What is the equation of a line containing the points (-3,2) and (-2,-1)

In a small town, electricity prices have been rising 2% each year since 2008. Which

mihalych1998 [28]

<h3>Answer: p = 0.12*(1.02)^t</h3>

Explanation:

The general exponential growth equation is

p = A*B^t

where t is the number of years that have gone by after 2008, A is the starting amount, B is the growth multiplier, and p is the price t years after 2008

We know that A = 0.12 is the starting price

The value of B is B = 1.02 which is in the form 1+r since 1.02 = 1 + 0.02 = 1+r

The r value is r = 0.02 and it is positive to represent growth. Keep in mind that 2% = 2/100 = 0.02

So we go from

p = A*B^t

to

p = 0.12*(1.02)^t

4 0

3 years ago

Mike runs for the president of the student government and is interested to know whether the proportion of the student body in fa

Alik [6]

Answer:

We conclude that the proportion of student body in favor of him is significantly less than or equal to 50%.

Step-by-step explanation:

We are given that Mike runs for the president of the student government and is interested to know whether the proportion of the student body in favor of him is significantly more than 50 percent.

A random sample of 100 students was taken. Fifty-five of them favored Mike.

Let p = proportion of the students who are in favor of Mike.

So, Null Hypothesis, $H_0$ : p $\leq$ 50% {means that the proportion of student body in favor of him is significantly less than or equal to 50%}

Alternate Hypothesis, $H_A$ : p > 50% {means that the proportion of student body in favor of him is significantly more than 50%}

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 of students body in favor of Mike = $\frac{55}{100}$ = 0.55

n = sample of students taken = 100

So, test statistics = $\frac{0.55-0.50}{\sqrt{\frac{0.55(1-0.55)}{100} } }$

= 1.01

The value of z test statistics is 1.01.

Now, at 0.05 significance level the z table gives critical value of 1.645 for right-tailed test.

Since our test statistic is less than the critical value of z as 1.01 < 1.645, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the proportion of student body in favor of him is significantly less than or equal to 50% or proportion of the students in favor of Mike is not significantly greater than 50 percent.

4 0

3 years ago

Are these ratios equivalent?

Rainbow [258]

Yes they are the both equal 5.25 when divided

4 0

3 years ago

Consider the function graphed below.

aivan3 [116]

Answer:

B. (see attached)

Step-by-step explanation:

All the answers agree that the function is x² for x < 1. Where they disagree is in the slope and y-intercept of the linear portion for x > 1.

The line has a slope that is less than 1 unit of rise for 1 unit of run, so will not be selections A or C, which have slopes of 3.

The y-intercept is clearly positive if we extend the line to the left until it reaches the y-axis. This eliminates selection D from consideration, leaving only selection B.

8 0

3 years ago

Type the correct answer in each box. If necessary, round your answers to the nearest hundredth.

disa [49]

Answer:

Perimeter = 32.44 units

Area = 30 square units

Step-by-step explanation:

Given

Vertices

A(2,8), B(16,2) and C(6,2)

WE have to determine the lengths of all sides before finding the perimeter and area.

The formula of modulus is:

$d = \sqrt{(x_{2}- x_{1})^{2} +(y_{2}-y_{1})^{2}}\\AB=\sqrt{(16-2)^{2} +(2-8)^{2}}\\=\sqrt{(14)^{2} +(-6)^{2}}\\=\sqrt{196+36}\\ =\sqrt{232}\\=15.23\\\\BC=\sqrt{(6-16)^{2} +(2-2)^{2}}\\=\sqrt{(-10)^{2} +(0)^{2}}\\=\sqrt{100+0}\\ =\sqrt{100}\\=10\\\\AC=\sqrt{(6-2)^{2} +(2-8)^{2}}\\=\sqrt{(4)^{2} +(-6)^{2}}\\=\sqrt{16+36}\\ =\sqrt{52}\\=7.21\\\\$

So the perimeter is:

$Perimeter=AB+BC+AC\\=15.23+10+7.21\\=32.44\ units$

Using hero's formula,

$s=\frac{perimeter}{2}\\s=\frac{32.44}{2}\\ s=16.22\\Area=\sqrt{s(s-a)(s-b)(s-c)}\\=\sqrt{16.22(16.22-15.23)(16.22-10)(16.22-7.21)}\\=\sqrt{(16.22)(0.99)(6.22)(9.01)}\\=\sqrt{899.91}\\=29.99\ square\ units$

Rounding off will give us 30 square units ..

4 0

3 years ago