The 40kg driver should be able to sit on the 12m driving platform to have equal potential energy.
What is potential energy?Potential energy is the energy held by an object as a result of its position relative to other objects, internal stresses, electric charge, or other factors.The gravitational potential energy of an object, which depends on its mass and distance from the center of mass of another object, the elastic potential energy of an extended spring, and the electric potential energy of an electric charge in an electric field are all examples of common types of potential energy. The joule, denoted by the symbol J, is the unit of energy in the International System of Units (SI).The formula of the potential energy of each driver:
Driver 1: PE = gmh = 9.8 · 80 · 6Driver 2: PE = gmh = 9.8 · 40 · hReplace the value of PE for driver 1 with the driver 2 formula.
9.8 · 80 · 6 = 9.8 · 40 · hNow, solve for (h) height:
9.8 · 80 · 6/9.8 · 40 ⇒ h - 12Therefore, the 40kg driver should be able to sit on the 12m driving platform to have equal potential energy.
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Seven-tenths of half a century is please help me
The meaning and equivalent of the word phrase; seven-tenths of half a century as given in the task content is; 35 years.
What is the meaning and equivalent the word phrase; seven-tenths of half a century as given in the task content?According to the task content, it follows that the meaning and equivalent of seven-tenths of half of a century is to be determined.
On this note, since it follows from place value that seven-tenths means; 7 × (1/10) = 7/10.
Also, since half a century means; (1/2) × 100 years = 50 years.
Ultimately, the word phrase given in the task content is equivalent to;
= (7/10) × 50 years.
= 35 years.
Ultimately, the meaning and equivalent of the word phrase; seven-tenths of half a century as given in the task content is; 35 years.
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How can representing sentences and phrases with symbols help you determine whether to apply the Law of Detachment or the Law of Syllogism
In the Law of Syllogism , Long sentences and phrases can occasionally be perplexing and written imprecisely at first glance.
What is the purpose of a syllogism?
The most typical format for organizing premises into a strong argument is a syllogism. In a syllogism, the conclusion derives from the truth of two or more premises, which is a type of deductive reasoning.Long sentences and phrases can occasionally be perplexing and written imprecisely at first glance.
Therefore, using symbols to denote various statements is quite helpful.
because the number of various statements we have and the relationship between them will then be much more obvious.
To put it another way, it would be simpler to decide which logical law to apply to a certain issue.
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Solve each equation.
2 e x-2=e x+7
After solving the given equation [tex]2 e^{x-2}=e^x+7[/tex], the value of [tex]x=\ln 7-\ln \left(2 e^{-2}-1\right)[/tex].
What is an equation, exactly?A mathematical statement made up of two expressions joined by an equal sign is known as an equation.3x - 5 = 16 is an example of an equation.We get the value of the variable x as x = 7 after solving this equation.So,
Given equation: [tex]2 e^{x-2}=e^x+7[/tex]
Then,
[tex]2 e^{x-2}=e^x+7\\2 \frac{e^x}{e^2}=e^x+7\\2 \frac{e^x}{e^2}-e^x=7\\e^x\left(2 e^{-2}-1\right)=7\\e^x=\frac{7}{\left(2 e^{-2}-1\right)}\\x=\ln \left(\frac{7}{\left(2 e^{-2}-1\right)}\right)\\x=\ln 7-\ln \left(2 e^{-2}-1\right)[/tex]
Therefore, after solving the given equation [tex]2 e^{x-2}=e^x+7[/tex], the value of [tex]x=\ln 7-\ln \left(2 e^{-2}-1\right)[/tex].
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Simplify each number. 25³/₂
Factorization of 25 yields 5×5. In index form, this is written as 5^2. Use the power rule (a^m)^n = a^mn
25=5^2
25^(3/2) = (5^2)^(3/2)
5^(2x3/2)= 5^3
5x5x5 = 125
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A square ABCD (shown below) is rotated 90° clockwise of the origin match the corresponding coordinates after rotation
The square is rotated 90° clockwise about the origin to new points A'(2, 2), B'(4, 2), C'(4, 4) and D'(2, 4)
What is transformation?Transformation is the movement of a point around the coordinate plane. Types of transformations are rotation, translation, reflection and dilation.
Rotation is the flipping of a figure about a fixed point.
Square ABCD have vertices at A(-2, 2), B(-2, 4), C(-4, 4) and D(-4, 2). The square is rotated 90° clockwise about the origin to new points A'(2, 2), B'(4, 2), C'(4, 4) and D'(2, 4)
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How do you write 4/25 as a percentage?
Answer: 16% :)
Step-by-step explanation: 25x4=100, and 4x4=16. so 16/100, which equals 16%
Answer:
[tex] \sf {\large{16 \: \%}}[/tex]
Step-by-step explanation:
We know that
4/25 is the same as 4÷25
Then using
Long Division for 4 divided by 25 gives us
0.16
Converting our number to a percentage:
0.16×100
=16%
In the morning, the temperature was 15°F. During the day, the temperature decreased 39°F. Which expression can be used to find the temperature at the end of the day?
Responses
The expression to find the temperature at the end of the day is Morning temperature + (Change in temperature) and we get the temperature as -24 degree Fahrenheit.
Given,
The Morning temperature = 15°F
Change in temperature during day time = fall by 39 degree Fahrenheit
The temperature of the end of the day:
Morning temperature + (change in temperature)
Fall by 39° = decrease in temperature by 39° = - 39°
Therefore,
Substitute the values in the expression:
That is,
15°F + (-39°F)
15°F - 39°F
= - 24°F
Therefore, the expression to find the temperature at the end of the day is Morning temperature + (Change in temperature) and we get the temperature as -24 degree Fahrenheit.
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For each function, find the inverse and the domain and range of the function and its inverse. Determine whether the inverse is a function. f(x)=√x+2
The inverse function of f(x) = √x + 2 would be f⁻¹(x) = x² - 2.
The domain of the function would be {x ∈ R, x ≥ −2}.
The range would be {y ∈ R, y ≥ 0}.
What is the inverse formula?The inverse function returns the original value for which the output of a function was given. When it comes to functions, f and g are inverse, with f(g(x)) = g(f(x)) = x. A function that is made up of its inverse returns the original value.
Considering f(x) = y, to find the inverse function, the x and y values are switched giving the new equation of
x = √y + 2
Simplifying the above equation, we get
x - 2 = √y
x² - 2 = y
x² - 2 = y is the inverse of the function f(x)=√x+2
The domain of the function would be all x, such that x + 2 ≥ 0, or x ≥ −2.
Hence it is {x∈R, x ≥ −2}
For range, consider y =√x + 2.
Since√x+2 ≥ 0, it is obvious that y ≥ 0.
The range would be {y ∈ R, y ≥ 0}
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Could someone please solve and explain this to me?
2ab^-2 • (b^2)^-2
(*if a number has ‘^’ before it, that means it’s an exponent).
Answer:
[tex]2ab^{(-6)}[/tex]
Step-by-step explanation:
Multiply exponents/group exponents
[tex]2ab^{(-2)} \times b^{(-4)}\\2ab^{-2 + -4}\\2ab^{-6}[/tex]
Sep 26, 8:04:36 AM
Watch help vide
For a given recipe, 24 cups of flour are mixed with 16 cups of sugar. How
many cups of flour should be used if 14 cups of sugar are used?
Assuming a constant ratio, fill out the table
A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. If For a given recipe, 24 cups of flour are mixed with 16 cups of sugar. then 21 cups of flour should be used if 14 cups of sugar are used.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
24 cups of flour are mixed with 16 cups of sugar.24:16
x cups of flour should be used if 14 cups of sugar .x:14
Now
24/16=x/14
Cross multiply
24*14=16x
336=16x
x=21.
Therefore 21 cups of flour should be used if 14 cups of sugar are used.
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Mathematical equation -
What is -3 x 5/9?
Answer:
=-1.66
Step-by-step explanation:
A triangle has two sides of lengths 4 and 7. What value could the length of the third side be? Check all that apply
A.7
B.17
C.11
D.5
E.9
F.3
Answer: E
Step-by-step explanation:
4 x 4 = 16
7 x 7 = 49
16 + 49 = 65
8.062 is the square root of 65.
Round 8.062 I guess you could round it to 9 but I believe the actual answer should be 8.
The larger of two numbers is three times the smaller. If ten is subtracted from the larger number then the result is eight more than the smaller number. What are the numbers?
The numbers are 8 and 24.
How to calculate the value?Let the smaller number be x.
Larger number = 3x
Therefore, the expression will be:
3x - 10 = x + 8
Collect like terms
3x - x = 8 + 10
2x = 18
Divide
x = 18/2
x = 9
The bigger number will be:
3x = 3 × 8 = 24
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i need help, i cant understand the steps to get it to where it needs to be.
The transformations that take rectangle ABCD to rectangle A'B'C'D' are given as follows:
Rotation of 90º over vertex B.Translation right.What are transformations on the graph of a function?Transformations in the graph of a function involve operations such as multiplication/division or sum/subtraction, either in the domain of the function, involving values of x, or the range, involving values of y.
Examples of transformations are as follows:
Translation: Translation left/right or down/up.Reflections: Over one of the axes or over a line.Rotations: Over a degree measure.Dilation: Coordinates of the vertices of the original figure are multiplied by the scale factor.For this problem, we have that:
Due to the orientation change, the figure was first rotated 90º over vertex B.Due to the position change, the function was translated right.More can be learned about transformations in a function at https://brainly.com/question/28687396
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Find the perimeter when 121 triangles are put together in the pattern shown below. Assume that all triangle sides are 1 cm long.
Applying the arithmetic sequence formula, the perimeter of the triangle is: 123 cm.
How to Apply the Arithmetic Sequence?An arithmetic sequence formula is given as, T(n) = a + (n - 1)d, where a is the first term; n is the nth number of terms; d is the common difference.
Applying the arithmetic sequence formula to this problem, we have the following:
n = 121
a = 3
d = 1
Substitute
T(121) = 3 + (121 - 1)1
T(121) = 3 + (120)1
T(121) = 3 + 120
T(121) = 123
Therefore, applying the arithmetic sequence formula, the perimeter of the triangle is: 123 cm.
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someone explain it step
The formula given in the question is Doughnuts are T=4 B+ 10C.
What is algebra?A part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.
Given:
The given question is Doughnuts are sold in bags and cartoons.
It contains 4 bags of Doughnuts and cartoon hold 10 Doughnuts.
According to given question we have
Let the total Doughnuts be T.
Let the bags of Doughnuts be B
Let the carton of Doughnuts be C.
1 bags of Doughnuts = B
4 bags of Doughnuts =4 B
1 carton of Doughnuts = C.
10 carton of Doughnuts = 10C.
To write the formula we gave,
T=4 B+ 10C.
Therefore, the formula given in the question is Doughnuts are T=4 B+ 10C.
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If x= 5 and y = 2 work out the value of 2x2
The value of the expression 2x^2 where x = 5 and y = 2 is 8
How to work out the value of the expression 2x^2?The expression is given as
2x^2
From the question, we have the values of the x and y to be
x = 5 and y = 2
Substitute x = 5 and y = 2 in the expression 2x^2
So, we have
2x^2 = 2 x 2^2
Evaluate the exponent
So, we have
2x^2 = 2 x 4
Evaluate the product
So, we have
2x^2 = 8
Hence, the value of the expression 2x^2 where x = 5 and y = 2 is 8
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A family spends 3/7 of their monthly income
on food,5/14
on clothing and 1/5
on rent.
What fraction of the family's income is
spent on other things? If in a particular
month, the family spends GH&2,400 on
other things, how much did the family
spend on clothing? What was the family's
income for the month.
They spent 1/70 of their monthly income on other things.
The family spent GH¢60,000 on clothing.
The monthly income of the family is GH¢168,000.
What is Fraction?
The number is expressed as a quotient in which the numerator is divided by the denominator is called fraction.
Since, The family spend;
On food = (3/7)*x
On clothing = (5/14)*x
On rent = (1/5)*x
Let the family's monthly income = x
Now, To find the fraction of the family's income is spent on other things, we can assume that y is spent on other things, then we should have;
(3/7)*x + (5/14)*x + (1/5)*x + y*x = x
We can divide both sides by x, we get:
(3/7) + (5/14) + (1/5) + y = 1
Now, we can solve this for y as;
3/7 + 5/14 + 1/5 + y = 1
6/14 + 5/14 + 1/5 + y = 1
(6 + 5)/14 + 1/5 + y = 1
11/14 + 1/5 + y = 1
The smallest common factor of 14 and 5 = 14*5 = 70
So, we can multiply in the first fraction by 5/5 and the second by 14/14,
(5/5)*(11/14) + (14/14)*(1/5) + y = 1
55/70 + 14/70 + y = 1
69/70 + y = 1
y = 1 - 69/70
y = 1/70
Hence, They spent 1/70 of their monthly income on other things.
And, On a particular month, the family spends GH¢2,400 on other things, then if the monthly income is x, we have:
(1/70)*x = GH¢2,400
x = 70* GH¢2,400
x = GH¢168,000
So, The monthly income of the family is GH¢168,000
And, we know that they spend (5/14)*x on clothing,
Then this month they spent on clothing,
⇒ (5/14)*GH¢168,000 = GH¢60,000
So, They spent 1/70 of their monthly income on other things.
The family spent GH¢60,000 on clothing.
The monthly income of the family is GH¢168,000.
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HELP ASAP!!! WILL MARK BRAINLIEST!!!
Line j: y = 2/3x + 1/2
Line k: y = 1/2x + 2/3
Line l: y = 2/3x + 3/2
Line m: y = 3/2x + 1/2
These four lines have been graphed on the same coordinate grid. Which lines are parallel to each other?
A. k & m
B. k & l
C. j & l
D. j & m
Answer:
line J and line L are parallel so C.
The parallel line are j and l.
Hence the correct answer is c.
Given are four lines that have been graphed on the same coordinate grid.
We need to check which of these are parallel to each other.
To determine which lines are parallel to each other, we need to compare their slopes. Parallel lines have the same slope.
The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
Let's identify the slopes of the given lines:
Line j: y = (2/3)x + 1/2
Slope of j: 2/3
Line k: y = (1/2)x + 2/3
Slope of k: 1/2
Line l: y = (2/3)x + 3/2
Slope of l: 2/3
Line m: y = (3/2)x + 1/2
Slope of m: 3/2
Now, let's see which lines have the same slope:
A. k & m - The slopes are different (1/2 and 3/2). These lines are not parallel.
B. k & l - The slopes are different (1/2 and 2/3). These lines are not parallel.
C. j & l - The slopes are the same (2/3). These lines are parallel.
D. j & m - The slopes are different (2/3 and 3/2). These lines are not parallel.
So, the correct answer is:
C. j & l
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PLEASE HELP ME ASAP!!!!!
What is the first step in making a frequency chart?
A) Doesn't matter
B) Write down numbers
C) Draw a box
D) Figure out what you are comparing
Solve for X
-1/2+6/7 x+9.7
The equation solved for x gives -0. 61
What are algebraic expression?
Algebraic expressions are expressions that comprise variables, terms, factors, constants and coefficients.
They are also made up of certain arithmetic operations such as addition, subtraction, multiplication, division, bracket, parenthesis, etc.
Given the expression;
-1/2 + 6/7 = x + 9.7
Find the lowest common multiple
-7 + 12/14 = x + 9. 7
Add the numerators
5/ 14 = x + 9. 7
Find the quotient
0. 36 = x + 0. 97
collect like terms
x = 0. 36 - 0. 97
x = -0. 61
Thus, the equation solved for x gives -0. 61
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Solve 5x-12-6x=-10x+7-1 (please fill out each step)
Step 1. Collect like terms
Step 2.Move variables to one side of the equation (addition/subtraction property of equalities)
Step 3. Move constant to the other side of equation (Addition/subtraction property of equalities)
Step 4.(multiplication/division property of equalities)
The solution to given equation 5x - 12 - 6x = -10x + 7 - 1 is x = 2.
In this question,
we have been given an equation 5x - 12 - 6x = -10x + 7 - 1
We need to solve above equation using given steps.
5x - 12 - 6x = -10x + 7 - 1 .................(Given equation)
Step 1. Collect like terms
⇒ (5x - 6x) - 12 = -10x + (7 - 1)
⇒ -x - 12 = -10x + 6
Step 2.Move variables to one side of the equation (addition/subtraction property of equalities)
⇒ -x + 10x -12 = 6
Step 3. Move constant to the other side of equation (Addition/subtraction property of equalities)
⇒ 9x = 6 + 12
⇒ 9x = 18
Step 4.(multiplication/division property of equalities)
⇒ x = 18 ÷ 9
⇒ x = 2
Therefore, the solution to given equation 5x - 12 - 6x = -10x + 7 - 1 is x = 2.
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Jeremy has volleyball practice every third day in soccer practice every 5th day today he had both practices and how many days will he have both practices on the same day again
Answer:
He will have it on the 15th day
Write an inequality that represents the situation using the variable x. then write the inequality in interval notation. an essay contest requires that entries be within 50 words of 1000 words long. inequality: ___ the interval notation is: ___
An inequality that represents the situation is 50 ≤ x ≤ 1000
And the inequality in interval notation is [50, 1000]
In this question, we have been given a situation - an essay contest requires that entries be within 50 words of 1000 words long.
We need to write an inequality that represents the situation using the variable x.
Also, we need to write the inequality in interval notation.
Let x represents the number of words.
An essay contest requires that entries be within 50 words of 1000 words long.
So, we get an inequality,
50 ≤ x ≤ 1000
and the corresponding interval notation for above inequality would be,
[50, 1000]
Therefore, an inequality that represents the situation is 50 ≤ x ≤ 1000
And the inequality in interval notation is [50, 1000]
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What is 25.9 rounded to the nearest whole number?
Answer:
26
Step-by-step explanation:
Answer: 26
Step-by-step explanation: When rounding you have to look and see if your number is above or below 5. Let's take your number for example.
25.9
Focus on the decimal point. If you notice, the number after the decimal point is above 5, therefore you should round it off to 26.
Hope it helps ^^
The following list has a mean of 24.
What would be the new mean if 17 was
added to the list?
12, 30, 19, 27, 21, 35
The mean would be 23.
GIven that
list of observations is: (12, 30, 19, 27, 21, 35)
Number of observations = 6
What is a mean?
The mean is the average or the most common value in a collection of numbers.
Mean = Sum of the numbers / Total no. of observation
Mean = (12+ 30+ 19+27+ 21+ 35)/6
Mean = 144 / 6
Mean =24
If 17 was added to the list the number of observations = 7
new obersation list = (12, 30, 19, 27, 21, 35 , 17)
Sum of the new observation = 161
mean = 161 /7
mean = 23
Hence, the mean would be 23 if 17 were added to the given list.
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Write each expression in simplest form. (x²/₃ )⁻³
The give expression can be written in the simplest form by solving the exponents.
The rules applicable to the expression are rule for negative exponent and power rule of exponents. Either one can be used first. In this case we will multiply the exponents and then solve for the negative exponent.
According to the power rule of exponents, when an exponential expression is raised to a new power, the exponents are multiplied i.e. (a^x)^y=a^xy
(x^2/3)^-3=x^(2/3)*-3=x^-2
According to the rule of negative exponents, the term with the negative exponent can be solved by expressing it as a reciprocal of the term i.e. a^-x=1/a^x
x^-2=1/x^2
The simplest form of the expression (x^2/3)^-3 is 1/x^2.
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What is the greatest common factor of 24 and 4?
Answer: 2
UvU This might help might not
20 customers are eating dinner at a local restaurant. The restaurant accepts cash or credit as forms of payment. Of the 20 customers, 4 have enough cash to pay for their meal, 16 have a credit card, and 3 have enough cash and a credit card. Using this information, answer the following questions. 1. What is P(A), the probability that a customer has enough cash? 2. What is A(B), the probability that a customer has a credit card? 3. What is P(A and B), the probability that a customer has enough cash and a credit card? 4. What is P(A or B), the probability that a customer has enough cash or a credit card?
P(A) = 4 / 20, this is the probability that a customer has enough cash
P (B) =16 / 20, this is the probability that a customer has a credit card.
P (A and B) = 3 / 20, this is the probability that a customer has enough cash and a credit card.
The probability that a customer has enough cash or a credit card is 0.85.
Probability is defined as the ratio of favorable outcomes to a total number of outcomes.
It is given that, 20 customers are eating dinner at a local restaurant.
The total number of customers = 20
Of the 20 customers,
4 have enough cash to pay for their meal
16 have a credit card and
3 have enough cash and a credit card.
Event A is the probability that a customer has enough cash
Event B is the probability that a customer has a credit card.
P(A) = 4 / 20 = 1 / 5, this is the probability that a customer has enough cash
P (B) =16 / 20 = 4 / 5, this is the probability that a customer has a credit card.
P (A and B) = 3 / 20, this is the probability that a customer has enough cash and a credit card.
To find the probability that a customer has enough cash or a credit card :
The formula used is P(A or B) = P(A) + P(B) - P(A∪B)
P (A or B) = P(A) + P(B) - P (A and B)
= 4 / 20 + 16 /20 - 3 / 20
= 17 / 20
= 0.85
Therefore, The probability that a customer has enough cash or a credit card is 0.85.
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(1/5) to the power of 2 X (1/5) to the power of 2
Answer: 0.0016
Step by step explanation:
Answer:
=1/5⁴ = 1/625
Step-by-step explanation:
(1/5)² (1/5)² = (1/5)⁴
= 1⁴ / 5⁴
= 1 / 625