What is the recursive formula for this sequence:
1,-1,-3, -5......

Answer:

a. 0.1038 = 10.38% probability that the sample mean is more than 59 pounds.

b. 0.6772 = 67.72% probability that the sample mean is more than 56 pounds.

c. 0.2210 = 22.10% probability that the sample mean is between 56 and 57 pounds.

d. 0.0146 = 1.46% probability that the sample mean is less than 53 pounds.

e. 0% probability that the sample mean is less than 49 pounds.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The Aluminum Association reports that the average American uses 56.8 pounds of aluminum in a year. The population standard deviation of annual usage is 12.3 pounds.

This means that [tex]\mu = 56.8, \sigma = 12.3[/tex]

Sample of 50:

This means that [tex]n = 50, s = \frac{12.3}{\sqrt{50}} = 1.74[/tex]

a. More than 59 pounds

This is 1 subtracted by the pvalue of Z when X = 59.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{59 - 56.8}{1.74}[/tex]

[tex]Z = 1.26[/tex]

[tex]Z = 1.26[/tex] has a pvalue of 0.8962

1 - 0.8962 = 0.1038

0.1038 = 10.38% probability that the sample mean is more than 59 pounds.

b. More than 56 pounds

This is 1 subtracted by the pvalue of Z when X = 56. So

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{56 - 56.8}{1.74}[/tex]

[tex]Z = -0.46[/tex]

[tex]Z = -0.46[/tex] has a pvalue of 0.3228

1 - 0.3228 = 0.6772

0.6772 = 67.72% probability that the sample mean is more than 56 pounds.

c. Between 56 and 57 pounds

This is the pvalue of Z when X = 57 subtracted by the pvalue of Z when X = 56.

X = 57

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{57 - 56.8}{1.74}[/tex]

[tex]Z = 0.11[/tex]

[tex]Z = 0.11[/tex] has a pvalue of 0.5438

X = 56

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{56 - 56.8}{1.74}[/tex]

[tex]Z = -0.46[/tex]

[tex]Z = -0.46[/tex] has a pvalue of 0.3228

0.5438 - 0.3228 = 0.2210

0.2210 = 22.10% probability that the sample mean is between 56 and 57 pounds.

d. Less than 53 pounds

This is the pvalue of Z when X = 53.

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{53 - 56.8}{1.74}[/tex]

[tex]Z = -2.18[/tex]

[tex]Z = -2.18[/tex] has a pvalue of 0.0146

0.0146 = 1.46% probability that the sample mean is less than 53 pounds.

e. Less than 49 pounds

This is the pvalue of Z when X = 49.

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{49 - 56.8}{1.74}[/tex]

[tex]Z = -4.48[/tex]

[tex]Z = -4.48[/tex] has a pvalue of 0

0% probability that the sample mean is less than 49 pounds.

Answer:

if x=4, the answer is -2.

Step-by-step explanation:

4x3-(3+4)2

12-7x2

12-14

= -2

i hope this helps :)

Answer: $21.99

Step-by-step explanation:

First, we need to solve for the total cost of 4 packs of football cards

We can either do: $3.97+$3.97+$3.97+$3.97

or

$3.97 x 4

This will equal: $15.88

Now we need to add $6.11 to $15.88

$6.11+$15.88

$21.99

Answer:

Hypotenuse= 97

Step-by-step explanation:

H² = B² + P²

H² = (65)² + (72)²

H² = 4225 + 5184

H²= 9409

Taking square root on both sides,

H= 97

Answer:

The missing side is 14.4

x=14.4

Answer:

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

+2($($;$)2:

hope it helps

Answer:

Step-by-step explanation:

[tex]\text{Show that a differentiable function f decreases most rapidly at x in the }[/tex]

[tex]\text{direction opposite the gradient vector, that is, in the direction of}[/tex] [tex]-\bigtriangledown f(x)[/tex][tex]\text{. Let}\ \theta \ \text{be the angle between} \bigtriangledown f(x) \ \text{and unit vector u. Then } D_u f = \mathbf{|\bigtriangledown f| \ cos \ \theta }}[/tex]

[tex]\text{Since the minimum value of} \ \ \mathbf{cos \ \theta} \ \ is \mathbf{-1} \ \text{occuring \ for \ 0} \le \ \theta \ < 2x, \\ \\ when \ \theta = \mathbf{\pi} , \text{the mnimum value of} \ D_uf \ is} -|\bigtriangledown f|, \text{occuring when the direction of u is } \\ \\ \ \mathbf{the \ opposite \ of} \ \text{the direction of } \ \bigtriangledown f (assuming \ \bigtriangledown f\ is \ not \ zero)[/tex]

b) [tex]\text{From part A:}[/tex]

[tex]If \ f(x,y) = x^4y -x^2y^2 \ \ decreases \ fastest \ at \ the \point \ (2,-5)\\ \\ F(x,y) = x^4y -x^2y^3 \\ \\ f_x = \dfrac{df}{dx}= \dfrac{d}{dx}(x^4y-x^2y^3) \\ \\ f_x = \dfrac{df}{dx}= y4x^3 -2y^3x \\ \\ For(2,-5) \\ \\ f_x = (-5)4(2)^3 -2(-5)^3(2) \\ \\ \mathbf{ f_x = 340}[/tex]

[tex]However; f_y = \dfrac{df}{dy} = \dfrac{d}{dy}(x^4y - x^2y^3) \\ \\ f_y = x^4 -3x^2y^2 \\ \\ Now, for (2, -5)\\ \\f_y = (2)^4 -3(2)^2(-5)^2 \\ \\ f_y = -284[/tex]

[tex]So; \bigtriangledown = < 340,-284> \text{this is the direction of fastest decrease}[/tex]

Answer: 80 degrees

Step-by-step explanation:

Answer:

B = 54 to the nearest degree.

Step-by-step explanation:

Remark

This is a sine law question. They can be rather nasty because no answer or 2 answers are possible. This one is well behaved because B, you are told, is acute. The two answer kind needs the supplement of an acute angle.

Sorry this blabs on and shouldn't. You are looking for <B

Formula

Sin(<B)/the side opposite = Sin(<A) / side opposite it

Simplified

Sin(<B) / 9 = Sin(A)/11

Sin(<B) / 9 = Sin(80) / 11             Multiply both sides by 9

9*Sin(B) / 9 = 9 * Sin(80) /11      The 9s Cancel

Now all you need to do is put it in your calculator. Do you need the steps?

Sin(B) = 9*sin(80) / 11

Sin(B) = 9 * 0.9848 /11

Sin(B)= 0.8058

B = Sin-1(0.8058)

B = 53.68

B = 54

Answer:

117

Step-by-step explanation:

By adding the percentages given: 3+16+14+18+10

you get 61%

multiply 300 by .61 or 61%

you get 183

subtract 183 from 300

you are left with 117 which is the answer

Answer:

y=2x+4

Step-by-step explanation:

Answer:

I think it's 20

Step-by-step explanation:

10x4÷2 because vase times height,the divide by 1/2 which it 2 so answer is 20

Answer:

$5740

Step-by-step explanation:

get 2.5% of 5600

5600/x=100/2.5

(5600/x)*x=(100/2.5)*x

5600=40*x

5600/40=x

140=x

x=140 <----- 2.5% of 5600

5600 + 140 = $5740

Answer:

I dont see any options....

But 1/4, 1/5, 1/6, 1/7, 2/7, etc

Step-by-step explanation:

Answer:

a lot but here are a few

Step-by-step explanation:

1/3 3/6 2/6 1/6 7/12 6/12 5/12 4/12 3/12 2/12 1/12 16/24 15/24 14/24 13/24 12/24 11/24 10/24 9/24 8/24 7/24 6/24 5/24 4/24 3/24 2/24 and 1/24

Answer:The answer is (1,-4).

Step-by-step explanation: Please mark this brainliest.

Answer:

m=17

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

m

=

17

Three times the quotient of 3 and 5 is equivalent to 1.8

The question asked us to convert the word problem to equation and solve.

The quotient of 3 and 5 is expressed as 3/5

Taking the product of the result and 3 will give;

Three times the quotient of 3 and 5 = 3 * 3/5

Three times the quotient of 3 and 5 = 9/5 = 1.8

Hence three times the quotient of 3 and 5 is equivalent to 1.8

Learn more on expressions here: https://brainly.com/question/723406

#SPJ6

Answer:

0 is a rational number, whole number, integer, and a real number.

Step-by-step explanation:

Answer:

where is the graph though?

Answer:

A

Step-by-step explanation:

Area = 1/2 * b * h

b = 4 in

h = 2.5 inches

Area = 1/2 * 4 * 2.5

Area = 2 * 2.5

Area = 5 in^2

Answer:

a) -150 feet per minute

b)-11,250 feet

c)240 minutes

Step-by-step explanation:

-3000/20 = -150 ft per minute

b) -150 times 75

c)-36000= -150x

Answer:

Each Shirt costs: $1.49

Each Slack costs: $4.49

Each Sport coat costs: $7.99

Answer:

1. Many possible solutions, two solutions would be: (-1,0) and (1,0)

2. x  =  −

2

±  i

Step-by-step explanation:

For the first equation, since its linear, there are many possible solutions!

two solutions would be: (-1,0) and (1,0)

For the second one, replace y with 0 and solve

x  =  −2 ±  i

Hope i helped, brainliest would be appreciated

Have a nice day!

  -Aadi x

Answer:

45535

Step-by-step explanation:

Answer:

45415

Step-by-step explanation:

Answer:

To maximize his earnings, Mr. Trenga must purchase 40 kayaks and 25 canoes.

Step-by-step explanation:

Since Mr. Trenga plans to start a new business called Rivers Explorers, which will rent canoes & kayaks to people to travel 10 miles down the Clarion River in Cook Forest State Park, and he has $ 45,000 to purchase new boats (canoes & kayaks) , and he can buy canoes for $ 600 each & kayaks for $ 750 each, and his facility can hold up to 65 boats, if the canoes will rent for $ 25 per day & the kayaks will rent for $ 30 per day, to determine how many canoes & how many kayaks should he buy to earn the most revenue, the following calculation should be performed:

65 x 750 = 48,750

48,750 - 45,000 = 3,750

750 - 600 = 150

3,750 / 150 = 25

25 x 600 + 40 x 750 = 45,000

25 x 25 + 30 x 40 = 1,825

600 x 5 = 3,000

750 x 4 = 3,000

40 x 30 + 25 x 25 = 1,825

60 x 30 + 0 x 25 = 1,800

56 x 30 + 5 x 25 = 1,805

52 x 30 + 10 x 25 = 1,810

48 x 30 + 15 x 25 = 1,815

44 x 30 + 20 x 25 = 1,820

Thus, to maximize his earnings, Mr. Trenga must purchase 40 kayaks and 25 canoes.

Answer:

28 Months

Step-by-step explanation:

(1140-1072)= 68

(1900/68)=27.9 ~ 28

Answer:

2,800

Step-by-step explanation:

700+900+1200=2800