Chemical reactions such as photosynthesis explains the manner in which green plants manufacture their own food using the energy derived from sunlight.
What is photosynthesis?
Photosynthesis is the process in which green plants prepare their own food in the presence of sunlight and light energy is converted into chemical energy by the process of cellular respiration.
The process of photosynthesis takes place in green plants only due to presence of chlorophyll and materials such as sunlight, water, carbon dioxide is required for the process of photosynthesis.
The equation of photosynthesis is represented below:
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂.
The process of food manufacturing in plant is done through photosynthesis and the plants are known as autotrophs as they are the producers.
In the process of photosynthesis the reactant have 6 carbon dioxide molecules and six water molecules, and light energy converted into chemical energy due to presence of chlorophyll.
Therefore, Chemical reactions such as photosynthesis explains the manner in which green plants manufacture their own food using the energy derived from sunlight.
Learn more about photosynthesis here: brainly.com/question/1388366
#SPJ4
A square frame has sides that measure 1.75 m when it is at rest. What is the area of the frame when it moves parallel to one of its diagonal with a speed of 0.88c as indicated in the figure ?
m²
Measurements taken in a different frame of reference reveal a decrease in their dimensions—the only component that is parallel to the motion—and a delay in time—commonly referred to as "Length Contraction" and "Time Dilation"
when the objects are moving at a speed that is comparable to the speed of light and is in the order of C. The following is a discussion of the given relativistic issue.
The length AC is the only length that observers using the platform frame of reference would perceive as being shorter (the length).
What is change in measurement?
Estimation of progress alludes to the evaluation of fluctuation from one viewpoint, and to the appraisal of progress in a smaller sense then again. Short-term and reversible fluctuations (such as mood state variability) are characteristics of variability.
To learn more about Measurements here
https://brainly.com/question/4725561
#SPJ4
Identify how long a player would have to practice batting to have 27 hits.
TIME (Hrs) 1 5 9 13 17
HITS 2 11 18 25 34
13.5 Hrs long a player would have to practice batting to have 27 hits.
Given:
TIME (Hrs) 1 5 9 13 17
HITS 2 11 18 25 34
To have 27 hits :
= 13 + 1 + 17 + 5 - 9 / 2
= 14 + 22 - 9 / 2
= 36 - 9 / 2
= 27 / 2
= 13.5 hours
Therefore 13.5 Hrs long a player would have to practice batting to have 27 hits.
Learn more about the times and hits here:
https://brainly.com/question/7161991
#SPJ1
Is it possible to construct a triangle with lengths of its sides as 3cm 4cm 8cm?.
Answer:
Step-by-step explanation:
Yes it is possible you start with one side worth 4 cm and the other two move on to the next
Starlin's goal is to spend less than $415 on a trip. So far, he has spent $25 on gas for his car. He will spend $100 each day on other expenses.
Let d represent the number of days for Starlin's trip.
Drag and drop the answer into the box to correctly complete the statement.
response - correct
Starlin's trip must last fewer than ___ days.
4
Answer: less than 4 days
Step-by-step explanation:
415 - 25 = 390
if ur spending 100 each day then
day 1 = 290
day 2 = 190
day 3 = 90
he needs to spend less than 4 days
a construction company is considering submitting bids for two contracts. it will cost the company \$10{,}000$10,000dollar sign, 10, comma, 000 to prepare and submit the bids, and if won, each bid would produce \$50{,}000$50,000dollar sign, 50, comma, 000 of income to the company. the company estimates that it has a 10\, percent chance of winning any given bid.
The expected value of the number of bids and profit are 0.2 and $220000
How to determine the expected value of the number of bids and profit?The possible question is added as an attachment
From the complete question, we have the following table of values
X (Number of bids) 0 1 2
M = Profit -$10000 $40000 $90000
Probability 0.81 0.18 0.01
Expected value of the number of bids
This is calculated as
E(x) = Sum of the products of the number of bids and the probability
This is represented as
E(x) = 0. * 0.81+1 * 0.18 + 2 * 0.01
Evaluate the products
E(x) = 0 + 0.18 + 0.02
Evaluate the sum
E(x) = 0.2
Expected value of the profit
This is calculated as
E(x) = Sum of the products of the number of profits and the probability
This is represented as
E(x) = 0 * -10000 + 1 * 40000 + 2 * 90000
Evaluate the products
E(x) = 0 + 40000 + 180000
Evaluate the sum
E(x) = 220000
Hence, the expected profit is $220000
Read more about expected values at
https://brainly.com/question/15858152
#SPJ1
the radius of the big circle is 6 inches long and the diameter of the small circle is 8 inches long. find the area of the shaded region.
[tex]20\pi in^{2}[/tex] is the area of the shaded region of the radius of the big circle is 6 inches long and the diameter of the small circle is 8 inches long.
What do you name a circle?The circle is a closed, two-dimensional object in which all points inside the plane are equally spaced out from the center. The reflection symmetry line is created by all lines that traverse the circle. Additionally, it is rotationally symmetric about the center for all angles.
The shaded area is the portion of the bigger circle that is not included in the smaller circle, assuming that the 8-inch diameter circle is entirely contained inside the 6-inch radius circle.
Therefore, the shaded area equals the large circle's area less the small circle's area.
The little circle has a radius of 4 inches since its diameter is 8 inches, so
[tex]A_{Shaded} = A_{l} - A_{s} \\A_{Shaded} = \pi 6^{2} - \pi 4^{2} \\A_{Shaded} = 36\pi - 16\pi \\A_{Shaded} = 20\pi in^{2}[/tex]
So, Area = [tex]20\pi in^{2}[/tex]
To know more about circle visit:
https://brainly.com/question/11833983
#SPJ4
a researcher calculated that the total sum of squares for a regression equation was 153.7, and the error sum of squares was 82.6. what is the proportionate reduction in error for knowing the value of the independent variable?
The proportionate reduction in error for knowing the value of the independent variable is 0.54.
What is independent variable ?The variable which does not depend on any variable and hence independent are known as independent variable.
Given that,
sum of squares for a regression equation was 153.7 = SST
error sum of squares was 82.6 = SSE
SS (reg) = SST - SSE
153.7 - 82.6
SS(reg) = 71.1
The proportionate reduction in error for knowing the value of the independent.
= 1 - [tex]\frac{(SS)reg}{SST}[/tex]
= 1 - [tex]\frac{71.1}{153.7}[/tex]
= 1 - 0.46
= 0.54
The proportionate reduction in error for knowing the value of the independent variable is 0.54.
To learn more about independent variable, visit:
https://brainly.com/question/29430246
#SPJ4
Which of the following is an example of an "experimenter-expectancy effect?"
a. participants come to experiments with preconceived notions of what they are supposed to do, and perform based on those notions rather than on what they are asked to do.
b. the experimenter "expects" females to experience more difficulty on a math task so the experimenter unintentionally behaves in ways that undermine the performance of females on the math task
c. participants in a study are nicebehave differently for the attractive experimenter than for the less attractive experimenter
d. a researcher finds that his participants did not behave as he expected them to, so he changes his statement of his hypothesis when he writes up his results
Answer: . the experimenter "expects" females to experience more difficulty on a math task so the experimenter unintentionally behaves in ways that undermine the performance of females on the math task
The example of the experimenter-expectancy effect is option (b) The experimenter "expects" females to experience more difficulty on a math task so the experimenter unintentionally behaves in ways that undermine the performance of females on the math task
The experiment-expectancy is defined as the unintended effect of the hypotheses that is obtained from the the result of the research participant.
It is also defined as how the perceived expectations of an observer can influence.
Hence, the example of the experimenter-expectancy effect is option (b) The experimenter "expects" females to experience more difficulty on a math task so the experimenter unintentionally behaves in ways that undermine the performance of females on the math task
Learn more about hypotheses here
brainly.com/question/21327731
#SPJ4
HURRY QUICK!!
Plot the points (-2, 0), (-1, -10), (4, 0) below. Find the equation of the parabola that fits these points, and graph.
After plotting all the three points, we get the parabolic equation in the form is 2(x - 1)²-34.
What is parabola?Any point on a parabola, which has the shape of a U, is situated at an equal distance from the focus, a fixed point, and the directrix, a fixed line.
General equation of the quadratic equation,
Y = ax² + bx +c
Given points,
(-2, 0),
(-1, -10),
(4, 0).
Putting the points in the general equation,
Putting (-2, 0), we get
0 = 4a - 2b + c
Putting (-1, -10), we get
-10 = a - b +c
Putting (4, 0), we get
0 = 16a + 4b +c
Solving all equations we get,
a = 2 , b = -4 , c = -16
After putting the values,
Y = 2x²- 4x- 16
2(x² - 2x - 8)
2(x²- 2x + 1 - 1 - 16)
=2(x - 1)²-34
Hence we get the required equation in the parabolic form.
To know more about parabola, visit :
https://brainly.com/question/21685473
#SPJ1
Which equation represents the line that passes
through the points (-3,7) and (3,3)?
Answer:
Step-by-step explanation:
First get the slope of the line. This is (7-3)/(-3-3)=4/-6=-4/6=-2/3
Using slope intercept form, we get the equation
(-2/3)x+5=y
a single card is drawn from a standard deck of 52 cards. what are the odds against drawing a card with a number less than 5?
If a single card is drawn from a standard deck of 52 cards, the probability it will be a card with a number less than 5 is 4/13.
Probability measures how likely an event occurs. The probability of an event A is defined as:
P(A) = number of ways A can occur / total possible outcomes
In the given problem, let an ace card is considered as 1. Then, for each suit of cards, the card numbers which are less than 5 are cards number: 1, 2, 3, 4.
There are 4 suits, hence:
number of ways the event can occur = 4 x 4 = 16
total possible outcomes = 52
Therefore,
P(<5) = 16/52 = 4/13
Learn more about probability here:
https://brainly.com/question/28528638
#SPJ4
Answer:14/52
Step-by-step explanation:
a norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window (see figure). find the dimensions of a norman window of maximum area if the total perimeter is 14 feet.
The dimensions of a norman window of maximum area if the total perimeter is 14 feet are 2 ft and 4 ft respectively.
Given:
a norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window
we are asked to find the dimensions of a norman window of maximum area if the total perimeter is 14 feet.
the area of the semicircle is given by:
A = πr²/2
The area of the rectangle is just the product of its length and width.
Letting A be the area of the window and adding the two ares, we have:
A = xy + π(y/2)²/2
= xy + π(y²/4)/2
= xy+πy²/8
we know the circumference = πd
the circumference of a semicircle is half of that. The perimeter of a rectangle is the sum of twice the length and twice the width. However, one of the sides is replaced by the semicircle, so we remove it from the equation.
Hence, we have the following equation for the perimeter.
14 = 2x+y+πy/2
let us isolate x from this equation
14 = 2x+y+πy/2
14-y-π/2 = 2x
x = 7-y/2-πy/4
substituting x to the equation for the area, w have:
A = xy + πy²/8
= (7 - y/2 - πy/4)y + πy²/8
= 7y - y²/2 - πy²/4 + πy²/8
= 7y - y²/2 - 2πy²/8 + πy²/8
= 7y - y²/2 - πy²/8
differentiating A with respect to x.
A = 7y - y²/2 - πy²/8
A' = 7 - y - πy/4
⇒ 7 - y - πy/4 = 0
⇒ 28 - 4y - πy=0
⇒ 28 = 4y+πy
⇒ 28=(4+π)y
⇒ y = 28/4+π ≈ 4 ft
perimeter:
14 = 2x+y+πy/2
14 = 2x + 28/4+π + π(28/4+π)/2
14(8+2π)=2x(8+2π)+28(2)+28π
112+28π = 16x+4πx+56+28π
112-56=16x+4πx
56=(16+4π)x
x=56/16+4π
= 14/4+π
x=14/4+π≈ 2 ft.
Hence the dimension are 2 ft and 4 ft.
Lean more about Maximum area here:
brainly.com/question/19819849
#SPJ4
find the extremum of each function using the symmetry of its graph. classify the extremum of the function as a maximum or a minimum and state the value of x at which it occurs. h(x)
Given the function h(x) = x² - 7x - 8. The extremum of the function is the minimum one and its value is h(x) = -32.5
The relation between symmetry of the graph and the extremum point is:
Suppose x = p is the line equation of the graph's symmetry, then f(p) is the extremum value.
The given function is:
h(x) = x² - 7x - 8
Find the x-intercepts:
h(x) = 0
x² - 7x - 8 = 0
(x + 1) (x - 8) = 0
x = -1 or x = 8
The symmetry lies in the middle of x-intercepts. Hence, the symmetry occurs at:
x = (-1 + 8) / 2
x = 3.5
The extremum point is:
h(3.5) = 3.5² - 7 x 3.5 - 8 = -32.5
Since the quadratic term x² has a positive coefficient, the graph is open downward, hence the extremum point is the minimum one.
Complete question:
Find the extremum of each function using the symmetry of its graph. classify the extremum of the function as a maximum or a minimum and state the value of x at which it occurs. h(x) = x² - 7x - 8
Learn more about extremum value here:
https://brainly.com/question/29500135
#SPJ4
suppose you lift a laptop that weighs 4.1 pounds off the floor onto a shelf that is 2 feet high. how much work have you done?
The required work done in lifting the laptop to a height of 2 feet will be 263.79 foot-poundal.
Total weight of the laptop is 4.1 pounds
Acceleration due to gravity = 32.17 ft/[tex]s^{2}[/tex]
Now the height to which the laptop has been lifted = 2 feet
Since, there is no mentioned velocity of the laptop, therefore the kinetic energy will be zero
Therefore, the total work in lifting the laptop will be equal to the change in potential energy.
Potential energy is the energy that comes by virtue of its position with reference to other
Therefore, potential energy = mgh
Where, m = mass of the laptop = 4.1 pounds
g = acceleration due to gravity = 32.17 ft/[tex]s^{2}[/tex]
h = height to which the laptop is lifted = 2 feet
Therefore potential energy = (4.1)(32.17)(2) = 263.79 foot-poundal
263.79 foot-poundal is the required work done.
To know more about the potential energy, visit here:
https://brainly.com/question/8664733
#SPJ4
Ahley buy a hamter wheel during the ale(25% off). If Ahley pay $6, what wa the original price?
Answer:
original price was $8
Step-by-step explanation:
Ashley buy a hamster wheel during the sale (25% off). If Ashley pay $6, what was the original price?
$6 = 75% of price
75% = 0.75
6 = 0.75x
divide both sides by 0.75:
6/0.75 = 0.75x/0.75
x = 8
original price was $8
simplify ((x-3)(x-3))/((3-x)(3+x))
Answer:
[tex]\frac{(x-3)^2}{(3-x)(3+x)}[/tex]
Step-by-step explanation:
1) Use Product Rule: [tex]x^ax^b=x^{a+b}[/tex].
[tex]\frac{(x-3)^2}{(3-x)(3+x)}[/tex]
Thanks.
The graph of f(x) |x] is reflected across the y-axis and
translated to the left 5 units. Which statement about the
domain and range of each function is correct?
A. Both the domain and range of the transformed
function are the same as those of the parent function.
B. Neither the domain nor the range of the transformed
function are the same as those of the parent function.
C. The range of the transformed function is the same as
the parent function, but the domains of the functions
are different.
D. The domain of the transformed function is the same
as the parent function, but the ranges of the functions
are different.
Answer:
A. Both the domain and range of the transformed function are the same as those of the parent function.
Step-by-step explanation:
Parent absolute value function:
[tex]f(x)=|x|[/tex]
Graph of the parent absolute value function:
Line |y| = -x where x ≤ 0Line |y| = x where x ≥ 0Vertex at (0, 0)Therefore:
The domain of the parent function is unrestricted: {-∞, ∞)The range of the parent function is restricted: [0, ∞)If function f(x) is reflected across the y-axis:
[tex]\implies f(-x)=|-x|[/tex]
The reflection does not change the graph as the parent function is symmetric about the y-axis.
If function f(x) is translated to the left 5 units:
[tex]\implies f(x+4)=|x+4|[/tex]
The domain remains unrestricted and the range remains [0, ∞).
Therefore, both the domain and range of the transformed function are the same as those of the parent function.
Factor this expression completely, then place the factors in the proper location on the grid. X 6 - y 6.
Factoring the expression [tex]x^{6} - y^{6}[/tex] is[tex](x^{3} +y^{3})(x^{3}-y^{3})(x^{2}+y^{2}+xy)(x^{2}+y^{2}-xy)[/tex]
Given expression = [tex]x^{6}-y^{6}[/tex]
= [tex](x^{3})^{2} - (y^{3})^{2}[/tex]
Now, using the formula [tex]a^{2}-b^{2} = (a+b) (a-b)[/tex]
= [tex](x^{3}-y^{3})(x^{3}+y^{3})[/tex]
Here, using the formulas
[tex]x^{3}-b^{3} = (a-b)(a^{2}+b^{2}+ab)[/tex] and [tex]a^{3} + b^{3} = (a+b)(a^{2}+b^{2} -ab)[/tex]
Therefore, [tex](x^{3} +y^{3})(x^{3}-y^{3})(x^{2}+y^{2}+xy)(x^{2}+y^{2}-xy)[/tex]
When a number or other mathematical object is expressed as the sum of several factors, usually smaller or easier versions of the same kind, this is referred to as factorization. When an expression has been fully factorized, it must be enclosed in brackets by removing the factors with the highest common denominator. The simplest method of factorization is to find the phrase's highest common factor among all of its terms. The highest common factor (HCF) should be placed in front of any brackets.
To learn more about factorization: https://brainly.com/question/18187355
#SPJ4
Jordan has some number cards that each have a whole number on them.
If he chooses a card at random, the probability that the number on it is even
is 2/7
Work out the ratio of even cards to odd cards that Jordan has.
Give your answer in its simplest form.
The ratio of even cards to odd cards that Jordan has is 2:5 or 2/3.
Given:
Jordan has some number cards that each have a whole number on them.
If he chooses a card at random, the probability that the number on it is even is 2/7.
Let x and y be the even and odd cards.
x / x+y = 2/7
cross multiplication
7*x = 2(x+y)
7x = 2x + 2y
7x - 2x = 2y
5x = 2y
divide by 5 on both sides
5x/5 = 2y/5
x = 2/5 y
x/y = 2/5
x:y = 2:5.
Learn more about the number here:
https://brainly.com/question/17429689
#SPJ1
Determine whether the relation is reflexive, symmetric, antisymmetric, transitive, and/or a partial order.
(x,y)∈???? if x≥y when defined on the set of positive integers.
For the given relation for (x , y) ∈R if x ≥ y defined on the set of positive integers only transitive relation holds true.
As given in the question,
Given (x , y) ∈R
To check whether relation reflexive, symmetric, antisymmetric, transitive, and/or a partial order is true or not:
a. Reflexive : If (x, x)∈R for all x ∈R
x ≥ x for all x ∈ R which is not true.
b. Symmetric : If 'x' is related to 'y' then 'y' is also related to 'x' for all (x, y) ∈R.
Here, x ≥ y ⇒ y ≥ x for all (x, y) ∈R , which is not true.
c. Antisymmetric : If 'x' is related to 'y' and 'y' is related to 'x' then x = y for all (x , y)∈ R.
Here, x ≥ y and y ≥ x ⇒ x = y is not true.
Not antisymmetric.
d. Transitive: If 'x' is related to 'y' and 'y' is related to 'z' then 'x' is related to 'z' for all x, y, z ∈R.
Here, x ≥ y , y ≥ z ⇒ x ≥ z for all x, y, z ∈R.
True.
Therefore, for the given relation for (x , y) ∈R if x ≥ y defined on the set of positive integers only transitive relation holds true.
The complete question is:
Determine whether the relation is reflexive, symmetric, antisymmetric, transitive, and/or a partial order.
(x, y)∈R if x ≥ y when defined on the set of positive integers.
Learn more about relation here
brainly.com/question/16862336
#SPJ4
How do you find the length width and height of a rectangular prism with the volume?.
To find the length, width, and height of a rectangular prism with the volume, you need to know the formula for volume of a rectangular prism. The formula is V=lwh, where l is the length, w is the width, and h is the height.
A rectangular prism is a three-dimensional figure with six faces that are all rectangles. The length, width, and height of a rectangular prism can be found using the formula V=lwh, where V is the volume, l is the length, w is the width, and h is the height. To solve for one of the variables, you need to rearrange the equation. For example, to solve for h, you would rearrange the equation to h=V/lw. This would give you the height in terms of the other two variables.
Learn more about prism at : https://brainly.com/question/13379929
#SPJ4
What is the range of f(x) = sin(x)? the set of all real numbers the set of all real numbers the set of all real numbers the set of all real numbers.
The range of function f(x) = sin(x) is the set of all real numbers lying between [-1, 1].
Define the function sin(x)?Although they can sometimes be written as functions, the sine, cosine, and tangent of such an angle really are defined on the basis of trigonometry.
All real numbers fall inside the domain of the function f(x) = sin x, but its range equals −1 ≤ sin x ≤ 1. If the angle is measured in degrees versus radians will affect the sine function's values. The periodicity of the function is 360 degrees, or 2π radians. As a result, sin x is just an odd function, and its algebraic expression is sin(x) = − sin x. Using the aforementioned numerical tables, you can verify this truth. When it comes to cos x, we could see that the graph has a symmetry axis along the y-axis, indicating that it's an even function that can be expressed algebraically; cos(−x) = cos x.Thus, range of function f(x) = sin(x) is the set of all real numbers lying between [-1, 1].
To know more about the function sin(x), here
https://brainly.com/question/21902442
#SPJ4
sixty-eight percent of online courses taught at community colleges nationwide were taught by full-time faculty. to test if 68% also represents california's percent for full-time faculty teaching the online classes, long beach city college (lbcc) in california was randomly selected for comparison. in the same year, 34 of the 44 online courses lbcc offered were taught by full-time faculty. conduct a hypothesis test at the 5% level to determine if 68% represents california. note: for more accurate results, use more california community colleges and this past year's data
The Confidence Interval for the hypothesis test at the 5% level to determine if 68% represents California is 0.65, 0.90.
First, we need to find H₀ and Hₐ. In this case, we want to check whether California community colleges take 68% of the online classes thought by full-time faculties, or not.
H₀ : p = 0.68; Hₐ : p ≠ 0.68
Second, we need to determine the distribution needed. State what our random variable P’ represents.
Normal: N
Test Statistic : z = 0.1873
Third, we have to calculate he p-value using the normal distribution for proportions.
p-value = 0.1873
If the null hypothesis is true (the proportion is 0.68), thus there is a 0.1873 probability which the estimated proportion is 0.773 or more.
Fourth, we need to compare [tex]\alpha[/tex] and the p-value, then indicate the correct decision (reject or do not reject the null hypothesis).
[tex]\alpha[/tex] = 0.05
Decision : Do not reject the null hypothesis
Reason for decision : p-value > 0.05
At the 5% level, the data do not provide statistically significant evidence that the true proportion of online courses taught by full-time faculty is not 68%.
Last, define the confidence interval. The confidence interval is (0.6275, 0.8725) = (0.65, 0.90).
Learn more about confidence interval at: https://brainly.com/question/24131141
#SPJ4
HELP!! (this is a math problem about angles)
Answer:
Below
Step-by-step explanation:
angle 1 + 120 = straight line = 180 so angle 1 = 60°
angles 1 3 4 7 are all equal
angle 2 = 120° = angles 5 and 6
need help finding this translation
a. up 2, right 3
b. right 3, down 2
c. left 3, down 2
d. down 3, right 3
To translate triangle A to B, left 3, down 2 and to translate triangle B to A, up 2, right 3
There are two triangles in the graph
Consider the triangle on top as triangle A and the triangle on bottom as triangle B
The translation is the process of the changing the coordinates of the given shapes in the graph. The shape and size will be same only the coordinates will vary
Consider the triangle A
If we want triangle A to translate to triangle B
First translate 3 units to left and translate 2 units down
Now consider the triangle B
If we want to translate triangle B to triangle B
First translate 2 units up and translate 3 units right
Hence, to translate triangle A to B, left 3, down 2 and to translate triangle B to A, up 2, right 3
Learn more about translation here
brainly.com/question/11805053
#SPJ1
The school year book had 50 ads placed last year. This year there was a 20% increase in the number of ads. What was the increase in the number of ads placed?
A: 20
B: 30
C: 40
D: 10
Show your work
Answer:
10
Step-by-step explanation:
20% of 50 ads
=20/100*50 ads
=10 ads
A diatance from school to priyanthas house is 700m and the distance from scool to lasntha house is 1km 300 m. find the ratio of the distance
Answer:
well 700m is 2296.59 feet
and 1km is 3280.84 feet
and 300m is 984.252 feet
Step-by-step explanation:
hope this helps :)
Write a linear function for the data in each table using function notation.
x 1, 2, 3, 4
y 4, 10, 16, 22
x 1, 2, 3, 4
y 1.5, 4, 6.5, 9
The linear functions of the tables are y = 6x - 2 and y = 2.5x - 1
How to determine the linear equation of the tables?Table 1
From the table, we have the following points that can be used in our computation:
(x, y) = (1, 4) and (2, 10)
The equation of the line is then calculated using the following equation
y = m(x - x₁) + y₁
Where
m = slope
The slope is then calculated as
slope = (y₂ - y₁)/(x₂ - x₁)
Substitute the known values in the above equation, so, we have the following representation
So, we have
m = (10 - 4)/(2 - 1)
Evaluate
m = 6
Recall that
y = m(x - x₁) + y₁
So, we have
y = 6(x - 1) + 4
So, we have
y = 6x - 6 + 4
Evaluate
y = 6x - 2
Table 2
From the table, we have the following points that can be used in our computation:
(x, y) = (1, 1.5) and (2, 4)
The equation of the line is then calculated using the following equation
y = m(x - x₁) + y₁
Where
m = slope
The slope is then calculated as
slope = (y₂ - y₁)/(x₂ - x₁)
Substitute the known values in the above equation, so, we have the following representation
So, we have
m = (4 - 1.5)/(2 - 1)
Evaluate
m = 2.5
Recall that
y = m(x - x₁) + y₁
So, we have
y = 2.5(x - 1) + 1.5
So, we have
y = 2.5x - 2.5+ 1.5
Evaluate
y = 2.5x - 1
Hence, the linear function is y = 2.5x - 1
Read more about linear equations at
brainly.com/question/2030026
#SPJ1
What is the slope of y =- 4x 10?.
The slope of the line y = - 4x + 10 is -4.
What is slope?
The slope of any line can be calculated using any two distinct points lying on the line. It is defined as the change in y coordinate with respect to the change in x coordinate of that line.
The net change in y coordinate is Δy, while the net change in the x coordinate is Δx, then the slope
m = Δy/Δx = dy/dx.
Here, we are given the line y = - 4x + 10
Differentiating the equation of line with respect to x, we get
dy/dx = - 4
⇒ slope m = dy/dx = -4.
Therefore, the slope of the line was found to be -4.
To learn more about slope, visit
brainly.com/question/16949303
#SPJ4
NOTE : The question given here is not complete. The complete question is given below.
Question: What is the slope of y = - 4x + 10?.
an airline offers a certain flight once per day that usually contains about 250250250 passengers. the flight offers seats in first class (most expensive), business class, and economy class (least expensive). the airline wants to survey 500500500 passengers of this flight about their overall satisfaction. the passengers will be selected using a cluster random sample where each flight is a cluster. Why might the airline choose a cluster random sample instead of a simple random sample in this setting?
The airline might choose cluster random sampling in this case.
Cluster Sampling:
It is a sampling method where the entire population under study is divided into homogeneous groups called clusters. The clusters are externally homogeneous and internally heterogeneous.
Simple Random Sampling:
It is a sampling technique where every unit in the population has an equal chance of being selected in the sample and the samples are selected at random. The airline wants to survey 500 passengers on this flight about their overall satisfaction. The passengers will be selected using a cluster random sample where each flight is a cluster.
Cluster sampling involves fewer resources for sampling compared to simple random sampling.
Here, the population under study is people travelling the flight which is externally homogeneous.
The people travelling in the flight are classified into three groups namely first class (most expensive), business class, and economy class (least expensive) which is internally heterogeneous. More number of persons can be included in the survey which acts as a good representative of the entire population. Thus, cluster sampling is suitable for this study. Simple random sampling may result in an unequal number of persons in each class if the persons are surveyed at random. So, cluster sampling better suits the scenario than simple random sampling.
Learn more about sampling:
https://brainly.com/question/16813351
#SPJ4
