Mathematical statements into logical statements with nested quantifiers. About Translate each of the following English statement
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Answer: Real world problem is "A student have c toffee he distribute th part of those toffees to his friends. He gave total 21 toffees to his friend".
Explanation:
Let a student have c number of toffees in his bag.
It is given that he distribute th part of those toffees to his friends.
The th part of c toffees is,
The total number of distributed toffees is 21.
It is the same as given equation.
If we change the equation in words it means the th part of a number c is 21.
Answer:
Step-by-step explanation:
Hello!
You have the math and writing SAT scores of twelve students.
There are two variables of interest X₁: Math SAT score of a student. and X₂: Writing the SAT score of a student.
These two variables aren't independent since both of them represent data corresponding to the same student, meaning, that the math and writing scores belong to the same students and not to two separate groups of students.
This is an example of paired samples, to make the statistical test you have to establish a third variable, this variable will be the difference between the other two:
Xd= X₁-X₂
Xd: "Difference between the Math and Writing SAT scores of a student.
This variable has a normal distribution Xd~N(μd;σd²)
a. Using a .05 level of significance and test for a difference between the population mean for the math scores and the population mean for the writing scores? Enter negative values as negative numbers. Round your answer to two decimal places.
The parameter of interest is μd is the population mean of the difference between the math and writing SAT scores of the students.
The hypotheses are:
H₀: μd=0
H₁: μd≠0
α: 0.05
The test statistic is a t-student for dependent samples and it's rejection region is two-tailed.
What is the p-value? Round your answer to four decimal places.
The p-value for this test is: 0.0394
The p-value is less than the level of significance, the decision is to reject the null hypothesis.
b. What is the point estimate of the difference between the mean scores for the two tests?
The sample mean for the variable "difference" is X[bar]d
You can calculate the point estimate of the sample mean of the variable Xd using two ways.
1) You calculate all the differences between the pairs of scores, add them and divide them by the sample size
X[bar]d= ∑di/n
∑di= 300
n=12
X[bar]d= 300/12= 25
2) You can calculate the sample mean for each variable and then calculate the difference between the two sample means
X[bar]₁= ∑X₁/n
∑X₁= 6168
X[bar]₁= 6168/12= 514
X[bar]₂= ∑X₂/n
∑X₂= 5868
X[bar]₂= 5868/12= 489
X[bar]d= X[bar]₁-X[bar]₂ = 514 - 489= 25
What are the estimates of the population mean scores for the two tests?
Math test X[bar]₁= 514
Writing test X[bar]₂= 489
Which test reports the higher mean score?
The Math test reports a higher mean score.
I hope it helps!
Answer:
Step-by-step explanation:
We know that:
- The initial conditions are -7 meters at 0 minutes.
- Then, after 6 minutes, he was 16 meters below the ground.
According to these two simple facts we can found the linear function that describes this problem. First, the problem says that Mr. Mole is descending at a constant rate, which is the slope of the function. Now, to calculate the slope we need to points, which are and
, where <em>t-values </em>are minutes, and <em>y-values </em>are meters. You can see, that the first point is the initial condition and the second point is 6 minutes later.
So, we calculate the slope:
From the slope we can see that Mr. Mole is descending, because it has a negative sign. Also, the point is on the <em>y-axis</em>, because <em>t</em> is null, so -7 is part of the function. Therefore the function that describes this problem is: