Answer:
2.3 lbs.
Step-by-step explanation:
Total=3.86
Cherry=1.56
3.86-1.56= 2.3
Recall that the Fibonacci Sequence is defined by the recurrence relation, a0 = a1 = 1 and for n ≥ 2, an = an−1 + an−2 . a. Show that f(x) = 1 1−x−x 2 is the generating function of the Fibonacci Sequence. b. Find ???? and β such that 1 − x − x 2 = (1 − ????x)(1 − βx). c. Find A and B in terms of ???? and β, such that 1 1−x−x 2 = A 1−????x + B 1−βx. d. Use the results of the previous parts to obtain a formula for an.
Answer:
Step-by-step explanation:
From the given information:
[tex]a_n = a_{n-1} + a_{n-2}; \ \ \ n \ge 2 \\ \\ a_o = 1 \\ \\ a_1 =1 \ \ \ \ \ since \ \ a_o = a_1 = 1[/tex]
A)
[tex]a_n - a_{n-1} - a_{n-2} = 0 \\ \\ \implies \sum \limits ^{\infty}_{n=2}(a_n -a_{n-1}-a_{n-2} ) x^n = 0 \\ \\ \implies \sum \limits ^{\infty}_{n=2} a_nx^n - \sum \limits ^{\infty}_{n=2} a_{n-1}x^n - \sum \limits ^{\infty}_{n=2}a_{n-2} x^n = 0 \\ \\ \implies (a(x) -a_o-a_1x) - (x(a(x) -a_o)) -x^2a(x) = 0 \\ \\ \implies a(x) (1 -x-x^2) -a_o-a_1x+a_ox = 0 \\ \\ \implies a(x)(1-x-x^2)-1-x+x=0 \\ \\ \implies a(x) (1-x-x^2) = 1[/tex]
[tex]\mathbf{Generating \ Function: a(x) = \dfrac{1}{1-x-x^2}=f(x)}[/tex]
B)
[tex]If \ \ 1 -x-x^2 = (1 - \alpha x) ( 1- \beta x) \\ \\ \implies 1 -x - ^2 = 1 + \alpha \beta x^2 - ( \alpha + \beta )x \\ \\ \text{It implies that:} \\ \\ \alpha \beta = -1 \\ \\ \alpha + \beta = 1 \\ \\ \implies \alpha = ( 1-\beta) \\ \\ ( 1- \beta) \beta = -1 \\ \\ \implies \beta - \beta^2 = -1 \implies \beta - \beta^2 -1 = 0\\ \\ \beta = \dfrac{-(-1) \pm \sqrt{(-1)^2 -4(1)(-1)}}{2(1)}[/tex]
[tex]\beta = \dfrac{1\pm \sqrt{5}}{2} \\ \\ \beta = \dfrac{1 + \sqrt{5}}{2} \ \ and \ \ \alpha = \dfrac{1 - \sqrt{5}}{2}[/tex]
C)
[tex]\dfrac{1}{1-x-x^2}= \dfrac{A}{1-\alpha x}+ \dfrac{\beta}{1-\beta x} \\ \\ = \dfrac{A(1-\beta x) + B(1-\alpha x)}{(1-\alpha x) (1 - \beta x)} \\ \\ = \dfrac{(A+B)-(A\beta+B\alpha)x}{(1-\alpha x) (1-\beta x)}[/tex]
[tex]\text{It means:} \\ \\ A+B=1 \\ \\ B = (1-A) \\ \\ A\beta+ B \alpha =0 \\ \\ A\beta ( 1 -A) \alpha = 0 \\ \\ A( \beta - \alpha ) = -\alpha \\ \\ A = \dfrac{\alpha}{\alpha - \beta } \\ \\ \\ \\ B = 1 - \dfrac{\alpha }{\alpha - \beta} \implies \dfrac{\alpha - \beta - \alpha }{\alpha - \beta } \\ \\ =\dfrac{-\beta }{\alpha - \beta} \\ \\ \mathbf{B = \dfrac{\beta }{\beta - \alpha }}[/tex]
D)
[tex]\text{The formula for} a_n: \\ \\ a(x) = \dfrac{\alpha }{\alpha - \beta }\sum \limits ^{\infty}_{n=0} \alpha ^n x^n - \dfrac{\beta}{\beta - \alpha }\sum \limits ^{\infty}_{n=0} \beta x^n \\ \\ \implies \sum \limits ^{\infty}_{n =0} \dfrac{\alpha ^{n+1}- \beta ^{n+1}}{\alpha - \beta}x^n \\ \\ a_n = \dfrac{\alpha ^{n+1}- \beta ^{n+1}}{\alpha - \beta } \\ \\ \\ a_n = \dfrac{1}{\sqrt{5}} \Big (\Big( \dfrac{\sqrt{5}+1}{2}\Big)^{n+1}- \Big ( \dfrac{1-\sqrt{5}}{2}\Big) ^{n+1}\Big)[/tex]
Factorise the following expressions.
Answer:
Q.1 a²+10a+24
splitting the middle.
a²+6a+4a+24
=a(a+6)+4(a+6)
(a+6)(a+4)
Q.2 x²+9x+18
splitting the middle
x²+6x+3x+18
x(x+6)+3(x+6)
(x+6)(x+3)
The 1st flat-bar, or cross, or other operator means:
-9-(-7)
-9-(-7)
-9--7
-9+7
7-9
-2
---
hope it helps
The excursion boat Holiday travels 35 km upstream and then returns to its starting point. The entire trip (both ways) took 4 hours and 48 minutes. If the speed of the boat in still water is 15 km /h and the current is 2.5km /h, how much longer is the trip upstream than the trip downstream?
Answer:
cundo estamos onectados me tocss
Step-by-step explanation:
An arch in the shape of the upper half of an ellipse is used to support a bridge that is to span a river 60 meters wide. The middle of the arch is 10 meters above the center of the river. Start by writing an equation for the ellipse if the x-axis coincides with the water level and the y-axis passes through the center of the arch. How high above the river is the arch at a distance of 8 meters from the center?
The arch is ____ meters above the river at a distance of 8 meters from the center. Do not round until the end. Round to the nearest tenth of a meter.
Answer:
Step-by-step explanation:
(y/10)^2+(x/30)^2=1
y^2/100+x^2/900=1
9y^2+x^2=900
9y^2=900-x^2
y^2=(900-x^2)/9, when x=8 we have
y^2=(900-8^2)/9
y^2=(900-64)/9
y^2=836/9
y=9.6 meters
The arch is 9.6 meters above the river at a distance of 8 meters from the center.
According to a survey, about 19% of all Americans are without health insurance. Assume that this estimate is reasonably accurate. Suppose that you select a random sample of 46 Americans. (a) Calculate the expected number of Americans without health insurance in the sample. Answer: (Keep at least four decimal places.) (b) Calculate the standard deviation of the number of Americans without health insurance in the sample. Answer: (Keep at least four decimal places.)
Answer:
a) 8.74
b) 2.6607
Step-by-step explanation:
For each American, there are only two possible outcomes. Either they are without health insurance, or they are not. In the sample, each person is independent of any other person, which means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
According to a survey, about 19% of all Americans are without health insurance.
This means that [tex]p = 0.19[/tex]
Suppose that you select a random sample of 46 Americans.
This means that [tex]n = 46[/tex]
(a) Calculate the expected number of Americans without health insurance in the sample.
[tex]E(X) = np = 46*0.19 = 8.74[/tex]
(b) Calculate the standard deviation of the number of Americans without health insurance in the sample.
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{46*0.19*0.81} = 2.6607[/tex]
Find the Surface area S of each prism (the numbers are 3,5,4,8)
Answer:
Did u ever get the answer to this?
Step-by-step explanation:
During the first 13 weeks of the television season, the Saturday evening 8:00 P.M. to 9:00 P.M. audience proportions were recorded as ABC 29%, CBS 28%, NBC 25%, and independents 18%. A sample of 300 homes two weeks after a Saturday night schedule revision yielded the following viewing audience data: ABC 95 homes, CBS 65 homes, NBC 87 homes, and independents 53 homes. Test with = .05 to determine whether the viewing audience proportions changed.
Required:
Compute the value of the 2 test statistic (to 2 decimals). The p value is Has a significant change occurred in viewing audience proportions?
Answer:
- The value of the 2 test statistic is 6.98
- There is no sufficient evidence to reject the claim of the specific distribution
Step-by-step explanation:
Given
Proportion (p)
[tex]ABC = 29\% = 0.29\\CBS = 28\% = 0.28\\NBC = 25\% = 0.25\\Others = 18\% = 0.18\\[/tex]
Samples
[tex]ABC = 95\\CBD = 65\\NBC = 87\\Others = 53\\\alpha = 0.05[/tex]
First, we formulate a table for chi square totals:
[tex]x^2 = \frac{(O - E)^2}{E}[/tex]
Where
O = Observed Frequency and E = Expected Frequency
So, we have:
[tex]\begin{array}{cccccc}{\ } & {O} & {E = np} & {O - E} & {(O -E)^2} & {x^2 = \frac{(O - E)^2}{E}} \ \\ \\ {0.29} & {95} & {87} & {8} & {64} & {0.736} &{0.28} & {65} & {84} & {-19} & {361} & {4.300} & {0.25} & {87} & {75} & {12} & {144} & {1.920} & {0.18} & {53} & {54} & {-1} & {1} & {0.019}\ \end{array}[/tex]
For ABC
[tex]E = np = 300 * 0.29= 87[/tex]
[tex]O-E =95 - 87 = 8[/tex]
[tex](O-E)^2 = 8^2 = 64[/tex]
[tex]x^2 = \frac{(O - E)^2}{E} = \frac{64}{87} = 0.736[/tex]
For CBS
[tex]E =np = 300 * 0.28 = 84[/tex]
[tex]O -E = 65 - 84 = -19[/tex]
[tex](O -E)^2 = (-19)^2 = 361[/tex]
[tex]x^2 = \frac{(O - E)^2}{E} = \frac{361}{84} = 4.300[/tex]
For NBC
[tex]E =np = 300 * 0.25 = 75[/tex]
[tex]O -E = 87 - 75 = 12[/tex]
[tex](O -E)^2 = (12)^2 = 144[/tex]
[tex]x^2 = \frac{(O - E)^2}{E} = \frac{144}{75} = 1.920[/tex]
For others:
[tex]E = np = 300 * 0.18 =54[/tex]
[tex]O - E = 53 - 54 = -1[/tex]
[tex](O - E)^2 = (-1)^2= 1[/tex]
[tex]x^2 = \frac{(O - E)^2}{E} = \frac{1}{54} = 0.019[/tex]
[tex]\sum x^2 = 0.736 + 4.300 + 1.920 + 0.019[/tex]
[tex]\sum x^2 = 6.975[/tex]
[tex]\sum x^2 = 6.98[/tex] --- approximated
The value of the 2 test statistic is 6.98
Next, is to determine the p value:
Calculate the degree of freedom
[tex]df = n - 1[/tex]
[tex]df = 4 - 1[/tex]
[tex]df = 3[/tex]
Using the [tex]x^2[/tex] table in the 3rd row,
[tex]\sum x^2 = 6.98[/tex] corresponds to:
[tex]p = 0.072699[/tex]
The value of p is:
[tex]0.05 < P < 0.10[/tex]
This implies that, we fail to reject H o
what is the H.C.F of 2³×3²
Can someone show me how to do this? I’m not sure how to do this
Directions: The points in the table lie on a line. Find the slope of the line. Then draw its graph.
Answer: Slope means the gradient. So find the equation of the line first then graph the points on the graph.
Step-by-step explanation:
y=mx+c *We want m*
m=(y2-y1)/(x2-x1)
m=(0-1)/(6-3)
m=-1/3
y=-1/3x+2 *(0,2) co-ordinate means it's the y-intercept=c*
I think the slope is -1/3 and then just plt the points on the graph manually.
Marking brainliest!!
What should I put for the second question? I am confused. HELPP
Which of the following is the correct factorization of the polynomial 4x2 - 11x +7?
A)
(4x - 1)(x - 7)
B)
(4x - 7)(x - 1)
C)
(4x - 7)(x + 1)
D)
(4x + 1)(x - 7)
pls help me im sooo stuck on math
The cost of making a chair is $28 correct to the nearest dollar. Calculate the lower and upper bounds for the cost of making 450 chairs
Answer:
$12,375
$12820.50
Step-by-step explanation:
To obtain a rounded value of $28 (to nearest dollar) the lowest and highest possible value before rounding will be : 27.50 and 28.49
Hence,
Lower bound = $27.50
Upper bound = $28.49
Therefore. Cost of making 450 chairs ;
27.50 * 450 = $12,375 (lower bound)
28.49 * 450 $12820.50 (upper bound)
a. Identify the relationship between the two
angles.
b. Write the equation used to represent the
relationship between the two angles.
c. Solve for the unknown variable.
Answer:
a - Mutual
b - (x+21)+(2x+3)=90
c - 3x +24 =90
3x=90-24
3x=66
X=22
Factorise the expressions.
Answer:
7 ([tex]y^{2}[/tex] + 6[tex]Z^{2}[/tex])
3a (x - 2y) - 4b(2y - x)
pq(p - 1) - [tex]r^{2}[/tex]( p - 1)
Step-by-step explanation:
(ii) 7y^2+35Z^2
=7(y^2+5Z^2)
(v) 3ax-6ay-8by+4bx
=x(3a+4b)-2y(3a+4b)
=(3a+4b)(x-2y)
viii)p^2q-pr^2-pq+r^2
=pq(p-1)-r^2(p-1)
=(p-1)(pq-r^2)
Please do not send links you will be reported and removed. What is this answer in feet please
Answer:
16.2 feet
Step-by-step explanation:
Reference angle = 62°
Opposite = x
Adjacent = 8.6
Apply trigonometric function, TOA:
Tan 62 = Opp/Adj
Tan 62 = x/8.6
8.6 × Tan 62 = x
16.1742476 = x
x = 16.2 ft (nearest tenth)
Solve the systems of equations problem using Elimination.
{3x+6y=27
{x+2y=11
Please clearly explain how you got your answer.
The cashier determines that the customer's groceries total $156.75. If the sales tax is four percent, how much will the customer have to pay for their groceries, including tax?
Determine whether the underlined number is a statistic or a parameter. Choose the correct statement below. because the value is a numerical measurement describing a characteristic of a . because the value is a numerical measurement describing a characteristic of a . because the value is a numerical measurement describing a characteristic of a . because the value is a numerical measurement describing a characteristic of a .
Complete question :
Determine whether the underlined number is a statistic or a parameter.
"In a study of all 4841 students at a college, it is found that 55% own a computer."
Answer:
because the value is a numerical measurement describing a characteristic of a population.
Step-by-step explanation:
The difference between statistic and parameter lies in the fact that, statistics are used in describing the numerical value obtained from a sample of data. While parameter are used to describe the numerical characteristics of a population.
Hence, all students of a college refers to the population(entire students). Therefore, the numerical characteristics obtained from such data would be called a parameter.
Four points are drawn on the coordinate plane and connected with straight lines to form a rectangle. Three of the vertices of the rectangle are located at (2, 1), (2, 4) and (4.4). a What are the coordinates of the fourth vertex of the rectangle? b. What are the dimensions of the rectangle? c What is the area of the rectangle?
You have 2 points with the same x value of 2 and 2 points with the same y value of 4.
You now need 2 points with the same x value of 4 ( you are given 1) and 2 y values of 1 ( you are given 1.
The missing point would need to be (4,1)
The width would be x2-x1 = 4-2 = 2 units
The length would be y2-y1 = 4-1 = 3 units
Area = 3x 2 = 6 square units
What is -1
What is the answer
Answer:
1
Step-by-step explanation:
The answer is actually just positive 1.
Absolute value is the direct opposite of a number with a positive value on a number line. However, the absolute value is always answered in a positive form of the number meaning that no matter what the number is (even if it's a positive number) the answer will always be that same number, but in positive form.
Remember, if a number is in between two of these " | " then the answer will be that same number but in positive form.
Hope this helps and have a nice day.
-R3TR0 Z3R0
In triangle ABC, angle C is a right angle. If cos A = 5 8, what is the value of cos B?
Answer:
65
Step-by-step explanation:
Please anyone help me on this
Answer:
y=-1/4x+21/4
Step-by-step explanation:
Slope=-2/8=-1/4
y=-1/4x+b
4=-1/4(5)+b
4=-5/4+b
5.25=b
21/4=b
What is the area of the shaded region?
Answer:
12 cm^2
Step-by-step explanation:
Pls answer correctly I’ll give you brainliest
Answer:
1=2(4)+b
Step-by-step explanation:
slope intercept looks like this y=mx(or y=#x+#
if the slope is 2 the equation will be y=2x+b
to find b so x=4 and y=1 we can plug those numbers into the equation to find b
Find the measure of 67.
81
96
90
47 = [?]
Entor
Answer
Correct option is
A
68
Answer:
96 is the answer because vertically opposite angles are always equal
Give me the correct answer
Answer:
[tex]71a(5a^{6} - 2b^{2} )[/tex]
Step-by-step explanation:
355 a3 a4 - 142 ab2
71a( 5a^6-2b^2)
I hope im right !!
GIVING 25 PTS URGENT
Answer:
D) 76 sq in
Step-by-step explanation:
It’s 4 triangles. A=1/2bh
1/2(8)(5)=20 (two of these)
1/2(8)(6)=24
1/2(4)(6)=12
20+20+24+12=76
the sum of the three sisters' ages is 51. If ava is 6 years older than
Camila, and Camila is twice as old as Luna, what are the ages of the
three sisters?
Create an equation with only one variable.
9514 1404 393
Answer:
Luna is 9Camila is 18Ava is 24Step-by-step explanation:
We can express all of the ages in terms of Luna's age. Letting L represent Luna's age, we have ...
Luna's age: LCamila's age: 2LAva's age: 2L +6The total of their ages is then ...
L +2L +(2L+6) = 51 . . . . an equation with one variable
5L = 45
L = 9
Luna is 9, Camila is 18, and Ava is 24.