Write each pair of quantities as a unit rate.

Which is the equation in slope-intercept form for the line that passes through (3, 7)

quester [9]

Answer:

$y = - \frac{5}{3} x + 12$

Step-by-step explanation:

First, rewrite the given equation in the form of y=mx+c.

m is the gradient while c is the y-intercept.

3x-5y=8

5y= 3x -8

$y = \frac{3}{5} x - \frac{8}{5}$

Thus, the gradient of the given equation is ⅗.

The product of the gradients of perpendicular lines is -1.

(gradient of line)(⅗) = -1

gradient of line= -1 ÷⅗

gradient of line= $- \frac{5}{3}$

$y = - \frac{5}{3} x + c$

To find the value of c, substitute a coordinate.

When x=3, y=7,

$7 = - \frac{5}{3} (3) + c$

7= -5 +c

c= 7+5

c= 12

Hence, the equation of the line is $y = - \frac{5}{3} x + 12$ .

6 0

2 years ago

What is the greatest common factor of 4k, 18k4, and 12?

Setler [38]

Answer: The greatest common factor is 2.

Step-by-step explanation: We are given to find the greatest common factor of the following expressions:

$E_1=4k,~~E_2=18k^4,~~E_3=12.$

<u>Greatest Common Factor:</u> The GCF of two or more numbers (expressions) is the greatest factor that divides all the numbers or expressions.

We have

$E_1=4k=2\times 2\times k,\\\\E_2=18k^4=2\times 3\times 3\times k\times k\times k\times k,\\\\E_3=12=2\times 2\times 3.$

Therefore, the greatest common factor will be

$G.C.F.=2.$

Thus, the required greatest common factor is 2.

6 0

2 years ago

Read 2 more answers

A medical researcher wondered if there is a significant difference between the mean birth weight of boy and girl babies. Random

Yuliya22 [10]

Answer:

b) independent samples t-test

$t=\frac{(5.92 -5.74)-(0)}{\sqrt{\frac{1.88^2}{5}}+\frac{1.81^2}{5}}=0.154$

$p_v =2*P(t_{8}>0.154) =0.881$

So with the p value obtained and using the significance level given $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the mean of the group 1 (boys) is NOT significantly different than the mean for the group 2 (Girls).

Step-by-step explanation:

The system of hypothesis on this case are:

Null hypothesis: $\mu_1 = \mu_2$

Alternative hypothesis: $\mu_1 \neq \mu_2$

Or equivalently:

Null hypothesis: $\mu_1 - \mu_2 = 0$

Alternative hypothesis: $\mu_1 -\mu_2\neq 0$

Our notation on this case :

$n_1 =5$ represent the sample size for group 1

$n_2 =5$ represent the sample size for group 2

We can calculate the mean and deviation for eaach group with the following formulas:

$\bar X= \frac{\sum_{i=1}^n X_i}{n}$

$s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

$\bar X_1 =5.92$ represent the sample mean for the group 1

$\bar X_2 =5.74$ represent the sample mean for the group 2

$s_1=1.88$ represent the sample standard deviation for group 1

$s_2=1.81$ represent the sample standard deviation for group 2

If we see the alternative hypothesis we see that we are conducting a bilateral test and with independnet samples t test.

b) independent samples t-test

The statistic is given by this formula:

$t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{\sqrt{\frac{s^2_1}{n_1}}+\frac{S^2_2}{n_2}}$

And now we can calculate the statistic:

$t=\frac{(5.92 -5.74)-(0)}{\sqrt{\frac{1.88^2}{5}}+\frac{1.81^2}{5}}=0.154$

The degrees of freedom are given by:

$df=5+5-2=8$

And now we can calculate the p value using the altenative hypothesis:

$p_v =2*P(t_{8}>0.154) =0.881$

So with the p value obtained and using the significance level given $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the mean of the group 1 (boys) is NOT significantly different than the mean for the group 2 (Girls).

7 0

3 years ago

if a square + b square + c square minus ab minus bc minus ca equals to zero, prove that A equals to B equal to C

lawyer [7]

A^2 + b^2 + c^2 - ab - bc - ca = 0
a.a + b.b + c.c = a.b + b.c + c.a

equating term by term:-
a = b
b = c
c = a

Therefore a = b = c

8 0

3 years ago

Circletown's limits form a perfectly circular shape. It has a population of

Iteru [2.4K]

Answer:

3.64 Km.

Step-by-step explanation: