Using Equivalence relation conditions ,
option (b) and option (c) are shows equivalence Relation.
Equivalence Relation : A relation is called (∼ ) an equivalence relation on a set A if it satisfies the following three properties:
a) reflexivity: for all a∈A,
a∼a
b) symmetry: for all a,b∈A,
if a∼b then b∼a.
c) transitivity: for all a,b,c∈A,
if a∼b and b∼c then a∼c.
first consider the matrix ,
A = [10100 ; 01000; 10100; 00010; 00001]
A = matrix form start [10100 end brackets
01000
10100
00010
00001]
it is a 5×5 matrix and row 1ˢᵗ and 3ʳᵈ are equivalent which implies determinnant is zero .
So, Matrix A is not equivalent relation.
b) let B = [00010;01000;00100;10010;00000]
we can see that last row (5ᵗʰ ) and last Colomn (5ᵗʰ )have zero enteries.
by simple row and column operation and proper arrangements we get an identity matrix of 4× 4 with 5ᵗʰcolumn and row zero enerties.
So, Identity matrix is always satisfied all three conditions of equivalence Relation.
c) Now, We have the first relation R defined as:
xRy : a relation between x and y exist if y can be obtained from x by swapping any two bits
i. Reflexivity: Any string is clearly related to itself as we can get the same string by swapping a bit with itself.
ii. Symmetry: Let xRy, then y is obtained from x by swapping two bits. Thus, x can be obtained from y by swapping the same bits. Hence the relation is symmetric.
iii. Transitive: Consider the three strings a = 1 0 1 0 1 0, b = 1 0 0 1 1 0, c = 1 0 0 1 0 1. Then b can be obtained from a by swapping the middle two bits, and c can be obtained from b by swapping the last two bits, but, c cannot be obtained from a by swapping two bits only. Hence aRb, bRc but a is not related to c. Therefore the relation is not transitive.
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g a fair coin is flipped n times and the results recorded. how many different sequences of heads and tails are possible?
The probability of heads and tail on coin flipped can be determined using Pascal's Triangle
Probability for flipping coin can be determined using Pascal's Triangle, here's how it's works:
1st level of Pascal's Triangle is 1, it means only 1 possibility when the coin not flipped
2nd level of Pascal's Triangle is 1 1, it means there's 2 possibility when the coin flipped 1 times, 1 heads and 1 tail
3rd level of Pascal's Triangle is 1 2 1, it means there's 3 possibility when the coin flipped 2 times, 2 heads (1 probability), 1 head 1 tail (2 probability), and 2 tails (1 probability)
4th level of Pascal's Triangle is 1 3 3 1, it means there's 4 possibility when the coin flipped 3 times, 3 heads (1 probability), 2 heads 1 tail (3 probability), 1 head 2 tails (3 probability) and 3 tails (1 probability)
And the list will go on depends how many the coins flipped
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a single card is drawn from a standard deck of 52 cards. what are the odds against drawing an odd numbered card?
Answer:26%
Step-by-step explanation:
Sam runs a large chain of car repair shops. He pays his employees for 8 hours of work each day. The employees
have to log the amount of time they spend working on each job, which results in a number of billable hours for
each employee each day. Sam would like to estimate the mean number of billable hours for the large number of
employees at the company. To do so, he selects a random sample of 10 employees and asks them how many
billable hours they tend to have each day. From their responses, he constructs a 95% confidence interval for the
true mean number of billable hours for all employees in the company. Which of the following may have an impact
on the confidence interval, but is not accounted for by the margin of error?
response bias
nonresponse bias
sampling variation
undercoverage bias
Sampling variation will have more impact on confidence interval, but is not accounted for by the margin of error.
What is Sampling variation?
Because each sample is unique, sampling variation describes how much a sample estimate (a statistic) is likely to change from sample to sample.What factors lead to sampling variation?
Sample Sizes and Variability
The variability of samples fluctuates as sample sizes are raised or lowered. For instance, if you select a sample size of 10 persons from a population of 1,000, you would almost certainly get a completely different conclusion than if you take a sample size of 100.What does the sample variation reveal?
To evaluate population group differences, statistical tests like variance tests and the analysis of variance (ANOVA) use sample variance. To determine whether the populations they represent significantly differ from one another, they use the variances of the samples.To know more about sample variation check the below link:
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What is the relationship between attending training and preferred source of ordering parts? which of these would be an appropriate Null Hypothesis?
1.
There is a relationship between attending training and the preferred source of auto parts.
2.
There should be a relationship between attending training and the preferred source of auto parts.
3.
There is no relationship between attending training and the preferred source of auto parts.
4.
There will be no difference in the number of auto parts ordered.
The correct option is,
There is no relationship between attending training and the preferred source of auto parts.
What is Null Hypothesis?
The null hypothesis in inferential statistics is that two possibilities are equal. The underlying assumption is that the observed difference is just the result of chance. It is feasible to estimate the probability that the null hypothesis is correct using statistical testing.
Null hypothesis always states that there is no significant difference between given observations. This also means that there is no such relationship between the two sets. That is, there is no effect of value in one set increases on value of another set will increase or decrease.
Hence the Null Hypothesis for given statement , "the relationship between attending training and preferred source of ordering parts " is :
H0 : There is no relationship between attending training and the preferred source of auto parts.
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g(x) = 3x^2+ 5
f(x) = x - 2
Find | g
The value of (gof)(x) is [tex]3x^2[/tex] - 12x + 17
The first function is
g(x) = [tex]3x^2[/tex] + 5
The second function is
f(x) = x - 2
The function is the mathematical statement that shows the relationship between one variable and another variable. If one variable is independent variable and another variable is dependent variable. The function consist of the different variable, numbers and mathematical operators
Then the value of (gof)(x) is
g(f(x) = g(x-2)
Then,
g(x - 2) = 3 × [tex](x-2)^2[/tex] + 5
Expand the terms
g(x - 2) = 3 × ([tex]x^2[/tex] - 4x + 4) +5
g(x - 2) = [tex]3x^2[/tex] - 12x + 12 +5
Add the terms
g(x - 2) = [tex]3x^2[/tex] - 12x + 17
Hence, the value of (gof)(x) is [tex]3x^2[/tex] - 12x + 17
The complete question is
If g(x) = 3x^2+ 5
f(x) = x - 2
Find the value of (gof)(x)
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A line passes through (0, 2) and has a slope of 13 . what is the equation of the line in slope-intercept form? responses y=13x 2 y equals 1 third x plus 2 y=13x−2 y equals 1 third x minus 2 y=−13x 2 y equals negative 1 third x plus 2 i don't know.
A line passes through (0, 2) and has a slope of 13. What is the equation of the line in slope-intercept form?
y = 1/3x + 2 (y equals 1 third x plus 2)
y = 1/3x − 2 (y equals 1 third x minus 2)
y = −1/3x + 2 (y equals negative 1 third x plus 2)
y-intercept is : (0 , 2)
slope = 13 or 13/1 (this is positive so slope will be positive)
slope = rise/run = y/x
what is the distance from amelia to the top of the tower? type your answer in the box. use numerals instead of words. the distance from amelia to the top of the tower is feet.
The distance from Amelia to the top of the tower is 100 feet.
Define trigonometric identities.Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate a triangle's side length and angle. Trigonometry is the study of angles and the angular relationships between planar and three-dimensional shapes. The cosecant, cosine, cotangent, secant, sine, and tangent are among the trigonometric functions (also known as the circle functions) that make up trigonometry.
Given,
Considering the query;
The tower has a 50-foot height.
Amelia's position and the top of the tower form a 30° angle.
Trigonometric identities, therefore;
Thus,
x = 50/sin30°
sin 30° = 50/x.
x = 50/0.5
x = 100 ft.
The distance from Amelia to the top of the tower is 100 feet.
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the cost in dollars of a class party is 59 13n, where n is the number of people attending. what is the cost for 44 people?
The total cost of 44 people in the class party will be $631
The total cost in dollars of a class party is 59 + 13n
Where n = number of people attending in the class party
Let F(n) be the function representing the total cost in dollars of a class party
Such as, F(n) = 59 + 13n
As per the question, the total cost of attending the 44 people will be:
For 44 people we have n = 44
As we had, F(n) = 59 + 13n
Here, F(n) will be treated as a function in which n will be its domain while F(n) will give the output as a range.
F(44) = 59 + 13(44)
= 59 + 572
= 631
Total cost will be $631
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What is called angle?.
When two rays intersect an angle is created, As different classification of angles are there on the basis of measurement of angles and on the basis of properties of angles.
What is definition of term "Angle" ?When two rays or straight lines intersect at one of their ends, an angle is created. Vertex of an angle refers to the point at which two points meet. The Latin word "angulus," which means "corner," is the origin of the English term "angle."
Symbol of Angle
The symbol ∠ represents an angle. Angles are measured in the form of degrees (°) using a protractor.
For example, 45 degrees is represented as 45°
Sections of Angles
A vertex is also the corner of an angle or at the place where two lines or sides come together to intersect at the point. In the above figure, O is the vertex.Arms: The angle's two sides which are connected at a single terminal. An angle's OA and OB are its arms.Initial Side: Also known to as the reference line, this is the first side of the angle that is to be drawn. The reference line is called OB.Terminal Side: The side that the angle measured is performed up to. OA is the terminal side.Types of Angles
Based on their measurements, here are the many types of angles:
An acute angle that measures less than 90° at the vertex of the lines.An obtuse angle measured between 90° to 180°.A right angle is exactly measures 90° at the vertex.An angle measuring precisely 180° is called a straight angle.A reflex angle is measured between 180°- 360°.A complete angle is measured is equal 360°.Interior and Exterior Angles:
Interior angles: Interior Angles are angle formed inside the shape.
Exterior angles: Exterior angles are to be angles that is formed outside a shape, between any side of shape and to an extended adjacent side.
Complementary and Supplementary Angles:
Complementary angles: Angles that add up to 90° (a right angle) are called complementary angles.
Supplementary angles: Angles that add up to 180° (a straight angle) are called supplementary angles.
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the least squares regression line is the line which minimizes the sum of the squared residuals for all the points in the scatterplot. the vertical distance between a point in the scatterplot and the predicted value on the regression line is the residual for the point. least square estimates from simple linear regression are the slope b1 estimates, on average, the change in the y variable associated with one unit increase in x variable.
The correct statements for least square estimates is the 3rd and 4th statements.
What is least square estimates?Least square estimates is method to predicted the observed Y value with minimized the sum of squared errors when using the fitted line.
The first and second statements is about simple linear regression. Simple linear regression is refers to linear line as parameter for fitting a model.
All statements are correct, but since the question asks for which statement is correct for least squares estimation, only the third and fourth statements are correct.
Thus, the 3rd and 4th statements is correct for least square estimates.
Your question is incomplete, but most probably your full question was (image attached)
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What number is 80% of 25?.
Can someone translate this photo it’s Russian
Giving 30 points
If not an appropriate answer
Report
Thankyou :D
The words in the image is translated from Russian language to English language as "Don't you really think you can learn something for yourself? - Ilya. She spoke with that goal that she hated in herself, i don't believe it. For example, here Vekshina! Exactly, I don't know"
Translating Russian to EnglishTo translate this paragraph to English, if you're not a native Russian speaker or fully understand the language to read and write, we can easily apply an online free tool for this type of text. This tool can translate texts as well as words in an image.
Using that here, the paragraph can roughly be translated as
"Don't you really think you can learn something for yourself? - Ilya. She spoke with that goal that she hated in herself, i don't believe it. For example, here Vekshina! Exactly, I don't know"
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What is the double plus 1 number sentence?.
The doubles Plus 1 is a strategy to learn addition and subtraction faster and make it easy to do.
we know that adding the same number twice is easier than adding two different numbers
like: 8+8 = 16 this is easier to remember and do
8+9 = 17 here we might make mistakes
so if we use the double plus one strategy to solve 8+9
we write it as 8+9 = (8+8)+1 = 16+1 = 17
hence this makes is easier for us to understand and do it faster.
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6. MODELING REAL LIFE The Navajo rug is made of
isosceles triangles. You know ZB = ZD. Use.
the SAS Congruence Theorem to prove that
AABC=ACDE.
A
B
D
E
By using SAS congruence theorem we have proved that ΔABC≅ΔCDE.
What is meant by SAS(Side-Angle-Side)?Two triangles are congruent if any two sides and the angle included between the sides of one triangle are equivalent to the corresponding two sides and the angle included between the sides of the second triangle.
Triangle SAS-Congruence
Example: AB= PQ, AC=PR, and the angle between AC and AB equals the angle between PR and PQ, i.e. A = P.
That is specifically stated in the SAS rule. When two sides and the included angle of one triangle equal two sides and the included angle of another, the triangles are congruent. An included angle is one that is formed by the intersection of two given sides.
In the illustration,
∠B≅∠D
By using SAS congruence,
If the two triangles are congruent then their sides are equal.
Therefore,
[tex]\bar{AB}[/tex]=[tex]\bar{CD}[/tex]
And [tex]\bar{AC}[/tex]=[tex]\bar{CE}[/tex]
[tex]\bar{BC}[/tex]=[tex]\bar{DE}[/tex]
ΔABC≅ΔCDE
Hence, Δ ABC ≅ Δ PQR.
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suppose that ab is the diameter of a circle with center o and that c is a point on one of the two arcs joining a and b. show that and are orthogonal.
For the circle , AC and CB are orthogonal
According to the question ,
AB is the diameter of a circle with center O and the C is a point on one
of the two arcs joining A and B
Let AO = -u and OB = u and CO = v
To prove that AC and AB is orthogonal .
We have to show their dot product is zero i.e. CA . CB = 0
=> CO + CA = -u
=> CA = -v -u
=> CO + CB = -v
=> CB = -v + u
So, the dot product,
CA . CB = (-v -u ) . ( -v +u)
=> v .v + u . v - v . u - u .u
=> |v|² +u . v - u . v - |u|²
=> |v|² - |u|² = 0
Hence , the length of v is same as the length of u
Therefore , AC and AB are orthogonal
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the regression sum of squares (ssr) can be greater than the total sum of squares (sst). group of answer choices true false
The given statement is False . That is regression sum of squares (ssr) can be greater than the total sum of squares (sst).
Regression sum of squares (ssr)
The sum of squares regression is the sum of the differences between the predicted value and the mean of the dependent variable.
SSR = ∑( yᵢ-cap - y-bar)² and i = 1 to N
Total Sum of Squares (SST) :
Total Sum of Squares is the deviation of the value of the dependent variable from the sample mean of the dependent variable. Essentially, the total sum of squares quantifies the total sample variation. It can be found using the formula:
SST = ∑(yᵢ - y-bar )²
The first is that the regression sum of squares cannot be computed as a total sum of squares. Let's find an explanation for this. We know that the sum of squares can be divided. There's the dualism of squares, some of the squares and regressions, sums of squares, dead food. A regression sum of squares is not formed, it is a total sum of squares. This means the statement is false. The next processing is the value, which is always positive, but we know that the value the confession of the adjustment, in the range -1 to 1.
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The y-intercept of f(x)=3(1/2)x is ____________________ the y-intercept of the function in the graph:
The y-intercept of f(x) = 3(1/2)x is less than the y-intercept of the graphed function.
What is the Y-intercept of a Function?The y-intercept of function, y = mx + b, is the value of b, which is the point on the graph where the line intersects the y-axis.
Given the function, f(x) = 3(1/2)x, the y-intercept is 0 because if we examine the equation given in slope-intercept form as y = mx + b, there is no value of b, or rather, the value of b is equal to 0.
In the given graph above, the line of the function intercepts the y-axis at 4. This implies that the y-intercept of the function on the graph is 4.
Therefore, f(x) = 3(1/2)x has a y-intercept that is less than that of the function in the given graph.
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in a baseball league of 9 teams, how many games are needed to complete the schedule if each team plays 12 games with each other?
Total number of games for 9 teams so that each team will play 12 games in the baseball league will be 432
Total number of teams in the baseball league is 9
Total number of games that each team will play is 12
Since, each team will have option of 8 teams to play with since no team can play with itself
Therefore, number of games that each team will play after playing 12 games will be 8 x 12 = 96
Since there are 9 teams, therefore total number of games that two teams will play = 96 x 9 = 864
Now, as it takes two teams to play a game therefore the required number of games for the 9 teams = 864/2 = 432
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The total cost for laundry service, in dollars, depends on the weight of the laundry, in pounds. This relationship is proportional, as it costs $24.65 for 29 pounds of laundry and $36.55 for 43 pounds of laundry. In words, describe the graph of the proportional relationship. A line from (0, 0) going through (24.65, 29) where the x-axis is labeled Weight (in pounds) and the y-axis is labeled Cost (in dollars) A line from (0, 0) going through (29, 24.65) where the x-axis is labeled Cost (in dollars) and the y-axis is labeled Weight (in pounds) A line from (0, 0) going through (43, 36.55) where the x-axis is labeled Cost (in dollars) and the y-axis is labeled Weight (in pounds) A line from (0, 0) going through (43, 36.55) where the x-axis is labeled Weight (in pounds) and the y-axis is labeled Cost (in dollars)
The best description of the graph of the proportional relationship is: D. A line from (0, 0) going through (43, 36.55) where the x-axis is labeled Weight (in pounds) while the y-axis is labeled Cost (in dollars).
What is the Graph of a Proportional Relationship?The graph that represents a proportional relationship is a straight line graph that passes through the origin (0, 0) and has a constant of proportionality, k, which is y/x.
Thus, given that the relationship between total cost for laundry service (y) is proportional to the weight of laundry (x), it means that the graph that will pass represent this would have the following features:
X-axis would be labelled weight (in pounds)Y-axis is labelled cost (in dollars)The line will pass through the following points, (0, 0), (29, 24.65), (43, 36.55)Therefore, the best description in words is: option D (last option).
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Answer:
Its A i did the practice exam test
Step-by-step explanation:
the guy above was wrong and didn't even make sense so here you go ;)
find two positive numbers that satisfy that the product is 147 and the sum of the first number plus three times the second number is a minimum.
Two positive numbers that satisfy x=21 and y=7
XY = 147
x +3y = x + 3(147/x) = (x²+ 441)/x = f(x)
0= f'(x) = (x ( 2x) - x² - 441)/x²
= 2x² - x² -441)/x²
= (x² - 441)/x²
So then x² - 441 = 0
x = 21 , as x>0
x=21 and y=7,
the max sum is 21 +3(7) = 42
Related to best a regular and a primary-order (linear) time period, in which m is the slope and b is the y-intercept. every so often, the above is referred to as a "linear equation of variables," where y and x are the variables. a linear feature is defined as a feature that has both one or two variables without exponents. it is a function that graphs to the direct line.
A linear equation in two variables is of the shape Ax + by way of + C = zero, in which A and B are the coefficients, C is a consistent term, and x and y are the two variables. Linear functions are those whose graph is an instant line. A linear feature has the subsequent shape. y = f(x) = a + bx. A linear characteristic has one impartial variable and one based variable. The independent variable is x and the base variable is y.
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Select the graph that correctly displays the solution of the system of inequalities.
y> 2x²+x-3
y<-x² + 5x
A graph that correctly displays the solution of the system of inequalities is graph D.
What are the rules for writing an inequality?In Mathematics, there are two (2) main rules that are generally used for writing and interpreting an inequality plotted on a graph and these include the following:
The line on a graph should be a dashed (dotted) line when the inequality symbol is (> or <).The line on a graph should be a solid line when the inequality symbol is (≥ or ≤).Additionally, the y-value for these system of inequalities intersects the x-axis at 5 and the boundary line is dashed (dotted) and shaded above to indicate that the boundary is not part of the solution, and this must be represented with the greater than (>) inequality symbol.
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Answer:
should be that graph, picture below!
Step-by-step explanation:
taking test!
1. Select all the correlation coefficients that indicate that an increase in one variable
results in a decrease in the other.
A. r=-0.9894
B. r=-0.5776
C.r=0.2361
D. T= 0.4429
E. r= 0.9919
The correlation coefficients that indicate that an increase in one variable results in a decrease in the other;
B. r=-0.5776
C.r=0.2361
What is correlation coefficient and how to interpret it?Correlation coefficient is a measure of how similar two datasets are acting.
When the correlation coefficient comes out as -1, it means that both the datasets are negatively oppositely correlated. One data increases, other data starts decreases in the opposite direction.
When the correlation coefficient comes out below 0, then values are negatively correlated. SO,
All of the given option are negatively correlated.
If the correlation coefficient comes out as 0, that means both the data sets are uncorrelated.
Therefore, the correlation coefficients that indicate that an increase in one variable results in a decrease in the other;
B. r=-0.5776
C.r=0.2361
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Find the number of elements inA_1 ∪ A_2 ∪ A_3if there are 100 elements in each set and if a) the sets are pairwise disjoint. b) there are 50 common elements in each pair of sets and no elements in all three sets. c) there are 50 common elements in each pair of sets and 25 elements in all three sets. d) the sets are equal.
a) Number of elements in the union of all three sets when the sets are pairwise disjoint is 300
b) Number of elements in the union of all three sets when there are 50 common elements in each pair of sets and no elements in all three sets is 150
c) Number of elements in the union of all three sets when there are 50 common elements in each pair of sets and 25 elements in all three sets is 175
d) Number of elements in the union of all three sets when the sets are equal is 100
What do you mean by relation and function?
(INPUT, OUTPUT) is a representation of an ordered pair.
The relationship between INPUT and OUTPUT is demonstrated by the relation. A function, on the other hand, is a relation that yields one OUTPUT for each given INPUT. Although all relations are functions, not all functions are relations. A function is a relationship that states that there should only be one output for each input, or we could refer to it as a particular category of relationship (a collection of ordered pairs) that adheres to a rule.
Given are three distinct sets, A1, A2, and A3, each with 100 members. The number of elements in the uninon set, A1 U A2 U A3, are as follows, according to the circumstances.
First off, if we remember the formula, it will be really simple to determine how many components make up the union set;
n(A1 U A2 U A3) = n( A1 ) + n( A2 ) + n( A3 ) - n( A1 ∩ A2 ) - n( A2 ∩ A3 ) - n( A1 ∩ A3 ) + n( A1 ∩ A2 ∩ A3 ),
a) This states that we dont have any common elemets in any pair of these sets,
n( A1 ∩ A2 ) = 0, n( A2 ∩ A3 ) = 0 , n( A1 ∩ A3 ) = 0 and also n( A1 ∩ A2 ∩ A3 ) = 0 and as given n( A1 ) = n( A2 ) = n( A3 ) = 100 .
Hence the no of elements in the union set A1 U A2 U A3 will be
n(A1 U A2 U A3)
= n( A1 ) + n( A2 ) + n( A3 ) - n( A1 ∩A2 ) - n( A2 ∩ A3 ) - n( A1 ∩ A3 ) + n( A1 ∩ A2 ∩ A3 )
= 100 + 100 + 100 - 0 - 0 - 0 + 0
= 300
b) We have
n( A1 ) = n( A2 ) = n( A3 ) = 100
n( A1 ∩ A2 ) = n( A2 ∩ A3 ) = n( A1 ∩ A3 ) = 50 and n( A1 ∩ A2 ∩ A3 ) = 0 .
Hence the no of elements in the union set A1 U A2 U A3 will be
n(A1 U A2 U A3)
= n( A1 ) + n( A2 ) + n( A3 ) - n( A1 ∩ A2 ) - n( A2 ∩ A3 ) - n( A1 ∩ A3 ) + n( A1 ∩ A2 ∩ A3 )
= 100 + 100 + 100 - 50 - 50 - 50 + 0
= 150
c) We have
n( A1 ) = n( A2 ) = n( A3 ) = 100
n( A1 ∩ A2 ) = n( A2 ∩ A3 ) = n( A1 ∩ A3 ) = 50 and
n( A1 ∩ A2 ∩ A3 ) = 25 .
Hence the no of elements in the union set A1 U A2 U A3 will be
n(A1 U A2 U A3)
= n( A1 ) + n( A2 ) + n( A3 ) - n( A1 ∩ A2 ) - n( A2 ∩ A3 ) - n( A1 ∩ A3 ) + n( A1 ∩ A2 ∩ A3 )
= 100 + 100 + 100 - 50 - 50 - 50 + 25
= 175
d) This states that all the common elemets are present in the three sets, so
n( A1 ) = n( A2 ) = n( A3 ) = 100 as well as n( A1∩ A2 ) = n( A2 ∩ A3 ) = n( A1 ∩ A3 ) = n( A1 ∩ A2 ∩ A3 ) = 100
Hence the no of elements in the unino set A1 U A2 U A3 will be
n(A1 U A2 U A3)
= n( A1 ) + n( A2 ) + n( A3 ) - n( A1 ∩ A2 ) - n( A2 ∩ A3 ) - n( A1 ∩ A3 ) + n( A1 ∩ A2 ∩ A3 )
= 100 + 100 + 100 - 100 - 100 - 100 + 100
= 100
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a pen in the shape of an isosceles right triangle with legs of length x ft and hypotenuse of length h ft is to be built. if fencing costs $5/ft for the legs and $10>ft for the hypotenuse, write the total cost c of construction as a function of h.
The total cost "C" for the construction as a function of h is C = 5h/√2 + 10h .
In the question ,
it is given that ,
the shape of the triangle is = isosceles triangle
length of the legs of the triangle = x ft ,
length of the hypotnuse of the triangle = f ft ,
the cost of fencing for legs = $5 per feet ,
the cost of fencing for hypotnuse = $0 per feet .
The pen is in shape of an isosceles right angle. This means one of angle is 90 degrees and 2 sides of triangle are equal and base angles are equal too.
So , By Pythagoras Theorem ,
x² [tex]+[/tex] x² [tex]=[/tex] h²
2x² = h²
x² = h² / 2
x = √h²/ √2 = h/√2
the cost will be written as ,
Cost = 5×(x) + 10×(h)
Cost = 5×(h/√2) + 10h
C = 5h/√2 + 10h
Therefore , The cost function is C = 5h/√2 + 10h .
The given question is incomplete , the complete question is
A pen in the shape of an isosceles right triangle with legs of length x ft and hypotenuse of length h ft is to be built. if fencing costs $5/ft for the legs and $10/ft for the hypotenuse, write the total cost c of construction as a function of h.
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I will give brainlest to first person to answer correctly!
Answer:
R = 1
Step-by-step explanation:
R = y/x
Substitute the x and y values, for example, the first row
5.8/5.8 = 1
Therefore the answer is 1
Fwam took a taxi from his house to the airport. The taxi company charged a pick-up fee of $3. 80 plus $2. 25 per mile. The total fare was $33. 05, not including the tip. Write and solve an equation which can be used to determine mm, the number of miles in the taxi ride.
The taxi company charged a pick-up fee of $3. 80 plus $2. 25 per mile. So, the number of miles in the taxi ride with the total fare $33. 05 is 13 miles.
How to determine the number of miles in the taxi ride?Write and solve an equation
Supppse, the number of miles = x
Total fare = a pick-up fee + fare per mile × the number of miles
Total fare = 3.80 + 2.25 x
Determine the number of miles
Total fare = 3.80 + 2.25 x
33.05 = 3.80 + 2.25 x
2.25 x = 33.05 - 3.80
2.25 x = 29.25
x = 29.25/2.25
x = 13
The number of miles in the taxi ride is 13 miles.
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A 16,000-gallon pool is being filled at a rate of 50 gallons per minute. At this rate, how many minutes will it take to fill this pool 3\4 full?
The amount of time it will take 16000 gallons to fill the pool 3/4 full is 320 minutes.
What is time?Time can be defined as an ongoing and continuous sequence of events that occur in succession, from past through the present, and to the future.
To calculate the amount of time it takes to fill 3/4 of the pool , we use the formula below.
Formula:
R = g/t............. Equation 1Where:
R = Rate at which the pool is being fiiledg = Gallons required to fill 3/4 of the poolt = TimeFrom the question,
Given:
g = (16000)×3/4 = 12000 gallonsR = 50 gallons per minuteSubstitute these values into equation 1 and solve for t
50 = 16000/tt = 16000/50t = 320 minutesHence, the time it will take is to fill the pool 3/4 full 320 minutes.
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Two quantities, x and y, are directly proportional. If x is doubled, what happens to y? clear check it is multiplied by 4. It is multiplied by 12. It depends on the starting value of x. It is doubled.
The two quantities x and y, are directly proportional. If x is doubled, then value of y will also be doubled.
Define the term directly proportional?If two quantities become directly proportional, it indicates that if one increases by a specific percentage, the other also increases by the same percentage.
The relationship between two values where their ratio equals a constant number is known as a direct proportion and direct variation. It is symbolized by the proportional sign (∝). Since the other variable is reversed in this case, the inversely proportional relationship is really represented by the same symbol.For the given situation;
x and y are in the direct proportional relation.
Thus,
x ∝ y
Thus,
x = k y
k = proportionality constant.
Thus,
multiplying both side by 2
2 x = 2 k y
Y also becomes twice .
If x is multiplied by 4 then,
4 x = 4 k y
y also get 4 times.
Thus, if x is doubled, then value of y will also be doubled and if x get 4 timed y also become 4 times.
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Describe the error sadie made, and explain how to find the correct answer.
Sadie didn't simplify the expression properly and made mistakes during the simplification. The correct answer after simplification will be [tex]3a^{3} b\sqrt{6ab }[/tex]
Whenever we are about to simplify an expression, we should do it till the most simplified answer we got and follows the maths rules properly.
Sadie simplified the expression [tex]\sqrt{54a^{7}b^{3} }[/tex].
He first made an error during the simplification step at
[tex]\sqrt{3^3 \cdot 6 \cdot a^2 \cdot a^5 \cdot b^2 \cdot b}[/tex] where it should be [tex]3^{2}[/tex] not [tex]3^{3}[/tex].
Secondly, he came to the answer [tex]3a b \sqrt{6 a^5 b}[/tex] but we can simplify it more by simplifying [tex]a^{5}[/tex].
We can find the correct answer by simplifying the expression [tex]\sqrt{54a^{7}b^{3} }[/tex] by the following:
[tex]\sqrt{54a^{7}b^{3} }[/tex] = [tex]\sqrt{3^2 \cdot 6 \cdot a^2 \cdot a^5 \cdot b^2 \cdot b}[/tex]
= [tex]3 \cdot a \cdot|b| \sqrt{6 \cdot a^5 \cdot b}[/tex]
= [tex]3 a b \sqrt{6.a^4.a.b}$[/tex]
= [tex]3.a.b.a^{2} \sqrt{6ab}[/tex]
[tex]= 3a^{3}b\sqrt{6ab}[/tex]
So the most simplified answer to the expression [tex]\sqrt{54a^{7}b^{3} }[/tex] is [tex]3a^{3}b\sqrt{6ab}[/tex].
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Your question is incomplete, but most probably your full question is:
Sadie simplified the expression [tex]\sqrt{54 a^7 b^3}[/tex], , where [tex]$a \geq 0$[/tex] as shown:
[tex]\sqrt{54 a^7 b^3}=\sqrt{3^3 \cdot 6 \cdot a^2 \cdot a^5 \cdot b^2 \cdot b}=3 a b \sqrt{6 a^5 b}[/tex]
Describe the error Sadie made, and explain how to find the correct answer.
A student-faculty government committee of 4 people is to be formed from 16 student volunteers and 5 faculty volunteers. Find the probability that the committee will consist of the following, assuming the selection is made at random: (a) All faculty members. Round your answer to five decimal places. The probability that the committee will consist of all faculty members is (b) Two students and two faculty members.Round your answer to five decimal places. The probability that the committee will consist of two students and two faculty members is (c) All students. Round your answer to five decimal places. The probability that the committee will consist of all students is (d) One faculty member and three students. Round your answer to five decimal places. The probability that the committee will consist of one faculty member and three students is
16 student volunteers and 5 faculty volunteers will make up the four-person student-faculty government committee. the probability of the likelihood that the following members will be on the committee:
A) All academic staff
Probability is equal to 5C4 / 21C4 or 5/5985.
The likelihood that the committee will be made up of only academics is 0.000835.
b) Two pupils and two professors equal (16C2 x 5C2) / 21C4.
There is a 0.40100 chance that the committee will be made up of two students and two faculty members.
b) All pupils = 16C4 / 21C4 = 1820 / 5985
The likelihood that every student will be represented on the committee is 0.30409
d) Three students and one professor equal 5c1 * 16c3 / 21c4 or 5 * 560 / 5985.
There is a 0.46783 percent chance that the committee will be made up of one professor member and three students.
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