Hanna Was Riding Her Bike For 11/12 Mile long. She Rode For 1/2 Mile And Then Stopped To Rest. She Rode Another 1/3 Mile And Then Had A Flat Tire. How Far Dose Hanna Have To Walk Her Bike To Complete The Loop?
Answers
Hanna have to walk her bike for 1/12 mile to complete the loop .
In the question , it is given that
distance Hanna had to ride to complete the loop = 11/12 mile
distance rode by Hanna before rest = 1/2 mile
distance rode by Hanna before flat tire = 1/3 mile
So the distance Hanna has to walk her bike to complete the loop = total distance of the loop - distance rode by Hanna before rest - distance rode by Hanna before flat tire .
On substituting the values from above we get ,
distance Hanna has to walk her bike to complete the loop = 11/12 - 1/2 - 1/3
taking the LCM of 12 , 2 and 3 as 12
we get ,
= 11/12 - 6/12 - 4/12
Simplifying further we get ,
= (11-6-4)/12
= (11-10)/12
= 1/12
Therefore , the distance Hanna have to walk her bike to complete the loop is 1/12 mile .
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Related Questions
Select the line segment Please helppppp !!!!
Answers
Answer:
C.
Step-by-step explanation:
A line is straight, and a segment is a part of a line.
A and D and lines because they have the arrows on the side, meaning they keep going and are not a segment.
B is not a line, it curves.
So that leaves C to be the answer because it is the only straight one with no arrows.
I will GIVE 45 POINTS!!!!!!
Shania plans to go on a vacation in a few months. She starts saving for the trip with a $100 bill. For the next four months, she saves 20% more than she did the previous month. Using the formula deduced in part C, find the total amount Shania will save at the end of 4 months.
Answers
Answer:
The question states that Shania saves 20% more than she did the previous month. Therefore, the amount she saves in the second month is 1.2 * $100 = $120.
To find the total amount saved in all four months, we need to calculate the sum of an arithmetic progression with first term $100 and common ratio 1.2.
The formula for the sum of n terms of an arithmetic progression is:
S_n = n/2 (first term + last term) = n/2 (a + a + (n-1)d)
Where a is the first term, d is the common difference and n is the number of terms.
In this case, the first term is $100, the common difference is $20(1.2-1)=$24, and the number of terms is 4.
So the total amount saved at the end of 4 months is:
S_4 = 4/2 (100 + 100 + 3 * 24) = 4/2 (100 + 100 + 72) = 4/2 (272) = $544
Therefore, at the end of 4 months, Shania will have saved $544 for her vacation.
The answer indicates that Shania saves 20% more money each month than she did the month before. She thus saves $120 (1.2 × $100) in the next month.
What is arithmetic progression?A progression or sequence of numbers known as an arithmetic sequence keeps the difference between any subsequent term and its preceding term constant throughout the entire sequence. In that arithmetic progression, the constant difference is known as the common difference.
According to the query, Shania saves 20% more each month than she did the previous one. As a result, she saves 1.2 × $100, or $120, in the second month.
Calculating the sum of an arithmetic progression with a first term of $100 and a common ratio of 1.2 will allow us to determine the total money saved over the course of the four months.
An arithmetic progression's formula for the sum of its n terms is as follows:
First term plus last term equals S n = n/2 (a + a + (n-1)d).
The initial term is denoted by the letter "a," the common difference is "d," and the number of terms is "n."
The first term here is for $100, the common difference is $20(1.2-1) = $24, and there are four terms altogether.
Consequently, the total amount saved after 4 months is:
S_4 = 4/2 (100 + 100 + 3 × 24) = 4/2 (100 + 100 + 72) = 4/2 (272) = $544
Shania will therefore have $544 saved for her vacation at the end of the four-month period.
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This exercise shows that if we bring the dual problem into stan- dord form and then apply the primal simplex method, the resulting algorithm is not identical to the dual simplex method. Consider the following standard form problem and its dual. minimize 21 +22 maximize Pi + P2 subject to x1 = 1 subject to P1 <1 22=1 P2 <1. 21,22 > 0 Here, there is only one possible basis and the dual simplex method must terminate immediately. Show that if the dual problem is converted into standard form and the primal simplex method is applied to it, one or more changes of basis may be required.
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The exercise highlights that converting the dual problem into standard form and applying the primal simplex method does not yield the same algorithm as the dual simplex method. By considering a specific standard form problem and its dual, it is shown that the primal simplex method applied to the dual problem may require one or more changes of basis, unlike the dual simplex method where termination occurs immediately due to the specific structure of the problem.
In the given exercise, we have a standard form problem and its dual:
Primal Problem:
minimize 21x1 + 22x2
subject to x1 = 1
x1, x2 ≥ 0
Dual Problem:
maximize P1 + P2
subject to P1 < 1
P2 < 1
P1, P2 ≥ 0
Since there is only one possible basis in this case, the dual simplex method terminates immediately because of the specific structure of the problem.
However, if we convert the dual problem into standard form and apply the primal simplex method to it, one or more changes of basis may be required. This is because the primal simplex method operates differently from the dual simplex method and may encounter different pivot elements and entering/leaving variables during the iterations. These differences in the algorithm can lead to changes in the basis during the primal simplex method's execution.
Therefore, it is evident that converting the dual problem into standard form and applying the primal simplex method does not result in the same algorithm as the dual simplex method. The primal simplex method may require one or more changes of basis during its execution, unlike the dual simplex method, which terminates immediately in this specific problem due to the singular structure of the basis.
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please help me i need to graduate
Answers
The statement that is true about the angle formed by the tangent JL and the secant JG is the option A.
A. The measure of ∠J is 25° and the triangle JKG is isosceles
What is a tangent (line)?A tangent is a straight line that touches a curve at (only) one point at which the slope of the tangent line and the slope of the curve are the same
The parameters of the circle are;
\(m\widehat{HK}\) = 50°
m∠GKL = 50°
m∠GKL = 0.5 × \(m\widehat{KG}\)
Therefore;
0.5 × \(m\widehat{KG}\) = 50°
\(m\widehat{KG}\) = 50° ÷ 0.5 = 100°
According to the angles formed by tangent and secant outside a circle theorem, the angle J formed by the tangent JL and the secant JG is half of the difference between arc \(m\widehat{KG}\) and arc \(m\widehat{HK}\)
Therefore;
\(\angle J = \dfrac{m\widehat{KG}-m\widehat{HK}}{2}\)
Which gives;
\(\angle J = \dfrac{100^{\circ}-50^{\circ}}{2}=25^{\circ}\)
The measure of ∠J = 25°
∠GKL = ∠J + ∠G (exterior angle of a triangle postulate)
Plugging in the values of ∠GKL, ∠J, and ∠G, we have;
50° = 25° + ∠G
∠G = 50° - 25° = 25°
∠G = 25°
The base angles of triangle ΔJKG (∠J and ∠G) are congruent by the definition of congruency, therefore, triangle ΔJKG is an isosceles triangle.
The correct option is therefore;
A. The measure of ∠J is 25°, and triangle JKG is an isosceles triangle
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- 7 + 6n - 9 = -4
Please help
Answers
Answer:
N = 2
Step-by-step explanation:
−7+6n−9=−4
−7+6n+−9=−4
(6n)+(−7+−9)=−4(Combine Like Terms)
6n+−16=−4
6n−16=−4
Step 2: Add 16 to both sides.
6n−16+16=−4+16
6n=12
Step 3: Divide both sides by 6.
6n
6
=
12
6
n=2
<3
Answer:
n = 2
Step-by-step explanation:
First combine like terms on the left of the equals sign, and get 6n - 16 = -4. Now add 16 to both sides. You should have 6n = 12. Now divide 6 from both sides and get n = 2
Two drivers, A and B, are archrivals competing in an automobile race. Driver A had been leading driver B for a while by a steady 3 miles, but at exactly 2 miles from the finish, driver A ran out of gas and decelerated thereafter at a rate proportional to the square of his remaining speed. One mile later, driver A's speed was exactly halved. If driver B's speed remained constant, who won the race? An outline for how to answer this question is given below: 1. Let s(t) denote the distance in miles traveled by driver A for t≥0, where t=0 is the point at which driver A ran out of gas. (Side note: As it turns out, we will not need to know the units for t to answer our given problem!). Let vA (t) be driver A's velocity, so that ds/dt=vA(t), and let vB be the constant velocity of driver B. Using k for the constant of proportionality, set up and solve an initial value problem to find an expression for vA(t) that depends only on vB,k, and t. 2. Using your result from problem 1, set up and solve an initial value problem to find an expression for s(t) that (again) only depends on vB,k, and t. 3. Let t=t1 be the moment when driver A's speed was halved-i.e., the moment when A has traveled for one mile after running out of gas. Use this to show that k=ln2. Write an expression for s(t) that depends only on vB and t. 4. Let tB be the moment when driver B crosses the finish line. Write tB as an expression depending only on vB, then evaluate s(tB). Did driver A cross the finish line before or after driver B?
Answers
By evaluating the expression for s(tB), we can determine whether driver A crossed the finish line before or after driver B. If s(tB) is positive, it means driver A crossed the finish line before driver B. If s(tB) is negative, it means driver A crossed the finish line after driver B.
To solve the initial value problem, we start with the equation vA'(t) = -k(vA(t))^2, where vA'(t) represents the derivative of vA with respect to t.
This equation describes the deceleration of driver A, proportional to the square of his remaining speed. Rearranging and solving the differential equation, we get vA(t) = 1 / (kt + C), where C is a constant determined by the initial conditions.
To find the expression for s(t), we integrate vA(t) with respect to t: s(t) = ∫(1 / (kt + C)) dt. Integrating this expression gives us s(t) = (1/k) ln(kt + C) + D, where D is another constant determined by the initial conditions.
At t = t1 (when driver A's speed is halved, i.e., one mile after running out of gas), we have vA(t1) = vA(0) / 2. Plugging this into the expression for vA(t) from step 1, we find 1 / (k * t1 + C) = (1 / (k * 0 + C)) / 2. Simplifying, we get k = ln(2) / t1.
Using the expression for s(t) from step 2, we can find tB by settings S(tB) = 3 (since driver A was leading by 3 miles). Simplifying this equation, we find tB = (e^(3k) - C) / k. Plugging in the value of k we found in step 3, we have tB = (e^(3ln2 / t1) - C) / (ln2 / t1).
To evaluate s(tB), we substitute t = tB into the expression for s(t) from step 2, resulting in s(tB) = (1/k) ln(ktB + C) + D. Since tB depends only on vB and t1, and C and D are constants determined by the initial conditions, s(tB) depends only on vB.
If s(tB) is positive, it means driver A crossed the finish line before driver B. If s(tB) is negative, it means driver A crossed the finish line after driver B.
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PLS NEED DONE ASAP 10 MINUTES TILL DUE
Answers
Then 3 red + 2 blue = 1 green + 2 blue, so 3 red = 1 green
If we know these facts then
3 red = 2 blue = 1 green
So the bottom one is 6 reds = 2 greens, or 1 green + 2 blue.
This makes my head hurt. They’re making it harder than it is.
Hope I didn’t confuse you more.
The diagram shows an open rectangular box ABCDEFGH.
A straight stick AGM rests against A and G and extends outside the box to M.
a. Calculate the angle between the stick and the base of the box.
b. AM= 30 cm.
Show that GM= 4.8 cm, correct
to 1 decimal place.
Answers
The angle between the stick and the base of the box is 77. 9 degrees
How to determine the angleTo determine the angle between the stick and the base, we have to know the trigonometric identities.
These identities are;
sinecosinecotangenttangentsecantcosecantFrom the information given, we have;
sin A = FB/AB
Given that;
GB = 14.5cm
AB = 18. 6cm
substitute for the length of the sides, we have;
sin A = 14.5/18. 6
Divide the values, we have;
sin A = 0. 7796
Find the inverse sine
A = 77. 9 degrees
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a probability distribution is: group of answer choices the average value that a random variable is expected to assume over a large number of trials. a summary of data into classes along with the number of occurrences in each class. a listing of all possible outcomes along with their likelihood of occurrence. a listing of the successes and failures from a given experiment.
Answers
A probability distribution is a listing of all possible outcomes along with their likelihood of occurrence.
It is a way of describing the likelihood of different outcomes in a statistical experiment or random event. It is used to calculate the probability of different events or outcomes in situations where there is uncertainty or variability. There are two types of probability distributions: discrete and continuous.
Discrete probability distributions are used when the possible outcomes of a statistical experiment are discrete or countable, such as the number of heads obtained in flipping a coin. Continuous probability distributions are used when the possible outcomes of a statistical experiment are continuous or uncountable, such as the height of people in a population.
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Approximate the area under the graph of f(x) over the specified interval by dividing the interval into the indicated number of subintervals and using the left endpoint of each subinterval. f(x)=x^3+x^2+1; interval [0,4]; 4 subintervals
Answers
Hello there. To solve this question, we'll have to remember some properties about Riemann sums.
When approximating the area under the graph of a function, we can make a partition of the interval in regular sub-intervals (that divides the former interval in smaller intervals with the same length) and add the areas of the polygons under the graph.
Usually, taking the left endpoint can lead to an under or overestimation, depending on the behavior of the function over the interval (if it is increasing or decreasing, respectively).
So, when approximating the area under the graph of the function f(x) over the interval [a, b], we're partitioning the interval [a, b] into n regular subintervals with length:
\(\frac{b-a}{n}\)This is also called the forward difference between two points in the endpoints of the interval, also known as:
\(\Delta x\)When taking the left endpoints, we start on x = a and will add it up to
\(a+(n-1)\Delta x\)In other words, we'll add all x_i values inside the interval as follows:
\(\sum_{i=0}^{n-1}f(x_i)\cdot\Delta x\)Where:
\(x_0=a\)Okay. With this, we can solve the question.
We want to estimate the area under the graph of the function:
\(f(x)=x^3+x^2+1\)over the interval
\([0,4\rbrack\)using 4 subintervals (that is, n = 4).
First, we find a and b:
From the interval, we get
\(a=0,b=4\)Calculating the difference:
\(\Delta x=\dfrac{4-0}{4}=\dfrac{4}{4}=1\)Finally, plugging these informations in the sum:
\(\sum_{i=0}^{4-1}f(x_i)\cdot1=\sum_{i=0}^3{x_i}^3+{x_i}^2+1\)Remember, in this case:
\(\begin{gathered} \Delta x=x_1-x_0=1 \\ \text{ but }x_0=a=0,\text{ hence} \\ \\ x_1=1 \\ x_2=2\text{ and} \\ x_3=3 \end{gathered}\)So we get:
\(\sum_{i=0}^3{x_i}^3+{x_i}^2+1=1+1^3+1^2+1+2^3+2^2+1+3^3+3^2+1=1+1+1+8+4+1+27+9+1=54\)This might be the approximate area under this graph.
When we want to find the real area, we take the limit as n goes to infinity (the partition becomes big enough such that the intervals have infinitesimal length), hence:
\(\underset{n\rightarrow\infty}{\lim}\sum_{i=0}^{n-1}f(x_i)\cdot\Delta x=\int_a^bf(x)\,\mathrm{d}x\)Plugging the function and the lower and upper bounds, we get:
\(\int_0^4x^3+x^2+1\,\mathrm{d}x\)Solving this integral, we get:
\(\dfrac{x^4}{4}+\dfrac{x^3}{3}+x\biggr|_0^4=\dfrac{4^4}{4}+\dfrac{4^3}{3}+4=64+\dfrac{64}{3}+4=\dfrac{268}{3}\approx89.34\)Hence this is why this was a case of underestimation.
ali and jake went on a cross country trip they took a train part of the way and a bus the rest of the way they traveled a total of 1050 kilometers riding on the train 200 more kilometers than in the bus how many kilo meters did they travel by
Answers
Answer:
1900 km
Step-by-step explanation:
train = 1050km
bus = 200 less than train or 1050-200 = 850
1050+850=1900
Answer:
625, just got it right
Step-by-step explanation:
a not-so-enthusiastic student has a predictable pattern for attending class. if the student attends class on a certain friday, then she is 2 times as likely to be absent the next friday as to attend. if the student is absent on a certain friday, then she is 4 times as likely to attend class the next friday as to be absent again. what is the long run probability the student either attends class or does not attend class? g
Answers
Therefore, the probability that the student attends class on a certain Friday is 1/2, and the probability that the student is absent is also 1/2. The long-run probability that the student either attends class or does not attend class is simply 1, since these are the only two possible outcomes.
Let's use A to represent the event that the student attends class on a certain Friday, and let's use B to represent the event that the student is absent on a certain Friday. We are asked to find the long-run probability that the student either attends class or does not attend class.
We can use the law of total probability and consider the two possible scenarios:
Scenario 1: The student attends class on a certain Friday
If the student attends class on a certain Friday, then the probability that she will attend class the next Friday is 1/3, and the probability that she will be absent is 2/3. Therefore, the probability that the student attends class on two consecutive Fridays is:
P(A) * P(A|A) = P(A) * 1/3
Scenario 2: The student is absent on a certain Friday
If the student is absent on a certain Friday, then the probability that she will attend class the next Friday is 4/5, and the probability that she will be absent again is 1/5. Therefore, the probability that the student is absent on two consecutive Fridays is:
P(B) * P(A|B) = P(B) * 4/5
The probability that the student attends class or is absent on a certain Friday is 1, so we have:
P(A) + P(B) = 1
Now we can solve for P(A) and P(B) using the system of equations:
P(A) * 1/3 + P(B) * 4/5 = P(A) + P(B)
P(A) + P(B) = 1
Simplifying the first equation, we get:
2/3 * P(B) = 2/3 * P(A)
P(B) = P(A)
Substituting into the second equation, we get:
2 * P(A) = 1
P(A) = 1/2
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mcgregor believed that theory x assumptions were appropriate for:
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Douglas McGregor believed that the Theory X assumptions were appropriate for traditional and authoritarian organizations.
Theory X is a management theory developed by Douglas McGregor, a management professor, and consultant. It is based on the idea that individuals dislike work and will avoid it if possible. As a result, they must be motivated, directed, and controlled to achieve organizational goals. The assumptions of Theory X are as follows:
Employees dislike work and will try to avoid it whenever possible. People must be compelled, controlled, directed, or threatened with punishment to complete work. Organizations require rigid rules and regulations to operate effectively. In conclusion, Douglas McGregor believed that Theory X assumptions were appropriate for traditional and authoritarian organizations.
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Can someone help me with this?
Answers
Answer:
(5, 1)
Step-by-step explanation:
The vertex is the turning point on the graph. Its coordinates are read from the axes labels.
VertexThe term vertex is used in several different contexts. A vertex of a polygon is a point where edges meet. A vertex of a curve is an extreme value of the curve.
When applied to an ellipse, the vertices are the ends of the major axis. The ends of the minor axis are the co-vertices.
ParabolaThe vertex of a parabola is the extreme value of the parabola. When it opens downward, as here, the vertex is the point where the curve is at its maximum.
As with any point on any graph, the coordinates of the vertex are read from the labels of the axes. The horizontal coordinate is customarily listed first.
The vertex is (x, y) = (5, 1).
Use factoring to solve the quadratic equation. Check by substitution or by using a graphing utility and identifying x-intercepts.
x² - 2x - 630
Answers
9514 1404 393
Answer:
x = -7, x = 9
Step-by-step explanation:
We presume your equation is ...
x² -2x -63 = 0
Factors of -63 that have a sum of -2 are -9 and +7. Then the factored equation is ...
(x -9)(x +7) = 0
Solutions make the factors zero.
x -9 = 0 ⇒ x = 9
x +7 = 0 ⇒ x = -7
The solutions to the quadratic equation are x = -7 and x = 9.
if its assumptions are met, the analysis of variance technique is appropriate when ____.
Answers
Answer:
comparing the means of three or more groups
Step-by-step explanation:
Find the missing angle measures?
Answers
Answer:
x)45
y)45
z)135
Step-by-step explanation:
Which of the following transformations would map CD on C'D'
Answers
hello, first we need to know what color represents each line segment.
Look at the figure: CD is represented in green, and C'D is represented in blue.
Now, let's look at the points of each one:
CD: (2,1) and (3(-4)
C'D': (-1,2) and (4,3)
To solve this question, we need to rotate the green line segment to the same position as the blue line segment.
So, if we rotate 90 degrees in the clockwise, we will have:
(-2, 1) and (-3, -4)
If we rotate 90 degrees in the counterclockwise, we will have:
(-1,2) and (4,3). This are the same points of the line segment C'D'
Check the picture and thanks
Answers
Answer:
I think the answer would be 'a'
An isosceles triangle has two sides of equal length, a, and a base, b. The perimeter of the triangle is 15.7 inches, so the equation to solve is 2a + b = 15.7.
Shana wants to use all 62 feet of the fencing she has to make a rectangular run for her dog. She decides to make the length of the run 20 feet. She writes and solves the equation 2 l plus 2 w equals 62 to find the width of the run.
Which statements are true of the solution? Check all that apply.
The value of w is 10 feet.
The value of w can be zero.
The value of w cannot be a negative number.
Substitution is used to replace the variable l with a value of 20.
The subtraction property of equality is used to isolate the term with the variable w.
Answers
Answer:
[c] The value of w cannot be a negative number.
[d] Substitution is used to replace the variable l with a value of 20.
[e] The subtraction property of equality is used to isolate the term with the variable w.
Step-by-step explanation:
To figure out which steps of the solution are true, let us solve.
2 l plus 2 w equals 62 -> 2l + 2w = 62
----
2l + 2w = 62
2(20) + 2w = 62 <- Substitution is used to replace the variable l with a value of 20.
40 + 2w = 62
2w = 22 <- The subtraction property of equality is used to isolate the term with the variable w.
w = 11
This means that the value of w is not 10 feet so the first option is incorrect. This shape is a rectangle, so the value of w cannot be 0. Since we cannot have a negative measurement, option three is incorrect. This leaves us with the last three options as our answer, shown by the work above.
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If sin0= 2/5, find csc0.
Answers
Answer: D I think
Step-by-step explanation:
Josiah plants vegetable seeds in rows. Each row has the same number of seeds in it. He plants more than one row of seeds. What could be the total number of seeds he plants?
Answers
The total number of seeds that Josiah would plant would be = nR×S
How to determine the total number of seeds that Josiah will plant?To determine the total number of seeds that Josiah will plant will be to add the seeds in the total number of rooms he planted.
Let each row be represented as = nR
Where n represents the number of rows planted by him.
Let the seed be represented as = S
The total number of seeds he planted = nR×S
Therefore, the total number of seeds that was planted Josiah would be = nR×S.
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Volume of a pentagonal prism is 360 inches cubed. The height of prism is 3 inches. What is the area of the pentagon base?
Answers
The pentagonal prism with volume 360 in³ and height of 3 inches have a base area of 120 in²
What is a pentagonal prism?A pentagonal prism is a prism that has two pentagonal bases like top and bottom and five rectangular sides.
Given that, the volume of a pentagonal prism is 360 in³, with a height of 3 inches,
We need to find the area of the base,
We know that, the volume of a pentagonal prism is =
V = 1/4 √(5(5+2√5)·a²h
Where a is the base edge and h is the height,
360 = 1/4·3 √(5(5+2√5)·a²
1/4·√(5(5+2√5)·a² = 120
Since, the base of a pentagonal prism is a pentagon, and the area of a pentagon = 1/4 √(5(5+2√5)·a²
And we have,
1/4 √(5(5+2√5)·a² = 120
Therefore, the base area is 120 in²
Hence, the pentagonal prism with volume 360 in³ and height of 3 inches have a base area of 120 in²
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Solve For X...
A, B, C, Or D.
Answers
Answer:
D.
Step-by-step explanation:
it literally can't be any of the other choices cause they don't have all the variables, variables can't disappear unless canceled and you can't cancel anything out in this problem
The length of a rectangular poster is 9 more inches than half its width. The area of the
poster is 20 square inches. Solve for the dimensions (length and width) of the poster.
Answers
The.dimensions (length and width) of the poster include 10 inches and 2 inches.
How to calculate the dimensions?Let the width be represented by w.
The length based on the information given will be: (w/2) + 9 = 0.5w + 9
The area is 20 inches²
It should be noted that length × width = area.
This will be:
= (0.5w + 9) × w = 20
0.5w² + 9w = 20
0.5w² + 9w - 20 = 0
Multiply through by 2
w² + 18w - 40 = 0
w² + 20w - 2w - 40 = 0
w(w + 20) - 2(w + 20)
(w - 2) = 0
w = 0 + 2
Width = 2 inches
Length = 0.5w + 9
= 0.5(2) + 9
= 1 + 9
= 10 inches.
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Please help, graph the line
Answers
Answer:
Step-by-step explanation:
15) x should +ve
16) x should be -ve
Question 3 Find whether the vectorrs are parallel. (-2,1,-1) and (0,3,1)
a. Parallel
b. Collinearly parallel
c. Not parallel
d. Data insufficient
Answers
To determine whether the vectors (-2,1,-1) and (0,3,1) are parallel, we need to compare their direction. If they have different directions, they are not parallel. the correct answer is option c) Not parallel.
To check if two vectors are parallel, we can compare their direction vectors. The direction vector of a vector can be obtained by dividing each component of the vector by its magnitude. In this case, let's calculate the direction vectors of the given vectors.
The direction vector of (-2,1,-1) is obtained by dividing each component by the magnitude:
Direction vector of (-2,1,-1) = (-2/√6, 1/√6, -1/√6)
The direction vector of (0,3,1) is obtained by dividing each component by the magnitude:
Direction vector of (0,3,1) = (0, 3/√10, 1/√10)
Comparing the direction vectors, we can see that they are not equal. Therefore, the vectors (-2,1,-1) and (0,3,1) are not parallel. Hence, the correct answer is option c) Not parallel.
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In reality, forecasts are typically not accurate. As such, it is typically most appropriate to use the std. deviation of demand as the primary measure of uncertainty. True/False
Answers
False. While it is true that forecasts can be subject to uncertainties and may not always be entirely accurate, it is not necessarily most appropriate to use the standard deviation of demand as the primary measure of uncertainty.
The standard deviation represents the dispersion of data points around the mean, and it is commonly used to measure variability within a dataset. However, it may not capture all the sources of uncertainty in demand forecasting.
Forecasts consider various factors such as historical data, market trends, customer behavior, and external influences to estimate future demand. Although they may not be entirely precise, they provide valuable insights and help organizations make informed decisions regarding production, inventory management, and resource allocation.
In addition to the standard deviation, other measures of uncertainty, such as confidence intervals or prediction intervals, can be used to quantify the range of possible outcomes and the associated level of uncertainty. These measures provide a more comprehensive understanding of the potential variations in demand, considering the inherent uncertainties in forecasting.
In conclusion, while forecasts may not always be completely accurate, they provide useful guidance for decision-making. The standard deviation of demand alone may not adequately capture the full range of uncertainties, and it is important to consider other measures of uncertainty when assessing the reliability and potential variations in demand forecasts.
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2. Landon, Wes, and Tim attempted 25 basketball shots each.
Landon made 36/100 of his shots.
Wes made 2/5 of his shots.
Tim made 32% of his shots.
Who shot the best % and why?
:,)
Answers
Answer: Wes shot the best because his percentage was 40% while Landon (36%) and Tim's (32%) percentage were lower than Wes's.
Step-by-step explanation: The best way to find out who shot the best is by first changing the denominator of the fraction to 25. This way, we can compare easily.
Landon:
36/100=9/25=36%
Wes:
2/5=10/25=40%
Tim:
32%
Hope this helped! ;)
In 2020, a total of 9559 Nissan Leafs were sold in the US. For the 12-month period starting January 2020 and ending December 2020, the detailed sales numbers are as follows: 651, 808, 514, 174, 435, 426, 687, 582, 662, 1551, 1295 and 1774 units.
before the Nissan plant in Smyrna, Tennessee, started to produce the Nissan Leaf they were imported from Japan. Although cars are now assembled in the US, some components still imported from Japan. Assume that the lead time from Japan is one weeks for shipping. Recall that the critical electrode material is imported from Japan. Each battery pack consists of 48 modules and each module contains four cells, for a total of 192 cells. Assume that each "unit" (= the amount required for an individual cell in the battery pack) has a value of $3 and an associated carrying cost of 30%. Moreover, assume that Nissan is responsible for holding the inventory since the units are shipped from Japan. We suppose that placing an order costs $500. Assume that Nissan wants to provide a 99.9% service level for its assembly plant because any missing components will force the assembly lines to come to a halt. Use the 2020 demand observations to estimate the annual demand distribution assuming demand for Nissan Leafs is normally distributed. For simplicity, assume there are 360 days per year, 30 days per month, and 7 days per week.
(a) What is the optimal order quantity?
(b) What is the approximate time between orders?
Answers
(a)The optimal order quantity is 4609 units.
(b)The time between orders is 1.98 months.
To determine the optimal order quantity and the approximate time between orders, the Economic Order Quantity (EOQ) model. The EOQ model minimizes the total cost of inventory by balancing ordering costs and carrying costs.
Optimal Order Quantity:
The formula for the EOQ is given by:
EOQ = √[(2DS) / H]
Where:
D = Annual demand
S = Cost per order
H = Holding cost per unit per year
calculate the annual demand (D) using the 2020
sales numbers provided:
D = 651 + 808 + 514 + 174 + 435 + 426 + 687 + 582 + 662 + 1551 + 1295 + 1774
= 9559 units
To calculate the cost per order (S) and the holding cost per unit per year (H).
The cost per order (S) is given as $500.
The holding cost per unit per year (H) calculated as follows:
H = Carrying cost percentage × Unit value
= 0.30 × $3
= $0.90
substitute these values into the EOQ formula:
EOQ = √[(2 × 9559 × $500) / $0.90]
= √[19118000 / $0.90]
≈ √21242222.22
≈ 4608.71
Approximate Time Between Orders:
To calculate the approximate time between orders, we'll divide the total number of working days in a year by the number of orders per year.
Assuming 360 days in a year and a lead time of 1 week (7 days) for shipping, we have:
Working days in a year = 360 - 7 = 353 days
Approximate time between orders = Working days in a year / Number of orders per year
= 353 / (9559 / 4609)
= 0.165 years
Converting this time to months:
Approximate time between orders (months) = 0.165 × 12
= 1.98 months
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