Answers
So the answer is choice B
Note: there are four zeros between the decimal point and the digit '4' in the value 0.0000416
Related Questions
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
Answers
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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PLEASE HELP.
Widget wonders produces widgets. They have found that the cost, c(x), of making x widgets is a quadratic function in terms of x.
The company also discovered that it cost $23 to produce 2 widgets, $103 to produce 4 widgets, and $631 to produce 10 widgets.
Find the total cost of producing 6 widgets.
Answers
y = ax^2 + bx + d
c (x) = ax^2 + bx + d
c (3) = a (3^2) + b (3) + d
c (3) = 9a + 3b + d = 15.50
c (7) = a (7^2 + b (7) + d
c (7) = 49a + 7b + d = 23.50
c (12) = a (12^2) + b (12) + d
c (12) = 144a + 12b + d = 56
solve using simultaneous equations... to get a b and d
use that to solve for x = 5
hope this helps?
Answer:
The total cost of producing 6 widgets is $231.
Step-by-step explanation:
Given : Widget wonders produces widgets. They have found that the cost, c(x), of making x widgets is a quadratic function in terms of x.
To find : The total cost of producing 6 widgets.
Solution :
Cost is given by [tex]c (x) = ax^2 + bx + d[/tex]
Cost $23 to produce 2 widgets,[tex]c(2) = a(2)^2 + b(2) + d[/tex]
[tex]23= 4a+2b+d[/tex] .........[1]
Cost $103 to produce 4 widgets,[tex]c(4) = a(4)^2 + b(4) + d[/tex]
[tex]103= 16a+4b+d[/tex] ............[2]
Cost $631 to produce 10 widgets.,[tex]c(10) = a(10)^2 + b(10) + d[/tex]
[tex]631= 100a+10b+d[/tex] ...........[3]
Now, we solve equation [1], [2] and [3]
Subtract equation [2]-[1] and [3]-[2]
[2]-[1] → [tex]12a+2b=80[/tex] ........[4]
[3]-[2] → [tex]84a+6b=528[/tex] .......[5]
Solving equation [4] and [5] by elimination method,
Multiply equation [4] by 3 and subtract from [5]
[tex]84a+6b-3(12a+2b)=528-3(80)[/tex]
[tex]84a+6b-36a-6b=528-240[/tex]
[tex]48a=288[/tex]
[tex]a=6[/tex]
Put in equation [4]
[tex]12(6)+2b=80[/tex]
[tex]72+2b=80[/tex]
[tex]2b=8[/tex]
[tex]b=4[/tex]
Substitute the value of a and b in [1] to get d
[tex]23= 4a+2b+d[/tex]
[tex]23= 4(6)+2(4)+d[/tex]
[tex]23= 24+8+d[/tex]
[tex]23= 32+d[/tex]
[tex]d=-9[/tex]
Substitute a=6,b=4,d=-9 in the cost equation,
The required equation form is [tex]c(x) = 6x^2 + 4x-9[/tex]
The total cost of producing 6 widgets.
Put x=6
[tex]c(6) = 6(6)^2 + 4(6)-9[/tex]
[tex]c(6) = 216+15[/tex]
[tex]c(6) =231[/tex]
Therefore, The total cost of producing 6 widgets is $231.
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
Answers
So its 82
Identify the number that does not belong with the other three. Explain your reasoning.
Answers
It is the only number in the set that cannot be expressed as a fraction (or ratio) meaning it is an irrational number
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
Answers
b,c,d are all numbers, so indeed, focus on a single number, say 'e'. Also a can't be zero, or there is no equation at all! So, again all numbers can be grouped:
a*sqrt(x) + b+c=d ---> sqrt(x) = f, f some number.
x = f^2 is the solution.
To be extraneous, means that it does not solve the equation.
Why here? Because by definition in mathematics sqrt( f^2) is not f! but abs(f), that is:
sqrt(9)=3,
So you just need to set the numbers to -3: (thinking x=9)
2*sqrt(x) + 7 -4 = -3
this gives: sqrt(x) = -3, from which x= 9, but sqrt(9) = 3.
It's kind of tricky, because many forget the definition that sqrt(a^2) = abs(a).
The same does not happen when looking for roots.
You should ask your teacher to make sure this is what they want.
Let me say that usually extraneous solutions are those which come out after solving an equation but make no sense when substituted in the original equation. But with sqrt(x) and your so particular equation, there is nothing else to say.
Use the equation and type the ordered-pairs.
y = log 3 x
{(1/3,____,)(1,___), (3,___),(9,____),(27,____),(81,___)}
Answers
-1,0,1,2,3,4 is the answer for y according to order
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]
write the expression in factored form: m²-n²
Answers
[tex]m^2 - n^2 = (m + n)(m - n)[/tex]
m^2 - n^2 = (m - n)(m + n)
Find the 6th term of the sequence with t1 = -4 and tn = 5tn-1
Answers
T2= 5(-4)= -20 don the same thing for all of them :
-100 t3
-500. T4
-2500 t5
-12500 is t6
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)
Answers
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
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
Answers
You will find its 3,000.
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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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)
Answers
The most consistent team is the team who has the lowest range, IQR and standard deviation (σ). From the table, the team who has the lowest range, IQR and the standard deviation is team Y.
Lower range indicates a small range of data interval, meaning that there is no extremely low or high value on a set. It also means that most of the data values are repeated and therefore is more consistent.
PART B:
Average of a data can be shown by the value of the mean or median. From the table, we can see that team A has the highest mean and median. These values indicate the earning by sales each team member would have made.
A ______ is an expression that can be written in the form of p/q where p and q are polynomials and q
Answers
The area of a square is 2500 cm .what is the side legth of the painting?
Answers
Area = 2500 sq. cm
s² = 2500
s = √(2500)
s = √(5² × 10²)
s = 5 × 10
s = 50 cm
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.
Answers
y = -10x² + 160x - 430
In order to generate $50 in daily profits, the number of T-shirts sold is determined by solving the equation
-10x² + 160x - 430 = 50
Divide through by -10.
x² - 16x + 43 = -5
x² - 16x + 48 = 0
Answer:
This quadratic equation can be solved by factorization.
Explanation:
Note that
48 = 4 x 12, and
4 + 12 = 16
Therefore
x² - 16x + 48 = (x - 4 )(x - 12 ) = 0
The solutions are
x - 4 = 0 => x = 4, and
x - 12 = 0 => x = 12
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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write the number 32.56 corrrect to one decimal place
Answers
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)
Answers
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
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
Answers
[tex]\bf \qquad \textit{Amount for Exponential Growth}\\\\ A=I(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\to &430\\ r=rate\to 0.9\%\to \frac{0.9}{100}\to &0.009\\ t=\textit{elapsed time}\to &10\\ \end{cases} \\\\\\ A=430(1+0.009)^{10}\implies A=430(1.009)^{10}[/tex]
Use newton's method to find the absolute minimum value of the function f(x)=x2+sinx correct to six decimal places.
Answers
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).
What reference angle in the first quadrant corresponds to theta = -120? Answer in radians.
Answers
This means that we pass the fourth quadrant and stop in the third quadrant.
The reference angle of an angle theta in the third quadrant, is theta + 180°.
So the reference angle of -120° is -120°+180°=60°.
360° are 2π Radians
then 60° are 1/6 of 2π Radians = π/3 Radians
Answer: Reference angle is π/3 Radians
Answer:
Answer: Reference angle is π/3 Radians
Step-by-step explanation:
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
Answers
g(f(x)) = (x-7)^3
Its D
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.
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)
Answers
15 x² + 3 x y + 10 x + 2 y =
= 3 x · ( 5 x + y ) + 2 · ( 5 x + y ) =
= ( 5 x + y ) ( 3 x + 2 ) = ( 3 x + 2 ) ( 5 x + y )
Answer:
A ) ( 3 x + 2 ) ( 5 x + y )
Answer:
the answer is the first option : A
Step-by-step explanation:
what is 17pi/4 in decimal form nearest the thousandth
Answers
17 x PI = 53.40707511
divided by 4 = 13.35176878
rounded to nearest thousandth = 13.352
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
Answers
$1 = .7306 Euros
She has to pay $3,500 per year to the University.
$3,500 * .7306 = 2,557.10 Euros
And since we have to find how many Euros can be except to pay per month:
2,557.10 : 12 = 213.09 ≈ 213 Euros
Answer:
She would pay 213 Euros per month.
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?
Answers
7x + 9y = 720
5x + 3y = 360.....multiply by -3
---------------
7x + 9y = 720
-15x - 9y = -1080 (result of multiplying by -3)
---------------add
-8x = - 360
x = -360/-8
x = 45 minutes <== plan A
5x + 3y = 360
5(45) + 3y = 360
225 + 3y = 360
3y = 360 - 225
3y = 135
y = 135/3
y = 45 minutes <== plan B
so both plans last 45 minutes <==
what is the domain and range for the following function and its inverse f(x) = x2 – 2
Answers
The domain is from -∞ to +∞, while the range is from -2 to +∞.
Answer:
x2-2 domain an range are 0, -2
Step-by-step explanation:
How high is a 40-foot ramp if it is propped at a 30 degree angle?
Answers
sin theta=[opposite]/[hypotenuse]
theta=30
opposite=x
hypotenuse=40 ft
hence;
sin 30=x/40
thus;
x=40sin30
x=20 ft
the ramp is 20 ft high
Express the number as a ratio of integers. 7.5336
Answers
division gives you 7.5336
HELP ROUND 1.75170179212 TO 6 DECIMAL PLACES
Answers
There are 11 decimal places here. We only need 7 to complete.
1.751701(7)xxxx
^
We need to round the 7th place to round to 6 decimals
If the 7th decimal place < 5, round to 1.
If the 7th decimal place > or = 5, round to 2.
Because 7 > 5, It rounds to 1.751702.
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
What is the surface area of the square pyramid?
(Figure is not drawn to scale.)
Answers
area of 1 traingle = 1/2 * 8 * 5.4 = 21.6
there are 4 triangular sides so their area = 4 * 21.6 = 86.4
Total surface area = 64 + 86.4 = 150.4 cm2
D
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?
Answers
mean=
mean=[90*4+70*3+2*60+80]/10
=[360+210+120+80]/10
=770/10
=77
the mean score is 77
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.