Answer:
count the number of places it is. The 5 in 458,039 is in the 10,000 place and the 5 in 271,145 is in the ones place so the 5 in 458,039 is 10,000 times greater
If y = ax^2 + bx + c passes through the points (-3,10), (0,1) and (2,15), what is the value of a + b + c?
Hi there!
[tex]\large\boxed{a + b + c = 6}[/tex]
We can begin by using the point (0, 1).
At the graph's y-intercept, where x = 0, y = 1, so:
1 = a(0)² + b(0) + c
c = 1
We can now utilize the first point given (-3, 10):
10 = a(-3)² + b(-3) + 1
Simplify:
9 = 9a - 3b
Divide all terms by 3:
3 = 3a - b
Rearrange to solve for a variable:
b = 3a - 3
Now, use the other point:
15 = a(2)² + 2(3a - 3) + 1
14 = 4a + 6a - 6
Solve:
20 = 10a
2 = a
Plug this in to solve for b:
b = 3a - 3
b = 3(2) - 3 = 3
Add all solved variables together:
2 + 3 + 1 = 6
help with q25 please. Thanks.
First, I'll make f(x) = sin(px) + cos(px) because this expression shows up quite a lot, and such a substitution makes life a bit easier for us.
Let's apply the first derivative of this f(x) function.
[tex]f(x) = \sin(px)+\cos(px)\\\\f'(x) = \frac{d}{dx}[f(x)]\\\\f'(x) = \frac{d}{dx}[\sin(px)+\cos(px)]\\\\f'(x) = \frac{d}{dx}[\sin(px)]+\frac{d}{dx}[\cos(px)]\\\\f'(x) = p\cos(px)-p\sin(px)\\\\ f'(x) = p(\cos(px)-\sin(px))\\\\[/tex]
Now apply the derivative to that to get the second derivative
[tex]f''(x) = \frac{d}{dx}[f'(x)]\\\\f''(x) = \frac{d}{dx}[p(\cos(px)-\sin(px))]\\\\ f''(x) = p*\left(\frac{d}{dx}[\cos(px)]-\frac{d}{dx}[\sin(px)]\right)\\\\ f''(x) = p*\left(-p\sin(px)-p\cos(px)\right)\\\\ f''(x) = -p^2*\left(\sin(px)+\cos(px)\right)\\\\ f''(x) = -p^2*f(x)\\\\[/tex]
We can see that f '' (x) is just a scalar multiple of f(x). That multiple of course being -p^2.
Keep in mind that we haven't actually found dy/dx yet, or its second derivative counterpart either.
-----------------------------------
Let's compute dy/dx. We'll use f(x) as defined earlier.
[tex]y = \ln\left(\sin(px)+\cos(px)\right)\\\\y = \ln\left(f(x)\right)\\\\\frac{dy}{dx} = \frac{d}{dx}\left[y\right]\\\\\frac{dy}{dx} = \frac{d}{dx}\left[\ln\left(f(x)\right)\right]\\\\\frac{dy}{dx} = \frac{1}{f(x)}*\frac{d}{dx}\left[f(x)\right]\\\\\frac{dy}{dx} = \frac{f'(x)}{f(x)}\\\\[/tex]
Use the chain rule here.
There's no need to plug in the expressions f(x) or f ' (x) as you'll see in the last section below.
Now use the quotient rule to find the second derivative of y
[tex]\frac{d^2y}{dx^2} = \frac{d}{dx}\left[\frac{dy}{dx}\right]\\\\\frac{d^2y}{dx^2} = \frac{d}{dx}\left[\frac{f'(x)}{f(x)}\right]\\\\\frac{d^2y}{dx^2} = \frac{f''(x)*f(x)-f'(x)*f'(x)}{(f(x))^2}\\\\\frac{d^2y}{dx^2} = \frac{f''(x)*f(x)-(f'(x))^2}{(f(x))^2}\\\\[/tex]
If you need a refresher on the quotient rule, then
[tex]\frac{d}{dx}\left[\frac{P}{Q}\right] = \frac{P'*Q - P*Q'}{Q^2}\\\\[/tex]
where P and Q are functions of x.
-----------------------------------
This then means
[tex]\frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^2 + p^2\\\\\frac{f''(x)*f(x)-(f'(x))^2}{(f(x))^2} + \left(\frac{f'(x)}{f(x)}\right)^2 + p^2\\\\\frac{f''(x)*f(x)-(f'(x))^2}{(f(x))^2} +\frac{(f'(x))^2}{(f(x))^2} + p^2\\\\\frac{f''(x)*f(x)-(f'(x))^2+(f'(x))^2}{(f(x))^2} + p^2\\\\\frac{f''(x)*f(x)}{(f(x))^2} + p^2\\\\[/tex]
Note the cancellation of -(f ' (x))^2 with (f ' (x))^2
------------------------------------
Let's then replace f '' (x) with -p^2*f(x)
This allows us to form ( f(x) )^2 in the numerator to cancel out with the denominator.
[tex]\frac{f''(x)*f(x)}{(f(x))^2} + p^2\\\\\frac{-p^2*f(x)*f(x)}{(f(x))^2} + p^2\\\\\frac{-p^2*(f(x))^2}{(f(x))^2} + p^2\\\\-p^2 + p^2\\\\0\\\\[/tex]
So this concludes the proof that [tex]\frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^2 + p^2 = 0\\\\[/tex] when [tex]y = \ln\left(\sin(px)+\cos(px)\right)\\\\[/tex]
Side note: This is an example of showing that the given y function is a solution to the given second order linear differential equation.
Please help no links.Mr. Longley is buying a $15 box of trail mix at Whole Foods, where tax is 6%. If Mr. Longley has
a coupon for 10% off the price of any item, how much does he end up paying?
I
Answer:
$14.40
Step-by-step explanation:
my way of doing things:
15/100=0.15=1%of total amount
0.15 x 6=0.9= the 6% which is the tax
0.15 x 10 = 1.5=the coupon
Take the coupon amount $1.50 minus the tax amount $0.90 =$0.60. Because the coupon amount is greater than the tax the 60 cents gets taken away from the original 15 dollars leaving Mr. Longely only having to pay $14.40.
A sample of 38 babies in the zinc group had a mean birth weight of 3328 grams. A sample of 31 babies in the placebo group had a mean birth weight of 3406 grams. Assume that the population standard deviation for the zinc group is 640 grams, while the population standard deviation for the placebo group is 851851 grams. Determine the 99% confidence interval for the true difference between the mean birth weights for "zinc" babies versus "placebo" babies.
Required:
Find the point estimate for the true difference between the population means.
Answer:
-78
Step-by-step explanation:
Zinc group :
Mean, x1 = 3328
σ1 = 640
Sample size, n1 = 28
Placebo group :
Mean, x2 = 3406
σ2 = 851
Sample size, n2 = 31
The point estimate for the true difference between the population means is obtained as :
Mean difference between population :
x1 - x2 = 3328 - 3406 = - 78
What is the minimum perimeter of a rectangle with an area of 625 mm^2
what is symmetrical line
Answer:
assuming youre asking for line of symmetry, it's a line that cuts a shape exactly in half.
for example, a square has 4 lines of symmetry
Charlie puts $50000 in a stock account, but it loses money at a rate of 20%
every month. Which of the expressions below models the number of dollars
Charlie's account has after t months?
Answer:
You dind't include the answer choices but it should look something like
[tex]50000(.8)^t[/tex]
Identify the factorization of 36 + 25x2.
Answer:
86
Step-by-step explanation:
First, we should use the rule of:
B: bracket
O: of
D: division
M: multiplication
A: addition
S: subtraction
so, before adding we should multiply
or;36+50
or;86 ans.
Calculate the GPA of a student with the following grades: B (77 hours), D (66 hours), F (2020 hours). Note that an A is equivalent to 4.04.0, a B is equivalent to a 3.03.0, a C is equivalent to a 2.02.0, a D is equivalent to a 1.01.0, and an F is equivalent to a 00. Round your answer to two decimal places.
Answer:
The student's GPA is of 0.82.
Step-by-step explanation:
GPA:
To find the student's GPA, we find his weighed mean.
Grades:
7 hours worth 3(B)
6 hours worth 1(D)
20 hours worth 0(F). So
[tex]M = \frac{7*3 + 6*1 + 20*0}{7+6+20} = 0.82[/tex]
The student's GPA is of 0.82.
9. The theater club of a local high school is planning a production. The amount of time t needed to assemble the set is inversely
proportional to the number people n working. Twelve people can assemble the set in 5 hours.
Write an equation to represent the situation.
Answer:
The situation that represents this situation is:
[tex]t = \frac{60}{n}[/tex]
Step-by-step explanation:
The amount of time t needed to assemble the set is inversely proportional to the number people n working.
This means that:
[tex]t = \frac{k}{n}[/tex]
In which k is the constant of proportionality.
Twelve people can assemble the set in 5 hours.
This means that for [tex]n = 12, t = 5[/tex]. We use this to find k.
[tex]t = \frac{k}{n}[/tex]
[tex]5 = \frac{k}{12}[/tex]
[tex]k = 12*5 = 60[/tex]
Write an equation to represent the situation.
[tex]t = \frac{60}{n}[/tex]
How many ways are there to choose three distinct integers between 1 and 20 inclusive such that the numbers form an arithmetic sequence?
*please try to answer by tomorrow/
Answer:
probability of the product of the chosen integers being a multiple of 3 is P(E)= 1 - (91/285)
=194/285 or 0.6807.
Step-by-step explanation:
The sample space of all possible choices of three integers from the set {1,2,…..,20} has C(20,3) = (20×19×18)/3! elements.
The complement of the event space E consists of all possible choices of three integers from the complement of the set of all the multiples of 3 in the above set because the product of the chosen integers is a multiple of 3 if and only if at least one of them is a multiple of 3. Hence we have to choose three elements from the set {1,2,4,5,7,8,10,11,13,14,16,17,19,20} which has 14 elements.
Hence
|E'| = C(14,3)
= 14×13×12/3!.
Therefore probability P(E')
= |E'|/|S|
= (14×13×12)/(20×19×18)
= (14×13×2)/(20×19×3)
=(7×13)/(5×19×3)
= 91/285.
Therefore the required probability of the product of the chosen integers being a multiple of 3 is P(E)= 1 - (91/285)=194/285 or 0.6807.
Please help me please please help ASAP
Step-by-step explanation:
70 + 45 = 115
180 - 115 = 65
angle c = 65
use sohcahtoa
cos angle = adjacent
hypotenuse
cos 65 = 2.5
b
b cos 65 = 2.5
use the calc for further answers
hope that helped
Water is flowing into a tank at a rate of 20 cm3/min. At the start, there is 250 cm3 of water in the tank.
(i) How much water will be in the tank after 30 minutes?
(ii) Find the time when there is 1210 cm3 of water in the tank.
Answer:
i) 410 cm³
ii) 48 min
Step-by-step explanation:
we start with 250 cm³.
and then we fill in 20 cm³ per minute.
i)
after 30 minutes we have
250 + 8×20 = 250 + 160 = 410 cm³
ii)
how long (how many minutes) does it take to reach 1210 cm³ in the tank ?
well, first we subtract the start amount (250).
and then we see how often 20 cm³ will "fit" into the remainder. and then we know how many minutes the water has to run.
1210 - 250 = 960 cm³
so, the incoming water needs to reach 960 cm³ to have a total of 1210 cm³.
and
960 cm³ / (20 cm³ / min) = 960 cm³ min / 20 cm³ =
= 960 min / 20 = 48 min
What is the correct way to read 43.106
Step-by-step explanation:
Forty three thousand one hundred and six
Answer:
Forty three AND one hundred six thousandths
Step-by-step explanation:
If there is a comma ( , ) between the two numbers, you are correct.
If there is a period / dot ( . ) between them, and you need to read the place values, you must read the numbers to the right of the . as decimals. Those are the "th" numbers. 1 is in the tenths place, 0 in the hundredths place and the 6 in the thousandths place.
If you are simply reading out the digit names, without assigning their value, you might say "forty three POINT one hundred six" or "forty three DOT one hundred six" or "forty three DECIMAL one hundred six".
I need help guys thanks so much
Answer: C
Step-by-step explanation:
Lucinda is writing a coordinate proof to show that a diagonal of a parallelogram partitions the parallelogram into two equal areas.
A parallelogram graphed on a coordinate plane. The vertices of rectangle are labeled as K L M and N. The vertex labeled as K lies on begin ordered pair 0 comma 0 end ordered pair. The vertex labeled as L lies on begin ordered pair x comma 2 y end ordered pair. The coordinate of vertex M is left blank. The vertex labeled as N lies on begin ordered pair 3 x comma 0 end ordered pair. A diagonal is drawn between points K and M.
Enter your answers in the boxes to complete Lucinda's proof.
Since KLMN is a parallelogram and a parallelogram's opposite sides are parallel and congruent, the coordinates for M are (4x, 2y).
In △KMN, the length of the base is and the height is . So an expression for the area of △KMN is .
In △KLM, the length of the base is 3x and the height is 2y. So an expression for the area of △KLM is .
Comparing the area of the two triangles that are formed by a diagonal of the parallelogram shows that a diagonal of a parallelogram partitions the parallelogram into two equal areas.
9514 1404 393
Answer:
ΔKMN: base, 3x; height, 2y; area, 3xyΔKLM: area, 3xyStep-by-step explanation:
ΔKMNThe base length is the length of the horizontal line segment KN. That length is the difference of the x-coordinates: 3x -0 = 3x.
The height is the difference of the y-coordinate of point M and the y-coordinate of horizontal segment KN. That difference is 2y -0 = 2y.
The area is half the product of base and height:
A = (1/2)bh
A = 1/2(3x)(2y) = 3xy
In ΔKMN, the length of the base is 3x and the height is 2y. So an expression for the area of ΔKMN is 3xy.
__
ΔKLMIn ΔKLM, the length of the base is 3x and the height is 2y. So an expression for the area of ΔKLM is 3xy.
y = 60x + 20
y = 65x
Answer:
4=x y=325
Step-by-step explanation:
60x + 20 = 65x
group the variables
20=5x
because you subtracted 60x from both
4=x
because you divided 5 from both
now substitute 5 for x
65×5 is 325
y=325
find the equation of straight line passes through point (3,1) such that the intercept on y-axis exceeds that on the x- axis by 4.
Answer:
Step-by-step explanation:
Write a rule to describe the transformation.
A. reflection across y=x
B. rotation 90º clockwise about the origin
C. rotation 180º about the origin
D. rotation 90º counterclockwise about the origin
Answer:
C. rotation 180º about the origin
Step-by-step explanation:
Given
Quadrilaterals GWVY and G'W'V'Y'
Required
Describe the transformation rule
Pick points Y and Y'
[tex]Y = (5,-4)[/tex]
[tex]Y' = (-5,4)[/tex]
The above obeys the following rule:
[tex](x,y) \to (-x,-y)[/tex]
When a point is rotated by 180 degrees, the rule is:
[tex](x,y) \to (-x,-y)[/tex]
Hence, (c) is correct
the art club held a show for 2 days a total 269 people attended the show. On the second day, 15 more people attended than had come to the show the first day how many people attended on the first day?
Answer:
127 peopleStep-by-step explanation:
Number of attendees the first day = x.
Solve the following equation for x:
x + (x + 15) = 2692x = 269 - 152x = 254x = 254/2x = 127In the figure, triangles ABC and DEF are congruent.
Find the measure of DF.
a. 13m
b. 13m
c. 7m
d. 13.928m
Please show work to help me understand.
since the two triangles are congruent..
AB=ED
AC=FD(side opposite to the right angle)
FD=AC
•°•FD=13m
Evaluate 20 + 16 ÷ 2 − 5.
is it 13 18 14 23
Answer:
it is 23
Step-by-step explanation:
first divide
then add
then subtract
Answer:
23
Step-by-step explanation:
Follow PEMDAS
16 ÷ 2 = 8
8 + 20 = 28
28 - 5 = 23
20 students were asked “How many pets do you have in your household?” and the following data was collected:
2 1 0 3 1 2 1 3 4 0
0 2 2 0 1 1 0 1 0 1
Select the type of the data ?
CHOOSE ONE PLEASE HELP
Discrete
Continuous
Categorical
Qualitative
Answer:
Discrete
Discrete data represent items that can be counted; they take on possible values that can be listed out. The list of possible values may be fixed (also called finite); or it may go from 0, 1, 2, on to infinity (making it countably infinite).
The manager of a movie theater is standing outside the theater complex one evening. He will be asking the moviegoers questions.
Which questions can the manager ask that will result in discrete quantitative data? Check all that apply.
What movie did you just see?
What genre of movie is your favorite?
How much did you spend at the movies today?
Did you order anything from the concession stand?
Answer:
It's How much did you spend at the movies today?
Step-by-step explanation:
The question can the manager asks "How much did you spend at the movies today?". Then the correct option is C.
What is discrete quantitative data?A discrete quantitative parameter has a clear mathematical explanation but could only take certain integer values (instead of every value in intervals).
The manager of a movie theater is standing outside the theater complex one evening.
He will be asking the moviegoers questions.
Then the questions can the manager ask that will result in discrete quantitative data will be
How much did you spend at the movies today?
The question can the manager asks "How much did you spend at the movies today?"
Then the correct option is C.
More about the discrete quantitative data link is given below.
https://brainly.com/question/12831013
#SPJ2
Help please if you know, thanks
Answer:
xsqrt(2)
Step-by-step explanation:
sqrt(a) / sqrt(b) = sqrt(a/b)
sqrt(22x^6) / sqrt(11x^4)
sqrt(22x^6/11x^4)
sqrt(2x^2)
We know sqrt(ab) = sqrt(a) sqrt(b)
sqrt(x^2) sqrt(2)
xsqrt(2)
answer the question
Answer:
g(1)=(1-1)*2 -2
= -2
g(2) = (2-1)*2 -2
= -1
g(3) = 1/2 (3) -2
= -1/2
Answer:
g(1) = -2
g(2) = -1
g(3) = -1/2 or -0.5
Step-by-step explanation:
you really need help for typing numbers into your calculator ? because there is nothing else to do here.
we get 3 values of x and need to calculate the functional values based on the given expressions by using each given value for x.
the only thing that requires a bare minimum of intelligence is to find the fitting expression.
so, for g(1) and g(2) we need to use the middle one, and for g(3) the third one. uhhhh, very difficult ...
typing it in here is way more effort than doing it directly on the calculator or really in the head.
so, g(1) = (1-1)² - 2 = -2
g(2) = (2-1)² - 2 = 1 - 2 = -1
g(3) = 1/2 ×3 - 2 = 3/2 - 2 = 3/2 - 4/2 = -1/2
uhhhh, come in, you could have done that too. and way faster.
Find the dimensions of the rectangle of largest area that can be inscribed in an equilateral triangle of side L if one side of the rectangle lies on the base of the triangle.
base=
height=
9514 1404 393
Answer:
base: L/2height: L√3/2Step-by-step explanation:
Let x represent the ratio of the rectangle base to the triangle side length. Then the height of the small triangle above the rectangle will be x times the height of the equilateral triangle. Then the height of the rectangle is (1-x) times the height of the equilateral triangle. The rectangle's area will be ...
A = bh
A = (xL)(1-x)(L·√3/2) = (L²√3/2)(x)(1-x)
This graphs as parabola opening downward with x-intercepts at x=0 and x=1. The vertex is on the line of symmetry, halfway between these zeros, at x = 1/2.
The base of the rectangle is L/2.
The height of the rectangle is L√3/2.
_____
The general solution to this sort of problem is that one side of the rectangle is the midsegment of the triangle.
The diameters of ball bearings are distributed normally. The mean diameter is 7373 millimeters and the variance is 44. Find the probability that the diameter of a selected bearing is less than 7676 millimeters. Round your answer to four decimal places.
Answer:
0.9332
Step-by-step explanation:
We are given that
Mean diameter, [tex]\mu=73[/tex]
Variance, [tex]\sigma^2=4[/tex]
We have to find the probability that the diameter of a selected bearing is less than 76.
Standard deviation, [tex]\sigma=\sqrt{variance}=\sqrt{4}=2[/tex]
[tex]P(x<76)=P(\frac{x-\mu}{\sigma}<\frac{76-73}{2})[/tex]
[tex]P(x<76)=P(Z<\frac{3}{2})[/tex]
Where [tex]Z=\frac{x-\mu}{\sigma}[/tex]
[tex]P(x<76)=P(Z<1.5)[/tex]
[tex]P(x<76)=0.9332[/tex]
Hence, the probability that the diameter of a selected bearing is less than 76=0.9332
Below is the graph of a polynomial function with real coefficients
(a) The function f is increasing over which intervals? Choose all that apply.
D(-0, -8)
O (-5,-2) O (-8, -2) O (-2,
2) (2,5)
O (5, 0 )
?
(b) The functionfhas local maxima at which x-values? If there is more than one value,
separate them with commas.
(c) What is the sign of the leading coefficient of f?
Select One
(d) Which of the following is a possibility for the degree of f? Choose all that apply.
4
5
6
Please help if you can thank you
9514 1404 393
Answer:
(a) (-∞, -8), (-5, -2), (2, 5)
(b) -8, -2, 5
(c) negative
(d) 6
Step-by-step explanation:
(a) The function is increasing on intervals where the graph slopes upward left-to-right. Those are (-∞, -8), (-5, -2), and (2, 5).
__
(b) The local maxima are at the right end of each interval on which the function is increasing: -8, -2, 5.
__
(c) The function opens downward (∩), so has a negative leading coefficient.
__
(d) There are three local maxima and two local minima (left end of an increasing interval), so a total o 5 turning points. The degree of the polynomial is at least one more than this: 6.
Four wires (red,green, blue and yellow) need to be attached to a circuit board. A robotic device will attach the wires. The wires can be attached in any order, and the production manager wishes to determnine which order would be the fastest for the robot to use.
Required:
Use the multiplication rule of counting to determine four choices for the first wire, three for the second wire, two for the third and only one for the fourth.
Answer:
24
Step-by-step explanation:
The topic here is COMBINATORICS.
The parent topic is PERMUTATIONS & COMBINATORICS.
Permutation deals with arrangement in a definite order while, as stated in the question here, definite order in not needed in Combinatorics.
Now, the multiplication rule of counting, also known as the rule of product, talks about the multiplication of the figures that represent the different ways of doing something.
For example, in this question, the robot needs to attach 4 wires to a circuit board. If you know how Physics or Electricity works, you'll that truly this is a combination matter and not permutation.
Putting/Connecting the 4 wires together (in a square shaped circuit for instance), the arrangement RGBY is different from RGYB or RBGY.
So there will be more ways to connect or combine these wires, than if we were to follow a definite rule like: "Red and Green must always stay together".
So using the multiplication rule of counting to determine 4 choices for the Red wire, 3 choices for the Green wire, 2 choices for the Blue wire, and 1 choice for the yellow wire, we have:
R4 x G3 x B2 x Y1 = 4 x 3 x 2 x 1 = 4! = 24
The term "4!" means "Four Factorial".
