The hypothesis in the given mathematical conditional statement 'If the sum of two angles is 90°, then the angles are complementary.' is 'the sum of two angles is 90°'.
Explanation:In a conditional statement in mathematics, the 'if' part of the statement is called the hypothesis and the 'then' part is termed the conclusion. Given the statement 'If the sum of two angles is 90°, then the angles are complementary.', the hypothesis of this statement is 'the sum of two angles is 90°'.
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In a conditional statement, the hypothesis is the condition that needs to be met. In this case, the hypothesis of the statement 'If the sum of two angles is 90°, then the angles are complementary,' is 'the sum of two angles is 90°.'
Explanation:In the context of the given conditional statement, 'If the sum of two angles is 90°, then the angles are complementary,' the hypothesis refers to the clause immediately after 'if.' This indicates the condition that needs to be fulfilled for the conclusion to be considered valid. Therefore, the hypothesis for this statement is 'the sum of two angles is 90°'.
After the 'if,' the hypothesis is given, and after the 'then,' you find the conclusion. The conclusion in this case is 'the angles are complementary.'
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The population of a town in 2000 was 430. The population is increasing at a rate of 0.9% every year. What will be the projected population of the town in 2010? Round your answer to the nearest whole number
If the mean of a symmetric distribution is 82, which of these values is most likely to be the median of the distribution? A.92 B. 85 C.78 D.82
Use newton's method to find the absolute minimum value of the function f(x)=x2+sinx correct to six decimal places.
The solution would be like this for this specific problem:
f(x) = x^2 + sin(x)
f '(x) = 2x + cos(x)
The minimum value is at f '(x) = 0,
So, let g(x) = 2x + cos(x)
Thus, g '(x) = 2 - sin(x)
x(new) = x - g(x) / g '(x)
or
x(new) = x - [2x + cos(x)] / [2 - sin(x)]
Calculation
x1 = -0.5 - [2 * -0.5 + cos(-0.5)] / [2 - sin(-0.5)]
= -0.4506266931
x2 = -0.4501836476
x3 = -0.4501836113
x4 = -0.4501836113
This value for x, f(x) = -0.2324655752.
After converting to 6 decimal places: the minimum point is (-0.450184,
-0.232466).
Final answer:
To find the absolute minimum value of f(x)=x^2+sin(x), use Newton's method with Newton-Raphson iteration x_{n+1} = x_n - f(x_n)/f'(x_n). Start with an initial guess and iterate until the result converges to six decimal places, ensuring the second derivative at the critical point is positive.
Explanation:
To find the absolute minimum value of the function f(x)=x^2+sin(x) correct to six decimal places, we can use Newton's method. Newton's method helps to find successively better approximations to the roots (or zeroes) of a real-valued function. First, we need to find the derivative of the function, which gives us f'(x) = 2x + cos(x). We are looking for a critical point where the derivative is zero because this could indicate a potential minimum (or maximum).
Starting with an initial guess, we can apply the Newton iteration formula x_{n+1} = x_n - f(x_n)/f'(x_n) to find a better approximation. In this case, let's choose an initial guess close to the root of f'(x). Since we do not have the specific initial guess, we would theoretically pick a value near the expected minimum and iterate until the difference between consecutive approximations is less than the desired tolerance, which is the change in six decimal places.
The Newton-Raphson iteration would be applied repeatedly until convergence is seen at six decimal places. Note that in practice, one must also check the second derivative f''(x) at the found critical point to confirm it is a minimum (it should be positive).
Express the number as a ratio of integers. 7.5336
Determine the factors of 15x2 + 3xy + 10x + 2y. (4 points)
(3x + 2)(5x + y)
(5x + y)(2x + 3)
(3x + y)(5x + 2)
(5x + 3)(2x + y)
Answer:
the answer is the first option : A
Step-by-step explanation:
What is the surface area of the square pyramid?
(Figure is not drawn to scale.)
A ______ is an expression that can be written in the form of p/q where p and q are polynomials and q
The quadratic function y = –10x2 + 160x – 430 models a store’s daily profit (y) for selling a T-shirt priced at x dollars. What equation do you need to solve to find the selling price or prices that would generate $50 in daily profit? What method would you use to solve the equation? Justify your choice.
a. The required equation is x² - 16x + 48 = 0
b. I would use factorisation to solve it and the selling prices that would generate a daily profit of $50 are $4 and $12 respectively.
a.
The required equation is x² - 16x + 48 = 0
The required equation
Since the quadratic function y = -10x² + 160x - 430 models a store’s daily profit (y) for selling a T-shirt priced at x dollars. Since we require a profit of $50, then y = 50.
So, y = -10x² + 160x - 430
-10x² + 160x - 430 = 50
-10x² + 160x - 430 - 50 = 0
-10x² + 160x - 480 = 0
Dividing through by -10, we have
x² - 16x + 48 = 0
So, the required equation is x² - 16x + 48 = 0
b.
I would use factorisation to solve it and the selling prices that would generate a daily profit of $50 are $4 and $12 respectively.
The methodTo determine the method you would use to solve the equation, you would need to determine the value of the discriminant.
DiscriminantFor a quadratic equation ax² + bx + c = 0, the discriminant is D = b² - 4ac
Since x² - 16x + 48 = 0 and its discriminant D = (-16)² - 4 × 48
= 256 - 192
= 48
= 64 > 0 and is a perfect square, so it is factorizable. The equation would have real and distinct roots,
So, x² - 16x + 48 = 0
x² - 4x - 12x + 48 = 0
x(x - 4) - 12(x - 4) = 0
(x - 4)(x - 12) = 0
x - 4 = 0 or x - 12 = 0
x = 4 or x = 12
I would use factorisation to solve it and the selling prices that would generate a daily profit of $50 are $4 and $12 respectively.
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Four students get 90s on a test, three get 70s, 2 get 60s and one gets an 80. what is the mean test score in this group?
Final answer:
The mean test score for the group is calculated by summing the products of each unique score and the number of students who received it, then dividing by the total number of students. In this case, the mean test score is 77.
Explanation:
To calculate the mean test score for the group, you multiply each score by the number of students who received it, then sum all those products, and finally divide by the total number of students. Four students scoring 90 would contribute 4 x 90 = 360 to the total sum. Three students scoring 70 contribute 3 x 70 = 210. Two students scoring 60 contribute 2 x 60 = 120. One student scoring 80 adds 80 to the sum. The total sum of all scores is 360 + 210 + 120 + 80 = 770. Since there are a total of 10 students (4 + 3 + 2 + 1), the mean score is calculated as 770 ÷ 10 = 77. Therefore, the mean test score in this group is 77.
what is 17pi/4 in decimal form nearest the thousandth
17 x PI = 53.40707511
divided by 4 = 13.35176878
rounded to nearest thousandth = 13.352
write the number 32.56 corrrect to one decimal place
Use the equation and type the ordered-pairs.
y = log 3 x
{(1/3,____,)(1,___), (3,___),(9,____),(27,____),(81,___)}
Answer:
[tex]{(1/3, 0) , ( 1, 0.477), (3, 0.954), (9, 1.43), (27, 1.90), (81, 2.385)}\\[/tex]
Step-by-step explanation:
Here the "X" Values are given, thus the corresponding "Y" values will be
[tex]Y = log (3 X)\\a) X = \frac{1}{1} , Y = log (3 * \frac{1}{3} ) = log (1) = 0\\b) X = 1, Y = log (3*1) = log (3) = 0.477\\c) X = 3, Y = log (3*3) = log (9) = 0.954\\d) X = 9, Y = log (3*9) = log (27) = 1.43\\e) X = 27, Y = log (3* 27) = log (81) = 1.90\\f) X = 81, Y = log (3 * 81) = log (243) = 2.385\\[/tex]
So the pattern would be
[tex]{(1/3, 0) , ( 1, 0.477), (3, 0.954), (9, 1.43), (27, 1.90), (81, 2.385)}\\[/tex]
what is the domain and range for the following function and its inverse f(x) = x2 – 2
Answer:
x2-2 domain an range are 0, -2
Step-by-step explanation:
Find the volume of a sphere that has a surface area of 16 sq. in.
A. (32/3) cubic inches
B.8 cubic inches
C.(4/3) cubic inches
Answer:
A is the answer
Which of the following statements are true? I. -(-6) = 6 and -(-4) > -4 III. 5 + 6 = 11 or 9 - 2 = 11 II. -(-4) < 4 or -10 > 10 - 10 IV. 17 > 2 or 6 < 9
The answer would be an option (D) 17 > 2 or 6 < 9 because 17 is greater than 2 and 6 is less than 9 is always true.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
I. -(-6) = 6 and -(-4) > -4
Here -(-4) > -4 is incorrect
-(-4) = 4 is correct
These statements are not true
III. 5 + 6 = 11 or 9 - 2 = 11
Here 9 - 2 = 11 is incorrect
So 9 - 2 = 7 is correct
These statements are not true
II. -(-4) < 4 or -10 > 10 - 10
Here -(-4) < 4 is incorrect
So -(-4) = 4 is correct
These statements are not true
IV. 17 > 2 or 6 < 9
Here 17 is greater than 2 and 6 is less than 9 is always true.
Hence, the correct answer would be an option (D)
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Video studying aboard and she's requested required to pay $3,500 in u.s. dollars per year to the university however she must pay in Euros how many euros can be there except to pay per month to the university round to the nearest Point 7306equals one u.s. dollar
The area of a square is 2500 cm .what is the side legth of the painting?
What reference angle in the first quadrant corresponds to theta = -120? Answer in radians.
Answer:
Answer: Reference angle is π/3 Radians
Step-by-step explanation:
HELP
There are 20 alligators in the swamp. Each year, the number of alligators increases by 25%. There are 25 crocodiles in the swamp. Each year, 10 new crocodiles join the swamp.
Part A: Write functions to represent the number of alligators and crocodiles in the swamp throughout the years. (4 points)
alligators:
x = total number of alligators
n = number of years
x=20x1.25^n
crocodiles:
y = total number of crocodiles
n = number of years
y=25+10n
How high is a 40-foot ramp if it is propped at a 30 degree angle?
A district manager rewards sales teams based on overall sales generated in a month. The data for earnings are shown in the table, where Low represents the lowest sales and High represents the highest sales generated by a single sales team member.Team Low High Range Mean Median IQR σTeam X 1970 2970 1200 2571.9 2684 426.3 313.8Team Y 250 375 125 315.8 311 59 37.8Team Z 950 1900 950 1529.9 1473 276 180.7Part A: If the manager wants to award the sales team that has the most consistent earnings among its team members, which team should it choose and why? Justify your answer mathematically. (5 points)Part B: If the manager wants to award the sales team with the highest average earnings, which team should it choose and why? Justify your answer mathematically. (5 points)
help me create an extraneous radical equation please using this model!! :) thank you.
[tex]a \sqrt{x}+b + c = d[/tex]
I don't need you to solve it, just help me pick numbers for variable a, b, c, and d to create an extraneous solutuion
The function h(x) = x2 + 6x + 7 represents a parabola.
Part A: Rewrite the function in vertex form by completing the square. Show your work. (6 points)
Part B: Determine the vertex and indicate whether it is a maximum or a minimum on the graph. How do you know? (2 points)
Part C: Determine the axis of symmetry for h(x). (2 points)
Part A.
The given equation is:
y = x^2 + 6x + 7
By completing the square:
y = (x^2 + 6x + 9) + 7 – 9
y = (x + 3)^2 – 2
y + 2 = (x + 3)^2
Part B.
The vertex form of a parabola is in the form:
y – k = 4p (x – h)^2
Where (h, k) is the vertex (x, y) of the parabola.
Therefore the vertex: (-3, -2)
Since 4p = 1, a positive number, therefore the parabola opens up which makes the vertex (-3, -2) the minima of the graph.
Part C.
The Axis of Symmetry is the x - coordinate of the vertex which is x = - 3
WILL GIVE BRAINLIEST PLEASE HELP!!
What is the fifth term of the recursive formula an=2an-1 with the first term of 3?
A.
7
B.
17
C.
33
D.
65
write the expression in factored form: m²-n²
The graph and table shows the relationship between y, the number of words Jean has typed for her essay and x, the number of minutes she has been typing on the computer.
According to the line of best fit, about how many words will Jean have typed when she completes 60 minutes of typing?
2,500
2,750
3,000
3,250
The number of words Jean will type when she completes 60 minutes of typing is 3,000, This is further explained below Option C is correct
What is correlation?Correlation is simply a relationship that exists between events or objects, A relationship between mathematical variables that are subject to variation.
In conclusion, The graph and table show the relationship between y and x
And the graph shows 3000 at "the number of words Jean has typed for her essay" axis denoted by y, for what she completes 60 minutes.
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Find the 6th term of the sequence with t1 = -4 and tn = 5tn-1
Donna the trainer has two solo workout plans that she offers her clients: Plan A and Plan B. Each client does either one or the other (not both). On Friday there were 7 clients who did Plan A and 9 who did Plan B. On Saturday there were 5 clients who did Plan A and 3 who did Plan B. Donna trained her Friday clients for a total of 12 hours and her Saturday clients for a total of 6 hours.
How long does each of the workout plans last?
HELP ROUND 1.75170179212 TO 6 DECIMAL PLACES
Answer:
The answer is 1.751702
Step-by-step explanation:
In this number there are 11 decimal places which can be found after the decimal point.
1.75170179212
As we want 6 decimal places, we need to look at the digit to the right of sixth decimal place. Therefore:
1.75170179212
So, in this case, the digit in the seventh place is a '7'.
If we want to round a number, there are two ways:
If the digit is less than 5, you leave the sixth decimal as it is.If the digit is equal or greater than 5, you add 1 up to the sixth decimal.As the seventh decimal is a '7' which is greater than '5'.
We add a 1 to the Sixth decimal place.
As the sixth decimal place was a '1'. When we round it, it will be a 2
1.751702
If f(x)=x-7 and g(x)=x^3, what is G(f(x))?
A. x^3+x-7
B. x^3(x-7)
C. X^3-7
D. (x-7)^3
Answer:
D. [tex](x-7)^3[/tex]
Step-by-step explanation:
Given functions are,
[tex]f(x) = x-7-----(1)[/tex]
[tex]g(x)=x^3-----(2)[/tex]
Now,
[tex]g(f(x))=g(x-7)[/tex] ( From equation (1) ),
[tex]=(x-7)^3[/tex] ( From equation (2) ),
[tex]\implies g(f(x)) = (x-7)^3[/tex]
Hence, Option D is correct.