Answer:
Isiah Thomas
Step-by-step explanation:
I amazing fact
Answer:
the correct answer is 4
Step-by-step explanation:
yea sorry i don’t know step-by-step
Which state is located at point C?
a map of the United States. New York, Indiana, and Kansas are labeled. There is an A marking the state south of New York along the Atlantic coast. There is a B marking the state east of Indiana. There is a C marking the state north of Indiana. There is a D marking the state northeast of Kansas. There is an E marking the state south of Kansas.
New Jersey
Ohio
Michigan
Iowa
According to the information provided, the state is at point C, Michigan.
Based on the information provided, the state located at point C is Michigan.
What is logical thinking?Logical reasoning consists of aptitude questions that require logical analysis to arrive at a suitable solution. Most of the questions are conceptual, the rest are unconventional.
Logical thinking follows he is divided into two types.
Oral reasoning:
It is the ability to logically understand concepts expressed in words and solve problems. Oral reasoning tests your ability to extract information and meaning from sentences. Non-verbal thinking:
It is the ability to logically understand concepts represented by numbers, letters, and combinations of numbers and words and solve problems. Nonverbal reasoning tests your ability to reason and guide the logic and implications of information in a problem.
Much of the logic curriculum can be classified into his two types above.
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Mr. Smith earns $23.20 per hour for the first 40
hours he works in a week. He earns 1.5 times that
amount per hour for each hour beyond 40 hours in
a week. Last week Mr. Smith worked 51.5 hours.
How much money did he earn last week?
A) $400.20
B) $1,328.20
C) $928.00
D) $1,194.80
Answer:For the first 40 hours, Mr. Smith earned:
$23.20/hour × 40 hours = $928.00
For the additional 11.5 hours, he earned:
$23.20/hour × 1.5 = $34.80/hour
So, for these hours, he earned:
$34.80/hour × 11.5 hours = $400.20
Adding these amounts together, we get:
$928.00 + $400.20 = $1,328.20
Therefore, Mr. Smith earned $1,328.20 last week.
Step-by-step explanation:
Miguel bought 22 pounds of flour for $12. How many dollars did he pay per pound of flour?
Jaxson has x nickels and y dimes, having a maximum of 26 coins worth at least
$1.80 combined. A maximum of 8 of the coins are nickels and no less than 18 of the coins are dimes. Solve this system of inequalities graphically and determine one possible solution.
One possible solution is for Jaxson to have 8 nickels and 18 dimes.
What exactly is a simple inequity?Inequality depicts the relationship of two objects or values. For instance, 3 is greater than 2, 1 is less than 5, and 5 is the same as 3. These are straightforward and well-known inequalities.
Begin by composing the inequalities that represent the given conditions:
Jaxson has a total of 26 coins: x + y ≤ 26
The total worth of the coins is at least $1.80: 0.05x + 0.1y ≥ 1.8
Jaxson has a total of eight nickels: x ≤ 8
Jaxson has a total of 18 dimes: y ≥ 18
To find the feasible region of solutions, we can graph these inequalities on a coordinate plane.
We can graph the inequality x + y 26 by drawing a line with slope -1 and y-intercept 26. The region beneath the line is shaded to indicate that the sum of x and y must be less than or equal to 26.
To graph the inequality 0.05x + 0.1y 1.8, rewrite it as 0.5x + y 18 and draw a line with slope -0.5 and y-intercept 18. The region above the line is shaded to indicate that the total value of the coins must be at least $1.80.
To graph the inequality x 8, we can draw a vertical line at x = 8 and shade the region to the left of the line to show that Jaxson can only have 8 nickels.
To graph the inequality y 18, draw a horizontal line at y = 18 and shade the region above the line to show that Jaxson has at least 18 dimes.
The shaded area that satisfies all four inequalities is the feasible region. In this region, one possible solution is the point (8, 18), which corresponds to Jaxson having 8 nickels and 18 dimes. We can verify that this point fulfils all four inequalities:
8 + 18 = 26 ≤ 26
0.05(8) + 0.1(18) = 1.8 ≥ 1.8
8 ≤ 8
18 ≥ 18
As a result, one solution is for Jaxson to have 8 nickels and 18 dimes.
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In the coordinate plane, the points X9, 5, Y−−3, 6, and Z−8, 4 are reflected over the x-axis to the points X′, Y′, and Z′, respectively. What are the coordinates of X′, Y′, and Z′?
Answer:
When a point is reflected over the x-axis, the x-coordinate remains the same, but the y-coordinate is multiplied by -1.
So, the coordinates of X' are (9, -5) since the x-coordinate remains the same and the y-coordinate is multiplied by -1.
Similarly, the coordinates of Y' are (-3, -6) and the coordinates of Z' are (-8, -4).
Therefore, X′ is (9,−5), Y′ is (−3,−6), and Z′ is (−8,−4).
4 letters are typed, with repetition allowed. what is the probability that all 4 will be vowels? write your answer as a percent. round to the nearest hundredth of a percent as needed.
Answer:
There are 5 vowels in the English alphabet: A, E, I, O, and U. Since repetition is allowed, each letter can be any one of the 5 vowels.
The probability of the first letter being a vowel is 5/26, since there are 5 vowels out of 26 letters in total. The probability of the second letter being a vowel is also 5/26, and so on for the third and fourth letters.
Since the events of each letter being a vowel are independent, we can use the multiplication rule to find the probability of all four letters being vowels:
P(all 4 vowels) = (5/26) x (5/26) x (5/26) x (5/26) = (5/26)^4
Using a calculator, we get:
P(all 4 vowels) ≈ 0.0023
To express the answer as a percent, we multiply by 100:
P(all 4 vowels) ≈ 0.23%
Therefore, the probability that all 4 letters typed will be vowels, with repetition allowed, is approximately 0.23%.
Step-by-step explanation:
Given a list (0, 1, 1, 2, 3, 5, 8, 13, 17), the binary search algorithm calls BinarySearch(list, 0, 8, 3). What is the index of the middle element?
The index of the middle element is 4.
The list (0, 1, 1, 2, 3, 5, 8, 13, 17), the binary search algorithm calls Binary Search (list, 0, 8, 3). The index of the middle element is 4. The binary search algorithm works by dividing a list into halves and looking at the value in the middle of the list. This is compared with the target value, and based on the comparison, one-half of the list is discarded as the search is continued in the other half. This is continued until the target value is found or it is clear that it is not on the list. In the given case, the list is (0, 1, 1, 2, 3, 5, 8, 13, 17), and the algorithm calls Binary Search(list, 0, 8, 3).
Here, the first parameter of the Binary Search function is the list, the second parameter is the lower index of the part of the list being searched, the third parameter is the upper index, and the fourth parameter is the value being searched. In the given case, the lower index is 0, the upper index is 8, and the value being searched is 3. The index of the middle element in the list is calculated as (0 + 8) / 2 = 4.
Therefore, the index of the middle element is 4.
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What value of x would make the denominator of the rational expression x2+2x+5/
x+5 equal to 0?
Answer:
The Answer is -5 (negative five)
A granola bar weighs 0.84 ounces. There are 8 bars in a box. What is the
total weight of the granola bars using the correct number of significant digits
it's not 6.72 i need the answer with significant digits
The total weight of the granola bars in the box is 6.7 ounces.
How to find the total weight of the granola barsTo calculate the total weight of the granola bars with the correct number of significant digits, we need to multiply the weight of a single bar by the number of bars in the box.
Given parameters:
Weight of a single bar = 0.84 ouncesNumber of bars in the box = 8Total weight of the granola bars
= Weight of a single bar x Number of bars in the box
= 0.84 ounces x 8
= 6.72 ounces
Since the weight of a single bar is given with two significant digits, and we have multiplied it by a whole number, the answer should be reported with two significant digits.
so we can say that, the total weight of the granola bars is 6.7 ounces.
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A tank is full of water when a valve at the bottom of the tank is opened. The equation V = 62(151 - t) gives the volume of water in the tank, in cubic meters, after t hours.What is the volume of water in the tank before the valve is opened?__ cubic metersHow long does it take the tank to fully empty?___ hoursFind an equation for DV/dtdV/dt = __ PreviewWhat is the flow rate after 23 hours? ____ Select an answerWhen is the water flowing out of the tank the fastest?t= ____ hours
1. The volume of water in the tank before the valve is opened is 9362 cubic meters. 2. It takes 151 hours for the tank to fully empty.
What is modelling in math?Modeling is the process of representing and analyzing real-world events using mathematical ideas and methods. It is a crucial component of mathematics because it enables systematic, quantitative prediction, problem-solving, and understanding of complicated processes.
We may learn about the behavior of systems, test hypotheses, and arrive at wise conclusions by using mathematical models. We may use models to enhance processes, forecast results, and discover key factors.
The equation of the volume is given as V = 62(151 - t).
At t= 0 we have the volume as:
V = 62(151 - 0) = 9362 cubic meters
To empty the tank we take V = 0:
0 = 62(151 - t)
151 - t = 0
t = 151
Hence, the volume of water in the tank before the valve is opened is 9362 cubic meters and it takes 151 hours for the tank to fully empty.
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Verify that W is a subspace of V. Assume that V has the standard operations.
W is the set of all 3x2 matrices of the form [a,b;(a+b),0;0,c] and V=M[-subscript-(3,2)]
The zero vector: The zero vector 0 = [0,0;0,0;0,0] is also a member of W. Thus, the third criterion is satisfied.
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The volume of a solid hemisphere of radius 2 cm
Answer:
The volume of a solid hemisphere with radius r is given by the formula:
V = (2/3)πr^3
In this case, the radius of the hemisphere is 2 cm. Substituting this value into the formula, we get:
V = (2/3)π(2 cm)^3
V = (2/3)π(8 cm^3)
V = (16/3)π cm^3
Therefore, the volume of the solid hemisphere is (16/3)π cubic centimeters.
Answer:
(16/3)π cm³ ≈ 16.76 cm³ (nearest hundredth)
Step-by-step explanation:
The volume of a solid hemisphere is given by the formula:
[tex]\boxed{V = \dfrac{2}{3}\pi r^3}[/tex]
where r is the radius of the hemisphere.
Substitute the given radius, r = 2 cm, into the formula, and solve for V:
[tex]\begin{aligned}\implies V &= \dfrac{2}{3}\pi(2)^3\\\\&= \dfrac{2}{3}\pi \cdot 8\\\\&= \dfrac{16}{3}\pi\; \sf cm^3\end{aligned}[/tex]
Therefore, the volume of the solid hemisphere of radius 2 cm is (16/3)π cm³ or approximately 16.76 cm³ (nearest hundredth).
The inside diameters of bearings used in an aircraft landing gear assembly are known to have a standard deviation of A random sample of 15 bearings has an average inside diameter of 8. 2535 cm. (a) Test the hypothesis that the mean inside bearing diameter is 8. 25 cm. Use a two-sided alternative and (b) Find the P-value for this test. (c) Construct a 95% two-sided confidence interval on the mean bearing diameter
(a) The hypothesis that the mean inside bearing diameter is 8. 25 cm is 6.78.
(b) The p value is zero because if we observe a sample that is unlikely to fall below zero (if the statistician can detect it, we can get a p-value of exactly zero.
(c) At 95% two-sided confidence interval on the mean bearing diameter is 8.2527 or 8.2543.
Hypothesis:
Hypotheses (plural hypotheses) are proposed explanations for phenomena. For a hypothesis to be a scientific hypothesis, the scientific method requires that it can be tested. Scientists often base scientific hypotheses on past observations that cannot be satisfactorily explained by existing scientific theories. Although the words "hypothesis" and "theory" are often used interchangeably, a scientific hypothesis is not the same as a scientific theory. A working hypothesis is a tentatively accepted hypothesis that is proposed for further research in a process that begins with an educated guess or idea.
(a) The hypothesis that the mean inside bearing diameter is 8. 25 cm. By Using the two sided alternative:
H₀= 8.25
H₁ ≠ 8.25
Z = X - 8.25÷ sd/√π
= x - 8.25÷ 0.002/3.14
= 6.78 > 1.96 (CV)
(b) the P-value for this test is:
p( value) = 0
because if we observe a sample that is unlikely to fall below zero (if the statistician can detect it, we can get a p-value of exactly zero.
(c) X ± Zᵃ ÷ sd/√π
= 8.2527 or 8.2543
At 95% two sided confidence interval on the mean bearing diameter is 8.2527 or 8.2543.
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find the circumference of each circle
Answer:
[tex]\large\boxed{\mathtt{C=100 \pi \ in.}}[/tex]
[tex]\large\boxed{\mathtt{C \approx314.16 \ in.}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked for the circumference of this circle.}[/tex]
[tex]\textsf{Let's review what the Circumference of a circle actually is.}[/tex]
[tex]\large\underline{\textsf{What is the Circumference?}}[/tex]
[tex]\textsf{The Circumference is is the length 'on' the circle.}[/tex]
[tex]\textsf{Circumference is the Perimeter of the Circle; The sum of all the curved edges.}[/tex]
[tex]\large\underline{\textsf{How do we find the Circumference?}}[/tex]
[tex]\textsf{To find the Circumference, we should use a common, and simple formula.}[/tex]
[tex]\mathtt{Circumference=(Diameter) \pi}[/tex]
[tex]\textsf{Pi will be multiplied by the Diameter of the Circle.}[/tex]
[tex]\textsf{Because we are given the Diameter, we can start solving for x.}[/tex]
[tex]\large\underline{\textsf{Substitute;}}[/tex]
[tex]\mathtt{Circumference \ (C)=(100 \ in.) \pi}[/tex]
[tex]\large\boxed{\mathtt{C=100 \pi \ in.}}[/tex]
[tex]\large\boxed{\mathtt{C \approx314.16 \ in.}}[/tex]
Rewrite the following in the form log(c).
log(15) -log(3)
The logarithmic expression given as log(15) -log(3) when simplified is log(5).
How to rewrite the logarithmic expressionGiven that
log(15) -log(3)
The form is
log(c)
Using the logarithmic identity that states log(a) - log(b) = log(a/b), we can rewrite the given expression as:
log(15) - log(3) = log(15/3)
And simplifying the expression inside the logarithm, we get:
log(15) - log(3) = log(5)
So the given expression, log(15) - log(3), can be written in the form log(c) as log(5).
This means that the logarithm of 5 is equivalent to the difference between the logarithms of 15 and 3.
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Your science teacher bought 6 posters for the classroom that cost $30. The rainforest posters cost $5.50 each and the ocean posters cost $4 each. How many of each did your teacher buy?
Answer: The science teacher bought 4 rainforest posters and 2 ocean posters.
Step-by-step explanation: Let x be the number of rainforest posters and y be the number of ocean posters that the science teacher bought.
We know that the teacher bought 6 posters in total, so we have:
x + y = 6 (equation 1)
We also know that the cost of the 6 posters was $30, so we have:
5.5x + 4y = 30 (equation 2)
To solve for x and y, we can use either substitution or elimination method. Let's use the elimination method by multiplying equation 1 by 4 and subtracting it from equation 2:
5.5x + 4y = 30
-4x - 4y = -24
Simplifying, we get:
1.5x = 6
x = 4
Substituting x = 4 into equation 1, we get:
4 + y = 6
y = 2
Therefore, the science teacher bought 4 rainforest posters and 2 ocean posters.
Please help me as I’m struggling
Therefore , the solution of the given problem of pie chart comes out to be number of adults who selected math (15) outnumbered the number of minors. (10).
Explain pie charts.
A pie chart, also referred to as a circle diagram, is a graphical representation of each of the values of a particular variable or a method to condense a collection of nominal data. (e.g. percentage distribution). A circle with many parts makes up this kind of chart. Each segment represents a particular group.
Here,
for a two-way table: Party A, Party B, and Party C
Men make up 12 8 % of the population while women make up 16 %.
Total 28 15 19
32 ladies make up the group, to start with.
b) 16 female voters plan to support Party A.
Math, English, and science are studied by adults aged 15 to twenty-one and by children aged ten to ten.
Total 25 24 31
15 people selected math.
b) Reeshma is mistaken. The number of adults who selected math (15) outnumbered the number of minors. (10).
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I NEED HELP ON THIS ASAP, IT'S DUE TODAY!
The inequalities which the number lines represent are as follows;
x > 3
x <= 2.
What are inequalities ?A mathematical comparison and expression of the relationship between two expressions is known as an inequality.
It can be seen as a generalization of an equation and is denoted by a symbol like ">", "", "", or "".
In contrast to an equation, which only has one solution, an inequality may have several answers or none at all.
The values that give rise to an inequity are its remedies.
The range of potential values for a variable is one example of how inequality models limits or limitations in the real world.
They can also be used to describe how two variables relate to one another, such as when one is more than or less than the other.
According to our question-
the inequality is; x <= 2
the inequality is; x > 3
x > 3
x <= 2
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Let k, a_2, a_3, and k, b_2, b_3 be nonconstant geometric sequences with different common ratios. If (a_3-b_3)=2(a_2-b_2) then what is the sum of the common ratios of the two sequences?
The sum of the common ratios is 2.
What is geometric sequences?A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio.
Let the common ratio of the first sequence be denoted by r₁ and the common ratio of the second sequence be denoted by r₂. Then we have:
a₂ = kr₁, a₃ = kr₁²
b₂ = kr₂, b₃ = kr₂²
Substituting these expressions into the given equation,
(a₃ - b₃) = 2(a₂ - b₂)
we get:
kr₁² - kr₂² = 2(kr₁ - kr₂)
Dividing both sides by k (since k is non-zero), we get:
r₁² - r₂² = 2(r₁ - r₂)
We can factor the left-hand side using the difference of squares formula:
(r₁ - r₂)(r₁ + r₂) = 2(r₁ - r₂)
Dividing both sides by (r₁ - r₂) (since r₁ ≠ r₂), we get:
r₁ + r₂ = 2
Therefore, the sum of the common ratios of the two sequences is 2.
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Subtract. Simplify, if possible.
4 1/2-2 3/2
(34
Give your answer as a mixed number.
Answer: 1
Step-by-step explanation:
To subtract mixed numbers, we need to convert them to improper fractions so that we can easily perform the subtraction.
4 1/2 can be written as (4 x 2 + 1) / 2 = 9/2
2 3/2 can be written as (2 x 2 + 3) / 2 = 7/2
Subtract the fractions:
Now that we have both numbers in the form of improper fractions, we can subtract them by finding a common denominator and then subtracting the numerators. In this case, the denominators are already the same, so we can just subtract the numerators.
9/2 - 7/2 = (9 - 7) / 2 = 2/2 = 1
Simplify the result:
Since the result is a proper fraction (i.e., the numerator is smaller than the denominator), we can simplify it to a mixed number. The mixed number that represents the fraction 1 is 1 0/2. However, this can be simplified further to just 1, which is our final answer.
So, the answer is 1.
Q-15) Ahmadi, Inc. has been manufacturing small automobiles that have averaged 50 miles per gallon of gasoline in highway driving. The company has developed a more efficient engine for its small cars and now advertises that its new small cars average more than 50 miles per gallon in highway driving. An independent testing service road-tested 64 of the automobiles. The sample showed an average of 51.5 miles per gallon with a standard deviation of 4 miles per gallon.
a.Formulate the hypotheses to determine whether or not the manufacturer's advertising campaign is legitimate.
b.Compute the test statistic.
c.What is the p-value associated with the sample results and what is your conclusion? Let a = .05.
It has been established that the manufacturer is legal.
The test statistic is 13
The p-value is 0.
a. Formulate the hypotheses:
The hypotheses for this test are:
H 0: μ ≤ 50
H a: μ > 50.
b. test statistic:
The test statistic will be a t-test because we do not know the population standard deviation.
Since this is a one-sided test, we will use a one-sample t-test.
The test statistic can be calculated using the formula below:
Substituting these values into the formula gives:
t = (51.5 - 50) / (4 / √64)
t = 6.5 / 0.5
t = 13
The test statistic is 13.
c. When the p-value associated with the sample results, using a t-distribution table with 63 degrees of freedom (64 - 1), we find that the p-value associated with a t-statistic of 13 is 0.
Therefore, we can reject the null hypothesis and conclude that the manufacturer's advertising is permitted.
The sample provides sufficient evidence to show that the new small cars average more than 50 miles per gallon of gasoline.
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Can someone help me out with these indices?
Using the law of indices, the values of the unknown are 1/2, -2/3, -3, 1, 10, 0, 7/12, and -4/17
What is the result of the indicesTo solve these problems, we need to apply the laws of indices to the question as required.
11. 10⁻³ˣ * 10ˣ = 1/10
using multiplication law of indices;
x = 1/2
12. 3⁻²ˣ ⁺¹ * 3⁻²ˣ ⁻³ = 3⁻ˣ
x = -2/3
13. 4⁻²ˣ * 4ˣ = 64
x = -3
14. 6⁻²ˣ * 6⁻ˣ = 1/216
x = 1
15. 2ˣ * 1/32 = 32
x = 10
16. 2^(-3p) * 2^(2p) = 2^(2p)
p = 0
17. 64 * 16⁻³ˣ = 16³ˣ⁻²
x = 7/12
18. 81^(3n + 2) / 243^(-n) = 3^4
n = -4/17
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A survey found that 34% of the students spend time with your family eating dinner. Oh the 500 student surveyed, about how many spend time with their family eating dinner?
Answer:
A survey found that 34% of the students spend time with your family eating dinner. Oh the 500 student surveyed, about how many spend time with their family eating dinner?
Step-by-step explanation:
If 34% of the students surveyed spend time with their family eating dinner, we can find the approximate number of students who do so by multiplying the percentage by the total number of students surveyed:
34% of 500 students = 0.34 x 500 = 170 students
Therefore, about 170 of the 500 students surveyed spend time with their family eating dinner.
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at a checkout counter customers arrive at an average of 1.5 per minute. find the probabilities that (a) at most 4 will arrive in any given minute. (b) at least 3 will arrive during an interval of 2 minutes.
(a) The probability of at most 4 customers arriving in any given minute is 0.835.
(b) The probability of at least 3 customers arriving in an interval of 2 minutes is 0.668.
Step by step explanation:
(a) To find the probability of at most 4 customers arriving in any given minute, we need to use the Poisson Distribution formula: P(X ≤ x) = Σ (e-λ λk) / k!
where λ is the mean number of customers arriving in one minute, which is 1.5.
Therefore, P(X ≤ 4) = Σ (e-1.5 (1.5)k) / k! = 0.835.
(b) To find the probability of at least 3 customers arriving in an interval of 2 minutes, we need to use the same Poisson Distribution formula.
This time, λ = 3 (the mean number of customers arriving in two minutes).
Therefore, P(X ≥ 3) = 1 - Σ (e-3 (3)k) / k! (where k ranges from 0 to 2)
= 1 - (0.224 + 0.452 + 0.224) = 0.668.
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Graph the system of equations {y=−12x+4y=−12x−2
Answer:
Step-by-step explanation: i hope this help if not let me know so i can fix it
(a) describe the relationship between distance and travel time. (select all that apply.) positive negative moderate weak linear nonlinear
The relationship between distance and travel time. It is not excessively strong or weak. In other words, the rate of change in journey time is moderate and constant with respect to distance.
positive negative moderate weak linear nonlinear relationship between distance and travel time can be described as follows:•
Positive• Linear• Moderate
Explain as we move from point A to point B, the distance covered and the travel time it takes to get there are positively correlated. As the distance increases, the travel time required to reach the destination also increases, resulting in a positive correlation.
The relationship between distance and travel time is linear because the rate at which distance is covered remains constant, resulting in a straight-line relationship on a graph. It means that if distance doubles, the travel time will also double, indicating a linear relationship.
Hence, the linear relationship is also referred to as a direct relationship. On a graph, the line that represents the relationship between distance and travel time is moderate. This implies that the slope of the line is neither too steep nor too gentle.
Thus, it is neither too strong nor too weak. In other words, the rate of change in travel time is consistent as distance changes, making it moderate.
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It takes 5 people 4 hours to clean a hall. How long will it take 8 people to clean the same hall at the same rate?
We can use the formula:
Work = Rate x Time
Let's assume that the amount of work involved in cleaning the hall is the same regardless of the number of people doing the job. Therefore, the amount of work done by 5 people in 4 hours is the same as the amount of work done by 8 people in t hours, where t is the time taken by 8 people to clean the hall.
We can set up an equation based on this:
5 people x 4 hours = 8 people x t hours
Simplifying this equation, we get:
20 = 8t/5
which implies, t = 25/8
Therefore, it will take 25/8 hours or 3 hours and 7.5 minutes for 8 people to clean the hall at the same rate as 5 people.
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FACTOR 6x²- 18x - 60
Answer: 6(x+2)(x-5)
Step-by-step explanation:
1: Factor by grouping- A 6 can be distributed in all 3 terms, when we do this we get 6(x²-3x-10).
2: This is in the form 6(x²+bx+c). So, to continue factoring, just forget about the six for a while and find two factors of c that add up to b. These two factors are -5 and 2.
3: Fill in the blanks with either factor. (x+?)(x+?) We get (x+2)(x-5).
4: Bring back the 6 to the beginning of the equation to get a final answer of 6(x+2)(x-5).
find a basis for the vector space of polynomials of degree at most two which satisfy the constraint . how to enter your basis: if your basis is then enter .
The vector space of polynomials of degree at most two that satisfies the constraint is given by the span
{1 + x + x², 1 - x + x²}.
To find a basis for the given vector space, we first determine the dimensions of the space.
The vector space of polynomials of degree at most two is of the form:
p(x) = a + bx + cx²
This vector space contains infinitely many vectors because it is a function space.
The constraint p(1) = 1 + 2a + b + c = 0 means that the dimension of the subspace is two rather than three.
Next, we will obtain a basis for the vector space of polynomials of degree at most two that satisfy the constraint:
span{1, x - 1, x(x - 1)} is a basis for the subspace of the vector space that satisfies the constraint.
To find the basis for the subspace, we can use the definition of a basis.
A basis is a set of vectors that spans the subspace, and that are linearly independent.
We must demonstrate that this basis spans the subspace and that it is linearly independent.
If p(x) = a + bx + cx² satisfies the constraint p(1) = 0, then we have
1 + 2a + b + c = 0, which means a = (-b - c + 1)/2.
Then p(x) = (-b - c + 1)/2 + bx + cx².
Now, we find a basis for the subspace that satisfies the constraint by selecting vectors and demonstrating that they are linearly independent.
span{1, x - 1, x(x - 1)} is a basis for the subspace because they are linearly independent and span the subspace.
Span{1, x - 1, x(x - 1)} spans the subspace because any polynomial in the subspace can be expressed as a linear combination of the elements of the basis.
1 = (1/2) (1 + x - x(x - 1) - x + x(x - 1)) = (1/2)(1 - x²)x - 1 = x - 1x(x - 1) = x² - x
Since the coefficients of 1, x - 1, and x² - x are unique, the three polynomials are linearly independent, so they form a basis.
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use the slicing method to find the volume of the solid whose base is the region inside the circle with radius 3 if the cross sections taken parallel to one of the diameters are equilateral triangles.
the volume of the solid is [tex]V = π r2 (sqrt(3/4)r) / 3 = π r3 sqrt(3/4) / 3.[/tex]
Plugging in the given values, we get[tex]V = π (3)3 sqrt(3/4) / 3 = 27π/4.[/tex]
The volume of a solid with a circular base and cross sections taken parallel to one of the diameters that are equilateral triangles can be found using the slicing method. The formula for the volume of such a solid is:[tex]V = π r2 h/3,[/tex]where π is the constant pi, r is the radius of the circular base, and h is the height of the solid.
In this case, the radius of the circular base is 3 and the height is equal to the length of the sides of the
equilateral triangles. To find the height, we can use the Pythagorean Theorem. The hypotenuse of the triangle is 2r, so the length of the sides is sqrt(r2 - (r/2)2), which simplifies to sqrt(3/4)r.
for such more questions on equilateral triangles
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