The arithmetic average return is found by adding up the returns and dividing by the number of years:
Arithmetic average = (22% + 9% - 7% + 13%) / 4 = 9.25%
To find the geometric average return, we need to use the formula:
Geometric average = (1 + R1) x (1 + R2) x ... x (1 + Rn) ^ (1/n) - 1
where R1, R2, ..., Rn are the annual returns.
So for this stock, the geometric average return is:
Geometric average = [(1 + 0.22) x (1 + 0.09) x (1 - 0.07) x (1 + 0.13)] ^ (1/4) - 1
= 0.0868 or 8.68%
Therefore, the arithmetic average return is 9.25% and the geometric average return is 8.68%.
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Question 23 of 25
Which inequality represents all values of x for which the quotient below is
defined?
√x+2+√5-F
O A. x≤5
OB. 25x55
OC. 2x<5
D. X2-2
unctions
To prevent division by zero errors, we once more ensure that x=5 is not permitted. The expression (5-x) underneath the other root is simultaneously set to be greater than 0.
what is inequality ?An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal symbol (). Different inequalities are used to contrast values, no matter how small or large. Many simple inequalities can be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.
given
We require the (x+2) expression to be either 0 or positive in order to ensure that the information under the square root is not negative.
The expression (5-x) underneath the other root is simultaneously set to be greater than 0. We do not allow (5-x) to equal 0.
As a result, 5-x > 0 becomes 5 > x or x 5 when x is removed. This is the result of adding x to both sides.
In addition to the two inequalities, we also have x < 5. In order to describe a number between -2 and 5, we must include -2 but not 5.
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What happens when a figure is dilated by a scale factor of less than 1?
When a figure is dilated by a scale factor of less than 1, it becomes smaller as the coordinates of each point on the figure will be multiplied by a value less than 1. This results in a reduction of the size of the figure while preserving its shape.
For example, if a figure is dilated by a scale factor of 0.5, the coordinates of each point on the figure will be multiplied by 0.5. This means that each point on the figure will be moved half as far from the origin as it was before the dilation.
The result of this is that the dilated figure will be smaller than the original figure and will have a scale factor of less than 1.
It's important to note that if the scale factor is less than 1, the dilation will reduce the size of the figure and if the scale factor is greater than 1, the dilation will increase the size of the figure.
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For the following data, find the correlation coefficient. Does the line of best fit have positive correlation, negative correlation, or no correlation?
X 4 2 8 3 4 8 5 1 2
y 3 6 7 8 9 1 2 3 5
The correlation coefficient of the given set of data is −0.17 which is negative correlation.
What is correlation coefficient?A correlation coefficient is a metric that expresses a correlation of some kind, or a statistical association between two variables. The variables could be two columns of a specific data set of observations, also known as a sample, or two parts of a multivariate random variable with a well-known distribution.
∑x = 4+2+8+3+4+8+5+1+2
∑x = 37
∑y = 3+6+7+8+9+1+2+3+5
∑y = 44
n = 9
[tex]$ \bar{\text x} = \frac{\Sigma \text x}{n} = \frac{37}{9} = 4.1[/tex]
[tex]$ \bar{\text y} = \frac{\Sigma \text y}{n} = \frac{44}{9} = 4. 8[/tex]
x - [tex]\bar{\text x}[/tex] y - [tex]\bar{\text y}[/tex] [tex](\text x -\bar{\text x} ) ( \text y - \bar{\text y} )[/tex]
−0.1 −1.8 0.18
−2.1 1.2 −2.52
3.9 2.2 8.58
−1.1 3.2 −3.52
−0.1 4.2 −0.42
3.9 −3.8 −14.82
0.9 −2.8 −2.52
−3.1 −1.8 5.58
−2.1 0.2 −0.42
[tex]\Sigma (\text x -\bar{\text x} ) ( \text y - \bar{\text y} )[/tex]
= −9.88
(x - [tex]\bar{\text x}[/tex])² (y - [tex]\bar{\text y}[/tex])²
0.01 3.24
4.41 1.44
15.21 4.84
1.21 10.24
0.01 17.64
15.21 14.44
0.81 7.84
9.61 3.24
4.41 0.04
∑(x - [tex]\bar{\text x}[/tex])² ∑(y - [tex]\bar{\text y}[/tex])²
= 50.89 = 62.96
Coefficient of correlation, r = [tex]$ \frac{\Sigma (\text x -\bar{\text y} ) ( \text y - \bar{\text y} )}{\sqrt{\Sigma(\text x -\bar{\text x} )^2} \sqrt{\Sigma(\text y-\bar{\text y} )^2}}[/tex]
r = [tex]$ \frac{-9.88} {\sqrt{50.89 } \sqrt{62.96}}[/tex]
r = [tex]$ -\frac{247\sqrt{8010086} } {4005043}[/tex]
r = −0.17
Thus, the correlation coefficient of the given set of data is −0.17 which is negative correlation.
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Please help! 50+ points!
Answer: x= 95° ; y= 35°
Step-by-step explanation:
If J II K (symmetrical), then x°= 180°- 85°
x°= 95°
In addition to this, because the J II K lines are symmetrical:
(5y-90)°= 85°
5y°- 90° = 85°
5y°= 85°+ 90°
5y° = 175°
5y°/ 5 = 175°/5
y°= 35°
Julia measured a line to be 16.6 inches long. If the actual length of the line is 16.4
inches, then what was the percent error of the measurement, to the nearest tenth of a
percent?
The percent error = 1.22% shown in nearest tenth.
What is percent error?
The difference between actual value and measured value is termed as percent error. It is shown in percentage unit. Generally, it is accepted that there may be some amount of percent error during our experiment and certain correction formula is always available to verify our result.
What was the percent error of Julia's measurement?Julia measured a line to be 16.6 inches in length.
but the actual length recorded is 16.4 inches.
The percent error of Julia's measurement = (experimental length - actual length) / actual length ×100
percent error = (16.6 - 16.4) / 16.4 ×100 = 1.22 %
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The equation for line g is y = 14x – 44. Suppose lines g and h are perpendicular, and the point (–2, 1) lies on line h. Write an equation in standard form for line h.
Answer:
Line h is y = -(1/14)x + (8/7)
Step-by-step explanation: A perpendicular line will have a slope that is the negative inverse of the reference line. The reference line in this problem is y=14x-44. The slope of 14 is inverted to 1/14 and multiplied by -1 to yield a new slope of -(1/14) for the perpendicular line. The perpendicular line will have the form of y = -(1/14)x + b.
Any value of b will still result in a line perpendicular to y=14x-44. But we want a line for h that goes through point (-2,1). To find a value of b that moves the line so that it intersects (-2,1), substitute the value (-2,1) for (x,y) in the equation y = -(1/14)x + b, and then solve for b.
y= -(1/14)*(x) + b
1 = -(1/14)*(-2) + b for (-2,1)
1 = (2/14) + b
1- (1/7) = b
b = (6/7)
The equation for line h becomes y = -(1/14)x + (6/7)
See the attached worksheet.
Answer: x+14y=12
Step-by-step explanation: got this off an assignment on mcgrawhill still dont know how to get that tho good luck
What is Heron's formula for area of triangle Class 9?
Heron's formula is a formula used to calculate the area of a triangle when the lengths of its three sides are known.
It is named after Hero of Alexandria, a Greek mathematician and engineer who first derived this formula.
The formula states that the area of a triangle is equal to the square root of the product of the semi-perimeter (half the sum of the three sides) and the differences of the semi-perimeter and each side.
Mathematically, Heron's formula can be written as:
A = √(s(s-a)(s-b)(s-c)),
where A is the area of the triangle, s is the semi-perimeter and a, b, c are the length of the three sides of the triangle.
For example, if the lengths of the three sides of a triangle are 5 cm, 6 cm and 7 cm, then the semi-perimeter (s) is (5 + 6 + 7)/2 = 9 cm.
Using Heron's formula, the area of the triangle is:
A = √(9(9-5)(9-6)(9-7)) = √(9*4*3*2) = √432 = 6.48 cm2
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What is the equation for the line in slope-intercept form?
Enter your answer in the box.
Answer: A
Step-by-step explanation: i took the test
Out of a journey of 300km;the firt part of ditance 85km i covered at a peed of 51km/h, the econd part of 90km at a peed of 135km/h and the remaining ditance at a peed of 75km/h. Find:
(1) the ditance covered at a peed of 75km/h. (2) the total time taken. (3) the average peed for the whole journey
125 km are traveled when traveling at a pace of 75 km/h.
The entire travel time to complete 300 km is 1.14 hours, with an average travel speed of 263.15 km/hr.
Given that,
The first 85 kilometers are traveled at a 51 km/hr pace.
A pace of 135 km/hr is used to cover the second 90 km stretch.
75 km/hr is used to cover the remaining distance.
Journey distance is 300 kilometers.
Distance traveled at 75 km/hr is equal to 300 - (85 + 90) = 125 kilometers.
The total time required was 300/261 miles per hour, or 1.14 hours.
The distance traveled divided by the time required equals 300/1.14, or 263.15 kilometers per hour, as the average speed for the whole trip.
Thus, 125 km are traveled when traveling at a pace of 75 km/h.
The entire travel time to complete 300 km is 1.14 hours, with an average travel speed of 263.15 km/hr.
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What is the formula for midpoint rule?
The formula for midpoint rule is M =∑ n i = 1 f ( m i ) Δx.
In this equation, I represents the ith rectangle, n the number of rectangles that comprise the area under the curve, f (m I) the function of the curve as defined by the ith rectangle's midpoint, and x the width of each rectangle. In calculus, the midpoint formula may be used to estimate the same area on an x-y plot. It is necessary to give an interval with a lower and upper border where the computed area will begin and stop, as well as the number of units, or subintervals, that the interval will be divided into when computing the area under the curve of a function. More rectangles enhance estimation precision (n).
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What are the two 2 main approaches of image classification for each explain the general steps involved?
The two main approaches for image classification are supervised learning, which uses labeled data and involves training a model to map features to labels, and unsupervised learning, which does not require labeled data and involves clustering images based on their features and assigning labels to the clusters.
There are two main approaches to image classification:
Supervised learning: This approach uses a labeled dataset, where the images and their corresponding labels are provided. The general steps involved in this approach are:Data pre-processing: This step includes cleaning, normalizing, and resizing the images.Feature extraction: This step involves extracting relevant features from the images that will be used to train the model.Model training: A supervised learning model is trained on the feature-label dataset, which learns to map the features to the corresponding labels.Model evaluation: The trained model is evaluated on a separate test dataset to measure its performance.Unsupervised learning: This approach does not require labeled data, the general steps involved in this approach are:Data pre-processing: This step includes cleaning, normalizing, and resizing the images.Feature extraction: This step involves extracting relevant features from the images that will be used to cluster the images.Clustering: The images are grouped into clusters based on their features using clustering algorithms like k-means or hierarchical clustering.Label assignment: Assign labels to the clusters based on the images they contain.Model evaluation: The performance of the model is evaluated by comparing the assigned labels with the ground truth labels if available.To learn more about image classification at
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What is midpoint formula Class 10?
The Midpoint Formula is given as, (x, y) = [(x₁ + x₂)/2, (y₁ + y₂)/2]
The midpoint formula is a mathematical equation that is used to locate the halfway point between two data points.
The key characteristic of this equation is that it calculates the percentage changes based on the difference between the beginning and the ending values.
Formula to Find the Midpoint:
To find the midpoint of the straight line in a graph, we use this midpoint formula that will enable us to find the coordinates of the endpoint of the given line.
Suppose the endpoints of the line is (x₁,y₁) and (x₂,y₂) then the midpoint is given as:
The Midpoint Formula is given as,
(x,y)=[x₁+x₂/2,y₁+y₁/2]
Where x₁ and x₂ are the coordinates of the x-axis. y₁ and y₂ are the coordinates of the y-axis.
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Are triangles ABC and ADC congruent?
No, triangles ABC and ADC are not congruent.
To determine if two triangles are congruent, we must use the Side-Angle-Side (SAS) Congruence Theorem. This theorem states that if two sides and the included angle of one triangle are equal to two sides and the included angle of a second triangle, then these two triangles are congruent.
In this case, we can see that sides AB and AD are equal, but angles A and D are not equal. Therefore, triangles ABC and ADC are not congruent. To prove this calculationally, we can use the Law of Cosines. First, we can calculate the length of side BC by using the Law of Cosines:
BC^2 = AB^2 + AC^2 - 2AB * AC * cos(A)
BC = √(AB^2 + AC^2 - 2AB * AC * cos(A))
Then, we can calculate the length of side DC by using the Law of Cosines:
DC^2 = AD^2 + AC^2 - 2AD * AC * cos(D)
DC = √(AD^2 + AC^2 - 2AD * AC * cos(D))
Finally, we can compare BC and DC. Since BC ≠ DC, we can conclude that triangles ABC and ADC are not congruent.
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a. Graph the system of equations.
b. What is the solution to the system of equations?
c. Verify the solution.
By graphing the system of equations, we can see that the solution of the system is (-5, -3).
How to solve the system of equations graphically?Here we want to solve the following system of equations:
y = (2/5)*x - 1
2x - 3y + 1 = 0
To solve a system of equations graphically, we just need to graph both equations on the same coordinate axis, and then find the point where the two lines do intersect.
The graph of the system of equations can be seen on the image below.
Below you can see the graph of the system of equations, and you can see that the graphs intercept at the point (-5, -3)
To check if this is a solution, just replace these values in both equations and see if you get the same thing.
For the first one:
-3 = (2/5)*-5 - 1
-3 = -2 - 1
-3 = -3
And for the other line
2*-5 - 3*-3 + 1 = 0
-10 + 9 + 1 = 0
0 = 0
So the point is a solution for both equations.
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Monica deposits $100 into a savings account that pays a simple interest rate of 3.7%. Paul deposits $200 into a savings account that pays a simple interest rate of 2.4%. Monica says that she will earn more interest in 1 year because her interest rate is higher. Is she correct? Justify your response.
No, Monica is incorrect. Paul will get more interest in 1 year
What is simple interest?Simple interest is the interest amount for a particular principal amount of money at some rate of interest
Formula: Simple interest :
Principal x rate x time/100
Given: For Monica, Principal =$100, rate = 3.7%
Interest in 1 year = 100 x 3.7 x 1/100
=$3.7
For Paul, Principal =$200, rate = 2.4%
Interest in 1 year =200 x 2.4 x 1/100
= $4.8
Thus , Paul will get more interest in 1 year.
Therefore, Monica is incorrect.
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Find the radius of a circle in which the central angle, 0, is 60° and intercepts an arc of length 77 cm.
The radius is ?cm
The radius of the circle is 73.6 cm
What is length of an arc?Arc length is the distance between two points along a section of a curve or circle.It is the measure of the distance along a curved line. In other words, it's the distance from one point on the edge of a circle to another, or just a portion of the circumference.
The length of an arc is given tetha/360× 2πr
where r is the radius and
tetha is the angle
Therefore 77 = /360 ×2×3.14×r
77 = 1/6× 6.28r
multiply both sides by 6
77×6 = 6.28r
462 = 6.28r
divide both sides by 6.28
r = 462/6.28
r = 73.6cm
Therefore the radius of the circle is 73.6 cm
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Explain why they are or not similar please!
Thank you!
We have proved that given polygons are similar polygons.
What are similar polygons?
Similar polygons are polygons that have the same shape, but possibly different sizes. Two polygons are similar if and only if their corresponding angles are congruent (equal in measure) and the ratio of the lengths of their corresponding sides is always the same, regardless of which pair of corresponding sides is chosen.
The similar polygons will have the same angles. in the given figure they all have the right-angle.
also if we take the ratio of their corresponding lengths, we get
12/8 = 24/16
3/2 = 3/2
So we can say that both polygons are similar.
Hence, we have proved that given polygons are similar polygons.
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Simplify the expression
using only positive exponents in the image
Answer:
option2 12x²/y⁹
Step-by-step explanation:
attached the solution below, hope that helps...
please help!
Find the measures of x and y. Explain your process
Using the fact that the sum of the interior angles of a triangle must be 180°, we will see that y = 70°, and x and y are vertical angles, so x = 70°.
How to find the measures of x and y?
First, remember that the sum of the interior angles of a triangle is always equal to 180°, then we can write a linear equation to find the value of y.
y° + 60° + 50° = 180°
We can solve that for y, we will get:
y° = 180° - 60° - 50°
y° = 180° - 110°
y° = 70°
Then the measure of angle y is 70 degrees.
Now, notice that angles x and y are vertical angles (have a common vertex but no common sides).
Vertical angles always have the same measure, then the measure of angle x is also 70°.
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PLEASE HELP ME I NEED AN EXPLINATION. IXL KEEPS ON DROPKICKING ME AND IM RUNNING OUT OF TIME
[tex]Answer: t=\boxed{5}\\.\ \ \ \ \ \ \ \ \ \ \ \ u=\boxed{9}[/tex]
Step-by-step explanation:
If ΔGHI=ΔFDE ⇒ we get a system of equations:
[tex]\displaystyle\\\left \{ {{5t+u+12=4u+2t\atop {u-2t+50=13u-9t-23}} \right. \\\\\\\\\left \{ {{3t-3u=-12\ (1)} \atop {7t-12u=-73\ (2)}} \right. \\[/tex]
Divide both parts of the equation (1) by 3:
[tex]\displaystyle\\\left \{ {{t-u=-4} \atop {7t-12u=-73}} \right. \\\\\\\left \{ {{t=u-4} \atop -{7(u-4)-12u=-73}} \right. \\\\\\\left \{ {{t=u-4} \atop {7u+28-12u=-73}} \right. \\\\\\\left \{ {{t=u-4} \atop {-5u=-45\ (3)}} \right.[/tex]
Divide both parts of the equation (3) by (-5):
[tex]\displaystyle\\\left \{ {{t=5} \atop {u=9}} \right.[/tex]
What is the coefficient of X²Y in the product 7x² 5y X² 3y?
So, on solving the provided question, we can say that coefficient of X²Y in the product 7x² +5y +X²- 3y is 7
What is the coefficient?A coefficient in mathematics is a polynomial, a series, or the multiplicative coefficient of a particular term in an expression. Typically numeric, however any expression is permitted. The term "parameter" can also refer to the coefficients themselves if they are variables. A number times a variable equals a coefficient. Coefficient examples include: The coefficient is 14 in phrase 14c 14c 14c. The coefficient is 1 for word g. multiplies the variable by this amount. example Given that "z" is a variable and that 6z is the definition of the term, the coefficient is 6. One is the coefficient of the square of x.
here,
coefficient of X²Y in the product 7x² +5y +X²- 3y is 7
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A person decides to buy a new home, which is selling for $275,000. The bank that is lending the money requires a 10% down payment. How much is required to be paid down on the home?
$27,500
$5,500
$11,000
$2,750
The graph of y = 4x? - 4x - 1 is shown.
Use the graph to find estimates for
the solutions of
i) 4x2 - 4x - 1 = 0
1%C
ii) 4x2 - 4x - 1 = 2
Then the two solutions are: x = (4 + 5.66) / 8 = 11.2075 and x = (4 - 5.66) / 8 = -0.2075
What is meant by Bhaskara's equation?The sine approximation formula of Bhaskara I is a rational equation in one variable for computing the approximations of the trigonometric sines found by Bhaskara I (c. 600–c. 680), an Indian mathematician of the seventh century.
Indian astronomer and mathematician Bhaskara II lived in the 12th century. He created a number of the same foundations and findings that are entirely attributable to Europeans and are still very helpful in modern science and forecasts, such as a basic form of calculus.
Here we have the equation:
y = 4 × x² - 4 × x - 1
And the graph should be available (you can see it below this answer)
Now, we're seeking answers to:
4 × x²- 4 × x - 1 = 0
The two x values at which the graph of our function intersects the y = 0 line, or the x-axis, will be these solutions.
The next step is to identify the two x values where our graph crosses the x-axis.
We can estimate the solutions in the graph as follows:
x = -0.2
x = 1.2
The Bhaskara's equation can be used to determine the precise solutions, and we will discover that the solutions are provided by:
[tex]$x=\frac{-(-4)+-\sqrt{(-4)^2-4 * 4 *(-1)}}{2 * 4}=\frac{4+-\sqrt{32}}{8}=\frac{4+-5.66}{8}[/tex]
Then the two solutions are:
x = (4 + 5.66) / 8 = 11.2075
x = (4 - 5.66) / 8 = -0.2075
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Carter walked for a while at three miles per hour, and then continued his journey on a bus travelling at 15 miles per hour. his time on the bus was twice as long as his time walking. how long did he ride on the bus if the total distance he covered was 66 miles? let t equal the time he walked (hours).
Answer: He rode on the bus for 3 hours
Step-by-step explanation:
1. We add 15 miles and 3 miles to get 18 miles.
2. Then 66/18 is 3.6666
3. Convert to whole number
Then 15x3 is 45
66-45 is 21
21/3=7
so he walked for 7 hours and rode the bus for 3 hours
A game includes spinning the spinner with 6 equal sections and then rolling a number
cube with numbers 1-6.
What is the probability of spinning yellow and having the number cube show an odd
number?
The probability of spinning yellow and having the number cube show an odd number = 1/12.
What is probability ?
probability can be defined as the ratio of number of favourable outcomes and total number of outcomes .
Given,
A game includes spinning the spinner with 6 equal sections
Then rolling a number cube with numbers 1-6.
Let the probability of spinning a yellow be x .
and the probability of having the number cube showing an odd number be y .
so,
The probability of spinning yellow and having the number cube show an odd number = x * y .
x = 1/6 .
y = 3/6
y = 1/2
So,
x*y = 1/6 * 1/2
x*y = 1/12
Hence, The probability of spinning yellow and having the number cube show an odd number = 1/12.
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What is the pixel size?
Pixel size refers to the physical dimensions of an individual pixel in a digital image. It is typically measured in micrometers (µm) or nanometers (nm).
The pixel size determines the resolution of an image, as a larger pixel size will result in a lower resolution image, and vice versa.
In digital cameras, the pixel size is directly related to the sensor size. A larger sensor will typically have larger pixels, which can result in better low-light performance and less noise in the final image.
However, larger pixels also mean that the sensor will have fewer pixels overall, which can result in a lower resolution image.
In conclusion, Pixel size is one of the factors that affect the resolution of the image. A larger pixel size will result in a lower resolution image but it is beneficial for low-light performance.
It is important to consider the pixel size when choosing a camera or device with a built-in camera. It is also important to consider the sensor size, as a larger sensor typically results in larger pixels.
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p = 9.7 inches, mm∠Q=93° and mm∠O=82°. Find the length of q, to the nearest 10th of an inch.
Answer:
its 9.7 bc if you insert P into V Is mutiply so it burst inside the mathmatic equation u get 9,7
Step-by-step explanation:
A. Complete the table to how the length of the field for each given width. Width (feet) Length (feet) 0 50 100 150 200 250 300
b. Define the function (w) to repreent the length of the field a
The length available will be (300-W) feet, where W represents the breadth (width) of the rectangle.
Let L, A, and W represent the length, area, and width of the rectangular field respectively.
A quadrilateral with parallel sides equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason.
The area a two-dimensional form occupies in a plane is known as its area. It has a square unit of measurement. As a result, the rectangle's area is the space enclosed by its exterior lines. It is the same as the length times the width calculation.
Rectangles can also be referred to as parallelograms since their opposite sides are equal and parallel.
Based on the data given we have,
2L + 2W = 60
=>2L=60-2W
=>L=(60-2W)/2
=>L=2(30-W)/2
∴ L=(30-W) feet
Thus, the length available will be (300-W) feet.
Therefore, Thus, the length available will be (300-W) feet.
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Nathan buys 9 items that cost b dollars each. She gives the cashier $100 dollars. Write
an expression for the change she should receive.
Answer:
100-9b
Step-by-step explanation:
equation: 100-9*b
simplified version: 100-9b
What is 2 with an exponent of 4?