The amount remaining out the money earned is $37.5
Sum of values and proportionGiven the following parameters
Amount earned by kevin = $80
If he spent $68/5 on shopping, $51/2 on food, and $22/5 for taxi, the total money spent is given as;
Total money spent = 51/2 + 68/5 + 22/5
Total money spent = 51/2 + 90/5
Total money spent = 25.5 + 18
Total money spent = 43.5
Amount remaining = 80. - 43.5
Amount remaining = 37.5
Hence the amount remaining out the money earned is $37.5
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Differentiation question, please explain :)
The Logistic Law of Population Growth, first proposed by Belgian mathematician
Pierre Verhulst in 1837, is given by [tex]\frac{dN}{dt}= kN-bN^2[/tex], where k and b are constants.
Show that the equation [tex]N= \frac{KN0}{nMN0+(k-bN0)e^{-kt} }[/tex] is a solution of this differential equation (N0 is a constant).
Answer:
dN)/(dt)=(rN(K-N))/K is the answer.
Step-by-step explanation:
The logistic equation (sometimes called the Verhulst model or logistic growth curve) is a model of population growth first published by Pierre Verhulst.
The continuous version of the logistic model is described by the differential equation is:
(dN)/(dt)=(rN(K-N))/K. (where r is the Malthusian parameter (rate of maximum population growth) and K is the so-called carrying capacity (i.e., the maximum sustainable population).
So, the correct option is ' (dN)/(dt)=(rN(K-N))/K'.
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How many different three-digit numbers can be written using digits from the set 2, 3, 4, 5, 6 without any repeating digits? A. 10 B. 120 C. 20 D. 60
The growth of the population over the years in a small town is represented by the
function: () = 3548 (0. 87)
Based on the given population function, the population of the town can be said to be increasing.
How do we know the population is increasing?The population of the town is increasing because the value of "b" is positive and greater than one.
"b" which in this case is 0.87, is the rate at which the population is growing overtime. If it is a positive figure, then the population is expanding.
The question is:
Is the town's population increasing or decreasing?
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the second statement is the blank of the first x ⇒ y ¬x = ¬y
The second statement is the inverse statement of the first conditional statement.
What is the second statement?If x and y are two propositions, then:
x ⇒ y
Is a conditional statement:
"If x, then y".
The other statement is:
¬x ⇒ ¬y
Where:
¬x means "not x"
So the statement is:
"If not x, then not y".
That would be the inverse statement of the given conditional statement.
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soybeans have a conversion factor of 36.744 (bu/t). how much do 45 bushels weight. Show your work pls
By using unit conversion and direct proportionality model, we find that 45 bushels of soybeans are equal to a weight of 1.225 tonnes.
How many tonnes are a given quantity of bushels?
In this question we have an application of direct proportionality model, whose form is shown below:
y = k · x (1)
Where:
x - Quantity of bushelsk - Conversion rate, in tonnes per bushel.y - Quantity of tonnesIf we know that x = 45 bu and k = 1/36.744, then the soybean quantity in tonnes is:
y = (1/36.744 t/bu) · (45 bu)
y = 1.225 t
By using unit conversion and direct proportionality model, we find that 45 bushels of soybeans are equal to a weight of 1.225 tonnes.
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A company has 12 000 employees. During the financial crisis in 2008, 2.5 % of them were retrenched
50.75 % of them had a pay cut and the rest were unaffected. Find the number of employees who
were unaffected by the financial crisis.
Answer:
5610
Step-by-step explanation:
unaffected people will be (100%-2.5\%-50.75%)=46.75% of 12000:
[tex]12000\cdot 46.75\%=12000\cdot \frac{46.75}{100} =120\cdot 46.75=5610[/tex]
a car travels 87 miles north and 114 miles west. what is the magnitude of the cars resultant vector
The magnitude of the resultant vector is 27 miles
How to determine the vector magnitudeResultant vector = Distance of A - Distance of B
This is so because of the opposite direction of the car's movement
A = 87 miles
B = 114 miles
Resultant vector = 114 - 87
Resultant vector = 27 miles
Thus, the magnitude of the resultant vector is 27 miles
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Y=
Help me please thank you
Answer:
-135689;456+((888888888
Can someone help me with these problems and can you number them
The correlation is a negative correlation, because weights and city MPG do not increase at the same time
The graph of the table of valuesTo graph of the table of values, we plot
The weights on the x-axisThe city MPG on the y-axisSee attachment for graph
Type of correlationThe correlation is a negative correlation, because weights and city MPG do not increase at the same time
The equation of the line of best fitTo do this, we make use of a graphing calculator.
From the graphing calculator, we have the following summary:
Sum of X = 463Sum of Y = 388Mean X = 28.9375Mean Y = 24.25Sum of squares (SSX) = 862.9375Sum of products (SP) = -857.75The line of best fit equation is
y = bx + a
Where
b = SP/SSX = -857.75/862.94 = -0.99
a = MY - bMX = 24.25 - (-0.99*28.94) = 53.0
So, we have:
y = -0.99x + 53
Hence, the equation of the line of best fit is y = -0.99x + 53
The weight for 30 MPGThis means that y = 30
So, we have:
-0.99x + 53 = 30
Subtract 53 from both sides
-0.99x = -23
Divide by -0.99
x =23
Hence, the predicted weight is 23 pounds
The city MPG for 1500 poundsThis means that x = 1500
So, we have:
y = -0.99 * 1500 + 53
Evaluate
y = -1432
Hence, the city MPG for 1500 pounds is -1432
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A cylinder has a cross-sectional area of 17m² and a length of 14 m what is the volume of the cylinder
Answer:
your answer please mark me as brainlist
Step-by-step explanation:
V
=
238
m³
4. 5. a) b) c) a) When the cost of 7kg of sugar is Rs 490, find the cost of 12 kg of sugar. If the cost of 5m of cloth is Rs 375, find the cost of 80m of cloth. If the cost of 70kg of rice is Rs 5600, find the cost of 1 quintal of rice. The cost of cloth com of 4 . 5 . a ) b ) c ) a ) When the cost of 7kg of sugar is Rs 490 , find the cost of 12 kg of sugar . If the cost of 5m of cloth is Rs 375 , find the cost of 80m of cloth . If the cost of 70kg of rice is Rs 5600 , find the cost of 1 quintal of rice . The cost of cloth com of
Answer:
B
Step-by-step explanation:
i took the test
Madeline uses a mirror on the ground to measure the height of her school building. She walks a distance of 9.5 m from the building, then place is a mirror flat on the ground. she then walks 2.75 more meters
The height of the building is 5.33m.
How to calculate the height?The question is to calculate the height of the building.
Based on the information given, the height will be:
Madeline eye height/Distance from X = Height of building/Building distance from X
1.55/2.75 = x/9.45
x = (1.55 × 9.45)/2.75
x = 5.33 m
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How does this graph change between point D and point G?
A graph increases from point D to point G, and then decreases.
The graph increases.
The graph decreases.
The graph increases, then decreases.
The graph remains constant.
Answer:
The graph increases.
Step-by-step explanation:
hope this helps!!
Answer: the graph increases
Step-by-step explanation: did test
Lacey has $36 to spend. She buys a pair of sunglasses for $14.89 and a hat for $9.33. Lacey buys a scarf with the remaining money. How much does Lacey spend buying a scarf?
Answer:
$11.78
Step-by-step explanation:
14.89+9.33=24.22
36-24.22=11.78
[tex]if a= \sqrt{3}+5/\sqrt{3}-5 and b= \sqrt{3}-5/\sqrt{3}+5 then find a^2 - b ^2[/tex]
The result of the evaluation as demanded in the task content is; -40 - 80√3.
What is the value of a²-b²?The expression; a² - b² can be evaluated by means of difference of two squares as follows;
a² - b² = (a+b)(a-b)
Therefore, we have;
= ((√3 +5√3 -5) + (√3 -5√3 -5)) ((√3 +5√3 -5) - (√3 -5√3 -5))
= (2√3 -10)(10√3 +10)
= 60 - 80√3 -100
= -40 - 80√3.
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By what factor should -1 - 4i/ 2 + 9i be multiplied to find the quotient? Enter any complex numbers in the form a + bi
The factor by which the complex rational number be multiplied is; 2 -9i.
What value should be used to multiply to find the quotient?The expression given in the task is a fraction made up of complex numbers.
Hence in a bid to evaluate the quotient of the expression; -1 - 4i/ 2 + 9i.
The numerator and denominator must be multiplied by the conjugate of the denominator which in this case is; 2 -9i.
This is to help reduce the denominator to a real number.
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Which of the following equations have no solutions? Choose all answers that apply: (Choice A) 40x+40=40x+20 (Choice B) 20x+40=40x+20 (Choice C) -20x+40=-20x+20 (Choice D) −40x+40=20x+20
The answer choice in which case the equation has no solution are; Choice A ; 40x+40=40x+20 and Choice C; -20x+40=-20x+20.
Which of the following equations have no solutions?A system of linear equations is determined to have no solutions when the variable coefficients diminish upon evaluation and hence, the value of the variable can not be determined.
Hence, Choices A and C; in which case; the coefficients of variable X amount to 0 upon evaluation are equations with no solution.
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. Expand: 31og2 (9n)
By definition of logarithm the value of [tex]$3log _2(9n)[/tex] exists
[tex]$ 6(log _2(3) +3 log _2(n))[/tex].
What is a logarithm?A logarithm exists as an amount that conveys power to a specified number contains to be raised to create the assigned number.
From the definition of a logarithm, we get
aˣ = b exists the same as x = logₐb
Given: [tex]$3log _2(9n)[/tex]
Simplifying [tex]$log _2(9n) = 2log _2(3) + log _2(n)[/tex]
[tex]$= 3(2log _2(3) + log _2(n))[/tex]
Expanding the equation, we get
[tex]$3(2log _2(3) + log _2(n))[/tex]
[tex]$= 6(log _2(3) +3 log _2(n))[/tex]
[tex]$= 6(log _2(3) +3 log _2(n))[/tex]
Therefore, the value of [tex]$3log _2(9n)[/tex] exists [tex]$ 6(log _2(3) +3 log _2(n))[/tex].
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A pyramid has 24 edges and 13 faces, find the number of vertices in the figure -geometry
Answer: 13 vertices
Step-by-step explanation:
We can use the following formula to find the number of vertices in the figure. V is the number of vertices, F is the number of faces, and E is the number of edges.
V = 2 - F + E
V = 2 - (13) + (24)
V = 13
How many solutions are there to the equation below?
√x = -7
Answer:
There are no solutions.
Step-by-step explanation:
Hope this helped! :D
Given: p: x is prime. q: x is even. What is the truth value of p^q when x is replaced by 2?
Truth Value for p^ q when x is replaced by 2 is also true. ( p^q is True)
What is a prime number?The prime numbers are those numbers that have only one factor namely 1 and the number itself.
Given that p = x is prime and q = x is even. If we replace x by 2 then we would get
p = 2 is prime
q = 2 is even
p^q will be held true only if p and q both are true.
The statement for p and q both are true because 2 only has two factors only 1 and 2 themselves.
2 is also considered an even number (2,4,6,8,...)
Since p = true and q = true then
p and q = p^q = true
Thus, p^q is True.
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Answer:
p^q is true
Step-by-step explanation:
If both p and q are true, the statement p^q is true. If both p and q are false, the statement p^q is still true. All other options yield a false result.
The side lengths of a 30-60-90 triangle are in the ratio 1:square root :2. What is the cos 60°?
A.square root 3
B.1/2
C.square root 3/2
D.square root 3/3
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PLEASE HELP ME
Which are dependent events? Check all that apply.
•choosing 2 socks from a drawer, •without replacement
•flipping a coin 4 times
•picking 4 cards from a deck, •one after the other
•rolling a number cube twice
•spinning a spinner and rolling a number cube
The dependent events are:
choosing 2 socks from a drawer, without replacementpicking 4 cards from a deck, one after the other.Which events are dependent?Two events are dependent when the outcome of the first event affects the probabilities for the outcomes of the second event.
The first pair:
"choosing 2 socks from a drawer, without replacement"
Is a pair of dependent events. Because the first pair chosen can't be chosen on the second event. Then, the outcome of the first event affects the second event.
The third option:
"picking 4 cards from a deck, one after the other"
Again, here we have dependent events, because the cards already picked can't appear in the next events.
The other 3 options are sets of independent events.
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Which equation represents a graph with a vertex at (–3, 2)?
The equation represents a graph with a vertex at (–3, 2) is y = a(x + 3)² + 2
Vertex of a functionThe standard vertex of a function is given as shown below
y = a(x - h)² + k
where (h, k) is the vertex of the function
Given the vertex of a function at (-3, 2). On substituting, we will have:
y = a(x - (-3))² + 2
y = a(x + 3)² + 2
Hence the equation represents a graph with a vertex at (–3, 2) is y = a(x + 3)² + 2
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What is the domain of the sine and cosine functions?
Answer:
domain of the sine and cosine functions is all real numbers
Step-by-step explanation:
range of both the sine and cosine functions is [−1,1]
graph can go left and right to infinity
graph goes up and down between 1 and -1
graph looks like a wave or
like U letters next to each other
UUUU
sine and cosine of an angle have the same absolute value as the sine and cosine of its reference angle.
mathlibretextsorg
HELP HELP HELP
Quick algebra 1 question for 50 points!
1. Provide a brief overview of graphing a linear equation using slope.
2. Create 2 original problems and solve it using the graphing a linear equation using slope method, show your work as you solve the problem and explain each step.
The standard equation of a straight line is given by y = mx + b, where m is the slope (rate of change) and b is the y intercept of the line.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The standard equation of a straight line is given as:
y = mx + b
Where m is the slope (rate of change) and b is the y intercept of the line.
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help me please im stuck here
The reciprocal relationship of the graph is graph (a)
How to determine the reciprocal relationship?The reciprocal relationship implies that:
The x and the y axes are swapped.
When the x and the y axes are swapped, the value on both axes swap their positions
For the given graph, the reciprocal relationship is graph (a)
This is shown in the attached graph
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Match the vocabulary word to its correct definition.
1. constant -----a mathematical phrase that cannot be determined true or false
2. coefficien-------- a mathematical expression containing one or more variables
3. variable------- the constant preceding the variables in a product
4. expression---- a numerical value
5. algebraic expression------- a letter or symbol used to represent an unknown
Answer:
Constant: A numerical value
Coefficient: The constant preceding the variables in a product
Variable: a letter or symbol used to represent and unknown
Expression: A mathematical phrase that cannot be determined by true or false
Algebraic expression: A mathematical expression containing one or more variables
Step-by-step explanation:
g = 15 - m/32
Alice fills up the gas tank of her car before going for a long drive, the equation above shows the amount of gas in gallons in Alice's car when she has driven m (miles). What does 32 mean in the equation?
The value of 32 in the equation will serve as the time taken by the driver to travel
Functions and valuesIf Alice fills up the gas tank of her car before going for a long drive, and the equation that shows the amount of gas in gallons in Alice's car when she has driven m (miles). is given as:
g = 15 - m/32
The value of 32 in the equation will serve as the time taken by the driver to travel
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The question is on the picture
Answer: 68
Step-by-step explanation:
By the inscribed angle theorem, arc BA measures twice of 34 degrees, which is 68 degrees.