Based on the equation for gravitational force, the value of radius (r) is equal to r = √(GM₁M₂/F).
What is a gravitational force?A gravitational force can be defined as a universal force of attraction which acts between two (2) physical objects, especially by pulling them together.
How to calculate the gravitational force?Mathematically, the gravitational force between two (2) planetary objects is given by this formula:
F = GM₁M₂/r²
Where:
r represents the radius or mean distance.G represents the gravitational constant.M represents the mass.F represents the gravitational force.Making r the subject of formula, we have:
Fr² = GM₁M₂
Divide both sides by F, we have:
r² = GM₁M₂/F
Taking the square root of both sides, we have:
r = √(GM₁M₂/F)
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I need help!
Estimate the instantaneous rate of change of the function f(x)=−4x2−3x+1 at x=−3 using the average rate of change over successively smaller intervals.
The instantaneous rate of change of the function f(x) = −4x² − 3x + 1 at the point x = -3 is 21.
What is the instantaneous rate of change of the function at the given point?The instantaneous rate of change is simply the change in the derivative value at a specific point.
Given the data in the question;
f(x) = −4x² − 3x + 1Point x = -3To determine the instantaneous rate of change of the function, first find the derivative of the function.
f(x) = −4x² − 3x + 1
Applying sum rule, with respect to x
d/dx[ -4x² ] + d/dx[ -3x ] + d/dx[ 1 ]
[ 2 × -4x¹ ] + [ 1 × -3x⁰ ] + d/dx[ 1 ]
[ -8x ] + [ -3 ] + d/dx[ 1 ]
-8x - 3 + d/dx[ 1 ]
Differentiate using constant rule
-8x - 3 + [ 0 ]
-8x - 3
f'(x) = -8x - 3
Next, plug x = -3 into the derivative and simplify.
f'(x) = -8x - 3
f'(-3) = -8(-3) - 3
f'(-3) = 24 - 3
f'(-3) = 21
Therefore, the instantaneous rate of change of the function f(x) = −4x² − 3x + 1 at the point x = -3 is 21.
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The lengths of pregnancies in a small rural village are normally distributed with a mean of 260 days and a standard deviation of 17 days. What percentage of pregnancies last beyond 221 days?
Answer:
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PLS PLS PLS PLS PLS PLS PLS PLS LAST QUESTION JUST HELP ME PLS I BEG U describe a real-world situation where you can apply finding the unit rate
the growth of a plant or the amount of money you'll have off a banks interest overtime
CAN YOU PLEASE HELP ME ON #18 PLEASE!!
Answer:
x=90, y= 130
Step-by-step explanation:
Given the function f(x) = 4x − 1 and the linear function g(x), which function has a greater slope?
f(x) has a greater slope.
g(x) has a greater slope.
The slopes of f(x) and g(x) are the same.
The slope of g(x) is undefined.
After the solution, we can conclude that (A) the slope of f(x) is higher.
What is the slope?A line's steepness can be determined by looking at its slope. The slope is calculated mathematically as "rise over run" (change in y divided by change in x). The letter M stands for the slope of a function of the form y=Mx+C, so the slope of the function F(x) =4.Now that you have a function but can only evaluate it using a table, you can determine the slope using the following formula:
[tex]m=\frac{y^2-y^1}{x^2-x^1}[/tex]
Simply choose two points from the table to enter into the formula; in this example, we'll use points (4, 7) as our points 1 and our second point is (6,9).
This implies:
x¹ = 4y¹ = 7x² = 6y² = 9You just need to enter it into the formula:
m = 9-7/6-4m = 2/2m = 1Now that we know both slopes, you can see that g(x) has a slope of 1, while f(x) has a slope of 4, indicating that f(x) has a steeper slope than g(x).
Therefore, (A) f(x) has a greater slope.
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The complete question is given below:
Given the function f(x) = 4x + 10 and g(x), which function has a greater slope?
x g(x)
2 5
4 7
6 9
f(x) has a greater slope.
g(x) has a greater slope.
The slopes of f(x) and g(x) are the same.
The slope of g(x) is undefined.
Answer:
After the solution, we can conclude that (A) the slope of f(x) is higher.
Step-by-step explanation:
What is the slope?
A line's steepness can be determined by looking at its slope.
The slope is calculated mathematically as "rise over run" (change in y divided by change in x).
The letter M stands for the slope of a function of the form y=Mx+C, so the slope of the function F(x) =4.
Now that you have a function but can only evaluate it using a table, you can determine the slope using the following formula:
Simply choose two points from the table to enter into the formula; in this example, we'll use points (4, 7) as our points 1 and our second point is (6,9).
This implies:
x¹ = 4y¹ = 7
x² = 6y² = 9
You just need to enter it into the formula:
m = 9-7/6-4
m = 2/2
m = 1
Now that we know both slopes, you can see that g(x) has a slope of 1, while f(x) has a slope of 4, indicating that f(x) has a steeper slope than g(x).
Therefore, (A) f(x) has a greater slope.
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The complete question is given below:
Given the function f(x) = 4x + 10 and g(x), which function has a greater slope?
x g(x)
2 5
4 7
6 9
f(x) has a greater slope.
g(x) has a greater slope.
The slopes of f(x) and g(x) are the same.
The slope of g(x) is undefined.
6.) Write another expression that is equivalent to 6.4 ÷ 0.08.
What company has the absolute advantage when it comes to producing phones?
a. Gonzalez and Bros. Inc
b. The G company Inc
c. they both do
d. neither
(Option a) Gonzalez and Bros . Inc has the absolute advantage when it comes to producing phones.
Absolute advantage theory
In his book The Wealth of Nations, the 18th-century economist Adam Smith proposed the concept of absolute advantage to describe how countries could benefit from trade by specializing in producing and exporting the goods that they can make more successfully than other countries.
On the other hand, China, Thailand, and Vietnam create and export low-cost manufactured goods. These three countries benefit greatly from their much lower unit labor costs.
Here, option a Gonzales and Bros. Inc has the absolute advantage when it comes to producing phones.
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-4(2w+7) simply with distributive property
Answer:
[tex]{ \tt{ - 4(2w + 7)}} \\ = { \tt{( - 4 \times 2w) + ( - 4 \times 7)}} \\ = { \tt{ - 8w - 28}}[/tex]
Is 0.6294 terminating or repeating
Answer:
This is terminating. As a fraction it would be: [tex]\frac{6294}{10000}[/tex] not simplified
Step-by-step explanation:
If it was repeating you would see a repeat bar over part of the number. Or 3 .... showing that the number goes on.
Working alone, Rob can mop a warehouse
in six hours. Molly can mop the same
warehouse in nine hours. How long would
it take them if they worked together?l
It will take Molly and Rob 54/15 hours to mop the warehouse.
What is defined as the concept of work and time?Work is described as anything that has an impact or has an outcome. When it is stated somebody has done a certain work, it means that he or she has completed all of the work. As a result, if Manu accomplishes his work in 5 days, he will complete 100% of the work in 5 days.As a result, we could indeed say that he completes 20% of a work in one day. Similarly, he completes 40% of a work in two days and 60% of a work in three days.For the given question;
Rob takes 6 hours for cleaning the ware house.
Let 'R' be the work done by rob.
Then, work done by Rob in 6 hours is 1/R = 1/6.
Similarly;
Let work by Molly is 'R'.
The, work done by Molly in 1 hour is 1/M = 1/9.
The total work done by both is 1 hour is;
1/R + 1/M = 1/6 + 1/9
Om simplification;
1/R + 1/M = 15/54.
Thus, the total time taken by doing the work is; 54/15 hours.
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A city has 27 fewer wooden park benches
than metal park benches. There are 24 wooden benches.
How many metal benches are there?
There are 51 metal benches in the park
According to the question we have been given that
Number of wooden benches = 24
We have to calculate number of metal benches.
Let the number metal benches be x.
The according to the question
W = x - 27 where, W = wooden benches
Here , W = 24
Putting the required in the above equation for x we get
24 = x - 27
x = 24 + 27
x = 51
Hence the number of metal benches = 51 and we can see that 27 less of metal benches is 24 which is the number of wooden benches.
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Among fatal plane crashes that occurred during the past 65 years, 260 were due to pilot error, 62 were due to other human error, 315
were due to weather, 682 were due to mechanical problems, and 313 were due to sabotage.
Fill in the relative frequency for each category. Write answers in percentage form and round to one decimal place as needed. Do not include the percent symbol.
Answer: Pilot Error: 15.9%
Human Error: 3.8%
Weather: 19.3%
Mechanical Problems: 41.8%
Sabotage: 19.2%
Step-by-step explanation:
260+62+315+682+313=
322+997+313=
1319+313=1632 total crashes
Pilot error: 260/1632=
0.159=
0.159*1=
0.159*100%=15.9%
Human error: 62/1632=
0.03799=
0.038=
0.038*100%=3.8%
Weather: 315/1632=
0.193=
0.193*100%=19.3%
Mechanical Problems: 682/1632=
0.41789=
0.418=41.8%
Sabotage: 313/1632=
0.191789=
0.192=19.2%
Help am i correct? I need help please give explanation
====================================================
Reason:
Focus on the numerator for now. The [tex](11^8)^2[/tex] is the same as [tex]11^{16}[/tex] because we multiply the exponents. The general rule is [tex](a^b)^c = a^{bc}[/tex]
Alternatively we can think of it like this
[tex](11^8)^2 = (11^8)(11^8) = 11^{8+8} = 11^{16}[/tex]
So far we have [tex]\frac{(11^8)^2}{11^3} = \frac{11^{16}}{11^3}[/tex]
------------
The last step is to subtract exponents due to the rule [tex]\frac{a^b}{a^c} = a^{b-c}[/tex] and the order of subtraction is important.
Therefore, [tex]\frac{(11^8)^2}{11^3} = \frac{11^{16}}{11^3} = 11^{16-3} = 11^{13}[/tex]
Two students start a club the first week of school. Each member invites three new members the second week of school. Each of these new members then invites three additional members the following week. If the pattern of each new member inviting three new members each week continues, how many members will be in the club after five weeks?
80 students
121 students
242 students
363 students
In linear equation ,242 total number of members within 5 weeks.
What is linear equation ?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."a manual computation on how 1 member recruits his members until week 5. Then multiply the sum by 2.
old new
1: 1
2: 1 x 3 = 3 ⇒ 1 3 *only new members recruit 3 more
3: 3 x 3 = 9 ⇒ 4 9
4: 9 x 3 = 27⇒ 13 27
5: 27 x 3 = 81 ⇒ 40 81
40 + 81 = 121. Total number of members under 1 founding member.
121 x 2 founding members = 242 total number of members within 5 weeks.
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Answer: Option C
Step-by-step explanation:
Alex is thinking of a number that is multiplied by 7 and the added with 27. The result is
equal to 111.
44) What is the equation that you can write to solve for the number if the unknown
number is x.c
The equation that can be used to solve for the unknown number that Alex is thinking is 7x + 27 = 111
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the unknown number. The number is multiplied by 7 and the added with 27. The result is equal to 111. Hence:
7x + 27 = 111
The equation that can be used to solve for the unknown number that Alex is thinking is 7x + 27 = 111
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which equation show the relationship between x,the number of minutes ,and y ,the price
Answer:
ummm idek
Step-by-step explanation:
Is y=10•0.93^x exponential decay, exponential growth or neither
Answer: Exponential decay
Explanation: The base of the actual exponential function, [tex]0.93^{x}[/tex], is less than 1, which means that the output will become smaller.
Two trains leave the same station at the same time but are headed in opposite directions. One train travels at 80 mph and the other train travels at 65 mph. How much time passes until the trains are 580 miles apart?
__Hours.
38.7 hours would have passed until the trains are 580 miles apart
How much time passes until the trains are 580 miles apart?The given parameters are
Train 1 = 80 mph
Train 2 = 65 mph
The difference in the speeds of the trains is
d = 80mph - 65mph
Evaluate
d = 15mph
The distance moved is
Distance = 15 * t
At 580 miles apart, we have
15 * t = 580
Divide by 15
t = 38.7 hours
Hence, 38.7 hours would have passed until the trains are 580 miles apart
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Y=(X-3)^2 from the parent function y=x^2
The parent function will shift the right side by 3 units after applying the transformation x → (x - 3).
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that:
The parent function is:
y = x²
After applying the transformation:
x → (x - 3)
The function will shift the right side by 3 units.
The equation of the function will be:
y = (x - 3)²
Thus, the parent function will shift the right side by 3 units after applying the transformation x → (x - 3).
The complete question is:
Describe the Transformation y=(x - 3)² if the parent function is y = x²
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Test scores for a class of 7 students are: 89, 72, 96, 87, 64, 93, 80 What is the mean test score? What is the median test score? What is the mode of this data set? Find the standard deviation of this data set using the table method that is in the Course Notes, please show your work. You can think of the class of 7 students as a population.
For the given set of data, the value of mean is 83, median is 87 and standard deviation is 11.03
What is standard deviation?Standard deviation is a measurement of how evenly distributed a set of numbers is. Since the variance is the average of the squared deviations from the mean, it is the square root of the variance.
The mean score is - Sum of all scores / total number of scores
= 89 + 72 + 96 + 87 + 64 + 93 + 80 / 7
= 83
So the mean of given scores is 83
Median = central term
= 64, 72, 80, 87, 89, 93, 96
Median = 87
Mode of the data is - no mode as there are no recurring terms given
Standard deviation -
variance = (89 - 83)² +(72 - 83)² + (96 - 83)² + (87 - 83)² + (64 - 83)² + (93 - 83)² + (80 - 83)² / 7
= 121.71
standard deviation = √variance
⇒ standard deviation = 11.03
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51 is 33 1/3 of what number
Step-by-step explanation:
33 1/3 = (3×33 + 1)/3 = 100/3
51 = 100/3 × x
153 = 100x
x = 153/100 = 1.53
1.53 × 33 1/3 = 51
so, "that" number is 1.53.
Jack works in a bookstore. He has 300 books to stock on the shelves. So far, he has stocked 120 books today. What percent of the books does he have left to stock?
A. 30%
B. 40%
C. 50%
D. 60%
Answer:Jack has 60% of the books left to stack.
Step-by-step explanation:
Answer:
Step-by-step explanation:
60% (300-120) 180/300*100=60. 60%
Students planted 360 tree saplings. which is 12% of the planned amount. How many seedlings are planned to be planted?
May I get help with my math?
Answer:
I don't know and your read in which class
In two or more complete sentences, explain how to use ordered pairs of points in f(x)=2x+5 and g(x)= x-5/2 to determine if f(x) and g(x) are inverses of each other.
The ordered pair given are not inverse to each other because:
Substituting a value say 5/2 into f(x)=2x+5 gives 10Substituting 10 into g(x)= x-5/2 does not return 5/2How to know inverse functionsWhen two functions are inverse to each other substituting a value A in function say AA will give answer say X, substituting the answer X to the the other function say BB returns the value A.
Instance
say function AA, plug in A gives X
the inverse will be:
say function BB plug in X gives A
So, we have f(x)=2x+5 and g(x)= x-5/2
plugging in say 5/2 in f(x) will give
f(x) = 2 * 5/2 + 5
f(x) = 5 + 5
f(x) = 10
We plug in 10 to g(x)= x-5/2
g(x) = 10 - 5/2
g(x)= 7/2
since 7/2 ≠ 5/2 the pair of functions are not inverse to each other
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Suppose in a class, 27 students got an A on the first exam and 15 students got an A on the third exam. Twelve students got an A on both the first and third exams. What is the conditional probabilty of getting an A on the third exam given that they got an A on the first exam, P(A third | A first)?
Given that:
In a class, 27 students got an A on the first exam.15 students got an A on the third exam.12 students got an A on both the first and third exams.To find:
What is the conditional probability of getting an A on the third exam given that they got an A on the first exam, P(A third | A first)?So, according the question,
Let's assume, total no. of students in class is x.
So, we know that
Conditional probability P( A IIIrd | A Ist ) = [tex]\frac{P(III^{rd} \cap I^{st}) }{P(I^{st})}[/tex]
From question,
P( A IIIrd ∩ A Ist) = 12/x. and
P(A Ist) = 27/12.
Now, putting the values
So, we will get
P( IIIrd | Ist ) = [tex]\frac{P(III^{rd} \cap I^{st}) }{P(I^{st})}[/tex]
P( IIIrd | Ist ) = [tex]{(\frac{12}{x})}\div {(\frac{27}{x} )}[/tex]
= [tex]\frac{12}{x} \times \frac{x}{27}[/tex]
= 12/27
= 4/9
Answer:
So, 4/9 is the Conditional probability of getting an A on the third exam given that they got an A on the first exam,To learn more about Conditional probability, please click on the link:
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Enter the sentence as an equation or inequality. Use x to represent any unknown number The sum of 2 and a number is 23.
The sentence can be written as:
x + 2 = 23
And the solution is x = 21.
How to write the sentence as an equation?Here we have the sentence:
" The sum of 2 and a number is 23."
Let's define x as the number, then we can write the equation:
x + 2 = 23
This is a simple linear equation, to solve this we need to subtract 2 in both sides of the equation, we will get:
x + 2 - 2 = 23 - 2
x = 21
We conclude that the number is 21.
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Which of the following is true of the composition G(F(y))?
The correct option is D.The function F(G(H(y))) depends on G(H(y)).
What is defined as the composite functions?The method by which two or even more functions into one function is identified as function composition.f(g(x)) or (f °g) represents this same composition of functions f(x) as well as g(x), where g(x) acts first (x). It integrates a number of functions to produce another. The output of one function inside the parenthesis is becoming the input of the other function in a function composition.For the given question-
A function is defined by its argument (values in parentheses after a function name). G(H(x)) is the argument of function F in F(G(H(x))).
F(G(H(x)) is dependent on G(H(x)).
Answers A and C make no statements about the particular composition. Answer option B depicts a composition (H(G(x)) that is unrelated to the argument of function F.
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The complete question is-
Which of the following is true of the composition F(G(HyX)))?
A. The function G(F(H(y))) depends on G(H(y)).
B. The function F(G(H(y))) depends on H(G(y)).
C. The function H(G(F(y))) depends on G(F(y)).
D.The function F(G(H(y))) depends on G(H(y)).
A shopper bought 15 apples and 5 oranges. Which statement describes the ratio of apples to oranges?
The statement which describes the ratio of apples to oranges is; Choice D; 3:1 because the shopper bought 3 apples for every orange.
What is the ratio of apples to oranges?It follows from the task content that the shopper in discuss bought; 15 apples and 5 oranges.
On this note, by dividing both numbers by their greatest common factor, it follows that the resulting ratio is;
(15/5) : (5/5)
= 3 : 1.
Hence, Choice D is correct; 3:1 because the shopper bought 3 apples for every orange.
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Which library has more volumes, Baton Rouge or El Paso? What number sentence shows the comparison? A. Baton Rouge; 1,232,185 < 1,277,003 B. El Paso; 1,232,185 > 1,277,003 C. Baton Rouge; 1,232,185 > 1,277,003 D. El Paso; 1,232,185 < 1,277,003
The library has more volumes in El Paso.
The number sentence that shows the comparison is 1,232,185 < 1,277,003
Hence, El Paso; 1,232,185 < 1,277,003. Option D
This is further explained below.
What is a library?Generally, A library is a collection of resources, such as books or other forms of media, that are made available for use rather than being kept only for the purpose of the show.
A library is a facility that makes resources available for physical or digital access, and it may exist either as a real place or as a virtual area, or both.
In conclusion, The library has more volumes in El Paso.
The number sentence that shows the comparison is 1,232,185 < 1,277,003
Hence, El Paso; 1,232,185 < 1,277,003.
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