Answer:
Solution: x=5, y=4
Step-by-step explanation:
System of Equations
We need to solve:
- 5x + 9y = 11
x - 3y = - 7
There are several ways to solve a system of linear equations. We'll take advantage of the second equation since it has the x with coefficient 1 and solve it for x:
x = - 7 + 3y
Now replace it into the first equation:
- 5(- 7 + 3y) + 9y = 11
Operate:
35 - 15y + 9y = 11
Simplify:
35 - 6y = 11
Rearrange:
- 6y = 11 - 35 = -24
Solve:
y = -24 / -6
y = 4
Finally, since
x = - 7 + 3y
x = - 7 + 3*4
x = - 7 + 12
x = 5
Solution: x=5, y=4
Answer:
64.0% is the correct answer.
Step-by-step explanation:
As per the given scatter plot of voter turnout every year:
X axis represents the year and
Y axis represents the percentage of people who voted.
The model was predicted as per the equation:
To find:Prediction for the year 1900.
Putting the value of , the value of y will be the predicted value of the model i.e. the value of percentage of voter turnout.
So, the model predicts for the year 1900.
Answer:
18
Step-by-step explanation:
Answer:
18
Step-by-step explanation:
If six loaves lasted seven days, and she is going for 21 days next time, that is three times the amount of days she went on her last camping trip. so you multiply the amount of loaves by 3.
Answer:
oh well thanks
Step-by-step explanation:
Answer:
Step-by-step explanation:
Corresponding heights of presidents and height of their main opponents form matched pairs.
The data for the test are the differences between the heights.
μd = the president's height minus their main opponent's height.
President's height. main opp diff
191. 166. 25
180. 179. 1
180. 168. 12
182. 183. - 1
197. 194. 3
180. 186. - 6
Sample mean, xd
= (25 + 1 + 12 - 1 + 3 + 6)/6 = 5.67
xd = 5.67
Standard deviation = √(summation(x - mean)²/n
n = 6
Summation(x - mean)² = (25 - 5.67)^2 + (1 - 5.67)^2 + (12 - 5.67)^2+ (- 1 - 5.67)^2 + (3 - 5.67)^2 + (- 6 - 5.67)^2 = 623.3334
Standard deviation = √(623.3334/6 sd = 10.19
For the null hypothesis
H0: μd ≥ 0
For the alternative hypothesis
H1: μd < 0
The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 6 - 1 = 5
The formula for determining the test statistic is
t = (xd - μd)/(sd/√n)
t = (5.67 - 0)/(10.19/√6)
t = 1.36
We would determine the probability value by using the t test calculator.
p = 0.12
Since alpha, 0.05 < than the p value, 0.12, then we would fail to reject the null hypothesis.
Therefore, at 5% significance level, we can conclude that for the population of heights for presidents and their main opponents, the differences have a mean greater than 0 cm.
The null hypothesis in this case would be that there is no average height advantage for presidents over their main opponents (µd ≤ 0), while the alternative hypothesis is that presidents are taller on average (µd > 0). A paired t-test with a significance level of 0.05 is usually employed in testing these hypotheses using the p-value and t-score.
In hypothesis testing, the goal is to determine the validity of a claim made. In this case, the claim is that the mean difference in height, where the difference is calculated as the president's height minus their main opponent's height, is greater than 0 cm. This represents the theory that taller presidential candidates have an advantage.
For setting up a null hypothesis and an alternative hypothesis, we consider the following parameters:
To test these hypotheses, we would typically use a one-sample t-test for paired differences with a significance level (alpha) of 0.05. A p-value less than this would allow us to reject the null hypothesis in favor of the alternative hypothesis that presidents are on average taller than their main opponents. Use of p-value and t-score is essential in conducting such a test.
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Answer:
most likely 3
Step-by-step explanation:
if ur asking for the exponent 3 is in the ones place