I would rlly appreciate it if someone helped me

What is the rule of a function of the form f(t)= a sin (bt+c) +d whose graph appears to be identical to the given graph?

olasank [31]

Answer:

Option A.

f(x) = -4*sin((1/3)*t + (π/6)) + 3

Step-by-step explanation:

We can easily solve this problem by using a graphing calculator or plotting tool.

The function is

f(t) = a*sin (b*t +c) + d

Please, see attached picture below.

By looking at the picture with all the possible cases, we can tell that the correct option is A.

The function has a period of T = 6π

Max . Amplitude = 7

Min . Amplitude = -1

7 0

3 years ago

Read 2 more answers

A fair coin is to be tossed 20 times. Find the probability that 10 of the tosses will fall heads and 10 will fall tails, (a) usi

lbvjy [14]

Using the distributions, it is found that there is a:

a) 0.1762 = 17.62% probability that 10 of the tosses will fall heads and 10 will fall tails.

b) 0% probability that 10 of the tosses will fall heads and 10 will fall tails.

c) 0.1742 = 17.42% probability that 10 of the tosses will fall heads and 10 will fall tails.

Item a:

Binomial probability distribution

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The parameters are:

x is the number of successes.
n is the number of trials.
p is the probability of a success on a single trial.

In this problem:

20 tosses, hence $n = 20$ .
Fair coin, hence $p = 0.5$ .

The probability is P(X = 10), thus:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 10) = C_{20,10}.(0.5)^{10}.(0.5)^{10} = 0.1762$

0.1762 = 17.62% probability that 10 of the tosses will fall heads and 10 will fall tails.

Item b:

In a normal distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

It measures how many standard deviations the measure is from the mean.
After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with $\mu = np, \sigma = \sqrt{np(1-p)}$ .

The probability of an exact value is 0, hence 0% probability that 10 of the tosses will fall heads and 10 will fall tails.

Item c:

For the approximation, the mean and the standard deviation are:

$\mu = np = 20(0.5) = 10$

$\sigma = \sqrt{np(1 - p)} = \sqrt{20(0.5)(0.5)} = \sqrt{5}$

Using continuity correction, this probability is $P(10 - 0.5 \leq X \leq 10 + 0.5) = P(9.5 \leq X \leq 10.5)$ , which is the p-value of Z when X = 10.5 subtracted by the p-value of Z when X = 9.5.

X = 10.5:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{10.5 - 10}{\sqrt{5}}$

$Z = 0.22$

$Z = 0.22$ has a p-value of 0.5871.

X = 9.5:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{9.5 - 10}{\sqrt{5}}$

$Z = -0.22$

$Z = -0.22$ has a p-value of 0.4129.

0.5871 - 0.4129 = 0.1742.

0.1742 = 17.42% probability that 10 of the tosses will fall heads and 10 will fall tails.

A similar problem is given at brainly.com/question/24261244

6 0

3 years ago

5. During the eruption of Mount St. Helens in 1980. debris was ejected at a speed of over 440 feet per second

skelet666 [1.2K]

Answer:

3500 ft

Step-by-step explanation:

We assume you intend the equations to be ...

$y(t)=-16t^2+425t+8200\\x(t)=113t$

Then we can solve the second equation for t and use that in the first equation. We can solve the first equation for y=6000.

x = 113t

t = x/113

y(t) = y(x/113) = -16(x/113)² +425(x/113) +8200 = 6000

(16/12769)x² -(425/113)x -2200 = 0 . . . . . . subtract 6000, multiply by -1

Using the quadratic formula, the positive solution is ...

x = ((425/113) +√((-425/113)² -4(16/12769)(-2200))/(2(16/12769))

The fraction in the denominator can be inverted and used as a multiplier. We also use a√b = √(a²b) to simplify the radical.

x = (48025 +√4104275825)/32

x ≈ 3502.8

Rock was thrown about 3500 feet horizontally.

7 0

3 years ago

1. Write an equation in slope intercept form for the line that passes through (-2,2) and is parallel to 2x+4y= 16

bija089 [108]

Answer:

The equation of this line would be y = -1/2x + 1

Step-by-step explanation:

In order to find this equation we must first find the slope of the original line. To do this, we need to solve the original equation for y.

2x + 4y = 16

4y = -2x + 16

y = -1/2x + 4

The original slope (the coefficient of x) is -1/2, which means the new slope will also be -1/2 because parallel lines have the same slope. Now, we can use this slope along with the point in point-slope form to find the equation of the line.

y - y1 = m(x - x1)

y - 2 = -1/2(x + 2)

y - 2 = -1/2x - 1

y = -1/2x + 1

8 0

3 years ago

Simplify: 3 + {[(8 ÷ 2) + 2] + 8} =

JulijaS [17]

Answer:

The answer is 17

hope this helped and good luck on your test! :D

Step-by-step explanation:

3 0

3 years ago