Which choice could be modeled by a linear function? A. The amount, y, of radioactive material remaining after x years when decay occurs at rate 30% each year.

B. The amount of money, y, In an account after x years earning 4% interest compounded annually.

C. The height, y, of a ball after bouncing x times, if each bounce reaches 2/3 the previous height.

D. The monthly cost, y, to use a cell phone for x minutes at a rate of 4 cents per minute.

Answers

Answer 1

Answer:

Final answer:

The monthly cost, y, to use a cell phone for x minutes at a rate of 4 cents per minute can be modeled by a linearfunction. This is because the cost increases at a constant rate with the number of minutes used. In contrast, options A, B, and C involve non-constant rates of change.

Explanation:

The answer is D. The monthly cost, y, to use a cell phone for x minutes at a rate of 4 cents per minute. This is a linear function because it describes a constant rate of change, as the cost changes linearly with the number of minutes used. Each additional minute costs the same amount: 4 cents. So, if we plot the minute (x) versus cost (y), we would get a straight line. This is different from the other options where the rate of change is not constant. For instance, options A, B, and C describe scenarios with exponential decay or growth.

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Answer 2

Answer:

Answer:

Step-by-step explanation:

D is linear because it increases the same amount each time

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A committee at the College Board has been asked to study the SAT math scores for students in Pennsylvania and Ohio. A sample of 45 students from Pennsylvania had an average score of 580, whereas a sample of 38 students had an average score of 530. The sample standard deviations for Pennsylvania and Ohio are 105 and 114 respectively. Does the study suggest that the SAT math score for students in Pennsylvania and Ohio differ

Answers

Answer:

Step-by-step explanation:

From the given information:

The null hypothesis and the alternative hypothesis can be computed as:

$H_0 :\mu_1 -\mu_2 = 0$ (i.e. there is no difference between the SAT score for students in both locations)

$H_1 :\mu_1 -\mu_2 \geq0$ (i.e. there is a difference between the SAT score for students in both locations)

The test statistics using the students' t-test for the two-samples; we have:

$t = \frac{\overline x_1 -\overline x_2}{\sqrt{(s_1^2)/(n_1)+(s_2^2)/(n_2) } }$

$t = \frac{580 -530}{\sqrt{(105^2)/(45)+(114^2)/(38) } }$

$t = \frac{50}{\sqrt{(11025)/(45)+(12996)/(38) } }$

$t = (50)/(√(245+342 ) )$

$t = (50)/(√(587) )$

$t = (50)/(24.228)$

t = 2.06

degree of freedom = ( $n_1 + n_2$ ) -2

degree of freedom = (45+38) -2

degree of freedom = 81

Using the level of significance of 0.05

Since the test is two-tailed at the degree of freedom 81 and t = 2.06

The p-value = 0.0426

Decision rule: To reject $H_o$ if the p-value is less than the significance level

Conclusion: We reject the $H_o$ , thus, there is no sufficient evidence to conclude that there is a significant difference between the SAT math score for students in Pennsylvania and Ohio.

One ticket is drawn at random from each of the two boxes.(A) 1 2 3 4 5

(B) 1 2 3 4 5 6

Find the chance that

(a) one of the number is 2 and the other is 5

(b) sum of the numbers is 7

(c) one number is bigger than twice the other

Answers

Answer:

a.1/15

b.1/6

c.1/3

Step-by-step explanation:

number of outcomes from box 1=5

number of outcomes from box 2=6

therefore total number of outcomes=6×5

=30

a. number of times receiving a ticket 2 and the other 5 =2

therefore probability= 2/30

=1/15

b.number of combinations for 7= 5 (1+6, 2+5,5+2,4+3,3+4.)

therefore probability= 5/30

=1/6

c.number of times one number was bigger than twice the other=10 (1+3,3+1,1+4,4+1,1+5,5+1,1+6,2+5,5+2,2+6)

therefore probability= 10/30

=1/3

I need to find the Missing angle of this equilateral triangle

Answers

Answer:

x = 120

Step-by-step explanation:

An equilateral triangle has 3 equal angles

The sum of the angles is 180

180/3 = 60

x + 60 = 180 since they form a straight line

x = 180-60

x = 120

Answer:

X...................

Please help with this fast

Answers

Answer:

integers from -1 ≤x≤2

Step-by-step explanation:

The domain is the value of the input or the x values

The domain is -1,0,1,2

integers from -1 ≤x≤2

Will give brainliest answer

Answers

Answer:

8- ff fj hfghgggģrdvbuhgffffgbhjjhhh

Determine which statements are true in the set of real numbers3. (Select all that apply.) (a) Two lines parallel to a third line are parallel. (b) Two lines perpendicular to a third line are parallel. (c) Two planes parallel to a third plane are parallel. (d) Two planes perpendicular to a third plane are parallel. (e) Two lines parallel to a plane are parallel. (f) Two lines perpendicular to a plane are parallel. (g) Two planes parallel to a line are parallel. (h) Two planes perpendicular to a line are parallel. (i) Two planes either intersect or are parallel. (j) Two lines either intersect or are parallel. (k) A plane and a line either intersect or are parallel. Incorrect: Your answer is incorrect.

Answers

Answer:

(a) True

(b) False

(d) False

(e) False

(f) True

(g) False

(h) True

(i) True

(k) True

Step-by-step explanation:

(a) Two lines parallel to a third line are parallel

True

(b) Two lines perpendicular to a third line are parallel

Only for lines on the same plane

Therefore, false

True

(d) Two planes perpendicular to a third plane are parallel

The two planes can be at an angle to each other and so intersect

Therefore, false

(e) Two lines parallel to a plane are parallel

Where the two lines are on a plane parallel to the first plane but the lines are not themselves parallel to each other they intersect

Therefore, false

(f) Two lines perpendicular to a plane are parallel

True

(g) Two planes parallel to a line are parallel

Where the planes are not parallel to each other, they will intersect

Therefore, false

(h) Two planes perpendicular to a line are parallel

True

(i) Two planes either intersect or are parallel

True

(k) A plane and a line either intersect or are parallel

True.

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