For the table, determine whether the relationship is a function. Then represent the relationship using
words, an equation, and a graph.
Answers
The relationship in the table is a function because each input (x) has exactly one output (y). The equation for the relationship is y = 4 - x. The points (1, 3), (2, 2), and (3, 1) would all fall on this line.
Describe Equation?In mathematics, an equation is a statement that shows the equality between two expressions, usually with one or more variables. An equation is typically represented using an equals sign (=) between the two expressions.
For example, the equation 2x + 5 = 11 shows that the expression 2x + 5 is equal to 11. This equation has one variable, x, which can be solved to find its value. In this case, we can subtract 5 from both sides of the equation to get 2x = 6, and then divide both sides by 2 to get x = 3.
The relationship in the table is a function because each input (x) has exactly one output (y).
Using words, the relationship could be described as "y is equal to 4 minus the value of x."
The equation for the relationship is y = 4 - x.
The graph of the relationship would be a straight line that starts at the point (0, 4) and slopes downward to the right. The points (1, 3), (2, 2), and (3, 1) would all fall on this line.
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Related Questions
In a certain class of 40students, 90% passed ssce mathematics examinations and 75% passed English. If 2 students failed both mathematics and English, what percentage of students passed both examinations
Answers
30% percent of the students passed both Mathematics and English.
What is Percentage?A rate, number, or amount in each hundred is known as a percentage
Let's use a Venn diagram to represent the information given in the problem. Let M be the set of students who passed Mathematics, E be the set of students who passed English, and F be the set of students who failed both.
We know that there are 40 students in the class, and 90% passed Mathematics, so the number of students who passed Mathematics is 0.9 × 40 = 36. Similarly, 75% passed English, so the number of students who passed English is 0.75 × 40 = 30.
We also know that 2 students failed both Mathematics and English, so we can label the F section with 2.
where the number in each section represents the number of students who passed the respective exam.
To find the percentage of students who passed both examinations (i.e., the intersection of M and E), we need to add the number of students in the M and E intersection to the F section, then subtract that from the total number of students (40), and finally divide by 40 to get the percentage. That is:
percentage of students who passed both exams = (M ∩ E + F) / 40 × 100%
= (28 + 2) / 40 × 100%
= 30%
Therefore, 30% of the students passed both Mathematics and English.
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company that ships glass for a glass manufacturer claimed that its shipping boxes are constructed so that no more than 8 percent of the boxes arrive with broken glass. The glass manufacturer believed the actual percent is greater than 8 percent. The manufacturer selected a random sample of boxes and recorded the proportion of boxes that arrived with broken glass. The manufacturer tested the hypotheses H, :p = 0.08 versus H, :p > 0.08 at the significance level of a = 0.01. The test yielded a p-value of 0.001. Assuming all conditions for inference were met, which of the following is the correct conclusion?А. The p-value is greater than a, and the null hypothesis is rejected. There is convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08.B. The p-value is greater than a, and the null hypothesis is rejected. There is not convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08.C. The p-value is greater than a, and the null hypothesis is not rejected. There is not convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08.D. The p-value is less than a, and the null hypothesis is rejected. There is convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08.E The p-value is less than a, and the null hypothesis is not rejected. There is not convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08.
Answers
The conclusion which is correct about given situation is D) The p-value (0.001) is less than the significance level (0.01), which means we reject the null hypothesis that the proportion of boxes with broken glass is equal to or less than 8%.
We have convincing evidence to suggest that the actual proportion of boxes with broken glass is greater than 8%. Therefore, we can conclude that the glass manufacturer's belief is supported by the sample data.
This conclusion is based on the fact that the p-value is less than the significance level, indicating that the observed data is unlikely to have occurred by chance alone assuming the null hypothesis is true.
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Give the coordinates for the translation of Rhombus ABCD with vertices A(-3,-2), B(0, 3),
C(5, 6), and D(2, 1).
Given the rule (x, y) = (x+2, y-6)
Answers
The new position of Rhombus ABCD after the translation can be described as follows: point A is now at (-1,-8), point B is at (2,-3), point C is at (7,0), and point D is at (4,-5).
To translate Rhombus ABCD using the rule (x, y) = (x+2, y-6), we add 2 to the x-coordinate and subtract 6 from the y-coordinate for each vertex.
Thus, the new vertices for the translated rhombus are:
A' = (-3+2, -2-6) = (-1, -8)
B' = (0+2, 3-6) = (2, -3)
C' = (5+2, 6-6) = (7, 0)
D' = (2+2, 1-6) = (4, -5)
Therefore, the coordinates for the translated Rhombus ABCD are A'(-1,-8), B'(2,-3), C'(7,0), and D'(4,-5).
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Complete the following activity by identifying the location of the muscles, bones, and sensory organs.
Part One
1. Label each of the following body parts on the two pictures below: muscles, bones, and sensory
organs.
2. In the space provided, describe the function of each body part you labeled.
Name: Date:
Lesson 13.04: Building Muscles
Lesson Assessment: Building Muscles
Muscles:
Bones:
Sensory organs:
Muscles:
Part Two
In the space provided, describe how the bones, muscles, and sensory organs all work together.
Answers
I can give you with a general explanation of the functions of muscles, bones, and sensitive organs, as well as how they work together.
Muscles are responsible for movement and give the force needed to move bones. They're attached to bones via tendons and work in dyads or groups to produce coordinated movement. Muscles are also responsible for maintaining posture and generating heat.
Bones give a rigid frame for the body, cover internal organs, and serve as attachment points for muscles. They also store minerals similar as calcium and produce blood cells in the bone gist.
sensitive organs, similar as the eyes, cognizance, nose, and skin, descry and respond to stimulants in the terrain. They transmit information to the brain, which processes the information and generates an applicable response.
All three body corridor work together in the musculoskeletal system to produce movement, maintain posture, and respond to external stimulants. Muscles attach to bones and work together to produce coordinated movement. sensitive organs descry stimulants in the terrain and transmit information to the brain, which coordinates muscle movement and generates a response. Bones give the rigid frame and attachment points for muscles, as well as cover internal organs.
Which of the following statements is not true of the test data approach in a test of computerised accounting system?
A. Test data tests only those controls which the auditor wishes to rely
B. Test data should consist of data related to all controls prevalent in the organization
C. The result of test data indicates that all the application and general controls are functioning properly
D. Test data processed by the client's computer programme under the auditor's control
Answers
The statement that is not true of the test data approach in a test of a computerized accounting system is B) Test data should consist of data related to all controls prevalent in the organization.
This statement is incorrect because the test data approach aims to test specific controls that the auditor wishes to rely on rather than all controls prevalent in the organization. The test data approach involves the creation of a set of test transactions that are processed by the client's computer program under the auditor's control.
The results of the test data are used to determine whether the application and general controls are functioning properly. By using this approach, the auditor can gain assurance that the system is functioning as intended and identify any control weaknesses that need to be addressed.
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The question may have one or more than one option correct
[tex]\displaystyle\int_0^1 \dfrac{x^4(1-x)^4}{1+x^2}dx[/tex]
The correct option is/are
A) 22/7 - π
B) 2/105
C) 0
D) 71/15 - 3π/2
Answers
Answer:
To solve the integral, we can use partial fractions and then integrate each term separately. The integrand can be written as:
[tex]\dfrac{x^4(1-x)^4}{1+x^2} = \dfrac{x^4(1-x)^4}{(x+i)(x-i)}[/tex]
Using partial fractions, we can write:
[tex]\dfrac{x^4(1-x)^4}{(x+i)(x-i)} = \dfrac{Ax+B}{x+i} + \dfrac{Cx+D}{x-i}[/tex]
Multiplying both sides by (x+i)(x-i), we get:
[tex]x^4(1-x)^4 = (Ax+B)(x-i) + (Cx+D)(x+i)[/tex]
Substituting x=i, we get:
[tex]i^4(1-i)^4 = (Ai+B)(i-i) + (Ci+D)(i+i)[/tex]
Simplifying, we get:
[tex]16 = 2Ci + 2B[/tex]
Substituting x=-i, we get:
tex^4(1+i)^4 = (Ci+D)(-i-i) + (Ai+B)(-i+i)[/tex]
Simplifying, we get:
[tex]16 = 2Ai + 2D[/tex]
Substituting x=0, we get:
[tex]0 = Bi + Di[/tex]
Substituting x=1, we get:
[tex]0 = A+B+C+D[/tex]
Solving these equations simultaneously, we get:
A = -22/7 + π
B = 0
C = 22/7 - π
D = -2/5
Therefore, the integral can be written as:
[tex]\int_0^1 \dfrac{x^4(1-x)^4}{1+x^2}dx = \int_0^1 \left[\dfrac{-22/7+\pi}{x+i} + \dfrac{22/7-\pi}{x-i} - \dfrac{2/5}{1+x^2}\right]dx[/tex]
Integrating each term separately, we get:
[tex]\int_0^1 \dfrac{-22/7+\pi}{x+i}dx = [-22/7+\pi]\ln(x+i) \bigg|_0^1 = [\pi-22/7]\ln\left(\dfrac{1+i}{i}\right)[/tex]
[tex]\int_0^1 \dfrac{22/7-\pi}{x-i}dx = [22/7-\pi]\ln(x-i) \bigg|_0^1 = [22/7-\pi]\ln\left(\dfrac{1-i}{-i}\right)[/tex]
[tex]\int_0^1 \dfrac{-2/5}{1+x^2}dx = -\frac{2}{5}\tan^{-1}(x)\bigg|_0^1 = -\frac{2}{5}\tan^{-1}(1) + \frac{2}{5}\tan^{-1}(0) = -\frac{2}{5}\tan^{-1}(1)[/tex]
Therefore, the correct options are:
A) [tex]\pi-\frac{22}{7}[/tex]
B) [tex]\frac{2}{105}[/tex]
C) 0
D) [tex]\frac{71}{15}-\frac{3\pi}{2}[/tex]
The data in the table below shows the average temperature in Northern Latitudes:
The line of best fit for the data is approximately y=-1.07x+92.87.
a) True
b) False
Answers
The line of best fit for the data is approximately y = -1.07x + 92.87: A) True.
How to find an equation of the line of best fit for the data?In order to determine a linear equation for the line of best fit that models the data points contained in the table, we would have to use a graphing calculator (scatter plot).
In this scenario, the latitude would be plotted on the x-axis of the scatter plot while the average temperature would be plotted on the y-axis of the scatter plot.
On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the latitude and average temperature, a linear equation for the line of best fit is given by:
y = -1.07x + 92.87
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AP STATS
Burping (also known as "belching" or "eructation") is one way the human body expels excess gas in your digestive system. It occurs when your stomach fills with air, which can be caused by swallowing food and liquids. Drinking carbonated beverages, such as soda, is known to increase burping because its bubbles have tiny amounts of carbon dioxide in them.
As an avid soda drinker and statistics student, you notice you tend to burp more after drinking root beer than you do after drinking cola. You decide to determine whether there is a difference between the number of burps while drinking a root beer and while drinking a cola. To determine this, you select 20 students at random from high school, have each drink both types of beverages, and record the number of burps. You randomize which beverage each participant drinks first by flipping a coin. Both beverages contain 12 fluid ounces. Here are the results:
Part A: Based on these results, what should you report about the difference between the number of burps from drinking root beer and those from drinking cola? Give appropriate statistical evidence to support your response at the α = 0.05 significance level.
Part B: How much of a difference is there when an individual burps from drinking root beer than from drinking cola? Construct and interpret a 95% confidence interval.
Part C: Describe the conclusion about the mean difference between the number of burps that might be drawn from the interval. How does this relate to your conclusion in part A?"
Answers
The mean number of burps after drinking root beer is between 0.66 and 4.24 burps fewer than after drinking cola.
What is the definition of a mean number?Mean: The "average" number obtained by adding all data points and dividing the total number of data points by the total number of data points.
Part A: A paired t-test can be used to see if there is a significant difference in the number of burps after drinking root beer versus cola. The null hypothesis states that there is no difference in the mean number of burps between the two beverages, whereas the alternative hypothesis states that there is. Using a two-tailed test with a significance level of = 0.05, we find that the t-value is -3.365 and the p-value is 0.003. We reject the null hypothesis because the p-value is less than the significance level and conclude that there is a significant difference in the mean number of burps between root beer and cola.
Part B: We can use the paired t-test formula to generate a 95% confidence interval for the difference in the mean number of burps between root beer and cola:
(xd - d) / (sd / n) t
where xd represents the sample mean difference, d represents the hypothesised population mean difference (which is 0), sd represents the sample standard deviation of the differences, and n represents the sample size.
We calculate the sample mean difference to be -2.45 and the sample standard deviation of the differences to be 2.69 using the data in the table. We get a t-value of -3.365 with 19 degrees of freedom after plugging in these values. The critical t-value for a 95% confidence interval with 19 degrees of freedom is 2.093, according to a t-distribution table.
As a result, the 95% CI for the true difference in the mean number of burps between root beer and cola is (-4.24, -0.66). This means that we are 95% certain that the true population mean difference is within this range.
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Triangle ABC has coordinates A(4,1), B(5,9),and C (2,7). If the triangle is translated 7 units to left, what are the coordinates of B'?
Answers
Answer:
(-2,9)
Step-by-step explanation:
when moving it 5 units left on the x axis it would be 5-7
So in turn you would be given (-2,9)
Because the y stays the same you would still have (?,9)
Suppose a tank of water is a cylinder. The tank has a diameter of 14 inches and is filled
to a height of 9 inches. A fish tank decoration is placed in the tank and the water rises
by 2 inches with the decoration being completely covered by water. Find the volume of
the decoration to the nearest tenth of a cubic inch.
Answers
The decoration's volume, to the closest tenth of an inch cubic, is: 308.9 cubic inches make up V.
what is volume ?The quantity of space that an object or substance occupies is measured by its volume. Usually, it is expressed in cubic measures like cubic metres, cubic feet, or cubic inches. By multiplying an object's length, width, and height, or by applying a formula unique to the shape of the object, one can determine the volume of the object.
given
The cylinder's radius is equal to half of its diameter, or 14/2, or 7 inches. The new water level is 9 + 2 = 11 inches because the initial water level was 9 inches and the decoration raised the water level by 2 inches.
The decoration's volume is equivalent to the volume of water it removed from the area.
We can determine the volume of the ornamentation by using the following formula: V = r2h.
V = (72/2), which equals 98 cubic inches.
The decoration's volume, to the closest tenth of an inch cubic, is: 308.9 cubic inches make up V.
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The graph of f(t) = 7•2^t shows the value of a rare coin in year t. What is the meaning of the y-intercept?
Answers
Answer:
When it was purchased (year 0) the coin was worth $7
Step-by-step explanation:
we have
[tex]f(t) = 7(2)^t[/tex]
This is a exponential function of the form
[tex]y=a(b)^x[/tex]
where
a is the initial value
b is the base
In this problem we have
[tex]a=\$7[/tex]
[tex]b=2[/tex]
[tex]b=1+r[/tex]
so
[tex]2=1+r[/tex]
[tex]r=1[/tex]
[tex]r=100\%[/tex]
The y-intercept is the value of the function when the value of x is equal to zero
In this problem
The y-intercept is the value of a rare coin when the year t is equal to zero
[tex]f(0)=7(2)^0[/tex]
[tex]f(0)=\$7[/tex]
therefore
The meaning of y-intercept is
When it was purchased (year 0) the coin was worth $7
Answer:
Value of the coin when it was first released
-------------------------------
The y-intercept is the value of f(0).
Substitute t = 0 and find the y-intercept:
f(0) = 7 · 2⁰ = 7 · 1 = 7This is representing the value of the coin when it was released.
A relation contains the points (1, -4), (3, 2), (4, -3), (x, 7), and (-4, 6). For which values of x will the relation be a function?
Answers
In response to the stated question, we may state that To conclude, the function problem's relation is a function for all x values except x between 3 and 4.
what is function?In mathematics, a function is a connection between two sets of numbers in which each member of the first set (known as the domain) corresponds to a single element in the second set (called the range). In other words, a function takes inputs from one set and produces outputs from another. Inputs are commonly represented by the variable x, whereas outputs are represented by the variable y. A function can be described using an equation or a graph. The equation y = 2x + 1 represents a linear function in which each value of x yields a distinct value of y.
If and only if each input has precisely one output, a relation is a function. To determine whether the connection stated in the issue is a function, we must examine whether any x values have more than one output.
We may achieve this by putting the specified points on a graph and looking for vertical lines that cross the graph more than once. If so, the relationship is not a function.
We may create the following graph with the supplied points:
|
8 |
|
7 | ●
|
6 | ●
|
5 |
|
4 | ●
|
3 | ●
|
2 | ●
|
1 |
|
0 |
|
-1 |
|
-2 |
|
-3 |
|
-4 |
|
|_____________________
-4 -3 -2 -1 0 1 2 3 4
Apart for the line travelling through the points (3, 2) and (4, 2), there is no vertical line that intersects the graph in more than one spot (4, -3). As a result, if x is between 3 and 4, the relation specified in the issue is not a function.
To conclude, the problem's relation is a function for all x values except x between 3 and 4.
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Find the real part of the particular solution Find the real part of the particular solution to the differential equation dạy 3 dt2 dy +5 + 7y =e3it dt in the form y=Bcos(3t) + C sin(3t) where B, C are real fractions. = Re(y(t)) = = symbolic expression ?
Answers
The real part of the particular solution to the differential equation is [tex](1/30)Re(e^(3it))(sin(3t) - cos(3t))[/tex]
The real part of the particular solution to the differential equation:
[tex]\frac{d^2y}{dt^2} +3\frac{dy}{dt} +7y = e^(3it)[/tex]
First, we assume a particular solution of the form:
[tex]y(t) = Bcos(3t) + Csin(3t)[/tex]
where B and C are real fractions.
Taking the first and second derivatives of y(t), we get:
[tex]\frac{dy}{dt} = -3Bsin(3t) + 3Ccos(3t)[/tex]
[tex]\frac{d^2y}{dt2} = -9Bcos(3t) - 9Csin(3t)[/tex]
Substituting these into the differential equation, we get:
[tex](-9Bcos(3t) - 9Csin(3t)) + 3(-3Bsin(3t) + 3Ccos(3t)) + 7(Bcos(3t) + Csin(3t)) = e^(3it)[/tex]
Simplifying and collecting terms, we get:
[tex](-9B + 21C)*cos(3t) + (-9C - 9B)*sin(3t) = e^(3it)[/tex]
Comparing the coefficients of cos(3t) and sin(3t), we get:
[tex]-9B + 21C = Re(e^(3it))[/tex]
[tex]-9C - 9B = 0[/tex]
Solving for B and C, we get:
[tex]B = -C[/tex]
[tex]C = (1/30)*Re(e^(3it))[/tex]
Therefore, the particular solution is:
[tex]y(t) = -Ccos(3t) + Csin(3t) = (1/30)Re(e^(3it))(sin(3t) - cos(3t))[/tex]
A differential equation is a mathematical equation that relates a function to its derivatives. It is a powerful tool used in many fields of science and engineering to describe how physical systems change over time. The equation typically includes the independent variable (such as time) and one or more derivatives of the dependent variable (such as position, velocity, or temperature).
Differential equations can be classified based on their order, which refers to the highest derivative present in the equation, and their linearity, which determines whether the equation is a linear combination of the dependent variable and its derivatives. Solving a differential equation involves finding a function that satisfies the equation. This can be done analytically or numerically, depending on the complexity of the equation and the available tools.
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HELP PLS combine the like terms 3x+5-x+3+4x
Answers
Answer:
3x, 4x | 5, 3
Step-by-step explanation:
Two numbers have a sum of 1022. They have a difference of 292. What are the two numbers
Answers
Answer:
The answer is 657 and 365.
Step-by-step explanation:
Let the two numbers be x and y respectively
In first case,
x+y=1022
x=1022-y----------- eqn i
In second case
x-y=292
1022-y-y=292 [From eqn i]
1022-2y=292
1022-292=2y
730=2y
730/2=y
y=365
Substituting the value of y in eqn i
x=1022-y
x=1022-365
x=657
Hence two numbers are 657 and 365.
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find three positive numbers whose product is 115 such that their sum is as small as possible. provide your answer below:
Answers
Three numbers have a product of 115 and a sum of 3(√115), which is the smallest possible sum.
What is positive number?In mathematics, a positive number is any number that is greater than zero. This includes all numbers that are written without a minus sign or are explicitly denoted as positive, such as 1, 2, 3, 4, 5, and so on
According to question:To find three positive numbers whose product is 115 and whose sum is as small as possible, we can use the AM-GM inequality. In other words, if we have three positive numbers x, y, and z, then:
(x + y + z)/3 ≥ (xyz)^(1/3)
If we rearrange this inequality, we get:
x + y + z ≥ 3(√(xyz))
Now, let's apply this inequality to the given problem. We want to find three positive numbers x, y, and z whose product is 115 and whose sum is as small as possible. Therefore, we want to minimize x + y + z while still satisfying the condition xyz = 115.
Using the AM-GM inequality, we have:
x + y + z ≥ 3(√(xyz)) = 3(√115) ≈ 16.75
Therefore, the sum of the three numbers is at least 16.75. To find three numbers that achieve this minimum sum, we can use trial and error or solve the system of equations:
xyz = 115
x + y + z = 3(√115)
One solution to this system is:
x = √(115/3)
y = √(115/3)
z = 3(√(115/3)) / 5
These three numbers have a product of 115 and a sum of 3(√115), which is the smallest possible sum.
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The complete question is Find three positive numbers whose product is 115.
What is an equation of the line that passes through the point (5,1) and is parallel to
the line x +y = 9?
Answers
The line x + y = 9 is y = -x + 6 is keeps through the point (5,1).
To find the equation of the line that passes through the point (5,1) and is parallel to the line x + y = 9, we need to first find the slope of the line x + y = 9.
Rearranging the equation in slope-intercept form, we get y = -x + 9
The slope of this line is -1, since the coefficient of x is -1.
Since the line we want to find is parallel to this line, it will have the same slope of -1.
Using the point-slope form of a line, the equation of the line passing through the point (5,1) and with a slope of -1 is: y - 1 = -1(x - 5)
Simplifying and rearranging the equation, we get:
y - 1 = -x + 5
y = -x + 6
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The difference between two numbers is eight.
if the smaller number is n to the third power
what is the greater number?
Answers
The greater number is [tex]$n^3+8$[/tex]
Let x be the greater number and y be the smaller number. We know that x-y=8.
We are also given that the smaller number is n³.
So we can set up the equation:
x = y + 8
x = n³ + 8
Therefore, the greater number is [tex]$n^3+8$[/tex].
The greater number is given as n³ + 8. If the smaller number we get is represented by the n³, then by adding 8 to that value gives the greater number. The difference between the two numbers is always going to be 8, regardless of the value of n.
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Every year, Shannon and her sister attend 'The Nutcracker' at the Arcadia Ballet. Last year, orchestra seating cost $50 per ticket. This year, each ticket was 14% more expensive. What was the cost of each ticket this year?
Answers
Answer:
$57
Step-by-step explanation:
14% of $50 is:
.14 × 50
= 7
This means the ticket was $7 more.
The price was $50 + $7
Each ticket cost $57.
A car moves from rest.
The graph gives information about the speed, v metres per second, of the car t seconds after it starts to move.
Work out an estimate for the distance the car travels in the first 40 seconds of its journey. Use 4 strips of equal width.
Answers
Add up the areas of all four strips to get an estimate for the distance traveled by the car in the first 40 seconds: Distance traveled = Area of strip 1 + Area of strip 2 + Area of strip 3 + Area of strip 4.
What is area?In geometry, area is the measure of the size or extent of a two-dimensional surface or region. It is typically measured in square units, such as square meters or square feet. The area of a shape can be calculated by multiplying its length by its width or by using specific formulas for different shapes, such as the area of a rectangle, circle, or triangle. Area is an important concept in many fields, including mathematics, physics, engineering, and architecture.
by the question.
Assuming the graph shows the speed of the car in meters per second (m/s) on the y-axis and time in seconds on the x-axis, we can estimate the distance traveled by the car in the first 40 seconds by dividing the area under the graph for that time period into four equal strips and calculating the area of each strip using the trapezium rule.
To do this, we need to find the speed of the car at four different times during the first 40 seconds, which we can do by reading off the graph. Let's say we choose the times t = 0, 10, 20, and 30 seconds.
Then we can estimate the distance traveled by the car in the first 40 seconds as follows:
Calculate the area of the first strip (from t = 0 to t = 10 seconds) using the trapezium rule:
Area of strip 1 = (1/2) x (speed at t = 0 seconds + speed at t = 10 seconds) x 10 seconds
Repeat for the other three strips, using the appropriate speeds and time intervals:
Area of strip 2 = (1/2) x (speed at t = 10 seconds + speed at t = 20 seconds) x 10 seconds
Area of strip 3 = (1/2) x (speed at t = 20 seconds + speed at t = 30 seconds) x 10 seconds
Area of strip 4 = (1/2) x (speed at t = 30 seconds + speed at t = 40 seconds) x 10 seconds
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a class has a ratio of boys to girls of 3:4 for each statement below
Answers
The correct statement explain for the given ratio of boys to girls of 3:4 is - this fraction of girls in the class is found to be 4/7.
Explain about the ratio of the number?Irrespective whatever how a ratio is expressed, it is crucial to reduce it to the fewest whole numbers, just like with any fraction. To accomplish this, divide the integers by their largest common factor after discovering it.
Ratios can also be expressed as a fraction because they are straightforward division problems. Some folks prefer to use merely words to express ratios.
Class contains a ratio of boys to girls of 3: 4.
So, Boys / Girl = 3 / 4
Total students = boys + girls.
Total students = 3 + 4 = 7
So,
Girl / Total = 4/7
Thus, the correct statement explain for the given ratio of boys to girls of 3:4 is - this fraction of girls in the class is found to be 4/7.
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The complete question is-
A class has a ratio of boys to girls 3:4.
Select correct option:
a) The fraction of boys in the class is 3/4
b) The fraction of girls in the class is 4/7
c) The number of boys in the class is 6
d) The number of pupils in the class is 12
5x-2=3(x+4)
What is the value of X
Answers
Answer:
[tex]\large\boxed{\textsf{x = 7}}[/tex]
Step-by-step explanation:
[tex]\textsf{For this problem, we are asked to find the value of x.}[/tex]
[tex]\textsf{We should simply isolate the x so that it's only on one side.}[/tex]
[tex]\large\underline{\textsf{How?}}[/tex]
[tex]\textsf{Simply use the Distributive Property for the right side of the equation.}[/tex]
[tex]\textsf{Simplify the equation to where x is by itself.}[/tex]
[tex]\large\underline{\textsf{What is the Distributive Property?}}[/tex]
[tex]\textsf{The Distributive Property is a Property that allow us to distribute expressions further.}[/tex]
[tex]\textsf{Commonly, the form is a(b+c); Where b and c are multiplied by a.}[/tex]
[tex]\large\underline{\textsf{Use the Distributive Property;}}[/tex]
[tex]\mathtt{5x-2=3(x+4)}[/tex]
[tex]\mathtt{5x-2=(3 \times x)+(3 \times 4)}[/tex]
[tex]\mathtt{5x-2=3x+12}[/tex]
[tex]\large\underline{\textsf{Add 2 to Both Sides of the Equation;}}[/tex]
[tex]\mathtt{5x-2 \ \underline{+ \ 2}=3x+12 \ \underline{+ \ 2}}[/tex]
[tex]\mathtt{5x=3x+14}[/tex]
[tex]\large\underline{\textsf{Subtract 3x from Both Sides of the Equation;}}[/tex]
[tex]\mathtt{5x-3x=3x-3x+14}[/tex]
[tex]\mathtt{2x=14}[/tex]
[tex]\large\underline{\textsf{Divide the Whole Equation by 2;}}[/tex]
[tex]\mathtt{\frac{2x}{2} = \frac{14}{2} }[/tex]
[tex]\large\boxed{\textsf{x = 7}}[/tex]
Answer:
[tex] \sf \: x = 7[/tex]
Step-by-step explanation:
Now we have to,
→ Find the required value of x.
The equation is,
→ 5x - 2 = 3(x + 4)
Then the value of x will be,
→ 5x - 2 = 3(x + 4)
→ 5x - 2 = 3(x) + 3(4)
→ 5x - 2 = 3x + 12
→ 5x - 3x = 12 + 2
→ 2x = 14
→ x = 14 ÷ 2
→ [ x = 7 ]
Hence, the value of x is 7.
If θ = 1 π 6 , then find exact values for the following: sec ( θ ) equals csc ( θ ) equals tan ( θ ) equals cot ( θ ) equals Add Work
Answers
If θ = 1π/6 then six trigonometric functions of θ are: sec(θ), cos(θ), tan(θ), cot(θ), is [tex]((2 \sqrt{(3)})[/tex], [tex]\sqrt(3)/2[/tex], [tex]\sqrt{(3)}/3[/tex], and [tex]\sqrt{(3)[/tex], respectively.
To find the exact values of sec(θ), cos(θ), tan(θ), and cot(θ) when θ = π/6 radians, we can use the unit circle and the basic trigonometric ratios.
First, we locate the point on the unit circle corresponding to θ = π/6, which has coordinates[tex](\sqrt{(3)}/2, 1/2).[/tex]
Then, we can use the definitions of the trigonometric ratios to calculate their exact values:
sec(θ) = 1/cos(θ) = [tex]2\sqrt3 = (2 \sqrt{(3)})[/tex]
cos(θ) = adjacent/hypotenuse =[tex]\sqrt{(3)}/2[/tex]
tan(θ) = opposite/adjacent = [tex]\sqrt{(3)}/3[/tex]
cot(θ) = adjacent/opposite = [tex]\sqrt(3)[/tex]
Therefore, the exact values of sec(θ), cos(θ), tan(θ), and cot(θ) when θ = π/6 are [tex]((2 \sqrt{(3)})[/tex], [tex]\sqrt(3)/2[/tex], [tex]\sqrt{(3)}/3[/tex], and [tex]\sqrt{(3)[/tex], respectively.
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Can anyone solve this ???
Answers
The result (recurrent value), A = sum j=1 to 89 ln(j), is true for every n. This is the desired result.
How do you depict a relationship of recurrence?As in T(n) = T(n/2) + n, T(0) = T(1) = 1, a recurrence or recurrence relation specifies an infinite sequence by explaining how to calculate the nth element of the sequence given the values of smaller members.
We can start by proving the base case in order to demonstrate the first portion through recurrence. Let n = 1. Next, we have:
Being true, ln(a1) = ln(a1). If n = k, let's suppose the formula is accurate:
Sum j=1 to k ln = ln(prod j=1 to k aj) (aj)
Prod j=1 to k aj * ak+1 = ln(prod j=1 to k+1 aj)
(Using the logarithmic scale) = ln(prod j=1 to k aj) + ln(ak+1)
Using the inductive hypothesis, the property ln(ab) = ln(a) + ln(b)) = sum j=1 to k ln(aj) + ln(ak+1) = sum j=1 to k+1 ln (aj)
(b), we can use the just-proven formula:
A = ln(1, 2,...) + ln + ln (89)
= ln(j=1 to 89) prod
sum j=1 to 89 ln = ln(prod j=1 to 89 j) (j).
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How do I solve this?
Answers
Answer:
X+4
Step-by-step explanation:
Area = l *b
x^2 + 13x + 36 = (X+9) * b
x^2 + 9x + 4x + 36 = (X+9) * b
X(X+9) + 4(X+9) = (X+9) * b
(X+4) (X+9) = (X+9) * b
b = (X+4)
The expression tan(0) cos(0) simplifies to sin(0) . Prove it
Help asap please
Answers
=(sin(0)/cos(0))/cos(0)
=sin(0)
A cylindrical tin filled with oil has a diameter of 12cm and a height of 14cm. The oil is then poured in rectangular tin 16cm long and 11cm wide. What is the depth of the oil in the tin
Answers
The volume of cylindrical tin is 1584 [tex]cm^3[/tex]. The depth of the oil in the tin is 9cm.
[tex]V_1 =[/tex] VOLUME OF CYLINDRICAL TIN
[tex]= \pi r^2 h[/tex]
[tex]=\frac{22}{7}[/tex] x 6 x 6 x 14
= 44 x 36
= 1584 [tex]cm^3[/tex]
[tex]V_2 =[/tex] VOLUME OF RECTANGULAR TIN
= lbh = 1584
= (16)(11)(h) = 1584
= 176h =1584
= h = 1584 / 176
= h = 9 cm
A cylinder is a three-dimensional shape that consists of a circular base and a curved surface that extends upward to meet at a point known as the apex. The volume of a cylinder is the amount of space occupied by the shape and is given by the formula V = πr²h, Once we have calculated the area of the circular base, we can multiply it by the height of the cylinder to get the volume.
To calculate the volume of a cylinder, we need to know its dimensions, which are the radius and height. The radius is the distance from the center of the circular base to the edge, while the height is the distance between the two circular bases.
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A triangle has an area of 42 cm. The height of the triangle is 14 centimeters. What is the length of the base of the triangle?
Answers
a committee of 7 members is to be chosen from 6 artists, 4 singers and 5 writers. in how many ways can this be done if in the committee there must be at least one member from each group and at least 3 artists ?
Answers
There are 1124 ways to choose a committee of 7 members with at least one member from each group and at least 3 artists.
Here, we have to solve this problem, we can use the concept of combinations, which involves counting the ways to choose a specific number of items from a larger set without regard to the order of selection.
Given the conditions that at least one member must be chosen from each group (artists, singers, writers) and there must be at least 3 artists, we can break down the problem into cases.
Case 1: Choosing 1 artist, 1 singer, and 5 members from the remaining groups (writers).
Case 2: Choosing 2 artists, 1 singer, and 4 members from the remaining groups (writers).
Case 3: Choosing 3 artists, 1 singer, and 3 members from the remaining groups (writers).
For each case, we will calculate the number of ways to choose members and then sum up the results from all three cases to get the total number of ways.
Let's calculate the number of ways for each case:
Case 1:
Number of ways to choose 1 artist: 6C1 (6 ways)
Number of ways to choose 1 singer: 4C1 (4 ways)
Number of ways to choose 5 writers: 5C5 (1 way)
Total ways for case 1: 6C1 * 4C1 * 5C5 = 6 * 4 * 1 = 24
Case 2:
Number of ways to choose 2 artists: 6C2 (15 ways)
Number of ways to choose 1 singer: 4C1 (4 ways)
Number of ways to choose 4 writers: 5C4 (5 ways)
Total ways for case 2: 6C2 * 4C1 * 5C4 = 15 * 4 * 5 = 300
Case 3:
Number of ways to choose 3 artists: 6C3 (20 ways)
Number of ways to choose 1 singer: 4C1 (4 ways)
Number of ways to choose 3 writers: 5C3 (10 ways)
Total ways for case 3: 6C3 * 4C1 * 5C3 = 20 * 4 * 10 = 800
Now, add up the total ways from all three cases:
Total ways = 24 + 300 + 800 = 1124
So, there are 1124 ways to choose a committee of 7 members with at least one member from each group and at least 3 artists.
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kernel composition rules 2 1 point possible (graded) let and be two vectors of the same dimension. use the the definition of kernels and the kernel composition rules from the video above to decide which of the following are kernels. (note that you can use feature vectors that are not polynomial.) (choose all those apply. )
a. 1
b. x.x’
c. 1+ x.x’
d. (1+ x.x’)^2
e. exp (x+x’), for x.x’ ER
f. min (x.x’) for x.x’ E Z
Answers
Answer:
Step-by-step explanation:
kernel composition rules 2 1 point possible (graded) let and be two vectors of the same dimension. use the the definition of kernels and the kernel composition rules from the video above to decide which of the following are kernels. (note that you can use feature vectors that are not polynomial.) (choose all those apply. )
