701-413 find rhe difference

Which ordered pair is a solution of the equation y = x - 3? (-2, 5) (-5, 2) (2, 5) (5, 2)

IceJOKER [234]

2=5-3 so the answer is (2, 5)

5 0

3 years ago

Please help asap!!!

sp2606 [1]

Answer:

$y=\frac{1}{6} (x+5)^2-4.5$

$y=\frac{-1}{20} (x-10)^2+1$

Step-by-step explanation:

focus at (-5, -3), and directrix y = -6

Directrix y=-6 so its a vertical parabola

so equation is

(x-h)^2 = 4p(y-k)

(h,k) is the center

P is the distance between focus and vertex

distance between focus and directrix = 2p

distance between -3 and y=-6 is 3

2p = 3

p = 3/2 or p = 1.5

Focus is (h, k+p)

given focus is (-5, -3) so h= -5 and k+p = -3

k+p=-3, plug in 1.5 for p

k + 1.5 = -3

subtract 1.5 on both sides

k = -4.5

(x-h)^2 = 4p(y-k)

$(x+5)^2= 4(1.5) (y+4.5)$

$(x+5)^2= 6(y+4.5)$

divide by 6 on both sides

then subtract 4.5 on both sides

$y=\frac{1}{6} (x+5)^2-4.5$

focus at (10, -4), and directrix y = 6.

Directrix y=6 so its a vertical parabola

so equation is

(x-h)^2 = 4p(y-k)

distance between focus and directrix = 2p

distance between -4 and y=6 is -4-6=-10

2p = -10

p = -5

Focus is (h, k+p)

given focus is (10, -4) so h= 10 and k+p = -4

k+p=-4, plug in 5 for p

k - 5 = -4

add 5 on both sides

k = 1

(x-h)^2 = 4p(y-k)

$(x-10)^2= 4(-5) (y-1)$

$(x-10)^2= -20(y-1)$

divide by -20 on both sides and add 1 on both sides

$y=\frac{-1}{20} (x-10)^2+1$

8 0

3 years ago

to convert feet per minute to inches per second which of the following conversion factors would be used select all that apply

Arisa [49]

1 feet = 12 inches

1 min = 60 s

1 feet/min = 12 in/60 s = 1 in/5 s = 0.2 in/s

7 0

3 years ago

PLEASE SOLVE THIS PROBLEM

schepotkina [342]

Answer:

18) Area= 5*5/2=25/2=12.5 unit ^2

19) Area=AB^2V3/4=8a^2*V3/4=2V3a^2

Step-by-step explanation:

18. A(-3,0)

B(1,-3)

C(4,1)

AB=V(-3-1)^2+(0+3)^2=V16+9=V25=5

AC=V(-3-4)^2+(0-1)^2=V49+1=V50=5V2

BC=V(1-4)^2+(-3-1)^2=V9+16=V25=5

so AB=BC=5

and AC^2=AB^2+BC^2

so trg ABC is an isosceles right angle triangle (<B=90)

Area= 5*5/2=25/2=12.5 unit ^2

19. A(a,a)

B(-a,-a)

C(-V3a, V3a)

AB=V(a+a)^2+(a+a)^2=V4a^2+4a^2=V8a^2

AC=V(a+V3a)^2+(a-V3)^2=Va^2+2a^2V3+3a^2+a^2-2a^2V3+3a^2=V8a^2

BC=V(-a+V3a)^2+(-a-V3a)^2=V8a^2

so AB=AC=BC

Area=AB^2V3/4=8a^2*V3/4=2V3a^2

7 0

3 years ago

Suppose that 500 parts are tested in manufacturing and 10 are rejected.

alexdok [17]

Answer:

a) $z=\frac{0.02 -0.03}{\sqrt{\frac{0.03(1-0.03)}{500}}}=-1.31$

$p_v =P(Z$

If we compare 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 proportion of rejected items is less than 0.03.

b) We can use a 95 percent upper confidence interval.

On this case we want a interval on this form : $(-\infty,\hat p +z_{\alpha}\sqrt{\frac{\hat p (1-\hat p)}{n}})$

So the critical value would be on this case $Z_{\alpha}=1.64$ and we can use the following excel code to find it: "=NORM.INV(1-0.05,0,1)"

We found the upper limit like this:

$0.02+1.64\sqrt{\frac{0.02 (1-0.02)}{500}}=0.03026$

And the interval would be: $(-\infty,0.03026)$

And since our value (0.02) is contained in the interval We fail to reject the hypothesis that p=0.03

Step-by-step explanation:

Part a

Data given and notation

n=500 represent the random sample taken

X=10 represent the number of objects rejected

$\hat p=\frac{10}{500}=0.02$ estimated proportion of objects rejected

$p_o=0.03$ is the value that we want to test

$\alpha=0.05$ represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that 70% of adults say that it is morally wrong to not report all income on tax returns.:

Null hypothesis: $p=0.03$

Alternative hypothesis: $p < 0.03$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.02 -0.03}{\sqrt{\frac{0.03(1-0.03)}{500}}}=-1.31$

Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.05$ . The next step would be calculate the p value for this test.

Since is a one tailed left test the p value would be:

$p_v =P(Z$

If we compare 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 proportion of rejected items is less than 0.03.

Part b

We can use a 95 percent upper confidence interval.

On this case we want a interval on this form : $(-\infty,\hat p +z_{\alpha}\sqrt{\frac{\hat p (1-\hat p)}{n}})$

So the critical value would be on this case $Z_{\alpha}=1.64$ and we can use the following excel code to find it: "=NORM.INV(1-0.05,0,1)"

We found the upper limit like this:

$0.02+1.64\sqrt{\frac{0.02 (1-0.02)}{500}}=0.03026$

And the interval would be: $(-\infty,0.03026)$

And since our value (0.02) is contained in the interval We fail to reject the hypothesis that p=0.03

3 0

3 years ago