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Pavel [41]
3 years ago
9

John has taken out a loan for college. He started paying off the loan with a first payment of $100. Each month he pays, he wants

to pay back 1.1 times the amount he paid the month before. Explain to John how to represent his first 20 payments in sequence notation. Then explain how to find the sum of his first 20 payments, using complete sentences.
Mathematics
1 answer:
sergeinik [125]3 years ago
8 0
<span>Let a_0 = 100, the first payment. Every subsequent payment is the prior payment, times 1.1. In order to represent that, let a_n be the term in question. The term before it is a_n-1. So a_n = 1.1 * a_n-1. This means that a_19 = 1.1*a_18, a_18 = 1.1*a_17, etc. To find the sum of your first 20 payments, this sum is equal to a_0+a_1+a_2+...+a_19. a_1 = 1.1*a_0, so a_2 = 1.1*(1.1*a_0) = (1.1)^2 * a_0, a_3 = 1.1*a_2 = (1.1)^3*a_3, and so on. So the sum can be reduced to S = a_0 * (1+ 1.1 + 1.1^2 + 1.1^3 + ... + 1.1^19) which is approximately $5727.50</span>
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A recent study focused on the number of times men and women who live alone buy take-out dinner in a month. Assume that the distr
Marianna [84]

Answer:

(a) Decision rule for 0.01 significance level is that we will reject our null hypothesis if the test statistics does not lie between t = -2.651 and t = 2.651.

(b) The value of t test statistics is 1.890.

(c) We conclude that there is no difference in the mean number of times men and women order take-out dinners in a month.

(d) P-value of the test statistics is 0.0662.

Step-by-step explanation:

We are given that a recent study focused on the number of times men and women who live alone buy take-out dinner in a month.

Also, following information is given below;

Statistic : Men      Women

The sample mean : 24.51      22.69

Sample standard deviation : 4.48    3.86

Sample size : 35    40

<em>Let </em>\mu_1<em> = mean number of times men order take-out dinners in a month.</em>

<em />\mu_2<em> = mean number of times women order take-out dinners in a month</em>

(a) So, Null Hypothesis, H_0 : \mu_1-\mu_2 = 0     {means that there is no difference in the mean number of times men and women order take-out dinners in a month}

Alternate Hypothesis, H_A : \mu_1-\mu_2\neq 0     {means that there is difference in the mean number of times men and women order take-out dinners in a month}

The test statistics that would be used here <u>Two-sample t test statistics</u> as we don't know about the population standard deviation;

                      T.S. =  \frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p \sqrt{\frac{1}{n_1}+\frac{1}{n_2}  } }  ~ t__n_1_-_n_2_-_2

where, \bar X_1 = sample mean for men = 24.51

\bar X_2 = sample mean for women = 22.69

s_1 = sample standard deviation for men = 4.48

s_2 = sample standard deviation for women = 3.86

n_1 = sample of men = 35

n_2 = sample of women = 40

Also,  s_p=\sqrt{\frac{(n_1-1)s_1^{2}+(n_2-1)s_2^{2}  }{n_1+n_2-2} }  =  \sqrt{\frac{(35-1)\times 4.48^{2}+(40-1)\times 3.86^{2}  }{35+40-2} } = 4.16

So, <u>test statistics</u>  =  \frac{(24.51-22.69)-(0)}{4.16 \sqrt{\frac{1}{35}+\frac{1}{40}  } }  ~ t_7_3

                              =  1.890

(b) The value of t test statistics is 1.890.

(c) Now, at 0.01 significance level the t table gives critical values of -2.651 and 2.651 at 73 degree of freedom for two-tailed test.

Since our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <u>we fail to reject our null hypothesis</u>.

Therefore, we conclude that there is no difference in the mean number of times men and women order take-out dinners in a month.

(d) Now, the P-value of the test statistics is given by;

                     P-value = P( t_7_3 > 1.89) = 0.0331

So, P-value for two tailed test is = 2 \times 0.0331 = <u>0.0662</u>

4 0
3 years ago
You roll a 6-sided die. What is P(factor of 10)? Write your answer as a percentage rounded to the nearest tenth.
exis [7]

Answer:

5 is the factor of 10. 5% of 10

6 0
3 years ago
Find the Maclaurin polynomials of orders n = 0, 1, 2, 3, and 4, and then find the nth Maclaurin polynomials for the function in
Zielflug [23.3K]

Answer:

Σ(-1)^kx^k for k = 0 to n

Step-by-step explanation:

The nth Maclaurin polynomials for f to be

Pn(x) = f(0) + f'(0)x + f''(0)x²/2! + f"'(0)x³/3! +. ......

The given function is.

f(x) = 1/(1+x)

Differentiate four times with respect to x

f(x) = 1/(1+x)

f'(x) = -1/(1+x)²

f''(x) = 2/(1+x)³

f'''(x) = -6/(1+x)⁴

f''''(x) = 24/(1+x)^5

To calculate with a coefficient of 1

f(0) = 1

f'(0) = -1

f''(0) = 2

f'''(0) = -6

f''''(0) = 24

Findinf Pn(x) for n = 0 to 4.

Po(x) = 1

P1(x) = 1 - x

P2(x) = 1 - x + x²

P3(x) = 1 - x+ x² - x³

P4(x) = 1 - x+ x² - x³+ x⁴

Hence, the nth Maclaurin polynomials is

1 - x+ x² - x³+ x⁴ +.......+(-1)^nx^n

= Σ(-1)^kx^k for k = 0 to n

6 0
3 years ago
Identify the slope represented in the graph below.
Vedmedyk [2.9K]
Answer:
The slope is -2
Explanation:
I choose two points on the graph (0,-2) and (-1,0) and put it into the slope form using two coordinate pairs which is y-y/x-x and got -2/1 which simplifies down to -2
5 0
2 years ago
A ball is kicked upward with an initial velocity of 32 feet per second. The ball's height, h (in feet), from the ground is model
stellarik [79]

Answer:

1.        t = 0.995 s

2.       h = 15.92  ft

Step-by-step explanation:

First we have to look at the following formula

Vf = Vo + gt

then we work it to clear what we want

Vo + gt = Vf

gt = Vf - Vo

t = (Vf-Vo)/g

Now we have to complete the formula with the real data

Vo = 32 ft/s      as the statement says

Vf = 0     because when it reaches its maximum point it will stop before starting to lower

g = -32,16 ft/s²        it is a known constant, that we use it with the negative sign because it is in the opposite direction to ours

t = (0 ft/s - 32 ft/s) / -32,16 ft/s²

we solve and ...

t = 0.995 s

Now we will implement this result in the following formula to get the height at that time

h = (Vo - Vf) *t /2

h = (32 ft/s - 0 ft/s) * 0.995 s / 2

h = 32 ft/s * 0.995 s/2

h = 31.84 ft / 2

h = 15.92  ft

4 0
2 years ago
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