The graph is a coordinate grid with one line that passes through the points 0 comma 1 and 3 comma negative 1 and another line that passes through the points 0 comma negative 1 and 2 comma negative 5.
The system of linear equations is:
y = -2/3x + 1
y = -2x - 1
To determine which graph shows the solution to the system, we need to graph the two equations on the same coordinate grid and find their intersection point, which represents the solution to the system.
For the first equation, y = -2/3x + 1, the y-intercept is 1 and the slope is -2/3. We can use this to find one more point, say by setting x = 3:
y = -2/3(3) + 1 = -1
So one point on the line is (3, -1), and we can plot it on the coordinate grid.
For the second equation, y = -2x - 1, the y-intercept is -1 and the slope is -2. We can use this to find another point, say by setting x = 0:
y = -2(0) - 1 = -1
So another point on the line is (0, -1).
Thus, the answer is a coordinate grid with one line connecting points 0 comma 1 and 3 comma negative 1 and another line connecting points 0 comma negative 1 and 2 comma negative 5.
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Let d be the relation defined on z as follows: for every m, n ∈ z, m d n ⇔ 3 | (m2 − n2). (a) prove that d is an equivalence relation
Since d satisfies all three properties of an equivalence relation, we conclude that d is indeed an equivalence relation on Z.
To prove that d is an equivalence relation on Z, we need to show that it satisfies three properties: reflexivity, symmetry, and transitivity.
Reflexivity: For any m ∈ Z, we have [tex]m^2 - m^2[/tex] = 0, which is divisible by 3. Therefore, m is related to itself under d, so d is reflexive.
Symmetry: If m d n, then [tex]3 | (m^2 - n^2)[/tex]). This means that there exists an integer k such that [tex]m^2 - n^2 = 3k.[/tex]
Rearranging this equation, we get n^2 - m^2 = -3k, which implies that 3 divides (n^2 - m^2) as well. Therefore, n d m, and d is symmetric.
Transitivity: Suppose m d n and n d p. Then, we have [tex]3 | (m^2 - n^2)[/tex] and [tex]3 | (n^2 - p^2)[/tex].
Adding these two equations, we get [tex]3 | ((m^2 - n^2) + (n^2 - p^2)),[/tex], which simplifies to [tex]3 | (m^2 - p^2).[/tex] Therefore, m d p, and d is transitive.
Since d satisfies all three properties of an equivalence relation, we conclude that d is indeed an equivalence relation on Z.
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This question has two parts.
A wooden block is a prism, which is made up of two cuboids with the dimensions shown. The volume of the wooden block is 427 cubic inches.
Part A
What is the length of MN?
Write your answer and your work or explanation in the space below.
Part B
200 such wooden blocks are to be painted. What is the total surface area in square inches of the wooden blocks to be painted?
A) The length MN of the given wooden block is: 12
B) 80400 in²
How to find the surface area and volume of the prism?1) The formula for volume of a cuboid is:
Volume = Length * Width * Height
Thus:
427 = (MN * 7 * 3) + (5 * 5 * 7)
427 = 21MN + 175
21MN = 252
MN = 252/21
MN = 12
2) Surface area of entire object is:
TSA = 2(12 * 3) + 2(12 * 7) - (5 * 7) + 2(7 * 3) + 3(5 * 7) + 2(5 * 5)
= 402 in²
For 200 blocks:
TSA = 200 * 402 = 80400 in²
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A recent study found that the weight of a certain species of fish living in the Bahamas can be modeled by the function 0. 034213, where w is measured in grams and L, the length of the fish is measured in centimeters. Calculate the approximate length of a fish that weighs 250 grams. Round your answer to the nearest tenth of a centimeter.
L=____ centimeters
To solve this problem, we need to use the given function to find the length of a fish that weighs 250 grams. We can do this by setting the weight of the fish (w) to 250 grams and solving for the length of the fish (L):
w = 0.034213 L
250 = 0.034213 L
L = 250 / 0.034213
L ≈ 7304.4
Rounding to the nearest tenth of a centimeter, the approximate length of the fish is:
L ≈ 730.4 centimeters
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Use the figure to find the Lateral Area.
15 un2
24 un2
12 un2
The lateral surface area of a cone is 15π units².
Option A is the correct answer.
We have,
The lateral area of a three-dimensional object is the total surface area of the object excluding the area of the bases.
So,
The given figure is a cone.
Now,
The lateral surface area of a cone = πrl
where r is the radius of the base of the cone, and l is the slant height of the cone.
The slant height is the distance from the apex of the cone to any point on the edge of the base.
Now,
Applying the Pythagorean,
l² = 4² + 3²
l² = 16 + 9
l² = 25
l = 5
So,
Substituting the values.
The lateral surface area of a cone
= πrl
= π x 3 x 5
= 15π units²
Thus,
The lateral surface area of a cone is 15π units².
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Place its midpoint I.
Draw the circle C of diameter [AB].
Draw the perpendicular bisector of the segment [AB]. It intersects circle C at points E and F.
Draw the half-lines [AE) and [BE).
Draw the arc of a circle with center A, radius [AB] and origin B. It intersects the half line [AE) at point H.
Draw the arc of a circle with center B, radius [BA] and origin A. It intersects the half line [BE] at point G.
Draw the quarter circle with center E, radius [EG] and bounded by points G and H.
Answer:
To complete the construction described:
Place the midpoint I of segment [AB]. Draw the circle C of diameter [AB]. Draw the perpendicular bisector of segment [AB]. Label the point where it intersects circle C as E and F. Draw half-lines [AE) and [BE). Draw an arc with center A and radius [AB] that passes through point B. Label the points where the arc intersects half-line [AE) as H and J. Draw an arc with center B and radius [BA] that passes through point A. Label the points where the arc intersects half-line [BE) as G and K. Draw the quarter circle with center E and radius [EG] that is bounded by points G and H. This completes the construction.
The final figure should consist of circle C, perpendicular bisector EF, half-lines [AE) and [BE), arcs passing through points B and A, and the quarter circle with center E, radius [EG], and bounded by points G and H.
Step-by-step explanation:
Quadratic function f has a vertex (4, 15) and passes through the point (1, 20). Which equation represents f ?
f(x)=−5/9(x−4)^2+15
f(x)=5/9(x−4)^2+15
f(x)=−35/9(x−4)^2−15
f(x)=35/9(x−4)^2−15
A standardized test is designed so that scores have a mean of 50 and a standard deviation of 4. What percent of scores are between 46 and 54?
Answer:
c
Step-by-step explanation:
c is correct
Figure these out ……….
Answer:
o
Step-by-step explanation:
Alex painted 178 ft2 of his apartment’s walls with 13 1 3 gallon of paint. He has 2 gallons of paint in all. If he wants to cover 1,000 ft2 of his apartment, does he have enough paint? Complete a true statement
From multiplcation operation, Alex has enough paint to cover 1,000 ft² of his apartment. The true statement is 2 gallons of paint will cover 1068 ft², Alex have enough paint of quantity 2 gallons.
We have Mr. Alex painted his apartment. Area of his apartment'walls = 178 ft²
Quantity of paint used by him to paint his apartment'walls with area 178 ft² =[tex] \frac{1}{3} \: \: gallons[/tex]
Total quantity of paint used in all
= 2 gallons
We have to check the provide paint is enough or not to cover 1,000 ft² of his apartment. Let the required paint for 1000 ft² be x gallons. Using multiplcation, 1/3 gallons quantity of paint will cover the area of apartment = 178 ft², so, 1 gallons quantity of paint will cover the area of apartment = 178 ×3 ft²= 534 ft²
Now, 2 gallons quantity of paint will cover the area of apartment = 2× 534 ft² = 1068 ft²> 1000 ft²
But he wants to paint 1000 ft² of his apartment in 2 gallons quantity (x=1.9 gal ). So, he has enough paint to paint his apartment.
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Complete question:
The above figure complete the question.
Alex painted 178 ft2 of his apartment’s walls with 1/3 gallon of paint. He has 2 gallons of paint in all. If he wants to cover 1,000 ft2 of his apartment, does he have enough paint? Complete a true statement
A sample of 33 blue-collar employees at a production plant was taken. Each employee was asked to assess his or her own job satisfaction (x) on a scale of 1 to 10. In addition, the numbers of days absent (y) from work during the last year were found for these employees. The sample regression line Y; = = 10.7 – – 0.2 x; was estimated by least squares for these data. Also found were T=Σ x = 7.0 Σ(x, -x = 50.0 SSE= 70.0 a. Test, at the 5% significance level against the appropriate one-sided alternative, the null hypothesis that job satisfaction has no linear effect on absenteeism. b. A particular employee has job satisfaction level 8. Find a 99% prediction interval for the number of days this employee would be absent from work in a year. 33 2 -X)=
Answer:
Step-by-step explanation :
I suggest you ask an expert
Here is a list of ingredients for making 10 cookies. Ingredients To make 10 cookies 120 g of butter 75 g of sugar 180 g of plain flour 150 g of chocolate chips 2 eggs Pam wants to make 25 cookies. Work out how much butter she needs.
Amount of butter that Pam needs is 300 g.
Given ingredients to make 10 cookies.
Ingredients needed for 10 cookies is,
Butter : 120 g
Sugar : 75 g
Plain flour : 180 g
Chocolate chips : 150 g
Eggs : 2
The proportion of each ingredient will be same.
To make 25 cookies,
Amount needed = 25 / 10 = 2.5
Amount of butter needed = 2.5 × 120 = 300 g
Hence the amount of butter needed is 300 g.
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Fill in the P(x - x) values to give a legitimate probability distribution for the discrete random vanuble X, whose possible values are 1, 2, 4, 5, and 6. Value of x P(X= ) 1 0.10 2 022 0.14 X 5 ?
The legitimate probability distribution for the discrete random variable X is:
Value of x P(X= )
1 0.10
2 0.22
4 0.14
5 0.18
6 0.36
To create a legitimate probability distribution, the sum of all the probabilities should be equal to 1. So, we can use the fact that the sum of all probabilities must equal 1 to find the missing probability for X = 5.
Value of x P(X= )
1 0.10
2 0.22
4 0.14
5 ?
6 0.36
To find P(X = 5), we can subtract the sum of the probabilities for X = 1, 2, 4, and 6 from 1:
P(X = 5) = 1 - (0.10 + 0.22 + 0.14 + 0.36) = 0.18
Therefore, the legitimate probability distribution for the discrete random variable X is:
Value of x P(X= )
1 0.10
2 0.22
4 0.14
5 0.18
6 0.36
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Rewrite the statements in if-then form.
Exercise
Catching the 8:05 bus is a sufficient condition for my being on time for work
The statement Catching the 8:05 bus is a sufficient condition for my being on time for work can be written as if a, then b, where, a is the case where I catch the 8:05 bus and b is the case where I reach the office on time.
Here we have been given that the sufficient condition for my being on time for work is catching the 8:05 bus.
Whenever we are denoting to cases say x and y, we say x being a sufficient condition for y by the notation
y ⇒ x
Here, let there be cases a and b
a is the case where I catch the 8:05 bus and
b is the case where I reach the office on time
Since a is a sufficient condition for b, we can write
a ⇒ b
In the If- then form, we say
If a, then b.
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Solve the following equation using the zero product property. Enter one solution per box. No brackets {} are needed.
The solution is, the solutions using the Zero Product Property: is x =8 and -5.
The expression to be solved is:
(x-8) (x + 5) = 0
we know that,
The zero product property states that the solution to this equation is the values of each term equals to 0.
now, we have,
(x-8) (x + 5) = 0
i.e. we get,
(x-8) × (x + 5) = 0
so, using the Zero Product Property:
we get,
(x-8) = 0
or,
(x + 5) = 0
so, we have,
x = 8 or, x = -5
The answers are 8 and -5.
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interior and exterior triangles
Answer:
∠ PQR = 18°
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ PQR is an exterior angle of the triangle , then
∠ PQR = ∠OPQ + ∠ QOP , that is
4x - 10 = x + 9 + x - 5
4x - 10 = 2x + 4 ( subtract 2x from both sides )
2x - 10 = 4 ( add 10 to both sides )
2x = 14 ( divide both sides by 2 )
x = 7
Then
∠ PQR = 4x - 10 = 4(7) - 10 = 28 - 10 = 18°
The alternating series test can be used to show convergence of which of the following alternating series?I. 4−19+1−181+14−1729+116−...,+an+...,where an={82nif n is odd−13nif n is evenII. 1−12+13−14+15−16+17−18+...+an+...,where an(−1)n+1nIII. 23−35+47−59+611−713+815−...+an+...,where an=(−1)n+1n+12n+1(A) I only(B) II only(C) III only(D) I and II only(E) I, II, and III
The alternating series test can be used to show convergence of the alternating series I, II, and III given in the options and the correct answer to this question is Option A. I only.
The alternating series test is a method used to determine the convergence or divergence of alternating series. According to the alternating series test, an alternating series converges if the absolute value of its terms decreases monotonically to zero. In other words, if the absolute value of the terms in an alternating series eventually becomes smaller and smaller until it is less than or equal to a certain positive number, then the series converges.
In series, I, the absolute value of the terms decreases monotonically to zero since the terms eventually become smaller and smaller. Therefore, series I converge by the alternating series test.In series II, the absolute value of the terms does not decrease monotonically to zero, since the terms eventually increase in magnitude. Therefore, the alternating series test cannot be used to show the convergence or divergence of series II.In series III, the absolute value of the terms decreases monotonically to zero since the terms eventually become smaller and smaller. Therefore, series III converges by the alternating series test.In conclusion, the alternating series test can be used to show the convergence of series I and III, but not for series II. Therefore, the answer is (A) I only.
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An investment of $10,000 earns interest at an annual rate of 6. 7% compounded continuously. Answer Part 1 and Part 2 with this information.
Part 1:
Find the instantaneous rate of change in the amount in the account after 2 years (in dollars per year). Round to the nearest cent.
$____per year.
Part 2
Find the instantaneous rate of change in the amount in the account at the time the amount is equal to $14,101. Round to the nearest cent.
$_____per year
1. The instantaneous rate of change in the amount after 2 years is [tex]$1,605.64[/tex] per year
2. The instantaneous rate of change in the amount at the time the amount is equal to [tex]$14,101[/tex] is approximately $994.78 per year
[tex]A = P[/tex]× [tex]e^{rt}[/tex]
where P is the principal (initial investment), r is the annual interest rate as a decimal, and t is the time in years.
For this problem, we have P = $10,000, r = 0.067 (6.7% as a decimal), and we want to find the instantaneous rate of change in the amount after 2 years, so t = 2.
Part 1:
To find the instantaneous rate of change, we need to take the derivative of the function A(t) with respect to t:
[tex]dA/dt = Pre^{rt}[/tex]
At[tex]t = 2[/tex], we have:
[tex]A(2) = $10,000e^{0.0672}[/tex]
[tex]= $11,868.94[/tex]
[tex]dA/dt = $10,0000.067e^{0.067}[/tex]×[tex]2)[/tex]
[tex]= $1,605.64[/tex]
So the instantaneous rate of change in the amount after 2 years is $1,605.64 per year
Part 2:
To find the time at which the amount in the account is $14,101, we need to solve the equation A = $14,101 for t:
[tex]$14,101[/tex][tex]= $10,000[/tex] × [tex]e^{0.067t}[/tex]
Dividing both sides by $10,000:
[tex]1.4101 = e^{0.067t}[/tex]
Taking the natural logarithm of both sides:
[tex]ln(1.4101) = 0.067t[/tex]
Solving for t:
[tex]t = ln(1.4101)/0.067[/tex]
≈ [tex]3.5 years[/tex]
So the time at which the amount in the account is $14,101 is approximately 3.5 years.
To find the instantaneous rate of change at this time, we need to evaluate the derivative at t = 3.5:
[tex]dA/dt = $10,0000.067e^{0.067}[/tex]×[tex]3.5)[/tex]
≈ [tex]$994.78[/tex]
So the instantaneous rate of change in the amount at the time the amount is equal to $14,101 is approximately $994.78 per year
Compound interest is the interest you earn on interest. This can be illustrated by using basic math: if you have $100 and it earns 5% interest each year, you'll have $105 at the end of the first year. At the end of the second year, you'll have $110.25
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Six hundred consumers were asked whether they would like to purchase a domestic or a foreign automoblie. Their reponses are given. domestic 240 foreign 360. Develop a 95% confidence interval for the proportion of all consumers who prefer to purcahse domestic automobiles
we can say with 95% confidence that the proportion of all consumers who prefer to purchase domestic automobiles is between 0.354 and 0.446.
To develop a 95% confidence interval for the proportion of all consumers who prefer to purchase domestic automobiles, we can use the formula:
CI = p ± z*(√(p*(1-p)/n))
where:
p = proportion of consumers who prefer domestic automobiles = 240/600 = 0.4
n = sample size = 600
z = z-score for 95% confidence level = 1.96
Plugging in the values, we get:
CI = 0.4 ± 1.96*(√(0.4*(1-0.4)/600))
= 0.4 ± 0.046
= (0.354, 0.446)
Therefore, we can say with 95% confidence that the proportion of all consumers who prefer to purchase domestic automobiles is between 0.354 and 0.446.
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solve for length of segment D a=4 cm b=12 cm c=6 cm 4 • ? = ? • D
The length of segment d is 8 when the value segment a is 4 cm, b is 12 cm , c is 6 cm
If two segments intersect inside or outside the circle then ab=cd
Given values of a is 4 cm, b is 12 cm , c is 6 cm and d is x
ab=cd
Plug in the values of a, b , c and d
4×12=6×d
48=6d
Divide both sides by 6
8=d
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j^2+6j-40. factor helpppp
The expression is factorized to give j = -10 and j = 4
How to factor the expressionFrom the information given, we have the quadratic equation as;
j²+ 6j - 40
Using the factorization method, we have to mulitply the coefficient of j² by the constant.
After this, find the pair factors of the product that adds up to give 6
Substitute the values
Then, we have;
j² + 10j - 4j - 40
group the expression in pairs
(j² + 10j) - (4j- 40)
factor the common terms
j(j + 10) - 4(j + 10)
We have;
(j + 10) (j - 4)
j + 10 = 0
collect the terms
j = -10
j = 4
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Simplify: 5m (5m^4 + 5m^2 -4)
please help!!
Using the Golfer Data in the Quiz Conf. Intervals Hypoth. Testing Templates compute a 90% confidence interval for the population proportion of females. a. 18 to 29 .19 to 28 20 to 27 9 d. 16 to 31 C
The 90% confidence interval for the population proportion of females is (0.261, 0.375). Answer: d. 16 to 31.
To compute a 90% confidence interval for the population proportion of females using the Golfer Data, you can use the following formula:
CI = p ± z*√(P(1-P)/n)
where P is the sample proportion, z is the z-score associated with the desired confidence level (in this case, 1.645 for 90% confidence), and n is the sample size.
From the Golfer Data, we can see that there are 84 females out of a total of 264 golfers:
n = 264
P = 84/264 = 0.318
Plugging these values into the formula, we get:
CI = 0.318 ± 1.645*√(0.318(1-0.318)/264)
CI = 0.318 ± 0.057
CI = (0.261, 0.375)
Therefore, the 90% confidence interval for the population proportion of females is (0.261, 0.375). Answer: d. 16 to 31.
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about 1 in 1,100 people have IQs over 150. If a subject receives a score of greater than some specified amount, they are considered by the psychologist to have an IQ over 150. But the psychologist's test is not perfect. Although all individuals with IQ over 150 will definitely receive such a score, individuals with IQs less than 150 can also receive such scores about 0.08% of the time due to lucky guessing. Given that a subject in the study is labeled as having an IQ over 150, what is the probability that they actually have an IQ below 150? Round your answer to five decimal places.
The probability that the subject actually has an IQ below 150 given that they are labeled as having an IQ over 150 is approximately 0.00073276, or 0.07328% when rounded to five decimal places.
Let's use Bayes' theorem to solve the problem. Let A be the event that the subject has an IQ over 150, and B be the event that the subject actually has an IQ below 150. We want to find P(B|A), the probability that the subject has an IQ below 150 given that they are labeled as having an IQ over 150.
From the problem, we know that P(A) = 1/1100, the probability that a random person has an IQ over 150. We also know that P(A|B') = 0.0008, the probability that someone with an IQ below 150 is labeled as having an IQ over 150 due to lucky guessing.
To find P(B|A), we need to find P(A|B), the probability that someone with an IQ below 150 is labeled as having an IQ over 150. We can use Bayes' theorem to find this probability:
P(A|B) = P(B|A) * P(A) / P(B)
We know that P(B) = 1 - P(B'), the probability that someone with an IQ below 150 is not labeled as having an IQ over 150. Since everyone with an IQ over 150 is labeled as such, we have:
P(B) = 1 - P(A')
where P(A') is the probability that a random person has an IQ below 150 or, equivalently, 1 - P(A).
Plugging in the given values, we have:
P(A|B) = P(B|A) * P(A) / (1 - P(A))
P(A|B) = P(B|A) * 1/1100 / (1 - 1/1100)
P(A|B) = 0.0008 * 1/1100 / (1 - 1/1100)
P(A|B) ≈ 0.00073276
Therefore, the probability that the subject actually has an IQ below 150 given that they are labeled as having an IQ over 150 is approximately 0.00073276, or 0.07328% when rounded to five decimal places.
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Which equality statement is FALSE?
Responses
A −1 = −(−1)−1 = −(−1)
B 7 = −[−(7)]7 = −[−(7)]
C 1 = −[−(1)]1 = −[−(1)]
D −(−14) = 14
The equality statement is False (b) 7= -(-(7)).
The expression on the right side of the equation simplifies to -(-7), which is equal to 7, making the statement untrue. Therefore, 7=-(-7) should be used as the right equality declaration.
In other words, 7 is equal to the opposite of -(-7)
The area of mathematics known as algebra aids in the representation of circumstances or problems as mathematical expressions. Mathematical operations like addition, subtraction, multiplication, and division are combined with variables like x, y, and z to produce a meaningful mathematical expression.
The associative, commutative, and distributive laws are the three fundamental principles of algebra. They facilitate the simplification or solution of problems and aid in illustrating the connection between different number operations.
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If a cell group is formatted with multiple conditional formats, the rules are applied _______.
a. based on the hierarchy of the rule type
b. in the order in which they are created
c. based on which rule best applies to the first cell in the range
d. in alphanumeric order by the name of the rule
If a cell group is formatted with multiple conditional formats, the rules are applied in the order in which they are created.
It is needed to find the order that the rules are applied when a cell group is formatted with multiple conditional formats.
For a cell group, when multiple conditional formats are used, then the last rule that is added is the one that will be done first
However, this can be changed by clicking on the conditional formatting and then manage rules.
So the order of the rules will be of the order that the rules are created.
Hence the correct option is b.
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Use the following notations: r = radius of a circle, v = linear velocity, w = angular velocity. Find the missing quantity. Round to the nearest tenth if necessary. V= 1235 m/min, r = 65 m, w = ?
The angular velocity of the circle is approximately 19 m/s.
In order to find the missing quantity, we can use the relationship between linear velocity and angular velocity in a circle. The linear velocity of a point on the edge of a circle is the product of the radius and the angular velocity. This can be expressed as:
v = r * w
where v is the linear velocity, r is the radius, and w is the angular velocity.
To find the value of w, we can rearrange this equation to solve for w:
w = v / r
Substituting the given values of v and r, we get:
w = 1235 m/min / 65 m
w = 19 m/s
It's important to note that units must be consistent when using formulas to solve problems. In this case, we converted the given linear velocity from m/min to m/s before plugging it into the formula. Also, we rounded the answer to the nearest tenth, as instructed, since the given values were rounded to the nearest unit.
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Partition each whole number interval into fourths. Label 7/4 and 9/4
We can see that 7/4 is located between 3/4 and 1 on the first interval, and 9/4 is located between 2 and 5/2 on the second interval.
To partition each whole number interval into fourths, divide each interval by 4. Label 7/4 between 3/4 and 1 and label 9/4 between 2 and 5/2 on an extended scale from 0 to 3.
To partition each whole number interval into fourths, we can divide each interval by 4. For example, the interval from 0 to 1 can be divided into fourths as follows:
0 -------- 1/4 -------- 1/2 -------- 3/4 -------- 1
Now, to label 7/4 and 9/4 on this scale, we can extend it by adding another interval from 1 to 2 and dividing it into fourths as well. This would give us the following scale:
0 -------- 1/4 -------- 1/2 -------- 3/4 -------- 1 -------- 5/4 -------- 3/2 -------- 7/4 -------- 2 -------- 9/4 -------- 5/2 -------- 11/4 -------- 3
So we can see that 7/4 is located between 3/4 and 1 on the first interval, and 9/4 is located between 2 and 5/2 on the second interval.
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What is the product of 1. 0 * 10^3 and 2. 0 x 10^5 expressed in scientific notation. HEEEELLLLPPPPP PLEASEEEEEEEE
The product of the exponents is given by A = 2.0 x 10⁸
Given data ,
Let the first number be p = 1 x 10³
Let the second number be q = 2 x 10⁵
From the laws of exponents , we get
mᵃ×mᵇ = mᵃ⁺ᵇ
A = p x q
On simplifying , we get
A = 1 x 10³ x 2 x 10⁵
A = 2 x 10³⁺⁵
A = 2.0 x 10⁸
Hence , the equation is A = 2.0 x 10⁸
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Suppose you are using α = 0. 05 to test the claim that μ = 1620 using a P-value. You are given the sample statistics n-35, X_bar=1590 and σ=82. Find the P-value. State the answer only and no additional work. Make sure to use the tables from the book. Do not round the final answer
The P-value is 0.0107 for the sample statistics n-35 and the coefficient of standard deviation is 82.
α = 0. 05
μ = 1620
size (n)= 35
X_bar=1590
σ=82
From the given sample statistics, the test statistics will be calculated as:
t = (X_bar - μ) / (σ / sqrt(n))
t = (1590 - 1620) / (82 / sqrt(35))
t = (-2.5411)
Using the t-distribution table with 34 degrees of freedom, the critical value will be:
t_critical = -1.6909
Here the calculated test statistic is less than the critical value.
P - value = 2*P(-100< t < -1.9720, when df = 34)
P = tcf (-100,-2.4103,34)
P = 0.0107
Therefore we can conclude that the P-value is 0.0107.
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Which equation represents this graph
The exponential function that represents the graph is given as follow:
y = 2^(x - 1) + 2.
How to define an exponential function?An exponential function has the definition presented as follows:
y = ab^x.
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The function in this problem has a horizontal asymptote at y = 2, hence:
y = ab^x + 2.
When x increases by one, y is multiplied by two, hence the parameters a and b can given as follows:
a = 1, b = 2.
The function is translated one unit right, hence it is defined as follows:
y = 2^(x - 1) + 2.
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