Drag the red and blue dots along the x-axis and y-axis to graph
−4+6=24
Answers
See the attached image for the plotted graph
What is a Graph?The graph of a function f in mathematics is the collection of ordered pairs where f(x)=y.
These pairs are Cartesian coordinates of points in two-dimensional space and so form a subset of this plane in the typical situation when x and f(x) are real integers.
4x -4y = 24
x - y= 6
y= x-6
Slope= 1, pass through (6,0), (0, -6)
Read more about graphs here:
https://brainly.com/question/19040584
#SPJ1
Related Questions
the average expenses of a sample of 200 patients who were hospitalized at rwj hospital in new brunswick is $4400. the standard deviation of average expenses for these patients is
Answers
The standard deviation of the average expenses of 200 patients who were hospitalized at RWJ Hospital in New Brunswick cannot be determined from the information provided. The average expenses of the sample is $4400, but the standard deviation of these expenses is not given.
The standard deviation is a measure of the variability or dispersion of the data in a set and is calculated using a complete dataset of the expenses of all 200 patients. Without this dataset, it is not possible to determine the standard deviation of the average expenses.
Option A, less than $400, Option B, at least $400, and Option C, between $0 and $400, are all based on assumptions about the standard deviation that cannot be made without a complete dataset of expenses.
In conclusion, the standard deviation of the average expenses of 200 patients who were hospitalized at RWJ Hospital in New Brunswick cannot be determined from the information provided and a complete dataset of expenses would be needed to make any assumptions about the standard deviation.
Learn more about standard deviation here:
https://brainly.com/question/23907081
#SPJ4
Complete Question: A sample of 200 patients who were hospitalised at the rwj hospital in New Brunswick incurred $4400 on average in costs. The patients' average monthly costs have a standard deviation of
A. less than $400.
B. $400 or more.
C. from $0 to $400
D. Unable to determine D.
The question is asking what the fraction would be, I find it difficult to figure the answer out. I added some pictures, there are actually 6 stages but I can only add 5 attachments.
Answers
The fraction of the area of the triangle that would be shaded in stage 7 is equal to 2,187/16,384.
No, there isn't a stage when the fraction of area shaded would be equal to 0.
What is a fraction?In Mathematics, a fraction simply refers to a numerical quantity which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.
Next, we would determine the area of the triangle that would be shaded in stage 2 is as follows;
Fraction of the area = 3/4 × 3/4 = 9/16.
The area of the triangle that would be shaded in stage 3 is as follows;
Fraction of the area = 3/4 × 3/4 × 3/4 = 27/64.
The area of the triangle that would be shaded in stage 4 is as follows;
Fraction of the area = 3/4 × 3/4 × 3/4 × 3/4 = 81/256.
Therefore, the area of the triangle that would be shaded in stage 7 is as follows;
Fraction of the area = 3/4 × 3/4 × 3/4 × 3/4 × 3/4 × 3/4 × 3/4 = 2,187/16,384.
In this context, we can reasonably infer and logically deduce that there isn't a stage when the fraction of area shaded in this triangle would be equal to zero (0) because there is a linear relationship between the shaded and unshaded area.
Read more on fraction here: brainly.com/question/2194108
#SPJ1
A dog sled driver added more gear to the sled, doubling its weight. This felt too heavy, so the driver removed 20 pounds to reach the final weight of 180 pounds. Write and solve an equation to find the sled’s original weight.
Answers
Answer:
Step-by-step explanation:
x will be the original weight.
2x - 20 = 180
2x = 200
x = 100
Mr Sharma deposit ₹250 per month every month in a reccuring deposit account for a period of 3 Years.At the time of maturity he gets ₹ 10,110.
I. Find the of interest per annum.
ii. Find the total interest earned by Mr Sharma .
Answers
Answer:
I. 11%
II. ₹ 1110 in interest over 3 years
Step-by-step explanation:
To solve for the interest rate and the total interest earned, we can use the formula for compound interest:
A = P * (1 + r/n)^(nt)
where A is the maturity amount, P is the principal, r is the interest rate, n is the number of times compounded per year, t is the time in years, and
Since we know the maturity amount (A = ₹ 10,110), the principal (P = 250 * 12 * 3 = 9,000), and the time (t = 3 years), we can rearrange the formula to solve for the interest rate:
r = n * ((A/P)^(1/nt) - 1)
We'll assume that the interest is compounded monthly, so n = 12. Then:
r = 12 * ((10110/9000)^(1/36) - 1)
r ≈ 0.11
So, the interest rate is approximately 11% per year.
To find the total interest earned, we can use the formula:
Interest = A - P
Interest = 10110 - 9000
Interest = 1110
So, Mr Sharma earned ₹ 1110 in interest over 3 years.
In the diagram, AC is a diameter of circle O. If the slope of Bis-
B
1
what is the slope of AB?
A. 1/2
B. -1/-4
C. 2
D. -2
E. -4
Answers
In the diagram, AC is a diameter of circle O. If the slope of BC is -1/2, then the slope of AB is 2.
What is the diameter of the circle?
The diameter of a circle is the length of the line starting from one point on a circle to another point and passing through the center of the circle. It is equal to twice the radius of the circle.
We have that,
ABC is a right triangle
so,
AB is perpendicular to BC
we know that
If two lines are perpendicular, then the product of their slopes is equal to -1.
so,
m1 * m2 = -1
in this problem
mAB * mBC =-1
solve for mAB
mAB = -1 / mBC
mAB = -1 / -1/2
mAB = 2
therefore, In the diagram, AC is a diameter of circle O. If the slope of BC is -1/2, then the slope of AB is 2.
To learn more about the diameter of a circle visit,
https://brainly.com/question/23220731
#SPJ1
Complete Question:
In the diagram, AC is the diameter of circle O. If the slope of BC is -1/2, what is the slope of AB?
Justin has two craft sticks that are 14 inches long and 11 inches long. Which ratio compares the length of the shorter stick to the length of the longer stick?
Answers
Answer: To find the ratio of the length of the shorter stick to the length of the longer stick, we need to divide the length of the shorter stick by the length of the longer stick:
11 inches ÷ 14 inches = 11/14
So, the ratio of the length of the shorter stick to the length of the longer stick is 11/14.
Step-by-step explanation:
urn i contains two red chips and four white chips: urn ii, three red and one white. a chip is drawn at random from urn i and transferred to urn ii. then a chip is drawn from urn ii. what is the probability that the chip drawn from urn ii is red?
Answers
The probability that the chip drawn from urn II is red is 4/15. Let's call the event that the chip drawn from urn I and transferred to urn II is red "R1", and the event that the chip drawn from urn II is red "R2".
The probability of event R1 is 2/6 = 1/3.
Given that event R1 has occurred, the number of red chips in urn II becomes 4, and the number of total chips becomes 4+1=5. The probability of event R2 is 4/5 = 4/5.
The probability of both events occurring is (1/3) * (4/5) = 4/15.
So, the probability that the chip drawn from urn II is red is 4/15.
To know more about Probability
https://brainly.com/question/13604758
#SPJ4
what is the surface area
Answers
The surface area of the cube of side length 0.125 inches is given as follows:
S = 0.09375 in².
How to obtain the surface area?The surface area for a cube of side length a is given by the equation presented as follows:
S = 6a².
The side length in this problem has the value given as follows:
a = 1/8 = 0.125 in.
Hence the surface area of the cube is calculated as follows:
S = 6(0.125)²
S = 0.09375 in².
More can be learned about the surface area of a cube at https://brainly.com/question/26403859
#SPJ1
sin ² (θ) - cos² (θ) = 2 sin² (θ) -1
Answers
Answer:
The equation is not true.
Step-by-step explanation:
Starting with the left side,
sin²(θ) - cos²(θ) = 1 - cos²(θ) - cos²(θ) = 1 - 2cos²(θ)
The right side,
2 sin²(θ) - 1 = 2(sin²(θ) - 0.5)
Thus, in general, sin²(θ) - cos²(θ) ≠ 2 sin²(θ) -1.
Name the place value to the immediate right of the ones place.
A) tens
B) hundredths
decimal point
D) tenths
Answers
Hope this helps!!
In a sale, a clothes shop reduces its prices by 15%. A shirt usually costs $37. How much is it in the sale? How do I work this out?
Answers
Answer:
$ 31.45
Step-by-step explanation:
15% = 0.15 x 37 = 5.55$ off the original price so 31.45$ is the final price for the tee shirt. Give brainlist please
Sale price for the given shirt will be $32.
According to question given are-
Percentage of the reduction rate of the shirt is = 15%
Reduction Percentage refers to the percentage rate at which the Initial Per Certificate Entitlement will diminish daily, assuming that the daily rate will be calculated as the annual rate given in the Final Terms divided by 365 and applied as necessary.
Actual cost of the shirt is = $37.
decreased rate "Reduced rate" refers to a contribution rate that is lower than the standard rate required by State law, while "standard rate" refers to the rate used to compute variances from that rate.
So, accordingly Reduction rate = (Actual rate X Reduction Percentage)/100
Reduction = (37×15)/100 = Rs 5.55$ ≅ 5$
So the sale price = 37−5 = 32$
To know more about Reduction rate
https://brainly.com/question/15400380
#SPJ1
BLACK HISTORY FACT OF THE DAY: 1998-Bryant is the youngest starter at first All-Star game UNIT 9 LESSON 4-SWBAI solve real-world and mathematical problems invol of polygons c. This week, the rolls of wallpaper are on sale for $11.99/rall Find the cost of covering the wall with wallpaper. d. A gallon of special textured paint covers 200 f12 and is on sale for $22.99/gallon. The wall needs to be painted twice (the wall needs two coats of paint). Find the cost of using paint to cover the wall.
Answers
The answers are a) the area of wallpaper needed to cover the wall is 84 ft², b) (i) the area of a roll = 49.5 ft², (ii) the number of the roll required to cover the wall is 2 rolls, c) the cost of the rolls needed to cover the wall = 2 x 11.99 = $23.98 and d) the cost of the paint for painting the wall is $19.3116
What is an area?Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.
Given that, a wall is 8 ft high and 16 ft long, having a window, mirror and a fireplace, with dimensions, 18 in(1.5 ft) by 14 ft, 5 ft by 3 ft and 4 ft by 2 ft respectively,
a) The area of wallpaper needed to cover the wall =
The area of wallpaper = area of wall - (sum of areas of the window, mirror and the fireplace)
= 8x16-(14x1.5+5x3+4x2)
= 128-(21+15+8)
= 84 ft²
Therefore, the area of wallpaper needed to cover the wall is 84 ft²
b) (i) The area of one roll =
The dimensions of the roll are 1.5 ft by 33 ft, area = 49.5 ft²
(ii) The number of the roll required to cover the wall = 84 ft² / 49.5 ft²
= 1.7 ≈ 2
Therefore, the number of the roll required to cover the wall is 2 rolls.
c) The cost of the rolls needed to cover the wall = 2 x 11.99 = $23.98
d) A gallon of the paint can cover 200 ft², costing $22.99/gallon,
1 ft² = 1/200 gallons
Therefore,
168 ft² = 168 x 1/200 = 0.84 gallons
Cost = 0.84 x $22.99
= $19.3116
Therefore, the cost of the paint for painting the wall is $19.3116
Hence, the answers are a) the area of wallpaper needed to cover the wall is 84 ft², b) (i) the area of a roll = 49.5 ft², (ii) the number of the roll required to cover the wall is 2 rolls, c) the cost of the rolls needed to cover the wall = 2 x 11.99 = $23.98 and d) the cost of the paint for painting the wall is $19.3116
Learn more about area, click;
https://brainly.com/question/27683633
#SPJ9
The complete question is attached :-
Find the Domain, Range, rel. Max and minimum, end behavior, and thr increasing and decreasing intervals.
EQUATION: f(x)=-x^3+8x^2-15x
Answers
Step-by-step explanation:
Domain: The domain of the function is all real numbers.
Range: The range of the function is all real numbers less than or equal to 8. To see this, note that the leading coefficient of the polynomial is negative (-x^3), so the function approaches negative infinity as x approaches positive or negative infinity. The largest y-value the function can attain is 8, which occurs at x = 2.
Relative maxima and minima: To find the relative maxima and minima, we find the critical points of the function, which are the values of x that satisfy f'(x) = 0 or f'(x) does not exist. The first derivative of the function f(x) is given by:
f'(x) = -3x^2 + 16x - 15
Solving f'(x) = 0, we get:
-3x^2 + 16x - 15 = 0
x = 1, 5
We also need to determine the concavity of the function near each critical point to determine whether each is a relative maximum or minimum. To do this, we find the second derivative of the function and evaluate its sign at each critical point. The second derivative of f(x) is given by:
f''(x) = -6x + 16
Since f''(x) is always negative, the function is concave down and therefore has a relative maximum at x = 1 and a relative minimum at x = 5.
End behavior: The leading term of the function is -x^3, which means the function approaches negative infinity as x approaches negative infinity and positive infinity as x approaches positive infinity. The end behavior of the function is therefore negative infinity as x approaches negative infinity and positive infinity as x approaches positive infinity.
Increasing and decreasing intervals: To find the increasing and decreasing intervals of the function, we find the critical points and the sign of f'(x) in the intervals between the critical points.
f'(x) = -3x^2 + 16x - 15
Since f'(x) is negative for x < 1 and positive for x > 1, the function is decreasing for x < 1 and increasing for x > 1. Similarly, since f'(x) is positive for x < 5 and negative for x > 5, the function is increasing for x < 5 and decreasing for x > 5. So, the increasing intervals are (negative infinity, 1) and (1, 5) and the decreasing intervals are (5, positive infinity).
At 6 a.m., the temperature was 50°F. For the next 4 hours, the temperature rose 3° per hour. The next 6
hours, it rose 2° per hour. The temperature then stayed steady until 6 p.m. For the next 2 hours, the
temperature dropped 1° per hour. The temperature then dropped steadily until the temperature was 56°F at
midnight. On the set of axes below, graph Elroy's data.
Temperature (°F)
70-
60-
4+2=4
6*2=12
6×2=0
Answers
The graph of the problem depicts the rate of the temperature change.
How to graph the temperature change?To graph temperature change, you can use a line graph. The horizontal axis represents time, while the vertical axis represents temperature. You plot points on the graph corresponding to the recorded temperature at specific times, and then connect the points to form a line.
The slope of the line represents the rate of temperature change, with a steep line indicating a rapid increase or decrease in temperature and a gentle slope indicating a slow change. The line graph helps to visually represent changes in temperature over time and can be used to analyze patterns and trends.
Learn more about temperature change:https://brainly.com/question/28884653
#SPJ1
9 pieces of Starburst candies contain 175 How many calories do 25 Starburst candies contain? Round your answer to the nearest calorie
Answers
Answer:
486 Calories
Step-by-step explanation:
175/9 = # of Calories for EACH Starburst
25 x 175/9
4375 / 9 = 486 1/9
Answer: 486 calories
Step-by-step explanation:
175 / 9 = 19.4444444444 calories per piece
25 starbursts = 19.4444444444 * 25= 486.111111111
Rounded = 486 calories
find the range of the following fiction for the domain {-4,-2,0,1.4,4}. f(x)=-2x-3
Answers
(5, 1, -3, 5.8, -11,)
Step-by-step explanation:
basically rage is y value. and domain is x value. so in this question the domain value are given so since domain is the value of x you have to substitute the number into the x. then you get the range. the answer are (5, 1, -3, 5.8, -11,)
Tanner collected 360 cans. This was 40% of what Reggie collected. How many cans did Reggie collect?
Answers
Answer:
Step-by-step explanation:
Let's call the number of cans Reggie collected as "x".
According to the problem, Tanner collected 360 cans, which was 40% of what Reggie collected, so:
360 = 40/100 * x
To find the value of x, we can isolate x by dividing both sides by 40/100:
x = 360 * 100/40
x = 900
So Reggie collected 900 cans.
Answer:
900 cans
Step-by-step explanation:
We know
360 cans = 40%
We have to find 1% by taking
360 divided by 40 = 9 cans
How many cans did Reggie collect?
We take
9 x 100 = 900 cans
Solve the polynomial (preferably with the X or Box method) g^2+9g+18=0
Answers
Answer:
To solve the polynomial (g^2 + 9g + 18 = 0) using the X or Box method, you need to factor the polynomial into two binomials. To do this, you need to find two numbers that multiply to 18 and add up to 9. The two numbers are 6 and 3, so the polynomial can be factored as:
g^2 + 9g + 18 = (g + 6)(g + 3) = 0
To find the solutions, you set each factor equal to 0 and solve for g:
g + 6 = 0, so g = -6
g + 3 = 0, so g = -3
The solutions to the polynomial are g = -6 and g = -3.
Step-by-step explanation:
find a geometric mean between 16 and 36
Answers
Answer:
5.196103885259%
Step-by-step explanation:
Negative values detected. All input values threated as percentages (e.g. an input of 0.1 is threated as 0.1%, -10 is threated as -10%).
Help……………………………………..
Answers
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Find the volume of the cylinder. Use 3.14 for T.
(E
34 m
drawing not to scale
27 m
Answers
The volume of the cylinder is approximately 6058.73 cubic meters.
Describe Cylinder?A cylinder is a three-dimensional geometric shape that is similar to a tube. It has two parallel bases that are circular in shape, and its lateral surface is a rectangle. The height of the cylinder is the distance between the two bases. The cylinder has a top base and a bottom base, and these are both circles with the same diameter. The volume of a cylinder can be found by multiplying the area of one of its circular bases by its height. The surface area of a cylinder can be found by adding up the areas of the two circular bases and the lateral surface. Cylinders are widely used in mathematics, engineering, and physics, and they play an important role in the study of various geometric and physical concepts.
Given the diameter of a cylinder is 34m and its height is 27m, we can find the volume of the cylinder using the formula:
Volume = π × (diameter / 2)² × height
Plugging in the values, we get:
Volume = 3.14 × (17 / 2)² × 27
Volume = 3.14 × (8.5)² × 27
Volume = 3.14 × 72.25 × 27
Volume = 6058.73 cubic meters
So, the volume of the cylinder is approximately 6058.73 cubic meters.
To know more about diameter visit:
https://brainly.com/question/5501950
#SPJ1
solve the question
in a group of 65 students 40students want to be a doctor and 20 wants to be a social worker. the number of students who want to be a doctor only and the student who wants to be a social worker only are in the ratio 3:1 by drawing venn diagram find.
1)how many students want to both?
2)how many want to be both?
Answers
Answer:To find the number of students who want to be both a doctor and a social worker, we can use the Principle of Inclusion-Exclusion (PIE). This principle states that the total number of elements in the union of two sets is equal to the sum of the number of elements in each set minus the number of elements in their intersection.
So, the number of students who want to be both a doctor and a social worker can be calculated as:
|Doctor ∩ Social worker| = |Doctor| + |Social worker| - |Doctor U Social worker|
|Doctor ∩ Social worker| = 40 + 20 - 65
|Doctor ∩ Social worker| = -5
However, this result is negative which is not possible, therefore, no students want to be both a doctor and a social worker.
To find the number of students who want to be both, we have to find the number of students who want to be both a doctor and a social worker which is 0 in this case.
Step-by-step explanation:
looking at the side-by-side boxplots from the previous question, should the mean for boxplot #3 be less than, greater than, or roughly equal to its median?
Answers
The mean for boxplot #3 should be less than its median. In a negatively skewed distribution, the mean is less than the median.
This is because the few small values in the data pull the mean down, while the median is still at the middle value. A boxplot can give us an idea of the shape of the distribution, and if it is negatively skewed, it suggests that the mean will be less than the median.
It's important to note that without actually seeing the boxplot, this conclusion may not be accurate. There could be other factors that affect the mean and median, such as outliers or the size of the sample. However, based on the information given that the boxplot is negatively skewed, it is likely that the mean will be less than the median.
Learn more about Boxplot:
https://brainly.com/question/24335827
#SPJ4
Is 6xy2 is the greatest common factor of 12xy2, 36x2y2, and 42xy4
Answers
Yes, 6xy² is the greatest common factor of 12xy², 36x²y², and 42 xy⁴. The Greatest common factor is the highest common factor of all the given numbers.
We can find the greatest common factor by applying the prime factorization method. There are two steps involved to find the highest common factor.
Find the factors 12, 36, and 42.Find the common factor for the variables i.e. xy², x²y², and xy⁴Step 1
The factors of the numbers are
Factors of 12 are 1,2,3,4,6,12
Factors of 36 are 1,2,3,4,6,9,12,18,36
Factors of 42 are 1,2,3,6,7,14,21,42
The common factor for 12,36,42 are 1,2,3,6
Therefore, the greatest common factor for 12,36,42 is 6.
Step 2
We have to find the common factors for the variable parts x¹,y²,x²,y²,x¹,y⁴
The factor for x¹ is x itself.
The factors for y² is y⋅y
The factors for x² are x⋅x
The factors for y² are y⋅y
The factor for x¹ is x itself.
The factors for y⁴ are y⋅y⋅y⋅y
Hence, the common factors for the variables
x¹,y²,x²,y²,x¹,y⁴ are x⋅y⋅y
The GCF for the variable part is xy².
Now, multiply the GCF of the numerical part i.e.6 and the GCF of the variable part i.e. xy².
Therefore, it comes out to be 6xy².
Learn more about the Greatest common factor here brainly.com/question/29065785
#SPJ4
Solve for x.
A) x = 4tan56°
B) x = 4sin34°
C) x = 4tan34°
D) x = 4sin56°
E) x = 4cos34°
Answers
The correct Option for this question is option C i.e. x= 4tan34°. The other options which are given in the question are incorrect.
The Right angled triangle along with the base angle of 34°. The base is equal to 4.
θ= 34°
To find the value of x which is equal to the perpendicular of the right-angled triangle
According to the trigonometric ratio
tanθ = Perpendicular ÷ base
According to the above formula
tan 34 = x ÷ 4
Now, we have to multiply each side by 4.
x= 4× tan34° which means x= 4tan34°
tan 34° = 0.6745
x= 4× 0.6745
X=2.70
Learn more about Trigonometry here brainly.com/question/22986150
#SPJ4
quinn is baking sweet potato pies. the table shows the ratio of cups of sugar to number of pies. number of pies359 cups of sugar1 and one half2 and one half4 and one half how many cups of sugar will quinn need to make 16 pies? 8 cups 8 and one half cups 9 and one half cups 11 cups
Answers
Quinn will need 8 cups of sugar to make 16 pies based on the table that shows the ratio of pies and sugar.
Dividing and Multiplying FractionWhat we know from the question:
3 pies = 1 ½ cups of sugar
5 pies = 2 ½ cups of sugar
9 pies = 4 ½ cups of sugar
16 pies = ?
To make it easier, the answer will be explained through sentence:
First, we find out how much sugar it takes to make one pie. Use one of the ratio provided above by dividing the pie amount with the sugar’s. For example, 3 divided by 1 ½ equals ½ .
Therefore, one pie would require only ½ cups of sugar. Crosscheck with the other ratio to make sure it is correct using the same method earlier.
Second, we find out how much sugar it takes to make 16 pies. Multiply the amount of pies with the amount of sugar. So 16 x ½ equals 8.
Here are the summary
1 pies = ½ cups of sugar
16 pies = 8 cups of sugar
Learn more about multiplying and dividing fraction, here:
https://brainly.com/question/2261275
#SPJ4
Part A: Describe in words how you can find the rate of change of a bushel of corn in the current year, and find the value. (5 points) Part B: How many dollars more is the price of a bushel of corn in the current year than the price of a bushel of corn in the previous year? Show your work. (5 points) Number of Bushels
Price of Corn (dollars)
2
10
4
20
6
30
8
40
Answers
The evaluation of the possible graph and table in the question, which indicates proportional relationships are presented as follows;
Part A: The rate of change of a bushel of corn in the current year is; 8 dollars per bushel of corn
Part B: Tnhe price of a bushel of corn in the current year is three dollars ($3) more than the price in the previous year.
What is a proportional relationship?A proportional relationship is one in which the output variable of the relationship, is a multiple of the input variable and factor.
The points on the graph in the question, obtained from a similar question posted on the website are;
(0, 0), (3, 24), (6, 46), (9, 72), (12, 76), (15, 120), (18, 144)
Part A: The slope is the rate of change of the bushel of corn. Therefore, the rate of change for the current year can be found by finding the slope as follows;
The graph is a straight line graph, indicating a proportional relationship therefore, the slope of the graph is a constant, which can be found as follows;
Slope = (24 - 0)/(3 - 0) = 8
The rater of change of the bushel for the current year is; 8 dollars per bushel of corn
Part B: Whereby the values in the table for the number of bushels to the price of corn for the previous year can be presented as follows;
Number of Bushels [tex]{}[/tex] Price of Corn (dollars)
2 [tex]{}[/tex] 10
4 [tex]{}[/tex] 20
6 [tex]{}[/tex] 30
8 [tex]{}[/tex] 40
The rate of change of the price for the previous year is therefore;
Rate of change = (20 - 10)/(4 - 2) = 5
The rate of change for the previous year is therefore 5 dollars per bushel
The price of a bushel in the current year is three more dollar than the price of a bushel in the previous year.
Learn more on proportional relationships here: https://brainly.com/question/11454559
#SPJ1
Determine whether each sequence is arithmetic, geometric, or neither. Find tn.
-k^2-k+1,k+2,k^2+3k+3,2k^2+5k+4,...
Answers
The given assertion states that the sequence's nth element is -k² + (2n-3)k + 1.
What are some examples of consecutive terms?Sequential is a derivative of the Latin word consecutus, which means "following closely" without a pause. Similar to those snowstorms, which occurred back-to-back each day for five months in a succession. Additionally, consecutive numbers progress in the correct sequence or follow one another. For instance, the numerals 5, 6, 7, 8, 9, and 10 follow one another.
Looking at the differences between consecutive terms, we have:
(k+2) - (-k²-k+1) = k²+3k+3 - (k+2) = k²+2k+1 = (k+1)²
(k²+3k+3) - (k+2) = k²+2k+1 = (k+1)²
(2k²+5k+4) - (k²+3k+3) = k²+2k+1 = (k+1)²
We can see that the differences between consecutive terms are all the same, which means that the sequence is an arithmetic sequence.
To find tₙ, we need to find the common difference d. From the differences above, we have:
d = (k+1)² - (k²+k-1) = 2k
So, the nth term of the sequence is given by:
tₙ = t₁ + (n-1)d
tₙ = (-k²-k+1) + (n-1)(2k)
tₙ = -k²-k+1 + 2nk - 2k
tₙ = -k² + (2n-3)k + 1
Therefore, the nth term of the sequence is -k² + (2n-3)k + 1.
To know more about consecutive terms visit:
https://brainly.com/question/28350604
#SPJ1
AABC has < A = 50⁰, < B = 72º and a = 10cm. Solve for side b.
Answers
The solution for side b is 12.4 cm
How to determine the solution for side bFrom the question, we have the following parameters that can be used in our computation:
< A = 50⁰, < B = 72º and a = 10cm.
Uing the law of sines, we have
a/sin(A) = b/sin(B)
Substitute the known values in the above equation, so, we have the following representation
10/sin(50) = b/sin(72)
So, we have
b = sin(72) * 10/sin(50)
Evaluate
b = 12.4
Hence, the length is 12.4 cm
Read more about triangles at
https://brainly.com/question/14285697
#SPJ1
You may have polarized sunglasses that eliminate glare by polarizing the light. When light is polarized, all of the waves are traveling in parallel planes. Suppose vertically polarized light with intensity strikes a polarized filter with its axis at an angle. Of with the vertical. The intensity of the transmitted light and are related by the equation write as a function
Answers
The intensity of the transmitted light, [tex]I_{t}[/tex], is equal to half of the original intensity, [tex]I_{0}[/tex].
Given θ = 45° and cosθ = [tex]\sqrt\frac{I_{t} }{I_{0} }[/tex]
When polarized light with intensity [tex]I_{0}[/tex] strikes a polarized filter with its axis at an angle θ with the vertical, the intensity of the transmitted light, [tex]I_{t}[/tex], depends on the angle θ and the original intensity [tex]I_{0}[/tex]. The relationship between [tex]I_{t}[/tex] and [tex]I_{0}[/tex] is described by the equation cosθ = [tex]\sqrt\frac{I_{t} }{I_{0} }[/tex].
If θ = 45°, then the equation θ can be simplified to cos 45° =[tex]\sqrt\frac{I_{t} }{I_{0} }[/tex].
The cosine of 45° is equal to [tex]\frac{1}{\sqrt{2} }[/tex], so we have:
[tex]\frac{1}{\sqrt{2} }=\sqrt\frac{I_{t} }{I_{0} }[/tex]
On Squaring both sides, we have:
[tex]\frac{1}{{2} }=\frac{I_{t} }{I_{0} }[/tex]
Multiplying both sides by [tex]I_{0}[/tex], we have:
[tex]I_{t}=\frac{I_{0} }{2}[/tex]
Therefore, if θ = 45°, the intensity of the transmitted light, [tex]I_{t}[/tex], is equal to half of the original intensity, [tex]I_{0}[/tex].
Learn more about polarized light here https://brainly.com/question/17003853
#SPJ4