All categories

1 year ago

Emma is planning her summer and would like to work enough to travel and buy a new laptop.

Mathematics

2 answers:

Pani-rosa [81]1 year ago

6 0

Answer:

(a) The required equation is $90x-150y=700$ .

(b) The graph of given relation is shown below.

(d) She needs to work for 18 days.

Step-by-step explanation:

Let x be the number of days she can work and y is the number of days she can travel.

She can earn $90 each day. She expects each day of travel will cost her $150 and the laptop she hopes to buy costs $700.

$90x-150y=700$

Therefore the required equation is 90x-150y=700.

(b)

The given relation is

$90x-150y=700$ .... (1)

Rewrite the above equation in slope intercept form.

$150y=90x-700$

Divide both sides by 150.

$y=\frac{90x-700}{150}$

$y=\frac{3}{5}x-\frac{14}{3}$

It is a straight line with slope 3/5 and y-intercept (14)/3. The graph of given relation is shown below.

(c)

The relation is

$y=\frac{3}{5}x-\frac{14}{3}$

Here, x is the number of days she can work and she can work a maximum of 40 days. So the domain of the function is

$Domain=\{x|x\in Z,0\leq x\leq 40\}$

At x=0,

$y=\frac{3}{5}(0)-\frac{14}{3}=-\frac{14}{3}$

At x=40,

$y=\frac{3}{5}(40)-\frac{14}{3}=\frac{58}{3}$

y is the number of days she can travel, so y cannot be negative.

The range of the relation is

$Range=\{y|y\in Z,0\leq x\leq \frac{58}{3}\}$

(d)

We need to find the number of days she need to work if she plans to travel for 6 days.

Substitute y=6 in equation (1) to find the value of x.

$90x-150(6)=700$

$90x-900=700$

$90x=700+900$

$90x=1600$

$90x=\frac{1600}{90}$

$x=17.77\approx 18$

Therefore she needs to work for 18 days.

V125BC [204]1 year ago

3 0

For the answer to the question above, f x is the number of days she works, she'll earn $90x 
After buying the laptop, she'll have $90x - $700 left over, which will pay for ($90x - $700) / $150 days of travel. So we have y = ($90x - $700) / $150 = (9x - 70) / 15 = 0.6x - (14/3) 
Note that y can't be negative. Also, if y = 0, then Emma doesn't get to travel at all, so we should avoid that. So we have: 
0.6x - (14/3) > 0 
0.6x > 14/3 
x > (14/3) / 0.6 
x > 70/9 
The question says that x can be up to 40, so the domain is 70/9 < x <= 40 
That's approximately 7.777... < x <= 40 
Multiply those numbers by 0.6 and then subtract 700 to get the range: 
0 < y <= 58/3 
That's approximately 0 < y <= 19.333

You might be interested in

Decide whether the function is an exponential growth or exponential decay function, and find the constant percentage rate of gro

frosja888 [35]

Consider the function f ( x ) = 2479 ⋅ 0.9948x First compare this with f ( x ) po ( 1 + r ) ^ 2 We get po = 2479 And 1 + r = 0.9948 = 1 – 0.0052 r = -0.0052 < 0 Therefore, f is an exponential decay function with a decay rate of 0.0052 x 100 = 0.52%

8 0

2 years ago

A member of a student team playing an interactive marketing game received the fol- lowing computer output when studying the rela

nirvana33 [79]

Answer:

$p_v = 2*P(t_{n-2} > |t_{calc}|)= 0.91$

So on this case for the significance level assumed $\alpha=0.05$ we see that $p_v >\alpha$ so then we can conclude that the result is NOT significant. And we don't have enough evidence to reject the null hypothesis.

So on this case is not appropiate say that :"the more we spend on advertising this product, the fewer units we sell" since the slope for this case is not significant.

Step-by-step explanation:

Let's suppose that we have the following linear model:

$y= \beta_o +\beta_1 X$

Where Y is the dependent variable and X the independent variable. $\beta_0$ represent the intercept and $\beta_1$ the slope.

In order to estimate the coefficients $\beta_0 ,\beta_1$ we can use least squares procedure.

If we are interested in analyze if we have a significant relationship between the dependent and the independent variable we can use the following system of hypothesis:

Null Hypothesis: $\beta_1 = 0$

Alternative hypothesis: $\beta_1 \neq 0$

Or in other words we want to check is our slope is significant (X have an effect in the Y variable )

In order to conduct this test we are assuming the following conditions:

a) We have linear relationship between Y and X

b) We have the same probability distribution for the variable Y with the same deviation for each value of the independent variable

c) We assume that the Y values are independent and the distribution of Y is normal

The significance level assumed on this case is $\alpha=0.05$

The standard error for the slope is given by this formula:

$SE_{\beta_1}=\frac{\sqrt{\frac{\sum (y_i -\hat y_i)^2}{n-2}}}{\sqrt{\sum (X_i -\bar X)^2}}$

Th degrees of freedom for a linear regression is given by $df=n-2$ since we need to estimate the value for the slope and the intercept.

In order to test the hypothesis the statistic is given by:

$t=\frac{\hat \beta_1}{SE_{\beta_1}}$

The p value on this case would be given by:

$p_v = 2*P(t_{n-2} > |t_{calc}|)= 0.91$

So on this case is not appropiate say that :"the more we spend on advertising this product, the fewer units we sell" since the slope for this case is not significant.

3 0

1 year ago

The table below represents Gerry's trip to school and back home. If the total time is 45 minutes, how far does Gerry live from s

lozanna [386]

Answer: X/8 + X/16 = 3/4

Step-by-step explanation:

you’re just dividing the distance by the rate you are going.

5 0

1 year ago

Read 2 more answers

Alexa borrowed some money from her friend in order to help buy a new video game system. Alexa agreed to pay back her friend $10

Ulleksa [173]