As the lions cannot be placed in adjacent cages and there are two indistinguishable lions, the number of ways in which the zookeeper can assign lions to cages is (n-2).
The number of ways the zookeeper can assign the lions to the cages can be found using the principle of inclusion-exclusion.
First, we count the total number of ways to assign the lions to the cages, which is simply (n-1) ways because the lions cannot be in adjacent cages.
Next, we subtract the number of ways the lions can be in adjacent cages. Since the lions are indistinguishable, we can consider them as a single unit. Thus, we have (n-2) ways to place this unit in the cages.
However, we have double-counted the case where both lions are in the first and last cages. This can only happen once, so we need to add it back in. Thus, we add 1 to our previous result.
Putting this all together, we have:
Total number of ways to assign lions to cages = (n-1) - (n-2) + 1 = n-2
Therefore, there are (n-2) ways for the zookeeper to assign the lions to the cages.
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Question 7(Multiple Choice Worth 2 points)
(Scatter Plots MC)
A marine biologist was interested in seeing the relationship between a manatee's weight and food consumption. She gathered data and wanted to construct a graph to display the data in order to observe this relationship.
Is a scatter plot or a line graph more appropriate to construct for the data, given the context of the problem? Explain.
A line graph, because it would show the association or relationship between two variables
A line graph, because it would show how a variable changes over time between each data point given
A scatter plot, because it would show the association or relationship between two variables
A scatter plot, because it would show how a variable changes over time between each data point given
A scatter plot would be more appropriate to construct for the data, given the context of the problem. The reason is that the marine biologist is interested in seeing the relationship between a manatee's weight and food consumption.
A scatter plot is a type of graph that displays the relationship between two variables, where each variable is plotted along one axis, and a point is placed at the intersection of the two values. In this case, weight would be plotted along one axis and food consumption along the other axis.
A scatter plot allows the researcher to see if there is a relationship between the two variables, and if so, what type of relationship it is (positive, negative, or no correlation). Therefore, a scatter plot is the most appropriate way to display the relationship between a manatee's weight and food consumption.
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Which equation represents the hanger balance?
hurry!!!!
The correct equation for the hanger balance is:= w = 2
How to balance equations?
The hanger balance equation is typically used in physics experiments to determine the weight of an object by comparing it to known weights on the other side of a balance. The equation is based on the principle of equilibrium, which states that the sum of the forces acting on an object must be zero for it to remain stationary.
The correct equation for the hanger balance is:
w = 2
This equation simply states that the weight of the object being measured (represented by "w") is equal to a known weight of 2 units. This indicates that the object being measured has a weight of 2 units.
The other equations provided, such as "6 = w + 2" and "6 = w - 2", do not accurately represent the hanger balance equation because they do not take into account the known weight on the other side of the balance. In order to determine the weight of an object using a hanger balance, it is necessary to have a known weight on the other side of the balance to compare it to.
In summary, the correct equation for the hanger balance is w = 2, which represents the weight of the object being measured as 2 units.
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Anyone help in number1 (d)
A pole leans away from the sun at an angle of 7° to the vertical. When the elevation of the sun is 44°, the
pole casts a shadow 49 ft long on level ground. How long is the pole?
The length of the pole is approximately 412.7 feet.
What is the tangent function?
The tangent function is a mathematical function that relates the ratio of the length of the side opposite to an acute angle in a right triangle to the length of the adjacent side. It is defined as the ratio of the sine of the angle to the cosine of the angle.
We can solve this problem using trigonometry. Let's call the length of the pole "x". We can then use the tangent function to relate the angle that the pole makes with the vertical to the length of the shadow cast by the pole.
The tangent of the angle between the pole and the vertical is equal to the opposite side (length of the shadow) divided by the adjacent side (length of the pole).
tan(7°) = opposite / adjacent
tan(7°) = 49 / x
We can solve for x by multiplying both sides by x and then dividing both sides by tan(7°):
x = 49 / tan(7°)
Now we know the length of the pole is:
x = 49 / tan(7°) = 412.7 ft (rounded to one decimal place)
Therefore, the length of the pole is approximately 412.7 feet.
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Graph g(x), where f(x) = 2x − 5 and g(x) = f(x + 1). a line labeled g of x that passes through points 0, negative 4 and 2, 0 a line labeled g of x that passes through points 0, negative 3 and 4, 5 a line labeled g of x that passes through points negative 5, negative 3 and 0, 7 a line labeled g of x that passes through points 0, negative 7 and 5, 3
To graph g(x), we must replace x with x + 1 in the function f(x) = 2x - 5: g(x) = f(x + 1) = 2(x + 1) - 5 = 2x - 3 (a) To display the g of x line that passes through the coordinates 0, -4, and 2, 0, we replace x = 0 and x = 2 in the equation g(x) = 2x - 3:
g(0) = 2(0) - 3 = -3
g(2) = 2(2) - 3 = 1
Hence the line's points are (0, -3) and (2, 1):
yaml Copy code | 5 |- * (2,1) | 4 |- | 3 |- * (0,-3) | 2 |- | 1 |- | 0 |—————————— 0 1 2 3 4 5\s(b) (b) To display the g of x line that passes through points 0, -3, 4, 5, we replace x = 0 and x = 4 in the equation g(x) = 2x. - 3:
g(0) = 2(0) - 3 = -3
g(4) = 2(4) - 3 = 5
Hence the line's points are (0, -3) and (4, 5):
Copy code in yaml | 5 |- * (4,5)
|\s4 |-\s |\s3 |- * (0,-3)\s |\s2 |-\s |\s1 |-\s |\s0 |
————————-\s 0 1 2 3 4 5\s(c) (c) To display the line labeled g of x that goes through points -5, -3, and 0, 7, we use the equation g(x) = 2x - 3:
g(-5) = 2(-5) (-5) - 3 = -13\sg(0) = 2(0) - 3 = -3
Thus the line points are (-5, -13) and (0, -3):
| 5 |- | 4 |- | 3 |- | 2 |- | 1 |- | 0 |- * (0,-3) | -1 |- (-5,-13)
\ \s ——————-\s -5 -4 -3 -2 -1 0\s(d) To draw the g of x line that passes between points 0, -7, and 5, 3, In the equation g(x) = 2x - 3 we substitute x = 0 and x = 5:
g(0) = 2(0) - 3 = -3
g(5) = 2(5) (5) - 3 = 7
Hence the line's points are (0, -3) and (5, 7):
| 7 |- * yaml Copy code (5,7)
|\s6 |-\s |\s5 |- \s | * (0,-3) (0,-3)
4 |-\s |\s3 |-\s |\s2 |-\s |\s1 |-\s |\s0 |
————————-\s 0 1 2 3 4 5.
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PLEASE HELP ILL GIVE BRAINLIEST
Answer:
True
Step-by-step explanation:
Since C has to add up to 180 and we already have 150 we can assume that that other angle is 30. The sum of angles in a triangle always has to equal 180. 120+30=150 meaning B also equals 30. B+A=150 therefore making it true.
any one know the answers?
The value of the boxes, A , B and C are 22/4, 15/4 and 9 1/4 respectively
How to determine the valuesNote that from the information given, we have that the number in a box is the sum of the two numbers below it.
Then, we can deduce that;
A = The sum of the two mixed fractions, 3 1/4 and 2 1/4
B = The sum of the two mixed fractions, 2 1/4 and 1 1/2
Now, add the values
A = 3 1/4 + 2 1/4
convert to improper fractions
A = 13/4 + 9/4
Add the values
A = 22/4
B = 2 1/4 + 1 1/2
convert to improper fractions
B = 9/4 + 3/2
B =9 + 6 /4
B = 15/4
Then , the value of C = A + B
C = 22/4 + 15/4
C = 37/4
C = 9 1/4
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10 to the 9th power is how many times 10 to the 8th power?
10 to the 9th power is 10 times 10 to the 8th power.
Which of the following uses the distributive property correctly?
3(x+5)=3-x+5
3(x+5)=3-x-3-5
3(x+5)=3+3.5
3(x+5)=3-x+3.5
Answer:
None of them, 3x + 15 is correct.
Step-by-step explanation:
In order to apply the distributive properly correctively, we need to multiply everything in the parentheses. For an example, lets look at the given expression:
[tex]3(x+5)[/tex]
We multiply everything in the parentheses by 3
[tex]3x+15[/tex]
Looking at out choices, none of them uses the distributive property correctly.
The following points represent a relation where x represents the independent variable and y represents the dependent variable.
three fourths comma negative 2, 1 comma 5, negative 2 comma negative 7, 1 comma negative one half, and 6 comma 6
Does the relation represent a function? Explain.
No, because for each input there is not exactly one output
No, because for each output there is not exactly one input
Yes, because for each input there is exactly one output
Yes, because for each output there is exactly one input
The correct answer is: No, because for each input there is not exactly one output.
What is function?In mathematics, a function is a relation between two sets, where each element in the first set (called the domain) is associated with exactly one element in the second set (called the codomain or range). A function assigns a unique output value (dependent variable) to each input value (independent variable) from the domain.
According to the given information:The given relation does not represent a function because for some inputs there are multiple outputs, violating the "one-to-one" or "vertical line test" rule.
The correct answer is: No, because for each input there is not exactly one output.
In this relation, we can see that x = 1 has two different outputs, y = 5 and y = -1/2. Therefore, the relation does not meet the criteria of a function as it violates the requirement of having exactly one output for each input.
Therefore, The correct answer is: No, because for each input there is not exactly one output.
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Given � ( � ) = − 2 � 2 − 4 � + 13 f(x)=−2x 2 −4x+13, find � ( − 7 ) f(−7)
The function g(-7) * f(-7) is approximately equal to *-8056.5*.
What is a function?
A function is a mathematical rule that assigns a unique output value to each input value from a given set. It represents a relationship between two sets of numbers in which each input has exactly one output. A function can be expressed symbolically, graphically, or verbally and is used to model real-world phenomena, solve equations, and make predictions in various fields of study.
According to the given information
To find g(-7) and f(-7), we need to substitute -7 for y in the function g(y) = -2ᵇ - 4b + 13 and x in the function f(x) = -2x² - 4x + 13.
g(-7) = -2⁻⁷ - 4⁻⁷ + 13
Simplifying this expression gives:
g(-7) = -1/128 + 28 + 13
g(-7) = 141 - 1/128
Therefore, g(-7) is approximately equal to 140.9922 .
f(-7) = -2(-7)² - 4(-7) + 13
Simplifying this expression gives:
f(-7) = -98 + 28 + 13
f(-7) = -57
Therefore, f(-7) is equal to -57.
So, g(-7) * f(-7) is approximately equal to -8056.5.
The correct question is
g(y ) = − 2ᵇ − 4b + 13 and f(x)=−2x² −4x+13, find g( − 7 ) f(−7)
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The numbers 2 through 16 are written on tiles and put into a hat. One number is drawn at random. Determine the theoretical probability of drawing a prime number.
Answer:
2/5 or 0.4, which is also equivalent to a 40% chance.
Step-by-step explanation:
To determine the theoretical probability of drawing a prime number from the numbers 2 through 16, we need to first identify the prime numbers in this range. The prime numbers between 2 and 16 are 2, 3, 5, 7, 11, and 13.
There are a total of 15 numbers in the hat, and 6 of them are prime. Therefore, the probability of drawing a prime number can be calculated as:
Probability of drawing a prime number = Number of favorable outcomes / Total number of possible outcomes
Number of favorable outcomes = 6 (since there are 6 prime numbers in the range of 2 through 16)
Total number of possible outcomes = 15 (since there are 15 numbers in the hat)
So, the probability of drawing a prime number is:
Probability of drawing a prime number = 6 / 15
Simplifying this fraction by dividing both numerator and denominator by 3, we get:
Probability of drawing a prime number = 2 / 5
Therefore, the theoretical probability of drawing a prime number from the numbers 2 through 16 is 2/5 or 0.4, which is also equivalent to a 40% chance.
Emily bought a car that depreciates at a
rate of 18% per year. She paid $55,000 for
the car. How much will her car be worth
after 8 years.
After answering the presented question, we can conclude that As a equation result, Emily's automobile will be valued roughly $19,105.25 after 8 years.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "[tex]2x + 3 = 9[/tex]" asserts that the phrase "[tex]2x + 3[/tex]" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "[tex]x2 + 2x - 3 = 0[/tex]." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
Emily's car will be worth 100% - 18% = 82% of its original value after one year, or 0.82 times its initial value.
After two years, the car is worth 0.82 times its initial value, or 0.822% of its original value.
Similarly, the car will be worth 0.828% of its initial value after 8 years.
Hence, after 8 years, Emily's automobile will be worth:
In 8 years, the value is $55,000 x 0.82.
After 8 years, the value is $19,105.25. (rounded to the nearest cent)
As a result, Emily's automobile will be valued roughly $19,105.25 after 8 years.
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A triangle has angles that measure 55°, 80°, and r. What is r?
Answer: r = 45°
Step-by-step explanation:
All triangles angles add up to 180 degrees.
With that said we can use the given information and create an equation to solve.
55° + 80° + r = 180°
Lets solve for r.
55° + 80° + r = 180°
first lets combine like terms.
135° + r = 180°
now lets subtract 143° from both sides
135° + r = 180°
-135° -135°
r = 45°
The expression 0.6y represents the result of
decreasing the quantity y by p%. What is the value
of p?
Answer:
P=40 and y was decreased by 40%
Step-by-step explanation:
Let's set up an equation as follows. In this case, we will set y will be equivalent to 1, as the number can be any value for this equation in the other fraction as the original number. Let us then represent the new number, 0.6y, or 0.6*1 which will be equivalent to 0.6 itself, and we will set that equal to 100-p as p will be the amount of percent it was decreased by. Here is the equation as follows:
[tex]\frac{1}{0.6} =\frac{100}{100-p}\\\\[/tex]We can use a method of solving fractions that is known as the Cross-multiplication property, which demonstrated in the image attached below this answer. Using this property, we can determine and simplify the equation to as follows:
[tex]1*(100-p)=0.6(100)[/tex], which can be simplified to [tex]100-p=60[/tex], and then solving the equation gives us the answer:
[tex]p=40[/tex]
P=40
make absolute value equation of
0 and 8
5 and 17
-4 and 6
in the form |x-c|=d
Please hurry!!!!
Answer:
Sure, here are the absolute value equations of 0 and 8, 5 and 17, and -4 and 6 in the form $|x-c|=d$:
* For 0 and 8, $|x-0|=8$. This means that $x-0=8$ or $x-0=-8$. Solving for $x$, we get $x=8$ or $x=-8$.
* For 5 and 17, $|x-5|=17$. This means that $x-5=17$ or $x-5=-17$. Solving for $x$, we get $x=22$ or $x=-12$.
* For -4 and 6, $|x-(-4)|=6$. This means that $x-(-4)=6$ or $x-(-4)=-6$. Solving for $x$, we get $x=10$ or $x=-2$.
I hope this helps! Let me know if you have any other questions.
Step-by-step explanation:
the infographic shows percentages of women overall in elected office as well as the share of latinas in elected office. women constitute approximately what percentage of members of congress, statewide executives, state legislators, and mayors in the top 100 cities? check all that apply.
According to the infographic, women constitute approximately 15-19% of members of Congress, less than 15% of state legislators, and 25-50% of statewide executives and mayors in the top 100 cities.
According to the information provided in the infographic, the following options apply:
Women constitute approximately 25-50% of statewide executives and mayors in the top 100 cities.
Women constitute approximately 15-19% of members of Congress.
Women constitute less than 15% of state legislators.
Therefore, the correct options are:
15-19%
Less than 15%
25-50%
The infographic presents data on the percentage of women overall in elected office and the share of Latinas in elected office. The data indicates that women constitute less than 15% of state legislators, approximately 15-19% of members of Congress, and 25-50% of statewide executives and mayors in the top 100 cities. This suggests that women are underrepresented in elected office at all levels of government, with the exception of statewide executives and mayors in the top 100 cities. The infographic underscores the need for greater gender diversity in elected office, and the importance of supporting and encouraging women to run for political office at all levels of government.
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Complete question:
The infographic shows percentages of women overall in elected office as well as the share of Latinas in elected office. Women constitute approximately what percentage of members of Congress, statewide executives, state legislators, and mayors in the top 100 cities? Check all that apply.
19-25%
Less than 15%
15-19%
25-50%
NEED HELP ASAP PLEASE.....
The output of the function g(x) = [tex]3^{(\frac{x}{2} )}[/tex] when x = 2 is 3.
How to solve function?g(x) is a function as defined as follows:
g(x) = [tex]3^{(\frac{x}{2} )}[/tex]
If we input n2 into the g(x), the output g(x) can be gotten as follows:
Therefore,
g(x) = [tex]3^{(\frac{x}{2} )}[/tex]
where
x = 2
Therefore,
[tex]3^{(\frac{2}{2} )}[/tex] = 3¹
Therefore,
the output is 3.
g(2) = 3
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a paperback book company charges $6 for each paperback book plus $4 for shipping and handling per order. what would the total cost for 3 books.
ANSWER FAST
Answer:
$30
Step-by-step explanation:
6x3=18
+
4x3=12
=30
Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options. 2(x2 + 6x + 9) = 3 + 18 2(x2 + 6x) = –3 2(x2 + 6x) = 3 x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot 2(x2 + 6x + 9) = –3 + 9
She could solve for (x+3)² and find two solutions, x = (-3 + √(33/2)) / 2 and x = (-3 - √(33/2)) / 2.
What is quadratic equation?it's a second-degree quadratic equation which is an algebraic equation in x. Ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form.
The three steps that Inga could use to solve the quadratic equation 2x² + 12x – 3 = 0 are:
1. Use the quadratic formula: Inga could use the quadratic formula x = (-b ± √(b² - 4ac)) / 2a, where a = 2, b = 12, and c = -3.
2. Factor the quadratic expression: Inga could factor the quadratic expression into (2x - 1)(x + 3) = 0 and then use the zero product property to find the solutions x = 1/2 and x = -3.
3. Complete the square: Inga could use the method of completing the square by adding and subtracting (6/2)² = 9 to the left side of the equation, giving 2(x+3)² - 33 = 0. Then she could solve for (x+3)² and find two solutions, x = (-3 + √(33/2)) / 2 and x = (-3 - √(33/2)) / 2.
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do you take the free samples offered in supermarkets? about 58% of all customers will take free samples. furthermore, of those who take the free samples, about 37% will buy what they have sampled. suppose you set up a counter in a supermarket offering free samples of a new product. the day you were offering free samples, 327 customers passed by your counter. (round your answers to four decimal places.)
a) The probability that more than 180 customers will take your free sample is approximately 0.9999.
b) The probability that fewer than 200 customers will take your free sample is approximately 0.0119.
c) Therefore, the probability that a customer will take a free sample and buy the product is 0.21.
d) The probability that between 60 and 80 customers will take the free sample and buy the product is approximately 0.043
a) Let X be the number of customers who take the free sample.
We know that X follows a binomial distribution with n = 327 and p = 0.58. To find the probability that more than 180 will take free sample, we need to find P(X > 180).
Using a binomial calculator or software, we get:
P(X > 180) = 1 - P(X ≤ 180) = 1 - binomial distribution (180, 327, 0.58, TRUE) ≈ 0.9999
Therefore, the probability that more than 180 customers will take your free sample is approximately 0.9999.
b) To find the probability that fewer than 200 will take your free sample, we need to find P(X < 200).
Using a binomial calculator or software, we get:.
P(X < 200) = binomial distribution (199, 327, 0.58, TRUE) ≈ 0.0119
Therefore, the probability that fewer than 200 customers will take your free sample is approximately 0.0119.
c) Let A be the event that a customer takes a free sample, and B be the event that the customer buys the product.
We are given P(B|A) = 0.35 and P(A) = 0.60.
Using the multiplication rule for dependent events, we get:
P(A ∩ B) = P(B|A) × P(A) = 0.35 × 0.60 = 0.21
Therefore, the probability that a customer will take a free sample and buy the product is 0.21.
d) Let Y be the number of customers who take the free sample and buy the product. We know that Y follows a binomial distribution with n = 327 and p = 0.21 (from part c). .
To find the probability that between 60 and 80 customers will take the free sample and buy the product, we need to find P(60 ≤ Y ≤ 80).
Using a binomial calculator or software, we get:
P(60 ≤ Y ≤ 80) = binomial distribution (80, 327, 0.21, TRUE) - binomial distribution (59, 327, 0.21, TRUE) ≈ 0.0434
Therefore, the probability that between 60 and 80 customers will take the free sample and buy the product is approximately 0.0434.
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Question: Do You Take The Free Samples Offered In Supermarkets? About 58 % Of All Customers Will Take Free Samples.
Furthermore, Of Those Who Take The Free Samples, About 37% Will Buy What They Have Sampled. Suppose You Set Up A Counter In A Supermarket Offering Free Samples Of A New Product. The Day You Were Offering Free Samples, 327Customers Passed By Your
Do you take the free samples offered in supermarkets? About 58% of all customers will take free samples. Furthermore, of those who take the free samples, about 37% will buy what they have sampled. Suppose you set up a counter in a supermarket offering free samples of a new product. The day you were offering free samples, 312 customers passed by your counter.(round your answers to four decimal places.)
a.) What is the probability that more than 180 will take your free sample?
b.) What is the probability that fewer than 200 will take your free sample?
c.) What is the probabilty that a customer will take a free sample and buy the product? Hint: Use the multiplication rule for dependent events. Notice that we are given the conditional probability P(buy|sample)=0.35, while P(sample)=0.60
d.) What is the probability that between 60 and 80 customers will take the free sample and buy the product? HInt: Use the probability of success calculated in part(c).
URGENT HELP NEEDED PLEASE
Step-by-step explanation:
Area of a triangle = 1/2 * base * height
For this triangle base = 9 m height = 8 m
1/2 ( 9 ) ( 8) = 36 m^2
What are the values of angle a c and f
Answer:
Step-by-step explanation:
f=133
a=93
c=140
Fill in the table for side length and area of different squares
a) The area of the square for side length [tex]3[/tex] is [tex]9[/tex][tex]cm^{2}[/tex].
The area of the square for side length [tex]100[/tex] is [tex]10000[/tex][tex]cm^{2}[/tex]
The area of the square for side length [tex]25[/tex] is [tex]625cm^{2}[/tex].
The area of the square for the side length [tex]s[/tex] is [tex]s^{2}cm^{2}[/tex].
b) No the side length of the square and area are not directly proportional.
What is the area of a square?The area of a square is the amount of space enclosed within the square, and it can be calculated using the formula A = [tex]s^{2}[/tex], where A is the area and s is the length of one side of the square.
According to the given information
The area of a square is the amount of space enclosed within the square, and it can be calculated using the formula A =[tex]s^{2}[/tex]
[tex]A = s^{2} = 3^{2} = 9cm^{2}[/tex]
[tex]A = s^{2} = 10^{2} = 10000cm^{2}[/tex]
[tex]A = s^{2} = 25^{2} = 625cm^{2}[/tex]
[tex]A = s^{2} = s^{2} = s^{2} cm^{2}[/tex]
Therefore area of the square are [tex]9cm^{2} ,10000cm^{2}, 625cm^{2} ,s^{2}cm^{2}[/tex]
Therefore the side length of the square and area are not directly proportional they are proportional to the square root of area.
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will give brainlest
|x+3|=9
you have to spilt the equation to get the absolute value
Answer:
To solve the equation |x+3|=9, we need to split it into two separate equations, one for the positive value and one for the negative value of the absolute value:
For the positive value:
x+3=9
Solving for x, we get x=6
For the negative value:
-(x+3)=9
Multiplying both sides by -1, we get:
x+3=-9
Solving for x, we get x=-12
Therefore, the solutions to the equation |x+3|=9 are x=6 and x=-12.
Hope This Helps!
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
For the the inequality –3(2x – 5) < 5(2 – x) the correct options are: x < 5, –6x + 15 < 10 – 5x
What is inequalities?
In mathematics, an inequality is a mathematical statement that indicates that two expressions are not equal. It is a statement that compares two values, usually using one of the following symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), or "≥" (greater than or equal to).
The correct representations of the inequality –3(2x – 5) < 5(2 – x) are:
x < 5 (obtained by simplifying the inequality and solving for x)
–6x + 15 < 10 – 5x (obtained by distributing the terms and simplifying the inequality)
Therefore, the correct options are:
x < 5
–6x + 15 < 10 – 5x
The options that describe number lines are not applicable to this inequality since they represent a single value, whereas an inequality represents a range of values that satisfy the inequality.
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in a binomial probability problem, if the nature of the problem is such that it is feasible to use either the binomial tables or the normal distribution to approximate the probability, which would give the more accurate answer?
If the sample size is large and the probability of success is not too close to 0 or 1, using the normal distribution to approximate the binomial probability will generally give a more accurate answer than using the binomial tables. However, if the sample size is small or the probability of success is very close to 0 or 1, using the binomial tables may be more accurate.
If the sample size is large (typically, n ≥ 30) and suppose that the probability of success (p) is not too close to 0 or 1, then we can use the normal distribution. As it gives more approximate value to the binomial probability which will generally give a more accurate answer than using the binomial tables.
This is because the normal distribution provides a more precise approximation of the binomial distribution as the sample size increases.
However, if the the probability of success is very close to 0 or 1 or sample size is small then using the binomial tables to calculate the probability directly may be more accurate. In general, it's important to check the conditions for using the normal approximation before using it and to use good judgment in deciding which method is more appropriate for a given problem.
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when a confounding variable is present in an experiment, one cannot tell whether the results were due to the a) independent variable or the dependent variable. b) independent variable or the confounding variable. c) dependent variable or the interval variable. d) dependent variable or the participant variable.
When a confounding variable is present in an experiment, one cannot tell whether the results were due to the independent variable or the dependent variable. The correct option is a) independent variable or the dependent variable.
A confounding variable is any variable that influences the dependent variable or response variable and is also
correlated with the independent variable. Because it is difficult to determine which variable is causing changes in the
dependent variable, it is also known as a confounding variable.
In other words, a confounding variable is a variable that can affect the dependent variable in an experiment, making it
impossible to determine the relationship between the independent variable and the dependent variable.
Therefore, when a confounding variable is present in an experiment, one cannot tell whether the results were due to
the independent variable or the dependent variable.
Consequently, researchers must take steps to identify and eliminate or control the effect of confounding variables to obtain valid and reliable results.
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the number 57 belongs to which of the following sets of the numbers? N only, N, W and Z only, N, W, Z, and Q only, All of the following: N, W, Z, Q, and R
The number 57 belongs to the sets Z, Q, and R, but not N or W.
What are natural numbers ?
Natural numbers are the counting numbers that we use to represent quantities and perform arithmetic operations. These are the numbers that we use to count objects, such as apples, books, or people.
The number 57 belongs to the following sets of numbers:
N (the natural numbers): No, because 57 is not a counting number.
W (the whole numbers): No, because 57 is not a non-negative integer.
Z (the integers): Yes, because 57 is an integer (a positive integer, in fact).
Q (the rational numbers): Yes, because 57 can be written as a ratio of two integers (57/1).
R (the real numbers): Yes, because every rational number is also a real number.
Therefore, the number 57 belongs to the sets Z, Q, and R, but not N or W.
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Complete question -
water is leaking out of an inverted conical tank at a rate of 10,500 cm3/min at the same time that water is being pumped into the tank at a constant rate. the tank has height 6 m and the diameter at the top is 4 m. if the water level is rising at a rate of 20 cm/min when the height of the water is 2 m, find the rate (in cm3/min) at which water is being pumped into the tank.
The rate at which water is being pumped into the tank is 11,760 cm3/min.
How to find rate?The formula for the volume of a conical tank is:V = (1/3)πr2h
Where r is the radius of the tank, and h is the height of the tank.Find the radius of the tank at a height of 2 m.Using similar triangles:
(r / 2) = (2 / 6)
r = 2/3 * 4r = 8/3 cm
The formula for the rate of change of volume of a conical tank is:dV / dt = (πr2 / 3)dh / dt
dV / dt = pump rate - leak rate
= pump rate - 10,500 cm3/mindh / dt
= 20 cm/minr = 8/3 cm
Plug in the values:pump rate - 10,500 = (π(8/3)2 / 3) * 20pump rate - 10,500
= 2114.67pump rate
= 11,760 cm3/min
Therefore, the rate at which water is being pumped into the tank is 11,760 cm3/min.
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