has a coupon for 15% off.
Percentage left = ( 1- 0.15)
Percentage left = 0.85 or 85%
Now let find the sales price
Sales price = 0.85(30)
Sales price = $25.50
Therefore the equation that can be used to find the sale price, S, of an oil change is: 3. s=0.85(30).
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The complete question is:
An oil change at city auto is regularly $30 Mr. Allen has a coupon for 15% off. Which equation can be used to find the sale price, S, of an oil change?
1. s=0.85 divided by 30
2. s=85 divided by 30
3. s=0.85(30)
4. s=85•30
a standard football field is 100 yards long from the end zone to the end zone and 160 feet wide. find the area of the field in square yards. hint: read carefully!
To find the football field's area in square yards, we need to multiply the length by the width, both of which are given in different units of measurement (yards and feet).
Steps:
1. Convert the width of the field from feet to yards: 160 feet / 3 feet/yard = 53.33 yards
2. Multiply the length and width of the field to find its area: 100 yards * 53.33 yards = 5,333 square yards. Therefore, the area of the football field is 5333.33 square yards.
The room is square since the length and range of the room are the same. Hence, we can apply the area of the square formula to cipher the area of the given carpet demanded to cover the room. Hence, the answer is 16 square yards.
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The area of the field in square yards will be 16 sq. yards.
To calculate the size of a football field in square yards, multiply the length by the width, which are both given in separate units of measurement (yards and feet).
First, we'll convert the field's width from feet to square yards.
There are 3 feet in 1 yard,
So 160 feet is the same as 160 / 3 = 53.333 yards.
Then we'll multiply the length by the width: 100 * 53.333 = 5333.33 square yards.
Therefore, the area of the football field is 5333.33 square yards.
The room is square since its length and width are equal.
As a result, we can use the area of the square formula to calculate the area of the provided carpet required to cover the room.
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Can you help me? I could use it.
The ratio of rubies to diamonds is equal to 1:4.
What is a ratio?In Mathematics, a ratio simply refers to a mathematical expression that is typically used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.
In this scenario, we would assign variables to the number of rubies and number of diamonds as follows;
Let the variable R represent number of rubies.Let the variable D represent number of diamonds.Since the number of rubies is four (4) times the number of diamonds, this can be represented as a ratio as follows;
R = 4D ⇒ R:D = 1:4.
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be Maps Desmos) Graphing
Analyzing Intersections of Lines and Planes
y
Z
x
B
Schoology
O
w
A
E
Use the given diagram to answer the question.
Which line is the intersection of two of the planes
shown?
Which line intersects one of the planes shown?
VZv
Which line has points on three of the planes shown?
Note that:
There are three separate planes and three different lines in the diagram. Line X crosses two of the planes, whereas Line Z intersects just one of the planes, and Line Y has points on all three planes.
Line y has points A and B in each of the three planes.
A plane is a flat surface that can be sliced across by a straight line connecting any two locations on the plane.
As a result of the diagram, we may deduce that
Line X is the line that connects two planes.Line Z is the line that intersects one of the planes.Line Y is the line with points on three of the planes displayed.Learn more about Planes:
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14.5x35 (if you do answer can you show work because it tells me to show work and if i don't ill get it wrong.)
The value of the expression 14.5 * 35 is 507.5
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
14.5 * 35
The given expression is a simple expression that can be solved using a calculator
Using a calculator, we have the following solution
14.5 * 35 = 507.5
Hence, the solution is 507.5
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Function Tables 2
Thank you!
To the function u=I+6, for the output 20 input is 14.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
For the table 2, the rule is u=I+6
For output u=14, we get
14=I+6
I=8 (Input)
For output u=28, we get
28=I+6
I=22 (Input)
For input I=24, we get
u=24+6
u=30 (Output)
For output u=16
16=I+6
I=10 (Input)
For output u=20
20=I+6
I=14 (Input)
For input I=48
u=48+6
u=54 (Output)
Therefore, to the function u=I+6, for the output 20 input is 14.
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Y=21(1.44)^x growth or decay
The exponential function [tex]Y=21{(1.44)}^x[/tex] represents growth when x ∈ N.
What is the formula for exponential growth and exponential decaying function?The formula for exponential growth is [tex]y = y_0.e^{(kt)}.[/tex]
The formula for exponential decay is [tex]y = y_0.e^{(-kt)}.[/tex].
Given, An exponential function [tex]Y=21{(1.44)}^x[/tex].
Now, This function can represent growth or decay depending upon the values of 'x'.
If x ∈ N, Then this exponential function [tex]Y=21{(1.44)}^x[/tex] represents growth.
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Last year, Dion gave $12, 848 to his local church, which he calculated as 27.5 % of his yearly salary.
How much money does Dion make in a year?
Dion will make $16381.2 in a year.
What is simple interest?
A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,
The formula for simple interest is:
S = p*t*r/100
where P is the principal amount of money, R is the interest rate as a decimal, T is the time.
Dion gave $12, 848 to his local church
which he calculated as 27.5 % of his yearly salary.
S = 12, 848 * 1*27.5 /100 = 3533.2
Total = 3533.2+12, 848 = $16381.2
Hence Dion will make $16381.2 in a year.
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You are curious about the accuracy of the estimates that the widget store owner gave you. If you wanted to take a random sample of daily customer arrivals, from which of the following is the population you should sample?1 баллThe number of arrivals each day for this widget store and the competing widget store down the street.The number of arrivals each day for all days this specific widget store has been open.The number of arrivals each day for this specific widget over the past month.A random, representative sample of the number of arrivals each day to this specific widget store.
The number of arrivals who came in each day while this particular widget shop was open. Therefore, statement 2 is correct.
The process by which a sample of observations is selected from a population to assume the population is known as random sampling. This process ensures that the results we get from your sample should be close to what we would have gotten if we measured the complete population. So that all the units in the population have an equal chance of being chosen using the simplest random sample.
In the given scenario, the number of arrivals each day for the widget store should have equal chance. To be specific, we should only take into account the number of visitors on the days when the store is open.
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