Therefore, we will need volume approximately 694.4 cubic feet of sand to fill the pit to a depth of 30 inches.
Describe volume.The volume of a three-dimensional item, which is measured in cubic units, describes how much room it occupies. Two instances of cubic units are cm3 and in3. To the contrary hand, a measurement of a thing's mass indicates how much material it includes. Typically, the weight of an item is measured in mass units the same as pounds or kilograms.
Here,
a.
Length: 30 feet 2 inches
Width: 9 feet 2 inches
Height: 30 inches (since the sand needs to be 30 inches deep)
To calculate the amount of wood required, we need to find the perimeter and area of the base of the frame.
Perimeter = 2(Length + Width) = 2(30 ft 2 in + 9 ft 2 in) = 2(39 ft 4 in) = 78 ft 8 in
Area of the base = Length × Width = (30 ft 2 in) × (9 ft 2 in) = 275 ft²
The amount of wood needed to surround the pit can then be calculated by finding the total surface area of the wooden frame.
Total surface area = 2(L × H) + 2(W × H) + Area of the base
= 2(30 ft 2 in × 30 in) + 2(9 ft 2 in × 30 in) + 275 ft²
≈ 240.5 square feet
Therefore, we will need approximately 240.5 square feet of wood to surround the pit.
b.
Length: 30 ft 2 in = (30 × 12) + 2 = 362 inches
Width: 9 ft 2 in = (9 × 12) + 2 = 110 inches
Depth: 30 inches
The volume of sand needed to fill the pit can be calculated using the formula:
Volume = Length × Width × Depth
Substituting the values, we get:
Volume = 362 in × 110 in × 30 in
= 1,198,800 cubic inches
To convert cubic inches to cubic feet, we divide by 12^3 (since there are 12 inches in a foot, and we need to cube this conversion factor):
Volume = 1,198,800 in³ ÷ (12³ in³/ft³)
= 694.4 ft³ (rounded to one decimal place)
Therefore, we will need approximately 694.4 cubic feet of sand to fill the pit to a depth of 30 inches.
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igure the amount of concrete (in cubic yards) required to pour a floor slab of the following dimensions: 18' by 24' by 4".
The amount of concrete required to pour a floor slab of the following dimensions: 18′ × 24′ × 4′′ is 5.34 cu.yard.
What is a Cuboid ?A cuboid is a three dimensional shape , with 6 faces , each face is a rectangle.
The concrete can be considered as in the shape of a cuboid.
Length = 18
Breadth = 24'
Height = 4"
Volume of Cuboid = Length * Breadth * Height
Volume of the cuboid = 18 * 24 * 4 *12*12 *(0.0278)³
=5.34 cu.yard.
Therefore the amount of concrete required to pour a floor slab of the following dimensions: 18′ × 24′ × 4′′ is 5.34 cu.yard.
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Which expression calculates the time in hours a person takes to walk 35 miles at a speed of 5 miles/hour
35 miles
5 miles
(Hint: 5x =35)
1/1 Pt
7
hours
1 hour
circle which one we are using
or
D Time=
35 miles
S
5 miles/ hour
miles or hours???
An expression that calculates the time in hours a person takes to walk 35 miles at a speed of 5 miles/hour is: T = 35/5 = 7 hours.
What is speed?In Mathematics, speed is the distance covered by a physical object per unit of time. This ultimately implies that, speed can be measured by using the following unit of measurement;
Meter per seconds (m/s).Miles per hour (mph).Kilometers per hour (kph).How to calculate the speed?Mathematically, the speed of any a physical object can be calculated by using this formula;
Speed = distance/time
Making time the subject of formula, we have:
Time = distance/speed
Time = 35/5
Time = 7 hours.
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Set up, but do not evaluate, the integral that expresses the surface area obtained by revolving the curvey2=x2−x5around thex-axis fory⩾0and0⩽χ⩽1. Simplify as much as possible.π∫01x25x6−24x3+8dx
The surface area ranges from 0 to 1, and is equal to the integral of the circumference of a circle with a radius of x2x5 times.
An integral can be used to define the surface area gained by rotating the curve y2=x2x5 around the x-axis for y0 and 0x1. This integral represents the circumference, from 0 to 1, of a circle with radius x2x5 multiplied by. This can be expressed as x25x624x3+8 times the integral of from 0 to 1 for. When the given curve is rotated about the x-axis over the specified range of y and x, this integral will evaluate to the surface area achieved. This integral can be expressed in the simplest possible form as 01 x25x624x3+8 dx.
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2.9. Consider the following nonstochastic models (i.e., models without the stochastic error term). Are they linear regression models? If not, is it possible, by suitable algebraic manipulations, to convert them into linear models? a Y₁ = A. Y₁ = Bi 1 + P₂X₂ X₂ B₁ + A₂X₁ 1 c. Y₁ = 1 + exp(-B₁ - B2X₁)
The first and second models are linear regression models as it follow the general form, while the third model is not a linear regression model
What are linear regression modelLinear Regression is a statistical method used to model the relationship between a dependent variable (also known as the response or output variable) and one or more independent variables (also known as predictor or input variables). It assumes that there is a linear relationship between the independent variables and the dependent variable.
A linear regression model takes the form:
Y = β0 + β1X1 + β2X2 + ... + βnXn + ε
Where Y is the dependent variable, X1, X2, ..., Xn are the independent variables, β0, β1, β2, ..., βn are the coefficients that represent the slope of the line for each independent variable, and ε is the error term. The goal of linear regression is to estimate the coefficients β0, β1, β2, ..., βn so that the model can be used to make predictions about the dependent variable.
a. Y₁ = A + B₁X₁ + B₂X₂
This is a linear regression model, as the relationship between Y₁ and X₁, X₂ is linear, with the coefficients A, B₁, and B₂.
b. Y₁ = B₁X₁ + A
This is also a linear regression model, as the relationship between Y₁ and X₁ is linear with the coefficients A and B₁.
c. Y₁ = 1 + exp(-B₁ - B2X₁)
This is not a linear regression model, as the relationship between Y₁ and X₁ is not linear. It is not possible to convert it into a linear regression model by suitable algebraic manipulations.
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Give a precise and thorough example of a function with a minimum at a value where its derivative is undefined.
The required example of a function with a minimum at a value where its derivative is undefined is f(x) = |x|.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
A function that has a minimum at a point where its derivative is undefined is the absolute value function. The absolute value function is defined as:
f(x) = |x|
At x = 0, the absolute value function has a minimum value of 0. However, the derivative of the absolute value function is undefined at x = 0, because the function is not differentiable there.
At x < 0, the absolute value function is decreasing and therefore has a negative derivative. At x > 0, the absolute value function is increasing and therefore has a positive derivative. At x = 0, the behavior of the function changes abruptly from decreasing to increasing, which makes the derivative undefined. Despite this, the absolute value function still has a minimum value of 0 at x = 0.
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Given the proportion a/b = 8/15, what ratio completes the equivalent proportion a/b
The ratio completes the equivalent proportion a/b is 16/30.
What is a proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".
The given proportion is a/b = 8/15.
To get the equivalent proportion multiply both the numerator and denominator by 2 we get
16/30
Multiply both the numerator and denominator by 3 we get
24/45
Therefore, the ratio completes the equivalent proportion a/b is 16/30.
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For the period 1995-2002, the total personal expenditures (in billions of dollars) in the United States for food, f(x), and for housing, h(x), can be described by the equations shown below, where x is the number of years past 1995.†
f(x) = 40.74x + 742.65 and h(x) = 47.93x + 725
Find the year in which these expenditures were equal and the amount spent on each. (Round the year up. Give the amount correct to the nearest whole billion.)
year______
amount ______
Years: 2.455 years
Amounts: $843 billions
This can be solved by using equation solving method.
What is personal expenditures?An expense classified as personal is one that is not related to a trade or enterprise, a passive activity, or an investment. Personal consumption spending is often divided into two categories: goods and services. Groceries, automobiles, and fuel are a few examples of products. Rent, medical treatment, and insurance are a few examples of services.
f(x) = 40.74x + 742.65
h(x) = 47.93x +725
For f(x) = h(x),
40.74x + 742.65 = 47.93x +725
47.93x - 40.74x = 742.65 - 725
x (47.93-40.74) = 17.65
x = 17.65 /7.19 = 2.455 years.
2.455 years after 1995, that is in 1998, these expenditures would be equal to each other.
The amount spent on each would be :-
40.74(2.455) + 742.65 = $842.667
= $843 billions.
Years: 2.455 years
Amounts: $843 billions
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Which team has the best record? Explain how you know.
The team that has the best record when compared to the other teams would be = team High - 5s which has the least number of losses.
How to calculate the team that has the best record?The team with the best score can be calculated by finding the difference between the games and the losses.
The difference between games and losses of team Jule's Rules = 36-12 = 24.
The difference between games and losses of Pink Sox= 68-17 = 51
The difference between games and losses Go-Girls =
52-13 = 51
The difference between games and losses High-5s = 72-8 = 64
Therefore the team with the best record = team High - 5s which has the least number of losses.
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It’s multi step word problems divide and multiply
The number of adults who attended the concert is 824.
Linear Equation:
The equation is said to be linear if the greatest power of a variable always equals 1. It is also known as a one-degree equation. The usual form of a linear equation with one variable is Ax + B = 0. In this case, the variables x and A are variables while the variable B is a constant.
It is given in the question that the number of adults are twice the number of children.
then,
Suppose there were x children present at the concert.
Then number of adults will be 2x.
According to the given question,
x + 2x = 1236
3x = 1236
dividing both sides by 3, we get
x= 412
therefore, number of children who attended the concert is 412.
Then the number of adults will be,
2x = 2 x 412 = 824
therefore, the number of adults who attended the concert is 824.
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The coffee variety Arabica yields about 750kg of coffee beans per hectare while Robusta yields about 1200kg/hectare. Suppose that a plantation has hectares of Arabica and r hectares of Robusta. On August 14th, 2003, the world market price of coffee was $1.42/kg for Arabica and $0.73 kg for Robusta.
Please show your work
Write an equation relating A and R if the plantation produces coffee worth $1,200,000.
Step-by-step explanation:
a)
Arabica coffee = 750a
Robusta coffee = 1200r
The total amount coffee beans 750a + 1200r = 1000000 kg
b)
The total amount of market price
1.42*750a +0.73*1200r 1000000
1065a + 876r = 1000000 dollars
step by step reading
The coffee variety Arabica yields about 750 kg of coffee beans per hectare, while
Robusta yields about 1200 kg per hectare. Suppose that a plantation has a
hectares of Arabica and r hectares of Robusta.
a. Write an equation relating a and r if the plantation yields 1,200,000 kg of coffee.
b. On August 14, 2003, the world market price of coffee was $1.42 per kg of Arabica
and $0.73 per kg of Robusta. Write an equation relating a and r if the plantation
produces coffee worth $1,200.000. what does that answer that means it would be
ANSWER
a
Arabica coffee = 750a
Robusta coffee = 1200r
The total amount coffee beans
750a + 1200r = 1.200,000 kg
b)
The total amount of market price
1.42*750a + 0.73*1200r = 1,200.000 ⇒
1065a + 876r = 1,200.000 dollar!!!!!!
Name:
Discrete Data:
Continuous Data:
Create a Histogram
Here are the times for swimming 100m from
several people:
113 124 108 89
103 114 125 136
Lowest Value:
Intervals:
93 92 102 98 88 104
79 123 90 93 87 99
Highest Value: 136
Interval Tally
1
Nuimperof,
people i
Skewedtsy
NO Outliers
Examples
Calculate the Average to check your answer.
Examples
Date,
17990 101 1 13 241130
Swinnming time
medo-110
136-8749
What do you think the average is? Draw a vertical line on the graph and label it "My Guess"
How does drawing the histogram help at guessing the average
Drawing the histogram helps in guessing the average by allowing us to visually see the distribution of the data.
What do you mean by histogram?It is used to show the frequency of occurrence of different values within a set of data. In a histogram, the data is divided into a set of intervals or "bins," and the height of each bar represents the number of data points that fall within that bin.
The x-axis of a histogram typically represents the range of values in the data, while the y-axis represents the frequency of occurrence of those values. The bars are positioned so that they touch each other, indicating that the data is continuous and that there are no gaps between the bins.
Discrete data refers to data that can only take certain values within a defined range, such as the number of candies sold. Continuous data refers to data that can take any value within a defined range, such as swimming time.
To create a histogram for the swimming times, we first need to determine the range of the data and choose an appropriate interval width. In this case, the lowest value is 87 and the highest value is 136, so the range is 87 to 136. A suitable interval width could be 5. This would give us 11 intervals, from 85 to 90, 90 to 95, and so on, up to 135 to 140.
Next, we would tally the number of swimming times that fall into each interval and plot this information as bars on the histogram. The height of each bar represents the frequency of the interval.
Drawing the histogram helps in guessing the average by allowing us to visually see the distribution of the data. Based on the shape of the histogram, we can make a guess as to where the average is likely to fall. If the histogram is symmetrical, the average is likely to be in the middle. If it is skewed, the average will be closer to the side with the longer bar. By drawing a vertical line labeled "My Guess" on the histogram, we can see how close our guess was to the actual average.
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can someone tell me how to find last three parts?
The population in the year 2000 is 1230 students.
The equation for the population, P, of the school t years after 2000 is P = 53t + 1389.
The population of the school in 2015 in 2025 students
How to find the population in the year 2000?The starting population in 2003 is 1389.
average population growth per year = 53
The population in the year 2000 will be:
number of year = 2000 - 2003 = -3 (3 years back)
population in the year 2000 = 1389 -3(53) = 1230
To find an equation for the population, P, of the school t years after 2000. We can write:
P = 53t + 1389
Using your equation, predict the population of the school in 2015:
t = 2015 - 2003 = 12
P = 53t + 1389
P = 53(12) + 1389
P = 2025 students
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20. What area of the figure below if one square is 1cm x 1cm? a. 6 cm ² b. 8cm ² c. 10 cm². d. 12cm ²
The area of figure above is a) 6cm²
Square Area FormulaIn addition to the circumference, a square shape also has an area, where the area of a square is calculated by squaring the length of its side.
Formula: Area of square= s²
The question above, the side of square is 1 cm.
so the area of one small square is 1×1= 1cm²
Because the shape is contain of 6 small square, therefore the total area is 6×1cm²=6cm²
Square propertiesA square has the following properties
Has 4 equal sides Every angle formed by a side is a right angle Each diagonal bisects the angle formed by the sides The intersection of the diagonals forms a right angleLearn more about square at
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Consider the following competing hypotheses: Hop=0, H₁0. The value of the test statistic is z = -3.38. If we choose a 5% significance level, then we
O reject the null hypothesis and conclude that the population mean is significantly different from zero
The required, we have strong evidence to suggest that the population means is not equal to zero.
What is the null hypothesis?The null hypothesis, denoted as H0, is a statistical hypothesis that assumes that there is no significant difference between a population parameter and a hypothesized value or between two or more population parameters.
Here,
If we choose a 5% significance level, this means that we are willing to reject the null hypothesis (Hop=0) if the probability of obtaining a test statistic as extreme as, or more extreme than, the observed value under the null hypothesis is less than 5%.
The observed value of the test statistic is z = -3.38. This means that the observed value is 3.38 standard deviations below the mean under the null hypothesis.
We can use a standard normal distribution table or calculator to find the probability of obtaining a z-score as extreme as -3.38 or less. The probability is approximately 0.0004, or 0.04%.
In other words, we have strong evidence to suggest that the population means is not equal to zero, and we can be 95% confident that the true population means falls within a certain range of values (based on the confidence interval).
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I’m not sure how to answer these questions can someone help
Step-by-step explanation:
14/16 = 7/8
3/12 = 1/4
16/28 = 4/7
A lot of 1000 components contains 300 that are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective, and let B be the event that the second component drawn is defective. Answer the following questions: a. Find P(A)= b. Find P(B|A)= c. Find P(A∩B)= d. Find P( Ac∩B)= e. Find P(B)=
The probability of A is 0.3, P(B|A) is 0.299, P(A∩B) is 0.3, P(Ac∩B) is 0.3 and P(B) is 0.3.
a. P(A) = The probability that the first component drawn is defective = Number of defective components/Total number of components
= 300/1000 = 0.3
b. P(B|A) = The probability that the second component drawn is defective given the first component is defective = Number of defective components remaining/Total number of components remaining
= (300-1)/(1000-1) = 0.299
c. P(A∩B) = The probability that both components are defective = Number of defective components/Total number of components
= 300/1000 = 0.3
d. P(Ac∩B) = The probability that the first component is not defective and the second component is defective = Number of defective components/Total number of components
= 300/1000 = 0.3
e. P(B) = The probability that the second component drawn is defective = Number of defective components/Total number of components
= 300/1000 = 0.3
The probability of A is 0.3, P(B|A) is 0.299, P(A∩B) is 0.3, P(Ac∩B) is 0.3 and P(B) is 0.3.
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Solve the following:
a)
4x3 2x + 7
Optional working+
b)
2x + 6 = 7x-
-
Optional wor
Cylinder B is the image of cylinder A after dilation by a scale factor of 4. If the surface area of cylinder A is 137 km, find the surface area of cylinder B, the image.
Answer:
Correct option is C)
Given s= 7m, h=9 m
Lateral surface area = Area of the curved surface =2πrh=2×
7
22
×7m×9m=396m
2
Total surface area = Area of curved surface + Area of two circular surfaces
=2πrh+2πr
2
=396m
2
+2×
7
22
×7m×7m=(396+308)m
2
=704m
2
The surface area of cylinder B is 548 square km.
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
The basic formula to find the scale factor of a figure is expressed as,
Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.
Given that, cylinder B is the image of cylinder A after dilation by a scale factor of 4.
The surface area of cylinder A is 137 km².
Then the surface area of cylinder B is 4×137
= 548 square km.
Therefore, the surface area of cylinder B is 548 square km.
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The length of a rectangle is 4 in longer than its width.
If the perimeter of the rectangle is 40 in, find its area.
Answer: 396
Step-by-step explanation:
length- x+4
width - x
perimeter = 40
40 = x+4+x
40-4=2x
36=2x
x=18
length - 18+4=22
width - 18
area = 22*18 = 396
The given diagram shows the steps for constructing a line parallel to line AB and passing through point P, but an error has occurred in the construction. What needs to be corrected in the diagram to fix the error?
The thing that needs to be corrected in the diagram to fix the error is that the third arc should be drawn centered at F.
How should the error be corrected?
Given:
Constructing a parallel line to line AB and passing through point P.
To find:
An error occurred in the construction.
The procedure is,
The first arc must be drawn centered at C.The second must be drawn centered at P.Finally, the third arc must be drawn centered at F.However, the third arc is drawn centered at D. This is wrong.
Therefore, the correct step is that the third arc must be centered at F.
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(GAME) You pay $1.00 to play a game that consists of rolling a colored die with three green sides, two red sides, and one blue side. A roll of a red loses. A roll of blue pays $6.00. A roll of green pays $2.00. What is the expected value of each game to the player? Round to the hundredths place.
The fair price to pay to play the game of rolling a colored die with three green sides, two red sides, and one blue side is; $2
How to Fair Price?
We are told that in the game of rolling the colored die;
- A roll of a red loses.
- A roll of blue pays 6.00.
- A roll of green pays 2.00.
Now, the best game to get the fairest price is to play; GGGRRB
Fair price = 2(3/6) + 6(1/6) + 0(2/6)
Fair price = $2
ATP singles rankings for tennis players rank Rafael Nadal as 2 and Roger Federer as 1. This is an example of an interval scale. True or false
The required ATP singles rankings for tennis players rank is false.
What are ATP signals?An interval scale is a type of measurement scale that has equal units of measurement and a zero point, meaning that differences between scale values can be meaningfully compared, but there is no meaningful interpretation of the zero point.
In tennis, ranking points are assigned based on a player's performance in a set number of tournaments over a rolling 52-week period, but the actual number of points assigned to a player is not an interval scale.
Thus, it is incorrect to say that the ATP singles rankings for tennis players are an example of an interval scale.
The given statement is false.
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PLEASE PLEASE HELP Solve and explain the method you chose to use (distributive property, FOIL, multiplying special cases): (c+3)^2
c² + 9 + 6c is the solution by distributive property .
What in mathematics is a distributive property?
This characteristic states that multiplying the total of two or more addends by a number will produce the same result as multiplying each addend separately by the number and then combining the products collectively.
When you multiply one value by another, you are using the distributive property of multiplication over addition. When multiplying 5 by the sum of 10 plus 3, for instance, add 3. We typically add the numbers first, then multiply the result by 5, since the terms are similar. However, in accordance with the property, you can first multiply each addend by 5.
= (c+3)^2
= c² + 9 + 2 * c * 3
= c² + 9 + 6c
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Translate the following verbal statement into an algebraic equation and then solve:
Use x for your variable.
The quotient of four more than a number and seven is ten.
the quotient of four (4) more than a number (x) and seven (7) is ten (10) equals (x +4)/7 = 10.
What is algebraic Expression?Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
Given The quotient of four is more than a number and seven is ten.
also given Use x for your variable.
In Mathematics, quotient literally means dividing a particular number by another number i.e the division of two (2) numbers.
Next, we would translate the word problem (sentence) into an algebraic expression as follows;
=> (x +4)/7 = 10
In conclusion, the algebraic expression for the quotient of four (4) more than a number (x) and seven (7) is ten (10) equals (x +4)/7 = 10.
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Eighth grade V.3 Area and perimeter: word problems 6MY
You have
A
Keith has a tent that is 3 feet wide by 8 feet long. Keith wants to buy a plastic tarp to go
under the tent. The tarps are sold for $1.00 per square foot. How much would it cost to buy a
tarp that is the same size as Keith's tent?
Submit
The total cost to purchase a tarp that is the same size as Keith's tent is given as follows:
$24.
How to obtain the area of a rectangle?The area of a rectangle is given by the multiplication of the width and the length of the triangle, as follows:
A = lw.
The dimensions for the tarp in this problem are given as follows:
Width of 3 feet.Length of 8 feet.Hence the area is given as follows:
A = 3 x 8 = 24 square feet.
As the cost is $1.00 per square feet and there are 24 square feet, the total cost is given as follows:
$24.00.
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Help me out I have been staring at this for hours what’s the answer
Triangle OGD and triangle ATC are similar triangles by the criteria of Side - Angle - Sides.
Similar triangles:The set of triangles with the same shape but different sizes are known as similar triangles. For example, all the equilateral triangles are similar triangles.
We can determine similar triangles by using the following conditions
Angle-Angle Similarity condition
Side-Angle-Side Similarity condition
Side-Side-Side Similarity condition
Here we have
Triangle OGD and triangle ATC
From the given triangles
=> Side OD = Side AC [ Equal sides ]
=> m ∠O = m ∠ A [ Equal angles ]
=> m ∠G = m ∠T [ Equal angles ]
Hence, By the criteria of Side - Angle - Side given triangles are similar triangles.
Therefore,
Triangle OGD and triangle ATC are similar triangles by the criteria of Side - Angle - Sides.
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Use a numerical solver and Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05. y' = (x − y)2, y(0) = 0.6; y(0.5) y(0.5) ≈ (h = 0.1) y(0.5) ≈ (h = 0.05)
Using Euler's method, y(0.5) ≈ 0.7052 when h = 0.1 and y(0.5) ≈ 0.6803 when h = 0.05.
What is Euler's method?
Ordinary differential equations (ODE) can be solved using the Euler's method, a first-order numerical technique, with a specified beginning value.
We are given an equation y' = f(x,y), a point ([tex]x_{o} ,y_{o}[/tex]) and a step value h.
We have
f(x,y) = (x − y)^2
Point is (0,0.6)
We need to find y(0.5).
So, using Euler's method with step h = 0.1, we get
⇒[tex]x_{1}[/tex] = [tex]x_{o}[/tex] + h
⇒[tex]x_{1}[/tex] = 0 + 0.1 = 0.1
⇒[tex]y_{1}[/tex] = [tex]y_{o}[/tex] + h * f([tex]x_{o} ,y_{o}[/tex])
⇒[tex]y_{1}[/tex] = 0.6 + 0.1 * (0 - 0.6)^2
⇒[tex]y_{1}[/tex] = 0.636
⇒[tex]x_{2}[/tex] = [tex]x_{1}[/tex] + h
⇒[tex]x_{2}[/tex] = 0.1 + 0.1 = 0.2
⇒[tex]y_{2}[/tex] = [tex]y_{1}[/tex] + h * f([tex]x_{1} ,y_{1}[/tex])
⇒[tex]y_{2}[/tex] = 0.636 + 0.1 * (0.1 - 0.636)^2
⇒[tex]y_{2}[/tex] = 0.6647296
⇒[tex]x_{3}[/tex] = [tex]x_{2}[/tex] + h
⇒[tex]x_{3}[/tex] = 0.2 + 0.1 = 0.3
⇒[tex]y_{3}[/tex] = [tex]y_{2}[/tex] + h * f([tex]x_{2} ,y_{2}[/tex])
⇒[tex]y_{3}[/tex] = 0.6647296 + 0.1 * (0.2 - 0.6647296)^2
⇒[tex]y_{3}[/tex] ≈ 0.6863
⇒[tex]x_{4}[/tex] = [tex]x_{3}[/tex] + h
⇒[tex]x_{4}[/tex] = 0.3 + 0.1 = 0.4
⇒[tex]y_{4}[/tex] = [tex]y_{3}[/tex] + h * f([tex]x_{3} ,y_{3}[/tex])
⇒[tex]y_{4}[/tex] ≈ 0.6863 + 0.1 * (0.3 - 0.6863)^2
⇒[tex]y_{4}[/tex] ≈ 0.7012
⇒[tex]x_{5}[/tex] = [tex]x_{4}[/tex] + h
⇒[tex]x_{5}[/tex] = 0.4 + 0.1 = 0.5
⇒[tex]y_{5}[/tex] = [tex]y_{4}[/tex] + h * f([tex]x_{4} ,y_{4}[/tex])
⇒[tex]y_{5}[/tex] ≈ 0.7012 + 0.1 * (0.5 - 0.7012)^2
⇒[tex]y_{5}[/tex] ≈ 0.7052
So, y(0.5) ≈ 0.7052
Similarly, with step h = 0.5, we will calculate the values till [tex]x_{10}[/tex] and [tex]y_{10}[/tex]
On doing this, we get y(0.5) ≈ 0.6803
Hence, using Euler's method, y(0.5) ≈ 0.7052 when h = 0.1 and y(0.5) ≈ 0.6803 when h = 0.05.
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This is a variation of problem 10 on page 141 of our textbook. You may want to solve this problem only after you solve the next one, which is the general version of this one. On the other hand, you also may want to solve this one first, and when solving the general one compare your evolving solution against your results in this problem.
A child is flying a kite. If the kite is 105 feet above the child's hand level and the wind is blowing it on a horizontal course at 6 feet per second, the child is paying out cord at _____________ feet per second when 165 feet of cord are out. Assume that the cord remains straight from hand to kite. (If you have ever flown a kite you know that this is an unrealistic assumption.)
For a solution of this problem (after the set closes) see the next problem.
The child is paying out the cord at a rate of 0 feet per second when 165 feet of cord are out.
What is Differential equation?A differential equation is an equation that contains one or more functions with its derivatives.
The distance between the kite and the child's hand level "d". Then, using the Pythagorean theorem, we can write:
d² + 105²= (165)²
d² = 165² - 105²
d = 129.1 ft
The length of the cord is increasing at a rate of 6 feet per second
Let us consider the length of the cord "L".
d² + L² = (165)²
Differentiating both sides with respect to time (t), we get:
2d(dd/dt) + 2L (dL/dt) = 0
We want to find (dL/dt) when L = 165 and d = 129.1.
(dL/dt) = -d × (dd/dt) / L
Substituting in the values we found for d and L, we get:
(dL/dt) = -(129.1 ft) × (0 ft/s) / (165 ft) = 0 ft/s
Therefore, the child is paying out the cord at a rate of 0 feet per second when 165 feet of cord are out.
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Which individual is eligible to use a 1040EZ form when filing a federal income
tax return?
A. Married person filing separately
B. Single person, with two dependents
C. Head of a household
D. Single person, with no dependents, who made $49,000 last year
Answer: A person who is eligible to use a 1040EZ form when filing a federal income tax return must meet certain criteria:
Must have taxable income of less than $100,000
Must not claim any dependents
Must only have wages, salaries, tips, taxable scholarship or fellowship grants, unemployment compensation, or Alaska Permanent Fund dividends, and your taxable interest is less than $1,500
Given these criteria, the correct answer is:
D. Single person, with no dependents, who made $49,000 last year.
Step-by-step explanation:
EASY POINTS!
Two runners are training for their next competitions. Each runner is able to run a certain
distance in proportion to the time. The table on the left displays the distance Runner A
can run in relation to the time. Meanwhile, the graph on the right displays the distance
Runner B can run in relation to time.
What are the unit rates for the two runners? Which runner can run faster?
Answer:
12 / 1 and runner B
Step-by-step explanation:
at 13 seconds runner a had only run 156 ft, however runner b had run 200 ft.