Answer:
There are six factors and two treatments.
Step-by-step explanation:
We can make this conclusion because treatments in experimentation refer to something that researchers use or administer to their subjects, while factors simply refer to the category of treatments; in other words, the number of various types of treatments.
Remember, the researchers stated that "the condition [treatments] randomly assigned to the subjects", is that the granola was labeled as either "Regular Rocky Mountain Granola" or "Low‑Fat Rocky Mountain Granola," which shows that the treatments are two (Rocky Mountain Granola and Low‑Fat Rocky Mountain Granola). Summing the factors (various types/categories of treatments) gives us six factors.
Sarah wants to know if there is a difference in the time it takes her to run the high trestle trail from Madrid to Woodward based on the type of her running shoes her Hokas or her Asics.
(7-2i)(-2-4i)
show all work
Answer:
Step-by-step explanation:
-14 - 28i + 4i + 28i^2
-14 - 24i + 28(-1)
-14 - 24i - 28
-42 - 24i
Find the slope of -5x+4Y=-16
Given parameters:
Find the slope of the line;
-5x + 4y = -16
To find the slope of this line, we must express it in linear form according to the equation below;
y = mx + c
Where x and y are the coordinates
m is the slope
c is the intercept
Now let us write the given equation in this form;
-5x + 4y = -16
Take add +5x to both sides;
-5x + 4y + 5x = 5x - 16
4y = 5x - 16
Now, divide through by 4;
[tex]\frac{4y}{4}[/tex] = [tex]\frac{5x}{4}[/tex] - [tex]\frac{16}{4}[/tex]
y = [tex]\frac{5x}{4} - 4[/tex]
So the slope of the line is [tex]\frac{5}{4}[/tex]
Consider the following. (A computer algebra system is recommended.) y'' + 3y' = 2t4 + t2e−3t + sin 3t (a) Determine a suitable form for Y(t) if the method of undetermined coefficients is to be used. Y(t) = t(A0t4 + A1t3 + A2t2 + A3t + A4) + (B0t2 + B1t + B2)e−t + C sin 3t + D cos 3t Y(t) = t(A1t3 + A2t2 + A3t + A4) + t(B0t3 + B1t2 + B2t + B3)e−3t + C sin 3t + D cos 3t Y(t) = (A0t4 + A1t3 + A2t2 + A3t + A4) + t(B0t2 + B1t + B2)e−3t + C sin t + D cos t Y(t) = t(A0t4 + A1t3 + A2t2 + A3t + A4) + t(B1t + B2)e−3t + C sin 3t + D cos 3t Y(t) = t(A0t4 + A1t3 + A2t2 + A3t + A4) + t(B0t2 + B1t + B2)e−3t + C sin 3t + D cos 3t (b) Use a computer algebra system to find a particular solution of the given equation. Y(t) =
First look for the fundamental solutions by solving the homogeneous version of the ODE:
[tex]y''+3y'=0[/tex]
The characteristic equation is
[tex]r^2+3r=r(r+3)=0[/tex]
with roots [tex]r=0[/tex] and [tex]r=-3[/tex], giving the two solutions [tex]C_1[/tex] and [tex]C_2e^{-3t}[/tex].
For the non-homogeneous version, you can exploit the superposition principle and consider one term from the right side at a time.
[tex]y''+3y'=2t^4[/tex]
Assume the ansatz solution,
[tex]{y_p}=at^5+bt^4+ct^3+dt^2+et[/tex]
[tex]\implies {y_p}'=5at^4+4bt^3+3ct^2+2dt+e[/tex]
[tex]\implies {y_p}''=20at^3+12bt^2+6ct+2d[/tex]
(You could include a constant term f here, but it would get absorbed by the first solution [tex]C_1[/tex] anyway.)
Substitute these into the ODE:
[tex](20at^3+12bt^2+6ct+2d)+3(5at^4+4bt^3+3ct^2+2dt+e)=2t^4[/tex]
[tex]15at^4+(20a+12b)t^3+(12b+9c)t^2+(6c+6d)t+(2d+e)=2t^4[/tex]
[tex]\implies\begin{cases}15a=2\\20a+12b=0\\12b+9c=0\\6c+6d=0\\2d+e=0\end{cases}\implies a=\dfrac2{15},b=-\dfrac29,c=\dfrac8{27},d=-\dfrac8{27},e=\dfrac{16}{81}[/tex]
[tex]y''+3y'=t^2e^{-3t}[/tex]
[tex]e^{-3t}[/tex] is already accounted for, so assume an ansatz of the form
[tex]y_p=(at^3+bt^2+ct)e^{-3t}[/tex]
[tex]\implies {y_p}'=(-3at^3+(3a-3b)t^2+(2b-3c)t+c)e^{-3t}[/tex]
[tex]\implies {y_p}''=(9at^3+(9b-18a)t^2+(9c-12b+6a)t+2b-6c)e^{-3t}[/tex]
Substitute into the ODE:
[tex](9at^3+(9b-18a)t^2+(9c-12b+6a)t+2b-6c)e^{-3t}+3(-3at^3+(3a-3b)t^2+(2b-3c)t+c)e^{-3t}=t^2e^{-3t}[/tex]
[tex]9at^3+(9b-18a)t^2+(9c-12b+6a)t+2b-6c-9at^3+(9a-9b)t^2+(6b-9c)t+3c=t^2[/tex]
[tex]-9at^2+(6a-6b)t+2b-3c=t^2[/tex]
[tex]\implies\begin{cases}-9a=1\\6a-6b=0\\2b-3c=0\end{cases}\implies a=-\dfrac19,b=-\dfrac19,c=-\dfrac2{27}[/tex]
[tex]y''+3y'=\sin(3t)[/tex]
Assume an ansatz solution
[tex]y_p=a\sin(3t)+b\cos(3t)[/tex]
[tex]\implies {y_p}'=3a\cos(3t)-3b\sin(3t)[/tex]
[tex]\implies {y_p}''=-9a\sin(3t)-9b\cos(3t)[/tex]
Substitute into the ODE:
[tex](-9a\sin(3t)-9b\cos(3t))+3(3a\cos(3t)-3b\sin(3t))=\sin(3t)[/tex]
[tex](-9a-9b)\sin(3t)+(9a-9b)\cos(3t)=\sin(3t)[/tex]
[tex]\implies\begin{cases}-9a-9b=1\\9a-9b=0\end{cases}\implies a=-\dfrac1{18},b=-\dfrac1{18}[/tex]
So, the general solution of the original ODE is
[tex]y(t)=\dfrac{54t^5 - 90t^4 + 120t^3 - 120t^2 + 80t}{405}\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,-\dfrac{3t^3+3t^2+2t}{27}e^{-3t}-\dfrac{\sin(3t)+\cos(3t)}{18}[/tex]
write and solve and equation to find ABE
Answer:
77
Step-by-step explanation:
<DBE and <ABE are supplementary angles so their sum is equal to 180
<DBE is given as 103
103 + <ABE = 180 subtract 103 from both sides
<ABE = 77
At Ariel's family reunion, Ariel hands out watermelon for the annual seed-spitting contest.
She gives a watermelon slice to each kid at the reunion. She also gives a slice to 40 adults.
Ariel hands out 90 watermelon slices in all.
Which equation can you use to find how many kids k are at the reunion?
k
90
K-40 = 90
k + 40 = 90
40k = 90
40
Solve this equation for k to find how many kids are at the reunion.
kids
How can i use scatter plots to analyze two sets of data?
Step-by-step explanation:
A Scatter Analysis is used when you need to compare two data sets against each other to see if there is a relationship. Scatter plots are a way of visualizing the relationship; by plotting the data points you get a scattering of points on a graph.
The sum of the measures of the three interior angles of any triangle is always 180°. The unmarked angles of the triangle below total 150°. angle A triangle.gif What is the measure of an angle that would be complementary to ∠ A ? A. 30° B. 60° C. 90° D. 150°
As rest angles have sum 150°
Using angle sum property
x+150=180x=30°Now
Complementary angles have sum 90°
So the complementary angle is 90-30=60°
Option B
An angle measures 70° more than the measure of its complementary angle. What is the measure of each angle?
Step-by-step explanation:
Let an angle = x
x= 70+(90-x)
x= 160-x
2x=160
x=80
So angle is 80 and it's complementary angle would be 10
Answer:
55∘ and 125∘
Step-by-step explanation:
Supplementary angles sum to
180∘
let one angle be [tex]x[/tex]
then the other angle is [tex]x+70[/tex]
summing the 2 angles gives
[tex]x+x+7=180[/tex]
[tex]2x+70=180[/tex]
subtract 70 from both sides
[tex]2x=180 -70=110[/tex]
divide both sides by
[tex]2x=\frac{110}{2} =55[/tex]
thus the angles are
55∘ and 55 + 70= 125∘
Help me with this please I gave you 30 points
Answer:
a reflection over the vertical axis, the coordinates would be (-2,5) the first number being the horizontal, second vertical
The circular floor of a teepee has a diameter of 9 yards. What is the circumference of the floor?
30 points pls show ur work thank u so much!!! :)
Answer:
28.26
Step-by-step explanation:
[tex]3.14\times9[/tex]
Calculate the product or quotient
[tex]28.26[/tex]
I hope this helps you
:)
For the function defined here, find
Answer:
f(0) = 2f(1) = 3f(2) = -2Step-by-step explanation:
The function value is the y-coordinate of the point having the given x-value.
f(0) = 2f(1) = 3f(2) = -2HELPPP PLS
Find the value of the variable.
Answer:
y = 90[tex]\sqrt{2}[/tex]
Step-by-step explanation:
using the sine ratio in the right triangle and the exact value
sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then using the 45° angle on the lower left
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{90}{y}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
y = 90[tex]\sqrt{2}[/tex]
For what value of x is the given parallelogram a rhombus?
Answer:
[tex]\sf x = 6[/tex]
solving steps:
[tex]\sf in \ a \ rhombus \ the \ opposite \ angles \ are \ equal[/tex]
[tex]\hookrightarrow \sf 7x + 4 = 9x - 8[/tex]
[tex]\hookrightarrow \sf 7x -9x = - 8-4[/tex]
[tex]\hookrightarrow \sf -2x = - 12[/tex]
[tex]\hookrightarrow \sf x = 6[/tex]
The area of a baseball field bounded by home plate, first base, second base, and third base is a square. If a player at first base throws the ball to a player at third base, what is the distance the player has to throw? 90 feet is first base 90 feet at third base
Answer:
ta side from one base to next has length of x. so we know each side has length x and the shape they make is a square. This means we are only searching for the diagonal of a square. remember that a diagonal forms and isoscoles right triangle with the 2 sides being equal and the diagonal as the hypotenuse. Using pythagoream theorem we can say
a^2 + b^2 = c^2 all side lengths are x so we can put x in for a and b to get
x^2 + x^2 = c^2
2x^2 = c^2
c = x * squareroot(2)
so if the length between bases is 90 ft
c = 90 ft * squareroot(2)
c = 127.28 ft
Step-by-step explanation:
Answer: C 16,200 squared
Step-by-step explanation:
The order of the first term more than 100 in the sequence (Tn)=(2+5n) is ……
Answer:
20
Step-by-step explanation:
T19 = 97
T20 = 102
The 20th term is the first term more than 100.
__
You can find the value of n from ...
2 +5n > 100
5n > 98
n > 19.6
The 20th term is the first term more than 100.
Could you please help me on this
Answer:
-x^2 +10x + 7
[tex]-x^2 +10x + 7[/tex]
Step-by-step explanation:
its the gray shaded area [(x+1)*(x+7)] minus the white area [(x-1)*(2x)]
AKA: [(x+1)*(x+7)] - [(x-1)*(2x)]
so first you foil to get both areas
gray region: (x+1)*(x+7) = x^2 + 8x + 7
white region: (x-1)*(2x) = 2x^2 - 2x
and then you subtract the white from the gray
[tex](x^2 + 8x + 7) - (2x^2 - 2x)[/tex]
-x^2 +10x + 7
what are the x- and y- intercepts for the graph of 3x + y = 15?
Answer:
X intercept=(5,0) and Y intercept=(0,15)
Step-by-step explanation:
3x + y = 15
to find the x int, sub in 0 for y and solve for x
3x + 0 = 15
3x = 15
x = 15/3
x = 5....so the x int is (5,0)
to find the y int, sub in 0 for x and solve for y
3(0) + y = 15
y = 15....so the y int is (0,15)
Which one is it?
A, B, C, or D?
Answer: I'd go with C
Step-by-step explanation:
A very large gardening business grows rose bushes for sale to garden stores around the world. The most popular colors are red, pink, and white. The business decides on 50% red roses, 30% pink, and 20% white. A gardener orders 10 rose bushes selected randomly from a huge field. Her primary interest is in pink roses. A good model for the number of bushes with pink roses is given by the binomial distribution. Probability calculations are quicker when using the Normal approximation to the binomial distribution. Which of the following is false
a. The approximation requires np 10 and n(1 â p) 10.
b. The sample size here is too small to use the Normal approximation to the binomial.
c. The approximation requires np 30.
d. The Normal approximation works better if the success probability p is close to p = 0.5.
Complete options are;
a. The approximation requires np > 10 and n(1 - p) > 10.
b. The sample size here is too small to use the Normal approximation to the binomial.
c. The approximation requires np > 30.
d. The Normal approximation works better if the success probability p is close to p = 0.5.
Answer:
Option C is false
Step-by-step explanation:
Looking at the options,
In normal approximation to the binomial,
n is the sample size,
p is the given probability.
q = 1 - p
Now, one of the conditions for using normal approximation to the binomial is that; np and nq or n(1 - p) must be greater than 10.
This means that option A is true because we require np or n(1 - p) to be greater than 10.
From Central limit theorem, the sample size needs to be more than 30 for us to use normal approximation. Our sample is 10. Thus, option B is true.
The approximation doesn't require np > 30. Rather it's the sample size that needs to be more than 30. Thus, option C is false.
Generally, when the value of p in a binomial is close to 0.5, the normal approximations will work better than when the value of p is closer to either 0 or 1. The reason is that: for p = 0.5, the binomial distribution will be symmetrical. Thus, option D is correct.
Find the slant height of this square pyramid Round to the neatest 10th
Answer: 21.9
Step-by-step explanation:
-Use Pythagoras theorem-
To find hypotenuse: square root 15 squared plus 16 squared
= 21.9
I need help with this math question
Answer:
-1/4x+3/4
or
-0.25x+0.75
Step-by-step explanation:
g(x) = mx + b
m = slope
b = initial value
m = -1/4
b = 3/4
g(x) = -1/4x+3/4
Hope this helped, let me know if you need more help!
Question 1 OT TU
A clothing store sells T-shirts, t, for $8 a shirt, shorts, s, for $12, and hats, h, for
$10 each. The store earned $464 revenue last month. The store sold three
times as many T-shirts than hats, and twice as many shorts as hats. Using the
substitution method, how many T-shirts, shorts, and hats did the store sell?
A. t=84; s = 12; h = 10
B. t = 24; s = 8; h= 16
C. t= 8; s = 16; h = 24
D. t = 24; s = 16; h=8
SUBMIT
The function f is defined by f(x)=x-2 . Find f(z-5) .
f(z-5)=z-5-2
f(z-5)=z-9
Help me out I’m also at done!!!
Answer: 68
Step-by-step explanation:
(7-(-1))^2+(-2)^2
8^2+4
68
Answer:
im sry if i get it wrong i think it is 32
Step-by-step explanation:
GIVING EXTRAS POINTS AND BRAINLIEST
Answer:
p<6
Step-by-step explanation:
this basically means she can buy 6 pounds or less
Answer:
p<7
Step-by-step explanation:
1 Suppose that $61,000 is invested at 55% interest, compounded quarterly. a) Find the function for the amount to which the investment grows after t years b) Find the amount of money in the account at t=0.3.7, and 10 years. 12 %
a) The function for the amount to which the investment grows after t years is A(t) = (Simplify your answer. Type an expression using t as the variable )
Answer:
i think its a
Step-by-step explanation:
Lucy invested for 15 years at 2.8%, compounded annually and ended with an account balance of $2250. What was her initial deposit?
Answer:1244
Step-by-step explanation:
Answer:
Step-by-step explanation:
Use the formula for calculating compound interest PN=P0(1+rk)Nk where N is the unknown, PN=2250, k=1, N=15, and r=0.028. Substitute the values into the formula and simplify.
2250=P(1+0.0281)1⋅15
2250=P(1.028)15
2250=P(1.5132...)
1486.91=P
Rounded to the nearest dollar, Lucy's initial deposit was $1487.
area of a trapezoid 6 mm 2 mm 4 mm
Answer:48 mm
Step-by-step explanation:
6 x 2 x 4= 48mm
Please answer quickly
The inequality below is equivalent to which of the following? 7−23x 9 B.x>−35 C.x<9 D.x<−35
WORTH ALL MY POINTS
If answers right i will give Brainliest
Answer:
?
Step-by-step explanation: