All categories

2 years ago

If k is a nonzero constant, what is the slope of the line containing the points (k,2k) and (3k,k)

Mathematics

1 answer:

ivolga24 [154]2 years ago

3 0

Answer:

The slope is -1/2

Step-by-step explanation:

$m=\frac{y_2-y_1}{x_2-x_1}\\ \\m=\frac{k-2k}{3k-k}\\ \\m=\frac{-k}{2k}\\ \\m=-\frac{1}{2}$

You might be interested in

Solve by using proper methods.

oksano4ka [1.4K]

Answer:

Approximately after 66.15 years, there will be 100 coyotes left

Step-by-step explanation:

We can use the formula $F=P(1+r)^t$ to solve this.

Where

F is the future amount (F=100 coyotes)

P is the initial amount (P=750 coyotes)

r is the rate of decrease per year (which is -3% per year or -0.03)

t is the time in years (which we need to find)

Putting all the information into the formula we solve.

Note: The logarithm formula we will use over here is $ln(a^b)=bln(a)$

So, we have:

$F=P(1+r)^t\\100=750(1-0.03)^t\\100=750(0.97)^t\\\frac{100}{750}=0.97^t\\\frac{2}{15}=0.97^t\\ln(\frac{2}{15})=ln(0.97^t)\\ln(\frac{2}{15})=tln(0.97)\\t=\frac{ln(\frac{2}{15})}{ln(0.97)}\\t=66.15$

Hence, after approximately 66.15 years, there will be 100 coyotes left.

Rounding, we will have 66 years

4 0

3 years ago

Can someone help pls

Iteru [2.4K]

I want to say 5.5 because I did 11 / 2 and got that so i know it’s wrong but yea

4 0

3 years ago

Read 2 more answers

The perimeter of parallelogram ABCD is 72cm. AD is 3cm more than twice AB. Find the lengths of all four sides of ABCD

GarryVolchara [31]

Answer:

AB=11, DC=11, AD=25, BC=25

Step-by-step explanation:

Opposite sides of parallelograms are congruent.

x+x+2x+3+2x+3=72

6x+6=72

6x=66

x=11

2(11)+3 = 25

6 0

3 years ago

A matched pairs experiment compares the taste of instant versus fresh-brewed coffee. Each subject tastes two unmarked cups of co

Bogdan [553]

Answer:

We conclude that the majority of people prefer the taste of fresh-brewed coffee.

Step-by-step explanation:

We are given that of the 50 subjects who participate in the study, 16 prefer the instant coffee.

We have to test the claim that a majority of people prefer the taste of fresh-brewed coffee.

Let p = proportion of the population who prefer fresh-brewed coffee

So, Null Hypothesis, $H_0$ : p $\leq$ 50% {means that the majority of people does not prefer the taste of fresh-brewed coffee}

Alternate Hypothesis, $H_A$ : p > 50% {means that the majority of people prefer the taste of fresh-brewed coffee}

The test statistics that would be used here One-sample z proportion statistics;

T.S. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion who prefer fresh-brewed coffee = $\frac{34}{50}$ = 0.68

n = sample of subjects = 50

So, test statistics = $\frac{0.68-0.50}{\sqrt{\frac{0.68(1-0.68)}{50} } }$

= 2.73

The value of z test statistics is 2.73.

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

P-value = P(Z > 2.73) = 1 - P(Z $\leq$ 2.73)

= 1 - 0.99683 = 0.0032

Since, in the question we are not given with the level of significance so we assume it to be 5%. Now, at 5% significance level the z table gives critical values of 1.645 for right-tailed test.

Since our test statistics is more than the critical value of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the majority of people prefer the taste of fresh-brewed coffee.

4 0

3 years ago

Consider the function g(x)=3x+2x-4 (a)(-2) (b)(0) (c)(4) (d)(15)

WINSTONCH [101]

Answer:

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers