The point 4 units along the curve (in the direction of increasing t) from P exists as t = ln |L/2 + 1|.
What is meant by arc length of the function?When a particle's position in space is represented as a function of time by a vector-valued function, the arc-length function calculates the particle's travel distance as a function of time.
The length of an arc is the separation of two locations along a segment of a curve. Curve rectification is the process of measuring an irregular arc segment's length by simulating the section as a network of connected line segments. A rectifiable curve can be broken down into a finite number of segments.
(a) Let the given function be r(t) = [tex]e^t[/tex] sin t i + √2 [tex]e^t[/tex] k
To find the arc length of the function, we have:
[tex]& \mathrm{r}^{\prime}(\mathrm{t})=\mathrm{e}^t \\[/tex]
[tex]& \mathrm{r}^{\prime}(t)=(\cos t+\sin t) e^t+(\cos t-\sin t) e^t+\sqrt{2} e^t \\[/tex]
[tex]& \left|r^{\prime}(t)\right|=\sqrt{\left[(\cos t+\sin t) e^t\right]^2+\left[(\cos t-\sin t) e^t\right]^2+\left(\sqrt{2} e^t\right)^2}[/tex]
simplifying the above equation, we get
[tex]& =\sqrt{\left(4 e^{(2 t)}\right)} \\[/tex]
[tex]& =2 \mathrm{e}^t[/tex]
(b) We have the arc length function, L to be the integral from 0 to t, so:
[tex]$& L=\int_0^t 2 e^v \\[/tex]
simplifying the above equation, we get
[tex]& L=2 e^t-2 e^0 \\[/tex]
[tex]& =2 e^t-2 \\[/tex]
[tex]& L=2\left(e^t-1\right) \\[/tex]
simplifying the above equation, we get
[tex]$& L / 2=e^t-1 \\[/tex]
[tex]& L / 2+1=e^t[/tex]
[tex]e^t[/tex] = L / 2+1
t = ln |L/2 + 1|
The complete question is:
A. Find the arc length function for the curve measured from the point P in the direction of increasing t and then reparametrize the curve with respect to arc length starting from P.
b. Find the point 4 units along the curve (in the direction of increasing t) from P.
r(t) = et sin t i + √2 et k, P(0, l ,√2)
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Car A travels 702 miles on 12 gallons of gasoline. Car B travels 873 miles on 15 gallons of gasoline. Hugo wants to buy a car with lower fuel consumption. Find out the distance each car could travel per gallon of gasoline. Then, tell which of the two cars (A or B) Hugo should buy.
Answer: Hugo should buy car A
Step-by-step explanation:
Car A
Take 702 divided by 12 = 58.5 miles per gallon of gas
Car B
Take 873 divided by 15 = 58.2 miles per gallon of gas.
So Hugo should buy car A
tell whether the orthocenter is inside, on, or outside the triangle. then find the coordinates of the orthocenter. x(-3,2)
Therefore , the solution of the given problem of triangle comes out to be
Orthocentre (0, - 5 ).
How do triangles function?Triangles are polygons with three sides and three vertices. The triangle's angles are created by joining its three sides end to end at a single point. The triangle has three angles, and the sum of them is 180 degrees.
Here,
We need the lengths of the triangle's three sides in order to identify which of the aforementioned cases the triangle fits into.
Make the length calculations using the distance formula.
d = [tex]\sqrt{(x2-x1)^{2}+(y2-y1)^{2}}[/tex]
L(0, 5) and M(3, 1)
LM =d = [tex]\sqrt{(3-0)^{2}+(1-5)^{2}}[/tex] = 5
L(0, 5) and (N(8, 1)
LN = d = [tex]\sqrt{(8-0)^{2}+(1-5)^{2}}[/tex] = √80
M(3, 1) and (N(8, 1)
MN = [tex]\sqrt{(8-3)^{2}+(1-1)^{2}}[/tex] = 5
If a triangle has three sides, a, b, and c, and side c is the longest, then
• Right triangle formed by a2 + b2 = c2
• a2 + b2 c2 - acute triangle
Triangle with angles a2, b2, and c.
A, B, and C are equal to five in this instance.
a² + b² = 5² + 5² = 25 + 25 = 50
c² = (4 )² = 80
A triangle is obtuse and the orthocentre lies outside the triangle because a2 + b2 c2.
The place where the triangle's three altitudes converge is known as the orthocentre.
For the orthocentre's coordinates, we only need to simultaneously solve
the equations for two of the altitudes.
A line drawn at a right angle from a vertex to the other side is known as an altitude.
Altitude from M to LN
Calculate the slope of LN using the slope formula
m = (y2 - y1 )/ (x2- x1 ) = 1-5/8-0 ⇒ = 2
Equation of altitude
y - 1 = 2(x - 3)
y - 1 = 2x - 6
y = 2x - 5 → (1)
Altitude between M and LN
Utilize the slope formula to determine LN's slope.
m = (y2 - y1)/ (x2- x1) = 1-5/8-0 ⇒ = 2
formula for altitude
y - 1 = 2(x - 3) (x - 3)
y - 1 = 2x - 6
y = 2x - 5 → (1) (1)
Altitude between N and LM
m = (y2 - y1)/ (x2- x1) = 1-5/3-0 ⇒ -3/4
formula for altitude
y - 1 = (x - 8) (x - 8)
y - 1 = x - 6
y = x - 5 → (2) (2)
Adding (1) to (2)
2x - 5 Equals x - 5 ( multiply through by 4 ) ( multiply through by 4 )
8x - 20 = 3x - 20
5x - 20 = - 20 ( add 20 on both sides ) ( add 20 to both sides )
5x = 0 ⇒ x = 0
Place x = 0 in place of (1)
y = 0 - 5 = - 5
It is the orthocentre (0, - 5 )
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which statement correctly describes the relationship between △def and △d′e′f′?
△DEF is congruent to △D'E'F' because you can map △DEF to △D'E'F' using a reflection across the x-axis, which is a rigid motion.
What does a math congruent mean?
Congruent refers to having precisely the same form and size. Even after the shapes have been flipped, turned, or rotated, the shape and size ought to remain constant.
1) Reflections, rotations and translations are rigid transformations, because they do not modify the lengths of the segments nor the angles, so the images and the preimages are congruents.
2) Let's see what transformation map △DEF is to △D'E'F' by analyzing the vertices of preimage and image:
Preimage Image
D (-3, -1) D' (-3, 1)
E (2, -4) E' (2, 4)
F (4, -4) F' (4, 4)
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given a function with one vector parameter scores. how should the parameter be defined if scores may be very large, and the function will modify the parameter? group of answer choices constant, and pass by value constant, and pass by reference not constant, and pass by reference not constant, and pass by value
Given a function with one vector parameter scores, if scores may be very large, and the function will modify the parameter, the parameter would be defined as pass by reference but not constant.
Pass-by-reference refers to passing the reference of an argument in the calling function to the corresponding formal parameter of the called function. The called function can modify the value of the argument by using its reference passed in. It refers to an alias or reference to the actual parameter that is passed to the method. Pass by reference makes the parameter modifiable, but constant prevents the parameter from being modified.
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1. Business is major
The sampling distribution of p
PROBLEM:
According to the National Center for Education Statistics, 20% of students who
recently earned bachelor's degrees were business majors. Imagine taking an SRS of
300 students who recently earned bachelor's degrees and calculating p = the
proportion of students in the sample who majored in business.
(a) Identify the mean of the sampling distribution of p.
(b) Calculate and interpret the standard deviation of the sampling distribution of p.
Verify that the 10% condition is met.
(c) Describe the shape of the sampling distribution of p. Justify your answer.
a) The mean of the sampling distribution of p is of 0.2.
b) The standard deviation of the sampling distribution of p is of: 0.0231, which is the amount that the sample proportions may differ from 0.2.
c) The shape of the sampling distribution of p is approximately normal.
How to define the sampling distribution of p?The sampling distribution of p is defined according to the Central Limit Theorem, which states that the sampling distribution of a proportion p in a sample of size n has:
Approximately normal shape.Mean equals to p.Standard deviation equals to [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex]The parameters for this problem are given as follows:
p = 0.2, n = 300.
The 10% condition is given as follows:
np = 300 x 0.2 = 60 > 10.n(1 - p) = 300 x 0.8 = 240 > 10.Then the standard error of the sampling distribution of p is calculated as follows:
[tex]s = \sqrt{\frac{0.2(0.8)}{300}} = 0.0231[/tex]
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homework due now!!!!!!!!!!!
Answer:
Option D: 7/3x
Step-by-step explanation:
Because this line passes through the origin (0,0), we know that there is know b-value according to the equation y = mx + b. To figure out the equation, we must first calculate the slope of the linear function.
Slope = △y/△x
△y (change in y) = -7
△x (change in x) = -3
Therefore, the slope is 7/3 and the equation is y = 7/3x.
HELPP!!!
angles of a triangle
Math
help please! Thank u.
Answer:
Step-by-step explanation:
40/20= 20
39/x=x
that woudl be how you would find it
what is arithmetic sequence
Answer: An arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence.
The constant difference in all pairs of consecutive or successive numbers in a sequence is called the common difference, denoted by the letter d.
Step-by-step explanation: Hope this was helpful
An arithmetic sequence (arithmetic progression) is a number sequence with a common difference between successive terms. By using the arithmetic sequence formula, we can easily find the value of a term and the common difference in the sequence.
Example: 5, 7, 9, 11, 13, 15
Find the two numbers which on multiplication with √360 gives a rational number. Are these numbers rational or irrational?
Answer:
The two numbers we are looking for are a rational number and an irrational number.
Step-by-step explanation:
To find the two numbers that, when multiplied by the square root of 360, give a rational number, we can consider the prime factorization of 360. 360 can be written as 2^3 * 3^2 * 5, so the square root of 360 is equal to √(2^3 * 3^2 * 5) = 2√(3 * 5) = 2√15.
Now, suppose we want to find a rational number that is equal to x * √15. We can rewrite this expression as x * √(3 * 5) = x * √3 * √5. For this expression to be rational, both x and √3 must be rational or both must be irrational.
If x is rational, then the expression x * √3 * √5 is rational. Therefore, one of the two numbers we are looking for is x, which is a rational number.
If x is irrational, then the expression x * √3 * √5 is irrational. Therefore, the other number we are looking for is √3, which is an irrational number.
Therefore, the two numbers we are looking for are a rational number and an irrational number.
Evaluate.
12÷(2+23)2
Responses
649
6 and 4 over 9
412
4 and 1 half
323
3 and 2 over 3
1 11/6
The evaluation of the given fraction expression is 1 11/16. The correct option is the last option
Evaluating a fraction expressionFrom the question, we are to evaluate the given expression.
The given expression is
[tex]12 \div (2+\frac{2}{3})^{2}[/tex]
Evaluating the expression
[tex]12 \div (2+\frac{2}{3})^{2}[/tex]
[tex]12 \div (\frac{8}{3})^{2}[/tex]
[tex]12 \div (\frac{8^{2}}{3^{2}})[/tex]
[tex]12 \div \frac{64}{9}[/tex]
= [tex]12 \times \frac{9}{64}[/tex]
= [tex]\frac{108}{64}[/tex]
= [tex]\frac{27 \times 4}{16 \times 4}[/tex]
= [tex]\frac{27}{16}[/tex]
= [tex]1\frac{11}{16}[/tex]
Hence, the fraction is 1 11/16
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b(x) = 6x², when x = 16
Answer:
Step-by-step explanation:
b(x)=6x^2
That is the same as b(x)=6*x*x
when x=16
b(16)=6*16*16=1536
what is geometric sequence
Answer: A Geometric sequence is a type of sequence in which each subsequent term after the first term is determined by multiplying the previous term by a constant (not 1), which is referred to as the common ratio.
Step-by-step explanation: Hope this was helpful
Step-by-step explanation:
The sequence
a, ar, ar^2, .....ar^n-1,...
where a is the first term and any two consecutive numbers differ by a factor r, is called a Geometric progression (G.P.).
Geometric progression also known as Geometric sequence.
Find the derivative please
Answer:
[tex] \displaystyle{ y' = \dfrac{2}{1 - {x}^{2} }}[/tex]
Step-by-step explanation:
Apply natural logarithm chain rule:
[tex] \displaystyle{y = \ln(u) \to y' = \dfrac{u'}{u}}[/tex]
Where u is a function. The ' symbol indicates that the function to be derived. From this formula, we will have:
[tex] \displaystyle{y' = \dfrac{ \left (\dfrac{1 + x}{1 - x} \right)'}{ \dfrac{1 + x}{1 - x}}}[/tex]
Now we have to derive quotient functions, we can use quotient rule for this:
[tex] \displaystyle{y = \dfrac{u}{v} \to y' = \dfrac{u'v - uv'}{ {v}^{2} }}[/tex]
Where u and v are functions. Therefore, from numerator:
[tex] \displaystyle{ \left( \dfrac{1 + x}{1 - x} \right)' = \dfrac{(1 + x)'(1 - x) - (1 + x)(1 - x)'}{ {(1 - x)}^{2} }}[/tex]
Derive using power rule and constant rule where:
[tex] \displaystyle{y = {x}^{n} \to y' = n {x}^{n - 1} } \\ \\ \displaystyle{y = c \to y' = 0 \: \: \: \: ( c \in \mathbb{R})}[/tex]
Thus:
[tex] \displaystyle{ \left( \dfrac{1 + x}{1 - x} \right)' = \dfrac{1(1 - x) - (1 + x)( - 1)}{ {(1 - x)}^{2} }} \\ \\ \displaystyle{ \left( \dfrac{1 + x}{1 - x} \right)' = \dfrac{1 - x- ( - 1 - x)}{ {(1 - x)}^{2} }} \\ \\ \displaystyle{ \left( \dfrac{1 + x}{1 - x} \right)' = \dfrac{1 - x + 1 + x}{ {(1 - x)}^{2} }} \\ \\ \displaystyle{ \left( \dfrac{1 + x}{1 - x} \right)' = \dfrac{2}{ {(1 - x)}^{2} }}[/tex]
Therefore, we will now have:
[tex] \displaystyle{y' = \dfrac{ \dfrac{2}{ {(1 - x)}^{2} }}{ \dfrac{1 + x}{1 - x}}}[/tex]
Simplify expressions:
[tex] \displaystyle{ \dfrac{ \dfrac{2}{ {(1 - x)}^{2} }}{ \dfrac{1 + x}{1 - x}} = \dfrac{2}{ {(1 - x)}^{2}} \times \dfrac{1 - x}{1 + x} } \\ \\ \displaystyle{ \dfrac{ \dfrac{2}{ {(1 - x)}^{2} }}{ \dfrac{1 + x}{1 - x}} = \dfrac{2}{ 1 - x} \times \dfrac{1 }{1 + x} } \\ \\ \displaystyle{ \dfrac{ \dfrac{2}{ {(1 - x)}^{2} }}{ \dfrac{1 + x}{1 - x}} = \dfrac{2}{ (1 - x)(1 + x)}}[/tex]
Therefore, the derived function is:
[tex] \displaystyle{ y' = \dfrac{2}{1 - {x}^{2} }}[/tex]
you have 3.35$ in quarters and nickels. If you have 31 coins how many each do you have?
a. Write a system for the problem
b. how many types of each coin do you have?
SOMEONE ANSWER PLSS IM DYING HERE
0.25Q+0.05N=3.25 and Q+N=31 is the required system of equation and nickels should be 22.5 and Quarters should be 8.5
What is Equation?Two or more expressions with an Equal sign is called as Equation.
From given,
3.35$ in quarters and nickels. If you have 31 coins
0.25Q+0.05N=3.25..(1)
Q+N=31
Q=31-N
Now substitute Q value in (1)
0.25(31-N)+0.05N=3.25
7.75-0.25N+0.05N=3.25
7.75-0.2N=3.25
Subtract 7.75 on both sides
-0.2N=3.25-7.75
-0.2N=-4.5
Divide both sides by 0.2
N=22.5
and Q+22.5=31
Q=31-22.5
Q=8.5
Hence, 0.25Q+0.05N=3.25 and Q+N=31 is the required system of equation and nickels should be 22.5 and Quarters should be 8.5
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Edwin wants to know the height of a water tower. If the water tower casts a shadow 12 yards
long and a nearby street sign that is 3 yards tall casts a shadow 4 yards long, then how tall is the water tower?
Find the difference. Enter your answer in the box below as a fraction, using the slash mark ( 1 ) for the fraction bar. 3/5 + 9/19
Therefore the solution to the difference of fraction comes out to be
12/95
What is fraction?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, and three-quarters, denotes the number of components of a specific size when used in conversational English.
Here,
the given fractions are 3/5 and 9/19
and to find the difference
we take lcm of both denominators
=> 3/5-9/19
=> (3*19-9*5)/5*19
=> (57-45)/95
=> 12/95
Therefore the solution to the difference of fraction comes out to be
12/95
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Give an example of each of the following: (a) A natural number (b) An integer that is not a natural number (c) A rational number that is not an integer (d) An irrational number
a) Natural number: [tex]12[/tex]
b) Integer that is not a natural number:[tex]-8[/tex]
c) Rational number that is not an integer: [tex]\frac{5}{10} or 0.5[/tex]
d) An Irrational number: [tex]\sqrt{3}[/tex]
A natural number is any whole number greater than zero, such as [tex]1,2,3,4,5,6[/tex] etc. Natural numbers are also known as counting numbers.
An integer is a whole number (not a fraction) that can be positive, negative, or [tex]0[/tex]. Examples of integers are: [tex]-5,0,1,5,10.[/tex]
Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are integers. Examples of rational numbers include [tex]-\frac{1}{2},\frac{3}{4},0.75, etc.[/tex]
Irrational numbers are numbers that cannot be expressed as a simple fraction and that cannot be written as a repeating or terminating decimal. Examples of irrational numbers include [tex]\pi (3.14), \sqrt{2}, etc.[/tex]
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a) Natural number: 12
b) Integer that is not a natural number:-8
c) Rational number that is not an integer: [tex]\frac{5}{10}[/tex]
d) An Irrational number: [tex]\sqrt{5}[/tex]
A natural number is any whole number greater than zero, such as [tex]1,2,3,4,5[/tex] etc. Natural numbers are also known as counting numbers.
An integer is a whole number (not a fraction) that can be positive, negative, or 0. Examples of integers are: [tex]-1,5, etc[/tex]
Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are integers. Examples of rational numbers include [tex]\frac{1}{2} ,0.5[/tex]
Irrational numbers are numbers that cannot be expressed as a simple fraction and that cannot be written as a repeating or terminating decimal. Examples of irrational numbers include [tex]\pi ,\sqrt{6}[/tex]
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A regular polygon is shown with one of its angle measures labeled a. 5 sided regular polygon with one angle labeled a If m∠a = (2z + 54)°, find the value of z.
The value of z if a 5-sided regular polygon with one angle labeled a, If m ∠ a = (2z + 54)° is 27.
What is a polygon?A polygon can be defined as a flat or plane, two-dimensional closed object circumscribed with straight sides. Its sides are not curled. A polygon's edges are another name for its sides. The vertices (or corners) of a polygon are the places where two sides converge.
Given:
m ∠ a = (2z + 54)°
The number of sides = 5,
Calculate the value of the sum of the interior angle by the formula given below,
[tex]S = 180(n - 2)[/tex]
S = 180 (5-2)
S = 180 × 3
S = 540°
Calculate the value of a as shown below,
[tex]a = S/5[/tex]
a = 540 / 5
a = 108
108 = 2z + 54
2z = 108 - 54
z = 54 / 2 = 27
Therefore, the value of z if a 5-sided regular polygon with one angle labeled a, If m ∠ a = (2z + 54)° is 27.
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one of the factors of g2 − 28g 196 is (1 point) g − 7 g − 14 g 14 g 7
( g - 14)² is factor of equation .
What is factor ?
A number that divides another number by itself with no residual is known as a factor.The factors of 8 are the numbers that divide 8 exactly without leaving any remainder. There are four factors of 8, they are 1, 2, 4, and 8.
In other words, if multiplying two whole numbers results in a product, the numbers we are multiplying are factors of the product since the product is divisible by them. Since the numbers we are multiplying are divisible by the product, they are factors of the product.
g2 − 28g + 196
= g² - 14g - 14g + 196
= g( g- 14 ) - 14( g - 14 )
= ( g - 14) ( g - 14)
= ( g - 14)²
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The complete question is -
One of the factors of g2 -28g + 196 is a. g-7 b. g-14 c. g+14 d. g+7
50 POINTS! Please Help!
Lola is making greeting cards, which she will sell by the box at an arts fair. She paid $50 for a booth at the fair, and the materials for each box of cards cost $8. She will sell the cards for $10 per box of cards. At some point, she will sell enough cards so that her sales cover her expenditures. How many cards will that take?
At some point, she will sell enough cards so that her sales cover her expenditures. So, the correct answer is ($40)
How did we figure this out?Lola is making greeting cards, which she will sell by the box at an arts fair. She paid $50 for a booth at the fair, and the materials for each box of cards cost $8. She will sell the cards for $10 per box of cards.
We are going to use 50, 8 and 10 to find are answer.
Therefore, we are going to divide the numbers:
[tex]\boxed{50/10}[/tex]
Division problem50/108 x ? = 40What is the missing number?First, we need to figure out 50/10:
[tex]\boxed{50/10=5}[/tex]
[tex]\boxed{8x5=40}[/tex]
[tex]5=40\\(50/10=5=8x5=40)[/tex]
Therefore, at some point, she will sell enough cards so that her sales cover her expenditures. So, the correct answer is ($40)
Answer:
40
Step-by-step explanation:
HELP ASAP WITH SLOPE PLEASE
the options are:
1
undefined
0
-1
Answer: 0
Step-by-step explanation:
Answer: 0
Step-by-step explanation:
Slope is a value that describes the steepness and direction of a line.
A line with a negative slope, said to be decreasing, runs downwards from left to right.
A line with a positive slops, said to be increasing, runs upwards from left to right.
A horizontal line has a slope of zero because y does not change. A vertical line has an undefined slope because you cannot divide by zero (x does not change).
I hope this helps to understand :)
Need help with this question, this is the unit about triangle mid segments
The length of the midsegment of the triangle DEF is 47 units.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know the midsegment of a triangle is half of the length of the parallel side.
∴ GH = (1/2)DF.
3x - 4 = (1/2)(9x - 59).
6x - 8 = 9x - 59.
- 3x = - 51.
x = 17.
So, The length of GH is 3(17) - 4 = 51 - 4 = 47 units.
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henry wants to earn at least trimming trees. he charges per hour and pays in equipment fees. what are the possible numbers of hours henry could trim trees?
The possible number of hours Henry could trim trees is t > 10.
The given information represents a scenario which demonstrates an inequality statement as Henry wants to earn at least $ 56, which means the amount earned should be greater than 56.
Let t be the possible number of hours Henry trim trees. As his per hour charge is $6 and he pays $4 in equipment fee, the inequality statement is:
6t – 4 > 56
Solving,
6t > 56 + 4
6t > 60
t > 10.
In order to earn at least $56, Henry must trim trees for at least 10 hours or more.
Note: The question is incomplete. The complete question probably is: Henry wants to earn more than $56 trimming trees. He charges $6 per hour and pays $4 in equipment rental fees. What are the possible number of hours Henry could trim trees?
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James is buying furniture for her new apartment. She buys one dining room table and four chairs and cost $265. Mark buys 2 tables and 6 chairs for the total cost of $470.
The system of equations below represents the scenario.
x + 4y = 265
2x + 6y = 470
Define the variables for x and y.
Determine the cost for one dining room table.
Using the system of equation, the cost of one dinning table is 145 dollars.
How to find the cost of one dinning table?James is buying furniture for her new apartment. She buys one dining room table and four chairs and cost $265. Mark buys 2 tables and 6 chairs for the total cost of $470.
The system of equation that represent the situation is as follows:
let
x = cost of one dinning room table
y = cost of one chair
Therefore,
x + 4y = 265
2x + 6y = 470
using substitution method,
x = 265 - 4y
2(265 - 4y) + 6y = 470
530 - 8y + 6y = 470
-2y = 470 - 530
-2y = -60
y = -60 / -2
y = 30
Hence,
x = 265 - 4(30)
x = 265 - 120
x = 145
Therefore,
cost of one dinning table = 145 dollars
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the average number of shoppers at a particular grocery store in one day is 505, and the standard deviation is 115. the number of shoppers is normally distributed. for a random day, what is the probability that there are between 250 and 450 shoppers at the grocery store?
For a random day with the standard deviation, the probability that there are less than 300 shoppers on a random day, is 0.00585.
Probability is a measure of the likelihood that an event will occur.
Many events cannot be predicted with absolute certainty. We can only predict the probability that an event will occur, i.e. how likely it is to occur, using it.The average total number of shoppers on a grocery store in 1 day is 505; the standard deviation is 115.
Let, X be the random variable denoting the number of shoppers on a random day.
Then, X follows normal with mean 505 and standard deviation of 115.
Then, we can say that,
Z=(X-505)/115 follows standard normal with mean 0 and standard deviation of 1.
We have to find
P (250 <X< 450)
= P {(250-505)/155} < Z < {(450-505)/155}
= P (-1.64 <Z< -0.03)
Where, Z is the standard normal variate.
ρ = -1.64 <ρ< -0.03
Where, ρ is the distribution function of the standard normal variate.
From the standard normal table, this becomes
=0.00585
For a random day, the probability that there are less than 300 shoppers on a random day, is 0.00585.
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Use Green's Theorem to calculate the circulation of G around the curve, oriented counterclockwise. G = 7yi + xyj around the circle of radius 6 centered at the origin. Close int C G. dr= [ ]
The circle's perimeter is determined by F = -9π, according to green's theorem.
What is Green's theorem?The simple formula for Green's theorem is the link between the total amount of microscopic circulation inside curve C and the macroscopic circulation revolving around it.
Remembering that we are talking about two dimensions, if C is a straightforward closed curve in the plane, it will enclose the region D (shown in red) in the plane.
So, knowing that this exercise should be solved using Green's theorem, then:
[tex]\begin{aligned}& \int 4 y d x+2 x y d y=\iint(d / d x)(2 x y)-(d / d y)(4 y) d A \\& =\iint 2 y-4 d A\end{aligned}[/tex]
You must convert in this manner to polar coordinates, and the result will be:
[tex]\begin{aligned}& \int_0^3 \int_0^{2 \pi}(2 r \sin (\theta)-4)(r) d \theta d r \\& =\int_0^3(-2 r \cos (\theta)-4 \theta)(-2 r \pi) d r \\& =-(\pi)\left(r^2\right)=-9 \pi\end{aligned}[/tex]
Therefore, the circle's perimeter is determined by F = -9π, according to green's theorem.
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Correct question;
Suppose F⃗ (x,y)=4yi⃗ +2xyj⃗ . Use Green's Theorem to calculate the circulation of F⃗ around the perimeter of a circle C of radius 3 centered at the origin and oriented counter-clockwise.
Mr. Callaway needs to purchase enough grass seed to cover a 3000-square-foot lawn and a
4200-square-foot lawn. If 40 ounces of grass seed will seed a 2400-square-foot lawn, how many ounces
does he need to seed both lawns?
Answer:
Mr. Callaway needs 120 ounces of seed to seed both lawns
Step-by-step explanation:
2400/40 = 60 ounces per square foot
3000 divided by 60 = 50 ounces
So, Mr. Callaway needs 50 ounces to cover a 3000-square-foot lawn
4200 divided by 60 = 70 ounces
So, Mr. Callaway needs 70 ounces to cover a 4200-square-foot lawn
50+ 70 = 120 ounces
So, Mr. Callaway needs 120 ounces to seed both lawns.
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Answer:
120 ounces pf grass seed
Step-by-step explanation:
[tex]\frac{40}{2400}[/tex] = [tex]\frac{x}{3000}[/tex] Cross multiply and solve for x
120000 = 2400x Divide both sides by 2400
\[tex]\frac{120000}{2400}[/tex] = [tex]\frac{2400x}{2400}[/tex]
50 = x
It will take 50 ounces of grass seed to cover 3,000 square foot lawn.
[tex]\frac{40}{2400}[/tex] = [tex]\frac{x}{4200}[/tex] Cross multiply and solve for x
168000 = 2400x Divide both sides by 2400
70 = x
It will take 70 ounces of grass seed to cover 4200 square foot lawn.
50 + 70 = 120
The line ax+by+c = 0 passes through the points (2 ,3) and (8 , 15). Find the ratio a :b :c.
The ratio of a : b : c in the linear equation is 2 : -1 : -1
How to determine the ratio of a : b : c?From the question, we have the following equation that can be used in our computation:
ax + by + c = 0
The points on the line are given as
(2 ,3) and (8 , 15)
A linear equation is represented as
y = mx + c
Where
Slope = m
y-intercept = c
This means that
3 = 2m + c
15 = 8m + c
Subtract the equations
So, we have the following representation
6m = 12
Divide by 6
m = 2
Substitute m = 2 in 3 = 2m + c
3 = 2 * 2 + c
So, we have
c = -1
Substitute m = 2 and c = -1 in y = mx + c
y = 2x - 1
So, we have
2x - y - 1 = 0
Recall that
ax + by + c = 0
This means that
a : b : c = 2 : -1 : -1
Hence, the ratio is 2 : -1 : -1
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The lifting force, F, exerted on an airplane wing varies jointly as the area, A, of the wing's surface and the square of the plane's velocity, v. The lift of a wing with an area of 250 square feet is 30,300 pounds when the plane is going at 190 miles per hour. Find the lifting force if the speed is 180 miles per hour. Round your answer to the nearest integer if necessary.
F= k*a*v^2
a= 250
v=190
30300=k*250*{190^2}
k= 0.003357
F= 0.003357*250*180*180
F=27135
The lifting force is 27135
What is surface area and an illustration?The total area that all of a 3D object's faces cover is the surface area. The surface area of a cube is its surface area, for instance, if we are trying to determine how much paint is needed to paint it. Always expressed in square units.
How does one determine surface area?The entire surface of a three-dimensional shape is referred to as its surface area. A cuboid with six rectangular faces has a surface area equal to the sum of the areas of each face. Alternatively, you can label the cuboid's length, width, and height (l, w, and h), then calculate its surface area (SA) using the formula: SA=2lw+2lh+2hw.
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