If it is 5 degrees outside and the temperature will drop 17 degrees in the next 6 hours how cold will it get?

In the diagram, angle 1 = 4x + 30, and angle 3 = 2x +48.

iragen [17]

Answer:

Since we have the information for Angles 1 and 3, and they are vertical, we can set them equal to each other. Once we have done this we can find the measures of them combined, and subtract it from 360 in order to only have the measure of 2 and its vertical angle. Finally, all we need to do now is divide the remaining measure by 2, and this will give us the measure of angle 2.

Angle 1=Angle 3

4x+30=2x+48

2x+30=48

2x=18

x=9

Angle 1=4(9)+30

Angle 1=36+30

Angle 1=66

Angle 1=Angle 3

Angle 1+ Angle 3=132

360-132=228

228/2=114

Angle 2= 114

6 0

3 years ago

you are rolling a 10-sided die with sides numbered 1-10. you keep rolling the die until you roll a prime number and then stop. l

evablogger [386]

The formula for E(x) would be SUM[ X(n)P(n)] from n = 1 to n = infinity until we get the prime number

In the given problem, a 10-sided die with 1-10 numbers is rolled until we get a prime number

Prime numbers between 1-10 = 2,3,5,7 (4 prime numbers)

Non - prime numbers = 1,4,6,8,9,10( 6 non-prime number)

Let X be the number of times the die is rolled

The probability of getting a prime =

$P(Prime) = \frac{4}{10}$

Now, the value of

E(X)=∑x.P(x) [ x-> {1, infinity}]

= P(1)X(1) +P(2)X(2)+P(3)X(3)+P(4)X(4)........+ P(n)X(n)

= 1. $\frac{4}{10}$ + 2. $\frac{6}{10}$ . $\frac{4}{10}$ + 3. $\frac{6}{10}$ . $\frac{6}{10}$ $\frac{4}{10}$ + 4. $\frac{6}{10}$ . $\frac{6}{10}$ . $\frac{6}{10}$ . $\frac{4}{10}$ .......

Hence, this is the value of E(x)

To learn more about Prime number, here

brainly.com/question/9315685

#SPJ4

4 0

2 years ago

3. Which ordered pair is a solution of the equation y = x – 2? (1 point) (3, 1) (1, 3) (–1, 3) (3, –1)

kozerog [31]

The answer is (3,1)

7 0

3 years ago

One circle has a circumference of 12 pie Another circle has a circumference of 32 pie What is the ratio of the radius of the sma

UNO [17]

Answer:

3 : 8

Step-by-step explanation:

The ratio of the radii is equal to the ratio of the circumference, then ratio is

12π : 32π ( divide both parts by 4π )

= 3 : 8

6 0

3 years ago

Suppose a poll is taken that shows that 765 out of 1500 randomly selected, independent people believe the rich should pay more

Zanzabum

Answer:

$z=\frac{0.51 -0.5}{\sqrt{\frac{0.5(1-0.5)}{1500}}}=0.775$

$p_v =P(z>0.775)=0.219$

So the p value obtained was a very high value and using the significance level given $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of interest is not significantly higher than 0.5

Step-by-step explanation:

Data given and notation

n=1500 represent the random sample taken

X=765 represent the successes

$\hat p=\frac{765}{1500}=0.51$ estimated proportion of successes

$p_o=0.5$ is the value that we want to test

$\alpha=0.05$ represent the significance level

Confidence=95% or 0.95

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 is higher than 0.5:

Null hypothesis: $p \leq 0.5$

Alternative hypothesis: $p > 0.5$

When we conduct a proportion test we need to use the z statistic, 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:

$z=\frac{0.51 -0.5}{\sqrt{\frac{0.5(1-0.5)}{1500}}}=0.775$

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 right tailed test the p value would be:

$p_v =P(z>0.775)=0.219$

So the p value obtained was a very high value and using the significance level given $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of interest is not significantly higher than 0.5

8 0

3 years ago