Answers
a = 5
b = 4
c= 0
Therefore, the equation for graph C is Y = a ^b + c
Y = 5 ^4 + 0
What is a graph?A graph is described as a diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.
Graphs are a popular tool for graphically illuminating data relationships.
A graph serves the purpose of presenting data that are either too numerous or complex to be properly described in the text while taking up less room.
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Related Questions
She wants to play cornhole, but she does not have enough pink bean bags
with her set. However, Sarah keeps a box of spare bean bags in her garage. If
the box contains one yellow, four blue, three red and two pink bean bags,
what is the probability to the nearest tenth of a percent that she will select
the two pink bean bags from the box on her first two attempts?
Answers
The probability that she will select the two pink bean bags from the box on her first two attempts is approximately 2.2%.
To calculate the probability that she will select the two pink bean bags from the box on her first two attempts, we need to;
1. Determine the total number of bean bags in the box. There is one yellow, four blue, three red, and two pink bean bags, which makes a total of 1 + 4 + 3 + 2 = 10 bean bags.
2. Calculate the probability of selecting a pink bean bag on the first attempt. There are two pink bean bags out of 10, so the probability is 2/10 or 1/5.
3. After selecting one pink bean bag, there are now nine bean bags left in the box. Calculate the probability of selecting the second pink bean bag on the second attempt. Since there is only one pink bean bag left, the probability is 1/9.
4. To find the overall probability of selecting two pink bean bags in the first two attempts, multiply the probabilities from steps 2 and 3. So, the probability is (1/5) * (1/9) = 1/45.
5. Convert the fraction to a percentage by dividing the numerator by the denominator and multiplying by 100. (1/45) * 100 = 2.22% (rounded to the nearest tenth of a percent).
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Please help im timed and im stuck
why were the testimonies of nazi officials at the nuremberg trials important?
their testimonies helped clear many nazis of their crimes.
the nazis denied that the events of the holocaust had occurred.
the confessions gave detailed accounts of the nazis’ crimes.
nazi officers got lighter sentences because they confessed.
Answers
The testimonies of Nazi officials at the Nuremberg Trials were incredibly important because they provided valuable insight into the atrocities committed by the Nazi regime.
Their testimonies helped to dispel any claims of denial that the events of the Holocaust had occurred. The confessions given by the Nazi officials gave detailed accounts of the crimes committed by the regime, and helped to hold those responsible accountable for their actions. It is important to note that while some Nazis did receive lighter sentences because of their confessions, the vast majority of those involved were held fully responsible for their crimes. Overall, the testimonies of Nazi officials played a crucial role in bringing justice to the victims of the Holocaust and shedding light on the horrific actions of the Nazi regime.
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You have a machine which can paint 20 bikes per hour. you purchase two additional, identical machines. how many bikes can you now paint per hour
Answers
The total number of bikes that can be painted in an hour would be 60 bikes.
With three identical machines,
the number of bikes machine can paint per hour = 20,
the number of machines bought again = 2,
so the total number of machines will be = 3,
when there are two same machines the productivity will be = 20 * 3 = 60 bikes.
This is because each machine works independently and can paint bikes simultaneously.
By adding two additional machines to the existing one,
the productivity of the painting process can be significantly increased. The new machines will not only increase the overall capacity but also reduce the turnaround time required for painting a large number of bikes.
By investing in additional machines,
the business can increase its output and generate more revenue,
which can be used to expand the operations further.
It's important to note that the investment in additional machines needs to be justified by the demand for painted bikes and the expected return on investment.
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Use the method of logarithmic differentiation to find the derivative of x^{sin x} with respect to x. (Your final answer should be in terms of x.) Hint: Let( y = x^{sin x})and your goal is to find dy/dx
Answers
The derivative of y = x^(sin x) with respect to x is:
dy/dx = x^(sin x) * (cos x * ln(x) + sin x * (1/x)).
To find the derivative of y = x^(sin x) with respect to x using logarithmic differentiation, follow these steps:
1. Take the natural logarithm of both sides of the equation:
ln(y) = ln(x^(sin x))
2. Use the properties of logarithms to simplify:
ln(y) = sin x * ln(x)
3. Differentiate both sides with respect to x, using the chain rule and product rule:
(1/y) * dy/dx = cos x * ln(x) + sin x * (1/x)
4. Multiply both sides by y to solve for dy/dx:
dy/dx = y * (cos x * ln(x) + sin x * (1/x))
5. Substitute the original expression for y (y = x^(sin x)) back into the equation:
dy/dx = x^(sin x) * (cos x * ln(x) + sin x * (1/x))
So the derivative of y = x^(sin x) with respect to x is:
dy/dx = x^(sin x) * (cos x * ln(x) + sin x * (1/x)).
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5-|p+6|=8
2 answers
NOT 19
Answers
5-|p+6|=8
Subtract 5 from both sides:
-|p+6|=3
Divide both sides by -1 (to isolate the absolute value term):
|p+6|=-3
Since absolute values cannot be negative, there is no solution to this equation.
A portion of an electrical circuit is displayed next. the switches operate independently of each other, and the probability that each relay closes when the switch is thrown is displayed by the switch. what is the probability that current will flow from s to t when the switch is thrown
Answers
If you provide me with a specific circuit diagram and the relevant details, I would be happy to help you determine the probability of current flowing from s to t when the switch is thrown.
What is the probability of current flowing from s to t when the switch is thrown?I apologize, but it seems that the circuit diagram you mentioned is not displayed here. Without the circuit diagram, it is not possible for me to provide a specific answer to your question.
However, in general, the probability of current flowing from s to t in an electrical circuit depends on several factors such as the voltage level, the resistance of the circuit components, and the state of the switches. If the switches are all closed, then the probability of current flowing from s to t will depend on the overall resistance of the circuit.
If you provide me with a specific circuit diagram and the relevant details, I would be happy to help you determine the probability of current flowing from s to t when the switch is thrown.
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what is the distinction between a positive and negative mean deviation in terms of meaning applied to the data values?
Answers
Positive mean deviation means that the data values are on average greater than the mean, while negative mean deviation means that the data values are on average lower than the mean. This provides insight into the distribution of the data and can help identify outliers or trends in the data.
Mean deviation is a measure of dispersion that indicates how much a set of data values varies from the mean value of the data set. A positive mean deviation indicates that the data values are larger than the mean value, while a negative mean deviation indicates that the data values are smaller than the mean value.
In other words, a positive mean deviation indicates that the data set tends to be higher than the average, while a negative mean deviation indicates that the data set tends to be lower than the average.
Therefore, the sign of the mean deviation reflects the direction of deviation of the data values from the mean value, whether above or below it, and it provides important information about the distribution of the data set.
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The scatter plot shows the number of miles per gallon (MPG) for trucks with different weights. Select all the associations shown by the scatter plot.
positive association
negative association
linear association
nonlinear association
no association
Answers
The associations rhat are shown by the graph are
negative associationlinear associationHow does a graph show negative association linear associationA graph depicting a negative linear association appears as points on the chart are concomitantly placed around a straight line that confidently descends from left to right. In simpler terms, there is a notable inverse correlation between the x and y variables, which can be best comprehended with the help of an illustration.
For instance, if one were to consider a dataset representing the age of an automobile (x) and its fuel efficiency in miles per gallon (y), a graph displaying a rigorous negative linear association implies that with an increase in the age of the car, its energy proficiency has an inclination to decrease.
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5.2 cm
4 cm
V = bh
V = ______ x 4
V=
3 cm
Area of base:_________x
cubic cm
11
sq. cm
Answers
Here is some information about 26 houses. A,b and c are all different numbers. Number of bedrooms:1,2,3,4,5. Number of houses:7,a,b,c,8. The median number of bedrooms is 3. 5 Work out a possible set of values for a,b and c
Answers
The possible set of values for a, b, and c could be: a=2, b=4, c=5.
Here is a possible set of values for a, b, and c,
- a = 2 (since there are 7 houses with 1-2 bedrooms and 8 houses in total, we know that there must be at least 1 more house with 1-2 bedrooms, which could be house a)
- b = 4 (since the median number of bedrooms is 3 and there are 7+1+1=9 houses total with either 1, 2, or 3 bedrooms, we know that the median house must have either 3 or 4 bedrooms. Since b must be different from a and c, we can assign it to 4)
- c = 5 (since there are only 3 houses left and we need to assign one to each remaining number of bedrooms, we can assign c to 5)
Therefore, a possible set of values for a, b, and c could be: a=2, b=4, c=5.
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For each set of data, describe the shape of the
distribution and determine which measures of
center and spread best represent the data.
15. 28, 13, 23, 34, 55, 38, 44, 65, 49, 33, 50, 59,
67, 45
Answers
The shape of the distribution in histogram is skewed left and mean=43.071429 and standard deviation= 15.886445 are used together to measure the center and spread of the data.
What is histogram?
A grouped frequency distribution with continuous classes is graphically represented by a histogram. It is an area diagram, and its size is proportional to the frequencies in the associated classes. Due to the base's coverage of the spaces between class boundaries, all of the rectangles in such representations are contiguous.
We can make a sideways histogram. (makes it easier if typing text, but if you are writing on paper then you don't have to make it sideways) Each row will represent a range of 10 (1st row is 10 to 19, 2nd row is 20 to 29, etc)
=> 13 23 28 33 34 38 44 45 49 50 55 59 65 67
The data looks like it is slightly skewed left (hump towards the right [down]). The mean and the standard deviation are used together to measure the center and spread of the data.
Mean = [tex]\frac{ 13+23+28+33+34+38+44+45+49+50+55+59+65+67}{14}=\frac{603}{14}[/tex] = 43.071429
Standard deviation = 15.886445
Hence the shape of the distribution in histogram is skewed left and mean=43.071429 and standard deviation= 15.886445 are used together to measure the center and spread of the data.
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there are 44 green balls, 65 blue balls, 14 yellow balls, and 2 red balls in a basket. a blind man goes to pick balls out of the basket. he does not know this, but all the blue balls and the red balls have a rough surface, and the green balls and yellow balls have a smooth surface. what is the lowest possible number of balls he needs to pick to ensure he has picked two balls of different colors?
Answers
The lowest possible number of balls blind man need to pick to ensure that he picked two different colors balls is equal to 48.
Number of green balls = 44
Number of blue balls = 65
Number of yellow balls = 14
Number of red balls = 2
To ensure the blind man picks two balls of different colors.
Maximum number of balls he can pick of a single color before he is guaranteed to have picked two of different colors.
All the blue and red balls have a rough surface.
All the green and yellow balls have a smooth surface.
Treat them as two distinct groups.
Let us consider the worst-case scenario,
where the blind man picks all the balls of one group before picking any ball of the other group.
Here, he could pick all 44 green balls or all 14 yellow balls before picking any blue or red ball.
Similarly, he could pick both red balls before picking any blue ball.
To ensure he has picked two balls of different colors, he needs to pick at least,
(44 green balls + 1 yellow ball) or 3 balls (2 red balls + 1 blue ball)
= 48 balls whichever is higher.
Therefore, the lowest possible number of balls he needs to pick to ensure he has picked two balls of different colors is 48.
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the Senators won 18 more games than they lost. they played 78 games. how many games did they win?
Answers
Answer:
let amount of games won and lost be x and y respectively
y+18=x
x+y=78
y+y+18=78
2y=78-18
2y=60
y=30
x=30+18
x=48
thus, games won is 48
Use linear approximation, i.e. the tangent line, to approximate (1/0.504) as follows: Find the equation of the tangent line to f(x)=1x at a "nice" point near 0.504. Then use this to approximate (1/0.504).
Answers
The equation of the tangent line to f(x) is y = -4x + 4
How to find the equation of the tangent line to f(x)?The equation of the tangent line to f(x) = 1/x at a point x = a is given by:
y - f(a) = f'(a) * (x - a)
where f'(x) is the derivative of f(x) with respect to x.
We can find a "nice" point near 0.504 by choosing a = 0.5, which is close to 0.504 and makes the calculation easy.
The derivative of f(x) = 1/x is given by:
[tex]f'(x) = -1/x^2[/tex]
At x = 0.5, we have:
f(0.5) = 1/0.5 = 2
[tex]f'(0.5) = -1/(0.5)^2 = -4[/tex]
Plugging these values into the equation of the tangent line, we get:
y - 2 = -4 * (x - 0.5)
Simplifying, we get:
y = -4x + 4
Now we can use this tangent line to approximate (1/0.504) as follows:
(1/0.504) ≈ y(0.504)
Plugging x = 0.504 into the equation of the tangent line, we get:
y(0.504) = -4(0.504) + 4 = 1.784
Therefore, (1/0.504) ≈ 1.784
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francisco had a rectangular piece of wrapping paper that was inches on two sides and 17 inches on the longer sides. monica has a similar piece of paper with two longer sides that each measure 34 inches. what is the measurement of the two shorter sides in monica's wrapping paper? a. inches b. inches c. inches d. inches
Answers
The measurement of the two shorter sides in Monica's wrapping paper is 17 inches.
How we can use proportions to solve this problem?We can use proportions to solve this problem. Since Francisco's piece of paper is similar to Monica's piece of paper, the ratios of the corresponding sides will be equal. Specifically, we have:
17 / x = 34 / y
where x is the length of one of Francisco's shorter sides, and y is the length of one of Monica's shorter sides.
To solve for y, we can cross-multiply and simplify:
17y = 34x
y = 2x
So the length of one of Monica's shorter sides is half the length of one of her longer sides, or:
y = 1/2 * 34 = 17
Therefore, the measurement of the two shorter sides in Monica's wrapping paper is 17 inches. Answer: a. inches.
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15
Find the first and second derivatives. y = - 5x4+1 dy dx 승 라 ||| dx2
Answers
The first derivative is dy/dx = [tex]-20x^3[/tex], and the second derivative is d^2y/dx^2 = -60x^2.
The function you provided is: y =[tex]-5x^4 + 1[/tex]
To find the first derivative (dy/dx), we'll use the power rule which states that if y = x^n, then dy/dx =[tex]n * x^(n-1)[/tex].
Applying this rule to each term, we get: dy/dx = [tex]d(-5x^4)/dx + d(1)/dx[/tex]dy/dx =[tex]-5(4x^(4-1)) + 0[/tex] (since the derivative of a constant is 0) dy/dx = [tex]-20x^3[/tex]
Now, to find the second derivative [tex](d^2y/dx^2)[/tex], we'll differentiate the first derivative again using the power rule: [tex]d^2y/dx^2 = d(-20x^3)/dx d^2y/dx^2 = -20(3x^(3-1)) d^2y/dx^2 = -60x^2[/tex]
So, the first derivative is dy/dx = [tex]-20x^3[/tex], and the second derivative is [tex]d^2y/dx^2 = -60x^2.[/tex]
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. Select two choices that are true about the function f(x)
A There is an asymptote at x = 0.
☐ B There is a zero at 23.
OC
There is a zero at 0.
D
There is an asymptote at y = 23.
23x+14
x
Answers
Answer:
A. There is an asymptote at x = 0.
D. There is an asymptote at y = 23.
F(x) and g(x) are polynomial functions.
determine whether each expression is always, sometimes, or never a polynomial.
f(x)+g(x)
and
f(x) / g(x)
Answers
F(x) and G(x) are polynomial functions in which the expression f(x) + g(x) is always a polynomial and f(x)/g(x) is sometimes a polynomial.
Let F(x) be a polynomial = 2x + 4
g(x) be a polynomial = 6x² + 12x
putting the value in the expression
f(x) + g(x) = 2x + 4 + 6x² + 12x
f(x) + g(x) = 6x² + 14x + 4
6x² + 14x + 4 is a polynomial
Now, putting the value in the equation
f(x)/g(x) = 2x + 4/6x² + 12x
Taking 3x common from 6x² + 12
We get 3x(3x+4)
f(x)/g(x) = 2x+4/3x(2x+4)
f(x)/g(x) = 1/3x
1/3x is not a polynomial
Hence, it sometimes a polynomial.
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Lokota wants to build a sandbox for his little brother. Determine the amount of sand he needs by finding the area of the sandbox. Use the drop-down menus to complete the statements.
First, write the
.
Next, use parentheses when you substitute
for b and
for h.
Now, simplify by
1
2
, 2. 4, and 3. 5.
The area of the sandbox is
m²
Answers
The area of the sandbox whose base is 3.5 meter and height is 2.4 meter is 4.2 m².
Given:
Base = 3.5 m
Height = 2.4 m
First, the area of the sandbox formula:
Area = 1/2 x base x height.
Next, substitute b = 3.5 meters and h = 2.4 meters.
Area = 1/2 * (3.5) * (2.4).
Now, simplify by multiplying 1/2, 2.4, and 3.5.
Area = 1/2 x 2.4 x 3.5
Area = 4.2 square meters.
Thus, The area of the sandbox is 4.2 m².
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The question attached here seems to be incomplete, the complete question is:
Lokota wants to build a sandbox for his little brother. Determine the amount of sand he needs by finding the area of the sandbox. Use the drop-down menus to complete the statements.
First, write the formula: A = 1/2 bh
Next, use parentheses when you substitute __ for b and __ for h.
Now, simplify by ___ 1/2, 2.4, and 3.5.
The area of the sandbox is ___ m²
Gabriella needs 120 meters of fence to surround a rectangular garden.
the length of the garden is three times its width, w.
how wide is the fence?
(please solve how the answer is formatted, i already looked at the other posts people made on this question and they did not help)
Answers
Answer is 15 meters
To solve this problem, we can use the formula for the perimeter of a rectangle, which is
P = 2l + 2w,
where P is the perimeter, l is the length, and w is the width.
We are given that Gabriella needs 120 meters of fence, which means that
P = 120.
We are also given that the length of the garden is three times its width, or
l = 3w.
Substituting these values into the formula, we get:
120 = 2(3w) + 2w
Simplifying this equation, we get:
120 = 8w
Dividing both sides by 8, we get:
w = 15
Therefore, the width of the garden is 15 meters.
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How Ex: A. Price of an item F is 280000L.L. After the discount the price is 235,000 1 item F 1x Calculate the percentage of discount d2=d1×3 ) if you buy 2 items of F 2 items of F the discount d₂=d₁ x 3 Calculate the price of F₁, F₂ 3) Adam had 1,000,000 L.L. How much he had after purchasing F1,F2
Answers
1) The discount percentage is 16.07%.
2) The discounted price of F₁, F₂ is $470,000
3) The amount that Adam had after purchasing F₁, F₂ is $530,000.
What is the discount percentage?The discount percentage is a product of the discount amount divided by the original cost, multiplied by 100.
Price of item F = $280,000
Discounted price = $235,000
Discount amount = $45,000 ($280,000 - $235,000)
Discount rate = 16.07% ($45,000/$280,000 x 100)
Discounted price of F₁, F₂ = $470,000 ($235,000 x 2)
The amount that Adam had before the purchase = $1,000,000
The amount he had after purchasing F₁, F₂ = $530,000 ($1,000,000 - $470,000).
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Arnold is looking at the building from 300 feet away at an angle of elevation of 22 grades when asked arnold says he’s 4.75 feet tall do you agree or desagree with arnold’s height explain your answer with matemátical support?
Answers
We can conclude that Arnold's height of 4.75 feet by using tangent function is not accurate based on the calculations.
To determine whether Arnold's height is accurate, we can use trigonometry and the given information about the angle of elevation and distance to the building.
Let's start by drawing a diagram to represent the situation. We have a right triangle with the opposite side being Arnold's height (h), the adjacent side being the distance to the building (300 ft), and the angle of elevation being 22 degrees.
Using the tangent function, we can write:
tan(22) = h / 300
Solving for h, we get:
h = 300 * tan(22)
Using a calculator, we find that h is approximately 122.8 feet.
Therefore, we can conclude that Arnold's height of 4.75 feet is not accurate based on the calculations. The height we calculated is over 25 times greater than Arnold's claimed height, which is not possible.
It is important to note that this assumes that Arnold's line of sight is parallel to the ground. If Arnold is on uneven ground, this could affect the calculations. Additionally, it is possible that Arnold may have misspoken about his height or the angle of elevation. However, based on the given information and calculations, we can confidently say that Arnold's claimed height is not accurate.
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State how many terms are in each algebraic expression:
(a) -112y2 ____________________ [1mark]
(b) 7x2 + 5y – 9xy + 3 __________________ [1mark]
Answers
(A) There is only one term in the expression:[tex]-112y^2.[/tex]
(B) There are four terms in the expression[tex]: 7x^2, 5y, -9xy, and 3.[/tex]
In A option, There is only one term within the algebraic expression [tex]-112y^2.[/tex]A term is a single numerical or variable expression this is separated from other expressions through addition or subtraction.
In B option, There are 4 terms within the algebraic expression[tex]7x^2 + 5y - 9xy +[/tex] 3. A time period is a single numerical or variable expression that is separated from other expressions through addition or subtraction.
In this situation, the primary term is[tex]7x^2[/tex], the second time period is 5y, the 0.33 time period is -9xy, and the fourth term is 3.
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The basketball started at a height of about 4 feet above the ground. While dribbling the ball traveled downward until it hit the ground, then it returned to its initial height. What is the distance and what is the displacement?
Answers
The distance traveled is 8ft and the displacement is 0ft.
What is the distance and what is the displacement?The distance traveled is equal to the total distance that the ball travels, in this case it starts 4ft above the ground, then goes to the ground, and then returns to the initial position which is 4ft above the ground, then the total distance is 4ft + 4ft = 8ft
The displacement is equal to the difference between the final position and the inital one, here we know that both are the same, thus, the displacement is 0ft.
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3. James has a box shaped as a rectangular prism. The container is 8 inches long, 4 inches wide, and 5 inches high. (a) Here is a model of the box. It is filled with unit cubes. Find the volume of the box using the unit cubes. Explain your answer. Answer: 160 cubic inches (b) Find the volume of the box using the formula. Answer: (c) Find the volume of the box using the formula. Answer: (d) How does using the volume formulas to find the volume of a rectangular prism compare to counting unit cubes? Compare your answers in parts (b) and (c) your answer in part (a) to answer the question. Answer:
Answers
The volume of the box is 160 cubic inches. Using the volume of a rectangular prism formula the volume of the box is 160 cubic inches. Using another formula base area times height, the area is the same.
The volume of James' rectangular prism box can be calculated using both unit cubes and a formula. Part (a) involves counting the unit cubes in the model and multiplying the number of cubes by their volume, which is 1 cubic inch. In this case, there are 160 unit cubes, so the volume of the box is 160 cubic inches.
Part (b) involves using the formula for volume of a rectangular prism, which is length times width times height. Plugging in the given dimensions, we get 8 x 4 x 5 = 160 cubic inches, which is the same as the answer in part (a) using unit cubes.
Part (c) involves using a different formula for volume, which is base area times height. In this case, the base of the rectangular prism is a rectangle with length 8 inches and width 4 inches, so the base area is 8 x 4 = 32 square inches. Multiplying by the height of 5 inches, we get 160 cubic inches, which is again the same as the answers in parts (a) and (b).
Using the volume formulas is much quicker and more efficient than counting unit cubes, especially for larger boxes. However, counting unit cubes can provide a more concrete visual representation of the volume and can be helpful for students who are just learning about volume. In this case, the answers obtained using the formulas were the same as the answer obtained by counting unit cubes, which reinforces the accuracy of the formulas.
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for an arc length s, area of sector a, and central angle of a circle of radius r, find the indicated quantity for the given value.
r= 4.27 m, 0 = 2.16, s = ?
s=
(do not round until the final answer. then round to two decimal places as needed.)
Answers
The arc length (s) for a circle with radius 4.27 meters and central angle 2.16 radians is approximately 9.22 meters.
To find the arc length (s) for a circle with radius (r) and central angle (θ), you can use the formula:
s = r * θ
In this case, the radius (r) is 4.27 meters, and the central angle (θ) is 2.16 radians. Plug these values into the formula:
s = 4.27 * 2.16
Now, multiply the values:
s ≈ 9.2232
Round the answer to two decimal places:
s ≈ 9.22 meters
So, the arc length (s) for a circle with radius 4.27 meters and central angle 2.16 radians is approximately 9.22 meters.
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Un árbol ha sido roto por el viento de tal manera que sus dos partes forman un triángulo rectángulo. la parte superior tiene una longitud de 10 m, y la distancia medida sobre el piso hasta la cúspide del árbol es de 6 m. hallar la altura que tenía el árbol.
Answers
Se puede utilizar el teorema de Pitágoras para resolver este problema. Si se considera que la altura del árbol es la hipotenusa del triángulo rectángulo,
entonces la parte superior de la parte rota del árbol es uno de los catetos, y la distancia medida sobre el piso hasta la cúspide del árbol es el otro cateto.
Por lo tanto, se tiene que:
[tex]altura^2 = cateto1^2 + cateto2^2[/tex]
Reemplazando los valores conocidos, se tiene:
[tex]altura^2 = 10^2 + 6^2[/tex]
[tex]altura^2 = 136[/tex]
Tomando la raíz altura^2 = 136, se obtiene:
[tex]altura = √136[/tex]
altura ≈ 11.66 m
Por lo tanto, la altura que tenía el árbol antes de ser roto por el viento es de aproximadamente 11.66 metros.
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Shelby multiplies 7,358.9 by a power of 10 and gets the product
73.589. select all possible factors.
(a) 1/100 "fraction"
(b) 1/10 "fraction"
(c) 1
(d) 0.1
(e) 0.01
(f) 0.001
Answers
(a) 1/100 (or 0.01)
(e) 0.01
This factor represents dividing the number by 100.
When Shelby multiplies 7,358.9 by a power of 10 and gets the product 73.589, we can determine the factor by comparing the two numbers.
7,358.9 → 73.589
We can see that the decimal point has moved two places to the left. Therefore, the factor is the one that will shift the decimal point two places to the left. Among the given options, the factor that does this is:
(a) 1/100 (or 0.01)
(e) 0.01
This factor represents dividing the number by 100. The other options (b, c, d, and f) do not represent the correct division by powers of 10 in this case.
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Find the equation of the tangent line of y=xlog(x) at the point(1,0).
Answers
The equation of the tangent line is y = x - 1.
To find the equation of the tangent line of y=xlog(x) at the point (1,0), we will first need to find the derivative of the function y=xlog(x) with respect to x.
Step 1: Find the derivative of y=xlog(x) with respect to x.
Using the product rule, (uv)' = u'v + uv', where u=x and v=log(x).
u' = derivative of x with respect to x = 1
v' = derivative of log(x) with respect to x = 1/x
Now, apply the product rule:
y' = u'v + uv' = 1*log(x) + x*(1/x) = log(x) + 1
Step 2: Find the slope of the tangent line at the point (1,0).
Evaluate y' at x=1:
y'(1) = log(1) + 1 = 0 + 1 = 1
The slope of the tangent line at (1,0) is 1.
Step 3: Find the equation of the tangent line.
We will use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) is the point (1,0) and m is the slope (1).
y - 0 = 1(x - 1)
y = x - 1
The equation of the tangent line of y=xlog(x) at the point (1,0) is y = x - 1.
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At the start of an observation, there are 7286.9 grams of a radioactive element present. The number of years t that must pass before N grams remain is given by the natural logarithm equation
t = 7,286.9 - 1,252 In(IV).
, dit
Find dt/dn When N = 15. Round to 2 decimal places, if necessary.
Answers
The value of dt/dN when N = 15 is -0.00509.
We are given the equation t = 7,286.9 - 1,252 ln(N/IV) which relates the number of years t that must pass before N grams of a radioactive element remain. We want to find the rate of change of t with respect to N, i.e., dt/dN when N = 15.
We can start by taking the derivative of both sides of the equation with respect to N:
dt/dN = -1252 / (N*ln(2))
Now we can substitute N = 15 into this equation to get:
dt/dN = -1252 / (15*ln(2))
Evaluating this expression, we get dt/dN ≈ -0.00509 (rounded to 2 decimal places). Therefore, the rate of change of t with respect to N when N = 15 is approximately -0.00509 years per gram.
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