A counterexample that shows that all the integers are not divisible by 3 is given as follows:
2.
How to obtain the counterexample?The statement for this problem is given as follows:
"All the positive integers are divisible by 3".
The statement is false, as only numbers whose sum of the digits is a multiple of 3 are divisible by 3, hence for example, the number 2 is not divisible by 3.
The counterexample is the statement that proves that a conjecture(another statement) is false, hence the number 2 is the counterexample showing that not all positive statements are divisible by 3.
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Find the shortest distance between the line L1 passing through the points A =
(3,2,1) and B = (2,1,0) and the line L2 passing through the points C = (2,4,−1) and
D = (3,0,−2)
The shortest distance between the two skew lines is equal to 11√38 / 38 units.
How to find the shortest distance between two skew lines in space
According to linear algebra, lines are defined by vectorial equations of the form:
(x, y, z) = P(x, y, z) + t · T(x, y, z)
Where:
P(x, y, z) - Point contained in the line.t - Parameter.T(x, y, z) - Vector slope.And the shortest distance between two skew lines is determined by the following expression:
[tex]d = \frac {|[P_{2} (x, y, z) - P_{1}(x, y, z)] \bullet [T_{1} (x, y, z) \times T_{2} (x, y, z)]|}{|T_{1} (x, y, z) \times T_{2} (x, y, z)|}[/tex]
First, determine the points contained in each line:
P₁(x, y, z) = (3, 2, 1)
P₂(x, y, z) = (2, 4, - 1)
Second, find each vector slope:
T₁(x, y, z) = (2, 1, 0) - (3, 2, 1)
T₁(x, y, z) = (- 1, - 1, - 1)
T₂(x, y, z) = (3, 0, - 2) - (2, 4, - 1)
T₂(x, y, z) = (1, - 4, - 1)
Third, determine the vector subtraction:
P₂(x, y, z) - P₁(x, y, z) = (2, 4, - 1) - (3, 2, 1)
P₂(x, y, z) - P₁(x, y, z) = (- 1, 2, - 2)
Fourth, determine the cross product:
T₁(x, y, z) × T₂(x, y, z) = (- 1, - 1, - 1) × (1, - 4, - 1)
T₁(x, y, z) × T₂(x, y, z) = (- 3, - 2, 5)
Fifth, use the dot product:
[tex][P_{2} (x, y, z) - P_{1}(x, y, z)] \bullet [T_{1} (x, y, z) \times T_{2} (x, y, z)] = (- 1, 2, - 2) \,\bullet\,(- 3, - 2, 5)[/tex]
[tex][P_{2} (x, y, z) - P_{1}(x, y, z)] \bullet [T_{1} (x, y, z) \times T_{2} (x, y, z)] = 3 - 4 - 10[/tex]
[tex][P_{2} (x, y, z) - P_{1}(x, y, z)] \bullet [T_{1} (x, y, z) \times T_{2} (x, y, z)] = - 11[/tex]
Sixth, calculate the norm of the cross product:
|T₁(x, y, z) × T₂(x, y, z)| = √[(- 3)² + (- 2)² + 5²]
|T₁(x, y, z) × T₂(x, y, z)| = √38
Finally, determine the shortest distance between the two skew lines:
d = |- 11| / √38
d = 11 / √38
d = 11√38 / 38
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Find the length of the third side. If necessary, round to the nearest tenth. 9 12
The required length of the third side of the right-angle triangle is 15 units.
What are Pythagorean triplets?In a right-angled triangle, its sides, such as the hypotenuse, are perpendicular and the base is Pythagorean triplets.
Here,
For the right triangle lenght of the two legs to be 9 and 12 units, a measure of the third side is to be determined.
So, Applying the Pythagoras theorem,
h² = p² + b²
h = √9² + 12²
h = √225
h = 15
Thus, the required length of the third side of the right-angle triangle is 15 units.
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A city has cone-shaped buildings for storing salt and sand for icy roads. Each
building has a radius of 50 feet and a height of 30 feet. Find the volume of the
building. Use 3.14 for 7.
OA. 19,625 ft³
OB. 78,500 ft3
O C. 4710 ft³
OD. 235,500 ft3
Which is the best estimate of the difference between 5 5/6 and 3 1/4
The best estimate of the difference between the two numbers is 31/12 or 2 7/12.
What are mixed fractions?A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.
to transform a mixed fraction into an incorrect fraction.
By denominator, divide the numerator.
Take the quotient as a whole number and use the remaining amount as the proper fraction's numerator while maintaining the original denominator.
Covert the mixed fraction into improper fractions:
5 5/6 = 35/6
3 1/4 = 13/4
The difference between the two numbers is:
35/6 - 13/4
Take the LCM.
70/13 - 39/12
(70 - 39) / 12
31/12 = 2 7/12
Hence, the best estimate of the difference between the two numbers is 31/12 or 2 7/12.
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for a certain kind of plaster work, 1.1 cu yd of sand are needed for every 100 sq yd of surface. How much sand will be needed for every 100 sq yd of surface. how much is sand will be needed for 380 sq yd of surface
The amount of sand needed for every 100 square yard of surface would be 1. 1 cubic yards.
The amount of sand needed for 280 square yards would be 4 .18 cubic yards of sand.
How to find the sand needed ?The question says that 1. 1 cubic yards of sand are needed for every 100 square yards of surface so this is the amount of sand needed per 100 square yards.
As for 380 square yards, the amount of sand needed can be found by the formula :
= ( 380 square yards of surface x 1. 1 cubic yards of sand ) / 100 square yards of surface
= 418 / 100
= 4 .18 cubic yards of sand
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the statistical methods of analysis of variance assume that the populations are normally distributed.A. TrueB. False
The statement of statistics "the statistical methods of analysis of variance assume that the populations are normally distributed" is true. So the correct answer is (a)True.
What is statistics?Statistics is a branch of applied mathematics that involves collecting, describing, analyzing, and drawing conclusions from quantitative data. It gives us information to figure out how things work. Statistics are used to conduct research, evaluate results, develop critical thinking, and make informed decisions. Statistics can be used to examine nearly any area of research to find out when and why things happen, and whether their recurrence is predictable.
Who uses statistics?Statistics are used in many different applications and professions. Statistics are generated each time data is collected and analyzed. This ranges from government agencies to academic research to investment analysis.
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Select the correct word in each sentence :) Thanks!
A phase change occurs when the kinetic energy increases/decrease enough so that the attraction between molecules pulls them together.
A substance with weaker molecular attraction will freeze at a higher/lower temperature because it requires more/less energy to be TAKEN OUT before the attraction pulls the molecules together.
A substance with stronger molecular attraction will evaporate at a higher/lower temperature because it requires more/less energy to be ADDED to overcome attraction between the molecules.
A phase change occurs when the kinetic energy decrease enough so that the attraction between molecules pulls them together.
A substance with weaker molecular attraction will freeze at a lower temperature because it requires more energy to be taken out before the attraction pulls the molecules together.
A substance with stronger molecular attraction will evaporate at a higher temperature because it requires less energy to be added to overcome attraction between the molecules.
What is a phase change?In Science, a phase change refers to the change in the state of matter of a given chemical compound or substance. Additionally, some examples of a phase change include the following;
Solid to liquidLiquid to gasGas to solidLiquid to solidGenerally speaking, a change in the state (phase) of matter that results in the release of energy is known as an exothermic reaction and they include:
Deposition.Condensation.Freezing.In conclusion, sublimation, melting, and evaporation are other processes that are associated with a change in the state (phase) of matter.
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Let V be an inner product space, S and S0 be subsets of V, and W be a finite-dimensional subspace of V.
Prove:S0⊂S implies S⊥⊂S⊥0
Pf: Let x∈S⊥, for all y∈S, the inner product ⟨x,y⟩ is given ⟨x,y⟩=0
, which implies y∈S0 Then S0⊂S, x∈S⊥0.Proved.
Prove: W=(W⊥)⊥
Pf: Let x∈W and y∈W⊥. By definition, for all y∈W⊥, the inner product is given by ⟨x,y⟩=0
. Using x∈W, this gives W⊂(W⊥)⊥
How to prove the other side?
Let V be an inner product space, S and S0 be subsets of V, and W be a finite-dimensional subspace of V. To prove the other side,
1 ) Suppose (e1,…,en) is basis for W. Suppose x∈(W⊥)⊥. Consider the projection w of x onto W, specifically:
w=⟨x,e1⟩e1+…+⟨x,en⟩en∈W.
Then, x−w is perpendicular to each ei, since
⟨x−w,ei⟩=⟨x,ei⟩−∑j=1n⟨⟨x,ej⟩ej,ei⟩=⟨x,ei⟩−∑j=1n⟨x,ej⟩⟨ej,ei⟩=⟨x,ei⟩−∑j=1n⟨x,ej⟩δij=⟨x,ei⟩−⟨x,ei⟩=0.
Since the linear map ⟨⋅,x−w⟩ is constantly 0 on the basis of W, it is constantly zero on all of W, hence x−w∈W⊥.
But then, since x∈(W⊥)⊥, we have ⟨x−w,x⟩=0, and since ⟨x−w,w⟩=0,
∥x−w∥2=⟨x,x−w⟩−⟨w,x−w⟩=0,
i.e. x=w∈W, completing the proof.
2 ) Suppose that w∈(W⊥)⊥
then ⟨w,x⟩=0
for all x∈W⊥
If w∉W, then w=v+v′ where v∈W and v′∈W⊥∖{0}.
Then.
0=⟨w,x⟩=⟨v,x⟩+⟨v′,x⟩=⟨v′,x⟩
for all x∈W⊥.
However, v′∈W⊥ and ⟨v′,v′⟩≠0 so it is a contradiction.
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What is the average atomic mass of the element in the data table?
37.96 is the average atomic mass of the element in the data table .
What does average mean?
The average is calculated by dividing the total number of values by the total number of values. It can also be described as mean. The mean in statistics is the average value across the specified sample or data set.
Mean, median, and mode are the three primary categories of average. Each of these methods operates a little bit differently and frequently yields values that diverge a little bit from the norm. The most popular type of average is the mean.
the average atomic mass = 35.97 + 37.96 + 39.96/3
= 113.89/3
= 37.96
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Answer:
39.96
Step-by-step explanation: I think
Scott deposits $300 into an account that pays a simple interest at a rate of 4% per year. How much interest will he be paid in the first 6 years?
Answer:
$72
Step-by-step explanation:
300
4% per year
so 12$ per year,
6 years = 12*6 = 72
Simplify the following union and or insection
(1,13] ∩ [13,19)
The intersection in the below problem is 13
Given equation is
[1,13] ∩ [13,19]
We need to simplify the expression and tell the intersection of the expression
After doing the intersection, we will take all the common elements in two sets
so , we have
[1,13] ∩ [13,9 ] = 13
therefore we get the intersection of the given expression by simplifying it as 13.
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Zak has 18 tennis balls. This i
Matt has 9 more tennis balls
How many tennis balls does
Answer:
The cost of 3 tennis balls and 2 golf balls is $7. The cost of 6 tennis balls and 3 golf balls is$12. Find the cost of 1 tennis ball and 1 golf ball.
Step-by-step explanation:
y = x - 11
7x+7y=-21
systems of equations by substitution
Answer: We can solve the system of equations using the substitution method.
First, we'll isolate "y" in one of the equations and substitute it into the other equation:
Y = x - 11
7x + 7y = -21
Substituting the first equation into the second equation:
7x + 7(x - 11) = -21
7x + 7x - 77 = -21
14x = 56
x = 4
Now that we have found the value of x, we can substitute it back into one of the original equations to find the value of y:
Y = x - 11
Y = 4 - 11
Y = -7
The solution to the system of equations is (x, y) = (4, -7).
Step-by-step explanation:
The value of x and y in the equation is 4 and -7 respectively
What is Simultaneous equation?Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 4x − 4y = 4.
Using substitution method to solve the system,
y = x-11 equation 1
7x+7y = -21 equation 2
substitute x-11 for y in equation 2
7x + 7( x-11) = -21
7x + 7x -77 = -21
14x = -21+77
14x = 56
divide both sides by 14
x = 56/14
x = 4
substitute 4 for x in equation 1
y = 4-11
y = -7
therefore the value of x and y is 4 and -7 respectively
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Consider an urn containing four balls, numbered 110, 101, 011 and 000, from which one ball is drawn at random. For k = 1, 2, 3 let Ak be the event of drawing a ball with 1 in the kth position. Show your work in answering the following:a) Are A1, A2, and A3 pairwise independent?b) Are A1, A2, and A3 mutually independent?
a)The events A1, A2, and A3 are pairwise independent.
b) The events are not mutually independent.
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
Observe the given numbers:
Out of 4 numbers, 2 have 1 at first position
so outcomes in event A1 is
A1 ={ 110, 101}
Similarly, possible outcomes in A2 is
A2 ={110, 011}
A3 = {101,111}
The probabilities of events are
P(A1) = 2/4 = 0.5
P(A2) = 2/4 = 0.5
P(A3) = 2/4 = 0.5
Also,
(A1 and A2) = {110}
(A1 and A3) = {101}
(A2 and A3) = {011}
The probabilities are
P(A1 and A2) = 1 /4 = 0.25
P(A1 and A3) = 1 /4 = 0.25
P(A2 and A3) = 1 /4 = 0.25
a)
From above we have
P(A1 and A2) = P(A1)P(A2) = 0.25
P(A1 and A3) = P(A1)P(A3) = 0.25
P(A2 and A3) = P(A2)P(A3) = 0.25
So events A1, A2, and A3 are pairwise independent.
b)
Since P(A1 and A2), P(A1 and A3) and P(A2 and A3) are not equal to zero so events are not mutually independent.
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a)The events A1, A2, and A3 are pairwise independent.
b) The events are not mutually independent.
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
Observe the given numbers:
Out of 4 numbers, 2 have 1 at first position
so outcomes in event A1 is
A1 ={ 110, 101}
Similarly, possible outcomes in A2 is
A2 ={110, 011}
A3 = {101,111}
The probabilities of events are
P(A1) = 2/4 = 0.5
P(A2) = 2/4 = 0.5
P(A3) = 2/4 = 0.5
Also,
(A1 and A2) = {110}
(A1 and A3) = {101}
(A2 and A3) = {011}
The probabilities are
P(A1 and A2) = 1 /4 = 0.25
P(A1 and A3) = 1 /4 = 0.25
P(A2 and A3) = 1 /4 = 0.25
a)
From above we have
P(A1 and A2) = P(A1)P(A2) = 0.25
P(A1 and A3) = P(A1)P(A3) = 0.25
P(A2 and A3) = P(A2)P(A3) = 0.25
So events A1, A2, and A3 are pairwise independent.
b)
Since P(A1 and A2), P(A1 and A3) and P(A2 and A3) are not equal to zero so events are not mutually independent.
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A flu epidemic occurs in Middletown schools and each student is either susceptible, sick, or infected. The percentage of students in each category by grade level is given below. Infected 70% 10% 20%
[S]= Sick 65% 15% 20%
Susceptible 60% 25% 15%
The population distribution of the Middletown school district is given below
HighSchool 1115 1100
[P] = MiddleSchool 830 795
Elementary 1610 1580
In this matrix question where percentages are listed, answers to all these questions are written below.
In the matrix given in the image, we can calculate following things:
a. S32 is a value that represents the percentage of sick students in the third grade of the elementary school. From data we can say it is 10%
b. P22 is a value that represents the number of middle school students in the second grade. From data we can say there are 795 such boys.
c. To find[tex][s] * [p][/tex] we need to multiply the percentage of students in each category by the corresponding population in each grade level.
[tex]\left[\begin{array}{ccc}1190.75&1311.75\\1194&1366.25\\1233&1405.5\end{array}\right][/tex]
Columns: Girls, Boys
Rows: Susceptible, Sick, Infected
d. [tex][[s] * [p]]21[/tex] represents the number of sick students in the second grade of the elementary school.
It represents that 1194 girls are sick.
e. To find the number of sick girls, we need to multiply the number of girls in each grade level by the corresponding percentage of sick students.
1194
f. To find the number of infected boys, we need to multiply the number of boys in each grade level by the corresponding percentage of infected students.
1406
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Complete Question: Image is uploaded for it.
a. Describe what S32 value is and what it will represent
b. Describe what P22 value is and what it will represent
c. Find [tex][s] * [p][/tex]
d. Describe what[tex][[s] * [p]]21[/tex] value is and what it will represent
e. How many sick girls are present?
f. Number of boys infected?
Consider a market characterized by the following inverse demand and supply functions: PX = 50 − 4QX and PX = 10 + 2QX. Compute the surplus producers receive when a $30 per unit price floor is imposed on the market.
A $75
B $35
C $25
D $50
Computing the surplus producers receive when a $30 per unit price floor is imposed on the market is option C.$25.
How did we get the value?To calculate the surplus producers receive, we need to find the difference between the price they receive at a given quantity and the price they would have received in the absence of the price floor.
When a price floor of $30 per unit is imposed on the market, the quantity supplied and demanded at this price are:
QX = (50 - 30)/4 = 5 units (demand)
QX = (30 - 10)/2 = 10 units (supply)
So, the surplus received by the producers is the difference between the price floor and the price they would have received in the absence of the price floor:
Surplus = 30 - (10 + 2 * 10) = 30 - 30 = $0.
However, the surplus for consumers is the difference between the price they would have paid in the absence of the price floor and the price floor:
Surplus = (50 - 4 * 5) - 30 = 25 - 30 = -$5.
So, the total surplus received by producers and consumers combined is $0 + (-$5) = -$5, which means that the price floor imposes a dead weight loss on the market.
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I already graphed it but I need yo figure out the solution. PLEASE HELP:)
I will give you brainlest!!!!
The solution of the system of equations is equal to (3, 4).
What is a point of intersection?In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect or cross each other, which is primarily represented as an ordered pair containing the point that corresponds to the x-coordinate (x-axis) and y-coordinate (y-axis) on a cartesian coordinate.
By critically observing the graph of the lines representing the given system of equations, we can reasonably and logically deduce that the correct solution set lies in Quadrant II and it is denoted by the point of intersection of both the x-coordinate (x-axis) and y-coordinate (y-axis), which is given by ordered pair (3, 4).
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Select the correct answer. If f(x)=x^2/x+3, find f(x+h)
The function operation f( x + h ) in the function f(x) = x² / (x + 3 ) is ( x + h )² / (x + h + 3 ).
What is the function operation f(x + h ) in the given function?A function is simply a relationship that maps one input to one output.
Given that;
f(x) = x² / (x + 3 )f( x + h ) = ?To determine f( x + h ), replace all the occurrence of x with (x + h) in the function and simplify.
f(x) = x² / (x + 3 )
f(x + h) = ( x + h )² / (( x + h ) + 3 )
f(x + h) = ( x + h )² / (x + h + 3 )
Therefore, the operation f(x + h) equals ( x + h )² / (x + h + 3 ).
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A box contains 16 square chips, 12 triangular chips, and 4 circular chips. Identify the ratio of circular chips to square chips in all three forms.
The ratio of circular chips to square chips is 1:4.
What is a ratio?The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.
Given:
A box contains 16 square chips, 12 triangular chips, and 4 circular chips.
The ratio of circular chips to square chips,
= Circular chips / square chips
= 4 / 16
= 1/4
= 1: 4
Therefore, the ratio is 1:4.
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Determine the tip percentage on a restaurant bill, given a subtotal of $41.00 and a total of $49.20. (2 points)
18%
25%
15%
20%
Determine the range, mean, variance, and standard deviation of the sample data set.
12,17,23,15,15,18,19,17,14,15
Statistics is a discipline, principally within applied mathematics, concerned with the systematic study of the collection, presentation, analysis, and interpretation of data.
The measures used in statistics are mean, range, standard deviation, variance etc.
The range can be calculated by finding the difference between the lowest and highest observation i.e. 23 - 12 = 11.
Variance is a measure of dispersion of data points from the mean. In the above given data, the variance is 9.389.
Standard deviation is the square root of the variance, hence, is 3.06.
Mean = sum of data divided by no of observations (10).
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find the ear in each of the following cases: input area: output area: stated rate (apr) compounding periods per year effective rate (ear) 7.80% 4 15.30% 12 12.40% 365 11.40% infinite
The effective annual rate (EAR) is the actual rate of interest that is earned or paid over a given period of time, taking into account the compounding of interest. For example, a stated rate of 7.80% with 4 compounding periods per year would result in an EAR of 15.30%.
The effective annual rate (EAR) is a measure of the actual rate of interest that is earned or paid over a given period of time. It takes into account the effect of compounding, which is the process of earning interest on both the principal and the accumulated interest. This means that the rate of return can increase over time. The EAR is calculated by taking the stated rate of interest, which is the rate of interest stated by the lender, and multiplying it by the number of compounding periods per year. For example, if the stated rate is 7.80% and the compounding periods per year are 4, then the EAR would be 15.30%. Similarly, if the stated rate is 12.40% and the compounding periods per year are 365, then the EAR would be 11.40%. If the compounding period is infinite, then the EAR will be the same as the stated rate, in this case 12.40%. Therefore, the EAR is the actual rate of return that is earned or paid over a given period of time.
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Find X and round to the nearest tenth.
The side length x of the triangle rounded to the nearest tenth is 31.3.
What is the numerical value of x?The figure in the image is a right triangle.
Angle θ = 38°Adjacent to angle θ = 40Opposite to angle θ = xTo determine the value of x, use trigonometric ratio.
Tangent = Opposite / Adjacent
tan( 38° ) = x / 40
Solve for x
x = tan( 38° ) × 40
x = 0.781285 × 40
x = 31.3
Therefore, the value of x is 31.3.
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Here is my question please show all of your work and answer as well
A shipment of 12 X-Ray machines includes 4 that are defective. In how many ways can a hospital purchase 5 of these machines and receive at least 2 of the defective machines
Answer:
Step-by-step explanation:
The number of ways the hospital can purchase 5 machines and receive at least 2 of the defective machines is calculated as follows:
The number of ways the hospital can receive exactly 2 defective machines is C(4,2) = 6, where C(n, k) is the number of combinations of n things taken k at a time.
The number of ways the hospital can receive exactly 3 defective machines is C(4,3) = 4.
The number of ways the hospital can receive exactly 4 defective machines is C(4,4) = 1.
So, the total number of ways the hospital can purchase 5 machines and receive at least 2 of the defective machines is 6 + 4 + 1 = 11.
Missing value in frequency distribution table
Based on the data, the total number of people would be 350. So the missing value in the table would be 54.
How to find missing value from table?To find the missing value of people in the graph we must do the following procedure. We must add the number of people who are already registered in the graph in the frequency column.
Additionally, we must establish a total number of people, for example 350. In this case we must subtract the result of the people registered in the graph from the total number of people:
350 - 295 = 54.
Then we can establish that the remaining number of people (54) corresponds to the frequency table.
Note: This question is incomplete. The complete information is here:
Total number of people: 350
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A large bowl can hold 3.5 pints. A smaller bowl can hold less than 60% of the amount. Graph the possible amounts, in quarts, that can be held by the smaller bowl.
Answer: qt=0.6
Step-by-step explanation:
3.5=
60%=0.6
qt=0.6
about two Daily Food Drive by Mr. Garcia's Homeroom Mean number of canned goods collected: 18.75 Median number of canned goods collected: 18 Range of data: 11 IOR of data: 4.25 The range for Mr. Garcia's homeroom is less than the range for Ms. Vicario's homeroom. The IQR for Mr. Garcia's homeroom is less than the IQR for Ms. Vicario's homeroom. The number of canned goods collected by Ms. Vicario's homeroom was more variable than the number of canned goods collected by Mr. Garcia's homeroom.
Mr. Garcia's homeroom had a more consistent collection of canned goods.
Ms. Vicario's homeroom varied more widely with the collection of canned goods.
What is the interquartile range?An interquartile range is a measure of the difference between the upper and lower quartiles of a dataset.
W can find the values of the upper and lower quartile and median from a box plot.
The middle line is the median and the first line is the lower quartile and the last line is the upper quartile.
The formula used is Upper quartile - Lower quartile.
We have,
The two daily food drives:
Mr. Garcia:
The mean number of canned goods collected = 18.75.
The median number of canned goods collected = 18.
The range of data for Mr. Garcia's homeroom = 11.
The IQR (interquartile range) of data = 4.25.
Ms. Vicario's homerooms:
The range of data = greater than 11.
The IQR of data = greater than 4.25.
The number of canned goods collected = more variable than the number of canned goods collected by Mr. Garcia's homeroom.
Based on these observations.
We can conclude that,
Mr. Garcia's homeroom had a more consistent collection of canned goods. i.e
Smaller range and IQR.
Ms. Vicario's homeroom varied more widely with the collection of canned goods.
i.e
Wider range and IQR
Thus,
Mr. Garcia's homeroom had a more consistent collection of canned goods.
Ms. Vicario's homeroom varied more widely with the collection of canned goods.
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approximatly 31,500 citizens of a country died in automobile accidents in 2015, express this toll in deaths per day. round to the nearest whole number. There are approximatly how many deaths due to automobile accidents
Using simple division we know that 86 people or citizens dies each day in 2015.
What is division?One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division.
The other operations are multiplication, addition, and subtraction.
Division in mathematics is the process of dividing an amount into equal parts.
For instance, we may split a group of 20 people into four groups of 5, five groups of 4, and so on.
So, we know that:
31,500 people died in 2015.
We also know that 2015 had 365 days.
Then, people died easily day would be:
= 31,500/365
= 86.30
Rounding off: 86 people
Therefore, using simple division we know that 86 people or citizens dies each day in 2015.
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Translate triangle P by the vector 2
y
P
4
3
No W
2
1
-5 -4 -3 -2 -10
-1
2344
-2
-3
-4
2 3 4 5
Step-by-step explanation:
The translation of triangle P by the vector (2, 3) results in the triangle being moved 2 units to the right and 3 units up. The new coordinates of the triangle are (6, 7), (4, 6), and (3, 5).
A city planner designs a park that is a quadrilateral with vertices at J(−3, 1), K(3, 3), L(5, −1), and M(−1, −3). There is an entrance to the park at the midpoint of each side of the park. A straight path connects each entrance to the entrance on the opposite side. Assuming each unit of the coordinate plane represents 10 meters, what is the total length of the paths to the nearest meter? Round your answer to the nearest whole number.
Answer: To determine the length of the paths connecting the entrance to the opposite entrance, we first need to find the midpoint of each side of the park. Then, we will use the distance formula to calculate the distance between each pair of midpoints.
Let's begin by finding the midpoint of each side of the park.
JK: (-3 + 3, 1 + 3) / 2 = (0, 2)
KL: (3 + 5, 3 - 1) / 2 = (4, 2)
LM: (5 - 1, -1 - -3) / 2 = (2, -2)
MJ: (-1 + -3, -3 + 1) / 2 = (-2, -1)
Next, we'll use the distance formula to calculate the distance between each pair of midpoints.
JK: sqrt((4 - 0)^2 + (2 - 2)^2) = sqrt(16 + 0) = 4
KL: sqrt((2 - 4)^2 + (-2 - 2)^2) = sqrt(16 + 16) = 4 sqrt(2)
LM: sqrt((-2 - 2)^2 + (-1 + 2)^2) = sqrt(16 + 9) = sqrt(25) = 5
MJ: sqrt((-2 - 0)^2 + (-1 - 2)^2) = sqrt(4 + 9) = sqrt(13)
The total length of the paths is 4 + 4 sqrt(2) + 5 + sqrt(13), which when rounded to the nearest whole number is 14.
Step-by-step explanation: