An exterior angle of a triangle measures 125° and one of the remote interior angles measures 35°. The triangle must be

A genetic experiment involving peas yielded one sample of offspring consisting of 420 green peas and 174 yellow peas. Use a 0.01

slavikrds [6]

Answer:

a) $z=\frac{0.293 -0.23}{\sqrt{\frac{0.23(1-0.23)}{594}}}=3.649$

b) For this case we need to find a critical value that accumulates $\alpha/2$ of the area on each tail, we know that $\alpha=0.01$ , so then $\alpha/2 =0.005$ , using the normal standard table or excel we see that:

$z_{crit}= \pm 2.58$

Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis at 1% of significance.

Step-by-step explanation:

Data given and notation

n=420+174=594 represent the random sample taken

X=174 represent the number of yellow peas

$\hat p=\frac{174}{594}=0.293$ estimated proportion of yellow peas

$p_o=0.23$ is the value that we want to test

$\alpha=0.01$ represent the significance level

Confidence=99% or 0.99

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion of yellow peas is 0.23:

Null hypothesis: $p=0.23$

Alternative hypothesis: $p \neq 0.23$

When we conduct a proportion test we need to use the z statisitc, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.293 -0.23}{\sqrt{\frac{0.23(1-0.23)}{594}}}=3.649$

Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.05$ . The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v =2*P(z>3.649)=0.00026$

So the p value obtained was a very low value and using the significance level given $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis.

b) Critical value

For this case we need to find a critical value that accumulates $\alpha/2$ of the area on each tail, we know that $\alpha=0.01$ , so then $\alpha/2 =0.005$ , using the normal standard table or excel we see that:

$z_{crit}= \pm 2.58$

Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis at 1% of significance.

5 0

2 years ago

there are 30 flowers in a vase 2.5 of flowers are roses. 1/6 of the flowers are daisies. the rest of the flowers are carnations.

tekilochka [14]

Answer:

13 carnations

Step-by-step explanation:

Assuming you meant 2/5 because 2.5 would mean there are more roses in the vase than there are flowers in the vase, heres how to solve this.

Understanding

Each fraction is referring to "flowers" not "remaining flowers" and as such each time we will be comparing to the total.

2/5 of the total flowers are roses. This is written in words as for every 5 flowers two are roses, which means we will multiply 2 by how many sets of five we have in 30 flowers.

(30/5) x 2 =

(6) x 2 = 12 roses

Though with fractions its written as 30/1*2/5 which is the same as (30 x 2)/5

60/5 = 12 roses

Following this logic for every 6 flowers one is a daisy.

30/1 * 1/6 = (30 x 1)/6 = 30/6 = 5 daisies

Because the rest are carnations we want to subtract the amount of daisies and roses from the total amount of flowers to find the remaining flowers.

30 - 5 - 12 = 13 carnations

Hope this helps,

8 0

2 years ago

Which of the following is the solution to the compound inequality below? 3x+5 2 -1 or -2x - 725

sashaice [31]

Answer:

x= -674

Step-by-step explanation:

Solve for x and check: x + 5 = 3

Solution

Solve for x and check: - 3x = 12

Dividing each side by -3, we obtain

Another way of solving the equation

3x - 4 = 7x + 8

would be to first subtract 3x from both sides obtaining

-4 = 4x + 8,

then subtract 8 from both sides and get

-12 = 4x.

Now divide both sides by 4 obtaining

- 3 = x or x = - 3

Solve for c: 3(x + c) - 4y = 2x - 5c

First remove parentheses.

Remember, abx is the same as 1abx.

We divide by the coefficient of x, which in this case is ab.

6 0

2 years ago

Solve This question for Me please I’ll give you brainliest

Lostsunrise [7]

Answer: I believe its the 3rd one

Step-by-step explanation: Because it's less than 97

5 0

2 years ago

An angle whose measure is -405° is in

lara [203]

Answer:

Quadrant IV

Step-by-step explanation:

Given

$\theta = -405^\circ$

Required

The quadrant of the terminal side

To do this, we simply rotate the given angle in a clockwise direction.

A complete rotation is $-360^\circ$

So, we have:

$\theta = -405^\circ$

$\theta = -360^\circ -45^\circ$

Remove the complete rotation

$\theta = -45^\circ$

When $45^\circ$ is rotated in the clockwise direction, it stops at the 4th quadrant.

Hence, the terminal side falls in the quadrant IV

8 0

2 years ago