The population grew to the number 7,723 in 27 years past 1940, i.e., 1967.
What is the linear function?
In mathematics, the term linear function refers to two distinct but related notions: In calculus and related areas, a linear function is a function whose graph is a straight line, that is, a polynomial function of degree zero or one.
We have,
The population of a small town, P, as a function of time, t, in years past 1940 is:
P = 2,323 + 200t
Let t be the year in which the population reached a count of 7,723. Solve for t:
P = 2,323 + 200t
7,723 = 2,323 + 200t
7,723 - 2,323 = 200t
5,400 = 200t
t = 5400/200
t = 27 years
Hence, The population grew to the number 7,723 in 27 years past 1940, i.e., 1967.
To learn more about the linear functionvisit,
https://brainly.com/question/4025726
#SPJ1
Alex has $170.42 in his account before making any transactions. Over the course of a week, Alex makes the following transactions:
At the end of the week, how much money is in Alex’s account?
$50.73
$114.13
$119.69
$226.71
Answer:
To find out how much money is in Alex's account at the end of the week, we need to add up all of the transactions that he made over the course of the week.
We start by adding the initial amount that Alex had in his account before making any transactions, which is $170.42.
Then we add the first transaction, which is $50.73. This brings the total to $221.15.
Next, we add the second transaction, which is $114.13. This brings the total to $335.28.
Then we add the third transaction, which is $119.69. This brings the total to $455.97.
Finally, we add the fourth and last transaction, which is $226.71. This brings the total to $682.68.
Therefore, at the end of the week, Alex has $682.68 in his account.
Step-by-step explanation:
Y/y-5+5/5-y= step bye step
The solution of the given equation is, y = -3.
what is solving an equation?
An effective method for solving linear equations can be found in the steps that follow. By deleting parentheses and combining like terms, each side of the equation can be made simpler. The variable term on one side of the equation can be separated using addition or subtraction. To find the variable, use multiplication or division.
Consider, the given equation
[tex]\frac{y}{y}-5 + \frac{5}{5}-y =0[/tex]
Since, If a/a then it is 1.
⇒ 1 - 5 + 1 - y = 0
-3 - y = 0
Add y on both sides,
-3 - y + y = 0 + y
-3 = y
y = -3
Hence, the solution of the given equation is, y = -3.
To know more about solving an equation, click on the link
https://brainly.com/question/22688504
#SPJ1
What is the range of linear function?
A linear function can only have one degree at most but the range of linear function is infinite.
In the given question, we have to explain what is the range of linear function.
A linear function can only have one degree at most. Therefore, it has at least most one x increased by one. The formula for them is f(x) = mx + b.
Nearly invariably, the domains and ranges of linear functions are infinite. When the graph is a horizontal line, there is an exception. This occurs when a function, like f(x) = b, equals a constant. These functions' domains are unlimited, but their range only contains the value b.
To learn more about range of linear function link is here
brainly.com/question/4786835
#SPJ4
What are the coordinates of the image of the point (-3, 6) after a dilation with a center of (0, 0) and scale factor of 1/3?
A. (-9, 18)
B. (-3, 6)
C. (-1,2)
D. (0,0)
Answer:
C
Step-by-step explanation:
since the dilatation is centred at the origin then multiply the coordinates of the point by scale factor of [tex]\frac{1}{3}[/tex]
(- 3, 6 ) → ([tex]\frac{1}{3}[/tex] (- 3), [tex]\frac{1}{3}[/tex] (6) ) → (- 1, 2 )
12.Todd's teacher asked him to construct a graph with the following specifications.
By studying the graph, it can be concluded that
Todd has done three mistakes
He has y increasing when x is between -5 and 0 instead of decreasing.
He has y decreasing when x is between 0 and 5 instead of increasing.
He has a non-linear relationship from x = 0 to 5 instead of a linear relationship.
What is graph of a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Graph of a function f(x) is the collection of points of the form (x, f(x))
Original specifications of the graph
y is decreasing when x is between -5 and 0
y is increasing when x is between 0 and 5
The relationship between x and y is non-linear from x = - 5 to x = 0
The relationship between x and y is linear from x = 0 to x = 5
From the graph it can be seen that Todd has done three mistakes
He has y increasing when x is between -5 and 0 instead of decreasing.
He has y decreasing when x is between 0 and 5 instead of increasing.
He has a non-linear relationship from x = 0 to 5 instead of a linear relationship.
To learn more about graph of a function, refer to the link-
https://brainly.com/question/24335034
#SPJ1
Given h(x)=4x-5 find h(4)
Step-by-step explanation:
16-5= 11
hope it's helpful
Nancy just became a personal trainer and is finalizing her pricing plans. One plan is to charge $41 for the initial consultation and then $83 per session. Another plan is to charge $43 for the consultation and $82 pse session. Nancy realizes that the two plans have the same same cost for a certain number of sessions. How many sessions is that? What is the cost?
The required number of sessions is obtained as 2.
How to balance a linear equation?A linear equation can be balanced by adding or subtracting the same number on both sides of the equality sign. Similarly, multiplication and division is also possible with the same numbers.
Suppose the number of sessions be x.
Then, the expression for the training cost as per the first plan is given as 41 + 83x.
And, for the another plan it is 43x + 82.
As per the question both the expressions has to be equated for the same cost as follows,
43 + 82x = 41 + 83x
=> 43 - 41 = 83x - 82x
=> x = 2
Hence, the number of sessions for both the plans to have same cost is 2.
To know more about linear equation click on,
https://brainly.com/question/11897796
#SPJ1
What is the slope of the line passing through the points P1 x1 y1 and P2 x2 y2?
(y2 - y1) / (x2 - x1) is the slope of the line passing through the points P1 x1 y1 and P2 x2 y2.
The slope of the line passing through the points P1 (x1, y1) and P2 (x2, y2) is calculated by: (y2 - y1) / (x2 - x1).
1. Subtract the y-coordinates of the two points: y2 - y1.
2. Subtract the x-coordinates of the two points: x2 - x1.
3. Divide the two results from steps 1 and 2: (y2 - y1) / (x2 - x1).
For example, if the two points are P1 (1, 5) and P2 (3, 8), then the slope is calculated by: (8 - 5) / (3 - 1) = 3 / 2 = 1.5. This means that the line has a slope of 1.5, which means that for every 1 unit increase in x, the y-coordinate increases by 1.5 units. So, for every 2 units increase in x, the y-coordinate increases by 3 units.
Learn more about slope here
https://brainly.com/question/3605446
#SPJ4
The lengths of the four sides of a quadrilateral (in feet) are consecutive even integers. If the perimeter is 92 feet, find the value of the longest of the four side lengths.
Answer:
The perimeter of the quadrilateral is the sum of the four side lengths. If the perimeter is 92 feet, then we can write the equation $x + (x+2) + (x+4) + (x+6) = 92$, where $x$ is the length of the shortest side. Solving this equation, we find that $x = 20$. This means that the side lengths are 20 feet, 22 feet, 24 feet, and 26 feet, so the longest side is 26 feet.
select all equations that are true with x=6
Answer:
A, C, and E
Step-by-step explanation:
Graph and label each figure and its image under a reflection in the given line.
Give the coordinates of the image
S'(4,-3),T'(7,-2),U'(8,-5),V'(2,-7), We must plot the graph using the above data for S(-3,6), T(0,7), U(1,4), and V(-52).
A graph is what?The link between lines and points is described by a graph, which is a mathematical description of a network.
The link between lines and points is described by a graph, which is a mathematical description of a network.
Plotting a graph based on the provided data is shown in the attachment.
Given, \s (x,y)=(x+7,y-9)
For example, S(-3,6)=S'(x+7,y-9)=S'(-3+7, 6-9)=S' (4,-3)
T(0, 7) = T' (x+7, y-9) = T' (0+7, 7-9) = T' (7,-2)
According to U(1,4)=U'(x+7,y-9)=U'(1+7, 4-9)=U' (8,-5)
Considering that V(-5,2)=V'(x+7,y-9)=V'(-5+7,2-9)=V' (2,-7)
To create the graph, we must plot the points S'(4,-3), T'(7,-2), U'(8,-5), and V'(2,-7).
S'(4,-3),T'(7,-2),U'(8,-5),V'(2,-7)
We must plot the graph using the above data for S(-3,6), T(0,7), U(1,4), and V(-52).
To learn more about Graph refer to:
https://brainly.com/question/19040584
#SPJ1
Diego charges $60 for the first hour of consulting and $30 for each additional hour or fraction of an hour.
the mean number of calls received in a certain office per day is 10 . what is the probability that in any given day the office receives exactly 3 calls ?
The probability that on any given day the office receives exactly 3 calls is 0.0076.
What is probability?
A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Here, we let
Let X be the number of calls received in an office per day.
X≈Poison(λ=10)
P(X = x) = e^(-λ)λˣ/x!; x = 0, 1, 2.....
= 0, otherwise
The probability that on any given day the office receives exactly 3 calls: 0.0076
P(X = 3) = e^(-10)10³/3!
P(X=3) = 0.0076
Hence, the probability that on any given day the office receives exactly 3 calls is 0.0076.
To learn more about the probability from the given link
https://brainly.com/question/25638875
#SPJ4
At this point, let us extend what you have done in Optimize. Consider the sets of
geometric figures below then answer the questions that follow.
10
1.
2.
3.
4.
5.
1
m
Q
How many points do OO and line / have in common?
How many points do OP and line m have in common?
How many points do OQ and line n have in common?
What kind of angle is formed by the line segments from the center of the
circles and their corresponding lines?
Are the line segments from the center of the circles parallel to their respective
lines? If not, write the correct term.
Answer:
No point,One Point.Reflex Angle Formed .
true or false: leagues with larger standard deviation values are more competitively balanced than other leagues
It is ''True'' that leagues with larger standard deviation values are more competitively balanced than other leagues.
What is Standard deviation?The standard deviation is a measure of how widely distributed or how much values vary. The expected value occurs when the standard deviation is low, which increases the likelihood that the values will fall within a small range. When the standard deviation is high, on the other hand, the expected value occurs when the values are closer to the mean.
Lets take an example to understand Standard deviation
Let's say the entire target population is comprised of eight students in a specific class. By subtracting the average of the values' squared deviations from it, one can calculate the population standard deviation for a finite set of numbers.
Eight of the following values represent the marks of an eight-student class (or a statistical population):
2,4,4,5,5,5,7,8
These eight data points have the mean (average) of 6;
[tex]\frac{2+4+4+5+5+5+7+8}{8}[/tex] = [tex]\frac{40}{8}[/tex]
= 5
First, calculate the deviations of each data point from the mean, and square the result of each:
[tex](2-5)^{2} =[/tex] [tex](-3)^{2}[/tex] = 9 [tex](5-5)^{2} =[/tex] [tex]0^{2}[/tex] = 0
[tex](4-5)^{2} =[/tex] [tex](-1)^{2}[/tex] = 1 [tex](5-5)^{2} =[/tex] [tex]0^{2}[/tex] = 0
[tex](4-5)^{2} =[/tex] [tex](-1)^{2}[/tex] = 1 [tex](7-5)^{2} =[/tex] [tex]2^{2}[/tex] = 4
[tex](5-5)^{2} =[/tex] [tex]0^{2}[/tex] = 0 [tex](8-5)^{2} =[/tex] [tex]3^{2}[/tex] = 9.
The variance is the mean of these values:
[tex](sigma)^{2}[/tex] = [tex]\frac{9+1+1+0+0+0+4+9}{8}[/tex] = [tex]\frac{24}{8}[/tex] = 3
and the population standard deviation is equal to the square root of the variance:
sigma = √3 = 1.732
This formula is valid only if the eight values with which we began form the complete population.
Learn more about Standard deviation from
https://brainly.com/question/475676
#SPJ4
4.Which of the following numbers are rational? Select three that apply.
Responses
The Rational number are 7/3, 8 and 72/8.
What is Rational Number?
Numbers that may be expressed in the form p/q, where p and q are integers and q0, are considered rational numbers. Because fractions cannot have a negative numerator or denominator, they differ from rational numbers in this respect. Because of this, the numerator and denominator of a fraction are whole numbers (denominator 0), unlike in the case of rational numbers, when they are both integers.
So to convert a fractional to reduce form we have to divide by 10 to power how many digits thereafter decimal point, and make sure that the numerator or denominator doesn't have commonly divisible.
√5 is not rational.
7/3 is rational
√17 is not rational
√64 = 8 is rational
72/8 is rational
Hence, The Rational number are 7/3, 8 and 72/8.
Learn more about Rational Number , by the following link
https://brainly.com/question/12088221
#SPJ1
Last year Raina biked n miles . This year She biked 575 miles . Using n , write an expression for the total number in of miles she Biked
Answer: n+575= total
or n+575=t
Step-by-step explanation:
n is what we start with, plus what she has this year. the total is unknown.
-5-5(3•5n)=-70
Find N
6x/4=12 what does x=?
Answer:
x = 8
Step-by-step explanation:
6x/4 = 12
Multiply 4 on both sides to get rid of it:
6x = 4(12) = 48
Divide 6 on both sides:
x = 48/6 = 8
Question
a. Write the formula for the area A of a trapezoid. Use b1 and b2 for the lengths of the bases, and use h for the height.
A=
b. Solve the formula for h.
h=
c. Use the new formula to find the height h of the trapezoid.
The height of the trapezoid is
centimeters.
The formula for the area of the trapezoid is A = 1/2(b₁ + b₂)h and the formula for height will be (2A)/(b₁ + b₂).
What is surface area?The quantity of space enclosing a three-dimensional shape's exterior is its surface area.
In other meaning, if we say side square then it is an area of the square but for a cuboid, there are 6 faces so the surface area will be external to all 6 surfaces area.
The area of a trapezoid is given as,
A = 1/2(b₁ + b₂)h
The formula for height h will be as,
A = 1/2(b₁ + b₂)h
h = (2A)/(b₁ + b₂)
Hence "The trapezoid's area is calculated using the calculation A = 1/2(b1 + b2)h, and its height is calculated using the formula (2A)/(b1 + b2).".
To learn more about surface area,
https://brainly.com/question/2835293
#SPJ1
Avani is designing a new board game, and is trying to figure out all the possible outcomes. How many different possible outcomes are there if she spins a spinner with four equal-sized sections labeled Red, Green, Blue, Orange and flips a coin?
The number of possible outcomes when she spins and flips a coin is 8.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The number of sections in the spinner = 4.
The number of possible outcomes in the coin = 2
Now,
The number of possible outcomes when she spins and flips a coin.
= 4 x 2
= 8
i.e
{Red, Green, Blue, Orange} x {H, T}
{Red:H, Red:T, Green:H, Green:T, Blue:H, Blue:T, Orange:H, Orange:T}
______(A)
Thus,
The number of possible outcomes from (A) is 8.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ1
A pyramid has a base with an area of 25 in² and a
volume of 100 in³. Find the height of the pyramid.
Answer:
12in
Step-by-step explanation:
Area and Volume (Proportion)Base Area and Volume are proportionalised based on their Height.
Eg. Base Area of Cube = Length × Width
Volume of Cube = Length × Width × Height
SolutionGiven from the Question:
Base Area of Pyramid =
[tex]25 \: {in}^{2} [/tex]
Volume of Pyramid =
[tex] \frac{1}{3} (base \: area)(height) = 100 {in}^{2} [/tex]
We already knew the Base Area, so we can substitute it into the Volume of Pyramid Formula to find the height.
[tex] \frac{1}{3} (25)(height) = 100 \\ height = \frac{100(3)}{25} \\ = 12in[/tex]
Therefore the height of the Pyramid is 12in.
Find The Missing Angles
The value of all the missing angles in the triangles are;
∠1 = 37°
∠6 = 30°
∠4 = 63°
∠3 = 133°
How to find the missing angles of the triangle?We know that the sum of angles in a triangle is equal to 180 degrees. Thus, with this knowledge, we can find the angles 1 and 6.
Therefore;
∠1 = 180 - (70 + 73)
∠1 = 180 - 143
∠1 = 37°
∠6 = 180° - (107° + 43°)
∠6 = 180° - 150°
∠6 = 30°
Now, we know that sum of angles on a straight line is 180 degrees. Thus, we can find angle 4 as follows;
∠4 = 180° - (65° + 42°)
∠4 = 180° - 117°
∠4 = 63°
∠3 = 90 + 43
∠3 = 133°
Thus, the conclusion is that the missing angles are ∠1 = 37°, ∠6 = 30°, ∠4 = 63°, ∠3 = 133°
Read more about missing angles at; https://brainly.com/question/28293784
#SPJ1
What is the value of t that satisfies the equation below? 3(t+4)-2(2t+3)=4
Explain how you got your answer
Answer:
t = 2
Step-by-step explanation:
First, we have to simplify the equation by multiplying 3 and -2 by everything in the corresponding parenthesis:
3(t+4) simplifies = 3t + 12
-2(2t+3) simplifies = -4t - 6
So:
3t + 12 - 4t - 6 = 4
Now we can combine like terms:
-t +6 = 4
Then we subtract 6 on both sides:
-t = -2
Then we divide by -1 in order to get rid of the negative:
t = 2, final answer.
What is an example of conceptual learning?
Conceptual Learning involves students engaged in quality learning experiences based around key concepts and central ideas rather than using the more traditional method of focusing on learning on topics.
Example of Conceptual Learning
A student with a conceptual understanding of decimals may readily work with fractions, percentages, and ratios. Students who just have traditional knowledge, on the other hand, may struggle to cope because they will have to recollect the information as different concepts.
Conceptual learning encourages active participation since it requires students to participate actively in the process, whereas traditional types of learning require the teacher to explain information
Learn more about conceptual learning here :-
brainly.com/question/21168020
#SPJ4
Express the radical using the imaginary unit,i .
Express your answer in simplified form.
√-30 = ±
Answer:
[tex] + - \sqrt{ - 30}[/tex]
Answer:
[tex]\sqrt{30i}[/tex]
Step-by-step explanation:
khan <3
Consider =) as a parametrized surface in the natural way. Write the equation of the tangent plane to the surface at the point 3.4.3) given that (48) = 4 and 14:32
The tangent planes to the surface are described by the equation "6x + 12y + 48z - 210 = 0" (3, 4, 3).
In this instance, the equation yields the parametrized surface "r(t) = (t², [tex]t^3[/tex], [tex]t^4[/tex]). On the surface, the issue that interests us is (3, 4, 3).
We may use the partial derivative concept to obtain the second derivative of the surface at points (3, 4, 3). Regardless of whether a change in the parameterization approaches zero, the time derivative of the parameter value of a variable serves as the upper estimate of the differentiating quotient.
[(r(3 + h) - r(3)) / h] as h approaches 0
For the x-coordinate of the surface, this limit is given by
[((3 + h)² - 3²) / h] as h approaches 0
which simplifies to
[(9 + 6h + h² - 9) / h] as h approaches 0
which simplifies to
[6h + h²] as h approaches 0
Since h is approaching 0, h2 is approaching it faster than h. As h approaches 0, the limit changes from 0 to 6, and the number of h2 decreases relative to the value of 6h.
Thus, the partial derivative of the x-coordinate of the surface concerning the time at the coordinates (3, 4, 3) is 6.
As a result, the vector is the normal vector to the ground at the location (3, 4, 3). (6, 12, 48). 6x + 12y + 48z + d = 0 is the equation of the tangent planes to the ground at this position.
Learn more about the tangent plane at
https://brainly.com/question/29589716
#SPJ4
0.0
1. Mei is shopping for the items shown in the
table. Write an expression to represent the
total cost of 6 bubbles, 2 beach balls, and
3 sand buckets. Then find the total cost.
(Example 3)
Item bubbles beach ball sand buckets
Cost $1.49
$2.00
$3.50
Bubble cost = $1.49
Beach ball cost = $2.00
Sand bucket cost = $3.50
Bubble = B
Beach Ball = A
Sand bucket = S
total cost = 6B + 2A + 3S
total cost = 6(1.49) + 2(2) + 3(3.5) = 23.44
Hope this helps :)
If you need any more explanation, feel free to ask. If this really helps, consider marking brainliest.
- Jeron
if a round analog clock featuring numbers 1-12 is hung on the wall upside down, the minute hand will point to the right of the viewer when the clock reads two forty-five.
The given statement is true, the minute hand will point to the right of the viewer when the upside down hung clock reads 2:45.
Here, we are given that a round analog clock featuring numbers 1-12 is hung on the wall upside down.
In order to solve this question, we need to visualize the situation very carefully.
When we hang the clock upside down, the numbers will switch their positions among their opposite pair.
For example, number 12 will be at the place of number 6 and vice versa.
Similarly, number 9 will be at the place of number 3.
When the clock strikes 2:45, the minute hand is pointing towards number 9.
However, since the clock is hung upside down, number 9 is at the place of number 3.
Number 3 is on the right side of the viewer who is standing in front of the clock.
Thus, the given statement is true, the minute hand will point to the right of the viewer when the upside down hung clock reads 2:45.
Learn more about clocks here-
https://brainly.com/question/24051741
#SPJ4
Elizabeth is going to roll a fair 666-sided die 600600600 times. Complete the following statement with the best prediction. Elizabeth will roll an even number.
The number of times getting an even number on the top of dice if dice is rolled 600 times is 300.
We know that probability is defined as the division of number of favorable outcomes to the total number of outcomes.
Here, favorable outcomes are even number from 6 possible numbers and those are =2,4,6
So, favorable outcomes are={2,4,6)
So, count of favorable outcomes is 3
Total number of outcomes are ={1,2,3,4,5,6}
So, count of total number of outcomes are =6
Therefore, probability of getting an even number on top of dice is =number of favorable outcomes/total number of outcomes
=>P(E) = 3/6
=>P(E)=1/2
Now, dice is rolled 600 times and probability of getting even number is 1/2,so total number of times even number comes on topo of dice is =(1/2)×600=300.
Hence, even number appearance is 300.
To know more about probability ,visit here:
https://brainly.com/question/11234923
#SPJ4