Convert y-1=7(x - 6) to standard form

What is the length of ML

Vlad [161]

first, find the circumference of the circle

2πr = 2π × 5

= 31.42 ft

then multiply the circumference with the angle given which is 50° divided by 360°.

31.42 × 50 ÷ 360 = 4.36 ft

answer = 4.36 ft

also can I get brainliest...plsss

8 0

3 years ago

Elderly drivers. In January 2011, The Marist Poll published a report stating that 66% of adults nationally think licensed driver

katrin [286]

Answer:

(a) Hence, the margin of error reported by The Marist Poll was correct.

(b) Based on a 95% confidence interval the poll does not provide convincing evidence that more than 70% of the population think that licensed drivers should be required to retake their road test once they turn 65.

Step-by-step explanation:

We are given that the Marist Poll published a report stating that 66% of adults nationally think licensed drivers should be required to retake their road test once they reach 65 years of age.

It was also reported that interviews were conducted on 1,018 American adults, and that the margin of error was 3% using a 95% confidence level.

(a) Margin of error formula is given by;

Margin of Error = $Z_(_\frac{\alpha}{2}_) \times \sqrt{\frac{\hat p(1-\hat p)}{n} }$

where, $\alpha$ = level of significance = 1 - 0.95 = 0.05 or 5%

Standard of error = $\sqrt{\frac{\hat p(1-\hat p)}{n} }$

Also, $\hat p$ = sample proportion of adults nationally think licensed drivers should be required to retake their road test once they reach 65 years of age = 66%

n = sample of American adults = 1.018

The critical value of z for level of significance of 2.5% is 1.96.

So, Margin of Error = $Z_(_\frac{\alpha}{2}_) \times \sqrt{\frac{\hat p(1-\hat p)}{n} }$

= $1.96 \times \sqrt{\frac{0.66(1-0.66)}{1,018} }$ = 0.03 or 3%

Hence, the margin of error reported by The Marist Poll was correct.

(b) Now, the pivotal quantity for 95% confidence interval for the population proportion who think that licensed drivers should be required to retake their road test once they turn 65 is given by;

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

So, 95% confidence interval for p = $\hat p \pm \text{Margin of error}$

= $0.66 \pm 0.03$

= [0.66 - 0.03 , 0.66 + 0.03]

= [0.63 , 0.69]

Hence, based on a 95% confidence interval the poll does not provide convincing evidence that more than 70% of the population think that licensed drivers should be required to retake their road test once they turn 65 because the interval does not include the value of 70% or more.

7 0

4 years ago

A line passes through the points (8,9) and (-2,4) .

MA_775_DIABLO [31]

A) Y1-Y2/X1-X2
9-4/8-(-2) = 5/10= 1/2

b) 1/2x+b=y <-- plug in a point
1/2(-2)+b=4 <--plugged in (-2,4)
-1+b=4 <-- simplify/solve
b=5

c) 1/2x+5=y

3 0

4 years ago

What is the value of x? Enter your answer in the box. x =

ivanzaharov [21]

The two angles shown ( 134 and X) make a straight line.

A straight line equals 180 degrees.

To find X subtract 134 from 180.

X = 180 - 134

x = 46

5 0

3 years ago

For each of the systems of equations that follow, use Gaussian elimination to obtain an equivalent system whose coefficient matr

noname [10]

Answer:

b) inconsistent

d) inconsistent

f) inconsistent

j) X_1 = 2 - 6a , X_2 = 4 + a , X_3 = 3 - a, X_4 = a (free variable)

Step-by-step explanation:

b)

Given: Augmented matrix

$\left[\begin{array}{ccc}2&-3&5\\-4&6&8\end{array}\right]$

Row operation : R_2 + 2*R_1

$\left[\begin{array}{ccc}2&-3&5\\0&0&18\end{array}\right]$

Looking at R_2 : 0 not equal to 18 ; Hence, inconsistent

c)

Given: Augmented matrix

$\left[\begin{array}{cccc}3&2&-3&4\\1&-2&2&1\\11&2&1&14\end{array}\right]$

Row operation : R_2 <---> R_1

$\left[\begin{array}{cccc}1&-2&2&1\\3&2&-3&4\\11&2&1&14\end{array}\right]\\$

Row operations : R_2 - 3*R_1 & R_3 - 11*R_1

$\left[\begin{array}{cccc}1&-2&2&1\\0&8&-9&1\\0&24&-21&3\end{array}\right]\\$

Row operations : R_3 - 3*R_2

$\left[\begin{array}{cccc}1&-2&2&1\\0&8&-9&1\\0&0&6&0\end{array}\right]\\$

Looking at R_3 : 0 not equal to 6 ; Hence, inconsistent

f)

Given: Augmented matrix

$\left[\begin{array}{cccc}1&-1&2&4\\2&3&-1&1\\7&3&4&7\end{array}\right]\\$

Row operations : R_2 - 2*R_1 & R_3 - 7*R_1

$\left[\begin{array}{cccc}1&-1&2&4\\0&5&-5&-7\\0&10&-10&-21\end{array}\right]\\$

Row operations : R_2 --> ( 1 / 5 )* R_2 & R_3 --> ( 1 / 10 )* R_3

$\left[\begin{array}{cccc}1&-1&2&4\\0&1&-1&-1.4\\0&1&-1&-2.1\end{array}\right]\\$

Row operations : R_3 - R_1

$\left[\begin{array}{cccc}1&-1&2&4\\0&1&-1&-1.4\\0&0&0&-0.7\end{array}\right]\\$

Looking at R_3 : 0 not equal to -0.7 ; Hence, inconsistent

j)

Given: Augmented matrix

$\left[\begin{array}{ccccc}1&2&-3&1&1\\-1&-1&4&-1&6\\-2&-4&7&-1&1\end{array}\right]\\$

Row operations : R_2 + R_1 & R_3 + 2*R_1

$\left[\begin{array}{ccccc}1&2&-3&1&1\\0&1&1&0&7\\0&0&1&1&3\end{array}\right]\\$

corresponding equations are:

X_1 + 2*X_2 - 3*X_3 + X_4 = 1

X_2 + X_3 = 7

X_3 + X_4 = 3

Free parameter : X_4 = a , then:

X_3 = 3 - a

X_2 = 4 + a

X_1 = 1 - a + 3*(3 - a) - 2*(4 + a) = 2 - 6 a

4 0

4 years ago