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3 years ago

7

Write an exponential function to describe the given sequence of numbers, assuming that the first number in the sequence correspo

nds to x = 0.
5.30, 180, 1080, 6480...

1 answer:

Fantom [35]3 years ago

6 0

Answer:

$y = 5(6) {}^{x}$

Step-by-step explanation:

A exponential function is represented by

$y = ab {}^{x}$

where a is the vertical stretch and b is the base and x is the nth

power of x

Since the first number corresponds with zero, that means our y intercept is the first number.

This means when x=0 , y=5 so let find the value of 5.

$5 = ab {}^{0}$

b to the 0th power equal 1 so

$5 = a \times 1$

$a = 5$

Our equation is for now

$y = 5b {}^{x}$

Now let plug in 1,30

$30 = 5b {}^{1}$

Divide 5 by both sides

$6 = b {}^{1}$

Anything to the 1st power is itself so b equal 6.

So our equation is

$y = 5(6) {}^{x}$

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3 years ago

kumpel [21]

Answer:

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Read 2 more answers

A clinical psychologist wants to test whether experiencing childhood trauma reduces one's self-efficacy in adulthood. He randoml

lidiya [134]

Answer:

No, there is not any sufficient evidence to conclude that individuals who have experienced childhood trauma have lower self-efficacy in adulthood.

Step-by-step explanation:

We are given that a clinical psychologist wants to test whether experiencing childhood trauma reduces one's self-efficacy in adulthood.

He randomly selects 22 adults who have experienced childhood trauma and finds that their mean self-efficacy score equals 118.1.

Self-efficacy scores in the general population of adults are distributed normally with a mean equal to 118.5 and a standard deviation equal to 18.8 .

<em>Let </em> $\mu$ <em> = mean self-efficacy score.</em>

So, Null Hypothesis, $H_0$ : $\mu \geq$ 118.5 {means that the individuals who have experienced childhood trauma have higher or same self-efficacy in adulthood}

Alternate Hypothesis, $H_A$ : $\mu$ < 118.5 {means that the individuals who have experienced childhood trauma have lower self-efficacy in adulthood}

The test statistics that would be used here <u>One-sample z test statistics</u> as we know about the population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean self-efficacy score = 118.1

$\sigma$ = population standard deviation = 18.8

n = sample of adults who have experienced childhood trauma = 22

So, <u><em>test statistics</em></u> = $\frac{118.1-118.5}{\frac{18.8}{\sqrt{22} } }$

= -0.0998

The value of z test statistics is -0.0998.

Since, in the question we are not given with the level of significance so we assume it to be 5%. <u>Now, at 5% significance level the z table gives critical value of -1.645 for left-tailed test.</u>

Since our test statistic is more than the critical value of z as -0.0998 > -1.645, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <u>we fail to reject our null hypothesis</u>.

Therefore, we conclude that the individuals who have experienced childhood trauma have higher or same self-efficacy in adulthood.

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4 years ago

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marysya [2.9K]

Answer:

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Step-by-step explanation:

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2 years ago

A ball is launched straight up in the air from a height of 6 feet. Its velocity (feet/second) t seconds after launch is given by

german

Step-by-step explanation:

A ball is launched straight up in the air from a height of 6 feet. The velocity as a function of time t is given by :

f(t) = -32 t+285

Height of the ball is :

$h(t)=\int\limits{f(t){\cdot} dt}\\\\h(t)=\int\limits{(-32t+285){\cdot} dt}\\\\h(t)=-16t^2+285t+C$

C is constant. Here the ball is launched from a height of 6 feet. So,

$h(t)=-16t^2+285t+6$

At t = 2 s, $h(t)=-16(2)^2+285(2)+6=512\ m$

At t = 9 s, $h(t)=-16(9)^2+285(9)+6=1275\ m$

Between 2 s and 9 s, the ball's height changed is : 1275 - 512 = 763 m.

6 0

4 years ago