The slice would be in the form of a pentagon.
What is meant by parallel lines?Parallel lines in geometry are coplanar infinite straight lines that don't intersect anywhere. When two planes in the same three-dimensional space are parallel, they never cross. Curves that maintain a set minimum distance from one another and do not touch or intersect are said to be parallel curves.
Parallel lines are those in a plane that are regularly spaced apart from one another. There is no crossing of parallel lines.
Wendell would need to make a parallel cut to the bases of the pentagons in order to split the doghouse in two.
Consequently, the section will be pentagonal in shape.
Consequently, the slice is pentagonal.
To learn more about the parallel lines refer to;
brainly.com/question/16701300
#SPJ4
can a triangle be formed with angles having measures of 30,70, and 110? explain using the model above.
Two cards are selected with replacement from a standard deck of 52 cards. Find the probability of selecting a spade and then selecting a heart.
A. 0.0625
B. 0.0637
C. 0.0588
D. 0.0250
The probability of selecting a spade and then selecting a heart is 0.0625, and the correct answer is option A.
What is probability?Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
Given that the cards are selected with replacement.
The probability of selecting a spade card is:
P(S) =13/52
Now, a heart card is selected.
Since, the previous card is replaced in the deck the total number of cards is 52.
The probability of selecting a heart card is:
P(H) = 13/ 52
The probability of selecting a spade and then selecting a heart is:
P = 13 / 52 × 13/52
P = 0.0625
Hence, the probability of selecting a spade and then selecting a heart is 0.0625, and the correct answer is option A.
Learn more about probability here:
https://brainly.com/question/30034780
#SPJ4
Round answer to the nearest hundredth
Using the cosine ratio, the measure of angle A, to the nearest hundredth is: 75.52°.
What is the Cosine Ratio?The cosine ratio, also known simply as the cosine, is a trigonometric function that represents the ratio of the adjacent side to the hypotenuse of a right triangle.
It is defined as cos(θ) = adjacent side/hypotenuse, where θ is the angle between the adjacent side and the hypotenuse.
Reference angle (∅) = A
Length of adjacent side = 2
Length of hypotenuse = 8
Therefore:
cos A = adj./hyp. = 2/8
cos A = 1/4
A = cos^(-1)(1/4)
A = 75.52°
Learn more about the cosine ratio on:
https://brainly.com/question/15793827
#SPJ1
what’s the answer to this question i’ve been trying my hardest and i still haven’t go it can somebody please help
a) Dilation 1 has a scale factor of 3 units.
b) Dilation 2 has a scale factor of 4 units.
c) Dilation 3 has a scale factor of 0 units.
What is a scale factor?
A scale factor is a number used to multiply the dimensions of a shape to enlarge or reduce its size. In geometry, the scale factor is used to create similar figures by preserving their shape while changing their size. If a figure is scaled up by a scale factor of 'k', its dimensions are increased by a factor of 'k'. If a figure is scaled down, its dimensions are reduced by a factor of 'k'.
For the triangle, the scale factor would be 3 units.
For the square, the scale factor would be 4 units.
For the line, the scale factor would be 0 units.
Hence,
a) Dilation 1 has a scale factor of 3 units.
b) Dilation 2 has a scale factor of 4 units.
c) Dilation 3 has a scale factor of 0 units.
To learn more about the scale factor, visit:
https://brainly.com/question/25722260
#SPJ1
Solve for x: 3 < x + 3 < 6
A. 6 < x < 9
B. 6 > x > 9
C. 0 < x < 3
D. 0 > x > 3
Answer:
C
Step-by-step explanation:
create two inequalities:
3 < x + 3 and x + 3 < 6
0 < x and x < 3
Under her cell phone plan, Aubree pays a flat cost of $50. 50 per month and $4 per gigabyte. She wants to keep her bill at $56. 10 per month. Choose the equation which could be used to determine g, the number of gigabytes of data Aubree can use while staying within her budget
54.10Answer:
Step-by-step explanation:
what is the time complexity of this pseudocode? for int i = 1; i<=n; i )
The size of the input is doubled, the time taken to execute the loop will also double.
The time complexity of this pseudocode is O(n). This can be determined by analyzing the number of times the loop is executed. The loop is entered once and is then executed n times, where n is the number of times the loop is executed. This can be expressed mathematically as T(n) = 1 + n. Since the loop is executed a constant number of times, regardless of the size of the input, the time complexity of the pseudocode is O(n). This means that the execution time of the loop grows linearly with the size of the input. Thus, if the size of the input is doubled, the time taken to execute the loop will also double.
Learn more about number of time here:
https://brainly.com/question/30061892
#SPJ4
Rebecca sells cupcakes for $3.50 each and charges customers an automatic $2 charge for a cupcake box as well. A customer walks in with $44 dollars. Represent the number of cupcakes that the customer can buy as an inequality.
Write the solution to the inequality in interval notation below.
The number of cupcakes that the customer can buy as inequality will be 3.5C + 2 < 44.
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.
Given that Rebecca sells cupcakes for $3.50 each and charges customers an automatic $2 charge for a cupcake box as well. A customer walks in with $44 dollars.
The inequality can be written as:-
3.5C + 2 < 44.
Where C is the number of cupcakes and $2 is the charge for the box. Which should be lesser than the total amount.
To know more about inequality follow
https://brainly.com/question/24372553
#SPJ1
The inequality equation is x ≤ 8 , where x is the number of cupcakes
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the number of cupcakes be represented as A
Now , the equation will be
The cost of each cupcake = $ 3.50
The cost per box of cupcake = $ 2.00
So , the total cost of x cupcakes = x ( 3.50 + 2.00 )
The total cost of x cupcakes = 5.50x
Now , The amount of money with Rebecca = $ 44
So , the maximum number of cupcakes she can buy is
total cost of x cupcakes < amount of money with Rebecca
Substituting the values in the equation , we get
5.50 x ≤ 44
Divide by 5.50 on both sides of the equation , we get
x ≤ 44/5.50
x ≤ 8 cupcakes
Hence , the inequality equation is x ≤ 8
To learn more about inequality equations click :
https://brainly.com/question/11897796
#SPJ1
Geometry
You roll a six-sided die. (Write your answer as a fraction, decimal, and percent)
a. What is the probability of rolling an odd number or rolling a 2?
b. What is the probability of rolling an even number or a 4?
the probability of rolling an odd number or rolling a 2 is 2/3
The probability of rolling an even number or a 4 is 2/3
How to find the probability of rolling an odd number or rolling a 2?Probability is a mathematical concept that measures the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 means an event is impossible and 1 means an event is certain to occur. The probability of an event can also be expressed as a percentage or as a fraction.
If you roll a six-sided die. The probability of rolling 1, 2, 3, 4, 5 and 6 are as follows:
P (1) = 1/6
P (2) = 1/6
P (3) = 1/6
P (4) = 1/6
P (5) = 1/6
P (6) = 1/6
a. Since there are three odd numbers, P(odd) = 3/6 = 1/2
Thus, the probability of rolling an odd number or rolling a 2 will be:
P(odd or 2) = P(odd) + P(2)
= 1/2 + 1/6 = 2/3
b. Since there are three even numbers, P(even) = 3/6 = 1/2
Thus, the probability of rolling an even number or a 4 will be:
P(even or 4) = P(even) + P(4)
= 1/2 + 1/6 = 2/3
Learn more about probability on:
brainly.com/question/251701
#SPJ1
find 6.50) The difference between annual compound interest on a ca sum of money for two years at 20% p.a. and semi- compound interest on the same sum of money at the same of interest and for the same period of time is Rs. 482 Calculate the sum (Ans: Rs. 20000
The sum of compound interest on a sum of money is (principal ) Rs 2000.
How is compound interest determined?CI = P*(1+R/100) is the formula for compound interest, which is computed by multiplying the starting principle amount by one and annual interest rate multiplied by the number of compound periods minus one (T)
CI = A – P
Periodic compounding formula is another name for this formula. In this case, A stands for the updated principle amount or the entire sum of money after the compounding period. P stands for the first or original quantity.
now we have :-
time (annual)=2
time (semi-annual)=4
rate (annual)= 20
rate (semi-annual=10
difference compound interest = 482
CI(semi-annual)-CI(annual) =482
P*(1+10/100)^(4) - P*(1+20/100)^(2)=482
P{ (14641/10000) - (36/25)}= 482
P(241/10000)=482
P=(482*10000)/241
P= 20000.
So, sum of money is (principal ) Rs 2000.
To know more about compound interest visit:-
https://brainly.com/question/13155407
#SPJ1
write each of these ratios in its simplest form 7:21:35
Answer:
1:3:5
Step-by-step explanation:
[tex]\frac{7}{7}=1\\\\\frac{21}{7}=3\\ \\\frac{35}{7}=5[/tex]
1:3:5
Which choice is equivalent to the product below?
√8 •√5
A. 4√10
OB. 10/2
OC. 2√10
OD. √13
The choice that is equivalent to the product given is 2√10
What are surds ?
Surds in mathematics are the square root values that can't be further condensed into whole numbers or integers. Numbers with surds are illogical.
Surds are the square roots of numbers ( √) that are not able to be divided into whole or rational numbers. It cannot be precisely described by a fraction. A surd, then, is a root of a whole number with an irrational value.
√8 •√5
= √(8*5) = √40
= √(10*4)
= √4 * √10
= 2√10
The choice that is equivalent to the product given is 2√10
To learn more about the surds from the given link
https://brainly.com/question/840021
#SPJ1
A 6-ft observer casts a 4-ft shadow at the same time a nearby chimney casts a 238-foot shadow. How tall is the chimney?
The height of the chimney is 357 feet according to mentioned dimensions of the chimney and observer.
The ratio of base and height according to angled of elevation will be -
tan theta = perpendicular ÷ base. The same will be for chimney. Hence, equating the ratio of both to find the height of chimney.
The formula will be -
Perpendicular ÷ base of observer = perpendicular ÷ base of chimney
6/4 = height/238
Rewriting the equation according to height of chimney
Height = (6 × 238)/4
Performing multiplication on Right Hand Side of the equation
Height = 1428/4
Performing division on Right Hand Side of the equation
Height = 357
Thus, chimney is 357 feet tall.
Learn more about height calculations -
https://brainly.com/question/27243378
#SPJ4
Jane has $14000 in a savings account that earns 2.5% annually. How much interest will she have earned after 9 months?
Answer:
Below
Step-by-step explanation:
Interest for a WHOLE 12 months would be 14 000 * .025 = 350
but Jane had the account for 9 out of 12 months
9/12 * 350 = 262.50 dollars
solve the initial value problem. ′=−2,(0)=−4 (express numbers in exact form. use symbolic notation and fractions where needed.)
According to the concept of fraction the value of the quantity at any time t is -4.
A fraction is a mathematical representation of division of two numbers. In this case, we will be using fractions to solve an initial value problem.
The initial value problem is ′=−2,(0)=−4.
This means that the rate of change of the quantity is -2 and its starting value at time 0 is -4.
To solve this problem, we need to find the value of the quantity at some other time.
Here the first step is to find the general solution to the differential equation ′=−2.
This can be done by integrating both sides, which gives us
=> −2.
Integrating, we get
=> −2 + C, where C is an arbitrary constant.
Next, we use the initial value to find the value of C.
We know that when t=0, the value of the quantity is -4, so we can substitute these values into the general solution to get
=> -4 = -2 + C.
Solving for C, we get C = -2.
Finally, we substitute C into the general solution to get
=> -2 -2 = -4.
To know more about fraction here.
https://brainly.com/question/10354322
#SPJ4
The volume of a gas was measured as
its temperature was increased from 10 K
to 15 K at intervals of 1 K. The volumes
were 1. 5, 2. 2, 3. 38, 5. 1, and 7. 6 cm.
Would a linear or exponential function
better approximate the data described?
Explain why.
An exponential function would better approximate the data described about the volume of a gas.
The relationship between the volume of a gas and its temperature is described by the Ideal Gas Law, which states that the volume of a gas is proportional to its temperature raised to the power of the ratio of specific heat to the universal gas constant. Therefore, as the temperature of a gas increases, its volume will increase exponentially.
The data given in the problem, with the volume increasing as the temperature increases, supports the use of an exponential function to model the relationship between temperature and volume. On the other hand, a linear function, which models a constant rate of change, would not accurately capture the exponential increase in volume as the temperature increases.
Learn more about An exponential function:
https://brainly.com/question/30127596
#SPJ4
1). What is the simplified form of 3a^4b^-2c^3?
2). What is -a^-2 if a = -5?
3). What is the simplified form of -(14x)^0y^-7z?
4). What is (-m)^-3n if m = 2 and n = -24
5). Which of the following simplifies to a negative number?
a). -4^-4
b). (-4)^-4
c). 4^-4
d). 1/4^-4
Answer:
1). 3a^4c^3 or D
2). -1/25 or C
3). -z/y^7 or D
4). 3 or A
5). -4^-4 or A
Step-by-step explanation:
I took the quick check already so enjoy your 100% :)
At the top of the mountain, you and your friend tart decending at the ame time. There i an angle of 18o between the two of you. You are travelling fater and therefore cover 250 m, while your friend only cover 195 m. How far apart are you at that point in time?
You and your friend are approximately 181.23 meters apart at that point in time.
Distance Between Friends On MountainTo find the distance between you and your friend, we can use the Pythagorean theorem. Let's call the distance between you two "d".
d² = 250² + 195² - 2 X 250 X 195 X cos(18)
d = √(250² + 195² - 2 X 250 × 195 X cos(18))
d ≈ 181.23 m
So you and your friend are approximately 181.23 meters apart.
The answer was determined using the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two smaller sides equals the square of the length of the largest side (the hypotenuse).
In this case, the two smaller sides represent the distances covered by you and your friend, and the hypotenuse represents the distance between you both.
We can use the theorem to calculate the distance "d" between you and your friend by rearranging the equation to isolate "d". We know the lengths of the two smaller sides (250 m and 195 m), and we also know the angle between them (18 degrees).
We can use the cosine formula to find the cosine of 18 degrees, and plug in all the values into the equation to find "d".
Learn more about Distance Between Friends On Mountain here:
https://brainly.com/question/9794375
#SPJ4
Why are there 52 weeks in a year and not 48 weeks given that there are only 4 weeks per month (4 x 12 = 48)?
A month does not have four weeks, nor does a year have 52 weeks.
The ISO week-numbering year, however, has 52 or 53 weeks.
That translates to 364 or 371 days rather than the typical 365 or 366 days.
Are there 4 weeks in every month?Since every month has at least 28 days, every month has 4 full weeks.
There are extra days in some months.
1 week = 7 days.
For the months of January, March, May, July, August, October, and December, a month has 4 weeks and 3 days.
A month in April, June, September, and November has 4 weeks and 2 days.
February in a leap year has 4 weeks and 1 day in a month.
There are around 29 days more than a calendar year.
Which means 4 weeks plus some days.
From 12 month: 4 × 12 = 48 weeks.
Form 29 extra days: 4 weeks and 1 days.
Total weeks: 52 weeks in a year.
Total days: 52 × 7 + 1 = 365 days in a year.
In a leap year, the month of February has 4 weeks and 1 day.
366 days make up a leap year.
To learn more about months refer to:
https://brainly.com/question/28664215
#SPJ4
Can someone PLEASE help? I will give brainliest if possible and lots of points
Part A: Find the value of x
Part B: Find ABK
Part C: Show your work to support your answer to Part A and Part B
Answer:
1. x = 20
2. m<ABK = 137
Step-by-step explanation:
1.
(3x - 5) + (4x + 2) + (2x + 3) = 180
9x = 180
x = 20
2.
3x - 5 + 4x + 2
7x - 3
7(20) - 3
140 - 3
m<ABK = 137
Point P i on line egment O Q. Given O Q = 11 OQ=11 and O P = 9 , OP=9, determine the length P Q ‾. PQ
The numerical length of PQ is 20
Determine the length P Q ‾. PQ ?A line segment in geometry is a section of a line that has two clearly defined endpoints and contains every point on the line that lies within its confines.
Given that the line segments are: -
OQ=11 O P = 9
The numerical value of PQ will be calculated as below.
OP+OQ=PQ
11+9=PQ=11+9=PQ
Therefore PQ=20=PQ
To know more about length visit:
https://brainly.com/question/8552546
#SPJ4
Select the shapes that have 8 or more edges.
Right circular cylinder
Right pyramid
Right triangular prism
Sphere
A and B
A and C
B and C
B and D
B and C
Right pyramid has 8, Right triangular prism has 9
The peak value of a sine wave is 80 VAC. What is the peak to peak value of this waveform?
The peak to peak value of a sine wave is twice the peak value. Therefore, total number of the peak to peak value of this waveform is 2 x 80 VAC = 160 VAC.
The peak to peak value of a sine wave is an important measure of the waveform's amplitude. It is calculated by multiplying the peak value of the waveform by two. The peak value of this particular waveform is 80 VAC, so the peak to peak value of the waveform is 2 x 80 VAC = 160 VAC. This peak to peak value is a measure of the total number voltage swing of the waveform, from its lowest point to its highest point. The peak to peak value of this waveform is a useful parameter for understanding the waveform's strength and potential for causing electrical damage. As such, it is important to measure and understand the peak to peak value of any sine wave in order to successfully manage its power and potential for causing harm.
learn more about number here
https://brainly.com/question/10547079
#SPJ4
Which equation represents a tangent function with a domain of all real numbers such that x is not equal to pi over 2 plus pi times n comma where n is an integer?.
y = tan(x) - (π/2 + πn)
This equation represents a tangent function with a domain of all real numbers, except for multiples of pi/2 plus pi.
The equation y = tan(x) - (π/2 + πn) represents a tangent function with a domain of all real numbers except for multiples of pi/2 plus pi. This equation is useful for finding the tangent value of any given x-value, as long as it is not equal to a multiple of pi/2 plus pi. The equation works by subtracting the multiple of pi/2 plus pi from the x-value, and then finding the tangent of the new value. This allows the tangent of the x-value to be found, regardless of whether or not it is equal to a multiple of pi/2 plus pi.
Learn more about equations: https://brainly.com/question/2972832
#SPJ4
Sandra, Davion, Taylor, and James each purchased a medium soda from the concession
stand at a soccer game. At the end of the game, Sandra drank of her soda, Davion drank
82% of his, Taylor drank 0.85 of hers, and James drank of his. Who drank the most soda
from their cup?
James and Sandra drank the most soda from their cup.
Why are they the persons that drank most?The information that was given gave specific amount that each person drank from their soda, but James and Sandra were not given a specific amount, so one can only assume they drank the most since their own percentage of drink is not disclose.
Percentage is a way to express a number as a fraction of 100. It's often denoted using the symbol "%". For example, 50% means 50 per 100, or one half
learn more about percentage: https://brainly.com/question/24877689
#SPJ1
Simplify the following expressions.
1. 11(5) - 11(4) =
2. 8(-3 + 2) =
3. 6(9) - 4(6) =
4. 7(4) - 2(0) =
5. 15(3) - 2(12) =
6. 9(5 + 3) =
7. 12(2) - 7(2) =
8. 8(3) =
9. (6)(6) =
10. 11(9) =
11. 8(5) - 2(7) =
12. 5(n) =
13. 5y(2) =
14. 13(x + 2) =
15. 16(5x - 8) =
16. 23y( 2 + 4) =
The simplification are as follows:
11(5) - 11(4) = 55 - 44 = 118(-3 + 2) = 8(-1) = -86(9) - 4(6) = 54 - 24 = 307(4) - 2(0) = 28 - 0 = 2815(3) - 2(12) = 45 - 24 = 219(5 + 3) = 9(8) = 7212(2) - 7(2) = 24 - 14 = 108(3) = 24(6)(6) = 3611(9) = 998(5) - 2(7) = 40 - 14 = 265(n) = 5n (Note: n is a variable)5y(2) = 10y13(x + 2) = 13x + 2616(5x - 8) = 80x - 12823y(2 + 4) = 23y(6) = 138y.What is simplification in mathematics?Simplification in mathematics refers to the process of making an expression, equation, or mathematical problem easier to understand, solve, or manipulate by reducing its complexity. This can be achieved by combining like terms, cancelling out common factors, reducing fractions, or using the properties of arithmetic operations.
The goal of simplification is to transform a complex expression into a simpler form that can be more easily understood or used in further mathematical analysis.
learn more about simplification: https://brainly.com/question/28595186
#SPJ1
A total cot of attending a tate univerity i 19,700 for thi year
a tudent grandparent will pay of thi half
an athletic cholarhip will pay another 5,000
Which amount i cloet to the minimum that the tudent will need to ave every month in order to pay off the remaining cot at the end of 12 month
The student will need to save approximately 488.33 dollars per month in order to pay off the remaining cost at the end of 12 months.
First, let's calculate the amount that the student's grandparent will pay: 19,700 / 2 = 9,850
Next, let's subtract the amount of the athletic scholarship: 19,700 - 9,850 - 5,000 = 5,850
Finally, to find the minimum amount that the student will need to save every month, we can divide the remaining cost by the number of months (12): 5,850 / 12 = 488.33
You can learn more about calculating total cost at
https://brainly.com/question/9063096
#SPJ4
PLEASE HELPPPPPLLLLPPP
In the given diagram, 4 = 45°, 5= 135°, and 10 11.
Part A: Solve for the values of the remaining angles. Show all of your work.
Part B: Use complete sentences to describe the angle relationship between the following angle pairs:
<4 and <1
<7 and <5
<9 and <10.
PLEASE HELP
Answer:
Step-by-step explanation:
Part A:
To find the value of the remaining angles, we can use the fact that the sum of the angles in a triangle is 180°.
First, let's find the value of <1. We have:
<4 + <1 + <2 = 180°
4 + <1 + (180° - 5 - 4) = 180°
4 + <1 + 171° = 180°
<1 = 5°
Next, let's find the value of <7. We have:
<7 + <5 + <6 = 180°
<7 + 135° + (180° - 10 - 5) = 180°
<7 + 135° + 165° = 180°
<7 = 0°
Finally, let's find the value of <9. We have:
<9 + <10 + <11 = 180°
<9 + 11° + (180° - 10 - 11) = 180°
<9 + 11° + 159° = 180°
<9 = 0°
Part B:
The angle <4 is supplementary to angle <1, meaning they add up to 180°.
The angle <7 is congruent to angle <5, meaning they have the same measure.
The angle <9 is congruent to angle <10, meaning they have the same measure.
A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is red.
Spinner divided evenly into eight sections with three colored blue, one red, two purple, and two yellow.
Determine the theoretical probability of the spinner not landing on blue, P(not blue).
0.375
0.625
0.750
0.875
Answer:
Below
Step-by-step explanation:
5 out of 8 are NOT blue 5/8=.625
Help please!!
Use the first and last data points to find the slop intercept equation of the trend line.
The slope-intercept equation of the line that best fits the data, with a slope of 5.3333 and a y-intercept of 9.6666.
What is the slope?
The slope of a line represents the change in the dependent variable (y) for a unit change in the independent variable (x). In this case, the slope of the line of best fit represents the average change in the test grade for a one hour increase in studying. To find the slope, you can use the formula:
m = (Σxy - (Σx)(Σy)/n) / (Σx² - (Σx)²/n)
To find the slope-intercept equation of the trend line using the first and last data points, we'll first find the slope (m) of the line. The slope can be found using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
where x₁ and y₁ are the values for the first data point, and x₂ and y₂ are the values for the last data point. In this case, the first data point is (1, 15) and the last data point is (7, 47):
m = (47 - 15) / (7 - 1) = 32 / 6 = 5.3333
Next, we'll use the slope and the first data point to find the y-intercept (b) using the formula:
b = y₁ - m * x₁
b = 15 - 5.3333 * 1 = 15 - 5.3333 = 9.6666
Finally, we'll use the slope and y-intercept to write the slope-intercept equation of the line:
y = mx + b
y = 5.3333x + 9.6666
Hence, the slope-intercept equation of the line that best fits the data, with a slope of 5.3333 and a y-intercept of 9.6666.
To learn more about slope, Visit
https://brainly.com/question/16949303
#SPJ1
Answer:
[tex]y=\dfrac{16}{3}x+\dfrac{29}{3}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]
The first and last data points of the given table are:
(1, 15)(7, 47)Substitute the data points into the slope formula to find the slope of the trend line:
[tex]\text{Slope}\;(m)=\dfrac{47-15}{7-1}=\dfrac{32}{6}=\dfrac{16}{3}[/tex]
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
Substitute the found slope and the first data point into the slope-intercept formula and solve for b:
[tex]\implies 15=\dfrac{16}{3}(1)+b[/tex]
[tex]\implies 15=\dfrac{16}{3}+b[/tex]
[tex]\implies b=15-\dfrac{16}{3}[/tex]
[tex]\implies b=\dfrac{45}{3}-\dfrac{16}{3}[/tex]
[tex]\implies b=\dfrac{45-16}{3}[/tex]
[tex]\implies b=\dfrac{29}{3}[/tex]
Therefore, the equation of the trend line in slope-intercept form is:
[tex]y=\dfrac{16}{3}x+\dfrac{29}{3}[/tex]