Which table idenifes points on the line defined by the equation y=3x+1?

The princess examines one plant and can’t seem to locate its roots. The plant is labeled as p(x)=x^2+x+3 Which values should the

AleksAgata [21]

Let's actually find the roots, using the quadratic formula:

p(x)=x^2+x+3 gives us a=1, b=1 and c=3.

-1 plus or minus sqrt(1^2-4(1)(3))
Then x = -----------------------------------------------
2

The discriminant here is negative, so the roots x will be complex:

-1 plus or minus sqrt(-11) -1 plus or minus i*sqrt(11)
x = ---------------------------------- = -------------------------------------
2 2

These are irrational roots; they cannot be expressed as the ratios of integers.

8 0

3 years ago

A local bottler in Hawaii wishes to ensure that an average of 22 ounces of passion fruit juice is used to fill each bottle. In o

Mandarinka [93]

Answer:

(a) Null Hypothesis, $H_0$ : $\mu$ = 22 ounces

Alternate Hypothesis, $H_A$ : $\mu\neq$ 22 ounces

(b) The value of the test statistic is -2.687.

(c) The critical values are -1.96 and 1.96.

(d) We conclude that Reject $H_0$ since the value of the test statistic is less than the negative critical value.

Step-by-step explanation:

We are given that a local bottler in Hawaii wishes to ensure that an average of 22 ounces of passion fruit juice is used to fill each bottle.

He takes a random sample of 65 bottles. The mean weight of the passion fruit juice in the sample is 21.54 ounces. Assume that the population standard deviation is 1.38 ounce.

Let $\mu$ = average ounces of passion fruit juice used to fill each bottle.

(a) So, Null Hypothesis, $H_0$ : $\mu$ = 22 ounces {means that the average of 22 ounces of passion fruit juice is used to fill each bottle}

Alternate Hypothesis, $H_A$ : $\mu\neq$ 22 ounces {means that the average different from 22 ounces of passion fruit juice is used to fill each bottle}

The test statistics that would be used here One-sample z test statistics 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 weight of the passion fruit juice = 21.54 ounces

$\sigma$ = population standard deviation = 1.38 ounce

n = sample of bottles = 65

So, test statistics = $\frac{21.54-22}{\frac{1.38}{\sqrt{65} } }$

= -2.687

(b) The value of z test statistics is -2.687.

(c) Since, in the question we are not given with the level of significance so we assume it to be 5%. Now, at 5% significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.

Since our test statistics does not lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that Reject $H_0$ since the value of the test statistic is less than the negative critical value which means that the average different from 22 ounces of passion fruit juice is used to fill each bottle.

6 0

3 years ago

Can you help me find t value in this problem?

Eduardwww [97]

we have a maximum at t = 0, where the maximum is y = 30.

We have a minimum at t = -1 and t = 1, where the minimum is y = 20.

<h3>How to find the maximums and minimums?</h3>

These are given by the zeros of the first derivation.

In this case, the function is:

w(t) = 10t^4 - 20t^2 + 30.

The first derivation is:

w'(t) = 4*10t^3 - 2*20t

w'(t) = 40t^3 - 40t

The zeros are:

0 = 40t^3 - 40t

We can rewrite this as:

0 = t*(40t^2 - 40)

So one zero is at t = 0, the other two are given by:

0 = 40t^2 - 40

40/40 = t^2

±√1 = ±1 = t

So we have 3 roots:

t = -1, 0, 1

We can just evaluate the function in these 3 values to see which ones are maximums and minimums.

w(-1) = 10*(-1)^4 - 20*(-1)^2 + 30 = 10 - 20 + 30 = 20

w(0) = 10*0^4 - 20*0^2 + 30 = 30

w(1) = 10*(1)^4 - 20*(1)^2 + 30 = 20

So we have a maximum at x = 0, where the maximum is y = 30.

We have a minimum at x = -1 and x = 1, where the minimum is y = 20.

If you want to learn more about maximization, you can read:

brainly.com/question/19819849

6 0

1 year ago

Please be kind enough to help me with this question in my geometry test thank you i’m very grateful

WARRIOR [948]

Answer:

yes

Step-by-step explanation:

5 0

3 years ago

Name 12 different rays

Digiron [165]

Los 12 rayos hijo el
azul, rosa, dorado, blanco, verde, oro rubí, violeta, oro naranja, lila esmeralda, dorado solar (blanca), melocoton solar (dorado sol), cristal celeste (diamante),

7 0

2 years ago

Read 2 more answers