MATHEMATICS COLLEGE

HELP!! Monette began heating a liquid with a starting temperature of 62.5°F. The temperature increased by 5° per minute.

What is the recursive rule that represents this situation?\
an=
a1=

Answers

Answer 1

Answer:

Greetings!

Answer:

an = 65 + 5 $_(n - 1)$

a1 = 65

Step-by-step explanation:

If the begining value is 65, then a1 has to be itL

a1 = 65

Then, if this amount increased every minute then 5 has to be added to this value each time:

an = 65 + 5

But this means that 5 is added to 65 every time with no increase, so the five must me multiplied by the n value:

an = 65 + 5 $_(n)$

a2 = 65 + 10 = 75

But this value should be 70 because it is the first point after 65 so it should be +5 not +10

To do this we can simply subtract one from the n value that is being multiplied by 5:

an = 65 + 5 $_(n - 1)$

Which is the recursive rule!

Hope this helps!

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What is the solution to x+5>-7

Answers

According to the given data we have the following inequality:

$x+5>-7$

To find the solution of the inequality above we would make the following:

$\begin{gathered} \mathrm{Subtract\: }5\mathrm{\: from\: both\: sides} \n x+5-5>-7-5 \end{gathered}$ $\begin{gathered} \text{Finally, simplify},\text{ and so:} \n x>-12 \end{gathered}$

Therefore, the solution to x+5>-7 would be x>-12

A social scientist believed that less than 30 percent of adults in the United States watch 15 or fewer hours of television per week. To test the belief, the scientist randomly selected 1,250 adults in the United States. The sample proportion of adults who watch 15 or fewer hours of television per week was 0.28, and the resulting hypothesis test had a p-value of 0.061. The computation of the p- value assumes which of the following is true? (A) The population proportion of adults who watch 15 or fewer hours of television per week is 0.28. Submit

(B) The population proportion of adults who watch 15 or fewer hours of television per week is 0.30.

(C) The population proportion of adults who watch 15 or fewer hours of television per week is less than 0.30.

(D) The population mean number of hours adults spend watching television per week is 15.

(E) The population mean number of hours adults spend watching television per week is less than 15.

Answers

The population proportion of adults who watch 15 or fewer hours of television per week is less than 0.30.

Given that,

A social scientist believed that less than 30 percent of adults in the United States watch 15 or fewer hours of television per week.

The scientist randomly selected 1,250 adults in the United States. The sample proportion of adults who watch 15 or fewer hours of television per week was 0.28,

And the resulting hypothesis test had a p-value of 0.061.

We have to determine,

The computation of the p- value assumes which of the following is true.

According to the question,

Let, The proportion of adults watching televisionless than or equal to 15% be = x

Null Hypothesis [H0] : x = 30% = 0.30

Alternate Hypothesis [H1] : x < 30% , or x < 0.30

P value is calculated at z value :

$= P_1- \sqrt(p_o(1-p_o))/(n)}$

Where p' = 0.28, $P_0$ = 0.30, $P_1$ = 0.70 ;

Then,

$= 0.70- \sqrt(0.30(1-0.30))/(1250)}\n\n= 0.70- \sqrt{(0.30 * 0.70 )/(1250) }\n\n= 0.70 - 0.012\n\n= 0.61$

Assuming 10% level of significance, p = 0.10

Therefore, p value 0.061 < 0.10, reject H0 & accept H1. This implies that we conclude that 'x i.e. proportion of adults watching television less than or equal to 15% < 30% or 0.30'

Hence, The population proportion of adults who watch 15 or fewer hours of television per week is less than 0.30.

To know more about Sample proportion click the link given below.

brainly.com/question/13846904

Answer:

Step-by-step explanation:

Let the proportion of adults watching television less than or equal to 15% be = x

Null Hypothesis [H0] : x = 30% = 0.30
Alternate Hypothesis [H1] : x < 30% , or x < 0.30

P value is calculated at z value : p' - [ √ { p0 (1- p0) } / n ] ;

where p' = 0.28, p0 = 0.30, p1 = 0.70 ; ∴ p ( z < -1.543) = 0.061

Assuming 10% level of significance, p = 0.10

As p value 0.061 < 0.10, we reject H0 & accept H1. This implies that we conclude that 'x ie proportion of adults watching television less than or equal to 15% < 30% or 0.30'

I need help with this question

Answers

Answer:
_______________________________________________
1) 72 $\pi$ cm² / min. ;
_______________________________________________
2) 192 $\pi$ cm² / min.
_______________________________________________
Explanation:
____________________________________________

Area of a circle: A = $\pi$ r² ;

Rate of change of Area is: da/dt = 2 $\pi$ r (dr/dt) ;

Given: dr/dt = 3 cm / min.
______________________________________________________
Problem 1)
____________________________________________________________
dA/dt = 2 $\pi$ *(12 cm)*(3 cm/ min) = 72 $\pi$ cm² / min. ;
____________________________________________________________
Problem 2)
____________________________________________________________
dA/dt = 2 $\pi$ *(32 cm)*(3 cm/ min) = 192 $\pi$ cm² / min.
_____________________________________________________________

A vehicle designed to operate on a drag strip accelerates from zero to 30m/s while undergoing a straight line path displacement of 45m. What is the vehicle's acceleration if its value may b assumed to be constant? A.2.0m/s
B.5.0m/s
C.10m/s
D.15m/s

Answers

The vehicle's acceleration if its value may b assumed to be constant is 10 m/s. Therefore, option C is the correct answer.

Given that, a vehicle designed to operate on a drag strip accelerates from zero to 30m/s while undergoing a straight line path displacement of 45m.

What is an acceleration?

Acceleration is the name we give to any process where the velocity changes. Since velocity is a speed and a direction, there are only two ways for you to accelerate: change your speed or change your direction-or change both.

Here, Δx = 45 m, v₀ = 0 m/s and v = 30 m/s

Using the formula v² = v₀² + 2aΔx

(30 m/s)² = (0 m/s)² + 2b (45 m)

b = 10 m/s

The vehicle's acceleration if its value may b assumed to be constant is 10 m/s. Therefore, option C is the correct answer.

Learn more about the acceleration here:

brainly.com/question/12550364.

#SPJ2

Answer:

C. 10 m/s²

Step-by-step explanation:

Given:

Δx = 45 m

v₀ = 0 m/s

v = 30 m/s

Find: a

v² = v₀² + 2aΔx

(30 m/s)² = (0 m/s)² + 2a (45 m)

a = 10 m/s²

(a)/(5h+q)=t Find a (a)/ means fraction

Answers

Answer:

Step-by-step explanation:

a/(5h+q) = t

multiply both sides by 5h + q

a / (5h + q) * (5h+q) = t * (5h + q)

a = t * (5h + q)

I would say this is your answer.

You could distribute the t

a = 5ht + tq

which could also be an answer.

In 2003, the population of an African country was about 10.2 million people, which is 1 million more than 4 times the population in 1950. Enter and solve an equation to find the approximate population p (in millions) in 1950. An equation is . The approximate population in 1950 was million people.