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.
Related Questions
The chess clubs of two schools consist of, respectively, 8 and 9 players. Four members from each club are randomly chosen to participate in a contest between the two schools. The chosen players from one team are then randomly paired with those from the other team, and each pairing plays a game of chess. Suppose that Rebecca and her sister Elise are on the chess clubs at different schools. What is the probability that
Answers
Answer:
A)1/18
B)1/6
C)13/18
Step-by-step explanation:
THIS IS THE COMPLETE QUESTION BELOW,
The chess clubs of two schools consist of, respectively, 8 and 9 players. Four members from each club are randomly chosen to participate in a contest between the two schools. The chosen players from one team are then randomly paired with those from the other team, and each pairing plays a game of chess. Suppose that Rebecca and her sister Elise are on the chess clubs at different schools. What is the probability that (a) Rebecca and Elise will be paired? (b) Rebecca and Elise will be chosen to represent their schools but will not play each other? (c) either Rebecca or Elise will be chosen to represent her school?
CHECK THE ATTACHMENT'S FOR STEP BY STEP EXPLANATION
Simplify the answer pls
Answers
Answer:
[tex]\frac{9}{8}[/tex]
Step-by-step explanation:
27 ÷ 9 = 3
3 * 3 = 9
9 ÷ 8 = [tex]\frac{9}{8}[/tex]
What is the value of n ??????????
Answers
Answer:
it's b 59° because it's at the side
In a survey, participants were asked how much confidence they had in the economy.
The results were as follows:
Response Number
A great 3,187
deal
Some
9,120
Hardly 5,149
any
What is the probability that a sampled person has either some confidence or a great
deal of confidence in the economy? Write only a number as your answer. Round to
two decimal places (for example: 0.43). Do not write as a percentage.
Answers
Answer:
0.71
Step-by-step explanation:
Great Deal or Some = 12,307
Total Participants = 17,456
Probability = 12,307/17,456 = 0.71
Jake made a rectangular garden area as shown in the figure. He wants to add 3 inches of topsoil to the entire area.
36 in
15 in
How much topsoil does Jake need to get at the nursery?
540 in.
1,080 in.
1,386 in.
1,620 in.
Answers
Answer:
1,620in
Step-by-step explanation:
LxWxH
36 x 15 x 3 = 1,620 in
Answer:
1620
Step-by-step explanation:
What is the slope of the lines 2,8 -6,-8
Answers
Answer:
2
Step-by-step explanation:
Slope is: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
We are given the points (2,8) and (-6, -8) .
[tex]m=\frac{-8-8}{-6-2} =\frac{-16}{-8}=2[/tex]
The slope is 2.
Determine the percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.20 kg. Interpret your answer in terms of sampling error.
Answers
Answer:
Percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.20 kg = 78.5%
The sampling error is 0.08083, in terms of the sampling error, 78.5% of samples of three men will have mean brain weights within (1.24×sampling error) of the mean.
Step-by-step explanation:
Complete Question
According to one study, brain weights of men are normally distributed with mean = 1.20 kg and a standard deviation = 0.14 kg.
Determine the percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.20 kg. Interpret your answer in terms of sampling error.
Solution
The Central limit theorem allows us to say
The mean of sampling distribution is approximately equal to the population mean.
μₓ = μ = 1.20 kg
And the standard deviation of the sampling distribution is given as
σₓ = (σ/√N)
σ = population standard deviation = 0.14 kg
N = sample size = 3
σₓ = (0.14/√3) = 0.08083
Percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.20 kg, that is, percentage of all samples of three men with mean brain weights within 1.10 kg and 1.30 kg.
P(1.10 ≤ x ≤ 1.30)
We first normalize or standardize 1.10 and 1.30
The standardized score for any value is the value minus the mean then divided by the standard deviation.
For 1.10 kg
z = (x - μₓ)/σₓ = (1.10 - 1.20)/0.08083 = -1.24
For 1.30 kg
z = (x - μₓ)/σₓ = (1.30 - 1.20)/0.08083 = 1.24
To determine the required probability
P(1.10 ≤ x ≤ 1.30) = P(-1.24 ≤ z ≤ 1.24)
We'll use data from the normal distribution table for these probabilities
P(1.10 ≤ x ≤ 1.30) = P(-1.24 ≤ z ≤ 1.24)
= P(z ≤ 1.24) - P(z ≤ -1.24)
= 0.89251 - 0.10749
= 0.78502 = 78.502%
The sampling error is 0.08083, in terms of the sampling error, 78.5% of samples of three men will have mean brain weights within (1.24×sampling error) of the mean.
Hope this Helps!!!
Reflect on the concept of function. What concepts (only the names) did you need to accommodate the concept of function in your mind? What is the simplest function you can imagine? In your day to day, is there any occurring fact that can be interpreted as a function? Is it possible to view a function? What strategy are you using to get the graph of a function?
Answers
Answer:
Step-by-step explanation:
For this kind of question you'd be better off if you'd write down and share your own answers to these conceptual questions and then ask for Brainly feedback on what you have written. You'll need to understand the concept of "function" often in algebra and beyond.
What concepts (only the names) did you need to accommodate the concept of function in your mind? input, output, rule, domain, range, mapping, variation (direct and inverse)
Simplest function: y = c (there's only one x-value and y equals that value)
In your day to day, is there any occurring fact that can be interpreted as a function? An electronic parking meter: the amount of time you can park at the meter without risking getting a ticket is dependent upon the number of quarters you insert into the meter, e. g, 15 minutes for 25 centers, 30 minutes for 50 cents, and so on.
Is it possible to view a function? Sure. Graph the function.
What strategy are you using to get the graph of a function? Set up a coordinate plane. Label the horizontal axis "x" and the vertical axis "y". Choose x (input) values that are included in the domain of the function. If the domain includes '0' you will be finding the 'y-intercept' of the function. Write the input and output as a point: (x, y). Plot that point. Choose other x values within the domain and calculate the corresponding y value for each. Plot several more points and draw a line or a curve through them. Of course there are more sophisticated strategies for graphing functions. Remember: If you're working with a function, there is never more than one output or y value for any particular input value.
Which explains why the graph is not a function?
Answers
Answer:
56
Step-by-step explanation:
I promise brainieliest for the first to answer What is the solution to the inequality 2x ≥ -4? Click the number line until the correct answer is shown.
Answers
Answer:
x ≥ -2
Step-by-step explanation:
Divide both sides of the inequality by 2.
2x ≥ - 4
2x / 2 ≥ -4 / 2
x ≥ -2
Answer:
the answer is the arrow going to the right because its not a negative number and a closed circle
Step-by-step explanation:
so that means that 2x is at LEASt more than -4 opposed to this sign> wich just means greater than
because when you work with variables you usually cannot find the exact amount especially when you are rounding so you know that its biigger than no less than or at least -4
i need to know £400 in euros and how to convert it
Answers
Answer:
449.40 Euro
Step-by-step explanation:
1 pound=1.12 euro
400*1.12=
Simplify the answer pls
Answers
Answer:
Step-by-step explanation:
24/3 - 4
8 - 4 = 4
what is the value sin(?)= cos 28
Answers
Answer: 62
Step-by-step explanation:
Using the fact that cos(90-x)=sin(x) we get that 90-x=28, so x=62 and the answer is simply 62.
Hope that helped,
-sirswagger21
A cylindrical metal pipe has a diameter of 8.4 millimeters and a height of 10 millimeters. A hole cut out of the center has a diameter of 6 millimeters.
A smaller cylinder is cut out of a larger cylinder. The smaller cylinder has a diameter of 6 millimeters. The larger cylinder has a diameter of 8.4 millimeters. Both cylinders have a height of 10 millimeters.
What is the volume of metal in the pipe? Use 3.14 for and round the answer to the nearest tenth of a cubic millimeter.
Answers
Answer:
[tex]271.3 mm^3\\[/tex]
Step-by-step explanation:
We have to find the volume of the hole and subtract it from the volume of the cylinder.
The volume of a cylinder is given as:
[tex]V = \pi r^2h[/tex]
where r = radius
h = height
A cylindrical metal pipe has a diameter of 8.4 mm and a height of 10 mm.
Its radius is 4.2 mm. Therefore, its volume is:
[tex]V = 3.14 * 4.2^2 * 10 = 553.9 mm^3[/tex]
A hole cut out of the center has a diameter of 6 mm. Its height is also 10 mm.
Its radius is 3 mm. Therefore, its volume is:
[tex]V = 3.14 * 3^2 * 10 = 282.6 mm^3[/tex]
Therefore, the volume of metal in the pipe is:
[tex]553.9 - 282.6 = 271.3 mm^3[/tex]
Answer:
B
Step-by-step explanation:
A study was conducted to determine how bacteria cells multiply over time in a controlled environment. In the study, the bacteria cells were counted once every hour for a total of 6 hours. which one is indepedent variable and dependent varible?
Answers
Answer:
Dependent variable → bacteria cell increase or population
Independent variable → time variable
Step-by-step explanation:
An independent variable has direct effect on the dependent variable. The independent variable can stand on it own and it is not change by the other variable you are trying to measure. The independent variable have direct effect on the dependent variable.
A dependent variable is actually the variable being tested in an experiment. The dependent variable is actually dependent on the independent variable.
The dependent variable in this scenario is the bacteria cell increase or the bacteria cell multiplication. The bacteria cell increase is dependent on the time . The time variable is the independent variable as it can stand on it own .
Dependent variable → bacteria cell increase or population
Independent variable → time variable
The graph of g(x) = ax^2 opens downward and is narrower than the graph of f(x) = x^2. Which of the following could be the value of a?
Answers
The value of a should be less than -1.
Equation of parabola,The equation of a parabola is given by the following function,
[tex]y=f(x)=\pm a(x-h)^2+k[/tex]
where,
(h, k) denotes the coordinates of its vertex,
a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.
Given to us,[tex]f(x) = x^2[/tex]
[tex]g(x)=ax^2[/tex]
SolutionFor the parabola,g(x) to be narrower than the parabola f(x) the value of a should be less than 1. also for the parabola to open downward the value of a is needed to be negative.
Hence, the value of a should be less than -1.
Learn more about Equation of parabola:
https://brainly.com/question/4443998
Calculating a correlation can help describe a relation between two quantitative variables' ___ and ___ . However, it is not sufficient to use a correlation coefficient to describe two variables. The addition of ___ can provide other helpful details such as __ _."
Answers
Answer:
direction
shape
scatter plots
shape and outliers
Step-by-step explanation:
Correlation is defined as the degree of correspondence between two variables.
When the values increase together, correlation is positive and when one value decreases as the other increases, correlation is negative .
Calculating a correlation can help describe a relation between two quantitative variables' direction and shape. However, it is not sufficient to use a correlation coefficient to describe two variables. The addition of scatter plots can provide other helpful details such as shape and outliers
e of Scores, a publication of the Educational Testing Service, the scores on the verbal portion of the GRE have mean 150 points and standard deviation 8.75 points. Assuming that these scores are (approximately) normally distributed, a. obtain and interpret the quartiles. b. find and interpret the 99th percentile.
Answers
Answer:
a) Q1= 144.10
Median = 150
Q3=155.90
b) The 99 percentile would be:[tex]a=150 +2.33*8.75=170.39[/tex]
And represent a value who accumulate 99% of the values below
Step-by-step explanation:
Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(150,8.75)[/tex]
Where [tex]\mu=150[/tex] and [tex]\sigma=8.75[/tex]
Part a
Lets begin with the first quartile:
[tex]P(X>a)=0.75[/tex] (a)
[tex]P(X<a)=0.25[/tex] (b)
We can find the quantile in the normal standard distribution and we got z=-0.674.
And we can apply the z score formula and we got:
[tex]z=-0.674<\frac{a-150}{8.75}[/tex]
And if we solve for a we got
[tex]a=150 -0.674*8.75=144.10[/tex]
The median for this case is the mean [tex]Median =150[/tex]
For the third quartile we find the quantile who accumulate 0.75 of the area below and we got z=0.674 and we got:
[tex]a=150 +0.674*8.75=155.90[/tex]
Part b
We can find the quantile in the normal standard distribution who accumulate 0.99 of the area below and we got z=2.33.
And we can apply the z score formula and we got:
[tex]z=2.33<\frac{a-150}{8.75}[/tex]
And if we solve for a we got
[tex]a=150 +2.33*8.75=170.39[/tex]
And represent a value who accumulate 99% of the values below
A laptop has a listed price of $875.98 before tax. If the sales tax rate is 6.5%, find the total cost of the laptop with sales tax included.
Round your answer to the nearest cent, as necessary.
please!
Answers
Answer:
$932.92
Step-by-step explanation:
6.5% = 0.065
(875.98) + (875.98)(0065)
(875.98) + (56.9387)
932.9187
$932.92
Answer:
$[tex]932.92[/tex]
Step-by-step explanation:
[tex]6.5/100=0.65[/tex]
Next, multiply the price by the sales tax.
[tex]875.98*0.65=56.94[/tex]
Then, add.
[tex]875.98+ 56.94=932.92[/tex]
$[tex]932.92[/tex] is the total cost of the laptop.
I promise brainliest and a exter 25 poinst to the first to answer What is the solution to the inequality 2x ≥ -4? Click the number line until the correct answer is shown...
Answers
:
Answer:
the answer is the arrow going to the right because its not a negative number and a closed circle
Step-by-step explanation:
so that means that 2x is at LEASt more than -4 opposed to this sign> wich just means greater than
because when you work with variables you usually cannot find the exact amount especially when you are rounding so you know that its biigger than no less than or at least -4
the answer is the arrow going to the right because its not a negative number and a closed circle
please please mark as brainliest
Find the slope of the line: 3x-2y=6
Answers
Answer:
slope = 3/2
Step-by-step explanation:
3x-2y=6
Get this equation in the form y = mx+b where m is the slope and b is the y intercept
Subtract 3x from each side
3x-3x-2y=-3x+6
-2y = -3x+6
Divide each side by -2
-2y/-2 = -3x/-2 +6/-2
y = 3/2x -3
The slope is 3/2 and the y intercept is -3
Answer:
3/2
Step-by-step explanation:
I got this answer by putting it in the form y=mx+b
Step 1: Subtract 3x from each side
-2y = -3x+6
Step 2: Divide each side by -2
y = 3/2x -3
The slope is 3/2 and the y intercept is -3 because m is the slope and b is the y-intercept.
Solve the two-step equation.
-9x + 0.4 = 4
Which operation must be performed to move all the constants to the right side of the equation?
Answers
Answer:
x = -0.4
multi-step equation
Step-by-step explanation:
subtract 0.4 from 4 and 0.4 so it cancells out,
0.4 - 0.4 = 0 (cancelled out)
4 - 0.4 = 3.6
then bring down -9x and divide -9 from both sides
-9/-9 = 0 (cancelled out)
3.6 / -9 = -0.4
x = -0.4
Answer:
x = -0.4
Step-by-step explanation:
We have the equation:
-9x + 0.4 = 4
First, the operation to move all the constants to the right side is subtraction since we would have to subtract 0.4 from each side, let's see this:
Now, we have all the constants on the right side of the equation.
Now, the operation we need to perform to isolate the variable is division (since the x has a -9 that is being multiplied by x) we need to do the opposite operation:
Thus, the answer to this equation is x= -0.4
To prove a polygon is a rectangle which of the properties listed must be included in the proof
Answers
Answer:
if the diagonals of a parallelogram are congruent, then it's a rectangle (neither the reverse of the definition nor the converse of a property). If a parallelogram contains a right angle, then it's a rectangle (neither the reverse of the definition nor the converse of a property).
Step-by-step explanation:
Entrance to a prestigious MBA program in India is determined by a national test where only the top 10% of the examinees are admitted to the program. Suppose it is known that the scores on this test are normally distributed with a mean of 420 and a standard deviation of 80. Parul Monga is trying desperately to get into this program. What is the minimum score that she must earn to get admitted?
Answers
Answer:
The minimum score that she must earn to get admitted is 523.
Step-by-step explanation:
As the scores are normally distributed, we can calculate the probability using the z-score.
The distribution has a mean of 420 and a standard deviation of 80.
We have to calculate the z-score z* that satisfies:
[tex]P(z>z^*)=0.1[/tex]
This happens for z*=1.28155.
Then, we can calculate the score as:
[tex]X=\mu+z\cdot\sigma=420+1.28155\cdot 80=420+102.524=522.524[/tex]
What is the answer to this question–1 × –5?
Answers
Answer:
5
Step-by-step explanation:
a minus times by another minus makes a positive, so it is basically 1 x 5
Answer:
5
Step-by-step explanation:
Since the you are multiplying 2 minuses together they will cancel each other out to form a positive number. However if you have an example like this
-6 × 7
Then the answer will be -42 because there is only one negative
A teacher wrote the equation 3y + 12 = 6x on the board. For what value of b would the additional equation 2y = 4x + b form a system of linear equations with infinitely many solutions?
b = –8
b = –4
b = 2
b = 6
Answers
Answer:
-8
Step-by-step explanation:
For a system to have infinitely many solutions the two equations must be the same line. We can simplify the first and second equations by dividing them by 3 and 2 respectively to get:
y + 4 = 2x
y = 2x + b/2 → y -b/2 = 2x
Since the constants must be equal, 4 = -b/2 which means b = -8.
Answer:
b=-8
Step-by-step explanation:
A baseball player comes up to bat 3 times during a league game. He either gets a hit or gets an out. What is the probability that the player gets 3 hits in the three bats ?
Answers
Answer:
Since there are 2 possibilities for each bat (hit or out), the amount of total possibilities is 2 * 2 * 2 = 8. There is only one possibility out of those eight that gives us three hits, therefore the probability is 1 / 8 or 0.125.
The weights of college football players are normally distributed with a mean of 200 pounds and a standard deviation of 50 pounds. If a college football player is randomly selected, find the probability that he weighs between 170 and 220 pounds.
Answers
Answer:
[tex]P(170<X<220)=P(\frac{170-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{220-\mu}{\sigma})=P(\frac{170-200}{50}<Z<\frac{220-200}{50})=P(-0.6<z<0.4)[/tex]
And we can find this probability with this difference:
[tex]P(-0.6<z<0.4)=P(z<0.4)-P(z<-0.6)=0.655-0.274= 0.381 [/tex]
Step-by-step explanation:
Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(200,50)[/tex]
Where [tex]\mu=200[/tex] and [tex]\sigma=50[/tex]
We want to find the following probability:
[tex]P(170<X<220)[/tex]
And we can use the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
And using this formula we got:
[tex]P(170<X<220)=P(\frac{170-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{220-\mu}{\sigma})=P(\frac{170-200}{50}<Z<\frac{220-200}{50})=P(-0.6<z<0.4)[/tex]
And we can find this probability with this difference:
[tex]P(-0.6<z<0.4)=P(z<0.4)-P(z<-0.6)=0.655-0.274= 0.381 [/tex]
I will give brainiest to the first to answer. The what
of the following set of data is 5.
13, 7, 9, 5, 2, 3, 5, 4, 10, 12
Answers
Answer:
it is the mode.
Step-by-step explanation:
i. e 5 is the most occuring number in the set of data listed above
Joshua has $4,200 to invest for college. If Joshua invests $4,200 for 3 years and earns $630, what is the simple interest rate? Joshua’s goal is to have $5,000 after 4 years. Is this possible if he invests with a rate of
return of 6%? Explain.
Answers
Answer:
The simple interest rate is 5%.
This is possible with a rate of 6%, since in this case, his amount earned will be $5,208.
Step-by-step explanation:
This is a simple interest problem.
The simple interest formula is given by:
[tex]E = P*I*t[/tex]
In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.
After t years, the total amount of money is:
[tex]T = E + P[/tex]
Joshua has $4,200 to invest for college. If Joshua invests $4,200 for 3 years and earns $630, what is the simple interest rate?
We have that [tex]P = 4200, E = 630, t = 3[/tex]. We have to find I.
[tex]E = P*I*t[/tex]
[tex]630 = 4200*I*3[/tex]
[tex]I = \frac{630}{4200*3}[/tex]
[tex]I = 0.05[/tex]
The simple interest rate is 5%.
Joshua’s goal is to have $5,000 after 4 years. Is this possible if he invests with a rate of return of 6%?
We have to find T when [tex]P = 4200, t = 4, I = 0.06[/tex]
So
[tex]E = P*I*t[/tex]
[tex]E = 4200*0.06*4[/tex]
[tex]E = 1008[/tex]
[tex]T = E + P = 4200 + 1008 = 5208[/tex]
This is possible with a rate of 6%, since in this case, his amount earned will be $5,208.