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1 year ago

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the graph plots four equations, a, b, c, and d: line a joins ordered pair negative 6, 16 and 9, negative 4. line b joins ordered

pair negative 2, 20 and 8, 0. line c joins ordered pair negative 7, negative 6 and 6, 20. line d joins ordered pair 7, 20 and 0, negative 7. which pair of equations has (4, 8) as its solution? equation a and equation c equation b and equation c equation c and equation d equation b and equation d

2 answers:

fomenos1 year ago

6 0

The pair of equations that has (4, 8) as its solution are the two equations represented by the lines which intersect at point (4, 8). The lines are line b and line d.
Therefore the equations are equation b and equation a.

IRISSAK [1]1 year ago

4 0

Answer with explanation:

Eqation of line joining two points (a,b) and (c,d) is given by

$\rightarrow \frac{y-b}{x-a}=\frac{b-d}{a-c}$

Eqation of line a, which joins two points (-6,16) and (9,-4) is

$\rightarrow \frac{y-16}{x+6}=\frac{16-(-4)}{-6-9}\\\\\rightarrow -15 y+240=20 x+120\\\\20x+15y=120\\\\4x+3y=24$

⇒Putting, x=4 and , y=8 in above equation

4 × 4+3×8=16+24=40≠24

Point (4,8) does not lie on this line.

⇒⇒Eqation of line b, which joins two points (2,20) and (8,0) is

$\rightarrow \frac{y-20}{x-2}=\frac{20-0}{2-8}\\\\\rightarrow -6 y+120=20 x-40\\\\20x+6y=160\\\\10x+3y=80$

⇒Putting, x=4 and , y=8 in above equation

10 × 4+3×8=40+24=64≠80

Point (4,8) does not lie on this line.

⇒⇒Eqation of line c, which joins two points (7,-6) and (6,20) is

$\rightarrow \frac{y-20}{x-6}=\frac{20-(-6)}{6-7}\\\\\rightarrow -y+20=26 x-156\\\\26x+6y=176\\\\13x+3y=88$

⇒Putting, x=4 and , y=8 in above equation

13× 4+3×8=52+24=76≠88

Point (4,8) does not lie on this line.

⇒⇒Eqation of line d, which joins two points (7,20) and (0,-7) is

$\rightarrow \frac{y-20}{x-7}=\frac{20-(-7)}{7-0}\\\\\rightarrow 7y-140=27x-189\\\\27x-7y=189-140\\\\27x-7y=49$

⇒Putting, x=4 and , y=8 in above equation

27× 4-7×8=108-56=52≠24

Point (4,8) does not lie on this line.

⇒None of the two lines has point of Intersection at point (4,8).

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The production department has installed a new spray machine to paint automobile doors. As is common with most spray guns, unsigh

Nesterboy [21]

Answer:

The numbers of doors that will have no blemishes will be about 6065 doors

Step-by-step explanation:

Let the number of counts by the worker of each blemishes on the door be (X)

The distribution of blemishes followed the Poisson distribution with parameter $\lambda =0.5$ / door

The probability mass function on of a poisson distribution Is:

$P(X=x) = \dfrac{e^{- \lambda } \lambda ^x}{x!}$

$P(X=x) = \dfrac{e^{- \ 0.5 }( 0.5)^ x}{x!}$

The probability that no blemishes occur is :

$P(X=0) = \dfrac{e^{- \ 0.5 }( 0.5)^ 0}{0!}$

$P(X=0) = 0.60653$

P(X=0) = 0.6065

Assume the number of paints on the door by q = 10000

Hence; the number of doors that have no blemishes is = qp

=10,000(0.6065)

= 6065

3 0

2 years ago

A pharmaceutical company proposes a new drug treatment for alleviating symptoms of PMS (premenstrual syndrome). In the first sta

Akimi4 [234]

Answer:

95% confidence interval for p, the true proportion of all women who will find success with this new treatment is [0.238 , 0.762].

Step-by-step explanation:

We are given that a pharmaceutical company proposes a new drug treatment for alleviating symptoms of PMS (premenstrual syndrome).

In the first stages of a clinical trial, it was successful for 7 out of the 14 women.

Firstly, the pivotal quantity for 95% confidence interval for the true proportion is given by;

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

where, $\hat p$ = sample proportion of women who find success with this new treatment = $\frac{7}{14}$ = 0.50

n = sample of women = 14

<em>Here for constructing 95% confidence interval we have used One-sample z proportion statistics.</em>

So, 95% confidence interval for the true proportion, p is ;

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5%

level of significance are -1.96 & 1.96}

P(-1.96 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < 1.96) = 0.95

P( $-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < ${\hat p-p}$ < $1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.95

P( $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < p < $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.95

<u />

<u>95% confidence interval for p</u> = [ $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ , $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ]

= [ $0.50-1.96 \times {\sqrt{\frac{0.50(1-0.50)}{14} } }$ , $0.50+1.96 \times {\sqrt{\frac{0.50(1-0.50)}{14} } }$ ]

= [0.238 , 0.762]

Therefore, 95% confidence interval for p, the true proportion of all women who will find success with this new treatment is [0.238 , 0.762].

4 0

2 years ago

Point R is at (3, 1.3) and Point T is at (3, 2.4) on a coordinate grid. The distance between the two points is ____. (Input numb

snow_lady [41]

Point R and point T have same x coordinate so their distance is by y axis.
Ty-Ry=2.4-1.3=1.1
So the distance between two points is 1.1

3 0

2 years ago

Read 2 more answers

Round 7905.68466806 to the nearest thousand.

mixas84 [53]

Answer:

8000 to the nearest thousand

7905.685 to the thousandth

Step-by-step explanation:

8 0

1 year ago

Suppose you are an expert on the fashion industry and wish to gather information to compare the amount earned per month by model

Ann [662]

Answer:

(1) The degrees of freedom for unequal variance test is (14, 11).

(2) The decision rule for the 0.01 significance level is;

If the value of our test statistics is less than the critical values of F at 0.01 level of significance, then we have insufficient evidence to reject our null hypothesis.

If the value of our test statistics is more than the critical values of F at 0.01 level of significance, then we have sufficient evidence to reject our null hypothesis.

(3) The value of the test statistic is 0.3796.

Step-by-step explanation:

We are given that you are an expert on the fashion industry and wish to gather information to compare the amount earned per month by models featuring Liz Claiborne's attire with those of Calvin Klein.

The following is the amount ($000) earned per month by a sample of 15 Claiborne models;

$3.5, $5.1, $5.2, $3.6, $5.0, $3.4, $5.3, $6.5, $4.8, $6.3, $5.8, $4.5, $6.3, $4.9, $4.2 .

The following is the amount ($000) earned by a sample of 12 Klein models;

$4.1, $2.5, $1.2, $3.5, $5.1, $2.3, $6.1, $1.2, $1.5, $1.3, $1.8, $2.1.

(1) As we know that for the unequal variance test, we use F-test. The degrees of freedom for the F-test is given by;

$\text{F}_(_n__1-1, n_2-1_)$

Here, $n_1$ = sample of 15 Claiborne models

$n_2$ = sample of 12 Klein models

So, the degrees of freedom = ( $n_1-1, n_2-1$ ) = (15 - 1, 12 - 1) = (14, 11)

(2) The decision rule for 0.01 significance level is given by;

If the value of our test statistics is less than the critical values of F at 0.01 level of significance, then we have insufficient evidence to reject our null hypothesis.

If the value of our test statistics is more than the critical values of F at 0.01 level of significance, then we have sufficient evidence to reject our null hypothesis.

(3) The test statistics that will be used here is F-test which is given by;

T.S. = $\frac{s_1^{2} }{s_2^{2} } \times \frac{\sigma_2^{2} }{\sigma_1^{2} }$ ~ $\text{F}_(_n__1-1, n_2-1_)$

where, $s_1^{2}$ = sample variance of the Claiborne models data = $\frac{\sum (X_i-\bar X)^{2} }{n_1-1}$ = 1.007

$s_2^{2}$ = sample variance of the Klein models data = $\frac{\sum (X_i-\bar X)^{2} }{n_2-1}$ = 2.653

So, the test statistics = $\frac{1.007}{2.653 } \times 1$ ~ $\text{F}_(_1_4,_1_1_)$

= 0.3796

Hence, the value of the test statistic is 0.3796.

3 0

1 year ago