The Fahrenheit is 51.8
What is Celsius and Fahrenheit?Celsius also called centigrade, scale based on 0° for the freezing point of water and 100° for the boiling point of water. Invented in 1742 by the Swedish astronomer Anders Celsuius, it is sometimes called the centigrde scale because of the 100° interval between the defined points.
Fahrenheit temperature scale based on 32° for the freezing point of water and 212° for the boiling point of water, the interval between the two being divided into 180 equal parts. The 18th-century German physicist Daniel Gabreil Fahrenheit originally took as the zero of his scale the temperature of an equal ice - salt mixture and selected the values of 30° and 90° for the freezing point of water and normal body temperature, respectively: these later were revised to 32° and 96°, but the final scale required an adjustment to 98.6° for the later value.
Conversion formula for °C to °F
°F = (9/5 × °C) + 32
Given:
Convert 11 °C to °F?
°F(11×1.8) + 32
= 19.8 + 32
= 51.8°F
Therefore 11 celsius (°c) is equal to 51.8 Fahrenheit (°F)
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Solve the inequality 4+p<11
Answer:
p<11-4
p<7
Step-by-step explanation:
we have 4+p<11 where we send 4 in another side and we get p<11-4 =p<7
How do you find the scalar and vector projection?
The scalar and vector projection of a vector onto another vector is found using dot product.
The scalar projection of a vector A onto a non-zero vector B is given by:
scalar projection = (A . B) / ||B||
where (A . B) is the dot product of vectors A and B and ||B|| is the magnitude of vector B.
The vector projection of A onto B is given by:
vector projection = (scalar projection) * (unit vector in the direction of B)
The unit vector in the direction of B is given by B/||B||. A unit vector has a magnitude of 1.
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Find the centroid of the triangle whose vertices are A(2, 6), B(4, 9), and C(6,15).
As a result, the triangle's centroid at vertices A(2, 6), B(4, 9), and C(6, 15) is (4, 10).
Given the vertices of a triangle, how do you get its centroid? The center of the thing is represented by the centroid.The centroid of a triangle is the location where the triangle's three medians cross.The junction of all three medians is another definition of it.A line connecting a side's midway to the triangle's opposite vertex is called the median.C = [(y1 + y2 + y3)/ 3, (x1 + x2 + x3)/ 3]. The triangle's centroid is indicated with the letter C.The x-coordinates of a triangle's three vertices are x1, x2, and x3.The y-coordinates for a triangle's vertices are y1, y2, and y3. As a result, the triangle's centroid at vertices A(2, 6), B(4, 9), and C(6, 15) is (4, 10).To learn more about triangle's centroid refer
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If the scores on an intelligence test form a normal curve with a standard deviation of 15,the mean, median, and mode are 100.68 percent of scores are between 85 and 115.60 percent of test-takers earned at least a 100.the first and second choices only are true.the first three choices are true.
The mean, median, and mode are all equal to 100, and 68% of the scores are between 85 and 115. The third choice is also true, as 60% of test-takers earned at least a 100.
The normal curve is a symmetrical bell-shaped distribution with the mean, median, and mode all equal to 100. If we take 15 as the standard deviation, then 68% of the scores will lie between 85 (100-15) and 115 (100+15). We can calculate this using the z-score formula: z=(x-μ)/σ, where x is the score, μ is the mean, and σ is the standard deviation.
In this case, the z-score for the lower limit (85) is (85-100)/15=-1. The z-score for the upper limit (115) is (115-100)/15=1. We can then use the z-score table to determine that the area between -1 and 1 is 68%. Therefore, 68% of the scores are between 85 and 115.
To determine the percentage of test-takers who earned at least a 100, we can use the same z-score formula. The z-score for x=100 is (100-100)/15=0. We can then use the z-score table to determine that the area above 0 is 60%. Therefore, 60% of test-takers earned at least a 100.
Therefore, the first two choices are true. The mean, median, and mode are all equal to 100, and 68% of the scores are between 85 and 115. The third choice is also true, as 60% of test-takers earned at least a 100.
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Evander King is ordering a luxury convertible. The base price is $81,975. Options include satellite radio, $475; keyless entry, $555; navigation system, $1,250; and custom paint, $983. The destination charge is $890. The dealer's costs are 90% of the base price and 88% of the options price. The dealer will sell Evander the car for $200 more than the dealer's cost plus a 6% sales tax. What is the total cost of the convertible, including tax?
Answer: $82,403.28
Step-by-step explanation:
475+555+1250+983 = 3263 (total option price)
81,975 (total base price)
0.9 * 81,975 = 73,777.5 + 200
.88 * 3263 = 2,871.44
1.06 * (73,977.5 + 2871.44 + 890) = 82,403.28 (Rounded to nearest tenth)
Which of the following describes the best time to begin protecting a seedling crop from infection by nematodes?
A. at the time of ordering the seedlings
B. before ordering the seedlings
C. at the time of planting the seedlings
D. at the first sign of damage to the seedlings
Utilize only nematode-free plants that you buy from reputable nurseries to keep nematodes out of your garden.
What does nematode prevention entail? Utilize only nematode-free plants that you buy from reputable nurseries to keep nematodes out of your garden.Avoid transferring plants or soil from the garden's affected areas to prevent the spread of nematodes.As this further spreads nematodes, don't let irrigation water from around infected plants run off.Warm moist soil in small amounts to 140°F in an oven or by solarization to destroy nematodes that are present in the soil.Nematodes can be eliminated from soil by baking it in an oven for the length of time required to bake a medium-sized potato placed in the middle of the soil, although this method is only viable for small amounts of soil.To learn more about nematode refer
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The best time to begin protecting a seedling crop from infection by nematodes is at the time of ordering the seedlings.
What is Nematodes ?Use only nematode-free plants that you buy from reputable nurseries to keep nematodes out of your garden. Move plants and soil away from nematode-infested areas of the garden to stop the spread of the parasite. Avoid letting irrigation water from plants that are infected run off since nematodes can also spread through this method.
Larvae go through four molts as they develop, with the third stage, the filariform larva, often being the infective stage.
Crop rotation is a cultural method of nematode management that has good potential. Even some cover crops generate compounds that are poisonous to worms. Finding a crop rotation that can starve out all of the nematodes in your soil, though, might be challenging if you have a variety of them there.
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As shown in the diagram, PQ/QR = 1/3. Find [PAB]/[QAB].
The ratio of [PAB]/[QAB]. is 1/3
How to determine the division of the anglesFrom the question, we have the following parameters that can be used in our computation:
The triangle
Also, we have
PQ/QR = 1/3
This means that;
The line segments divide PAB to 1/3
So, we have
PAB = 1
QAB = 1 - 1/3 = 2/3
When represented as quotient, we have
[PAB]/[QAB] = 3/2
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What is the letter name of the point (-3, 4)?
Answer: R
Step-by-step explanation: you are gonna go left 3 and up 4.
x=-3 and y=4
elementary statistics, a step-by-step approach, 10th ed., bluman
The subject is taught in a non-theoretical manner in Al Bluman's Elementary Statistics. Today's world speaks statistics, and Bluman's market-leading Step-by-Step Approach makes it simple to learn and comprehend.
Bluman gives your students all the assistance they need to understand the foundations of statistics and draw that link by assisting them in transitioning from the computational to the conceptual.
Elementary Statistical Methods are the collection, analysis, presentation, and interpretation of data, and probability. The analysis includes descriptive statistics, correlation and regression, confidence intervals, and hypothesis testing.
Thus, The subject is taught in a non-theoretical manner in Al Bluman's Elementary Statistics. Today's world speaks statistics, and Bluman's market-leading Step-by-Step Approach makes it simple to learn and comprehend.
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The base of a solid oblique pyramid is an equilateral triangle with a base edge length of 18 inches.
The base of a solid oblique pyramid is an equilateral triangle with a base edge length of 18 inches has height of triangular base as 9√2 inches.
We are given that.
Length of equilateral triangle = a =18 inches
Base is an equilateral triangle.
height of the triangular base of the pyramid
h= a.cosθ
Each angle of equilateral triangle is equivalent to 60 degree
θ = 60/2
θ = 30 degree
Substitute the values,
Height of triangular base of the pyramid,
h=18.cos30
h = 18x √3/2 in
Using the value of
Cos30 = √3/2
Height of triangular base of the pyramid, h= 9√3 inches
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find the function f(x) whose tangent line has the slope (1 x√)127x√ for any x≠0 and whose graph passes through the point (9,89).
therefore, the function [tex]f(x)=\frac{1}{6}(1+\sqrt{x})(\sqrt{1+\sqrt{x})}-7/12[/tex] whose tangent slope is given.
In Geometry, the tangent is defined as a line touching circles or an ellipse at only one point. Suppose a line touches the curve at P, then the point “P” is called the point of tangency. In other words, it is defined as the line which represents the slope of a curve at that point.
We have the slope of the function as-
[tex]=\sqrt{\frac{1+\sqrt(x)}{8 \sqrt{x}}[/tex]
passes through the point (9,3/4).
Now, from the Fundamental Theorem of Calculus, we can integrate f′(x)
to get f(x). And then using the point that they gave us we can solve for the constant of integration. Do you know how to proceed from here? Do you know how to integrate that?
[tex]f'(x)=\sqrt{1+\sqrt{x}}/8 \sqrt{x}\\\\x=u^2\\\\2uf'(u^2)=\frac{\sqrt{1+u}}{{4}}}\\\\f(u^2)=\frac{1}{6}(1+u)\sqrt{1+u}+c\\\\f(x)=\frac{1}{6}(1+\sqrt{x})(\sqrt{1+\sqrt{x})+c[/tex]
the tangent passes through the (9,3/4)
[tex]\frac{3}{4}=\frac{1}{6}(1+3)(\sqrt{1+3})+c\\\\3/4=8/6+c\\3/4-4/3=c\\\\c=-7/12[/tex]
therefore, the function [tex]f(x)=\frac{1}{6}(1+\sqrt{x})(\sqrt{1+\sqrt{x})}-7/12[/tex]
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what is joule equal to
The work (or energy expended) by a one newton (N) force applied across a one meter distance is equivalent to one joule (m).
The SI unit of energy, the joule (symbol J), measures the ability to do work or produce heat. One newton is equal to a force that accelerates a mass of one kilograms (kg) by one meter per second (s) per second. As a result, one joule is equal to one newton meter.
In SI Unit
1 Joule = 1 kgm^2/s^2
In CGS units:
1 Joule = 1 kgm^2/s^2
As we know that 1 kg = 1000 g and 1 m = 100 cm. Now
1 Joule = 1(1000 g) × (100cm)^2/(1s)^2
Now solving
1 Joule = 1000 × 10^4 gcm^2/s^2
1 Joule = 10^7 gcm^2/s^2
As we know that 1 gcm^2/s^2 = 1 erg. So
1 Joule = 10^7 erg
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Equation: &-
Solution:
,. © Justify Conclusions Seventy-five percent, or 15, of the students in Emily's homeroom class are going on a field trip. Two thirds, or 12, of the students in Santiago's homeroom class are going on the field trip. Which class has more students? Justify your answer.
The class that has more students, given the percentage of students in both classes is Emily's homeroom tab .
How to find the class with more student ?To find the class with the higher number of students, you need to find the total number of students in these classes.
The number of students in Emily's homeroom class is:
= Number of students / Percentage of students
= 15 / 75 %
= 20 students
Students in Santiago's homeroom class is :
= 12 / ( 2 / 3 )
= 12 x 3 / 2
= 18 students
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How do you recruit people for research?
Recruiting participants for research can be done through various methods such as:
1. Online advertisements
2. Flyer distributions in public places
3. Collaboration with organizations or schools
4. Referral from previous participants
5. Direct mailing to potential participants
6. Social media promotion.
It is important to consider ethical guidelines and informed consent procedures when recruiting participants for research.
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Let u and v be vectors in R^2. Which of the following is/are true?(select all that apply)[ ] None of the choices is correct.[ ] The set of all vectors which are scalar multiple of a nonzero vector u is a line through u and 0.[ ] The operation of vector addition is not commutative.[ ] A column vector in R^2 is a 1x2 matrix.[ ] The magnitude of a vector cv is c times the magnitude of v, where c is any scalar.
None of the choices is correct, and a column vector in R^2 is not a 1x2 matrix.
[ ] The set of all vectors which are scalar multiple of a nonzero vector u is a line through u and 0.
[ ] The operation of vector addition is not commutative.
[ ] The magnitude of a vector cv is c times the magnitude of v, where c is any scalar.
None of the choices is correct, and a column vector in R^2 is not a 1x2 matrix.
None of the choices is correct. The set of all vectors which are scalar multiple of a nonzero vector u is a line through u and the origin (not just 0). The operation of vector addition is not commutative, meaning that the order of addition matters. The magnitude of a vector cv is c times the magnitude of v, where c is any scalar and v is a vector. A column vector in R^2 is a matrix with two columns and one row (1x2 matrix).
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How do pattern in mathematic help individual better undertand the world and predict what come next?
Pattern in mathematic help individual better undertand the world and predict what come next because patterns follow a predictable rule and that rule allows us to predict what will come next.
What is Predictable Rule?
A prediction function is a mathematical function that predicts a future occurrence based on past events. Many other types of functions can be classified as prediction functions, such as those based on likelihood, sufficiency, and plausibility.
Reasons:
Patterns are more than just beautiful designs (though they frequently are), they follow a predictable law, and that rule allows us to forecast what will happen next. Mathematics, according to mathematicians, is the study of patterns—patterns and structure in numbers, as well as patterns and structure in geometry.
Mathematical tools can explain and improve the way the world works. Mathematical modeling has the potential to save lives, aid in policy and decision-making, and optimize economic growth. It can also be used to better understand the Universe and the conditions required for life to thrive.
Scientists, like everyone else, rarely, if ever, make accurate predictions. The future remains unpredictable regardless of the data and mathematical models available. As a result, scientists must account for mistake in our fundamental equation. In other words, Y = f(X) + E, where "E" represents our incapacity to forecast accurately.
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Patterns in mathematic help individual better understand the world and predict what comes next because patterns follow a predictable rule and that rule allows us to predict what will come next.
What is the Predictable Rule?
A prediction function is a mathematical function that predicts a future occurrence based on past events. Many other types of functions can be classified as prediction functions, such as those based on likelihood, sufficiency, and plausibility.
Reasons:
Patterns are more than just beautiful designs (though they frequently are), they follow a predictable law, and that rule allows us to forecast what will happen next. Mathematics, according to mathematicians, is the study of patterns—patterns and structure in numbers, as well as patterns and structure in geometry.
Mathematical tools can explain and improve the way the world works. Mathematical modeling has the potential to save lives, aid in policy and decision-making, and optimize economic growth. It can also be used to better understand the Universe and the conditions required for life to thrive.
Scientists, like everyone else, rarely, if ever, make accurate predictions. The future remains unpredictable regardless of the data and mathematical models available. As a result, scientists must account for mistake in our fundamental equation. In other words, Y = f(X) + E, where "E" represents our incapacity to forecast accurately.
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the angle bisectors of a triangle are concurrent, and their point of concurrency is called the of the triangle.
The point of concurrency of the angle bisectors of a triangle is known as the incenter of a triangle.
The confluence point of the elevations in a triangle is known as the orthocenter. The intersection of three or more lines, rays, segments, or planes is referred to as a point of concurrency.
One of a triangle's concurrent points, the orthocenter. The incenter, circumcenter, and centroid make up the remaining three.The intersection of all three of the triangle's interior angle bisectors is where a triangle's incenter is located. In other words, it can be defined as the point where the internal angle bisectors of the triangle cross.This point will be equidistant from the sides of a triangle, as the central axis’s junction point is the center point of the triangle’s inscribed circle.
A point that is equally spaced from a triangle's sides contains all three of its angle bisectors simultaneously.
Therefore, the point of concurrency of the angle bisectors of a triangle is known as the incenter of a triangle.
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2. Is the following inequality always, sometimes, or never true?
2(3x - 1) +4> 6x + 2
The two sides of an inequality are not the same so inequality can never be true.
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.
Given that the inequality is 2(3x - 1) +4> 6x + 2. The inequality will be solved as below;-
2(3x - 1) +4> 6x + 2
6x - 2 + 4 > 6x + 2
6x + 2 > 6x + 2
The two sides are equal so inequality can never be true.
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Drag the tiles to the correct boxes to complete the pairs.
Jeff is a bird watcher. Every year in the first week of spring, he visits the Hawk Mountain Sanctuary in Pennsylvania. Last year, he saw 12 Turkish vultures, 2 bald eagles, 4 northern goshawks, and 7 red-tailed hawks. Jeff didn’t see any other birds. This year, the sanctuary authorities are expecting 175 birds during the time he visits. Use this data to predict the count of each bird that will be in the sanctuary during this year’s visit.
red-tailed hawks
bald eagles
Turkish vultures
northern goshawks
Predicted Count
Bird
49
arrowBoth
28
arrowBoth
14
arrowBoth
84
arrowBoth
Data to predict the count of each bird that will be in the sanctuary during this year's visit is red-tailed hawks, Turkish vultures, northern goshawks and bald eagles.
What does predict mean in math?
In general, prediction is the process of determining the magnitude of statistical variates at some future point of time.
12 + 2 + 4 + 7 = 25 (The total number of birds observed in the last year)
Turkish vultures = 175 × 12 / 25 = 84
bald eagles = 175 × 2 / 25 = 14
northern goshawks = 175 × 4 / 25 = 28
red-tailed hawks = 175 × 7/ 25 = 49
So,
49 ↔ red-tailed hawks
84 ↔ Turkish vultures
28 ↔ northern goshawks
14 ↔ bald eagles
Hence, data to predict the count of each bird that will be in the sanctuary during this year's visit is red-tailed hawks, Turkish vultures, northern goshawks and bald eagles.
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To predict the count of each bird that will be in the sanctuary during this year's visit, we need to assume that the proportion of each bird species in the sanctuary remains the same as it was last year when Jeff visited.
Last year, Jeff saw a total of 12 Turkish vultures + 2 bald eagles + 4 northern goshawks + 7 red-tailed hawks = 25 birds.
So, the proportion of each bird species in the sanctuary last year was:
Turkish vultures: 12/25 = 48%
Bald eagles: 2/25 = 8%
Northern goshawks: 4/25 = 16%
Red-tailed hawks: 7/25 = 28%
Using these proportions, we can predict the count of each bird species in the sanctuary this year:
Turkish vultures: 48% of 175 birds = 84 birds
Bald eagles: 8% of 175 birds = 14 birds
Northern goshawks: 16% of 175 birds = 28 birds
Red-tailed hawks: 28% of 175 birds = 49 birds
These are the predicted counts of each bird species in the sanctuary during this year's visit.
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Consider the system of equations 2x + 5y = 1 3x - 4y = 2 How many solutions does this system have? Explain.
The system of equations 2x + 5y = 1 and 3x - 4y = 2 has one solution.
How is the system of equations classified?A pair of equations system can be categorized as follows:
The system has no solution if the y-intercepts are varied but the slopes are the same.
The system has a single solution if the slopes are different.
The system has an endless number of solutions if the slopes and y-intercepts match.
The given system of equations are:
2x + 5y = 1
3x - 4y = 2
Write the equations in the standard form:
5y = -2x + 1
4y = 3x - 2
Here, the slope of equation 1 is -2 and the slope of equation 2 is 3.
We know that if the slope is different the system of equations has one solution.
Hence, the system of equations 2x + 5y = 1 and 3x - 4y = 2 has one solution.
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if 3/4 quart of lemonade concentrate is mixed with 6 and 2/3 quarts of water to make lemonade for 40 people, how many uarts of lemonade concentrate are needed to make the lemonade for 24 people
[tex]\frac{9}{20}[/tex] Quarts of lemonade concentrate are needed to make the lemonade for 24 people.
What is the meaning of multiple proportion?The law of many proportions states that when two components combine to generate more than one compound, the combined weights of each element are in a ratio of tiny whole numbers.The right response is John Dalton. Due to the fact that the English chemist John Dalton first declared this law of multiple proportions in 1803, it is also known as Dalton's law.Factor: A quantity or number that, when multiplied by another, yields the specified expression or number. a number that may be divided by another without leaving a residual is said to be multiple.A fraction multiplied by another fraction, an integer, or a set of variables is referred to as a fraction. The steps for multiplying fractions are as follows: Add the numerator to the numerator to multiply. Add the denominator to the denominator and multiply.Given data :
For 40 people = 3 / 4 quart lemon + 6 and 2/3 quarts of water
For 24 people = ?
Multiply proportion the given :
[tex]\frac{3}{4}[/tex] x [tex]\frac{24}{40}[/tex] = [tex]\frac{9}{20}[/tex] Quarts
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The lifetime of the timing belt of a certain make of cars is normally distributed with mean 125,000 miles and standard deviation 10,000 miles.
a) Find the probability that a timing belt lasts until the car runs 140,000 miles.
b) The auto maker recommends that owners have the timing belt replaced when the mileage reaches 90,000 miles. What is the probability that the timing belt fails before the car reaches the manufacturer’s recommended mileage?
c) An owner of this type of car wants to take a chance and replace the timing belt at the 1st percentile of the distribution. What should be the mileage of the car when he has the timing belt replaced?
The probability that a timing belt lasts until the car runs 140,000 miles is 0.9332.
a) The probability that a timing belt lasts until the car runs 140,000 miles can be found using the Z-score formula. The Z-score is calculated as (140,000 - 125,000)/10,000 = 1.5. The probability can be found using the Z-score table or by using a calculator, and is equal to 0.9332.
b) The probability that the timing belt fails before the car reaches the manufacturer’s recommended mileage of 90,000 miles can be found using the Z-score formula. The Z-score is calculated as (90,000 - 125,000)/10,000 = -2.5. The probability can be found using the Z-score table or by using a calculator, and is equal to 0.0062.
c) The 1st percentile of a normal distribution is the Z-score corresponding to the cumulative probability of 0.01. The Z-score for the 1st percentile is -2.33. The mileage of the car when the timing belt should be replaced can be found using the Z-score formula. The mileage is equal to 125,000 - (2.33 * 10,000) = 110,700 miles.
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Eric meaure a line to be 2. 98 in long. If the actual meaurement i 3 in, find Eric' relative error to the nearet thouandth
So Eric's relative error to the nearest thousandth is 0.007 or 0.7%.
Relative error can be calculated using the following formula:
Relative error = (|measured value - actual value|) / actual value
In this case, the actual value is 3 inches, and the measured value is 2.98 inches. So, we can calculate the relative error as follows:
Relative error = (|2.98 - 3|) / 3 = (0.02) / 3 = 0.0067
To find the relative error to the nearest thousandth, we round the result to three decimal places:
Relative error = 0.007
So Eric's relative error to the nearest thousandth is 0.007 or 0.7%.
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So Eric's relative error to the nearest thousandth is 0.007 or 0.7%.
The relative error can be calculated using the following formula:
Relative error = (measured value - actual value|) / actual value
In this case, the actual value is 3 inches, and the measured value is 2.98 inches. So, we can calculate the relative error as follows:
Relative error = (|2.98 - 3|) / 3 = (0.02) / 3 = 0.0067
To find the relative error to the nearest thousandth, we round the result to three decimal places:
Relative error = 0.007
So Eric's relative error to the nearest thousandth is 0.007 or 0.7%.
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What is the Slope of (8,6) and (16,11)
Answer:
5/8
Step-by-step explanation:
[tex]\textrm{Slope } = $\dfrac{y_2 - y_1}{x_2 - x_1}$[/tex]
where[tex](x_1, y_1) \;\; (x_2, y_2)[/tex] are two points on the graph
The given points on the graph are (8,6) and (16,11)
Difference in y values, y2 - y1 = 11 - 6 = 5
Difference in x values,: x2 - x1 = 16 - 8 = 8
Slope = 5/8
Please answer the question :)
According to the information in the graph, it can be established that the profit for 600 people would be $3,013.96
How to calculate the profit for 600 people?To calculate the profit for 600 people we must take into account the information in the graph. In this case we must establish how many people participated in the survey and how much was the total profit of the store with these customers.
11 + 8 + 9 + 19 + 3 = 5087.98 + 66.45 + 32.50 + 34.50 + 29.95 = 251.08Now we must make a rule of three to establish how much the profit would be in a group of 600 buyers.
50 - $251.08600-x600 * 251.08 / 50 = 3,012.96According to the above, the profit of the store with a group of 600 buyers would be 3,012.96
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How tall will each candle be at 11:00 PM when
the Johnsons put the candles out for the night?
3
in.
4
Each candle will be
inches tall
8 in.
5:00 PM
6:00 PM
7:00 PM
The height of each candle at 11:00 PM will be 3.5 inches.
This is because each candle starts at 8 inches tall and decreases by 3/4 of an inch per hour as it burns
To find out the height of each candle at 11:00 PM, we need to calculate the total change in height of each candle over the 6 hours it was burning.
Each hour, the height of each candle changes by -3/4 inch. So over 6 hours, the height of each candle changes by:
= -3/4 * 6= -4.5 inches.Since each candle started at 8 inches, the height of each candle at 11:00 PM will be:
= 8 - 4.5 = 3.5 inches.This question is incomplete and should be provided as:
When the Johnson family lights candles at 5:00 PM, each candle is 8 inches tall. The height of each candle changes by -3/4 inch for each hour that it burns. How tall will each candle be at 11:00 PM when the Johnsons put the candles out for the night? Each candle will be___inches tall.Learn more about candle length here: brainly.com/question/30364605
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What are the coordinates of point B on AC such that the ratio of AB to AC is 5:6
Coordinates of point B are (5x₂+6x₁)/11 and (5y₂+6y₁)/11
What is the section formula in coordinate geometry?
When the line segment is divided internally in the ratio m:n, we use this formula. That is when point C lies somewhere between points A and B. p= (mx₂+nx₁)/(m+n) & q= (my₂+ny₁)/(m+n)
Given here, point B on AC such that the ratio of AB to AC is 5:6
Let the point B(p,q) internally divide the line joining points A(x₁, y₁) and C(x₂, y₂) in the ratio m : n , then,
p= (mx₂+nx₁)/(m+n)
q= (my₂+ny₁)/(m+n)
Here. m=5 and n=6
p=(5x₂+6x₁)/11 , q=(5y₂+6y₁)/11
Hence, the Coordinates of point B are (5x₂+6x₁)/11 and (5y₂+6y₁)/11
I hope this helps <3
Find the values of a and b that make the following piecewise defined function both continuous and differentiable everywhere. f(x) = 3x + 4, X<-3
2x2 + ax + b. X>-3
The values of a and b that make the function both continuous and differentiable everywhere are a = -3 and b = 19.
What do you mean by function?A function is a mathematical concept that assigns a unique output value for each input value. It is a rule that takes in an input or set of inputs and maps it to a specific output. Functions are represented by symbols, usually denoted by a letter, such as "f".
In mathematical notation, a function is usually expressed as "f(x)" where "x" is the input and "f(x)" is the corresponding output. For example, a function could be defined as f(x) = x^2, which means that for any value of x, the function will calculate and return the square of that value.
Functions play a central role in mathematics and are used to model real-world phenomena and to study the relationships between variables. They are also used in computer programming to perform specific tasks, such as converting temperatures from Celsius to Fahrenheit or calculating the square root of a number.
To make the function continuous at x = -3, the value of f(-3) must be equal for both the first and second parts of the definition. That is, 3 * -3 + 4 = -3 * -3 + a * -3 + b. Solving for a and b gives us:
a = -3
b = 19
To make the function differentiable at x = -3, the limits of the first and second parts of the definition must be equal, and their derivatives must also be equal.
The limit from the left of f(-3) is:
[tex]\lim_{x \to \ -3}[/tex]f(x) = 3 * -3 + 4 = 5
The limit from the right of f(-3) is:
[tex]\lim_{x \to \ -3}[/tex] + f(x) = -3 × -3 + a × -3 + b = -3 × -3 + 19 = 19
So the function is continuous at x = -3. To check for differentiability, we find the derivative of the first part:
f'(x) = 3
And the derivative of the second part:
f'(x) = -6x + a
The derivative of the two parts must be equal at x = -3, so we have:
3 = -6 × -3 + a
3 = 18 - a
a = -15
This value of a is different from the value we found in the first step, so the function is not differentiable at x = -3. To make it differentiable, we must choose the value of a that makes the function continuous, which is a = -3.
So the values of a and b that make the function both continuous and differentiable everywhere are a = -3 and b = 19.
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In thi lab, we will examine the Law of Large Number and ue it to determine if a coin i unfair. A fair coin i equally weighted on each ide. An unfair coin i a coin that weigh more on one ide o that the chance of it landing on a certain ide i more likely. In thi activity, H will repreent the coin landing head up and T will repreent the coin landing tail up. Before you to the coin, ue theoretical probability to determine the probability of the coin landing head up and the probability of the coin landing head down
The probability of a fair coin landing heads up is 0.5
The probability of a fair coin landing heads up is 0.5 and the probability of it landing tails up is also 0.5.
Theoretically, this means that if a fair coin is flipped an infinite number of times, half of the flips will result in heads and half of the flips will result in tails.
In the case of an unfair coin, the probability of landing heads up and the probability of landing tails up will not be equal.
The exact probabilities will depend on the weight of the coin, but one side will have a greater probability of landing face up.
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In Exercises 17-20, find the volume of the solid generated by revolv- ing ` the shaded region about the given axis. 17. About the x-axis 18. About the J-axis x + 2 = 2 1 19. About the y-axis 20. About the x-axis sin x cOS X Lan'
the volume of the solid generated by revolving the shaded region about the given axis x- axis is: 2π/3
What is shaded region?The difference between the area of the complete polygon and the area of the unshaded portion inside the polygon is the area of the shaded region. There are two methods for the area of the darkened component to appear in polygons. The darkened area can be found either in the polygon's center or on one of its sides.
We first solve for y from the equation:
x+2y=2
or, 2y = 2 - x
or, y = (2 - x) / 2
From the graph we see that the equation is from x=0 to x=2
And it is rotating about the x axis. We can use the Disk method to find the volume of the solid:
= π [tex]\int\limits^2_0 {((2 - x)/2)^2} \, dx[/tex]
= π/4 [4x - 2x² + x³/3]₀²
= 2π/3
so, 2π/3 is the volume of the solid, it is rotating about the x axis.
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