With the beam being held still at a height of 40 m, the crane breaks and the beam falls to the ground. Assuming no air resistance, how much total energy will the beam have just as it hits the ground?
The total energy of the beam just as it hits the ground would be equivalent to the initial potential energy when it was held at a height of 40 m, assuming no air resistance.
Explanation:The question is about understanding the concept of conservation of energy, specifically the transformation of potential energy to kinetic energy. When the beam was held at a height of 40 m, it had potential energy given by the formula:
PE = mgh
where m is the mass of the beam, g is the acceleration due to gravity, and h is the height. Assuming no air resistance, when the beam falls, all of its potential energy will be converted to kinetic energy, which can be determined by the formula:
KE = 1/2 mv^2
However, as we don't know the exact speed of the beam just as it's hitting the ground, we don't need it because the total energy remains constant. So, just as the beam hits the ground the total energy will be the same as the initial potential energy when it was still.
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find the sum of the first 25 terms. 2,8,14,20
Answer:
1850
Step-by-step explanation:
Suppose a $75,500 mortgage is to be amortized at 6.5% interest. Find the total amount of interest that would be paid for a 40 year term. What is the amount of interest for a 40 year mortgage?
What is the arc measure of an arc with length 4.189 cm and radius equal to 3 cm.'?
what is the prime factorization of 204
David earns $8.59 an hour. His benefits package is equal to 18 percent of his hourly wages. When you include the value of his benefits, how much does David earn per hour?
Answer:
David earns $10.14 per hour.
Step-by-step explanation:
David earns for an hour = $8.59
He gets benefits package that is equal to 18% of his hourly wages.
18% of 8.59
[tex]\frac{18}{100}[/tex] × 8.59
= 0.18 × 8.59
= $1.5462 ≈ $1.55
David's per hour earning = $8.59 + $1.55 = $10.14
David earns $10.14 per hour.
Answer: David earns $10.14 per hour.
Step-by-step explanation:
We are given that , David earns for an hour = $8.59
He gets benefits package that is equal to 18% of his hourly wages.
Now, When we include the value of his benefits, then the amount earned by David per hour as benefit will be :
Benefit = 18% of $8.59
[We write 18% as 0.18 (To convert a percent into decimal or fraction we divide it by 100.)]
Benefit = 0.18 × $8.59
Benefit = $1.5462 ≈ $1.55
David's per hour earning = original earning + Benefit
=$8.59 + $1.55 = $10.14
Hence , David earns $10.14 per hour.
how many cubic blocks of side length 1/7 inch would it take to fill a cube with a side length of 3/7 inch?
the price of a pair of shoes plus 5% sales tax
Marisa hiked 1 3/4 miles and 3/4 hours at that rate how far can she hike in one hour
Answer:
2.33 miles/hour
Step-by-step explanation:
If Marisa hiked a distance of 1 3/4 miles in a time of 3/4 hours we can determine her speed as miles per hour. Speed is defined as the distance(d) per time(t). Let speed equal to v:
[tex]v=d/t[tex]
We can determine the decimal numbers of the distance and time:
1 3/4 = 7/4 = 1.75 miles
3/4 = 0.75 hours
∴ [tex]v=1.75/0.75=2.33[/tex]
Marisa can hike 2.33 miles per hour.
Bari Jay, a gown manufacturer, received an order for prom dresses from China. Her cost is $35 a gown. If her markup based on selling price is 79%, what is the selling price of each gown?
To calculate the selling price of a gown with a cost of $35 and a markup of 79%, convert the markup to a decimal, subtract from 1, and divide the cost by this number. The selling price is $166.67 per gown.
Explanation:Calculating the Selling Price with MarkupThe problem involves finding the selling price of a gown given the cost and the markup based on selling price. Markup based on selling price is calculated using the formula: Selling Price = Cost / (1 - Markup Percentage), where the Markup Percentage is expressed as a decimal. Here, the cost of a gown is $35, and the markup based on the selling price is 79%. Let's calculate the selling price.
Convert the markup percentage to a decimal by dividing by 100: 79% / 100 = 0.79.Subtract the markup percentage as a decimal from 1: 1 - 0.79 = 0.21.Divide the cost by the result to find the selling price: $35 / 0.21 = $166.67.The selling price of each gown is $166.67.
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7^16/7^12=7^-18/? what is the missing denominator
Write this number in standard form. 12 ten thousands, 8 thousands, 14 hundreds and 7 ones
domain and range of x^2+x-2/x^2-3x-4
Assume that a procedure yields a binomial distribution with n trials and the probability of success for one trial is p. use the given values of n and p to find the mean muμ and standard deviation sigmaσ. also, use the range rule of thumb to find the minimum usual value mu minus 2 sigmaμ−2σ and the maximum usual value mu plus 2 sigmaμ+2σ.
A binomial distribution is an experiment where there are two outcomes; Success and failure. For instance, you are given n = 128 and p = 0.27. The formula for the variance of a binomial distribution is n*p(1 – p) or n*p*q*. They are equivalent because q = 1- p. We will use the first equation.
Variance = n*p*(1 – p)
Variance = 128*0.27*(1 – 0.27)
Variance = 25.23
To get the standard deviation, find the square root of the variance.
Standard deviation = sqrt (Variance)
Standard deviation = sqrt (25.23)
Standard deviation = 5.02
Brainiest To Best Answer: Are Guidance Counselors allowed to lie or give false information about a class and force a math-genius to take an intensive math class? I took Algebra I Honors, Geometry Honors, and Algebra II Honors and scored in the 99th percentile on their EOCs and aced the classes. For my 10th grade year, my Guidance Counselor claimed that for my blank-period, I should take "Advanced Math Topics" because I would get 2 math credits that year (Pre-Calculus Honors was the other class I was taking). The Guidance Counselor did not mention it being an intensive class and this class was only for those who fail their math classes, exams, or other national math-portion of tests. It would look horrible for a math-major to have taken an intensive math class and would look weird that I was also taking a high-level math course at the same time. When we were informed about this, we were outraged and research does suggest that having such a class on your transcript will eliminate the possibility for getting into a good competitive college or getting the scholarship for out-of-state colleges in academics. I took many extra-classes and aced them online and we want to have this class removed from our transcript considering the fact that by rules, they cannot place a student performing as well as I am into a class lower than the classes previously taken. Do you agree with this? We are bringing this to the District Officer and the class was so basic, that I would be the only one in the class getting an A, "100%" every test and I would finish the questions in 5-10 minutes at most for any classwork given. Was the Guidance Counselor wrong to do this? What consequences might he face for this and will we be compensated for these troubles or have this transcript recording of this intensive class removed, exempt, or clarified?
Final answer:
Guidance counselors should not mislead students; it is worthwhile to challenge placement of a high-achieving math student in an unnecessary remedial class and seek to correct the record.
Explanation:
Guidance counselors should provide accurate information to students regarding class choices, particularly for students excelling in certain subjects like math.
It seems inappropriate for a counselor to enroll a high-achieving student in an intensive class designed for remediation without discussing the nature of the class and reviewing the student's academic history and test scores.
There may be rules or guidelines, possibly at the district level, outlining the circumstances under which a counselor can place a student in a specific class. If these procedures were not followed, bringing the issue to the attention of a District Officer is reasonable.
The aim would be to correct the student's academic record, ensuring it reflects their true capabilities and doesn't unfairly disadvantage them in future educational or scholarship opportunities. Corrective actions could include exemption, removal, or clarification of the intensive math class on the student's transcript.
The counselor in question may face a review of their practices or disciplinary action if they are found to have acted against established policies. However, the outcome will depend on the investigation conducted by the school district.
what is the point slope form of an equation with the slope of 3/5 that passes through the point (10,-2)
The sales tax in Bill's state is 6%. Bill bought a Scion having a sales tax of $820. What was the cost of the car, rounded to the nearest dollar.
A firm has $100 of average inventory, operating profit of $500 and sales of $1,500. its days in inventory is:
The inventory in days is 36.5 days
Further Explanation:
Inventory Turnover Ratio: It is an activity ratio which measure of how suitably a company is handling its inventory to generates sales. The inventory turnover ratio is calculated as:
[tex]\text{Inventory Turnover Ratio}=\dfrac{\text{Cost of goods sold}}{\text{Average Inventory}}[/tex]
Calculate the days in inventory:
[tex]\begin{aligned}\text{Days in inventory}&=\dfrac{\text{365}}{\text{Inventory Turnover Ratio}}\\&=\frac{365}{10}\\ &=36.5\text{days}\end{aligned}[/tex]
Therefore, the inventory in days is 36.5 days
Working note 1:
Calculate the cost of goods sold:
[tex]\begin{aligned}\text{Cost of goods sold}&=\text{Sales}-\text{Operating profit}\\ &=\$1,500-\$500\\ &=\$1,000\end{aligned}[/tex]
Working note 2:
Calculate the inventory turnover ratio:
[tex]\begin{aligned}\text{Inventory Turnover Ratio}&=\frac{\text{Cost of goods sold}}{\text{Average Inventory}}\\ &=\frac{\$1000}{\$ 100}\\ &=\$10\end{aligned}[/tex]
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Answer details:
Grade: High School
Subject: Financial Accounting
Chapter: Ratio Analysis
Keywords: A firm has $100 of average inventory, operating profit of $500, sales of $1,500, days in inventory.
simplify b^2/6a^2 - 1/3a^3 + 3b/8a
Help me please!! SOS!!
If 7-y=6 then y =what
Answer:
-29
Step-by-step explanation:
The Correct Answer:
A. -29
Square both sides of the equation.
7−y−−−−√
=
6
(7−y−−−−√)2
=
(6)2
7−y
=
36
−7
−7
Subtract 7 from both sides
−y
=
29
y
=
−29
7−(−29)−−−−−−−−√
=?
6
Check your answer
7+29−−−−−√
=?
6
36−−√
=?
6
6
=
6
So m=−29 is a solution.
A company that creates model cars uses a 1.5 foot : 1 inch ration when creating the models. If a real car is 12 feet long, how long will the model car be?
Triangle ABC has coordinates A(3,3), B(0,0) and C(3,0) if the triangle is rotated 180 degrees about point B what will the coordinates of the images of A and C
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The rule for G -1(x) in G(x)=3x-5/4 is G^-1(x)=
(4x-5)/3
(4x+5)/3
(3x+5)/-4
Answer:
(4x+5)/3=y
Step-by-step explanation:
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Maria and Ming start at the same point and drive in opposite directions. Maria drives 50 mph and Ming drives 30 mps. How far apart will they be in 2 hours
Maria and Ming, driving in opposite directions at speeds of 50 mph and 30 mph respectively, will be 160 miles apart after 2 hours due to their combined relative speed of 80 mph.
The question you've asked is a relative speed problem in Mathematics, specifically dealing with the concept of adding distances when objects move in opposite directions. To solve this, we take the sum of the two speeds and multiply by the time they travel to get the total distance between them.
Maria drives at 50 mph and Ming drives at 30 mph. Since they are driving in opposite directions, you add their speeds together to find the relative speed at which they are moving apart. This gives us a relative speed of 50 mph + 30 mph = 80 mph. If they drive for 2 hours, you multiply the relative speed by the time to get the distance:
Distance = Speed times Time
Distance = 80 mph times 2 hours = 160 miles apart.
Therefore, Maria and Ming will be 160 miles apart after 2 hours.
Tina wants to save money for school. Tina invests 400$ in an account that pays interest rate of 8%. How many years will it take if her goal is 5500$
In the middle of the page draw a equilateral triangle with 2 inch sides and the bottom parallel to the of the page
The sum of the angle of a triangle is 180 degrees. If you are to draw a pattern of equilateral triangles then you know that an equilateral triangle has three equal sides. Also, its angles are the same, having 60 degrees at each corner of the triangle. A triangle cannot qualify as an equilateral triangle if it is greater than 180 degrees or less than 180 degrees as a total angle. Also if a triangle that has no two right angles, then it is called a scalene triangle. If the triangle has two right angles, it is called isosceles triangle. A triangle with equal sides is called an equilateral triangle.
What's the average of 200 and 300
A ball is thrown from an initial height of 7 feet with an initial upward velocity of 30ft/s . The ball's height h (in feet) after t seconds is given by the following. h=7+30t-16t^2
Find all values of t for which the ball's height is 20 feet.
Round your answer(s) to the nearest hundredth.
t = —— seconds
The values of t for which the ball's height is 20 feet, after solving the quadratic equation using the appropriate values for a, b, and c, are approximately t = 3.79 seconds and t = 0.54 seconds. These values represent the time it takes for the ball to reach 20 feet on its way up and on its way down.
Explanation:To find all values of t for which the ball's height is 20 feet, we need to set the ball's height equation h = 7 + 30t - 16t2 equal to 20 and solve for t. This means solving the quadratic equation: 16t2 - 30t + (7 - 20) = 0, which simplifies to 16t2 - 30t - 13 = 0.
We can solve this quadratic equation using the quadratic formula, t = (-b ± √(b2 - 4ac)) / (2a), where a = 16, b = -30, and c = -13. After applying the quadratic formula, we find two potential solutions for t, which are t = 3.79 seconds and t = 0.54 seconds. Since time cannot be negative, both of these times represent the moments when the ball is at 20 feet: once on the way up and once on the way down.
The values of t for which the ball's height is 20 feet are approximately [tex]\(t \approx 2.76\)[/tex] seconds and [tex]\(t \approx 0.14\)[/tex] seconds (rounded to the nearest hundredth).
To find the values of [tex]\(t\)[/tex] when the ball's height is 20 feet, you can set the equation for height [tex]\(h\)[/tex] to 20 and solve for [tex]\(t\)[/tex]:
[tex]\[h = 7 + 30t - 16t^2\][/tex]
Setting [tex]\(h\)[/tex] to 20:
[tex]\[20 = 7 + 30t - 16t^2\][/tex]
Rearranging the equation:
[tex]\[16t^2 - 30t + 7 = 0\][/tex]
Now, you can solve this quadratic equation for t. You can use the quadratic formula:
[tex]\[t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\][/tex]
In this case, the coefficients are [tex]\(a = 16\), \(b = -30\), and \(c = 7\)[/tex].
[tex]\[t = \frac{30 \pm \sqrt{(-30)^2 - 4(16)(7)}}{2(16)}\][/tex]
[tex]\[t = \frac{30 \pm \sqrt{900 - 448}}{32}\][/tex]
[tex]\[t = \frac{30 \pm \sqrt{452}}{32}\][/tex]
[tex]\[t = \frac{30 \pm 2\sqrt{113}}{32}\][/tex]
Now, you have two possible solutions for t:
[tex]\[t_1 = \frac{30 + 2\sqrt{113}}{32} \approx 2.76 \text{ seconds}\][/tex]
[tex]\[t_2 = \frac{30 - 2\sqrt{113}}{32} \approx 0.14 \text{ seconds}\][/tex]
Solve for x & y. 30x−42y=−6 and 5x−7y=−1