I need help with this

Mrs.Lopez has two kinds of flowers in her garden. The ratio of lilies to daisies in the garden is 5:3. If there are 10 lilies, w

aliya0001 [1]

Answer:

16

Step-by-step explanation:

8 0

3 years ago

A candidate for a US Representative seat from Indiana hires a polling firm to gauge her percentage of support among voters in he

UkoKoshka [18]

Answer:

a) The minimum sample size is 601.

b) The minimum sample size is 2401.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

For this problem, we have that:

We dont know the true proportion, so we use $\pi = 0.5$ , which is when we are are going to need the largest sample size.

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

a. If a 95% confidence interval with a margin of error of no more than 0.04 is desired, give a close estimate of the minimum sample size that will guarantee that the desired margin of error is achieved. (Remember to round up any result, if necessary.)

This is n for which M = 0.04. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.04 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.04\sqrt{n} = 1.96*0.5$

$\sqrt{n} = \frac{1.96*0.5}{0.04}$

$(\sqrt{n})^2 = (\frac{1.96*0.5}{0.04})^2$

$n = 600.25$

Rounding up

The minimum sample size is 601.

b. If a 95% confidence interval with a margin of error of no more than 0.02 is desired, give a close estimate of the minimum sample size necessary to achieve the desired margin of error.

Now we want n for which M = 0.02. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.02 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.02\sqrt{n} = 1.96*0.5$

$\sqrt{n} = \frac{1.96*0.5}{0.02}$

$(\sqrt{n})^2 = (\frac{1.96*0.5}{0.02})^2$

$n = 2401$

The minimum sample size is 2401.

4 0

3 years ago

. Two bicyclists, Sarah and Emily, depart from the same location. Sarah heads N55°E at an average speed of 6 km/hr. Emily heads

Liula [17]

Answer:

The distance between them after 30 minutes is 6.5 km.

Step-by-step explanation:

Speed = $\frac{distance}{time}$

Sarah's speed = 6 km/hr = 1.6667 m/s

Emily's speed = 10 km/hr = 2.7778 m/s

The measure of angle between their bearings = $105^{o}$

After 30 minutes (1800 seconds);

distance = speed x time

Sarah would have covered a distance = 1.6667 x 1800

= 3000 m

= 3 km

Emily would have covered a distance = 2.7778 x 1800

= 5000 m

= 5 km

The distance between them, a, can be determined by applying the cosine rule;

$a^{2}$ = $b^{2}$ + $c^{2}$ - 2bcCos A

= $5000^{2}$ + $3000^{2}$ -2(5000 x 3000) Cos 105

= $5000^{2}$ + $3000^{2}$ -2(5000 x 3000) x (-0.2588)

= 2.5 x $10^{7}$ + 9 x $10^{6}$ + 7764000

= 41764000

a = $\sqrt{41764000}$

= 6462.5073

a = 6462.5 m

The distance between them after 30 minutes is 6.5 km.

4 0

3 years ago

According to the synthetic division below, which of the following statements are true? Check all that apply. -5(2 6 -8) -10 20 _

Sunny_sXe [5.5K]

***(2x²+6x-8):(x+5)=2x-4
     -2x²-10x
    ⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
   -4x-8
          4x+20
    ⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
              12 ⇒ A. statement is true.

***When x=-5⇒2*(-5)²+6*(-5)-8=12⇒B. statement is true.

***2x²+6x-8 can also be written as (x+5)*(2x-4)+12 so (x+5) is a factor of 2x²+6x-8⇒C. statement is true.

***When x=5⇒2*5²+6*5-8=72 is not 12⇒D. statement is not true

***(2x²+6x-8):(x+5)=2x+16
     -2x²+10x
    ⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
        16x-8
             -16x+80
      ⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
                     72⇒F. statement is not true

***E. statement is not true.

8 0

4 years ago

Read 2 more answers

Is -2.54 greater or less than -2 and 27/50

zloy xaker [14]

-2.54 is equal to -2 27/50

7 0

3 years ago

Read 2 more answers