For f(x) = 3x³ + 20x² + 14x - 65, there are no vertical, horizontal, or oblique asymptotes.
For f(x) = x² + 8x + 15, there are no vertical, horizontal, or oblique asymptotes either.
To find the vertical, horizontal, and oblique asymptotes of a function, we need to analyze its behavior as x approaches positive or negative infinity.
For the function f(x) = 3x³ + 20x² + 14x - 65:
Vertical asymptotes occur when the function approaches infinity or negative infinity as x approaches a certain value. By observing the coefficients of the terms, we can see that there are no factors in the denominator that would cause vertical asymptotes. Hence, there are no vertical asymptotes for this function.
Horizontal asymptotes are determined by analyzing the leading terms of the function as x approaches positive or negative infinity. In this case, the leading term is 3x³. As x approaches infinity or negative infinity, the cubic term dominates, so the horizontal asymptote is y = 3x³.
Oblique asymptotes (also known as slant asymptotes) occur when the degree of the numerator is one greater than the degree of the denominator. In this case, the degree of the numerator is 3 and the degree of the denominator is 0. Therefore, there are no oblique asymptotes.
For the function f(x) = x² + 8x + 15:
Vertical asymptotes: Again, there are no factors in the denominator that would cause vertical asymptotes. Thus, there are no vertical asymptotes.
Horizontal asymptotes: The degree of the numerator (2) is equal to the degree of the denominator (0), so there is no horizontal asymptote.
Oblique asymptotes: As the degree of the numerator is equal to the degree of the denominator, there are no oblique asymptotes.
In summary, for f(x) = 3x³ + 20x² + 14x - 65, there are no vertical, horizontal, or oblique asymptotes.
For f(x) = x² + 8x + 15, there are no vertical, horizontal, or oblique asymptotes either.
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The path a character takes to navigate a level of a video game is given in the follo
What is the domain?
uestion
-6 ≤ x≤4
-6 ≤ x ≤4,x ≠-6,2
-12 ≤x ≤10
-12 ≤x ≤10,x≠-6,6
The domain refers to the set of possible input values for a function. In the given question, the character's path in a video game is described using different inequalities. To find the domain, we need to identify the valid values for the variable x that satisfy all the given conditions.
From the first inequality, -6 ≤ x ≤ 4, we see that x can take any value between -6 and 4, inclusive.
Moving to the second inequality, -6 ≤ x ≤ 4, x ≠ -6, 2, we can see that x cannot be equal to -6 or 2, but it can still take any other value between -6 and 4.
Finally, in the third inequality, -12 ≤ x ≤ 10, x ≠ -6, 6, we find that x cannot be equal to -6 or 6, but it can still take any other value between -12 and 10.
Therefore, the domain of the character's path in the video game is the set of values for x that satisfy all the given conditions, which is -12 ≤ x ≤ 4, x ≠ -6, 2, 6.
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An experiment was used to test a new migraine medicine. Each participant took either the new medicine or a placebo
then waited for one hour to see if the headache went away or remained. The results are compiled in the contingency
table below. Use the table to answer the questions.
Went Away| Medicine| Placebo
Remained|. 120. |. 68
18. | 44
Your answers should be exact numerical values.
There were
participants whose headache remained.
The probability of randomly selecting an individual whose headache remained is
There were
participants whose headache remained and took a placebo.
The probability of randomly selecting an individual whose headache remained and took a placebo is
1) Number of participants whose headache remained is: 62
2) The probability of randomly selecting an individual whose headache remained is: 0.4133
3) The probability of randomly selecting an individual whose headache remained and took a placebo is: 0.2933
How to find the probability of random selection?From the table, we have the parameters as:
Number of participants that took medicine and headache went away = 120
Number of participants that took placebo and headache went away = 68
Number of participants that took and headache remained = 18
Number of participants that took placebo and headache remained = 44
1) Number of participants whose headache remained = 18 + 44 = 62
2) The probability of randomly selecting an individual whose headache remained is:
62/(62 + 120 + 68)
= 62/150
= 0.4133
3) The probability of randomly selecting an individual whose headache remained and took a placebo is:
44/150 = 0.2933
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Please help! Will give brainliest
Which is a step in proof by mathematical induction?
Substitute n = k + 2 into the formula.
Prove the formula is true for n = k.
Assume that the formula is true for the (k + 1) term.
Assume the formula is true for some other value.
Answer:
Assume that the formula is true for the (k + 1) term
Step-by-step explanation:
Proof by mathematical induction is a method of proving that a statement is true for all natural numbers.
The proof has three steps:
Base case: Prove that the statement is true for n = 1.Inductive step: Assume that the statement is true for n = k. Prove that the statement is also true for n = k + 1.Conclusion: By the principle of mathematical induction, the statement is true for all natural numbers n.In the step "Assume that the formula is true for the (k + 1) term", we are assuming that the statement is true for some value of n, say k.
We then use this assumption to prove that the statement is also true for the next value of n, k + 1.
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a sprayer discharges 600cc of herbicide in 45 sec. For what period of the time should be discharged in order to apply 2000 cc of herbicide
We have:
[tex]$\frac{600\text{ cc}}{45\text{ seconds}} = \frac{2000\text{cc}}{x \text{ seconds}}[/tex]
Cross multiplying, we get:
[tex]$600x = 90000$[/tex]
We divide both sides by 600 and get:
[tex]$\frac{600x}{600} = \frac{90000}{600}$[/tex]
[tex]$x=\boxed{150}$[/tex]
It takes 150 seconds (2 minutes and 30 seconds) for the sprayer to disperse 2000 cc of herbicide. Hope this helps!
the drawing for a rectangular room is 3 3/8 in wide by 5 3/4 in long. if the room is actually 124 ft long, find the actual width of the room to the nearest tenth of a foot
Answer:
Width = 7.3 feet
Step-by-step explanation:
Step 1: Find the scale of the drawing:
The scale is the ratio of the length of the drawing to the actual length of the room. In this case, the scale is 5 3/4 in / 124 ft.Step 2: Convert feet to inches:
Since we need to work with the same units, let's convert feet to inches: 1 ft = 12 in, so 124 ft = 124 * 12 in = 1488 in. Now, the scale is (5 3/4 in) / (1488 in).Step 3: Simplify the fraction:
Simplifying this fraction, we get (23/4) / (1488) = 23 / (4 * 1488) = 23 / 5952.Thus, the simplified fraction is 23/5952.
Step 4: Find the actual width of the room:
The actual width is the width of the drawing divided by the scale: (3 3/8 in) / (23 / 5952).Step 5: Simplify the fraction:
Simplifying this fraction, we get: (27/8 in) / (23 / 5952) = (27/8) * (5952/23) in = (27 * 5952) / (8 * 23) in ≈ 87.30434782608696 in.Step 6: Convert inches to feet:
Converting inches to feet, we get `87.30434782608696 in = 87.30434782608696 / 12 ft ≈ 7.27536231884058 ft`.Step 7: Round to the nearest tenth of a foot:
Rounding to the nearest tenth of a foot, we get **7.3 ft**.
Thus, the actual width of the room is about 7.3 ft.
classify the following differential equation s given in both standard and differential form. Q5 only
Which solution below is considered to have basic character? Group of answer choices pOH = 13 pH = 2 None of these pOH = 7 pOH = 4
The correct answer would be "None of these" since none of the provided options indicate a basic solution.
The solution with a pH of 2 is considered to have basic character. The pH scale measures the acidity or alkalinity of a solution, ranging from 0 to 14. A pH value below 7 indicates acidity, while a pH above 7 indicates alkalinity. Thus, a pH of 2 is highly acidic and not basic.
On the other hand, the pOH scale is the inverse of the pH scale and measures the concentration of hydroxide ions (OH-) in a solution. A higher pOH value indicates a higher concentration of hydroxide ions and a more basic solution. Therefore, a pOH of 13 or 4 would suggest a basic solution.
Considering the given answer choices, neither pOH = 13 nor pOH = 4 is considered to have basic character.
It's important to note that the pOH scale is less commonly used in everyday situations compared to the pH scale when discussing the acidity or basicity of a solution. So, the correct answer is none of these.
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HCF of 560 and 729 :)
The HCF of 560 and 729 is 1.
To find the HCF of 560 and 729, we use the Euclidean algorithm as follows;HCF of 560 and 729:Step 1: Divide the larger number by the smaller number, then find the remainder.729 ÷ 560 = 169 remainder 169Step 2: Divide the smaller number (i.e., 560) by the remainder (i.e., 169).560 ÷ 169 = 3 remainder 53.
Step 3: Divide the remainder from step 1 (i.e., 169) by the remainder from step 2 (i.e., 53).169 ÷ 53 = 3 remainder 10Step 4: Divide the remainder from step 2 (i.e., 53) by the remainder from step 3 (i.e., 10).53 ÷ 10 = 5 remainder 3Step 5: Divide the remainder from step 3 (i.e., 10) by the remainder from step 4 (i.e., 3).10 ÷ 3 = 3 remainder 1.
Step 6: Divide the remainder from step 4 (i.e., 3) by the remainder from step 5 (i.e., 1).3 ÷ 1 = 3 remainder 0The HCF of 560 and 729 is the last non-zero remainder, which is 1.
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4y=2x nonportional or portional
The relationship described by the equation 4y = 2x is proportional.
The relationship in the equation 4y = 2x is proportional. By simplifying the equation, we got that y = (1/2)x, which shows that y is directly proportional to x. In a proportional relationship, the ratio of y to x always remains constant.
In this scenerio, the constant of proportionality is 1/2. As x increases or decreases, y also increases or decreases by half of x.
So, the relationship between y and x in this equation is proportional, indicating that changes in x will result in corresponding proportional changes in y.
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The question is:-
Is the relationship described by the equation 4y = 2x proportional or non-proportional?
State the restrictions then simplify
Answer:
Restrictions:
x ≠ -1/5; x ≠ 1
Answer:
[tex] \dfrac{5x - 9}{x - 1} [/tex]
Step-by-step explanation:
[tex] \dfrac{25x^2 - 40x - 9}{5x^2 - 4x - 1} = [/tex]
[tex] = \dfrac{25x^2 - 45x + 5x - 9}{5x^2 - 5x + x - 1} [/tex]
[tex] = \dfrac{5x(5x - 9) + 1(5x - 9)}{5x(x - 1) + 1(x - 1)} [/tex]
[tex] = \dfrac{(5x + 1)(5x - 9)}{(5x + 1)(x - 1)} [/tex]
[tex] = \dfrac{5x - 9}{x - 1} [/tex]
5x + 1 = 0
x = -1/5
x - 1 = 0
x = 1
Restrictions:
x ≠ -1/5; x ≠ 1
Answer:
[tex] \dfrac{5x - 9}{x - 1} [/tex]
Mr. Selan gave his class two tests. 32% of the class passed both tests. and 70% of the
class passed the first test. What percent of those who passed the first test also passed the
second test?
A. About 22%
B. About 32%
C. About 38%
D. About 46%
o find the percent of those who passed the first test and also passed the second test, we can use the concept of conditional probability.
Given that 32% of the class passed both tests, and 70% of the class passed the first test, we want to determine the percentage of those who passed the first test and also passed the second test.
We can set up the calculation as follows:
Percentage = (Number of students who passed both tests) / (Number of students who passed the first test)
Since 32% of the class passed both tests and 70% of the class passed the first test, we can substitute these values into the equation:
Percentage = (0.32) / (0.70)
Calculating this division, we find:
Percentage ≈ 0.4571
Converting this to a percentage, we get approximately 45.71%.
Therefore, the correct answer is:
D. About 46% (rounded to the nearest percent).
The question is about percentages and the correct answer is that approximately 46% of the students who passed the first test also passed the second one.
Explanation:The student's question is about the concept of percentages, a basic concept in Mathematics. The problem mentioned is about calculating the percentage of students who passed both tests out of those who passed the first one.
Given that 32% of the entire class passed both tests and that 70% of the class passed the first test, to find the percentage of students who passed the first test and also the second one, one can use the following steps:
First, write down the percentages as fractions. In this case, the percentage of those who passed both tests is 0.32 and for those who passed the first test is 0.70.Second, divide the two fractions. That is, divide 0.32 by 0.70.Third, multiply the resulting number by 100 to get the percentage.Using these steps, you would find out that approximately 46% of the students who passed the first test also passed the second one. Therefore, D. About 46% is the correct answer.
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Explain why all solutions must be non-zero for this polynomial function. An algebraic argument must be provided for full credit. Graphing by hand or with technology will be granted partial credit unless the evidence on the graph is supported with algebra.
Answer:
For a polynomial function, if any of its solutions were zero, that would mean that its corresponding factor is zero. Thus, the polynomial would have a factor of zero, which would make the entire polynomial zero. In other words, if there were a solution of zero, that solution would be a root of the polynomial function.
However, a polynomial function can only have a finite number of roots, which is equal to its degree. Therefore, if a polynomial function had a solution of zero, that would mean that it has one more root than its degree, which is impossible. This is because a polynomial function with degree n can have at most n roots.
Therefore, all solutions of a polynomial function must be non-zero, or in other words, the function must have no roots of zero. This ensures that the polynomial function has the correct number of roots, which is equal to its degree.
This argument applies to all polynomial functions, regardless of their degree or coefficients. Therefore, it is a general property of polynomial functions that all of their solutions must be non-zero.
Here is a list of numbers. 51 38 48 36 39 40 39 47 a) Work out the range of the numbers in the list. b) Work out the median of the numbers in the list.
Answer:
a) Range = 15
b) Median = 39.5
Step-by-step explanation:
Here, we are given a list of numbers and asked to find the range and median.
In a data set, range is the difference between the highest and lowest numbers. On the other hand, the median is the middle number when the data is in ascending order (from lowest to highest). When there are two middle numbers, add the numbers and divide by two to find the median of the data set.
Given data set: 51, 38, 48, 36, 39, 40, 39, 47
Step 1: List the data in ascending order.
36, 38, 39, 39, 40, 47, 48, 51
Step 2: Find the range (highest - lowest).
36, 38, 39, 39, 40, 47, 48, 51
51 - 36 = 15
Step 3: Find the median (middle number).
36, 38, 39, 39, 40, 47, 48, 51
(39 + 40)/2 = 79/2 = 39.5
Range:
15
Median:
39.5 (79/2 in fraction form)
Explanation:
When looking for the range, just remember that it is the difference between the largest number and the smallest one. In other words:
[tex]\textsf{Range = Largest Number - Smallest Number}[/tex]
The largest number is 51, an the smallest one is 36. So the range is:
Range = 51 - 36
= 15
To find the median, we'll first list the numbers from least to greatest:
36, 38, 39, 39, 40, 47,48, 51
Since we have 8 numbers in the list, we find the mean of the two numbers in the middle, i.e., 39 and 40:
39 + 40
79 / 2
39.5
Hence, these are the answers.
2. Find the linear approximation to ()=√3 at =64. Use it to approximate √653. Report your answer to 4 decimal places.
Answer:1.9975
Step-by-step explanation:
The computation of the linear approximation of the given function is shown below:
L(x) = 2 - 1 ÷ 4(x)
As we are looking for √3.9
So here
x = 0.1
So
= 4 - 0.1
= 3.9
Now
L(0.1) = f(3.9) = 2 - (0.1 ÷ 4)
= 1.975
now
substitute the x = 0.01
Then
L(0.01) = f(3.99) = 2 - (0.01 ÷ 4)
= 1.9975
We simply applied the above equations
At the pharmacy, there are two shelves that contain customer prescriptions. frac(3,6) of the first shelf and frac(2,6) of the second shelf have been picked up by customers. How many shelves of prescriptions in total have been picked up? Add frac(3,6)+frac(2,6), and write the answer in lowest terms.
Answer:
[tex]\frac{5}{6}[/tex] of the shelves of prescriptions have been picked up.
Step-by-step explanation:
First, let's write out the problem they want us to solve.
[tex]\frac{3}{6} +\frac{2}{6}[/tex]
Since the denominators are the same, we know our answer will have the same denominator, 6, and a numerator of whatever the two numerators, 3 and 2, totals.'
[tex]\frac{3}{6} +\frac{2}{6}=\frac{3+2}{6} =\frac{5}{6}[/tex]
Since 5 can't go into 6, we know the fraction can't be simplified. So, [tex]\frac{5}{6}[/tex] of the shelves of prescriptions have been picked up.
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Determine la fuerza electrostática ejercida por una carga de 16.9 µC sobre otra carga de 60.7 µC si se encuentran separadas a una distancia de 3.93 cm.
hagan paro neta estoy en examen
The electrostatic force between the two charges is 5,977.68 N.
What is the electrostatic force between the two charges?The electrostatic force between the two charges separated by the given distance is calculated by applying Coulomb's law.
F = kq₁q₂ / r²
where;
k is the Coulomb's constantq₁ is the magnitude of the first chargeq₂ is the magnitude of the second charger is the distance between the charges = 3.93 cm = 0.0393 mThe electrostatic force between the two charges is calculated as follows;
F = (9 x 10⁹ x 16.9 x 10⁻⁶ x 60.7 x 10⁻⁶ ) / ( 0.0393 )
F = 5,977.68 N
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Find an equation of the ellipse that has center (4,0), a minor axis of length 4, and a vertex at (4,-4)
Answer:
(x-4)²/16 + y²/4 = 1
Step-by-step explanation:
To find the equation of the ellipse, we need to determine the length of the major axis. Since the minor axis has length 4, and the vertex is at (4,-4), the distance from the center to the vertex is 4. Therefore, the major axis has length 8. Thus, the equation of the ellipse is
(x-4)²/16 + y²/4 = 1.
Althea needs 106 ounces of cold cuts for a party. How many pounds and ounces does she need?
Find the sample variance of the following set of data: 5, 6, 11, 11, 9, 6. Select the correct answer below: 10.2 8.2 9.2 5.2 7.2
The sample variance of the given set of data is 7.2. The correct answer is 7.2.
To find the sample variance of the given set of data, follow these steps:
1. Calculate the mean of the data set:
Mean (μ) = (5 + 6 + 11 + 11 + 9 + 6) / 6 = 48 / 6 = 8
2. Calculate the difference between each data point and the mean, and square each difference:
[tex](5 - 8)^2 = 9 \\ (6 - 8)^2 = 4 \\ (11 - 8)^2 = 9 \\ (11 - 8)^2 = 9 \\ (9 - 8)^2 = 1[/tex]
[tex](6 - 8)^2 = 4[/tex]
3. Calculate the sum of all the squared differences:
9 + 4 + 9 + 9 + 1 + 4 = 36
4. Calculate the sample variance:
Variance [tex](s^2)[/tex] = sum of squared differences / (n - 1)
= 36 / (6 - 1)
= 36 / 5
= 7.2
Therefore, the provided set of data has a sample variance of 7.2. The right response is 7.2.
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Ashley is serving her child french fries and chicken wings for lunch today. Let f be the number of french fries in the lunch, and let c be the number of chicken wings. Each french fry has 25 calories, and each chicken wing has 100 calories.
Ashley wants the total calorie count from the french fries and chicken wings to be less than 500 calories. Using the values and variables given, write an inequality describing this.
The difference is: [tex]500 = (25 \times f) + (100 \times c)[/tex]
To write the inequality describing the total calorie count, we need to consider the calorie count of the french fries and chicken wings and ensure that it is less than 500 calories.
Let's start by defining the variables:
Let f be the number of french fries.
Let c be the number of chicken wings.
Next, we can determine the total calorie count for the french fries and chicken wings:
The number of calories per french fry is 25.
The number of calories per chicken wing is 100.
To calculate the total calorie count, we multiply the number of french fries by the calorie count per french fry and the number of chicken wings by the calorie count per chicken wing. Then, we sum the two values:
Total calorie count = [tex](25 \times f) + (100 \times c)[/tex]
We want this total to be less than 500 calories, so we can write the inequality as:
[tex](25 \times f) + (100 \times c) < 500[/tex]
This inequality ensures that the sum of the calories from the french fries and chicken wings is less than 500.
By varying the values of f and c within the constraints of the inequality, Ashley can ensure that the total calorie count for the lunch remains within her desired limit.
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find the sum of the angle measures of the polygon.
a 17 sided polygon.
Answer:
The sum of the interior angles =
(n-2)*180
= (17-2)*180
= 2700°
hope this helps
Help please!!! What was the number of small, medium, and large pizzas delivered to the college?
In the word problem above, 0 small pizzas, 1 medium pizza, and 5 large pizzas were delivered to the college.
How is this so?Let S = number of small pizzas delivered
Let M = number of medium pizzas delivered
Let L = number of large pizzas delivered
We'll start by solving equation 1 for one variable and substituting it into the other equations.
S + M + L = 12
We can rewrite this equation as -
S = 12 - M - L
Now, substitute this value of S in equations 2 and 3 -
4S + 10M + 15L = 109
4(12 - M - L) + 10M + 15L = 109
48 - 4M - 4L + 10M + 15L = 109
6M + 11L = 61
2S + 4M + 13L = 81
2(12 - M - L) + 4M + 13L = 81
24 - 2M - 2L + 4M + 13L = 81
2M + 11L = 57
Now we have a system of two equations with two variables -
6M + 11L = 61 ...(4)
2M + 11L = 57 ...(5)
Subtract equation (5)from equation (4) -
(6M + 11L) - (2M +11L) = 61 - 57
4M = 4
M = 1
Substitute the value of M into equation (5) -
2(1) + 11L = 57
2 + 11L = 57
11L = 55
L = 5
Now substitute the values of M and L into equation (1) -
S + 1 + 5 = 12
S + 6 = 12
S = 6 - 6
S = 0
Therefore, the solution is -
S = 0 (no small pizzas)
M = 1 (1 medium pizza)
L = 5 (5 large pizzas)
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Full Question:
Although part of your question is missing, you might be referring to this full question:
a pizza shop delivered 12 pepperoni pizzas to a college on the first night of final exams. the total cost of the pizzas was $109. a small pizza costs $4 and contains 2 ounces of pepperoni. a medium pizza costs $10 and contains 4 ounces of pepperoni. a large pizza cost $15 and contains 13 ounces of pepperoni. the owner of the pizza shop used 5 pounds 1 ounces of pepperoni in making the 12 pizzas. how many pizzas of each size were delivered to the college?
In an alloy of gold and silver the ratio of the amount of gold to the amount of silver is 2:5. What is the weight of gold in the alloy if there are 80g of silver?
Answer:
2/5 = g/80
5g = 160, so g = 32 grams of gold
Solve for x. cos(6x) = sin(3x - 9)
A. x = 10 B. x = 11 C. x = -10 D. x = 12
The solution to the equation cos(6x) = sin(3x - 9) from the given options is x = -10. Option C.
To solve the equation cos(6x) = sin(3x - 9) according to the given options, we can substitute each option into the equation and check if it satisfies the equation.
A. x = 10:
cos(6 * 10) = sin(3 * 10 - 9)
cos(60) = sin(21)
However, cos(60) does not equal sin(21), so x = 10 is not a solution.
B. x = 11:
cos(6 * 11) = sin(3 * 11 - 9)
cos(66) = sin(24)
Again, cos(66) does not equal sin(24), so x = 11 is not a solution.
C. x = -10:
cos(6 * -10) = sin(3 * -10 - 9)
cos(-60) = sin(-39)
Interestingly, cos(-60) does equal sin(-39). Therefore, x = -10 satisfies the equation cos(6x) = sin(3x - 9). Thus, C. x = -10 is a solution.
D. x = 12:
cos(6 * 12) = sin(3 * 12 - 9)
cos(72) = sin(27)
Once again, cos(72) does not equal sin(27), so x = 12 is not a solution.
In summary, the solution to the equation cos(6x) = sin(3x - 9) from the given options is x = -10, which corresponds to option C.
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Answer: Its B (11)
Step-by-step explanation:
I did the test
find x.
please and thank youuu
Answer:
x = 4√2
Step-by-step explanation:
Identifying the triangle in the diagram:
Whenever you see a right angle (its measure is 90°) and a 45°, the measure of the third angle is also 45° and the triangle is called a 45-45-90 triangle which has special rules, as it relates to the lengths of its sides.45-45-90 triangle rules:
The two sides across from the 45° are congruent and their lengths are x units long.The hypotenuse (always across from the right angle) is the longest side and its length is x√2 units long.Finding x:
Since the hypotenuse is 8 units long and, we can find x by setting 8 equal to x√2:
(8 = x√2) / √2
8/√2 = x
Rationalize the denominator to simplify:
When you have a fraction with a root as the denominator, we simplify (i.e. rationalize the denominator) by multiplying both the numerator and denominator by the root, which clears the root on the denominator:(8/√2) * (√2/√2)
8√2 / 2
4√2
Thus, x = 4√2
“ select two points to the final line where the polygon will break into two pieces find the area of each figure to determine the area of a composite figure. The area of the rectangle is 44M squared the area of the circle is about _M squared. _The area of the circle by two to find the area of a semicircle to find the area of the composite figure, _The area of the rectangle and the area of a semicircle
The area of the composite figure is
Area of the semi circle + Area of the rectangle.
Formula for the area of a circle is
π x r²
= 3.14 x (2)²
= 3.14 x 4
≈ 12.57
Formula for the area of the rectangle is
L x B
= 4 x 11
= 44m²
Since the area of the semi circle = Area of circle /2
⇒ (πr²)/2
= 12.57/2
= 6.29
Hence are of the composite shape is
6.29 + 44
≈ 50.29m²
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Full Question:
See attached image.
A 2010 U.S. Census Bureau report indicated there are 4,229,138 residents of Indiana’s aged 25 and older. What percentage of the residents aged 25 and older have a degree if there are 326,036 residents with an associates degree, 623,200 with a bachelor’s, and 348,807 with either a graduate or professional degree? Write your answers as a percent rounded to the nearest whole number.
The percentage of residents aged 25 or older with Associate degrees, Bachelor,s degrees, and either graduate or professional degrees is 31%.
Given: Let the total number of residents aged 25 and older with associate degrees, bachelor,s degrees, and either graduate or professional degrees be "x" and the total number of residents of Indiana’s aged 25 and older be "y".
Therefore,
x= 326036 + 623200 + 348807
x=1298043 &
y=4,229,138
Percentage = (x/y)*100
Percentage = (1298043/4229138)*100
Percentage = 30.6% = 31%
So, the percentage of residents aged 25 or older with Associate degrees, Bachelor,s degrees, and either graduate or professional degrees is 31% (rounded to the nearest whole number).
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2. Find the linear approximation to ()=√3 at =64. Use it to approximate √653. Report your answer to 4 decimal places.
The linear approximation of √653 is approximately 24.8163.
To find the linear approximation to a function at a given point, we can use the formula:
L(x) = f(a) + f'(a)(x - a)
where L(x) is the linear approximation, f(a) is the value of the function at point a, f'(a) is the derivative of the function at point a, and (x - a) represents the difference between the given point x and the approximation point a.
In this case, we are given f(x) = √3 and we want to approximate √653 using the linear approximation. Let's find the linear approximation first.
Taking the derivative of f(x) = √3, we get:
f'(x) = 1 / (2√3)
Now, let's evaluate the linear approximation at a = 64:
L(x) = √3 + (1 / (2√3))(x - 64)
Substituting x = 653 into the linear approximation equation:
L(653) = √3 + (1 / (2√3))(653 - 64)
L(653) ≈ √3 + (1 / (2√3))(589)
L(653) ≈ √3 + (1 / (2√3))(589)
Calculating this approximation, we get:
L(653) ≈ √3 + (1 / (2√3))(589) ≈ 24.8163
Therefore, the linear approximation of √653 is approximately 24.8163, rounded to 4 decimal places.
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Apply fourth-order Runge-Kutta method to find an approximate value of y when x = 1/5, given that
[tex] \frac{dy}{dx} = x + y[/tex]
y = 1, when x = 0 with h = 0.1
Answer:
To apply the fourth-order Runge-Kutta method, we can use the following steps:
Given:
Initial condition: y = 1 when x = 0
Step size: h = 0.1
We want to find the approximate value of y when x = 1/5.
The fourth-order Runge-Kutta method involves the following steps:
Set up the following equations:
k1 = hf(x, y)
k2 = hf(x + h/2, y + k1/2)
k3 = hf(x + h/2, y + k2/2)
k4 = hf(x + h, y + k3)
Update the values:
y = y + (k1 + 2k2 + 2k3 + k4)/6
x = x + h
Repeat steps 1 and 2 until the desired x-value is reached.
Let's apply these steps to find the approximate value of y when x = 1/5:
Step 1:
x = 0, y = 1
h = 0.1
k1 = 0.1 * f(x, y) = 0.1 * f(0, 1)
k2 = 0.1 * f(x + h/2, y + k1/2) = 0.1 * f(0 + 0.1/2, 1 + k1/2)
k3 = 0.1 * f(x + h/2, y + k2/2) = 0.1 * f(0 + 0.1/2, 1 + k2/2)
k4 = 0.1 * f(x + h, y + k3) = 0.1 * f(0 + 0.1, 1 + k3)
Step 2:
y = y + (k1 + 2k2 + 2k3 + k4)/6
x = x + h
Repeat steps 1 and 2 until x = 1/5.
Performing these calculations step by step will yield the approximate value of y when x = 1/5 using the fourth-order Runge-Kutta method.
Step-by-step explanation:
A stockholder sold her shares and made a profit of 1328 if that is a profit of 25% how much were the shares worth when she originally purchased them?
To determine the original worth of the shares, we can use the concept of profit as a percentage of the original value. Since the profit is 25% of the original value, we can set up the following equation:
Profit = Original Value x Percentage
1328 = Original Value x 0.25
To solve for the Original Value, we can divide both sides of the equation by 0.25:
Original Value = 1328 / 0.25
Original Value = 5312
Therefore, the shares were worth $5312 when she originally purchased them.
