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3 years ago

6

On the first swing, a pendulum swings through an arc of length 65 cm. On the successive swing, the length of the arc is 85% of t

he length of the previous swing.
Write a rule to model this situation.

1 answer:

Crazy boy [7]3 years ago

3 0

you mutliply 65 to 85%/0.85 and you get 55.25cm as your answer

You might be interested in

How do you do this??

astra-53 [7]

welll...you have there written just one relationship...it is berween 280 and 4 hours...you have to figure out speed:

$280 \div 4 = 70$

it is speed per hour

then you just connect time and speed:

140 - 2
280 - 4
350 - 5
420 - 6
560 - 8
700 - 10

6 0

3 years ago

Of 575 broiler chickens purchased from various kinds of food stores in different regions of a country and tested for types of ba

chubhunter [2.5K]

Answer:

a) $0.68 - 2.58 \sqrt{\frac{0.68(1-0.68)}{575}}=0.630$

$0.68 + 2.58 \sqrt{\frac{0.68(1-0.68)}{575}}=0.730$

And the 99% confidence interval would be given (0.630;0.730).

b) We are 99% confident that the true proportion of infected chickens are between 0.63 (63%) and 0.73 (73%)

c) For this case the answer would be No. Since all the required assumptions in order to construct the confidence interval are satisfied, so then the results can be assumed for all the population

Step-by-step explanation:

Previous concepts

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".

$p$ represent the real population proportion of interest

$\hat p =0.68$ represent the estimated proportion

n=575 is the sample size required (variable of interest)

$z$ represent the critical value for the margin of error

The population proportion have the following distribution

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

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 99% confidence interval the value of $\alpha=1-0.99=0.01$ and $\alpha/2=0.005$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=2.58$

And replacing into the confidence interval formula we got:

$0.68 - 2.58 \sqrt{\frac{0.68(1-0.68)}{575}}=0.630$

$0.68 + 2.58 \sqrt{\frac{0.68(1-0.68)}{575}}=0.730$

And the 99% confidence interval would be given (0.630;0.730).

Part b

We are 99% confident that the true proportion of infected chickens are between 0.63 (63%) and 0.73 (73%)

Part c

For this case the answer would be No. Since all the required assumptions in order to construct the confidence interval are satisfied, so then the results can be assumed for all the population

4 0

4 years ago

Suppose that E and F are two events and that P(E)=0.3 and P(F|E)=0.5. What is P(E and F)?

Sergio [31]

E and F are two events and that P(E)=0.3 and P(F|E)=0.5. Thus, P(E and F)=0.15

Bayes' theorem is transforming preceding probabilities into succeeding probabilities. It is based on the principle of conditional probability. Conditional probability is the possibility that an event will occur because it is dependent on another event.

P(F|E)=P(E and F)÷P(E)

It is given that P(E)=0.3,P(F|E)=0.5

Using Bayes' formula,

P(F|E)=P(E and F)÷P(E)

Rearranging the formula,

⇒P(E and F)=P(F|E)×P(E)

Substituting the given values in the formula, we get

⇒P(E and F)=0.5×0.3

⇒P(E and F)=0.15

∴The correct answer is 0.15.

If, E and F are two events and that P(E)=0.3 and P(F|E)=0.5. Thus, P(E and F)=0.15.

Learn more about Bayes' theorem on

brainly.com/question/17010130

#SPJ1

4 0

2 years ago

Please anyone answer me

ollegr [7]

Let's divide the shaded region into two areas:

area 1: x = 0 ---> x = 2

ares 2: x = 2 ---> x = 4

In area 1, we need to find the area under g(x) = x and in area 2, we need to find the area between g(x) = x and f(x) = (x - 2)^2. Now let's set up the integrals needed to find the areas.

Area 1:

$A\frac{}{1} = ∫g(x)dx = ∫xdx = \frac{1}{2} {x}^{2} | \frac{2}{0} = 2$

Area 2:

$A\frac{}{2} = ∫(g(x) - f(x))dx$

$= ∫(x - {(x - 2)}^{2} )dx$

$= ∫( - {x}^{2} + 5x - 4)dx$

$= ( - \frac{1}{3}{x}^{3} + \frac{5}{2} {x}^{2} - 4x) | \frac{4}{2}$

$= 2.67 - ( - 0.67) = 3.34$

Therefore, the area of the shaded portion of the graph is

A = A1 + A2 = 5.34

3 0

3 years ago

Alex bought string for $125. Other materials for $18. What is the total cost to make 50 puppets?

Lesechka [4]

(125+18) 50 = $7,150

6 0

3 years ago