The required Missing Frequency is 3.
What is frequency ?Frequency is a measure of the number of occurrences of a given event within a specified period of time. It can refer to the number of times a particular event happens in a unit of time.
Such as the number of times a wave or vibration occurs in a second, or the number of times an action occurs in a given period. In physics, frequency is measured in hertz (Hz); in electrical engineering, it is measured in cycles per second (cps). Frequency is also used in mathematics, music, and sound engineering.
Value Frequency
1 2
2 4
3 9
4 ?
5 6
6 8
7 2
8 4
Total 40
We have to find the Missing frequency:
Computation:
Missing frequency = Total frequency - Counted
Missing frequency = 40 - 37
Missing frequency = 3
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In the equation y = 2x + 3 , what is the output if the input is 6?
Answer:
[tex]x=\frac{y-3}{2\\}[/tex]
Step-by-step explanation:
Swap sides so that all variable terms are on the left-hand side. Subtract 3 from both sides. Divide both sides by 2. Dividing by 2 undoes the multiplication by 2.
Can you please help me answer these math problems.
1. Find the equation of a line in slope-intercept form that passes through a given point or has a slope of m. x-intercept = - 2 and y-intercept = -10.
2. Find the equation of a line in slope-intercept form that passes through a given point or has a slope of m. (0, - 6); m = 8
3. Find the equation of a line in slope-intercept form that passes through a given point or has a slope of m. Parallel to y = 5; passing through (4,9)
4. Find the equation of a line in slope-intercept form that passes through a given point or has a slope of m. Perpendicular to x = -4; passing through (3, 7)
5. What is the slope of the line?
6. What does it mean if the slope of a line is undefined?
A vertical line can be written in the form x = a, where a is the x-coordinate of any point on the line.
What is equation?In mathematics, an equation is a statement that asserts the equality of two expressions. It contains an equals sign (=) and one or more variables, which represent unknown values. Equations are often used to solve problems and find the values of the variables that make the equation true. There are many types of equations, including linear equations, quadratic equations, and systems of equations, among others.
Here,
1. To find the equation of a line in slope-intercept form, we need to use the formula y = mx + b, where m is the slope of the line and b is the y-intercept. We are given the x-intercept and y-intercept of the line, so we can use them to find the slope and y-intercept:
x-intercept = -2, y-intercept = -10
To find the slope, we can use the formula:
m = (y2 - y1)/(x2 - x1), where (x1, y1) = (-2, 0) and (x2, y2) = (0, -10)
m = (-10 - 0)/(0 - (-2)) = -10/2 = -5
So the slope of the line is -5.
Now we can use the slope-intercept form equation to find the equation of the line:
y = mx + b
Substituting the values of m and b, we get:
y = -5x - 10
Therefore, the equation of the line in slope-intercept form that passes through the x-intercept = -2 and y-intercept = -10 is y = -5x - 10.
2. We are given a point (0, -6) and the slope m = 8. We can use the slope-intercept form equation to find the equation of the line:
y = mx + b
Substituting the values of m and the point (0, -6), we get:
-6 = 8(0) + b
b = -6
Therefore, the equation of the line in slope-intercept form that passes through the point (0, -6) and has a slope of m = 8 is y = 8x - 6.
3. We are given that the line is parallel to y = 5 and passes through the point (4, 9). Since the line is parallel to y = 5, it has the same slope as y = 5, which is 0. We can use the point-slope form equation to find the equation of the line:
y - y1 = m(x - x1)
Substituting the values of m, x1, and y1, we get:
y - 9 = 0(x - 4)
y - 9 = 0
y = 9
Therefore, the equation of the line in slope-intercept form that is parallel to y = 5 and passes through the point (4, 9) is y = 9.
4. We are given that the line is perpendicular to x = -4 and passes through the point (3, 7). Since the line is perpendicular to x = -4, it is a vertical line and its slope is undefined. We can use the equation x = 3 to represent the line.
5. To find the slope of a line, we can use the formula:
m = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.
6. If the slope of a line is undefined, it means that the line is vertical. This happens when the change in the x-coordinates between any two points on the line is zero, which makes the denominator in the slope formula zero. In this case, the line does not have a slope, since the slope is defined as the ratio of the change in y-coordinates to the change in x-coordinates.
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You have 2 different savings accounts. For Account A, the simple interest earned after 18 months is $8.10. For Account B, the simple interest earned after 18 months is $16.50. If the interest rate is 3.6% for Account A and 2.2% for Account B, how much is the principal in each account? Which account earned you the most interest the first month? Explain your answer.
The required principal in accounts A and B are $150 and $500 respectively, while the interest earned by account B is greater than the interest earned by account A.
What is simple interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan.
SI = Principal [rate×time]
Here,
For Account A,
SI = Principal [rate×time]
8.10 = P [0.036 × 18 / 12]
P = $150
Similarly
For Account B,
P = $500
Now,
for an account, A interest earned in the first month is given as,
SI = 150 × 0.036 × 1 / 12
SI = $0.45
Similarly,
for account B interest earned in the first month is given as,
SI = $0.92
Thus, the required principal in accounts A and B are $150 and $500 respectively, while the interest earned by account B is greater than the interest earned by account A.
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Select the correct answer. Which value is not part of the five-number summary needed for a box plot of this data? { 5, 6, 1, 27, 2, 7, 12, 15, 9, 18, 19} A. 1 B. 5 C. 9 D. 11
Answer:
Step-by-step explanation:nnbjnj
Answer:
Order the row {5, 6, 1, 27, 2, 7, 12, 15, 9, 18, 19} from the smallest number to the biggest number:
{1, 2, 5, 6, 7, 9, 12, 15, 18, 19, 27}.
The minimum is 1, the maximum is - 27.
The median is the middle number in this row - 9.
The median of left part {1, 2, 5, 6, 7} is 5 and the median of the right part {12, 15, 18, 19, 27} is 18.
From the option A-D only number 11 is absent (numbers 1, 5 and 9 are part of the five-number summary).
Answer: correct choice is D.
Step-by-step explanation:
11
10
9
7
6
5
4
D
E
G
L
0 1 2 3 4 5 6 7 8 9 10 11 12*
The farmer wants to provide an area of 20 square meters for each rabbit.
Which of these statements are true? Choose all that are correct.
O The perimeter of the field is approximately 300 meters.
O
The area of the field is 5,400 square meters.
The area of the field is 6,000 square meters.
The perimeter of the field is approximately 316 meters.
The field will hold a total of 300 rabbits.
The field will hold a total of 270 rabbits.
None of the given statements are true.
What are the area and perimeter of a rectangle?We are aware that a rectangle's area is equal to the product of its length and breadth, and that the perimeter of any 2D shape is equal to the sum of the lengths of its other sides, excluding the circle.
Given:
The rectangular shape has a width of 4 units and a length of 6 units.
So, The perimeter of the rectangle is,
= 2(6 + 4)
= 20 meters.
and, The area of the rectangle is,
= (6×4)
= 24 square meters.
From the given statements none of the statements are true.
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can someone help me on IREADY AREA problem? thank you so much !
Answer:
494ft^2
Step-by-step explanation:
Area of trapezoid = [ (20 + 32) / 2 ] * 3 = 78 ft^2
Area of square = 32 * 13 = 416 ft^2
Total area: 78ft^2 + 416ft^2 = 494ft^2
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Triangle XYZ is a right triangle with ZQ¯¯¯¯¯⊥XY¯¯¯¯¯¯ . A right triangle with vertices labeled X, Y, and Z. Side Y Z is the base. Angle Z is marked as a right angle. Side X Y contains a midpoint labeled Q. A line segment is drawn through vertex Z to the point Q that bisects angle X Z Y into two parts. Angle X Q Z is marked as a right angle. Side Z X is labeled as a. Side Y Z is labeled as b. Side X Y is labeled as c. Segment X Q is labeled as f. Segment Q Y is labeled as e. Segment Q Z is labeled as d. Drag and drop a correct answer into each box to complete the proof of the Pythagorean theorem. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. By the angle-angle similarity postulate, △YXZ∼△YZQ and △YXZ∼△ZXQ. Since similar triangles have Response area sides, ac=fa and bc=eb . Solving the equation for a² and b² gives a2=cf and b2= Response area. Adding these together gives a2+b2=cf+ce. Factoring out the common segment gives a2+b2=c(f+e). Using Response area gives a2+b2=c(c), which simplifies to a2+b2=c2 .
The answers are proportional , ce, segment addition postulate if the Triangle XYZ is a right triangle with ZQ XY.
What is triangle ?
Triangle can be defined in which it consists of three sides , three angles and sum of three angles is always 180 degrees.
Given,
Triangle XYZ is a right triangle with ZQ XY.
proportional
ce
segment addition postulate
You want the words that finish the proof of the Pythagorean theorem.
Similar triangles
The proof makes use of the fact that the right triangles in the figure are all similar, and the fact that similar triangles have proportional sides.
The proportion b/c = e/b can be rearranged to b² = ce.
Then the segment addition theorem is invoked to let you use the fact that f+e = c.
Therefore, The answers are proportional , ce, segment addition postulate if the Triangle XYZ is a right triangle with ZQ XY.
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Ally is planning on saving money for a new computer. She currently has $100 in her bank account. She plans on saving an additional $25 each month. a.) Write a linear equation to model how much Ally saves for a computer each month. b.) What will her savings be after 6 months? c.) Ally decides that she will need $1200 to purchase the computer she wants. How many months will it take her to reach this goal?
The linear equation that models how much Ally saves for a computer each month is y = 25x + 100, where x is the number of months that have passed, and y is the total amount saved. After 6 months, her savings will be $250. It will take her 44 months to have $1200 to purchase the computer.
An equation is a mathematical statement that shows that two expressions are equal. Equations use an equals sign (=) to show that the values of the expressions on either side of the sign are equal. It can include variables, numbers, and mathematical operations such as addition, subtraction, multiplication, and division
Let x = the number of months
y = total amount she saves
If she currently has $100 in her bank account and she plans on saving an additional $25 each month, then the linear equation to model how much she saves is:
y = $25x + $100
y = 25x + 100
After 6 months, the equation becomes:
y = 25(6) + 100 = 150 + 100 = $250
So after 6 months, Ally will have saved $250.
To find the number of months it will take to reach the goal of $1200, we can rearrange the equation and solve for x:
$1200 = 25x + 100
$1100 = 25x
x = 44
It will take 44 months, or approximately 3 years and 8 months, for Ally to reach her savings goal of $1200.
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A local grocery delivery time has a uniform distribution over 0 to 60 minutes. What is the probability that the grocery delivery time is more than 15 minutes on a given day? Answer
The probability that the grocery delivery time is more than 15 minutes on a given day is P ( x > 15 ) = 0.75
What is Probability?The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
Probability = number of desirable outcomes / total number of possible outcomes
The value of probability lies between 0 and 1
Given data ,
Let the probability that the grocery delivery time is more than 15 minutes on a given day be P
Now , the equation will be
The density function is f ( x ) = 1 / ( b - a )
And , the uniform distribution is over 0 to 60 minutes
So , a = 0
b = 60
Substituting the values in the equation , we get
f ( x ) = 1 / ( 60 - 0 )
f ( x ) = 1/60
f ( x ) = 0.01667
Now , the probability P = P ( x > 15 ) , where the termination point is 60 minutes
So , P ( x > 15 ) = ( 60 - 15 ) f ( x )
P ( x > 15 ) = 45 x 0.01667
P ( x > 15 ) = 0.75
Hence , the probability is 0.75
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Please help me with this question.
The solution of the given differential initial value problem is
y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6).
What is initial value problem?In multivariable calculus, an initial value problem is an ordinary differential equation together with an initial condition which specifies the value of the unknown function at a given point in the domain.Given is the initial value problem -
y''' + 10y'' + 25y' = 0
We can write the -
[tex]$25 \frac{d}{d x} y{\left(x \right)} + 10 \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} = 0$[/tex]
The given differential equation can be solved and written as -
y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6)
Therefore, the solution of the given differential initial value problem is
y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6).
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The table of values forms a quadratic function F(x)
The equation that represents f(x) is f(x) = x²-2x-8.
What is the equation that represents f(x)?This equation is a parabola in the form of y = ax² + bx + c, where a, b, and c are constants.The value of a is 1, b is -2, and c is -8.The domain of this equation is all real numbers and the range is all real numbers greater than or equal to -8.The parabola of this equation is a "U" shape that opens upwards.The vertex is located at (x,y) = (1, -8) and the axis of symmetry is the line x = 1.The y-intercept is -8, which can be seen in the table of values.As x increases, the parabola will move up, and as x decreases, the parabola will move down.The graph of this equation is symmetrical around the y-axis.The equation that represents f(x) is d. f(x) = x²-2x-8. This is a quadratic function, which is a type of polynomial equation with one variable (in this case, x). A quadratic equation is defined as an equation of the form ax² + bx + c = 0, where a, b, and c are constants and a is not equal to 0.To find the equation that represents f(x), we can use the values given in the table and solve for the constants a, b, and c. For example, when x = 0, f(x) = -8, so we can set -8 = c. When x = 1, f(x) = -2, so we can set -2 = -a + b. Finally, when x = 2, f(x) = 6, so we can set 6 = 4a - 2b.We can then use these three equations to solve for the constants a, b, and c, and find that a = 1, b = -2, and c = -8. This gives us the equation f(x) = x² - 2x - 8, which represents the given table of values.To learn more about quadratic function refer to:
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Please help me solve this problem
Extra points
Answer:
C
Step-by-step explanation:
you open up the brackets and multiply 2 to whatever is inside and you'll get C
Sum = 1/1-r is the formula for an infinite series sum. If the sum is 5, find R
Answer:
Below
Step-by-step explanation:
5 = 1 / (1-r)
1-r = 1/5
r = 4/5
2. A colony of bacteria has an initial population of 5,000. After applying a test serum to the bacteria, the population decreases 7% each day. Which equation rep change in bacteria population?
If a colony of bacteria has an initial population of 5,000. After applying a test serum to the bacteria, the population decreases 7% each day. The equation that represent change in bacteria population is: P(t) = 5000(1-0.07)^t.
How to find the equation that represent change in population?The equation for the change in bacteria population over time can be represented as:
P(t) = P0(1-r)^t
Where:
P(t) = population at time t (in days)
P0 = initial population = 5,000
r = rate of change = -0.07 for a 7% decrease per day
t = number of days
So, the equation is:
P(t) = 5000(1-0.07)^t
Therefore the equation that represent change in bacteria population is: P(t) = 5000(1-0.07)^t.
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A study shows that 80% of the population of a city have brown eyes and 20% do not. The study also shows that 20% of the people who do not have brown eyes do not have brown hair, while 90% of the people who have brown eyes have brown hair. A relative frequency table was constructed for this data. What is the largest marginal relative frequency and its interpretation?
0.90; Individuals with brown hair
0.88; Individuals with brown hair
0.80; Individuals with brown eyes
0.72; Individuals with brown eyes
The largest marginal relative frequency and its interpretation is
0.80; Individuals with brown eyes.
What is probability?Probability is a way to gauge how likely something is to happen. According to the probability formula, the likelihood that an event will occur is equal to the proportion of positive outcomes to all outcomes. The probability that an event will occur P(E) is equal to the ratio of favorable outcomes to total outcomes.
Given, 80% of the population of a city have brown eyes and 20% do not,
let B for brown eyes and B' for nonbrown eyes
p(B) = 0.80
p(B') = 0.20
The study also shows that 20% of the people who do not have brown eyes do not have brown hair, while 90% of the people who have brown eyes have brown hair,
here H for brown hair and H' for non-brown hairs
p(H given B) = 0.90
p(H given B') = 0.20
using bays theorem for calculation,
p(H ∩ B) = p(H given B) x p(B)
p(H ∩ B) = 0.90 x 0.80
p(H ∩ B) = 0.72
p(H' ∩ B) = p(B) - p(H ∩ B)
p(H' ∩ B) = 080 - 0.72
p(H' ∩ B) = 0.08
p(H ∩ B') = p(H given B') x p(B')
p(H ∩ B') = 0.20 x 0.20
p(H ∩ B') = 0.04
p(H' ∩ B') = p(B') - p(H ∩ B')
p(H' ∩ B') = 0.20 - 0.40
p(H' ∩ B') = 0.16
Hair/eyes Brown other total
Brown 0.72 0.04 0.76
other 0.08 0.16 0.24
total 0.80 0.20 1
so 0.80 is the highest which is for brown eyes.
Hence option C is correct.
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EASY POINTS!
The subtotal of items in your online shopping cart, before sales tax, is $210. After sales tax is applied, the total becomes $219.66. What is the sales tax percentage?
4.4%
95.4%
7.2%
4.6%
Answer:
4.6%
Step-by-step explanation:
Correct me if I'm wrong
219.66-210=9.66
210x4.6%=9.66
Answer: 4.6%
Step-by-step explanation:
I just took the test :)
Question 1(Multiple Choice Worth 2 points)
(Graphing Linear Equations MC)
A gymnast joined a yoga studio to improve his flexibility and balance. He pays a monthly fee and a fee per class he attends. The equation y = 10 + 20x represents the amount the gymnast pays for his membership to the yoga studio per month for a certain number of classes.
Which graph represents this situation?
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 20 through the point 1 comma 30
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 20 through the point 1 comma 10
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 10 through the point 1 comma 30
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 10 through the point one half comma zero
Question 2(Multiple Choice Worth 2 points)
(Graphing Linear Equations MC)
A eyeglasses store is checking their inventory. The table shows the relationship between the number of days since the opening of the eyeglasses store and the total amount of sunglasses in their inventory.
Sunglasses Inventory
Number of Days Total Amount of Sunglasses
2 54
5 48
7 44
10 38
Which of the following graphs shows the relationship given in the table?
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 52 through the point 1 comma 50
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 52 through the point 1 comma 49
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 58 through the point 1 comma 56
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 58 through the point 1 comma 55
Question 3(Multiple Choice Worth 2 points)
(Graphing Linear Equations LC)
The table represents a linear relationship.
x −1 0 1 2
y 2 0 −2 −4
Which of the following graphs shows this relationship?
graph of a line passing through the points negative 2 comma negative 4 and 0 comma 0
graph of a line passing through the points negative 2 comma negative 1 and 0 comma 0
graph of a line passing through the points negative 2 comma 4 and 0 comma 0
graph of a line passing through the points negative 2 comma 1 and 0 comma 0
Question 4(Multiple Choice Worth 2 points)
(Graphing Linear Equations LC)
Which of the following graphs has a slope of negative three halves and a y-intercept of 2?
graph of a line passing through the points 0 comma 2 and 3 comma 0
graph of a line passing through the points 0 comma 2 and 2 comma negative 1
graph of a line passing through the points 0 comma 3 and 2 comma 0
graph of a line passing through the points 0 comma 3 and 3 comma 1
Question 5(Multiple Choice Worth 2 points)
(Graphing Linear Equations MC)
A middle school club is planning a homecoming dance to raise money for the school. Decorations for the dance cost $100, and the club is charging $10 per student that attends.
Which graph describes the relationship between the amount of money raised and the number of students who attend the dance?
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 100 through the point 2 comma negative 80
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 100 through the point 2 comma negative 120
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma 100 through the point 2 comma 80
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma 100 through the point 2 comma 120
Question 6(Multiple Choice Worth 2 points)
(Graphing Linear Equations MC)
Which graph represents the equation y equals one half times x minus 1?
graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1
graph of a line passing through the points negative 2 comma 0 and 0 comma 1
graph of a line passing through the points negative 2 comma negative 3 and 0 comma negative 2
graph of a line passing through the points negative 4 comma 0 and 0 comma 2
Step-by-step explanation:
and a line going from the point 0 comma 100 )
Which graph represents the equation
graph of a line passing through the points negative
From a random sample of potential voters in an upcoming election, 47% indicated they intended to vote for Candidate R. A 95 percent confidence interval was constructed from the sample and the margin of error for the estimate of 5%. Which of the following is the best interpretation of the interval?
A) We are 95% confident that the proportion who intend to vote for Candidate R from the random sample is between 42% and 52%
B) We are 95% confident that the proportion who intend to vote for Candidate R from the population is between 42% and 52%
C) We are 95% confident that the proportion who intend to vote for Candidate R from the random sample is 47%
D) We are 95% confident that the proportion who intend to vote for Candidate R from the population is 47%
E)We are confident that 95% of the population intended to vote for Candidate R
The best interpretation is A) We are 95% confident that the proportion who intend to vote for Candidate R from the random sample is between 42% and 52%.
The confidence interval is constructed based on the sample data, not the population. The interval represents the range in which the true proportion of people who intend to vote for Candidate R in the population is likely to fall, given the sample data. The margin of error of 5% indicates that the estimate may be off by up to 5%. So, there is a 95% chance that the true proportion is between 42% (47% - 5%) and 52% (47% + 5%).
Option D) We are 95% confident that the proportion who intend to vote for Candidate R from the population is 47% is not correct because there is always some degree of uncertainty in sample estimates. The confidence interval takes into account this uncertainty by providing a range of possible values.
Option E) We are confident that 95% of the population intended to vote for Candidate R is not correct because the confidence level refers to the level of confidence in the estimate, not the proportion of people who actually intend to vote for the candidate.
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
Answer:
Step-by-step explanation:
The two correct representations of the inequality -3(2x - 5) < 5(2 - x) are:
-6x + 15 < 10 - 5x
6x - 15 > 5x - 10
Derrick would like to explore his area. He estimates that his walking speed is 3.5 mph in the difficult terrain he has been given. If Derrick leaves at around 12 pm, and the sun sets at 4:45 pm, how far can he explore and still make it back by sunset?
If Derrick leaves at around 12 pm, and the sun sets at 4:45 pm, the distance he can explore and still make it back by sunset is : 1.24 miles.
How to find the distance?In order to find how far Derrick can explore, we need to know how much time he has before sunset.
If the sun sets at 4:45 pm, and he leaves at 12 pm, we can find the amount of time he has by subtracting 12 pm from 4:45 pm.
4:45pm - 12:00pm
= 4:45pm
We can convert the hours and minutes to minutes only.
4 hours × 60 minutes/hour + 45 minutes
= 260 minutes
Since Derrick's walking speed is 3.5 mph, let convert this to minutes per mile by using the conversion factor 1 hour = 60 minutes.
Now let find the distance Derrick can travel
Distance = 260 minutes / 3.5 mph × 60 minutes/hour
Distance = 260 minutes / 210 minutes/mile
Distance = 1.24 miles
Therefore Derrick can explore 1.24 miles before sunset.
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Prove whether each argument is valid or invalid. First find the form of the argument by defining predicates and expressing the hypotheses and the conclusion using the predicates. If the argument is valid, then use the rules of inference to prove that the form is valid. If the argument is invalid, give values for the predicates you defined for a small domain that demonstrate the argument is invalid.
The domain for each problem is the set of students in a class.
(c)Every student who missed class got a detention.
Penelope is a student in the class.
Penelope got a detention.
Penelope missed class.
(e)Every student who missed class or got a detention did not get an A.
Penelope is a student in the class.
Penelope got an A.
Penelope did not get a detention.
(c) The argument is valid, and we can conclude that Penelope missed class because she got a detention.
(e) The argument is valid, and we can conclude that Penelope did not miss class because she got an A and did not get a detention.
(c) To prove this argument's validity, we need to define the predicates and express the hypotheses and conclusion using them:
Let "M(x)" be the predicate "x missed class", and "D(x)" be the predicate "x got a detention".
Hypotheses: M(Penelope), D(Penelope)
Conclusion: M(Penelope)
Using modus ponens, which states that if P implies Q and P is true, then Q must be true, we can conclude that M(Penelope) is true:
From M(Penelope) and "Every student who missed class got a detention", we have D(Penelope)
From D(Penelope), we have M(Penelope)
So, the argument is valid, and we can conclude that Penelope missed class because she got a detention.
(e) To prove this argument's validity, we need to define the predicates and express the hypotheses and conclusion using them:
Let "M(x)" be the predicate "x missed class", "D(x)" be the predicate "x got a detention", and "A(x)" be the predicate "x got an A".
Hypotheses: A(Penelope), ~D(Penelope)
Conclusion: ~M(Penelope)
Using modus tollens, which states that if P implies Q and Q is false, then P must be false,
we can conclude that M(Penelope) is false:
From A(Penelope) and "Every student who missed class or got a detention did not get an A",
we have ~M(Penelope) & ~D(Penelope)
From ~D(Penelope), we have ~M(Penelope)
So, the argument is valid, and we can conclude that Penelope did not miss class because she got an A and did not get a detention.
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Housing prices in a small town are normally distributed with a mean of $174,000 and a standard deviation of $9,000. Use the empirical rule to complete the following statement. Approximately 95% of housing prices are between a low price of Ex: 5000 and a high price of $ SA
The Leona Vicario school cooperative will deliver to its 96 members this year's profits, which were $5,616. How much will each receive if the division is equitable?
Answer:
$58.50
Step-by-step explanation:
5616/96
Find BDC
A. 75
B. 79
C. 43
D. 41
Answer:
B. 79.
Step-by-step explanation:
1. to connect two points C and T with line;
2. m∠ACT=(63/2)° and m∠BTC=(95/2)°, then
3. in ΔCDT m∠CDT=180-(m∠ACT+m∠BTC)=101°;
4. finally, m∠BDC=180-101=79°.
for more details find the attachment.
[tex]\int tanx dx\\[/tex]
The value of the integrand is -ln | cos(x) | + C
How to evaluate the integrandFrom the question, we have the following parameters that can be used in our computation:
Integral of tan(x) w.r.t x
The antiderivative (indefinite integral) of the tangent function, tan(x), with respect to x cannot be expressed in terms of elementary functions
However, it can be expressed in terms of special functions, such as the hyperbolic tangent and the dilogarithm.
One possible representation of the antiderivative of tan(x) is:
∫tan(x) dx = -ln | cos(x) | + C
where C is an arbitrary constant of integration.
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You have a box that measures 2 meters x 2 meters x 6 meters. What is the longest piece of rebar (inside diagonal) that could fit in this box? What assumption is necessary for this calculation?
A box that measures 2 meters × 2 meters × 6 meters. So the longest piece of rebar (inside diagonal) that could fit in this box is 2√11 cm.
Determine the longest piece of rebar (inside diagonal)These are the specified parameters:
Length of the box (l) = 2 m
Breadth of the box (b) = 2 m
Height of the box (h) = 6 m
The longest piece of rebar (inside diagonal)
For example, inside diagonal = x
x² = l² + b² + h²
= 2² + 2² + 6²
= 4 + 4 + 36
= 44
x = √44
x = 2√11 cm
So the longest piece of rebar (inside diagonal) is 2√11 cm.
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The diagonals of rectangle QRST intersect at P. Given that
m/PTS= 34° and
QS=10, find mSRT.
Note that since the diagonals of rectangle QRST intersect at P and m∠PTS = 34°, thus, m∠SRT is 56°.
What are the properties of a rectangle?A rectangle is a quadrilateral with four right angles in Euclidean plane geometry. Rectangles have the following fundamental properties: A rectangle is a quadrilateral.
The two opposite sides are parallel and equal.Each inside angle measures 90 degrees.The total of all internal angles is 360 degrees.The diagonals cut each other in half.The diagonals are both the same length.With regard to the above problem:
Since ∠QRS = 90° (based on the qualities of a rectangle) ; and
∠QRT ≅ ∠RTS = 34° (based on the rule of alternate angles,
Thus, m∠SRT = 90° - 34°
∠SRT = 56°
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Full Question:
The diagonals of the rectangle QRST intersect at P. Given that
m∠PTS= 34° and QS=10, find m∠SRT.
See attached image.
The table represents a linear relationship.
x −1 0 1 2
y 2 0 −2 −4
Which of the following graphs shows this relationship?
graph of a line passing through the points negative 2 comma negative 4 and 0 comma 0
graph of a line passing through the points negative 2 comma negative 1 and 0 comma 0
graph of a line passing through the points negative 2 comma 4 and 0 comma 0
graph of a line passing through the points negative 2 comma 1 and 0 comma 0
The graph that shows the relationship would be C. graph of a line passing through the points negative 2 comma 4 and 0 comma 0
How to find the graph ?To find the graph, first find the slope of the line using the points from the table, ( - 1, 2 ) and ( 1, - 2).
The slope is:
= ( Y2 - Y1) / ( X 2 - X 1 )
= ( - 2 - 2 ) / ( 1 - ( - 1 ))
= - 2
This means that if a point on the graph has the x value of - 2, the y value would be:
= x - value x slope
= - 2 x - 2
= 4
The point would therefore be ( -2, 2 ) which makes option C correct.
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Any help please, thanks
The answer should be
B, The price of each cup of lemonade is $0.25, less at Florence's Lemonade Stand.
If I'm right Your Welcome, I'm glad I can help.
I'm just finishing the challenge answer 5 math questions.
So hope I helped. Your Welcome.
Mardea's age is 10 less than 3 times Togar's age.
Together their ages add to 50. Which equations best
represent these relationships?
A. M-10-3T
M + T = 50
B. M-3T-10
M + T = 50
C.T-3M-10
M+T=50
D. T-10-3M
M+T=50
These connections are best represented using equations. M-3T-10 as well as M + T = 50 are in Option B.
What does age actually mean?a time frame in a person's life, defined in years from birth, that is frequently characterized by a distinct stage or stage of physical and mental development and involves the development of legal ability and responsibility: the legal age of majority; the legal age of consent; The legal drinking age was increased by the state from 18 to 21.
What does it mean to be under 21?As of 1971, a minor in the U.s. is typically considered to be someone who is underneath the age age 18. However, those below the age of twenty-one may also occasionally be referred to that as minors in the framework of drinking or gambling legislation.
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