What is the solution to the system of equations? -4y – 3x = -11 x

The population of a small town on January 1, 2005, was 7,200. On January 1, 2006, the population was 7,416. On January 1, 2007,

gogolik [260]

Answer:

(c) 8597

Step-by-step explanation:

A tool for regression analysis shows the given population values fit an exponential curve better than they fit a line. The exponential function for the population can be written as approximately ...

p(x) = 6211.54(1.02998^x) . . . . . x is years after 2000

Then for x=11, the population is about ...

p(11) ≈ 8596.4

The closest answer choice is 8597.

5 0

2 years ago

2. A marketing firm is trying to estimate the proportion of potential car buyers that would consider

Maurinko [17]

Answer:

a. The number of people that should be in the pilot study are 600 people

b. The point estimate is 0.62 $\overline 6$

c. At 95% confidence level the true population proportion of potential car buyers of hybrid vehicle is between the confidence interval (0.588, 0.6654)

d. Two ways to reduce the margin of error are;

1) Reduce the confidence interval

2) Use a larger sample size

Step-by-step explanation:

a. The given parameters for the estimation of sample size is given as follows;

The margin of error for the confidence interval, E = 4% = 0.04

The confidence level = 95%

The sample size formula for a proportion as obtained from an online source is given as follows;

$n = \dfrac{Z^2 \times P \times (1 - P)}{E^2}$

Where, P is the estimated proportions of the desired statistic, therefore, we have for a new study, P = 0.5;

Z = The level of confidence at 95% = 1.96

n + The sample size

Therefore, we have;

$n = \dfrac{1.96^2 \times 0.5 \times (1 - 0.5)}{0.04^2} = 600.25$

Therefore, the number of people that should be in the pilot study in order to meet this goal at 95% confidence level is n = 600 people

b. The point estimate for the population proportion is the sample proportion given as follows;

$\hat p = \dfrac{x}{n}$

Where;

x = The number of the statistic in the sample

n = The sample size

From the question, we have;

The number of potential car buyers, n = 600

The number of respondent in the sample that indicated that they would consider purchasing a hybrid, x = 376

Therefore, the point estimate, for the proportion of potential car buyers that would consider buying a hybrid vehicle, $\hat p$ = 376/600 = 0.62 $\overline 6$

c. The confidence interval for a proportion is given as follows

$CI=\hat{p}\pm z\times \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

Therefore, we get;

$CI=0.62 \overline 6\pm 1.96\times \sqrt{\dfrac{\hat{0.62 \overline 6}\cdot (1-\hat{0.62 \overline 6})}{600}}$

C.I. ≈ 0.6267 ± 0.0387

The 95% confidence interval for the true population proportion of potential buyers of hybrid vehicle, C.I. = (0.588, 0.6654)

d. The margin of error is given by the following formula;

$MOE_\gamma = z_\gamma \times \sqrt{\dfrac{\sigma ^2}{n} }$

Where;

$MOE_\gamma$ = Margin of error at a given level of confidence

$z_\gamma$ = z-score

σ = The standard deviation

n = The sample size

Therefore, the margin error can be reduced by the following two ways;

1) Reducing the confidence interval and therefore, the z-score

2) Increasing the sample size

6 0

3 years ago

-3x + 4x + 1- 8 whats the answer

Marta_Voda [28]

Answer:

x - 7

Step-by-step explanation:

just add/substract like terms only

3 0

3 years ago

You are given the following data, where X1 (final percentage in history class) and X2 (number of absences) are used to predict Y

vaieri [72.5K]

Answer:

Step-by-step explanation:

Hello!

Given the variables

Y: standardized history test score in third grade.

X₁: final percentage in history class.

X₂: number of absences per student.

Determine the following multiple regression values.

I've estimated the multiple regression equation using statistics software:

^Y= a + b₁X₁ + b₂X₂

a= 118.68

b₁= 3.61

b₂= -3.61

^Y= 118.68 + 3.61X₁ - 3.61X₂

ANOVA Regression model:

Sum of Square:

SS regression: 25653.86

SS Total: 36819.23

F-ratio: 11.49

p-value: 0.0026

Se²= MMError= 1116.54

Hypothesis for the number of absences:

H₀: β₂=0

H₁: β₂≠0

Assuming α:0.05

p-value: 0.4645

The p-value is greater than the significance level, the decision is to not reject the null hypothesis. Then at 5% significance level, there is no evidence to reject the null hypothesis. You can conclude that there is no modification of the test score every time the number of absences increases one unit.

I hope this helps!

5 0

4 years ago

Directions - For the following problem, write a paragraph proof to justify each step you make. All work must be neat,

nlexa [21]

$$ PS = \frac{4}{3} x$