a crane is oriented so that the end of the 25-m boom ao lies in the yz plane. at the instant shown, the tension in cable ab is 4.8 kn. determine the moment about each of the coordinate axes of the force exerted on a by cable ab.
Answers
Applying Pythagoras theorem, and drawing free body diagram we can measure the moments required.
First of all draw the free body diagram.
Now, in triangle AOC, apply Pythagoras theorem,
Now, write the coordinates of the points,
O (0, 0, 0) m
A (0, 15, 20) m
C (0, 0, 20) m
B (2.5, 0, 20) m
Now, write the position vector from A to B,
Now, write the unit vector rAB
Now, write the tensional force on the point A due to the cable AB,
Now, calculate the force ‘T’ about the origin,
Hence the moments about the coordinate axes are,
Mx = 78.9 kN.m
Mx = 13.15 kN.m
Mx = -9.86 kN.m
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Related Questions
Help please
Determine whether the statement is true or false. If the statement is false, make the necessary changes) to produce a true statement.
Image attached
Answers
The complex number statement (3+8i)/(2+8i)=3/2 is false. The correct complex number statement is (3+8i)/(2+8i) = (24i + 6)/(-64i² + 16).
What is a complex number?
Complex numbers are those that are expressed as a+ib, where a and b are actual numbers and i is a imaginary number called a "iota."
The given complex number equation is (3+8i)/(2+8i)=3/2
Simplify both sides of the equation.
On the left side, there is -
= (3+8i)/(2+8i)
= (3+8i)/(2+8i) × (2-8i)/(2-8i)
= (6+24i-24i-64i²)/(2² + 2×8i-8i²)
= (-64i² + 24i + 6)/(-64i² + 16)
= (24i + 6)/(-64i² + 16)
On the right side, there is -
3/2 = 3/2
It can be seen that the simplified forms of both sides are not equal, so the original statement is false.
To make the statement true, change the right side of the equation to the left side simplified form.
(3+8i)/(2+8i) = (24i + 6)/(-64i² + 16)
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1. (04.03 MC)
If a household is saving 35% of their total bi-weekly gross pay of $1,546.00, determine how many months it will take to save a 20% down payment and 2.5% for closing costs for a
property with a purchase price of $195,450.00. (2 points)
Answers
Answer:
38
Step-by-step explanation:
NO LINKS!!! NOT MULTIPLE CHOICE!!
59. You put $500 into a bank account that earns 2% interest. Determine each of the following.
a. The value of the account after 3 years if compounded annually.
b. The value of the account after 5 years if compounded quarterly.
c. The value of the account after 10 years if compounded monthly.
d. The value of the account after 20 years if compounded continously.
Answers
Answer:
[tex]a. \;\; \boxed{\$ 530.60}[/tex]
[tex]b.\; \;\boxed{ \$552.45}[/tex]
[tex]c,\;\;\boxed{\$610.60}[/tex]
[tex]d. \;\; \boxed{\$745.91}[/tex]
Step-by-step explanation:
All four cases deal with compound interest on the same amount of $500 and same interest rate of 2%.
The only difference is in the frequency of compounding and time
Compound Interest Formula
[tex]\boxed{A = P\left(1 + \dfrac{r}{n}\right)^{n\cdot t}\\\\}[/tex]
where
This will depend on the frequency of compounding - daily, monthly, quarterly or yearly
t = number of number of years under consideration
In this particular problem we have
P = $500
r = 2% = 0.02
These are common for all parts of the question
Only n an t are different for each of the question sub-parts
Part a
Compounding is done annually (once a year) for 3 years
n = 1
t = 3 years
n · t = 3
[tex]A = 500\left(1 + \dfrac{0.02}{1}\right)^3\\\\A = 500\left(1.02\right)^3\\\\A = 500(1.061208)\\\\A=\boxed{\$ 530.60}[/tex]
For accuracy of calculations, I will not compute and store the exponent part, I will perform the calculations in one shot
Part b
Here the compounding is done quarterly (4 times a year) for 5 years
n = 4
t = 5 years
nt = 4 · 5 = 20
[tex]A = 500\left(1 + \dfrac{0.02}{4}\right)^{20}\\\\\\A = 500(1.005)^{20}\\\\A =\boxed{ \$552.45}[/tex]
Part c
Compounding done monthly(12 times a year) for 10 years
n = 12
t = 10
nt = 120
[tex]A = 500\left(1 + \dfrac{0.02}{12}\right)^{120}\\\\\\A = \boxed{\$610.60}[/tex]
Part d
First let's figure out what continuous compounding means
[tex]\fbox{\begin{minipage}[t]{1\columnwidth \fboxsep - 2\fboxrule}%\textsf{What is continuous compounding?} \\\textsf{Continuous compounding is the mathematicallimit that compound interest can reach if it's calculated and reinvestedinto an account's balance over a theoretically infinite number ofperiods. While this is not possible in practice, the concept of continuouslycompounded interest is important in finance. (Investopedia)}\}%\end{minipage}}[/tex]
The formula for continuous compounding can be determine by using the standard formula for periodic compounding and taking limits as
[tex]n \rightarrow \infty[/tex]
Therefore, for compounding continuously , the formula can be derived from
[tex]\lim _{n\to \infty } P\left(1 + \dfrac{r}{n}\right)^{nt}\\\\[/tex]
One of the limit formulas states
[tex]\lim _{x\to \infty } \left(1 + \dfrac{a}{x}\right)^{x} = e^a\\\\[/tex]
Therefore
[tex]\lim _{n\to \infty } \left(1 + \dfrac{r}{n}\right)^{n} = e^r\\\\[/tex]
So for the continuous compounding case, the formula is
[tex]\boxed{A = P \cdot e^{rt}}[/tex]
Here we have
r = 0.02
t = 20 years
rt = 20(0.02) = 0.4
Plugging in P = 500, and rt = 0.4 we get
[tex]A = 500 \cdot e^{0.4}\\\\A = \boxed{\$745.91}[/tex]
Answer:
a) $530.60
b) $552.45
c) $610.60
d) $745.91
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]
Part aGiven:
P = $500r = 2% = 0.02t = 3 yearsn = 1 (annually)Substitute the given values into the compound interest formula and solve for A:
[tex]\implies A=500\left(1+\dfrac{0.02}{1}\right)^{1 \cdot 3}[/tex]
[tex]\implies A=500\left(1.02\right)^{3}[/tex]
[tex]\implies A=500(1.061208)[/tex]
[tex]\implies A=530.604[/tex]
Therefore, the value of the account after 3 years if interest is compounded annually is $530.60 (nearest cent).
Part bGiven:
P = $500r = 2% = 0.02t = 5 yearsn = 4 (quarterly)Substitute the given values into the compound interest formula and solve for A:
[tex]\implies A=500\left(1+\dfrac{0.02}{4}\right)^{4 \cdot 5}[/tex]
[tex]\implies A=500\left(1.005\right)^{20}[/tex]
[tex]\implies A=500(1.10489557...)[/tex]
[tex]\implies A=552.447788...[/tex]
Therefore, the value of the account after 5 years if interest is compounded quarterly is $552.45 (nearest cent).
Part cGiven:
P = $500r = 2% = 0.02t = 10 yearsn = 12 (monthly)Substitute the given values into the compound interest formula and solve for A:
[tex]\implies A=500\left(1+\dfrac{0.02}{12}\right)^{12 \cdot 10}[/tex]
[tex]\implies A=500\left(1.0016666...\right)^{120}[/tex]
[tex]\implies A=500(1.22119943...)[/tex]
[tex]\implies A=610.599716...[/tex]
Therefore, the value of the account after 10 years if interest is compounded monthly is $610.60 (nearest cent).
Part d[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Interest Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\\phantom{ww}$\bullet$ $P =$ principal amount \\\phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\\phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\\phantom{ww}$\bullet$ $t =$ time (in years) \\\end{minipage}}[/tex]
Given:
P = $500r = 2% = 0.02t = 20 yearsSubstitute the given values into the continuous compounding interest formula and solve for A:
[tex]\implies A=500e^{0.02 \cdot 20}[/tex]
[tex]\implies A=500e^{0.4}[/tex]
[tex]\implies A=500(1.49182469...)[/tex]
[tex]\implies A=745.912348...[/tex]
Therefore, the value of the account after 20 years if interest is compounded continuously is $745.91 (nearest cent).
lan collects stamps. He put 34% of his stamp collection in an album. If there are
204 stamps in the album, how many stamps does he have in his collection?
Answers
well, there are a total of "x" stamps in his collection, which oddly enough is 100%.
now, we know that 34% of "x" is 204, what the heck is "x"?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 204& 34 \end{array} \implies \cfrac{x}{204}~~=~~\cfrac{100}{34} \\\\\\ \cfrac{ x }{ 204 } ~~=~~ \cfrac{ 50 }{ 17 }\implies 17x=10200\implies x=\cfrac{10200}{17}\implies x=600[/tex]
factor $(x^2 y^2-z^2)^2-4x^2y^2$ as the product of four polynomials of degree $1$, each of which has a positive coefficient of $x$. all coefficients appearing in your factorization should be integers. within each factor, arrange the terms so that variables appear in alphabetic order and the constant term, if any, is at the end. (this will help ensure accurate grading.)
Answers
We can factor [tex]$(x^2 y^2-z^2)^2-4x^2y^2$[/tex]as:
[tex]$(x^2 y^2-z^2)^2-4x^2y^2 = (x^2 y^2-z^2-2xy\sqrt{2})(x^2 y^2-z^2+2xy\sqrt{2})$[/tex]
To calculate this:
We can see that each factor is of degree 1 and has a positive coefficient of x.
In each factor, the variables appear in alphabetic order, with the constant term at the end.
In order to factor this expression, we first use the difference of squares, by breaking it down [tex]$(x^2 y^2-z^2)^2$[/tex] as [tex]$(x^2 y^2-z^2)(x^2 y^2-z^2)$[/tex]
We can then add and subtract a suitable term, here we added and subtract 2xy * √2, to make one of the terms in each of the brackets match one of the terms of the original expression, so we can factor it out.
So, [tex]$(x^2 y^2-z^2)^2-4x^2y^2 = (x^2 y^2-z^2-2xy\sqrt{2})(x^2 y^2-z^2+2xy\sqrt{2})$[/tex].
Factors are the numbers that divide into a given number without leaving a remainder.
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what is the answer!??
Answers
Answer:
8.75 miles
Step-by-step explanation:
using the equation for the line of best fit
y = 0.8x + 0.75
substitute x = 10 into the equation
y = 0.8(10) + 0.75 = 8 + 0.75 = 8.75
the equation predicts she will run 8.75 miles in week 10
Joseph buys 11 bottles of apple juice at the corner store for a total cost of $9.68. If
each bottle costs the same amount, how much is 12 bottles of juice?
Answer: $
Submit Answer
Answers
Answer:
10.56
Step-by-step explanation:
Explanation: To find out the total cost for each apple juice, you have to divide 9.68 by 11 (also known as 11.00 in cash) which comes out as 0.88. After you get that you at the amount to the total cost (which is 9.68) to get to 12 bottles of juice. 9.68 + 0.88 is 10.56.
if a pizza feeds 3 kids, but you need to feed 6, what would the scale factor be for calculating how many pizzas you need?
Answers
Answer:
2
Step-by-step explanation:
If a pizza feeds 3 kids and you need to feed 6 kids, the scale factor for calculating how many pizzas you need would be 2.
A scale factor is used to determine the relationship between the size of an object and a similar or corresponding object. In this case, you have a pizza that can feed 3 kids and you need to feed 6 kids, so the relationship between the number of kids that can be fed by one pizza and the number of kids you need to feed is 6/3 = 2
So, you need to double the quantity of pizza to feed 6 kids, therefore the scale factor would be 2.
Find the average rate of change of the function on the interval specified for real number b.
f(x) = 4x2 − 7 on [1, b]
Answers
The average rate of change on the interval [1, b] is:
r = 4*(b + 1)
How to find the average rate of change?For a function f(x), we define the average rate of change on the interval [a, b] as:
r = ( f(b) - f(a))/(b - a)
Here we have the function:
f(x) = 4x² - 7
And the interval is [1, b]
Then the average rate of change is:
r = (f(b) - f(1))/(b - 1)
r = ( 4b² - 7 - 4 + 7)/(b - 1)
r = (4b² - 4)/(b - 1)
r = 4*(b² - 1)/(b - 1)
r = 4*(b + 1)*(b - 1)/(b - 1)
r = 4*(b + 1)
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TRUE OR FALSE deciding that a process that fills bottles with soda is functioning properly by checking the weights for a sample of bottles is an example of inferential statistics.
Answers
True, Deciding that a process that fills bottles with soda is functioning properly by checking the weights for a sample of bottles is an example of inferential statistics.
A subset of statistics known as inferential statistics uses a variety of analytical techniques to extrapolate conclusions about population data from sample data.
It is an example of inferential statistics because you are using a sample of data to make inferences about the population of bottles being filled, rather than measuring the weight of every bottle.
Hence, Deciding that a process that fills bottles with soda is functioning properly by checking the weights for a sample of bottles is an example of inferential statistics.
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I need the answers for this whole side work must be shown or you get reported please don’t make me waste my points
Answers
a. The percentage of the original price that the consumers are going to pay will be 8.57%.
b. The markup percentage of the gallons will be
c. The percentage that decided not to sell the juice is 41.7%.
d. The price of each bottle will be:
How to calculate the percentage?a. The percentage of the original price that the consumers are going to pay will be:
= (3.50 - 3.20) / 3.50 × 100
= 0.30 / 3.50 × 100
= 8.57%
b. The markup percentage of the gallons will be:
= (3.20 - 2.70) / 2.70 × 100
= 0.50 / 2.70 × 100
= 18.5%
c. The percentage that decided not to sell the juice is:
= 125 / 300 × 100
= 41.7%
d. The price of each bottle will be:
= (1 - 15%) × $2.25
= $1.91
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1) Identify the quadrant in which the point belongs. (-17,-87)
Answers
The point (-17, -87) belongs to the third quadrant
How to determine the quadrant of the pointFrom the question, we have the following parameters that can be used in our computation:
Point = (-17, -87)
In the above point, we have
x = -17 and y = -87
This means that the x and the y coordinates are negative
The quadrant where the x and the y coordinates are negative is the third quadrant
Hence, the point is in the third quadrant
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Using the volume of the cylinder and the prism, find the volume of the composite shape. Remember, the prism has been removed from the cylinder.
Diameter of cylinder base - 19.8
base area of cylinder - 307.8
volume of cylinder - 9.234
base area of the prism - 196
volume of the prism - 6.186
Answers
When the prism is taken out of the cylinder, the composite shape's volume is 3.048.
what is volume ?The volume of an item in three dimensions is the area that is enclosed by its boundaries. The space that an object occupies in three dimensions is measured by its volume, which is given in cubic units. A few of illustrations of cubic units are cm3 and in3. On the other side, an item's mass is used to measure how much matter it contains. One typical method to ascertain an object's mass is to weigh it, either in pounds or kilogrammes. Unlike the primary equation for the square of a rectangular box, which would be length, breadth, and height, the primary equation in capacity is length, width, and height.
given
volume of cylinder - 9.234
volume of the prism - 6.186
the volume of composite shape is = volume of cylinder - volume of prism
= 9.234 - 6.186
= 3.048
When the prism is taken out of the cylinder, the composite shape's volume is 3.048.
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Please answer this question
Answers
Answer:
Step-by-step explanation:
7x9=63
because 7 down times 9 across
Davis burns 1,080 calories when he runs for 2.5 Chours.)The number of calories he burns while
swimming Y)can be described using the
equation y = 266x, where Prepresents the number of hours Davis swims. How many more calories will Davis burn running for 30 minutes) than swimming for 30 minutes assuming the rates remain constant
Answers
Answer:
...
Step-by-step explanation:
To find the number of calories Davis burns while running for 30 minutes, we can use the information that he burns 1080 calories running for 2.5 hours.
We know that 30 minutes is 1/120 of 2.5 hours. So, we can divide the total number of calories by 120 and we get the calorie burn for 30 minutes:
1080 calories / 120 = 9 calories
The number of calories Davis burns while swimming for 30 minutes can be determined by using the equation y = 266x, where x represents the number of hours he swims. We know that he swims for 30 minutes, or 1/120 hours, so we can plug that value into the equation:
y = 266(1/120) = 2.216 calories
So, Davis burns 7 calories more running for 30 minutes than swimming for 30 minutes, assuming the rates remain constant.
Let f(x) = 2√x.
If g(x) is the graph of f(x) shifted down 1 units and right 6 units, write a formula for g(x).
Answers
The formula for g(x) is 2√(x-6) + 1. The solution has been obtained using the concept of translation.
What is translation?
In mathematics, a translation involves moving a shape up, down, left, or right. The translated shapes appear to be exactly the same size as the original ones; thus, the shapes are consistent with one another. Just one or more directions have been changed. There is no change to the shape because it is simply being moved from one location to another.
The object's shift in location can occur in a variety of ways, such as initially moving left, then turning right, and so on. Each point on the form will translate by the same number of units.
We are given f(x) = 2√x
Now, shifted down 1 unit, we get
2√x + 1
Also, shifted right 6 units, we get
2√(x-6)
So, g(x) = 2√(x-6) + 1
Hence, the formula for g(x) is 2√(x-6) + 1.
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consider the expresson 1/2x to the second power +x+7. complete 2 descriptions of the part of the expression
Answers
The entire expression is a sum with 0 factors
The coefficients are 1/2, 1 and 7
How to describe the expressionFrom the question, we have the following parameters that can be used in our computation:
1/2x² + x + 7
The above expression is a quadratic expression and it has three terms
Quadratic expressions with real roots have 2 factors, otherwise it would have 0 factor
The expression 1/2x² + x + 7 does not have a real root because
b² < 2ac
Also in the expression, the coefficients are 1/2, 1 and 7
i.e. a = 1/2, b = 1 and c = 7
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Complete question
consider the expresson 1/2x² + x + 7.
complete 2 descriptions of the part of the expression
The entire expression is a sum with __ factors
The coefficients are _
which of the following expressions have dimensions of length? assume the standard variables have the following dimensions: t is in units of s, x is in units of m, v is in units of m/s, and a is in units of m/s2.a. atb. 1/2at^2c. x^3/td. √2axe. v^2/a
Answers
The following expressions have length dimensions: a. at b. x3/t
d. √2ax
a. at: has a dimension of m because it is the product of acceleration (m/s2) and time(s). b. 1/2at2: has a dimension of m because it is the product of acceleration (m/s2) and time(s) squared. c. x3/t: has a dimension of m because it is the product of distance x (m) cubed and time(s).
e. v2/a: is a product of velocity (m/s) squared and acceleration (m/s2) thus it doesn't have a dimension of length. d. 2ax: is a product of 2, distance x (m), and acceleration (m/s2) so it has dimension of m.
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A northbound train and a southbound train meet each other on parallel tracks heading in opposite directions. The northbound train travels 16 miles per hour faster than the southbound train. After 2.5 hours, they are 265 miles apart. At what speeds are the two trains traveling?
Answers
If a northbound train and a southbound train meet each other on parallel tracks heading in opposite directions. The speeds that the two trains are traveling is:61 mph.
How to find the speedSpeed of westbound train = x mph
Speed of eastbound train = x+16
2.5x + 2.5(x+16) = 265
2.5x + 2.5x + 40 = 265
Combine like terms
5x = 225
Divide both side by 5x
x =225/5
x = 45 mph
Westbound train = 45mph
Eastbound train =45 mph +16 mph = 61 mph
Therefore the speed is 61mph.
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all of the following are precautions to prevent static electricity damage when replacing a control module except
Answers
To stop electrostatic discharge from harming your hardware, fasten a wrist strap to a painted metal surface.
Static electricity discharge can damage disc drives, media drives, electronic boards, and adapters. To avoid this harm, these gadgets are enclosed in antistatic bags. Take the following safety measures to guard against static electricity discharge harming this equipment.
To stop electrostatic discharge from harming your hardware, fasten a wrist strap to a painted metal surface.
Be sure to observe all electrical safety precautions while utilizing a wrist strap. For static control, a wrist strap is used. When you use or work on electrical equipment, your risk of getting shocked by electricity is not increased or decreased.
If you do not have a wrist strap, you must touch an unpainted metal surface of the system for at least 5 seconds before removing it from the ESD packing and installing or replacing components.
When you're ready to install the device in the system, take it out of the antistatic bag.
Touch the gadget to the system's metal frame while it is still in its antistatic bag.
Grasp the edges of the cards and boards. On the adaptor, stay away from the parts and gold connectors.
The complete question is :-
All of the following are precautions to prevent static electricity damage when replacing a control module EXCEPT:
Touch a known good ground before opening the package.
Wipe the terminals clean before installing the component.
Ground the package to a known good ground before opening.
See Electronic Service Precautions
Open the package only when ready to install the component.
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Find all the complex roots. Leave your answer in polar form with the argument in degrees. The complex fifth roots of 3. Zo= ___ (cos ___º + i sin ___º)z₁=___(cos___º + i sin ___º)z2=___(cos___º + i sin___º) z3=___ (cos___º + i sin___º) z4=___(cos___º + i sin___º)
Answers
The complex fifth roots of 3 are Z₀ = ∛3 (cos 0° + i sin 0°), Z₁ = ∛3 (cos 72° + i sin 72°), Z₂ = ∛3 (cos 144° + i sin 144°), Z₃ = ∛3 (cos 216° + i sin 216°) and Z₄ = ∛3 (cos 288° + i sin 288°)
The complex fifth roots of 3 can be found by finding the roots of the equation z^5 = 3. To find the roots in polar form, we first convert 3 to polar form:
3 = |3| (cos 0 + i sin 0) = 3 (cos 0 + i sin 0)
Next, we find the argument of the fifth roots, which is equal to 360°/5 = 72°. The polar form of the first root is then:
z₁ = ∛3 (cos 0° + i sin 0°) = ∛3 (cos 0° + i sin 0°)
The polar form of the other roots can be found by rotating the argument by 72°, 144°, 216°, and 288° respectively. The result is:
z₂ = ∛3 (cos 72° + i sin 72°)
z₃ = ∛3 (cos 144° + i sin 144°)
z₄ = ∛3 (cos 216° + i sin 216°)
z₅ = ∛3 (cos 288° + i sin 288°)
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Can a slope have two negative signs
Answers
If the slope of the line has two negative signs, then it is positive.
How to obtain the slope of a linear function?The slope of a linear function represents the rate of change of the linear function.
If we have two points on the linear function, then the slope is obtained by the division of the change in the output by the change in the input.
If both changes are negative, then we are dividing two negative numbers, meaning that the slope is positive, as the quotient of two negative numbers is positive.
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In circle O O, O P = 2 OP=2 and the length of ⌢ = 7 9 π PQ ⌢ = 9 7 π. Find the area shaded below. Express your answer as a fraction times π π.
Answers
The measure of angle POQ is given as follows:
30º.
What is the area of a circle?The area of a circle of radius r is given by π multiplied by the radius squared, as follows:
A = πr²
The radius of the circle in this problem is given as follows:
r = OP = 2.
(distance of the center O to point P on the circumference).
Hence the area of the circle is given as follows:
A = 4π.
The area of the sector is given as follows:
π/3.
The ratio of the area of the sector and the area of the circumference is given as follows:
(π/3)/(4π) = 1/12.
The entire area has a measure of 360º, hence the angle measure is obtained as follows:
1/12 x 360 = 30º.
Missing InformationThe problem is given by the image presented at the end of the answer.
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The point A, B and C are (9,8),(12,4) and (4,-2).
1.) Find the gradient of the line through a and b.
2.) The equation of the line through C which is parallel to AB.
3.) Calculate the length of the line segment AB and bc.
4.) Show that AB is perpendicular to Bc.
Answers
Therefore , the solution of the given problem of gradient comes out to be
It has been established that line BC and AB are parallel option 2 is correct.
How do you find the gradient of a line A and B?Pick two points on a graph that has a straight line as the direction. Change in y-coordinate divided by change in x-coordinate is the gradient of the line.In a visual representation, parallel lines encircle one another like train tracks. Parallel lines AB and CD go side by side.
Here,
Two lines that are parallel are denoted by the symbol ||. To indicate that AB is parallel to CD, we write AB||CD.
As a result, line segment AC's length is equal to the sum of line segments AB and BC.
The product of AB's and BC's slopes must be negative because AB and BC are obviously perpendicular to one another.
It has been established that line BC and AB are parallel.
Therefore , the solution of the given problem of gradient comes out to be
It has been established that line BC and AB are parallel.
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Please help me I need this.
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Answer:
y= - 2,0
x=0,-5
slope would be y=MX+Y
so -2= -5(0)+0
A rectangle has length x and width y. Select all the statements that must be true.
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The area of a rectangle with length x and width y is xy unit square.
What is an equation?An equation is an expression that shows the relationship between numbers and variables.
Area is the amount of space occupied by a figure. Area is usually calculated for a two dimensional shape while volume is calculated for a three dimensional shape.
A rectangle have equal opposite sides which are parallel to each other and all angles are at 90 degrees.
Area of rectangle = length * width
Area = x * y = xy
The area is xy unit square.
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While playing a board game, Vy noticed that the die landed on the number 1 more often than usual.
Part A: Describe a simulation that could be run to test how many times out of 100 a fair die should land on the number 1. State the representations and possible outcomes. Be sure to give enough detail that another person could replicate your simulation. (7 points)
Part B: While running a simulation, the die landed on the number 1 a total of 26 times out of the 100 rolls. Construct and interpret a 95% confidence interval for the true proportion of rolls that will land on the number 5. Show all work. (7 points)
Part C: Does the confidence interval in part B support Vy's suspicions that the die is not fair? Explain your reasoning. (6 points)
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a) A procedure that could be run to test how many times out of 100 a fair die should land on the number 1 is given as follows: Select a random number out of six 100 times, with 1 constituting a success and the remaining five numbers constituting a failure.
b) The 95% confidence interval for the true proportion of rolls that will land on the number 1 is given as follows: (0.174, 0.346). The interpretation is that we are 95% sure that the proportion of all rolls that land in one is between these two values.
c) As the lower bound of the interval is above the expected proportion of 0.1667, the confidence interval supports Vy's suspicions that the die is not fair.
How to design the procedure?A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
A die has six sides, one out of which is one, hence the probability of a one being rolled is given as follows:
p = 1/6 = 0.1667.
Hence 100 trials of a procedure with 6 results should be used, in which:
One result represents a success.The remaining five results represent failure.What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The parameters for this problem are given as follows:
[tex]n = 100, \pi = \frac{26}{100} = 0.26[/tex]
Then the lower bound of the interval is calculated as follows:
[tex]0.26 - 1.96\sqrt{\frac{0.26(0.74)}{100}} = 0.174[/tex]
The upper bound is calculated as follows:
[tex]0.26 + 1.96\sqrt{\frac{0.26(0.74)}{100}} = 0.346[/tex]
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You use beads to make design. Of the beads, 1/3 are red and 1/6 are blue. The rest are white. What fraction of the beads are red red or blue?
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Answer:
1/2
Step-by-step explanation:
First, let's find the GCF of 3 and 6. In this case, it's 6.
Then, lets convert every fraction so that the denominator is 6. 1/6 already has this property, so let's convert 1/3. And to do that, we multiply the fraction by 2/2.
[tex]\frac{1}{3} * \frac{2}{2} = \frac{2}{6}[/tex]
Finally, we add the fraction of beads that are red and blue together, then simplify.
[tex]\frac{2}{6} + \frac{1}{6}=\frac{3}{6} =\frac{1}{2}[/tex]
Therefore, the answer is 1/2.
Convert the decimal
0.9
2
¯
to a fraction.
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the charge of sphere 2 is twice that of sphere 1. which vector below shows the force of 2 on 1 if the distance
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The vector representing the force of sphere 2 on sphere 1 is[tex]$\frac{2}{5} \vec{i}$[/tex] because the charge of sphere 2 is twice that of sphere 1 and they are separated by a distance of 5 cm.
Step 1: Calculate the charge of sphere 2. Since it is twice that of sphere 1, the charge of sphere 2 is 2 x the charge of sphere 1.
Step 2: Calculate the distance between the two spheres. This is given as 5 cm.
Step 3: Calculate the force. The force is equal to the product of the charges of the two spheres divided by the square of the distance between them.
Step 4: Construct the vector. The vector representing the force of sphere 2 on sphere 1 is[tex]$\frac{2}{5} \vec{i}$.[/tex]
The vector representing the force of sphere 2 on sphere 1 is [tex]$\frac{2}{5} \vec{i}$[/tex], as the charge of sphere 2 is twice that of sphere 1 and they are separated by a distance of 5 cm. This is calculated by multiplying the charges of the two spheres and dividing by the square of the distance between them.
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