Answers
Answer: choice A
Step-by-step explanation:
by rearranging the initial inequality you’ll get
[tex]\frac{3}{2} x\leq 5-\frac{1}{3}[/tex]
which equals
[tex]\frac{3}{2} x\leq\frac{14}{3}[/tex]
then multiply both sides by 2/3
[tex]x\leq \frac{28}{9}[/tex]
Related Questions
Jose runs a factory that makes stereo tuners. Each S100 takes 8 ounces of plastic and 4 ounces of metal. Each FS20 requires 4 ounces of plastic and 6 ounces of metal. The factory has 312 ounces of plastic, 372 ounces of metal available, with a maximum of 20 S100 that can be built each week. If each S100 generates $7 in profit, and each FS20 generates $13, how many of each of the stereo tuners should Jose have the factory make each week to make the most profit
Answers
Answer: Jose should have the factory make 50 FS20 stereo tuners and 14 S100 stereo tuners each week to make the most profit
Step-by-step explanation:
Since each S100 takes 8 ounces of plastic and 4 ounces of metal. Each FS20 requires 4 ounces of plastic and 6 ounces of metal. And the factory has 312 ounces of plastic, 372 ounces of metal available, then,
For plastic
8 ounces + 4 ounces = 12 ounces
The number of stereo tuners it can produce will be
312/12 = 26 stereo tuners
For metal
4 ounces + 6 ounces = 10 ounces
The number of stereo tuners it can produce will be
372/10 = 37.2 = 37 approximately
Since FS20 generate more profit than S100, let assume that Jose produces 50 FS20 by consuming
4 × 50 = 200 ounces of plastic
6 × 50 = 300 ounces of metal
The remaining plastic will be
312 - 200 = 112
The remaining plastic will be
372 - 300 = 72
Divide 112 by 8 in order to make S100
112/8 = 14
Also 72/4 = 18.
Therefore, Jose should have the factory make 50 FS20 stereo tuners and 14 S100 stereo tuners each week to make the most profit
Confidence Intervals for Curved Gaussian Family Bookmark this page (a) 1 point possible (graded) Let X1,…,Xn be i.i.d. random variables with distribution N(θ,θ) , for some unknown parameter θ>0 . True or False: The sample average X¯¯¯¯n follows a normal distribution for any integer n≥1 .
a. true
b. false
Answers
Answer:
True
True
Step-by-step explanation:
The unknown parameters are treated as variable and data serve as coefficients. The random variables are value whose outcome depends on some random event. The θ can exist when n ≥ 0. A sample mean is a sequence which has normal distribution and n ≥ 1. The sample average of X-n follows normal distribution for all integer and n is greater or equal to 1.
The given statement is True
Random variable:The unknown parameters should be considered variable and data represent the coefficients. The random variables refers to the value where outcome based on some random event. The θ could exist at the time when n ≥ 0. A sample mean represent the sequence that contains normal distribution and n ≥ 1.
Learn more about distribution here: https://brainly.com/question/24520301
The area of a circle is 18 pi square inches. If the area of a sector of this circle is 6 pi square inches, then
which of the following must be the sector's central angle?
Answers
Answer:
120°Step-by-step explanation:
Area of a sector = [tex]\frac{\theta}{360} * \pi r^{2}\ where\ \pi r^{2} \ is\ the\ area\ of\ the\ circle[/tex]
theta is the sector's central angle
Area of the sector = [tex]\frac{\theta}{360} * \ area\ of\ a\ circle[/tex]
Given area of a circle = 18πin² and area of a sector = 6πin²
On substituting;
6π = [tex]\theta/360 * 18 \pi[/tex]
Dividing both sides by 18π we have;
1/3 = [tex]\theta/360[/tex]
[tex]3 \theta = 360\\\theta = 360/3\\\theta = 120^{0}[/tex]
The sector's central angle is 120°
angle x is coterminal with gale y. if the measure of angle x is greater than the measure of angle y which statement is true regarding the values of x and y
Answers
Answer:
The answer is C
Step-by-step explanation:
did the quiz
Answer:
He is right it C just did the quiz let him have the brainly ;)
Step-by-step explanation:
3. (05.01)
A pair of linear equations is shown below:
y = -x + 1
y = 2x + 4
Which of the following statements best explains the steps to solve the pair of equations graphically? (4 points)
On a graph, plot the line y = -x + 1, which has y-intercept = -1 and slope = 1, and y = 2x + 4, which has y-intercept = 2 and slope = 4, and write the coordinates of the point of
Intersection of the two lines as the solution.
On a graph, plot the line y = -x + 1, which has y-intercept - 1 and slope = 1, and y = 2x + 4, which has y-intercept = 1 and slope = 4, and write the coordinates of the point of
intersection of the two lines as the solution.
On a graph, plot the line y = -x + 1, which has y-intercept = 1 and slope = -1, and y = 2x + 4, which has y-intercept = -2 and slope = 2, and write the coordinates of the point
of intersection of the two lines as the solution.
On a graph, plot the line y = -x + 1, which has y-intercept = 1 and slope = -1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of
intersection of the two lines as the solution.
Answers
Answer:
On a graph, plot the line y = -x + 1, which has y-intercept = 1 and slope = -1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution.
Step-by-step explanation:
Each equation is in slope-intercept form:
y = mx + b . . . . . where m is the slope, and b is the y-intercept
The first equation is ...
y = -x +1
so the slope is -1, and the y-intercept is +1.
__
The second equation is ...
y = 2x +4
so the slope is 2, and the y-intercept is 4.
__
The slopes and intercepts are properly described in the last selection.
76,80,88,95,100,101,? Which number comes next in this sequence?
Answers
Answer:
112
Step-by-step explanation:
Difference between each 4,8,7,5,1
Add numbers next to each other in pairs = 12
So 12-1= 11 and
101+11=112
simplify 8-(3a+8)=
havent done these in a while so...
Answers
Answer:
3
Step-by-step explanation:
8-(3a+8)
8-(11a)
8-11a
a=11-8
a=3
Answer:
0
Step-by-step explanation:
8-(3a+8)=0
8-3a-8=0
-3a=0
a=0
what is the x-intercept of the line 10x-5y=40
Answers
Answer:
4
Step-by-step explanation:
The x-intercept occurs when y=0, if you think about it graphically. Plug y=o into your equation:
10x - 5(0) = 40
10x = 40 (divide each side by 10)
x=4
k(x)=-2x^2+10x+5, Evaluate k(3)
Answers
Answer:
17
Step-by-step explanation:
k(x)=-2x^2+10x+5
k(3)=-2(3)^2+10(3)+5
k(3)=-2(9)+30+5
k(3)=-18+35
= 17
Answer:
71
Step-by-step explanation:
-2(3)^2+ 10(3)+5
So first you multiply the -2 by the 3
(-6)^2+10(3)+5
then you do the exponents
36+10(3)+5
then you multiply the 10 by 3
36+30+5
then you would add 36 and 30
66+5
then add the 5
71
What’s the correct answer for this question?
Answers
Answer:
B) (1,2,3,4,5,6,7,8)
Step-by-step explanation:
The answer is B because the union of a set represents everything thing that is within the sets.
Eliminate the variable t from the set of parametric equations. Graph the equation X=5cost Y=5sint Please explain this, I need to know how to do these kinds of equations for my trig final
Answers
Answer:
x^2 + y^2 = 25
Step-by-step explanation:
x = 5 cos t
cos t = x/5
y = 5 sin t
sin t = y/5
cos^2 t + sin^2 t = 1
(x/5)^2 + (y/5)^2 = 1
x^2/25 + y^2/25 = 1
(x^2 + y^2)/25 =1
x^2 + y^2 = 25
Assignment
Use the function f(x) = 2x3 - 3x2 + 7 to complete the exercises.
f(-1) =
f(1) =
f(2)=
>
Answers
Answer:
The value of the function f(x) at x=a can be determined by substituting a instead of x into the function expression.
1. When x=-1, then
f(-1) = 2 * (-1)^3 - 3 * (-1)^2 + 7 = -2 - 3 + 7 = 2.
2. When x=1, then
f(1) = 2 * 1^3 - 3 * 1^2 + 7 = 2 - 3 + 7 = 6.
3. When x=2, then
f(-1) = 2 * 2^3 - 3 * 2^2 + 7 = 16 - 12 + 7 = 11.
Step-by-step explanation:
Answer:
f(−1) =✔ 2
f(1) = ✔ 6
f(2) =✔ 11
Step-by-step explanation:
Let A be an n # n matrix, b be a nonzero vector, and x0 be a solution vector of the system Ax D b. Show that x is a solution of the nonhomogeneous system Ax D b if and only if y D x!x0 is a solution of the homogeneous system Ay D 0.
Answers
Complete Question
Let A be an n x n matrix, b be a nonzero vector, and x_0 be a solution vector of the system Ax = b. Show that x is a solution of the non-homogeneous system Ax = b if and only if y = x - x_0 is a solution of the homogeneous system Ay = 0.
Answer:
Step-by-step explanation:
From the question we are told that
A is an n × n matrix
b is a zero vector
[tex]x_o[/tex] us the solution vector of [tex]Ax = b[/tex]
Which implies that
[tex]Ax_o = b[/tex]
So first we show that
if [tex]x[/tex] is the solution matrix of [tex]Ax = b[/tex]
and [tex]y= x-x_o[/tex] is the solution of [tex]Ay = 0[/tex]
Then
[tex]A(x-x_o) = 0[/tex]
=> [tex]Ax -Ax_o = 0[/tex]
=> [tex]b-b = 0[/tex]
Secondly to show that
if [tex]y= x-x_o[/tex] is the solution of [tex]Ay =0[/tex]
then x is the solution of the non-homogeneous system
[tex]Ax = b[/tex]
Now we know that [tex]y = x-x_o[/tex] is the solution of [tex]Ay =0[/tex]
So
[tex]Ay = 0[/tex]
=> [tex]A(x- x_o) = 0[/tex]
=> [tex]Ax - Ax_o = 0[/tex]
=> [tex]Ax - b = 0[/tex]
=> [tex]Ax = b[/tex]
Thus this has been proved
You get tired of the sand and head up to the amusement park. You can purchase 20 ride tickets for $14 or you can purchase 30 ride tickets for $22.50. Which is a better deal?
Answers
Answer:
The one with the better deal would be 30 ride tickets for $22.50 this is because you pay less money for more rides.
Step-by-step explanation:
First you divide 20 by 14. Doing this will give you the cost of a ride per ticket.
20/14 = 1.42
Then you do the same thing to 30 and 22.50.
30/22.50 = 1.30
Last you compare which deal has less money per ride.
1.42 > 1.30
The differential equation below models the temperature of a 91°C cup of coffee in a 17°C room, where it is known that the coffee cools at a rate of 1°C per minute when its temperature is 70°C. Solve the differential equation to find an expression for the temperature of the coffee at time t. dy dt = − 1 53 (y − 17)\
Answers
Answer:
[tex]t \approx 17.690\,min[/tex]
Step-by-step explanation:
This differential equation is a first order linear differential equation with separable variables, whose solution is found as follows:
[tex]\frac{dy}{dt} = - \frac{1}{53} \cdot (y - 17)[/tex]
[tex]\frac{dy}{y-17} = -\frac{1}{53} \, dt[/tex]
[tex]\int\limits^{y}_{y_{o}} {\frac{dy}{y-17} } = -\frac{1}{53} \int\limits^{t}_{0}\, dx[/tex]
[tex]\ln \left |\frac{y-17}{y_{o}-17} \right | = -\frac{1}{53} \cdot t[/tex]
[tex]\frac{y-17}{y_{o}-17} = e^{-\frac{1}{53}\cdot t }[/tex]
[tex]y = 17 + (y_{o} - 17) \cdot e^{-\frac{1}{53}\cdot t }[/tex]
The solution of the differential equation is:
[tex]y = 17 + 74\cdot e^{-\frac{1}{53}\cdot t }[/tex]
Where:
[tex]y[/tex] - Temperature, measured in °C.
[tex]t[/tex] - Time, measured in minutes.
The time when the cup of coffee has the temperature of 70 °C is:
[tex]70 = 17 + 74 \cdot e^{-\frac{1}{53}\cdot t }[/tex]
[tex]53 = 74 \cdot e^{-\frac{1}{53}\cdot t }[/tex]
[tex]\frac{53}{74} = e^{-\frac{1}{53}\cdot t }[/tex]
[tex]\ln \frac{53}{74} = -\frac{1}{53}\cdot t[/tex]
[tex]t = - 53\cdot \ln \frac{53}{74}[/tex]
[tex]t \approx 17.690\,min[/tex]
An engineer believes that there is a linear relationship between the thickness of an air filter and the amount of particulate matter that gets through the filter; that is, less pollution should get through thicker filters. The engineer tests many filters of different thickness and fits a linear model. If a linear model is appropriate, what should be apparent in the residual plot
Answers
Answer:
There should be no pattern in the residual plot.
Step-by-step explanation
Remember a residual plot is calculating if a linear model is appropriate or not and since the engineer is trying to find a linear relationship with his air filters then he should be looking for no pattern.
Here, we are required to determine what should be apparent in the residual plot.
The residual plot will have a negative slope, i.e the residual plot descends from the top left to the bottom right.
According to the Engineer's believe, the thicker the air filter, the less pollution that gets through it.
By plotting each of the quantities on either of x and y axis on the residual plot, The residual plot therefore, has a negative slope.
Read more:
https://brainly.com/question/7412322
A credit card company monitors cardholder transaction habits to detect any unusual activity. Suppose that the dollar value of unusual activity for a customer in a month follows a normal distribution with mean $250 and variance $2400.
(a) What is the probability of $250 to $294 in unusual activity in a month? Round your answer to four decimal places (e.g. 98.7654) P-0.4861
(b) What is the probability of more than $294 in unusual activity in a month? Round your answer to four decimal places (e.g. 98.7654) P 0.0139
(c) Suppose that 10 customer accounts independently follow the same normal distribution. What is the probability that at least one of these customers exceeds $294 in unusual activity in a month? Round your answer to four decimal places (e.g. 98.7654)
Answers
Answer:
Step-by-step explanation:
Let x be the random variable representing the dollar value of unusual activity for a customer in a month. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = standard deviation
From the information given,
µ = 250
σ = √variance = √2400 = 48.99
a) the probability of $250 to $294 in unusual activity in a month is expressed as
P(250 ≤ x ≤ 294)
For x = 250,
z = (250 - 250)/48.99 = 0
Looking at the normal distribution table, the probability corresponding to the z score is 0.5
For x = 294
z = (294 - 250)/48.99 = 0.9
Looking at the normal distribution table, the probability corresponding to the z score is 0.8159
Therefore,
P(250 ≤ x ≤ 294) = 0.8159 - 0.5 = 0.3159
b) the probability of more than $294 in unusual activity in a month is expressed as
P(x > 294) = 1 - P(x < 294)
P(x > 294) = 1 - 0.8159 = 0.1841
c) since n = 10, the formula becomes
z = (x - µ)/(σ/n)
z = (294 - 250)/(48.99/√10) = 2.84
Looking at the normal distribution table, the probability is 0.9977
Therefore, the probability that at least one of these customers exceeds $294 in unusual activity in a month is
1 - 0.9977 = 0.0023
Richard and Stephen win some money and share it in the ratio 6:1. Richard gets £60 more than Stephen. How much did they get altogether?
Answers
Answer:
They got £84 altogether.
Step-by-step explanation:
We can see that Richard get's 6 parts and Stephen gets 1 part. We can subtract these two to get 5 parts. We know that five parts equals £60, so we can divide by 5 to get 1 part equals £12. We are looking for the amount they got altogether, which is equal to 7 parts, 6 parts + 1 part. We multiply £12 by 7, leaving us with £84, which is our answer.
Does this graph represent a function? Why or why not?
10+
8+
6-
110884
-8
O
A. No, because it is not a straight line.
B. Yes, because it passes the horizontal line test.
Ο Ο Ο
C. Yes, because it passes the vertical line test.
D. No, because it fails the vertical line test.
Answers
Answer:
Option (C).
Step-by-step explanation:
In the graph attached,
An absolute function has been given.
To check a graph whether it's a relation or a function, vertical line test is a trusted tool.
In vertical line test a vertical line (parallel to y-axis) is drawn passing through the graph.
If the vertical line cuts the graph at only one point then the graph is said to be a function.
The given graph passes the vertical test.
Therefore, it's a function.
Option C. will be the answer.
Yes, this graph represents a function, because it passes the vertical line test. Option C is correct
What exactly is a function?A function is a statement, rule, or law that specifies the connection between two variables. Functions are common in mathematics and are required for the formulation of physical connections.
An absolute function is shown in the graph that is attached. The vertical line test is a reliable method for determining if a graph represents a relation or a function.
In the vertical line test, a vertical line that is parallel to the y-axis and cuts through the graph is created. The graph is considered to be a function if the vertical line only intersects it once.
The vertical test is passed by the shown graph. It serves a purpose as a result.
Hence option C is correct.
To learn more about the function, refer to:
https://brainly.com/question/5245372
#SPJ5
Triangle XYZ, XY= 80, ZY= 64 XZ= 48 what is the cosine
Answers
Answer:
[tex]cos=\frac{4}{5}[/tex]
Step-by-step explanation:
Cosine is the adjacent side over the hypotenuse (You can remember sin, cos, and tan by using sohcahtoa or sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite over adjacent). I think a picture would help, too.
I attached a picture of what I think the triangle would look like.
If the picture is right (we're assuming it is) and going with what we're given (the triangle was addressed as triangle XYZ, meaning that angle Y is in the middle and that's the one we'll use).
Looking at my picture then:
[tex]cos=\frac{64}{80} \\cos=\frac{8}{10} \\cos=\frac{4}{5}[/tex] .
TWO PLANES INTERSECT IN A
A. point
B. Ray
C. Line
D. Line segments
Answers
Answer:
c. line
Step-by-step explanation:
the intersection of two planes is called a line
Answer:
Hello dear,
two planes intersect and forms line
so yaa your answer is C)
Hope I helped you ;)
please thank me !!!
satsriakal ji
what is the value of this expression plssssss 8z-3 when z =7
Answers
Answer:
53
Step-by-step explanation:
8•7 is 56
56 - 3 is 53
Answer:
53
Step-by-step explanation:
z = 7
8z is the same as saying 8×z
8×7-3 (do multiplication first)
56-3 = 53
How many pound are in 28 ounces
Answers
Answer:
1.75
Step-by-step explanation:
Divide the ounces by 16 to get the value.
If a procedure meets all the conditions of a binomial distribution except that the number of trials is not fixed, then the geometric distribution can be used. The probability of getting the first success on the xth trial is given by
P
(
x
)
=
p
(
1
−
p
)
x
−
1
where
p
is the probability of success on any one trial.
Assume that the probability of a defective computer component is 0.21. Find the probability that the first defect is found in the fifth component tested.
(Round answer to four decimal places.)
P
(
5
)
=
Answers
Answer:
M.
Step-by-step explanation:
There is a bag with only milk and dark chocolates.
The probability of randomly choosing a dark chocolate is
2/9.
There are 24 dark chocolates in the bag and each is equally likely to be chosen.
Work out how many milk chocolates there must be.
Answers
Answer:
80 milk chocolates
Step-by-step explanation:
Probability of choosing a dark chocolate= number of dark
chocolate/number of total
chocolate
But the probability of choosing dark chocolate= 2/9
The number of dark chocolate= 24
Total chocolate= number of dark
chocolate/probability
of choosing dark
chocolate
Total chocolate= 24/(2/9)
Total chocolate=( 24*9)/2
Total chocolate= 108
Number of milk chocolate= total- dark
Number of milk chocolate
= 108-28
= 80
As a birthday gift, you are mailing a new personal digital assistant (PDA) to your cousin in Toledo. The PDA cost $414. There is a 3 percent chance it will be lost or damaged in the mail. Is it worth $4 to insure the mailing?Explain, using the concept of expected value.
Answers
Answer:
It is worth $4 to insure the mailing.
Step-by-step explanation:
The random variable X can be defined as the money value.
The PDA costs, $414.
It is provided that there is a 3% chance it will be lost or damaged in the mail.
So, there is 97% chance it will not be lost or damaged in the mail.
The insurance costs $4.
If the PDA is lost or damaged in the mail when there is no insurance the money value would be of -$414.
And if the PDA is lost or damaged in the mail when there is an insurance the money value would be of $414 - $4 = $410.
Compute the expected value of money as follows:
[tex]\text{E (X)}=(0.97\times 410)+(0.03\times -414)[/tex]
[tex]=397.7-12.42\\=385.28[/tex]
The expected value of money in case the PDA is lost or damaged in the mail or not is $385.28.
Thus, it is worth $4 to insure the mailing.
A broker has calculated the expected values of two different financial instruments X and Y. Suppose that E(x)= $100, E(y)=$90 SD(x)= 90$ and SD(y)=$8. Find each of the following.
a. E(X+ 10) and SD(X+ 10)
b. E(5Y) and SD(5Y)
c) E(X+ Y) and SD(X+ Y)
d) What assumption must you make in part c?
Answers
Expectation is linear, meaning
E(a X + b Y) = E(a X) + E(b Y)
= a E(X) + b E(Y)
If X = 1 and Y = 0, we see that the expectation of a constant, E(a), is equal to the constant, a.
Use this property to compute the expectations:
E(X + 10) = E(X) + E(10) = $110
E(5Y) = 5 E(Y) = $450
E(X + Y) = E(X) + E(Y) = $190
Variance has a similar property:
V(a X + b Y) = V(a X) + V(b Y) + Cov(X, Y)
= a^2 V(X) + b^2 V(Y) + Cov(X, Y)
where "Cov" denotes covariance, defined by
E[(X - E(X))(Y - E(Y))] = E(X Y) - E(X) E(Y)
Without knowing the expectation of X Y, we can't determine the covariance and thus variance of the expression a X + b Y.
However, if X and Y are independent, then E(X Y) = E(X) E(Y), which makes the covariance vanish, so that
V(a X + b Y) = a^2 V(X) + b^2 V(Y)
and this is the assumption we have to make to find the standard deviations (which is the square root of the variance).
Also, variance is defined as
V(X) = E[(X - E(X))^2] = E(X^2) - E(X)^2
and it follows from this that, if X is a constant, say a, then
V(a) = E(a^2) - E(a)^2 = a^2 - a^2 = 0
Use this property, and the assumption of independence, to compute the variances, and hence the standard deviations:
V(X + 10) = V(X) ==> SD(X + 10) = SD(X) = $90
V(5Y) = 5^2 V(Y) = 25 V(Y) ==> SD(5Y) = 5 SD(Y) = $40
V(X + Y) = V(X) + V(Y) ==> SD(X + Y) = √[SD(X)^2 + SD(Y)^2] = √8164 ≈ $90.35
THIS QUESTION IS KILLING ME
Calculate the volume of the object by using the triple integral.
Answers
The volume of the solid (call it S) in Cartesian coordinates is
[tex]\displaystyle\iiint_S\mathrm dV=\int_{-1}^1\int_{-\sqrt{1-x^2}}^{\sqrt{1-x^2}}\int_{(x^2+y^2)^2-1}^{4-4(x^2+y^2)}\mathrm dz\,\mathrm dy\,\mathrm dx[/tex]
but I suspect converting to cylindrical coordinates would make the integral much more tractable.
Take
[tex]\begin{cases}x=r\cos\theta\\y=r\sin\theta\\z=z\end{cases}\implies\mathrm dV=r\,\mathrm dr\,\mathrm d\theta\,\mathrm dz[/tex]
Then
[tex]4-4(x^2+y^2)=4-4r^2=4(1-r^2)[/tex]
[tex](x^2+y^2)^2-1=(r^2)^2-1=r^4-1[/tex]
and the integral becomes
[tex]\displaystyle\iiint_S\mathrm dV=\int_0^{2\pi}\int_0^1\int_{r^4-1}^{4(1-r^2)}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]=\displaystyle2\pi\int_0^1r(4(1-r^2)-(r^4-1))\,\mathrm dr[/tex]
[tex]=\displaystyle2\pi\int_0^1r(5-4r^2-r^4)\,\mathrm dr[/tex]
[tex]=\displaystyle2\pi\int_0^15r-4r^3-r^5\,\mathrm dr[/tex]
[tex]=2\pi\left(\dfrac52-1-\dfrac16\right)=\boxed{\dfrac{8\pi}3}[/tex]
I really need help :( anybody ??
Answers
_______________________________
Hey!!
Answer:{2,4,5}
Explanation:
RangeLet R be relation from A to B.The set of second components or the set of elements of B are called range.
Hope it helps..
_______________________________
1. OSHA is an agency responsible for workplace safety, read its rule and sketch a diagram that shows the proper relationship between the ladder, wall and ground
Answers
Completed Question
1. OSHA is an agency responsible for workplace safety, read its rule and sketch a diagram that shows the proper relationship between the ladder, wall and ground .
Rule: Non-self-supporting ladders, which must lean against a wall or other support, are to be positioned at such an angle that the horizontal distance from the top support to the foot of the ladder is about the 1/4 working length of the ladder.
2. Calculate the angle that the ladder makes with the ground using a trigonometric ratio.
3. If a ladder is x feet long, how high up a wall can it safely reach?
4. Would a 51-foot ladder be long enough to climb a 50-foot wall?
Answer:
(a)See attachment
(b)75.52 degrees
(c)[tex]Height ,h=\dfrac{x\sqrt{15}}{4} $ feet[/tex]
(d) NO
Step-by-step explanation:
Part 1
Let the length of the ladder =x
Since by the given rule, Horizontal Distance =[tex]\dfrac14$ of the length of the ladder[/tex]
Horizontal Distance = [tex]\dfrac14x[/tex]
In the sketch of the problem attached below,
The length of the ladder=ACHorizontal distance =BCPart 2
From Triangle ABC
[tex]\cos C=\dfrac{BC}{AC} \\\cos C=\dfrac{x/4}{x} \\\cos C=\dfrac{1}{4}\\ C=\arccos \dfrac{1}{4}\\C \approx 75.52^\circ[/tex]
The angle that the ladder makes with the ground is 75.52 degrees.
Part 3
If the ladder is x feet long
Using Pythagoras theorem in Triangle ABC below
[tex]x^2=(x/4)^2+h^2\\h^2=x^2-\dfrac{x^2}{16}\\ h^2=\dfrac{15x^2}{16}\\h=\sqrt{\dfrac{15x^2}{16}} \\h=\dfrac{x\sqrt{15}}{4}$ feet[/tex]
Part 4
If x=51 feet
[tex]Height ,h=\dfrac{51\sqrt{15}}{4}$ = 49.38 feet[/tex]
Therefore, a 51 feet ladder would not be enough to climb a 50 feet wall as it would violate the safety rule.