Answer: n=40
Step-by-step explanation:
let me know if i got this right for you broski
now dance
The rectangular garden is 175 m long and 96 m broad . find the cost of fencing it at 17.50per m.also find the cost of ploughing it at 4.50 paise per square metre
Hence, the cost of fencing the garden is ₹9485. Hence, the cost of plowing the garden is ₹756.
What is perimeter?Perimeter is the total distance around the outside of a closed two-dimensional shape. It is the sum of the lengths of all the sides of the shape. For example, the perimeter of a rectangle is found by adding the lengths of all its four sides, whereas the perimeter of a circle is found by multiplying the diameter by π (pi). Perimeter is usually expressed in units of length, such as meters, centimeters, feet, or inches.
Here,
The perimeter of the rectangular garden is twice the sum of its length and width. So, the length of the fence needed to enclose the garden is:
2 × (length + width) = 2 × (175 m + 96 m) = 542 m
Therefore, the cost of fencing the garden at 17.50 per meter is:
Cost of fencing = length of fence × cost per meter
= 542 m × 17.50
= 9485
Hence, the cost of fencing the garden is ₹9485.
To find the cost of plowing the garden, we need to first calculate its area, which is given by:
Area = length × width
= 175 m × 96 m
= 16800 m²
Therefore, the cost of plowing the garden at 4.50 paise per square meter is:
Cost of plowing = area of garden × cost per square meter
= 16800 m² × 0.045
= 756
Hence, the cost of plowing the garden is ₹756.
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Where did my dad go? He went to get milk but never came back
The phrase "He went to get milk but never came back" is often used as a humorous way to explain someone's absence or to imply that someone is unreliable or untrustworthy.
The phrase likely originates from a common experience where a child's parent, often their father, promises to go out to get something, like milk, but never returns. This can be a source of disappointment and confusion for the child, and the phrase has since been used in a joking manner to explain someone's failure to show up or fulfill a promise.
However, it is important to recognize that this experience can also be a source of trauma and should not be used to make light of someone's pain or loss.
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The village of Hampton has 436 families 238 of the families live within 1 mile of the village square use mental math to find how many families live farther than 1 mile from the square show your work
Answer: 198 families live farther than 1 mile from the square.
Step-by-step explanation:
We know that there are 238 families that live within 1 mile of the village square. To find the number of families that live farther than 1 mile from the square, we can subtract 238 from the total number of families:
436 - 238 = 198
Therefore, 198 families live farther than 1 mile from the square. We can do this subtraction mentally without needing a calculator.
Hi. Please help me convert this non-linear to linear form y=mx+c. The answer is square root of y= 6/p x - 2/q .
Thank you so much.
Answer: To convert the given equation, √y = (6/p)x - (2/q), into the linear form y = mx + c, we can use the following steps:
Square both sides of the equation to eliminate the square root:
√y = (6/p)x - (2/q)
√y^2 = (6/p)x - (2/q)^2
Simplifying the right-hand side, we get:
y = (36/p^2)x - (4/q) + 4/q^2
Rearrange the equation to the form y = mx + c:
y = (36/p^2)x + (4/q^2 - 4/q)
So the linear form of the given non-linear equation is y = (36/p^2)x + (4/q^2 - 4/q).
Step-by-step explanation:
8. Using only a compass and straightedge, find the image of A after a rotation by 180° counterclockwise about point B. Label the image A', please provide a picture of the answer
When a point is rotated, it must be rotated around a point.
See attachment for the image of the rotation about point K
How to construct triangles?We should note the following:
In order to construct triangles, you will need a protractor, a pair of compasses and a ruler. To draw the triangle, three properties must be taken into account: length, angle and shape
The given parameters are:
ΔEFG
The angle of rotation is
∅ = 180⁰
The above angle of rotation means that:
The translated triangle will be 180 degrees from ΔEFG about point K.
It also means that:
ΔEFG and ΔE'F'G' will be equidistant from point K
See attached image for ΔE'F'G'
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3. any time you are presented with data or statistics are many things you should consider. list two examples of things you need to consider when evaluating a data set or statistics. why do you need to consider them?
When evaluating a data set or statistics, the things to consider are sample size and data quality. It's important to consider these things because they provide insight into the validity of the data and the accuracy of the statistics that are being used.
When presented with a dataset or statistics, there are several things to consider.
Here are two examples of what you need to consider when evaluating a dataset or statistics:
1. Sample size: It's important to consider the sample size because small sample sizes are more likely to be biased. For example, a small sample size might be unrepresentative of a larger population. A sample size of 30 is commonly used to distinguish between small and large samples in statistics. Larger sample sizes are often more representative of the population and produce more reliable statistics.
2. Data quality: The quality of the data is also an important consideration. When evaluating statistics, you must ensure that the data is accurate, relevant, and up-to-date. This is important because using incorrect or outdated data can lead to incorrect conclusions. Additionally, if the data is missing or incomplete, you may not be able to get an accurate picture of the population that the dataset is supposed to represent. This can skew the results, making them less reliable or even completely useless. Therefore, data quality is an important consideration when evaluating statistics.
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Use substitution to solve -4x + y = 3, 5x - 2y = -9
Using the substitution method, the solution of the system of equations -4x + y = 3 and 5x - 2y = -9 is (x, y) = (1, 7)
We can solve this system of equations using the substitution method by solving for one variable in terms of the other in one equation, and then substituting that expression into the other equation. Here's how:
-4x + y = 3 (Equation 1)
5x - 2y = -9 (Equation 2)
Solving Equation 1 for y, we get:
y = 4x + 3
Now, we substitute this expression for y into Equation 2 and solve for x:
5x - 2(4x + 3) = -9
5x - 8x - 6 = -9
-3x = -3
x = 1
We have found the value of x to be 1. Now, we substitute this value back into Equation 1 to find the value of y:
-4(1) + y = 3
y = 7
Therefore, the solution to the system of equations is (x, y) = (1, 7)
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Bella is splitting her rectangular backyard into a garden in the shape of a trapezoid and a fish pond in the shape of a right triangle. What is the area of her garden?
The Area of Bella's garden as required to be determined in the task content is the difference of the area of the rectangular backyard and the right triangular fish pond.
What is the area of Bella's trapezoidal garden?It follows from the task content that the area of Bella's trapezoidal garden is to be determined from the given information.
Since the garden and the fish pond are from the rectangular backyard; the sum of their areas is equal to the area of the backyard.
Ultimately, the area of the garden is the difference of the area of the rectangular backyard and the right triangular fish pond.
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what is the variance inflation factor measuring? (select all that apply) group of answer choices the variance of the error term how much the explanatory variables are associated with one another the variance of the coefficient estimates the collinearity of the explanatory variable
The Variance Inflation Factor (VIF) measures the degree of correlation or the collinearity of the explanatory variables.
VIF quantifies how much each explanatory variable is correlated with a linear combination of the other variables in a multiple regression model. This can help identify variables that are redundant, irrelevant, or harmful to the model's accuracy. The VIF is calculated for each explanatory variable by dividing the variance of the regression coefficient estimates by the variance of the regression coefficient estimates when that variable is excluded from the model.
If the VIF is greater than 1, it indicates that the variance of the regression coefficient estimate for that variable is inflated by the presence of the other variables, which reduces the model's accuracy. Therefore, a VIF greater than 1 is considered to be an indication of collinearity or multicollinearity in the explanatory variables. The VIF measures the degree of correlation or the collinearity of the explanatory variables, and it can identify variables that are redundant, irrelevant, or harmful to the model's accuracy.
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Given the lengths of two sides of a triangle, write an equality to indicate between which two numbers the length of the third side must fall.
The sides are:
8 and 13
I will award brainliest to the first correct answer with a decent explanation
The length of the third side must fall between 8 and 13. This is because the sum of the lengths of any two sides of a triangle must always be greater than the length of the third side.
an equation of a circle is given by (x+3)^2+(y_9)^2=5^2 apply the distributive property to the square binomials and rearrange the equation so that one side is 0.
The equation of the circle is [tex]x^2 + y^2 + 6x - 18y + 65 = 0[/tex].
Given:
Equation of the circle is [tex](x+3)^2+(y-9)^2=5^2[/tex]
Expand the equation
[tex](x+3)^2 = (x+3)(x+3) = x^2 + 3x + 3x + 9 = x^2 + 6x + 9[/tex]
[tex](y-9)^2 = (y-9)(y-9) = y^2 - 9y - 9y + 81 = y^2 - 18y + 81[/tex]
[tex]5^2 = 25[/tex]
Then, substitute the expanded expressions into the equation
[tex](x+3)^2+(y-9)^2=5^2\\(x^2 + 6x + 9) + (y^2 - 18y + 81) = 25\\[/tex]
Simplify and combine like terms
[tex](x^2 + 6x + 9) + (y^2 - 18y + 81) = 25\\x^2 + y^2 + 6x - 18y + 90 = 25[/tex]
Rearrange the equation so that one side is 0
[tex]x^2 + y^2 + 6x - 18y + 90 = 25\\x^2 + y^2 + 6x - 18y + 90 - 25 = 0\\x^2 + y^2 + 6x - 18y + 65 = 0[/tex]
Thus, the equation of a circle [tex](x+3)^2+(y-9)^2=5^2[/tex] can be rearranged using the distributive property to form [tex]x^2 + y^2 + 6x - 18y + 65 = 0[/tex], with one side equaling 0.
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I need help, what does this mean
Answer:
2125 ft/min
33,000 ft
y = -2125x + 33,000
Step-by-step explanation:
A. -2125 feet per minute. You get this number when you divide 17,000 by 8 (rise over run). You could also use the formula y2-y/x2-x1 with the points (0, 33,000) and (8, 17,000).
B. 33,000 feet is the height of the plane before it starts descending, so it must be the starting value.
C. Plug in the values you got for A and B into the slope formula y = mx + b
y = -2125x + 33,000
Can someone just help me on 19, it’s pretty confusing. Just look around at the other questions so it’ll help with answering it.
Answer:
0% (0/40)
Step-by-step explanation:
I feel like this is a trick question. since chicken is not indicated on the graph, I believe chicken is nobodies favorite food
Darnel is studying the movement of glaciers, which are bodies of dense ice. The median
annual movement of the Blue Valley Glacier is about 300.2 feet, and the interquartile range is
14 feet. The median annual movement of the Silver Lake Glacier is about 300.4 feet, and the
interquartile range is about 14 feet.
4) What can you conclude from these statistics? Complete the sentence.
Over a year, the Blue Valley Glacier typically moves about
the Silver Lake Glacier, and Blue Valley has
its annual movement compared to Silver Lake.
as
▾ variability in its annual movement compared to silver lake
Over a year, the Blue Valley Glacier typically moves about the same distance as the Silver Lake Glacier, and Blue Valley has the same variability in its annual movement compared to Silver Lake.
How to interpret the statisticsThe median annual movement of the Blue Valley Glacier is 300.2 feet, and the interquartile range is 14 feet.
The interquartile range indicates the spread of the data within the middle 50% of the data
So we know that the annual movement of the Blue Valley Glacier falls within a range of 300.2 ± 7 feet (i.e. 293.2 to 307.2 feet)
Similarly, the median annual movement of the Silver Lake Glacier is 300.4 feet, and the interquartile range is also 14 feet
So the annual movement of the Silver Lake Glacier also falls within a range of 300.4 ± 7 feet (i.e. 293.4 to 307.4 feet)
Since the ranges for both glaciers overlap and have the same size, we can conclude that they typically move about the same distance over a year, and that the variability in the annual movement of Blue Valley is comparable to that of Silver Lake.
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Bonny has 3 cards and a standard rolling cube. She wants to pick a card and spin the rolling cube at random. How many outcomes are possible?
There are 18 possible outcomes for Bonny to pick a card and spin a rolling cube at random.
How to calculate How many outcomes are possibleThere are a total of 6 outcomes for the rolling cube and 3 outcomes for picking a card. To find the total number of outcomes, we can use the multiplication rule of counting:
Total number of outcomes = number of outcomes for picking a card x number of outcomes for rolling a cube
Total number of outcomes = 3 x 6 = 18
Therefore, there are 18 possible outcomes for Bonny to pick a card and spin a rolling cube at random.
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In order to make the same amount of money, they would have to each sell ______ bicycles. They would both make $______.
They would each need to sell 5 bicycles to make the same amount of money and if they both sell 5 bicycles, they would each make $500.
What do you mean by finding the break-even point ?
The key concept used here is the idea of finding the break-even point between two scenarios. In this case, the break-even point is the number of bicycles that Jim and Tom each need to sell in order to make the same amount of money. This is found by setting their total earnings equal to each other and solving for the number of bicycles. Once the break-even point is found, the total earnings for that number of bicycles can be calculated by plugging it back into the original equations. This concept is commonly used in business and finance to determine the minimum level of sales needed to cover costs and make a profit.
Calculating the number of bicycle and money :
To make the same amount of money, Jim and Tom would have to each sell the same number of bicycles, let's call it "b".
So Jim would make a total of:
250 + 50b dollars
Tom would make a total of:
400 + 20b dollars
To find the value of "b" where they both make the same amount of money, we can set the two expressions equal to each other and solve for "b":
250 + 50b = 400 + 20b
30b = 150
b = 5
Therefore, they would each need to sell 5 bicycles to make the same amount of money.
To find out how much they would make, we can substitute "b=5" into either of the expressions above:
Jim:
250 + 50(5) = $500
Tom:
400 + 20(5) = $500
Therefore, if they both sell 5 bicycles, they would each make $500.
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Ten cards are selected out of a 52 card deck without replacement and the number of Jacks is observed. This is an example of a Binomial Experiment.
true
false
The statement "Ten cards are selected out of a 52 card deck without replacement and the number of Jacks is observed. This is an example of a Binomial Experiment" is false.
What is a Binomial Experiment?A binomial experiment is an experiment that is repeated multiple times with each repetition having only two potential outcomes. In a binomial experiment, the probability of success remains constant from trial to trial.
The criteria for a binomial experiment are as follows:
The experiment is made up of a fixed number of trials.There are only two possible results for each trial: success and failure.The probability of success for each trial is the same.The trials are all independent of one another.The formula for calculating the probability of x successes in n trials is:P(x) = (ⁿCₓ)(pˣ)(q^(n-x))
Where p is the probability of success, q is the probability of failure (q = 1 - p), and ⁿCₓ is the combination formula.
Therefore, the statement "Ten cards are selected out of a 52-card deck without replacement and the number of Jacks is observed. This is an example of a "Binomial Experiment" being false. This is because the probability of drawing a jack changes with each trial, as the deck's composition changes after each card is drawn.
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if one response is selected at random, what is the probability the response indicated that the dog is small-sized given that they enjoyed the treat? express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
The probability that the response indicated that the dog is small-sized given that they enjoyed the treat is 0.286 (or 2/7) in fraction in the lowest terms.
What is Bayes' theorem?Bayes' theorem is used to update probabilities of a hypothesis or an event in light of new data or evidence. It is used to calculate the conditional probability of an event based on prior knowledge of the conditions that might be relevant to the event.In the given problem, we have to find the probability that the response indicated that the dog is small-sized given that they enjoyed the treat.
The probability that the dog is small-sized given that they enjoyed the treat is the conditional probability P(S|T), where S is the event that the dog is small-sized and T is the event that they enjoyed the treat. To find the value of P(S|T), we will use Bayes' theorem. Bayes' theorem states that P(S|T) = P(T|S) * P(S) / P(T) where P(T|S) is the probability that they enjoyed the treat given that the dog is small-sized, P(S) is the prior probability that the dog is small-sized, and P(T) is the probability that they enjoyed the treat.
P(S) = 3/7P(T|S) = 2/3P(T) = (2/3 * 3/7) + (1/4 * 4/7) = 18/84 + 4/28 = 1/3
(adding the probabilities of T given S and T given L)Therefore, P(S|T) = (2/3 * 3/7) / (1/3) = 2/7 = 0.285714...Rounding off to the nearest millionth, the probability is 0.286. Therefore, the probability that the response indicated that the dog is small-sized given that they enjoyed the treat is 0.286 (or 2/7) in fraction in the lowest terms.
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an ore sample weighs 18.5 n n in air. when the sample is suspended by a light cord and totally immersed in water, the tension in the cord is 11.8 n n .find the total volume and density of the sample
The total volume of the sample is 0.0067 m³ and the density of the sample is 2753.73 kg/m³.
An ore sample weighs 18.5 N in air. When the sample is suspended by a light cord and totally immersed in water, the tension in the cord is 11.8 N. When the ore sample is immersed in water, the tension in the cord is given as 11.8 N.
Thus, the buoyancy force experienced by the ore sample is given by the difference between the weight of the sample in the air and the tension in the cord.
Buoyancy force experienced by the ore sample = Weight of the sample in the air - Tension in the cord
Buoyancy force experienced by the ore sample = (18.5 N) - (11.8 N)
Buoyancy force experienced by the ore sample = 6.7 N
Also, we know that the weight of the ore sample in air is equal to the weight of the ore sample when immersed in water.
Weight of the ore sample = Weight of the displaced water
Weight of the ore sample = Buoyancy force experienced by the ore sample
Weight of the ore sample = 6.7 N
The density of the ore sample
Density is given by the formula Density = Mass/Volume
Where Density is measured in kg/m³
Mass is measured in kg
Volume is measured in m³
Also, the density of water is given as 1000 kg/m³.
The density of the ore sample = Mass/Volume
Mass = Density x Volume
Volume of the ore sample can be obtained from volume of the displaced water.
Volume of the displaced water = Weight of the ore sample/Density of water
Volume of the displaced water = (6.7 N)/(1000 kg/m³)
Volume of the displaced water = 0.0067 m³
Density of the ore sample = (18.5 N)/(0.0067 m³)
Density of the ore sample = 2753.73 kg/m³
Therefore, 0.0067 m³ is the sample's total volume and 2753.73 kg/m³ is the density of the sample.
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Use the formula pH=log(1/[H^+]) to write an expression for the concentration of hydrogen ions in a liter of a sports drink that has a pH of 2. 4. What is the concentration of hydrogen ions?
The concentration of hydrogen ions in a liter of the sports drink is approximately 3.98 x 10^(-3) moles per liter.
The pH of a substance is a measure of its acidity or basicity and is defined as the negative logarithm (base 10) of the hydrogen ion concentration [H+]. The formula for pH is given as pH = -log[H+].
To find the concentration of hydrogen ions in a liter of a sports drink that has a pH of 2.4, we can use the formula pH = -log[H+]. Rearranging this formula, we get [H+] = 10^(-pH).
Substituting the given value of pH into this expression, we get [H+] = 10^(-2.4).
It's worth noting that the hydrogen ion concentration is related to the acidity of a solution; the higher the hydrogen ion concentration, the more acidic the solution. The pH scale ranges from 0 (most acidic) to 14 (most basic), with a pH of 7 being neutral. The sports drink in question has a relatively low pH, indicating that it is quite acidic.
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using the net below find the area of the triangular prism
6 cm
3 cm
4 cm
6 cm
5 cm
2 cm
Answer:153
Step-by-step explanation:
Y=3x+3 what is the slope and y intercept
Answer:
y-intercept is (0,3) and the slope is 3
Step-by-step explanation:
Answer: the slope is 3x while 3 is the y-intercept.
Step-by-step explanation:
Identify three points that are solutions to
each system.
The solutions for the systems of inequalities are:
a) (0, -100), (0, -150), (0, -1000)
b) (0, 50), (0, 55) , (0, 1,204).
How to identify 3 solutions of each system?When we have a system of inequalities, a solution is a point that solves both ienqualities at the same time.
The first one is:
y ≤ x - 8
y < -3x - 9
Here y must be smaller than x, then we can define x like x = 0, and really small values for y, like y = -100, replacing that we will get:
-100 ≤ 0 - 8 = -8
-100 < - 3*0 - 9 = -9
Both of these are true, so (0, -100) is a solution, and trivially, (0, -150) and (0, -1000) are other two solutions.
For the second system:
y > 5x + 1
y > 3
Let's do the same thing, x = 0 and y gets really large values, like y = 50
50 > 5*0 + 1 = 1 this is true.
50 > 3 this is true.
so (0, 50) is a solution, and also are (0, 55) and (0, 1,204).
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Find the value of N.
4 + 5 -3 = N
8 x 3 - 5 = N
15 ÷ 3 + 10 = N
8 + 3 -1 x 2 = N
14 x 3 - 2 = N
( 3 + 5 ) x 2 = N
10 + 7 + 2 x 1 = N
16 ÷ 8 + 4 = N
7 + 5 ÷ 5 = N
20 ÷ 4 x 6 = N
Answer:
1. n=6
2. n=19
3. n=15
4. n=20
5. n=40
6. n=16
7. n=19
8. n=6
9. n=2.4
10. n=30
Step-by-step explanation:
remember the priorities :
1. brackets
2. exponents
3. multiplications and divisions
4. additions and subtractions
inside every category you go usually from left to right, but you can use the commutative property where applicable.
4 + 5 - 3 = 4 + 5 - 3 = 4 + 5 - 3 = 4 - 3 + 5 = 6
8×3 - 5 = 24 - 5 = 19
15/3 + 10 = 5 + 10 = 15
8 + 3 - 1×2 = 8 + 3 - 2 = 9
14×3 - 2 = 42 - 2 = 40
(3 + 5)×2 = 8×2 = 16
10 + 7 + 2×1 = 10 + 7 + 2 = 19
16/8 + 4 = 2 + 4 = 6
7 + 5/5 = 7 + 1 = 8
20/4×6 = 5×6 = 30
The average between 3. 15 and x is 40 what is x?
The value of x that makes the average between 3.15 and x equal to 40 is 76.85.
In this problem, we are given two numbers, 3.15 and x, and told that the average between them is 40. We can set up an equation to solve for x as follows:
(3.15 + x) / 2 = 40
To find the average between 3.15 and x, we add the two numbers together and divide by 2, which gives us the equation above.
To solve for x, we can start by multiplying both sides of the equation by 2:
3.15 + x = 80
Next, we can subtract 3.15 from both sides of the equation:
x = 76.85
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In a regular pentagon PQRST. PR intersects QS
at O. Calculate angle ROS.
Answer: 72°
Step-by-step explanation:
To find the interior angle of this shape, use the formula 180(n-2)/n, where n is the amount of sides. Plugging 5 in for the interior angle of a pentagon, you get 180(3)/5, or 108°.
Using the statement that PR intersects QS, we can see that triangle QOR is isosceles (to get this, look at triangle PQR, and note that because it has 2 equal side lengths, and its last length is not equivalent to the other 2 sides, it is isosceles). Solving for angle PRQ, we know one angle is 108°, and the other two are equal. The total angle in a triangle is 180°, so (180°-108°)/2 = 36° (angles QPR and PRQ).
Since the angle of R = 108°, we can find angle PRS as 108° - 36°, or 72°. Since triangles PQR and QRS are similar (share the same angles and side lengths), we can see that angle RQS and RSQ are both 36°.
Since ORS is a triangle, its angle total is 180°. Since we know the angles ORS and OSR (respectively) already as 72° and 36°, we can subtract these angles to find angle ROS. 180°-72°-36° = 72°
find the number of ways of arranging the numbers ${}1,$ ${}2,$ ${}3,$ ${}4,$ ${}5,$ $6$ in a row so that the product of any two adjacent numbers is even.
Combining these, we have[tex]$6 \times 6 = \boxed{36}$[/tex] different arrangements of the numbers [tex]${}1,$ ${}2,$ ${}3,$ ${}4,$ ${}5,$ $6$[/tex] in a row where the sum of any adjacent numbers is even.
What are the fundamental products?Products intended for exporting after processing into goods or processed products are referred to as "basic products," as are goods planned for export after processing. Samples 1 - 3 Samples 2 - 3.
We may start by noting that at minimum one of the neighboring numbers must be even for the sum of both numbers to be even. This means that a even numbers (2, 4, 6) as well as the odd numbers (1, 3, 5) should be arranged in the appropriate positions.
Let's start by thinking about the even positions. The second, fourth, and sixth places are the only even positions. We can choose any variant of the 3 even numbers to occupy these spots, giving us[tex]$3! = 6$[/tex] ways.
Let's now think about the unusual positions. The first, third, and fifth positions are the only ones that are odd. We have an additional [tex]$3! = 6$[/tex]ways to fill these spots by using any combination of the 3 odd numbers.
Consider the odd locations now. The first, third, and fifth places are the three odd positions. We have an additional[tex]$3! = 6$[/tex]ways by using any permutation of the three odd numbers to fill these positions.
Together, this give us [tex]$6 \times 6[/tex] = [tex]\boxed{36}$[/tex] different ways to arrange the numbers [tex]${}1,$ ${}2,$ ${}3,$ ${}4,$ ${}5,$ $6$[/tex]in a row so that the sum of any two adjacent numbers is even.
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The interest $I on a loan of $P for a year at a rate of 6% varies directly as the loan
find the formula relating I and P
a) I when P = 800 b)P when I = 72
The formula relating I and P is I = kP
a) When P= $800, then I = $48
b) When I = $72, then P = $1200
If the interest $I on a loan of $P for a year at a rate of 6% varies directly as the loan, we can write:
I = kP
where k is a constant of proportionality. To find the value of k, we can use the given information that the interest rate is 6%, or 0.06 as a decimal. We know that when P = 100, the interest I = 0.06 × 100 = 6. Therefore:
I/P = 6/100 = 0.06 = k
Now we can use this value of k to answer the given questions,
a) When P = 800, the formula relating I and P is:
I = kP
I = 0.06 × 800
I = 48
Therefore, the interest on a loan of $800 for a year at a rate of 6% is $48.
b) When I = 72, the formula relating I and P is:
I = kP
72 = 0.06P
Solving for P:
P = 72/0.06
P = 1200
Therefore, a loan of $1200 for a year at a rate of 6% would have an interest of $72.
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Fatoumata is working two summer jobs, making $15 per hour lifeguarding and making $10 per hour tutoring. In a given week, she can work at most 12 total hours and must earn a minimum of $140. Also, she must work at least 8 hours lifeguarding. If � x represents the number of hours lifeguarding and � y represents the number of hours tutoring, write and solve a system of inequalities graphically and determine one possible solution.
Answer:
not sure if this sign � was important did it the best way I could
Step-by-step explanation:
To solve this problem graphically, we will first set up a system of inequalities based on the given information:
x ≥ 8 (Fatoumata must work at least 8 hours lifeguarding)
y ≤ 12 - x (Fatoumata can work at most 12 total hours)
15x + 10y ≥ 140 (Fatoumata must earn a minimum of $140)
To graph these inequalities, we can plot the points (8,0), (12,0), and (0,14) on a coordinate plane and draw lines connecting them. The line between (8,0) and (12,0) represents the constraint on the number of hours Fatoumata can work, while the line between (8,0) and (0,14) represents the constraint on the amount of money she must earn. The shaded region that satisfies all three inequalities is the feasible region.
To find one possible solution, we can pick any point within the feasible region. One such point is (8,6), which represents working 8 hours lifeguarding and 6 hours tutoring. This point satisfies all three inequalities:
x ≥ 8 is true since x = 8
y ≤ 12 - x is true since y = 6 ≤ 12 - 8
15x + 10y ≥ 140 is true since 15(8) + 10(6) = 180 ≥ 140
Therefore, one possible solution is for Fatoumata to work 8 hours lifeguarding and 6 hours tutoring to earn at least $140 while not exceeding 12 total hours worked.
Let A, B, and C be subsets of some universal set U. (a) Draw two general Venn diagrams for the sets A, B, and C. On one, shade the region that represents A - (B nC), and on the other, shade the region that represents (A -B) U (A C). Based on the Venn diagrams, make a conjecture about the relationship between the sets A-(BnC) and (A -B)U (A -C). (b) Use the choose-an-element method to prove the conjecture from Exer- cise (5a). (c) Use the algebra of sets to prove the conjecture from Exercise (5a).
In conclusion, we can prove that[tex](A -B) U (A C)[/tex] is a superset of[tex]A - (B nC)[/tex] using both the choose-an-element method and the algebra of sets.
To answer this question, let's first draw two Venn diagrams to represent the sets A, B, and C. In the first Venn diagram, shade the region that represents[tex]A - (B nC)[/tex].
This is the region outside of the intersection of B and C and inside of A. In the second Venn diagram, shade the region that represents [tex](A -B) U (A C).[/tex] This is the union of the region outside of B and the region outside of C, both of which are inside of A. Based on these diagrams, we can make the conjecture that (A -B) U (A C) is a superset of A - (B nC).
To prove this conjecture, we can use the choose-an-element method. Let a be an element of A - (B nC). This means that a is in A, but not in B or C. Since a is in A, it is also in (A -B) U (A C), and therefore (A -B) U (A C) is a superset of A - (B n C).
We can also use the algebra of sets to prove this conjecture.[tex]A - (B n C) = (A -B) U (A -C) since A - (B n C)[/tex]is the union of the regions outside of B and outside of C, both of which are inside of A. This implies that (A -B) U (A C) is a superset of A - (B nC).
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