What is the equation of the line that passes through the point(-6,-5) and has a slope of -1/2

suter [353]

Answer:same :(

Step-by-step explanation:

6 0

2 years ago

Claire is a manager at a toy packaging company. The company packs 80 boxes of toys every hour for the first 3 hours of the day.

Stells [14]

Answer:

See the attached figure.

Step-by-step explanation:

Modeling each part as a function.

Let x is hours of the working day

The company packs 80 boxes of toys every hour for the first 3 hours of the day. ⇒ y₁ = 80 x , x ∈ [0,3]

At the end of the 3 hours The company packs = 80 * 3 = 240

They stop packaging for the next 2 hours in order to carry out a training session. ⇒ y₂ = 240 , x ∈ [3,5]

Then, for the next 4 hours, they pack 20 boxes of toys every hour

y₃ = 20x + c , x ∈ [5,9]

To find c, y₂ = y₃ at x =5

∴ 240 = 20 * 5 + c

∴ c = 240 - 20 * 5 =240 - 100 = 140

∴ y₃ = 20x + 140 , x ∈ [5,9]

So,

y₁ = 80 x , x ∈ [0,3]

y₂ = 240 , x ∈ [3,5]

y₃ = 20x + 140 , x ∈ [5,9]

The graph models the piecewise function for the given situation is as shown in the attached figure.

8 0

2 years ago

Read 2 more answers

Consider A (-9, 4) and B (11, 17), find the coordinates for point P that partition A to B in a 3: 5 ratio.

Talja [164]

Answer:

C. (-1.5, 8.875)

Step-by-step explanation:

on a coordinate plane if point(x1,y1) and (x2,y2) is divided by a point p in ratio of m:n then coordinate of point p is given by

p = (nx1 + mx2/ m+n, ny1+my2/m+n)

_______________________________________________

Given point

A (-9, 4) and B (11, 17)

ratio 3:5

m:n = 3:5

m+n = 3+5 = 8

coordinate of point p that partition AB

x = (5*-9 + 3*11) / 5+3 y = (5*4 + 3*17) / 5+3

x = (-45 + 33) / 8 y = (20 + 51) / 8

x = (-12) / 8 y = (71) / 8

x = -3 / 2 = -1.5 y = 8.875

Thus, coordinate of point p is (-1.5, 8.875).

7 0

2 years ago

A Pew Internet poll asked cell phone owners about how they used their cell phones. One question asked whether or not during the

EastWind [94]

Answer:

a) $\hat p=\frac{471}{1024}=0.460$

The standard error is given by:

$SE= \sqrt{\frac{\hat p(1-\hat p)}{n}}=\sqrt{\frac{0.460(1-0.460)}{1024}}=0.0156$

And the margin of error is given by:

$ME=z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}=1.96\sqrt{\frac{0.460(1-0.460)}{1024}}=0.0305$

b) The 99% confidence interval would be given by (0.429;0.491)

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Data given and notation

n=1024 represent the random sample taken

X=471 represent the people responded that they had used their cell phone while in a store within the last 30 days to call a friend or family member for advice about a purchase they were considering

$\hat p=\frac{471}{1024}=0.460$ estimated proportion of people responded that they had used their cell phone while in a store within the last 30 days to call a friend or family member for advice about a purchase they were considering

p= population proportion of people responded that they had used their cell phone while in a store within the last 30 days to call a friend or family member for advice about a purchase they were considering

Part a

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

The standard error is given by:

$SE= \sqrt{\frac{\hat p(1-\hat p)}{n}}=\sqrt{\frac{0.460(1-0.460)}{1024}}=0.0156$

And the margin of error is given by:

$ME=z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}=1.96\sqrt{\frac{0.460(1-0.460)}{1024}}=0.0305$

Part b

If we replace the values obtained we got:

$0.460-1.96\sqrt{\frac{0.460(1-0.460)}{1024}}=0.429$

$0.460+1.96\sqrt{\frac{0.460(1-0.460)}{1024}}=0.491$

The 99% confidence interval would be given by (0.429;0.491)

8 0

2 years ago

Mike and Ike are twins. Mike’s age is one more than twice a certain number. Ike’s age is 10 less than triple that same number. F

Misha Larkins [42]

Mike age is 3 less then twice the age of his brother nuke.
M = Mike's age now
N = Nuke's age now
M = 2N - 3

Ten years ago, four times nuke's age was one more mike's age.
M-10 = Mike's age 10 years ago
N-10 = Muke's age 10 years ago
4(N - 10) = 1 + M -10

what are their present ages

find M and N

substitute M = 2N - 3 into 4(N - 10) = 1 + M -10:

4(N - 10) = 1 + [2N - 3] - 10
4N - 40 = 2N - 12
2N = 28
N = 14

M = 2(14) - 3 = 28 - 3 = 25

Mike is 25 and Nuke is 14.

check:
4(14 - 10) = 4(4) = 16 = 26 -10 = 1 + 25 - 10

4 0

2 years ago