Answer: Option a) 33 1/3 lbs
Solution:
Be
Attraction force (F) varies inversely as the square of the distance between them:
F=k/d^2
Constant of proportionality: k
Distance between the two masses: d
F=75 lbs when d=8 feet
Replacing in the formula above:
F=k/d^2
75 lbs=k/(8 feet)^2
Squaring in the denominator:
75 lbs=k/(64 feet^2)
Solving for k: Multiplying both sides of the equation by 64 feet^2:
(64 feet^2)(75 lbs)=(64 feet^2)[k/(64 feet^2)]
4,800 lbs*feet^2=k
k=4,800 lbs*feet^2
F=k/d^2
F=4,800 lbs*feet^2/d^2
Find the attraction when the masses are twelve feet apart:
F=?
d=12 feet
Replacing in the formula:
F=4,800 lbs*feet^2/(12 feet)^2
Squaring in the denominator:
F=4,800 lbs*feet^2 / (144 feet^2)
Dividing:
F=(4,800/48)/(144/48) lbs
F=100/3 lbs
F=(99+1)/3 lbs
F=(99/3+1/3) lbs
F=33 1/3 lbs
Final answer:
Using Newton's inverse square law for gravitational force, it is determined that the force of attraction will be a) 33 1/3 lbs when the distance between the masses is increased from 8 to 12 feet.
Explanation:
The scenario described falls under the gravitational force law stated by Isaac Newton, which is a fundamental concept in Physics. The force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them (F ∝ 1/d²). We are given that the gravitational attraction is 75 lbs when the bodies are 8 feet apart. To find the force at a distance of 12 feet, we use the inverse square law which indicates that increasing distance reduces gravitational force.
Let F1 be the initial force and d1 be the initial distance, and let F2 be the force at a new distance d2. According to the inverse square law, we have F1/F2 = (d2/d1)². Plugging in the values F1 = 75 lbs, d1 = 8 feet, and d2 = 12 feet, we get 75/F2 = (12/8)² = 2.25. Solving for F2, we find that F2 = 75 / 2.25 = 33.33 lbs.
Therefore, the gravitational attraction when the masses are twelve feet apart is 33 1/3 lbs.
Dividing whole numbers if insulation can be installed at a rate of 1,400 square feet per hour and 29,400 square feet needs to be installed,how many hours will the job take?
It will take approximately 21 hours to install the insulation.
Explanation:To determine the number of hours it will take to install 29,400 square feet of insulation at a rate of 1,400 square feet per hour, we can use division. We can divide the total square footage by the rate of installation per hour:
Number of hours = Total square footage / Rate of installation per hour
Number of hours = 29,400 square feet / 1,400 square feet per hour
Number of hours = 21 hours
Therefore, it will take approximately 21 hours to install the insulation.
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which lists all the integer solutions of the equation x = l21l ?
A.21 only
B.21 and -21
C.0 and 21
D.-21 only
What does this complex fraction equal??? Please help me
Answer:
16/3
As a decimal, 5.3 with a line other the "3" which means it's repeating
As a mixed fraction, 5 1/3
Hope this helps :-)
Solve. - 1 3 x > 5
A) x < -15
B) x > -15
C) x > 5/3
D) x < -5/3
its none of them... x<-5/13 divide each term by -13 and simplify.
I'm assuming by the answer choices that you're question is:
-1/3x > 5
Isolate the x. Multiply -3 to both sides
(-3)(-1/3)x > 5(-3)
x > 5(-3)
Remember to flip the sign when you multiply by a negative number
x > 5(-3)
Multiply
x < -15
x < -15, or (A) is your answer
hope this helps
~Rise Above the Ordinary
Three years ago, Claire borrowed money from her father to pay for a class trip. She agreed to pay 6% simple annual interest on the loan. Now she owes him $90 in interest, plus the principal amount. How much did Claire borrow?
Answer:
D 500
Its been 2 years since you asked this but I hope I can help!
What can you say about the marked angles in these parallelogram?
A Opposite angles of a parallelogram are congruent. ( the same measure)
B Consecutive angles of a parallelogram are supplementary (measure add to 180)
C consecutive angles of a parallelogram are congruent. (The same measure)
D Opposite angles of a parallelogram are supplementary (measure add to 180)
Please need help on this don’t understand this one
Answer: A and B both are correct statements.
Step-by-step explanation:
Let ABCD is a parallelogram then its properties are as follows:-
1. Opposite angles and sides of parallelogram are always congruent.
i.e.AB=CD and AD=BC and ∠A=∠C and ∠B=∠D
2.Consecutive angles are supplementary.
i.e. ∠A+∠B=180° and ∠B+∠C=180°
3. Its diagonals bisect each other.
4. The sum of all the angles is 360°.
I NEED HELP WITH #36
Answer:
2 3/4 in
Step-by-step explanation:
The sum of the marked distances is equal to the total distances shown:
... (1 5/8) + ? + (1 5/8) = 6
... ? = 6 - (1 5/8 + 1 5/8) . . . . . subtract the constants on the left
... ? = 6 - (2 5/4) . . . . . . . . . . . add the numbers in parentheses
... ? = 6 - 3 1/4 . . . . . . . . . . . . rewrite the number in parentheses (2+5/4 = 2 + 1 1/4)
... ? = (6 -3) -1/4 = 3 -1/4 . . . . . see below
... ? = 2 3/4
_____
Comment on subtacting mixed numbers
Some folks find it convenient to subtract by adding. To find the difference between 3 1/4 and 6, they would start by adding 3/4 to make 4, then add 2 to make 6. Then they see the difference is 3/4 + 2 = 2 3/4.
Here, I chose to subtract 3 1/4 by subtracting 3, then subtracting 1/4. After subtracting 3 from 6, I get 3, from which I now need to subtract 1/4. It should be clear that taking 1/4 away from 3 will leave 2 3/4. (One of the units has been converted to 4/4 to make the subtraction of 1/4 possible.)
_____
Comment on doubling a fraction
As part of this problem, we needed to add 1 5/8 to itself. We did that by doubling the integer part, and doubling the fraction. When a fraction has an even denominator, it is easy to double it: replace the denominator with half its value — 2×(5/8) = 5/4, where the denominator 4 is half the denominator 8.
Identify the smallest numbers that can actually belong to a class in a frequency distribution
Answer: Lower class limits.
Step-by-step explanation:
1. By definition, a frequency distribution lists classes of values and the frequency of ocurrency.
2. The class limits is define as the minimum and maximum values that can belong to the different clases. The class limits are: Lower class limits and Upper class limit.
3. Lower class limits is define as the smallest numbers that can belong to a class.
Answer:
Does the frequency distribution appear to have a normal distribution using a strict interpretation of the relevant criteria?
A. Yes, all the requirements are met.
Does the frequency distribution appear to have a normal distribution using a strict interpretation of the relevant criteria?
C. No, the distribution is not symmetric.
Identify the class width for the given frequency distribution.
B. 5
Identify the class midpoints for the given frequency distribution.
C. 202 207 212 217 222 227 232 237
A survey of statistics students asked the students for their favorite music genre. The results of the survey are provided in the table. Identify the model class from the distribution.
A. Blues
A recent survey asked 874 people to identify what education they have achieved. The accompanying table summarizes the result. Does this table describe a relative frequency distribution? Why or why not?
C. No, the sum of the percentages is not 100 percent.
Find the midpoint of the FICO score interval 550-599.
D. 574.5
Listed below are blood groups of O, A, B, and AB of randomly selected blood donors (based on data from the Greater New York Blood Program)
Identify the frequency of the blood group O.
D. 22
A sample value that lies very far away from the majority of the other sample values is _______
A. An outlier
Identify the smallest numbers that can actually belong to a class in a frequency distribution.
A. Lower class limit.
An elevator started on the first floor and went up 18 floors. It then comes down 11 floors and went back up 16 floos. At what floor did this stop.
zoe watched 6 episodes of her favorite online video series in 1.5 hours. she spent the same amount of time watching each episode. what is the unit rate of hours to episodes
Tracie rides the bus home from school each day. The graph represents her distance from home relative to the number of minutes since the bus left the school.
What does the slope of the graph mean?
Tracie’s bus travels towards her home at an average speed of mile per minute.
Tracie’s bus travels towards her home at an average speed of 2 miles per minute.
Tracie’s bus travels away from her home at an average speed of mile per minute.
Tracie’s bus travels away from her home at an average speed of 2 miles per minute.
Answer:
Tracie’s bus travels towards her home at an average speed of 1/2 mile per minute.
Step-by-step explanation:
The labels on the graph tell us that the independent variable, x, represents time in minutes, and the dependent variable, y, represents distance from home in miles.
Looking at the graph, we can see that the number of miles from home decreases by 1 for every two minutes. Since the distance is decreasing, this means that the bus is getting closer to home. Since it decreases by 1 mile every 2 minutes, this means that the speed is 1/2 mile per minute.
The answer is : A, Tracie's bus travels towards her home at an average speed of 1/2 mile per minute.
You have invested in three different stocks: Engineering Aces, Upton Clothiers, and Thompson Musical Instruments. Because you have diversified your stocks so well, the way they change is independent. The probabilities of the stocks changing in value by more than 10% in a given week are listed below.
P(E) = 19%
P(U) = 11%
P(T) = 6%
What is the probability that all three will change by more than 10% in the same week?
Answer:
answer is 0.001254.
Step-by-step explanation:
Given that you invested in 3 stocks of Engineering Aces, Upton Clothiers, and Thompson Musical Instruments.
Also given that each stock value is independent of the other.
Let E be the event changing in value by more than 10% in a given week for Engineering Aces,
U be the event changing in value by more than 10% in a given week for Upton Clothiers, and T be the event changing in value by more than 10% in a given week for Thompson Musical Instruments.
Given that P(E) = = 19%
P(U) = 11%
P(T) = 6%
probability that all three will change by more than 10% in the same week
= P(EUT)
= P(E) P(U) P(T) since three events are independent.
=0.19(0.11)0.06
= 0.001254
Final answer:
The probability that all three stocks, Engineering Aces, Upton Clothiers, and Thompson Musical Instruments, will change by more than 10% in the same week is calculated by multiplying their individual probabilities together, resulting in a probability of 0.1254%.
Explanation:
The question asks for the probability that all three stocks will change by more than 10% in the same week, given their individual probabilities.
To find this probability, since the changes in stocks are independent of each other, we multiply the probabilities of each event occurring together. The formula for the joint probability of independent events is P(E and U and T) = P(E) × P(U) × P(T).
Using the given probabilities:
P(E) = 19% or 0.19P(U) = 11% or 0.11P(T) = 6% or 0.06We calculate:
P(E and U and T) = 0.19 × 0.11 × 0.06
Which equals:
P(E and U and T) = 0.001254 or 0.1254%
Therefore, the probability that all three stocks will change by more than 10% in the same week is 0.1254%.
what is the square root of 28
The decimal form would be 5.29150262
What is 5103 to the nearest thousands
5,103 rounded to the nearest thousands is 5,000
In order to round a number to the nearest thousand, we must see if the digit in the hundreds position is greater or less than 5.
In this case, 1 is less than 5
If the number is less than five, we round the number down, and in this case, to the nearest thousand.
Therefore, the nearest thousand would be 5000
One square tile on your kitchen floor is 11.25 inches long. It takes 12.5 tiles to cover the length of the floor. About how long is the floor?
1 Square = 11.25 inches
You need 12.50 Squares
So, that means that you should do 11.25 × 12.50 which equals 140.625 and 140.625 is your length. Let me know if this is right and if it helped you.
What is the common denominator of 1/a+1/b in the complex fraction 1/a-1/b/1/a+1/b
Answer:
common denominator is ab.
Step-by-step explanation:
Given : [tex]\frac{1}{a} +\frac{1}{b}[/tex] ; complex fraction [tex]\frac{\frac{1}{a} - \frac{1}{b}}{\frac{1}{a}+\frac{1}{b}}[/tex].
To find : What is the common denominator.
Solution : We have given that [tex]\frac{\frac{1}{a} - \frac{1}{b}}{\frac{1}{a}+\frac{1}{b}}[/tex].
For this, we subtract fractions in the numerator and the sum of fractions in the denominator.
[tex]\frac{\frac{b-a}{ab}}{\frac{b+a}{ab}}[/tex].
We observe that the common denominator is given by the product: ab
Therefore, common denominator is ab.
Answer: is D
Step-by-step explanation:
No really getting this please help
Hi,
From simplifying the expression I can see your answer in it's exact form is 35/6. Based off of your multiple choice answers, your answer is 5 5/6.
Hope this helps.
Is .634 an integer ??
No.
An integer is a whole number.
In the case of .634 (or 0.634), we see that it is not a whole number, as there is a decimal point, and numbers to the right of the decimal points.
hope this helps
No, because .634 is an odd number and odd numbers cannot be integers.
Wouldn't let me type the question so I just attached an image.
a restaurant owner bought 6 boxes of disposable cups for $81 with each box containing 3741 cups if he wanted to divvy up the Cups among his 3 restaurants with with each restaurant getting the same number of cups how many cups of each do I get
An isosceles triangle has an angle that measures 80°. Which other angles could be in that isosceles triangle? Choose all that apply
In an isosceles triangle with an angle measuring 80°, the other two angles could be 50° each.
An isosceles triangle has two sides of equal length and two angles of equal measure. Since one angle measures 80°, the other two angles must be equal to each other. To find the measure of these angles, we subtract 80° from 180° (the sum of all angles in a triangle) and divide the result by 2. So, each of the other two angles in the isosceles triangle could be 50°.
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The other angles that could be in the isosceles triangle are:[tex]\[\boxed{50^\circ \text{ and } 20^\circ}\][/tex]
In an isosceles triangle, two sides are of equal length, and the angles opposite those sides are equal. The sum of the angles in any triangle is always [tex]\(180^\circ\).[/tex] Given that one angle measures [tex]\(80^\circ\)[/tex], we need to determine the possible configurations for the remaining angles.
Case 1: 80° is the vertex angle
If the [tex]\(80^\circ\)[/tex] angle is the vertex angle (the angle between the two equal sides), the remaining two angles must be equal. Let x be the measure of each of the remaining angles.
Since the sum of the angles in a triangle is [tex]\(180^\circ\):[/tex]
[tex]\[80^\circ + x + x = 180^\circ\]\[80^\circ + 2x = 180^\circ\][/tex]
[tex]\[2x = 100^\circ\][/tex]
[tex]\[x = 50^\circ\][/tex]
So, the other angles in this case are [tex]\(50^\circ\)[/tex] each.
Case 2: 80° is one of the base angles
If the [tex]\(80^\circ\)[/tex] angle is one of the base angles (the angles opposite the equal sides), there will be two such angles. Let y be the measure of the vertex angle.
Since the sum of the angles in a triangle is [tex]\(180^\circ\):[/tex]
[tex]\[80^\circ + 80^\circ + y = 180^\circ\]\[160^\circ + y = 180^\circ\][/tex]
[tex]\[y = 20^\circ\][/tex]
So, the other angles in this case are [tex]\(80^\circ\) and \(20^\circ\).[/tex]
Possible angles
Given that one angle is [tex]\(80^\circ\),[/tex] the possible configurations for the angles in the isosceles triangle are:
- [tex]\(80^\circ, 50^\circ, 50^\circ\)[/tex]
- [tex]\(80^\circ, 80^\circ, 20^\circ\)[/tex]
So, the other angles that could be in the isosceles triangle are:
[tex]\[\boxed{50^\circ \text{ and } 20^\circ}\][/tex]
These are the angles that apply based on the given conditions.
which unit is most appropriate to use to measure the volume of a bathtub
The most appropriate unit to measure the volume of a bathtub is liters.
When considering the volume of a bathtub, the most appropriate unit of measure would be liters. Milliliters are too small for such a large volume, and while gallons could be used, liters are more standard for this type of measurement in many parts of the world, including in scientific contexts.
For example, if we have a common bathtub that is 13.44 dm long, 5.920 dm wide, and 2.54 dm deep, we would calculate its volume in liters. Since a bathtub has a capacity similar to a large container, liters are an appropriate choice because they give a manageable number for the volume. In measuring smaller volumes, like that of a water balloon or a chemical solution in a lab, milliliters or a graduated cylinder may be used instead.
What the length of a cube having a volume of 1331 ft3
You just have to take the cube root of 1331. So ³√1331 = 11
A line has a slope of -1/2 and a y-intercept of –2. So what is the x intercept on the line.
A. -4
B. -1
C. 1
D. 4
Answer:
(4,0)
Step-by-step explanation:
The equation of the line is y = (-1/2)x - 2. At the x-intercept, y = 0. Setting y = (-1/2)x - 2 to zero, we get (1/2)x = 2, and thus x = 4.
How many inches are in 5 1/2
There are 12 inches in every foot 5 x 12 is 60 half a foot would be 12÷2=6 so 60+ 6=66 inches
David plants a tree that is 3 feet tall. at the end of the 4 years it has grown to be 6 feet tall, and then stops growing. after 7 years, david cuts down the tree to put in a pool. what is the domain, in years, of the function that represents the height of the tree?
The domain of the function is (0, 7) years.
The function that represents the height of the tree is defined over the period during which the tree's height changes. Given that,
The tree starts growing at 0 years (the time when it is first planted). It grows for 4 years, reaching a height of 6 feet by the end of that period. After 4 years, the tree stops growing and remains at 6 feet for the remaining 3 years. After 7 years total (4 years of growth + 3 years of constant height), the tree is cut down.
The domain of the function that represents the height of the tree is the time interval from when the tree is planted until it is cut down.
Multiply.
1.25(−3.6)
Enter your answer as a decimal in the box.
Answer:
-4.5
Step-by-step explanation:
the multiplication of 1.25(−3.6) is -4.5.
What are mathematics operations?
• A mathematical operation is a function that converts a set of zero or more input values (also called "b" or "arguments") into a defined output value. The number of operands determines the operation's arity. Most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive and multiplicative inverses.
• Zero-arity operations, or nullary operations, are constants, and mixed products are arity three operations, or ternary operations.
Here, the given expression is :
1.25(−3.6)
Now after removing the bracket multiplication sign will apply :
1.25 x −3.6 = -4.5
Therefore, the multiplication of 1.25(−3.6) is -4.5.
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can someone please help me with this plss and thanks
4x + 32 - 4 = 34 - 2x
4x + 28 = 34 - 2x
4x = 34 - 2x - 28
4x = -2x + 6
4x + 2x = 6
6x = 6
x = 1
clara wants to run a total od 5 1/2 miles each lap around the track is 0.25 miles how many laps around the track does clara need to run to complete 5 1/2
Final answer:
Clara needs to run 22 laps around the track, at 0.25 miles per lap, to reach her goal of 5 1/2 miles.
Explanation:
The question is about calculating the number of laps Clara needs to run to cover a distance of 5 1/2 miles, with each lap being 0.25 miles long. To find the number of laps, we divide the total distance she wants to run by the distance of one lap.
Total distance Clara wants to run: 5 1/2 miles or 5.5 miles (converting 1/2 into decimal for easier calculation).
Distance of one lap around the track: 0.25 miles.
To find the number of laps, we perform the division:
5.5 miles ÷ 0.25 miles/lap = 22 laps.
Therefore, Clara needs to run 22 laps around the track to complete her goal of 5 1/2 miles.
what is and why 41/2+31/4=
41 divided by 2 plus 31 divided by 4 equals to 28.225
In order to add these fractions, you must make sure that the denominators are the same. Since one of the denom. is 4 and the other is 2, we can just multiply the fraction of 41/2 by 2. Remember to multiply top and bottom.
41/2 * 2/2 = 82/4 Now that the denom. are 4 you may now add the numerators.
82/4 + 31/4 = 113/4 if you are asked to give it as a mixed fraction then it will be 28 1/4
hope this helps