Determine the standard form of the equation of the line that passes through (-7,8) and (0,2)

Natalia is writing a recursive formula to represent the sequence 8,12,18,27 what value should she use as the common ratio in the

Marrrta [24]

Common ratio = second term / first term = 12 / 8 = 1.5

7 0

2 years ago

Read 2 more answers

A karate center has 120 students. The director wants to set a goal to motivate her instructors to increase student enrollment. U

iVinArrow [24]

A) Plan A requires for a percentage increase of a number of students. This means that year after year the number of new students will increase. Plan B requires for a constant number of new students each year. This means that year after year the percentage increase would get smaller.

B) To solve this problem we will use formula for a growth of population:
$final = initial * (1+percentage)^{t}$
Where:
final = final number of students
initial = initial number of students
percentage = requested percentage increase
t = number of years

We can insert numbers and solve for t:
$240= 120* (1+0.12)^{t} \\ 2=1.12^{t} \\ log2=log(1.12^{t} ) \\ log2=t*log1.12 \\ t= \frac{log2}{log1.12} \\ t=6.12years$

For Plan B we can use simple formula
increase = 120
increase per year = 20
number of years = increase / (increase per year) = 120 / 20 = 6 years

Plan B is better to double the <span>enrollment.

C)We use same steps as in B) to solve this.
</span>

$360= 120* (1+0.12)^{t} \\ 3=1.12^{t} \\ log3=log(1.12^{t} ) \\ log3=t*log1.12 \\ t= \frac{log3}{log1.12} \\ t=9.69years$

For Plan B we can use simple formula
increase = 240
increase per year = 20
number of years = increase / (increase per year) = 240 / 20 = 12 years

Plan A is better to triple the enrollment.

3 0

2 years ago

Lucy has to run two errands. She starts from home and travels 3 miles south to the post office. From the post office, she travel

alexira [117]

Answer:

the correct choice is A. At the gas station

Step-by-step explanation:

Lucy starts at home and travels 3 miles south to the post office. From the post office, she travels 4 miles east to the gas station. As it is known south and east directions form right angle. Since the entire trip forms a triangle, this triangle is right with right angle at the post office.

Call the vertices of this triangle P - post office, G - gas station, H - home. Then HP and PG are legs of this triangle and GH is hypotenuse.

From the given data:

HP=3;

PG=4;

GH=5;

∠P=90°.

The smallest angle is opposite to the smallest side. The smallest side is leg HP, so the smallest angle is G that is the angle at gas station.

6 0

2 years ago

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Employment data at a large company reveal that 74% of the workers are married, 42% are college graduates, and that 56% are marri

ValentinkaMS [17]

Answer:

(E) None of these above are true.

Step-by-step explanation:

Married = 74% or 0.74

College graduates = 42% or 0.42

pr(married | college graduates) = 0.56

(A) These events are pairwise disjoint. This is false. Pairwise disjoint are also known as mutually exclusive events. Here we can see that both events are occurring at same time.

(B) These events are independent events. This is also false.

(C) These events are both independent and pairwise disjoint. False

(D) A worker is either married or a college graduate always. False

Here Probability(A or B) shall be 1

= Pr(A) + Pr(B) - Pr( A and B) = 0.74 + 0.42 - 0.56 * 0.42 = 0.9248

This is not equal to 1.

(E) None of these above are true. This is true.

8 0

2 years ago

g In a survey of 500 residents, 300 were opposed to the use of the photo-cop for issuing traffic tickets.The standard error of t

Evgesh-ka [11]

Answer:

Z-score 1.96

Margin of error d= 0.04323

Step-by-step explanation:

Hello!

The study variable in this case is

X: Number of people that oppose the use of photo-cop for issuing traffic tickets in a sample of 500.

n= 500

The parameter of interest is the proportion of people that opposes it.

The estimated proportion is p'= 300/500= 0.6

To estimate the population proportion per Confidence interval you have to approximate the distribution of the sample proportion p' to normal:

p'≈N(p;p(1-p)1/n)

The mean of this distribution is p and the variance is p*(1-p)*1/n

To construct the Confidence interval, since the value of the population proportion is unknown, an estimated variance is used:

p'(1-p')*1/n ⇒ then the estimated standard error is √(p'(1-p')*1/n)

The formula for the confidence interval is:

p' ± $Z_{1-\alpha /2}$ * $\sqrt{\frac{p'(1-p')}{n} }$

Where " $Z_{1-\alpha /2}$ * $\sqrt{\frac{p'(1-p')}{n} }$ " represents the margin of error of the interval.

Now for a confidence level of 0.95 the value of Z is $Z_{0.975}= 1.965$

The estimated standard error is already calculated: $\sqrt{\frac{p'(1-p')}{n} } = 0.022$

The margin of error (d) is then:

d= $Z_{1-\alpha /2}$ * $\sqrt{\frac{p'(1-p')}{n} }$ = 1.965 * 0.022

d= 0.04323

I hope it helps!

7 0

1 year ago