The Transformation of the function f(x) = log₅(x) to g(x) = 3 - log₅(x) is a vertical reflection followed by a vertical translation.
(i) The original function f(x) = log₅(x) is first reflected over the x-axis, which changes the sign of the function. The result is a graph that is upside-down compared to the original. the function becomes -log₅(x) .
(ii) Next, the transformed function g(x) is shifted up by 3 units, which results in the vertical translation of the graph. This transformation changes the range of the original function, but the shape of the graph remains unchanged.
So , the function becomes g(x) = 3 - log₅(x).
Therefore , The transformation of f(x) to g(x) changes the orientation of the graph and shifts it vertically, but does not affect its shape.
The given question is incomplete , the complete question is
The function f(x) = log₅(x) , is transformed to g(x) = 3 - log₅(x).
Describe the transformation.
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point-slope(urgent please,will give brainliest)
a. Plot the points (-3, 17) and (-1, 1) and draw a line through them.
b. Plot the points (-3, -14/3) and (-1, -2/3) and draw a line through them.
c. Plot the points (3, 2) and (5, 4) and draw a line through them.
What is the stepwise explanation of plotting the points?a. Point slope form equation for a line with slope m that passes through a point (x1, y1) is given by:
y - y1 = m(x - x1)
Using the given point (-2, 5) and slope -6, we have:
y - 5 = -6(x + 2)
Graph: The graph of the line can be drawn by finding two points on the line and plotting them, then drawing a line through the points.
For example, to plot the line when x= -3 and x = -1, we can substitute the respective x-values into the equation to find the corresponding y-values, then plot the points:
when x = -3, y = -3 * -6 + 5 = 17
when x = -1, y = -1 * -6 + 5 = 1
Plot the points (-3, 17) and (-1, 1) and draw a line through them.
b. Using the given point (-2, -8) and slope 5/6, we have:
y + 8 = (5/6)(x + 2)
Graph: Plotting the line using the same steps as above, for example, when x= -3 and x = -1,
when x = -3, y = (5/6)(-3 + 2) - 8 = -14/3
when x = -1, y = (5/6)(-1 + 2) - 8 = -2/3
Plot the points (-3, -14/3) and (-1, -2/3) and draw a line through them.
c. Using the given point (4, 3) and slope -1/2, we have:
y - 3 = -1/2 (x - 4)
Graph: Plotting the line using the same steps as above, for example, when x= 3 and x = 5,
when x = 3, y = -1/2 (3 - 4) + 3 = 2
when x = 5, y = -1/2 (5 - 4) + 3 = 4
Plot the points (3, 2) and (5, 4) and draw a line through them.
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calculate -8000 * 41 with long division
The solution to the expression is -328000
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
calculate -8000 * 41 in long division
The above expression is a product expression
This means that it cannot be evaluated using long division
When the expression is evaluated. we have
-8000 * 41 = -328000
Hence, the solution is -41000
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Launch Problem
The Martinez twins, Carlos and Clarita, are trying to find a way to make money during summer
vacation. When they overhear their aunt complaining about how difficult it is to find someone to
care for her pets while she will be away on a trip, Carlos and Clarita know they have found the
perfect solution. Not only do they have a large, unused storage shed on their property where
they can house animals, they also have a spacious fenced backyard where the pets can play.
Carlos and Clarita need to clean the storage shed where they plan to board the pets. They have
decided to hire a company to clean the windows. After collecting the following information, they
have come to you for help deciding which window cleaning company they should hire.
• Sunshine Express Window Cleaners charges $50 for each service call, plus $10 per window.
• "Pane "less Window Cleaners charges $25 for each service call, plus $15 per window.
1. Which company would you recommend, and why? Prepare an argument to convince Carlos
and Clarita that your recommendation is reasonable. (It is always more convincing if you
can support your claim in multiple ways. How might you support your recommendation
using a table? A graph? Algebra?)
I recommend hiring "Pane "less Window Cleaners since it's less expensive compared to Sunshine Express Window Cleaners.
What is the recommendations about?I recommend hiring "Pane "less Window Cleaners". This is because for a fixed number of windows, "Pane "less Window Cleaners" is less expensive compared to Sunshine Express Window Cleaners. The difference in cost can be calculated by subtracting the cost of "Pane "less Window Cleaners" from that of Sunshine Express Window Cleaners.
For example, for 10 windows, the cost of Sunshine Express Window Cleaners is $50 + 10 * $10 = $150, whereas the cost of "Pane "less Window Cleaners" is $25 + 10 * $15 = $175.
Therefore, the difference in cost is $175 - $150 = -$25, meaning that "Pane "less Window Cleaners" is cheaper. This recommendation is reasonable because it provides the best value for their money.
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what is an irreflexive closure
Irreflexive closure is the creation of a new binary relation by adding irreflexivity property, meaning no element is related to itself.
What is binary ?
A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" and "1".
An irreflexive closure is a mathematical concept that refers to the creation of a new binary relation from a given binary relation by adding the property of irreflexivity. A binary relation is irreflexive if it does not relate any element to itself. The irreflexive closure of a binary relation is the smallest irreflexive relation that contains it.
In other words, the irreflexive closure of a binary relation is a modified version of the original relation where no element is related to itself. The process of finding the irreflexive closure involves removing all self-referential relationships and adding new relationships to preserve the original relationships between elements.
Irreflexive closure is the creation of a new binary relation by adding irreflexivity property, meaning no element is related to itself.
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If No, give a reason.Let if be a function. Is it possible that f(2)=9 and f(3)=9 Multiple choiceA. Yes.B. No. A function assigns each value of x in its domain to exactly one value of fox).C. No. A function assigns each value of Fx) in its range to exactly one value of x.D. No. A function expecting a variable cannot be called with a constant argument.E. No. There is no possible function operations that would yield 9 from 3
(a) Yes,f(x)=9 since every point on this line would have a y-coordinate of 9.
(b) No. A function can have only one value of y corresponding to each value of x.
A function is an equation where each value of x corresponds to exactly one value of y, This means that different x-values can correspond to the same y value but different y-values cannot correspond to the same x value.
(a)
if f(1)=9and f(2)=9 then both x=1 and x=2 corresponds to y=9.
Since different x-values can go to the same y-value for a function, then it is possible that f(1)=9 and f(2)=9
For example, the function could be the horizontal line
f(x)=9 since every point on this line would have a y-coordinate of 9 .
b) If
f(1)=9 and f(1)=3, then y=3 and y=9correspond to x=1. Since functions cannot have different y-values corresponding to the same x-value, then it is not possible for f(1)=9 and f(1)=3
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What is the samole variance for the data given:
5,10,7,12,0,20,15,22,8,2
The Samole variance for the given data is 0.
What is the variance of the data?The variance is mean squared difference between each data point and the center of the distribution measured by the mean.
The given data is 5,10,7,12,0,20,15,22,8,2.
We know that, Variance = [tex]\frac{\sum( {\bar x-x} )}{Number of observations }[/tex]
Here, [tex]\bar x[/tex] = (5+10+7+12+0+20+15+22+8+2)/10
= 101/10
= 10.1
Now, variance = [(10.1-5)+(10.1-10)+(10.1-7)+(10.1-12)+(10.1-0)+(10.1-20)+(10.1-15)+(10.1-22)+(10.1-8)+(10.1-2)]/10
= 0/10
= 0
Therefore, the Samole variance for the given data is 0.
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2/5x10/7 in simplest form
Answer:
4/7
Step-by-step explanation:
Solve the equation: 2x + x + (x + 20) = 180
What is the value of x?
35, 40, 50, or 90
Answer:
x=40
Step-by-step explanation:
Pls help ASAP the question is in the picture
Given Tables does not represents a quadratic function.
What is a function?A set of inputs with one output per input is referred to as a function. Simply put, a function is an association between inputs in which every input is coupled to exactly one output. Each function has a range and a co-domain, or domain.
There are numerous function types in mathematics. Among the crucial types are the following:
An injective function, also referred to as a one-to-one function, is a mapping between two sets that accounts for a range for each domain.
Onto functions or surjective functions when a range to a domain mapping involves more than one element.
A function composed of polynomials is known as a polynomial function.
Inverse functions are those that have the ability to invert other functions.
Now,
As we can see from the image that the graph for the function is a straight line but for quadratic function or parabola the graph is parabolic.
Hence,
Given Tables does not represents a quadratic function.
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a different poll of households had a sample mean of children and a sample standard deviation of children. what is the -statistic? type as:
The number of the degrees of freedom for the data given below is 14.
Given that ,
According to data from the US Census Bureau, there are 1.86 children on average in each American home. In a specific city, 15 households were polled.
To find : The degree of the freedom ?
The mean number of children in an
American House hold is 1.86
Polls of 15 households were conducted in a city.
So, No . of households sampled
D = 15
Degrees of freedom of = n- 1
= 15 - 1
=14
Therefore, the degree of the freedom is 14.
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The United States Census Bureau determined that the mean number of children in an American household is 1.86. Polls of 15 households were conducted in a certain city. What is the number of degrees of freedom?
1 Gallon = 4 Quarts 1 Quart = 2 Pints 1 Pint = 2 Cups 1 Cup = 8 Fluid Ounces. answer choices. a. 100 Fluid Ounces. b. 8 Pints. c. 5 Quarts. d. 1 Gallon.
The correct answer is d. 1 Gallon is equal to 4 Quartz.
To determine the correct conversion, we can work backwards from the given answer choices.
a. 100 Fluid Ounces: Since 1 cup equals 8 fluid ounces, 100 fluid ounces would be equivalent to 100/8 = 12.5 cups, which is not one of the answer choices.
b. 8 Pints: Since 1 pint equals 2 cups, 8 pints would be equivalent to 8 * 2 = 16 cups. However, this is not one of the answer choices.
c. 5 Quarts: Since 1 quart equals 2 pints, 5 quarts would be equivalent to 5 * 2 = 10 pints. However, this is not one of the answer choices.
d. 1 Gallon: Since 1 gallon equals 4 quarts, each quart is 2 pints, and each pint is 2 cups, the conversion can be calculated as follows:
1 gallon = 4 quarts = 4 x 2 pints = 8 pints = 8 x 2 cups = 16 cups = 16 x 8
fluid ounces = 128 fluid ounces.
Therefore, the correct answer is d. 1 Gallon.
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The table below represents the value of the equation 2x+y=7 for x=0,1,2.....8
1. Find the value of A
2. Find the value of 2b
Answer:
Q10: a = 1 (Choice D)
Q11. 2b = -10 (Choice A)
Step-by-step explanation:
The given equation is
[tex]2x + y = 7[/tex]
We can rewrite this equation with y on the left side and other terms on the right:
Subtract [tex]2x[/tex] from either side:
[tex]2x + y - 2x = 7 - 2x\\\\y = 7 - 2x\;\;\cdots \cdots(1)\\[/tex]
Q10
The value of [tex]y = a[/tex] corresponds to an [tex]x[/tex] vlaue of [tex]6[/tex]
Plug in [tex]x = 3[/tex] into the equation [tex](1)[/tex] :
[tex]a = 7-2(3)\\\\a = 7 - 6\\\\a = 1\\\\[/tex] ANSWER
Q11
We can find b using the same technique as Q10
[tex]b = 7 - 2(6)\\\\b = 7-12\\\\b = -5\\\\[/tex]
Therefore
[tex]2b = 2(-5) = -10[/tex] ANSWER
What is the rule of greater than?
Greater than or less than symbols are used when a number is greater or less than another number. A greater than sign (>) is used if the first number is greater than the second number. If the first number is less than the second number, the less than sign (<) is used.
What is the greater than sign?In mathematics, the greater-than sign represents an inequality between two values. A common form of > joining two strokes of equal length at an acute angle on the right is found in documents dating from 1631.
> is the greater than sign. So 9>7 is interpreted as "9 is greater than 7".
less than icon. (greater than or equal to) and two other comparison characters (less than or equal to). Think of the symbol as something like a crocodile's mouth, with numbers representing small fish on either side.
Alligators always prefer to eat more fish. The higher the number, the more the crocodile's mouth opens.
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The speed of a boat in still water is 15Km/hr. It needs four more hours to travel 63 Km against the current river than it needs to travel down the river. Determine the speed of the current of the river.
Answer:
The speed of the current of the river is 6 km/hr--------------------------------
Let the speed of the current be x.
The speed with current is 15 + x and the speed against current is 15 - x.
The time difference to travel the distance of 63 km is 4 hours:
63/(15 - x) - 63/(15 + x) = 463(15 + x - 15 + x) = 4(15 + x)(15 - x)63*(2x) = 4(225 - x²)63x = 450 - 2x²2x² + 63x - 450 = 0x = (-63 + √(63² + 2*4*450))/4 (negative root is discarded)x = (-63 + 87)/4x = 6Am truck weigh 4,725 pound. The truck can carry 7,500 pound. What i the total weight of the truck and full load
The total weight of the truck is 7,500 pounds and the full load weighs 2775.
This is a simple subtraction problem and we can easily find out the required values by subtracting the correct values. It has been mentioned that the Truck can carry 7500 pounds and that the Truck's weight is 4725 pounds.
The weight of the load can be calculated as follows-
= 7500 - 4725 pounds
= 2775 pound
So, the total weight of the truck same as its total capacity with which it can carry, that is, 7500 pounds, and the weight of its full load which can be put in the truck is 2775 pounds.
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help_outline (a) what is the cardinality of p({1, 2, 3, 4, 5, 6})?
Cardinality of the power set of the given set = 64
Power set is the set of all the possible subsets that can be formed from the given set including the null set and the set itself.
Example set:
{1,2,3}
All the possible subsets of this set:
{}; {1}; {2}; {3}; {1,2,3}; {1,2}; {1,3}; {2,3}
The power set of the above set is written as:
P({ {}, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3} })
Since the no. of elements in the above power set in this example is 8 therefore its cardinality is 8.
Cardinality of the power set of a given set is expressed by a formula:
where n is the cardinality (no. of elements) of the given set whose power set is to be formed for determining cardinality of the power set.
Hence in the given case, we have n = 6.
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Explain the answer step by step please
The answer is D.
The portion of the statement [tex]{x\to 0}[/tex] says we're looking at the graph as the x-values get closer to 0. So we're looking at x-values like 0.1, 0.01, 0.001, 0.0001, etc and -0.1, -0.01, -0.001, -0.0001, etc.
The [tex]\lim\limits_{x\to 0}f(x)[/tex][tex]\lim\limits_{x\to 0}f(x) = 1[/tex] as a whole is asking "are the y-values on the graph headed towards a specific y-value as x-values get closer to 0?"
As you move towards x = 0 from either side, the y-values get closer to y=1.
So [tex]\lim\limits_{x\to 0}f(x)=1[/tex].
differences between mean and median 1. you're given n = 5 measurements: 0, 7, 1, 1, 4. find the mean, median, and mode. show your work (don't use the calculator; show the calculations.) (2 points)
The mode of this set of numbers is 1,the median of this set of numbers is 1.
Mean: To find the mean of this set of 5 numbers, we first add them together and divide by the number of measurements. 0 + 7 + 1 + 1 + 4 = 13. 13 divided by 5 (the number of measurements) is 2.6. Therefore, the mean of this set of numbers is 2.6.
Median: To find the median of this set of 5 numbers, we first need to arrange them in order from least to greatest. 0, 1, 1, 4, 7. The median is the middle number, so it is 1. Therefore, the median of this set of numbers is 1.
Mode: To find the mode of this set of 5 numbers, we need to look for the number that appears most often. In this set, the number 1 appears twice while the rest of the numbers appear only once. Therefore, the mode of this set of numbers is 1.
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Solve for x ∼
[tex]\color{purple} \large\frak{3x + 5 = 3(x - 5)}[/tex]
[tex] \\ \\ \\ \\ \\ \\ \\ \\ [/tex]
Ty
————————————————————————
[tex]3x+5=3(x-5)[/tex]
Distribute numbers outside of parentheses:
[tex]3x+5=(3)(x)+(3)(-5)[/tex]
[tex]3x+5=3x-15[/tex]
Subtract 3x from both sides:
[tex]3x+5-3x=3x-15-3x[/tex]
[tex]5=-15[/tex]
Subtract 5 from both sides:
[tex]5-5=-15-5[/tex]
[tex]0=-20[/tex]
[tex]\fbox{No solution}[/tex]
Solve the equation7(x+4)=-21. X=
Answer: x = -7
Step-by-step explanation:
7(x + 4) = -21
x + 4 = -3
x = -7
Answer:
-7 because -7 + 4 is -3 and 7 x -3 is -21
Step-by-step explanation:
Pleaseee help :) thank you!
Salut/Hello!
Answer: C. SAS~
Step-by-step explanation:
I left a photo for you so you can tell what I'm talking about.
1. The angles are equal because they are opposites.
2. Side AE is congruent with side ED.
3. Side BE is congruent with side EC.
I hope it was helpful! :]
Answer: SAS~
Step-by-step explanation:
a fair die is rolled six times. what is the probability that the rolls are 1, 2, 3, 4, 5, and 6, in any order?
The probability that the rolls are 1, 2, 3, 4, 5, and 6, in any order is [tex]\frac{1}{46656}[/tex].
A fair die is rolled six times.
The rolls are 1, 2, 3, 4, 5, and 6.
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur. The probability of all the events in a sample space adds up to 1.
Probability of event to happen P(E) = Number of favourable outcomes/Total Number of outcomes.Hence there is a [tex]\frac{1}{6}[/tex] chance a 1 will be rolled first, [tex]\frac{1}{6}[/tex] chance a 2 will be rolled second, [tex]\frac{1}{6}[/tex] that a 3 will be rolled third, etc. Therefore the probability of the sequence appearing is [tex]\frac{1}{6}[/tex]. [tex]\frac{1}{6}[/tex]. [tex]\frac{1}{6}[/tex]. [tex]\frac{1}{6}[/tex]. [tex]\frac{1}{6}[/tex]. [tex]\frac{1}{6}[/tex].
On each of the six independent rolls there is a probability of 1/6
for rolling the desired number, so by the multiplicative principle, the probability for rolling the required sequence is:
Since each sequence of six rolls is equally likely, the answer is
[tex]\frac{1}{number of possible sequences of six rolls}[/tex]=[tex](\frac{1}{6} )^{6} =\frac{1}{46656}[/tex]
Therefore, the probability is [tex]\frac{1}{46656}[/tex].
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a bacteria colony initially has 85 million bacteria, and is growing at a rate of f(t)=2e0.1t million bacteria per hour. what is the new bacteria population after 6 hours? the units of your answer should be million bacteria. only enter the numerical value and round your answer to three decimals.
The new bacteria population after 6hours is 101.442 million.
The integration denotes the summation of discrete data. The integral is calculated to find the functions which will describe the area, displacement, volume, that occurs due to a collection of small data, which cannot be measured singularly.
integration is a method of adding or summing up the parts to find the whole. It is a reverse process of differentiation, where we reduce the functions into parts.
Given initially bacteria 85 million.
and the growing rate of bacteria 10 is given by.
[tex]$f(t)=2 e^{0.1 t}[/tex] million/hour
Let [tex]$y$[/tex] be number of bacteria (In millions) at t hour.
so, [tex]\frac{dy}{dt} =2e^{0.1t}[/tex]
Integrating both side
[tex]$$\begin{aligned}& y=\int 2 e^{0.1 t} d t \\& y=\frac{2 e^{0.1 t}}{0.1}+c \\& y=20 e^{0.1 t}+c\end{aligned}$$[/tex]
So, at t=0, y=85
[tex]$$\begin{aligned}& \Rightarrow \quad 85=20 e^{0.1 \times 0}+c \\& \Rightarrow \quad 85=10+c \\& \ C_2\quad=85-20 \\& \Rightarrow C=65 \\& \Rightarrow y=20 e^{0.1 t}+65 \\& \text { when } t=6 \\& y=20 e^{0.1 \times 6}+65 \\& y=20 x e^{0.1 \times 6}+65 \\& y=36.442376+65 \\& y=101.442376 \\& y \cong 101.442 \text {million bacteria } \\&\end{aligned}$$[/tex]
so, at t=6 hour the population of bacteria are 101.442 million.
Therefore, the new bacteria population after 6hours is 101.442 million.
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3) Mrs. Ramirez is planning a family reunion and deciding where to buy food and drinks. She considers the information below. She expects 96 family members to attend. How much would it cost to buy 96 hotdogs purchased from Value Market? Show your work.
b) How much would 96 hotdogs cost from Sammy's Bulk Store? Show your work. c) Which store offers the better buy for bottled water? Explain your reasoning. PLEASE HELP ME GUYS IM DESPERATE !!
The cost of 96 hotdogs from Value Market would be $94.04.
The cost of 96 hotdogs from Sammy's Bulk Store would be $75.84.
The better buy for bottled water would be from Value Market.
What is a Value Market?Value Market is a store that offers products at low prices, usually with a focus on basic household items, food and drink.
a) The cost of 96 hotdogs from Value Market would be 96 × $0.99 = $94.04.
b) The cost of 96 hotdogs from Sammy's Bulk Store would be 96 × $0.79 = $75.84.
c) The better buy for bottled water would be from Value Market. Value Market offers bottled water for $0.69 per bottle while Sammy's Bulk Store offers bottled water for $0.89 per bottle. Therefore, buying bottled water from Value Market would result in a lower cost for 96 bottles, which would be $0.69 × 96 = $66.24, compared to $0.89 × 96 = $83.84 from Sammy's Bulk Store.
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Y=-1.5. Graph linear equations
Plot the coordinate points (0, 0), (1, -1.5), (2, -3.0), (-1, 1.5) and (-2, 3) on graph as below.
What is the graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.
The given linear equation is y= -1.5x.
Substitute, x=0, 1, 2, 3, 4, 5, .......
So, y=0, -1.5, -3, -4.5, -6.0, ....
Plot the coordinate points (0, 0), (1, -1.5), (2, -3.0), (-1, 1.5) and (-2, 3)
Therefore, plot the coordinate points (0, 0), (1, -1.5), (2, -3.0), (-1, 1.5) and (-2, 3) on graph as below.
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"Your question is incomplete, probably the complete question/missing part is:"
Graph linear equations y= -1.5x.
at his school's spring carnival, javier is in charge of the balloon-launcher contest. in this contest, each team builds a catapult to launch water balloons at a target. javier gives a bucket of 12 water balloons to each team in the contest. in all, he gives out 48 water balloons.which equation can you use to find the number of teams t in the contest?
The equation which represents the number of the team 't' participated in the water balloon contest is equal to 12t = 48 and number of teams are 4.
Let us consider 't' represents the number of teams participated in the water balloon contest.
Total number of water balloons given by Javier to each team is equal to 12
Total number water balloons distributed by the Javier is equal to 48.
The equation which represents the number of the team in the water balloon contest is given by :
12t = 48
Number of teams participated in contest are:
⇒ t = 48 / 12
⇒ t = 4
Therefore, the equation represents the number of teams in the balloon contest is equal to 12t = 48 and number of teams are 4.
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A store sells packages of comic books with a poster. a poster and 5 comic books cost $11.50. a poster and 10 comic books cost $16.50. write a linear function rule that models the cost of y of a package containing x number of comic books
The linear function rule that models the cost of 'y' of a package containing 'x' number of comic books is y = x + 6.50.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
Given, A poster and 5 comic books cost $11.50 and a poster and 10 comic books cost $16.50.
slope(m) = (16.50 - 11.50)/(10 - 5).
slope(m) = 5/5.
slope(m) = 1.
16.50 = 10(1) + b.
b = 6.50.
y = x + 6.50.
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On average yasmin drinks 3/4 of an 8 ounce glass of water in 1 1/4 hours how much can she drink per hour
Answer:
She drinks 4.8 ounces of water per hour
Step-by-step explanation:
We know
Yasmin drank 3/4 of an 8-ounce glass of water in 1 1/4 hours
3/4 of 8 ounce = 6 ounces
1 1/4 = 5/4 = 1.25 hours
How much can she drink per hour?
6 divided by 1.25 = 4.8 ounces of water per hour
So, she drinks 4.8 ounces of water per hour.
Use the branch-and-bound method to find the optimal solution to the following IP: max z = 7x1 + 3x2 s.t. 2x1 + x2 ≤ 9 3x1 + 2x2 ≤ 13 x1, x2 ≥ 0; x1, x2 integer
As per the branch and bound method, the optimal solution of IP is (0,6.5).
The term called branch and bound method is defined as an algorithm design paradigm which is generally used for solving combinatorial optimization problems
Here we have know that following equation and they are written as,
=> z = 7x₁ + 3x₂
=> 2x₁ + x₂ ≤ 9
=> 3x₁ + 2x₂ ≤ 13
where the value of x₁, x₂ ≥ 0 and the value of x₁, x₂ integer
In order to solve this one then we have to make the table for each of the constraint given here.
Then we get,
=> 2x₁ + x₂ ≤ 9
When x₁=0 then x₂=?
⇒2(0)+ x₂ =9
⇒x₂=9
Similarly When x₂=0 then x₁=?
⇒2x₁+(0)=9
⇒2x₁=9
⇒x₁= 9/2 = 4.5
Then the table for the constraint is written as
x₁ 0 4.5
x₂ 9 0
Similar way the table for the constraint 3x₁ + 2x₂ ≤ 13 is written as,
x₁ 0 4.33
x₂ 6.5 0
When we plot the graph, then we get the graph like the following.
The value of the objective function at each of these extreme points is as follows:
Extreme Point Lines through Objective
Coordinates Extreme Point function value
(x1,x2) Z=3x1+5x2
O(0,0) 3→x1≥0,4→x2≥0 3(0)+5(0)=0
A(4.33,0) 2→3x1+2x2≤13 4→x2≥0 3(4.33)+5(0)=13
B(0,6.5) 2→3x1+2x2≤13 3→x1≥0 3(0)+5(6.5)=32.5
Here the maximum value of the objective function Z=32.5 occurs at the extreme point (0,6.5).
Hence, the optimal solution to the given LP problem is : x1=0,x2=6.5 and max Z=32.5.
To know more about branch and bound method here.
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I really need help with this question . Please and thank you . I got 136 but I do not know the square root of 136.
Answer:
It's the other way around, subtract 36 from 100, and you will get 8
Step-by-step explanation:
a^2+b^2=c^2
a and b are the sides, and c is the longest side.
6x6=36
10x10=100
100-36=64
square root of 64 is 8
