Yes, this is true. Safety stock is an inventory strategy used to ensure that a company has enough of a particular item in stock to meet customer demand.
It is typically used to protect against unexpected changes in demand and/or supply, and is most applicable to independent demand inventory.
Safety stock is an inventory strategy used to ensure that a company has enough of a particular item in stock to meet customer demand. It is typically used to protect against unexpected changes in demand and/or supply. These changes can include anything such as supplier delays, unexpected customer orders, or seasonal fluctuations. Safety stock is most applicable to independent demand inventory, which is inventory that is driven by customer demand and not production requirements. Therefore, the statement that safety stock only applies to independent demand inventory is true.
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The pattern in this table continues. Which equation below relates the number of squares to the figure number?
a) s=4 f+1
b) s=2 f+3
c) s=f+2
d) f=2 s+3
A
B
C
D
The final equation that represent the given table is s=f+2. So the option c is correct.
In the given question, the pattern in this table continues.
We have to check which equation below relates the number of squares to the figure number.
a) s=4f+1
b) s=2f+3
c) s=f+2
d) f=2s+3
From the given table;
f(1) = 5, f(2) = 7, f(3) = 9, f(4) = 11, f(5) = 13
If we check closely the value of f(x), we can see that the difference between each number is of 2.
So if we want to write the function as
f(1) = 5,
f(2) = f(1)+2 = 7,
f(3) = f(2)+2 = 9,
f(4) = f(3)+2 = 11,
f(5) = f(4)+2 = 13
So the final equation that represent the given table is;
s=f+2
So the option c is correct.
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8x + 9y = 3 and x + y = 0
Answer:
x is 3 and y is -3
Step-by-step explanation:
[tex]x + y = 0 \\ x + y - y = 0 - y \\ x = - y \\ \\ 8x + 9y = 3 \\ (8 \times - y) + 9y = 3 \\ - 8y + 9y = 3 \\ y = 3[/tex]
X = -3
Which is true?
A. 0.0093>0.01
B. 0.2673>0.2562
C. 0.5330>0.533
D. 0.6409>0.641
Answer: B; B. 0.2673>0.2562
Step-by-step explanation: So, let's focus on the decimals, we already know that 0.26 IS GREATER than 0.25. All the other expressions are showing the smaller number as greater, or equal to, I hoped this helped!
Someone please help me! Find the cotangent! Thank you!
The value for cotangent of ∠V is 55.6°.
What is pythagora's theorem?
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side. When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.Cotangent = adjacent / opposite
Pythagoras theorem,
WV² = XW² + VW²
9² = x² + (√57)²
x² = 81 - 57
= 24
x = √24
= 4.89
cot (v) = √24 / √57
v = cot⁻¹ (0.6488)
v = 55.6°
Hence, the value for cotangent of ∠V is 55.6°.
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X is the midpoint of UV. Y is the midpoint of UW. If mZUYX= 46, find mZW.
mZW=
U
Y
W
Answer:
46°
Step-by-step explanation:
As m<UYX and m<W is corresponding angle because X is the midpoint of UV and Y is the midpoint of UW, therefore
m<W = 46°
I hope my answer helps you.
Answer:
m<W = 46 degrees
Step-by-step explanation:
UX = UV/2 ==> This is because X is the mid-point of UV, dividing UV by 2
to make UX
UY = UW/2 ==> Y is the mid-point of UW, dividing UW by 2 to make UY
XY = VW/2 ==> Since X is the midpoint of UV and Y is the midpoint of UW,
segment XY is exactly in the middle of point U and
segment VW, so segment XY is half of segment VW.
Since all sides of the small triangle(ΔUXY) are exactly half of all sides in the big triangle(ΔUVW), The corresponding angles in each triangle are equal to each other:
Hence, m<UYX = m<UWV
m<UWV ==> m<W = 46 degrees ==> since m<UYX=46, m<W = 46 as well
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Which angle is an adjacent interior angle to
The required adjacent interior angle is the angle angles that lie later or former to the given angle.
Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
Here,
Consider a triangle,
In triangle, there are three angles in triangle
Each of the angle is adjacent with the other two lying former and later in the sequence.
Thus, the required adjacent interior angle is the angle angles that lie later or former to the given angle.
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a child is riding in a boat in a 12-m-deep pond. while in the boat he plays with a stone sphere of radius 2.0 cm. a). if the sphere has a mass of 89 g. what is its density?b). if the child holds the sphere under water, what is the difference in pressure between the top and bottom of the sphere?c). as you kne would happen, the child drops the stone sphere in the pond. what is the total pressure exerted on the sphere when it is at the bottom of the pond?
the total pressure exerted on the sphere when it is at the bottom of the pond is 8∛2 ≈ 10.08
The volume of a hemisphere is given by the formula ...
V = (2/3)πr³
Then the radius is ...
r = ∛(3V/(2π))
r = ∛(3·1071.79/(2·3.14)) ≈ ∛512.00 ≈ 8.00
The radius of Sarah's pond is 8 inches.
We can see from the above that the radius is proportional to the cube root of the volume. If Sarah wants to double the volume, she needs to multiply the radius by ∛2 ≈ 1.260.
The pressure will be 8∛2 ≈ 10.08
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The Support Vector Classifier includes a tuning parameter C that controls the bias-variance trade-off. Which of the following statements is correct?
a) As C increases, the margin becomes smaller, which increases bias but potentially decreases variance
b) As C increases, the margin becomes smaller, which decreases bias but potentially increases variance
c) As C increases, the margin becomes larger, which increases bias but potentially decreases variance
d) As C increases, the margin becomes larger, which decreases bias but potentially increases variance
The correct answer is D) As C increases, the margin becomes larger, which decreases bias but potentially increases variance.
In the Support Vector Classifier (SVC), the parameter C controls the trade-off between the model's complexity and the amount of training error that it is allowed to have. A larger value of C means that the model will be more complex, and therefore will have a larger margin.
This will decrease the bias of the model but may increase the variance.
On the other hand, a smaller value of C means that the model will be less complex and will have a smaller margin, which will increase the bias of the model but potentially decrease the variance.
So, in summary, as C increases, the margin becomes larger, which decreases bias but potentially increases variance.
Hence, the correct answer would be an option (D).
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Use the marginal tax rate chart to answer the question.
Tax Bracket Marginal Tax Rate
$0–$10,275 10%
$10,276–$41,175 12%
$41,176–$89,075 22%
$89,076–$170,050 24%
$170,051–$215,950 32%
$215,951–$539,900 35%
> $539,901 37%
Determine the effective tax rate for a taxable income of $192,700. Round the final answer to the nearest hundredth.
32.00%
21.77%
24.00%
18.57%
PLEASE HELP
Answer: B. 21.77%
Step-by-step explanation: See picture. I'm currently taking the test right now
Answer:
(b) 21.77%
Step-by-step explanation:
Using the given tax rate table, you want to know the effective tax rate on a taxable income of $192,700.
TaxThe tax will be the sum of the taxes due in each of the brackets. This sum can be simplified to make the tax computation a little less work.
tax = 0.10(10275) +0.12(41175 -10275) +0.22(89075 -41175) +0.24(17050 -89075) +0.32(192700 -170050)
= 10275(0.10 -0.12) +41175(0.12 -0.22) +89075(0.22 -0.24) +170050(0.24 -0.32) +192700(0.32)
= 192700(0.32) -(10275(0.02) +41175(0.10) +89075(0.02) +170050(0.08))
= 192,700(0.32) -19708.50
tax = 41955.50
Effective rateThe tax as a percentage of the taxable income is ...
tax/income × 100% = 41955.50/192700 × 100% ≈ 21.77%
The effective tax rate is about 21.77%.
__
Additional comment
We can use this same idea to simplify the tax table all around. The various tax computations are shown in the second attachment. Interestingly, the tax due is the maximum of the computations for the different brackets. The graph shows the effective tax rate (%) as a function of income. The effective rate for $192,700 is marked.
Because the tax tables are written with discontinuities, there can be some confusion about the amount that fits in each bracket. For example, the tax on 10276 is not 10% of 10275 plus 12% of zero. Rather it is 10% of 10275 plus 12% of (10276 -10275), for a total of $1027.62.
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the following are midterm scores of an algebra class of 20 students in a high school: 69 84 52 93 81 74 89 85 88 63 87 64 67 72 74 55 82 91 68 77 find the interquartile range using r.
13.3 is the interquartile range of the data set.
Given,
The midterm scores of an algebra class of 20 students;
69 84 52 93 81 74 89 85 88 63 87 64 67 72 74 55 82 91 68 77
We have to find the interquartile range using r.
Interquartile Range;-
The second and third quartiles, or the centre half of your data set, are contained in the interquartile range (IQR). The interquartile range provides the range of the middle half of a data set, whereas the range provides the spread of the entire data set.
Interquartile range = Q3 - Q1
Q1 is the lower quarter
Q3 is the upper quarter
Q2 is the median
Here,
Q2 = 63 + 87 / 2 = 150 / 2 = 75
Q1 = 81 + 74 / 2 = 77.5
Q3 = 74 + 55 / 2 = 64.5
Then,
Interquartile range = Q3 - Q1 = - (64 . 5 - 77.5) = 13.3
That is,
The interquartile range for the given data set is 13.3
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HELP IM IN K12 PLEASE HELP
Step-by-step explanation:
p = a + 3
Three more a than p
A population of squirrels lives in a forest with a carrying capacity of 1800 Assume logistic growth with growth constant k = 0.8 yr-1 . (a) Find a formula for the squirrel population P(t) , assuming an initial population of 450 squirrels_ P(t) 1800/(1+3e^(-0.8t)) (b) How long will it take for the squirrel population to double? doubling time ~ 83 years
By applying formulas of logistic growth we can find the answers as part (a) P(t) = 1800 / (1+3e^(-0.8t)) and part(b) 1.37 years
What is logistic growth?In a logistic growth the growth rate decreases with the passage of time until the growth reaches the maximum capacity at infinite time.
What is formula for logistic growth?The formula is f(t) = L / (1+ ye^(-kt))
where L is the maximum value, k is the growth rate, y is a constant and t is time.
Part(a)
In this case, L = 1800, k = 0.8 yr-1
f(t) = 1800 / (1 + ye^(-0.8)t)
at t = 0 , f = 450,
450 = 1800/ (1+y)
solving this gives, y = 3
Thus the final answer is f(t) = 1800/ (1+ 3e^(-0.8t))
Part(b)
we need to find the time when f(t) = 900
900 = 1800/(1+3e^(-0.8t))
t = 1.37 years
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Professor Bowdidge taught four business statistics classes during the fall semester with the following grade averages for each class: 74%, 82%, 86%, and 91%. Calculate the mean (round to the nearest hundredth). A. 83.00% B. 83.12% C. 85.00% D. 83.25%
By using the mean formula, the mean grade across all four classes was 83.25%.
What is mean?The mean is a measure of central tendency that represents the average value of a set of data
What is formula to calculate mean?The formula for calculating the mean:
Mean = (x1 + x2 + x3 + ... + xn) / n
Where:
x1, x2, x3, ..., xn are the individual values in the set
n is the total number of values in the set
Mean = (74 + 82 + 86 + 91) / 4
Mean = 333 / 4
Mean = 83.25
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UX ≅ UY, YZ ≅ WX, TZ ≅ VW, and UV ≅ TU. Complete the proof that ∠W≅∠Z.
This is the first question I have seen with this type of two column proof, and i do not want to get it wrong as a large portion of my score will be taken from me.
(There may have to be another row(s) added, which can be done with the "Add line" button)
Geometry, Proofs involving SSS(and CPCTC)
https://www.ixl.com/math/geometry/proofs-involving-sss
You are just couple of steps away from completing the proof.
So far you have concluded that two sides of triangles ZTX and WVY are congruent. You need to complete it for the third side and prove the triangles are congruent. Then use it to complete the proof.
Missing statement and reasons given below.
Statement Reason
12. WY = XZ Transitive property13. ΔZTX ≅ ΔWVY SSS congruency14. ∠W ≅ ∠Z CPCTCTriangle TVW is dilated according to the rule
(x,y)(three-fourths x, three-fourths y) to create the image triangle T'V'W', which is not shown.
On a coordinate plane, triangle T V W has points (negative 4, 8), (0, 4), and (4, 4).
What are the coordinates of the endpoints of the segment T'V'?
T'(-3, 6) and V'(0, 3)
T'(-3, 6) and V'(0, 1)
T'(-1, 2) and V'(0, 3)
T'(-1, 2) and V'(0, 1)
The coordinates of the endpoints of the segment T'V' are equal to: A. T'(-3, 6) and V'(0, 3).
What is dilation?In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.
Next, we would have to dilate the coordinates of triangle TVW by using the following transformation rule with a scale factor of 3/4: (x, y) → (3x/4, 3y/4)
For coordinate T, we have;
Coordinate T = (-4, 8) → (3/4(-4), 3/4(8)) = Coordinate T' = (-3, 6).
For coordinate V, we have;
Coordinate V = (0, 4) → (3/4(0), 3/4(4)) = Coordinate V' = (0, 3).
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Answer:
A. T'(-3, 6) and V'(0, 3)
Step-by-step explanation:
5 + 2a = a - 9 what does a equal
a= -14.
Step-by-step explanation:1. Write the expression.[tex]5 + 2a = a - 9[/tex]
2. Subtract 5 from both sides of the equation.[tex]5 + 2a -5= a - 9-5\\ \\2a=a-14[/tex]
3. Subtract "a" from both sides of the equation.[tex]2a-a=a-14-a\\\\a=-14[/tex]
4. Verify.[tex]5 + 2(-14) = (-14) - 9\\ \\5-28=-23\\ \\-23=-23[/tex]
Both sides are equal to each other, hence a= -14 is the correct solution.
5. Conclude.a= -14.
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Determine which of these are linear homogeneous recurrence relations with constant coefficients. Also, find the degree of those that are:
a) an = 3an-1 + 4an-2 +5an-3
b) an = 2nan-1 + an-2
c) an = an-1 + an-4
A linear recurrence relation is homogeneous if f(n) = 0. The order of the recurrence relation is determined by k. We say a recurrence relation is of order k if an = f(an−1,...,an−k).
Given: a) an = 3an-1 + 4an-2 +5an-3
We note that the given recurrence relation is linear, because the right-hand side is a linear combination of previous terms. We note that the given recurrence relation is homogeneous, because the recurrence relation does not contain any constant terms. The degree of the recurrence relation is the largest value k for which are occurs in the recurrence relation.
k=3
Given: b) an = 2nan-1 + an-2
We note that the given recurrence relation is not linear, because the right-hand side is not a linear combination of previous terms (due to the
fact that 2n is not a constant). We note that the given recurrence relation is homogeneous, because the recurrence relation does not contain any constant terms.
Given: c) an = an-1 + an-4
Because the right-hand side is a linear combination of the prior terms, we observe that the provided recurrence relation is linear. Given that there are no constant terms in the recurrence relation, it is important to observe that it is homogenous. The biggest value k for which are k appears in the recurrence relation is the recurrence relation's degree.
Degree of linear homogeneous recurrence are k=3 .
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For a standard normal distribution, find: P(Z > -1.56) Express the probability as a decimal rounded to 4 decimal places. For a standard normal distribution, find: P(Z < 0.26) Express the probability as a decimal rounded to 4 decimal places.
the value of P(Z>-1.56) is 0.9406
The value of P(Z<0.26) is 0.6026
For a standard normal distribution,
the standard normal distribution is also known as the Z - distribution
it is a very special type of distribution in which the value of mean is zero and the value of standard deviation is one.
the formula of standard normal distribution is
[tex]f(x)=\frac{1}{\sigma\sqrt{2\pi } } e^{\frac{-1}{2}(\frac{x-\mu}{\sigma})^2 }[/tex]
(OR)
Z=[tex]\frac{x-\mu}{\sigma}[/tex]
where
[tex]\mu[/tex] is the value of mean
[tex]\sigma[/tex] is the value of standard deviation
f(x) is the probability density function
now,
the value of P(Z>-1.56) is
P(Z> -1.56) = 1 - P(Z< -1.56)
=> 1 - 0.05938
=> 0.94062 (By rounding to 4 decimal places we get)
=> 0.9406
P(Z<0.26) = 1 - P(Z<0.26)
=> 0.60257 (By rounding to 4 decimal places we get )
=> 0.6026
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find the critical values for a 95% confidence interval using the chi-square distribution with 15 degrees of freedom
The critical values for a 95% confidence interval using the chi-square distribution with 15 degrees of freedom are roughly 21.02 and 32.36.
The critical value for the 95% confidence interval using the 15 degrees of freedom chi-square distribution is the value that divides the distribution into two;
lower tail and upper tail. These values are calculated such that the area under the curve of the chi-square distribution between the critical values represents 95% of the total area under the curve.
To find critical values, you can use a chi-square table or a computer program that calculates critical values for a given confidence level and degree of freedom.
In this case, the critical value for the 95% confidence interval with 15 degrees of freedom can be determined as follows:
Lower critical value:
The lower critical value is the value corresponding to the area under the chi-square distribution curve to the left of the value, equal to 2.5% (half of 5% not included in the confidence interval). Using a chi-square table or computer program, we can find that the lower critical value for the 95% confidence interval with 15 degrees of freedom is approximately 21.02. Upper critical value:
The upper critical value is the value corresponding to the area under the chi-square distribution curve to the right of the value, equal to 2.5% (half of 5% is not included in the confidence interval).
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a company's sales in year 1 were $330,000 and in year 2 were $367,500. using year 1 as the base year, the percent change for year 2 compared to the base year is:
Percentage change in company's sales is 11%
What is percentage?
In arithmetic, a proportion may be a range or magnitude relation expressed as a fraction of a hundred. it's usually denoted victimisation the percentage sign, "%", d. A proportion may be a dimensionless number; it's no unit of measuring.
Main body:
According to the question:
company's sales in year 1 = $330,000
company's sales in year 2 =$367,500
Change = $ 367500 – 330000 = $ 37,500
Percentage change = $ 37500 / $ 330000 = 0.11
Percentage change = 11%
Hence ,Percentage change in company's sales is 11%.
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refer to the work hrs.rds dataset. in this problem, we want to examine the effect of an hourly wage (wage), education (educ), and the number of children (nchild) on the hours worked per week by married women (hrswork).
The coefficient values will indicate the change in the dependent variable (hrswork) for a one-unit change in the independent variable (wage, educ, and nchild).
To examine this, we would use a regression analysis to look at the relationship between each of these variables and the hours worked per week. We would create a model with wage, educ, and nchild as the independent variables, and hrswork as the dependent variable. We can then analyze the coefficient of each of these variables to measure the effect they have on the hours worked per week. The coefficient values will indicate the change in the dependent variable (hrswork) for a one-unit change in the independent variable (wage, educ, and nchild).
1. Load the work hrs.rds dataset.
2. Examine the data to identify the independent and dependent variables. In this case, the independent variables are wage, educ, and nchild, and the dependent variable is hrswork.
3. Use a regression analysis to examine the relationship between the independent and dependent variables.
4. Create a model with wage, educ, and nchild as the independent variables, and hrswork as the dependent variable.
5. Analyze the coefficient of each of the independent variables to measure the effect they have on the dependent variable (hrswork).
6. Interpret the results to determine the effect of the independent variables on the dependent variable.
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in a certain quadrilateral, the three shortest sides are congruent and both diagonals are as long as the longest side. what is the degree measure of the largest angle of tihs quadrilateral
The measurement of the largest angle of the quadrilateral is 108°
Given,
Quadrilateral;
A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.
Here,
Three shortest sides of the quadrilateral are congruent.
Both diagonals are as long as the longest side.
That is,
Side 1 ≅ Side 2 ≅ Side 3
Side 4 = Diagonal 1 = Diagonal 2
Then,
The largest angles of the quadrilateral will be 108°
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Determine the number and type of solutions for the equation x^2+8x+15=0
Two different irrational-number solutions
One repeated irrational-number solution
One repeated rational-number solution
Two different rational-number solutions
Two imaginary-number solutions
Answer:
Step-by-step explanation:
disc=8²-4×1×15=64-60=4=2²>0
it is a perfect square and >0
so it has one repeated rational number solution.
1. A survey of local car dealers revealed that 64% of all cars sold last month had CD players,
28% had alarm systems, and 22% had both CD players and alarm systems.
a.
What is the probability one of these cars selected at random had neither a CD player nor
an alarm system?
b. What is the probability that a car had a CD player unprotected by an alarm system?
C.
What is the probability a car with an alarm system had a CD player?
D.
Are having a CD player and an alarm system disjoint events? Explain.
apply dijkstra's algorithm to find the shortest path from vertex a to vertex g in h. for full credit you must show your work, follow dijkstra's algorithm approach explicitly, and indicate both the shortest path and cumulative weight at the end
On solving the provided question, Mark the remaining distances with infinite and your chosen beginning node with a current distance of 0.
What is Dijkstra's algorithm?In a graph that may, for instance, represent a network of roads, Dijkstra's Method is an algorithm for determining the shortest routes between nodes. Computer scientist Edsger W. Dijkstra created it in 1956, and it was published three years later. Algorithms come in a wide variety.
Here is how the algorithm is described:
Mark the remaining distances with infinite and your chosen beginning node with a current distance of 0.Make current node C the non-visited node with the shortest current distance. You should double the distance between your current node C and each of its neighbors, N, by the weight of the edge that connects C and N. Make it the new current distance of N if it is less than the current distance of N. C is the current node; mark it as visited.
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a church window is bounded above by a parabola and below by the arc of a circle (see figure). find the surface area of the window. (round your answer to three decimal places.)
The surface area of a church window bounded above by a parabola and below by the arc of a circle is 2.750x^2, rounded to three decimal places.
Let x be the length of the window. The radius of the arc of a circle is x/2.
Surface area = [Area of parabola] + [Area of arc of a circle]
= (1/2)x^2 + (π/2)*(x/2)^2
= (1/2)x^2 + (π/4)x^2
= (π/4 + 1/2)x^2
= (1 + π/4)x^2
= 2.75x^2
Answer: 2.750
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PLS HELP QUICK! 20 POINTS
Can a triangle be formed with side lengths 5, 6, 12? Explain.
No, because 5 + 6 < 12
Yes, because 5 + 6 > 12
No, because 12 − 6 < 6
Yes, because 12 − 6 < 5
Answer:
No, because [tex]5+6<12[/tex]
Step-by-step explanation:
The side lengths do not satisfy the triangle inequality.
find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = 1 + 10. Vt, y+t^5 -t, and z + t^5 + t; (11, 0, 2)?
Dy/dx = (dy/dt)/(dx/dt) denotes the slope of the tangent line of a parametric curve whose parametric equations are x = /(t) and y = g(t). Wherever dy/dt is zero and dx/dt is zero, a parametric curve has a horizontal tangent.
What is the formula for parametric equations?The x and y coordinates are defined as functions of t when parametric form is used to represent angles: Plot the entire circle by using the equations x = r cos t and y = r sin t. Polar equations are the name given to these parametric equations.
The given x=1+12+ dx=dt 0+12(1) =12
Parametric y Curve is as follows: ts-t dy 5t-1 dt z = ts+t dz dt 5t +1 (dz, dy, dz) = (12, 5t-1, St+1) dt 7 dt dt x = 13 =) When, 1+12 t = 13 12
(x(t), y(t), and z(t)) = (13,0,2) + + (12, 4, 6) x(t), y(t), and 2(t)) = (13+12t, ut, 2+ 6+) x(t) = 13+12t, y(t) = ut, 2(t).
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Full Question = Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.
x = 1 + 12 t , y = t5 − t, z = t5 + t; (13, 0, 2)
x(t), y(t), z(t) =
4. *
This pattern of squares continues. Which equation below relates the number of squares, n, in a picture to the size number, s ?
Size 1
Size 2
a) n=s+4
b) n=4 s
c) n=4 s+1
d) s=4 n
A
B
c
D
The required equation that following the pattern is n = 4s+1. So the option c is correct.
In the given question, we have to choose which equation below relates the number of squares, n, in a picture to the size number, s.
The given options are:
a) n = s+4
b) n = 4s
c) n = 4s+1
d) s = 4n
We find the pattern we firstly observe the given diagram closely.
As we can see that in first diagram have 5 blocks.
In second diagram have 9 blocks.
In third diagram have 13 blocks.
So, if the number of squares, represent by n, in a picture and the size number, represented by s, so the required equation that following the pattern is n = 4s+1. So the option c is correct.
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Find the area of the parallelogram with vertices P(1, 0, 2), Q(3, 3, 3), R(7, 5, 8), and S(5 , 2, 7).
The area of parallelogram with the vertices is √269 when vertices are P(1, 0, 2), Q(3, 3, 3), R(7, 5, 8), and S(5 , 2, 7).
Given that,
The vertices are P(1, 0, 2), Q(3, 3, 3), R(7, 5, 8), and S(5 , 2, 7).
We have to find the area of parallelogram with the vertices.
We know that,
PQ=Q-P=(3,3,3) -(1,0,2)=(2,3,1)
PR=R-P=(7,5,8) -(1,0,2)=(6,5,6)
Find area using cross product as
Area= |PQ x PR|
=|i (3(6)-1(5)) - j (2(6)-1(6)) + k (2(5)-3(6)) |
= |i (18 - 5) - j (12 -6) + k (10 -18) |
= |{13; 6; -8}|
=√(13²+6²+(-8)²)
=√269
Therefore, the area of parallelogram with the vertices is √269 when vertices are P(1, 0, 2), Q(3, 3, 3), R(7, 5, 8), and S(5 , 2, 7).
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