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3 years ago

A system of linear equations is shown on the graph. The equation of one of the lines is y = 1/2x + 4

Mathematics

1 answer:

ra1l [238]3 years ago

7 0

Answer:

$y = 3x - 1$

Step-by-step Explanation:

From the graph given, let's label the lines as line A and line B. As indicated in the attachment below.

The equation of a line is given as y = mx + b

Where, m is the slope, which is:

$m = \frac{y2 - y1}{x2 - x1}$

b is the y-intercept. It is the point at which the line crosses or intercepts the y-axis. At this point, x = 0.

Having known this, let's figure out which of the lines has the equation, y = ½x + 4

From the equation given, it means the line's m = ½, and it's y-intercept (b), where the line intercepts the y-axis = 4.

Taking a look at line A and B that we've labelled in the attachment below, line A intercepts the y-axis at 4. This means value of b for line A = 4.

If we calculate the slope (m) for line A using the points labelled in the attachment below, we would arrive at ½ as the slope (m) of line A.

Therefore, the equation y = ½x + 4 is for line A.

Let's find the equation for line B.

=>Find the slope (m) of line B using any 2 coordinate pairs of line B.

We're using the 2 coordinates points, (0, -1), (-1, -4) as indicated in the attachment below.

$m = \frac{y2 - y1}{x2 - x1}$

$m = \frac{-4 - (-1)}{-1 - 0}$

$m = \frac{-4 + 1)}{-1}$

$m = \frac{-3)}{-1}$

$m = 3$

Line B intercepts the y-axis at -1. Therefore, the y-intercept (b) for line B = -1

The equation for line B would be:

$y = 3x - 1$

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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

if a model of a tower uses a scale of 1/3 inch=2ft and the actual tower is 207 feet tall what's the height of the model

stepladder [879]

Answer:

The height of the model is 2 feet 10.5 inches.

Step-by-step explanation:

Given:

scale of 1/3 inch=2ft

actual tower is 207 feet

To Find:

The height of the model = ?

Solution:

We know that 1 feet is 12 inches

Then 2 feet is $12 \times 2$ = 24 inches

24 inches= $72 \times \frac{1}{3}$ of a inch.

The tower is 72 times the scale of the model.

Now the actual tower is 207 feet

$\frac{207}{72}$ = $\frac{23}{8}$ , units feet

=> $2 \frac{7}{8} feet$

=> 2 feet 10.5 inches.

7 0

3 years ago

Interest earned:$45 Principal: ? Interest rate: 3% Time: 2 years

Yakvenalex [24]

Answer:

The Principal = $75,000

Step-by-step explanation:

Formula for finding the principal:

I × 100/ R × T

Therefore;

Principal = 45 × 100 / 3/ 100 × 2

$= \: \frac{45 \times 100}{ \frac{3}{100} \times 2} \\ = \frac{4500}{ \frac{3}{50} } \\ = 4500 \times \frac{50}{3} \\ = 1500 \times 50 \\ = 75000.00$

Which means that the Principal is $75,000.00

8 0

3 years ago

Equations of Exponential Functions

andriy [413]

Answer:

B. B is 0.535; It is a decay factor.

Step-by-step explanation:

I calculated it logically

3 0

3 years ago

Read 2 more answers

A: {71,73,79,83,87} B:{57,59,61,67}

Jobisdone [24]

Answer:

$\frac{3}{5}$ .

Step-by-step explanation:

We have been given two sets as A: {71,73,79,83,87} B:{57,59,61,67}. We are asked to find the probability that both numbers are prime, if one number is selected at random from set A, and one number is selected at random from set B.

We can see that in set A, there is only one non-prime number that is 87 as it is divisible by 3.

So there are 4 prime number in set A and total numbers are 5.

$P(\text{Prime number from A})=\frac{4}{5}$

We can see that in set B, there is only one non-prime number that is 57 as it is divisible by 3.

So there are 3 prime number in set B and total numbers are 4.

$P(\text{Prime number from B})=\frac{3}{4}$

Now, we will multiply both probabilities to find the probability that both numbers are prime. We are multiplying probabilities because both events are independent.

$P(\text{Prime number from A and B})=\frac{4}{5}\times \frac{3}{4}$

$P(\text{Prime number from A and B})=\frac{1}{5}\times \frac{3}{1}$

$P(\text{Prime number from A and B})=\frac{3}{5}$

Therefore, the probability that both numbers are prime would be $\frac{3}{5}$ .

4 0

3 years ago