According to the Florida Agency for Workforce, the monthly average number of unemployment claims in a certain county is given by ????????(tt) = 24.31tt2 − 276.58tt + 2035, where t is the number of years after 1990. a) During what years did the number of claims decrease? b) Find the relative extrema and interpret it.

Answers

Answer 1

Answer:

a) The number of claims decrease from 1990 to 1996.

b) The relative extrema is a minimum and happens approximately in 1996 (t=5.688). This means the moment when the number of claims stop decreasing and start to increase.

Step-by-step explanation:

The monthly average number of unemployment claims in a certain county is given by:

[tex]C(t)=24.31t^2-276.58t+2035[/tex]

With t: number of years after 1990.

We have to determine in what years the number of claims decrease and the relative extreme value.

We can find this by analizing the first derivative.

When the first derivative is equal to zero, this indicates an extreme value, which can be a maximum or minimum.

When the first derivative is positive, it indicates that the function is increasing. On the contrary, when the first derivative is negative, it indicates that the function is decreasing.

The first derivative is:

[tex]\dfrac{dC}{dt}=24.31(2t)-276.58(1)+0\\\\\\\dfrac{dC}{dt}=48.62t-276.58[/tex]

Then, we can calculate the extreme value:

[tex]\dfrac{dC}{dt}=48.62t-276.58=0\\\\\\48.62t=276.58\\\\\\t=\dfrac{276.58}{48.62}=5.688\approx 6[/tex]

This extreme value happens for t=6 (year 1996).

If we calculate the value of the first derivative for t=5, that is previous to the extreme value, we can find if the function was increasing or decreasing:

[tex]\dfrac{dC}{dt}(5)=48.62*5-276.58=243.10-276.58=-33.48<0[/tex]

As the value is  negative, we know that the number of claims was decreasing from t=0 to t=6 (from 1990 to 1996), and then reach a minimum and start to increase from them (from 1996 onwards).


Related Questions

Three black beads, two red beads, and a yellow bead are arranged in a line. What is the probability that no black bead is adjacent to the yellow bead?

Answers

Answer:

Probability of no black bead is adjacent to the yellow bead is = 0.966

Step-by-step explanation:

First to arrange all the beads without restrictions = 6! = 720

Probability the black bead is adjacent to Yellow bead = 4!/6! = 24 /720

= 0.0333

Probability of no black bead is adjacent to the yellow bead is

= 1- Probability the black bead is adjacent to Yellow bead

= 1-0.033

= 0.966

What is the length of AC? Brainliest for right answer

Answers

Answer:

2.3 units

Step-by-step explanation:

Complete A and B for 5-8 points.

Answers

Answer:

a) 4 hours

b) 11 am

Step-by-step explanation:

So say the number of hours is x

a) 72 + 6x = 96

6x = 24

x = 4

b) 7am + 4 hours = 11am

Question 11 of 15

Micah is filling up his cone-shaped cup with water. The cup (as shown) has a diameter of 72 millimeters and a slant height of 45

millimeters. How much water can Micah fill in his cup?

Answers

Answer:

  36.644 mL . . . . depending on your value of π (see below)

Step-by-step explanation:

The height of Micah's cup is found from the radius and slant height. The radius is half the diameter, so is 36 mm. Then the height h is ...

  45² = 36² +h²

  h = √(45² -36²) = 27 . . . . . mm

The volume is given by the formula ...

  V = (1/3)πr²h

  V = (1/3)π(36 mm)²(27 mm) = 11664π mm³

For π = 3.14

  11664(3.14) mm³ ≈ 36,625 mm³ = 36.625 mL

For π = 3.14159265

  11665π mm³ = 36,644 mm³ = 36.644 mL

_____

Comment on units

A unit of measure used for relatively small volumes, especially of liquid, is milliliters (mL). 1 mL = 1000 mm³.

Answer:

The answer is 11664pimm^3

Step-by-step explanation:

Find the supplement of an angle that measures 20 degrees.
A) 50 degrees
B) 70 degrees
C) 90 degrees
D) 160 degrees

Answers

Answer:

160 degrees

Step-by-step explanation:

Answer:I think it is D

Step-by-step explanation:

What is the circumference of the following circle?
9 cm

Answers

Answer:

9π or 28.27 cm

Step-by-step explanation:

The circumference formula is 2πr or dπ. The diameter is 9 cm so we multiply 9 with pi to get the answer.

The value of the circumference of the given circle is 9π cm OR 28.278 cm

Calculating circumference of a circle

From the question, we are to determine the circumference of the circle.

The circumference of a circle can be calculated by using the formula,

C = πd

Where C is the circumference of the circle

and d is the diameter

From the diagram,

d = 9 cm

Therefore,

Circumference of the circle = π × 9

Take π = 3.142

Then,

Circumference of the circle = 28.278 cm

Hence, the value of the circumference of the given circle is 9π cm OR 28.278 cm

Learn more on Calculating circumference of a circle here: https://brainly.com/question/12823137

−5y=−5
7x+6y=7

Is (5,1) a solution of the system

Answers

Answer:no, (5,1) is not a solution for the equation. (1/7,1) will be a solution for the equation.

Step-by-step explanation:

one way to do it is to plug 1 as the y-value into the first equation which does work but when you plug 5 as the x-value and 1 as the y-value in the second equation, it will get you to 41 which does not match so it will not be an equation. the other way to check is to solve by substitution which for the first equation, you divide both side by -5 and get y=1 then substitute y with 1 in the second equation and subtract both side by 6 and get 7x=1 and divide both side by 7 to get 1/7. the y-value match but the x-value don't so (5,1) is not a solution.

Sound travels about 750 miles per hour. If you stand in a canyon and sound a horn, you will hear an echo.

Suppose it takes about 0.5 seconds to hear the echo. How far away is the canyon wall, in feet?
feet

Now let's generalize that result. Suppose it takes n seconds to hear the echo. How far away is the canyon wall, in terms of n?

Answers

Answer:

The sound takes time to go to a point and reflect back to your position.

It means the sound went twice a distance.

=> Suppose it takes about 0.5 seconds to hear the echo, the canyon wall would be [750 x (0.5/3600)]/2 = 0.052 miles

=> Suppose it takes about n seconds to hear the echo, the canyon wall would be [750 x (n/3600)]/2 miles

Hope this helps!

:)

The distance the canyon wall is away is 33000 feet.

The distance the canyon is away in terms of n is 66000n feet.

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Speed = 750 miles per hour

Time = 0.5 seconds

Distance = Speed x Time

Now,

1 mile = 5280 feet

750 miles = 3960000 feet

1 hour = 60 seconds

So,

Speed = (3960000/60) feet per second

Distance = 66000 x 0.5 feet = 33000 feet

This means,

The canyon wall is 33000 feet away.

Now,

For n seconds,

The canyon wall is 66000n feet away.

Thus,

The canyon wall is 33000 feet away.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ2

What’s the correct answer for this?

Answers

Answer:

C

Step-by-step explanation:

HJN IS SIMILAR TO PQN

faz um bom tempo que não faço expressões numéricas,vcs podem me ajudar!

Answers

Answer:

English Plz

Step-by-step explanation:

A family plan to catch a ferry and need to book in at 12:02 am. The journey to the ferry port will take 2 hours 45 minutes. What time should they leave home in order to get to the ferry port on time?

Answers

Answer:

DEEZNUUTZZZ

Step-by-step explanation:

what are the steps for using integar tiles to evaluate the expression 45 divided by 15

Answers

Answer:

1. Gather 45 tiles

2. Split them up into groups of 15. Your answer will be the amount of piles you  end up with. Hope this helps!

What is the volume of a sphere with a diameter of 6 m, rounded to the nearest tenth of a cubic meter?

Answers

Answer:113 cubic meter

Step-by-step explanation:

Diameter=6

Radius=r=6/2

Radius=r=3

π=3.14

Volume of sphere=4/3 x π x r x r x r

Volume of sphere=4/3 x 3.14 x 3 x 3 x 3

Volume of sphere=(4x3.14x3x3x3) ➗ 3

Volume of sphere=339.12 ➗ 3

Volume of sphere=113.04

Volume of sphere =113 cubic meter

How many fish a are in the box

Answers

Answer:

Where is the box?

Step-by-step explanation:

So I can help you

This area model shows 50 X 38 Which number is missing from the model

Answers

Answer:

69

Step-by-step explanation:

list all the factor means use divisibility rules of 102,232​

Answers

Answer:

  102,232​ = 2·2·2·13·983

Step-by-step explanation:

  102,232​ ends in 32, so is divisible by 4

  102,232/4 = 25558 ends in 2, so is divisible by 2

  25558/2 = 12779

     is not even, so is not divisible by 2

     has a sum of digits mod 9 of 8, so is not divisible by 3 or 9

     does not end in 0 or 5, so is not divisible by 5

     gives the result 1277-2·9 = 1259; 125-2·9 = 107; 10-2·7 = -4, which is not zero, so 12779 is not divisible by 7

     gives the result (1+7+9)-(2+7) = 8, which is not divisible by 11, so 12779 is not divisible by 11

     gives the result 1277 +4·9 = 1313, which is divisible by 13, so 12779 is divisible by 13

  12779/13 = 983 needs to be tested for divisibility by primes between 17 and 31, namely 17, 19, 23, 29, 31. It is not divisible by any of these, so this is the last prime factor of 102,232:

  102,323 = 2·2·2·13·983

_____

Divisibility rules:

Note that for any transformation rule, the rule can be repeated on the reduced result. The digits of a sum of digits can be summed, for example.

  2: ends in even digit

  3: sum of digits is divisible by 3

  5: ends in 0 or 5

  7: subtracting 2 times the last digit from the rest is divisible by 7

  11: difference of sums of alternate digits is divisible by 11

  13: there are several rules. A couple of useful ones are

the sum of 4 times the last digit and the remaining number will be divisible by 13 (used above)the difference of the sums of alternate groups of 3 digits will be divisible by 13 (232-102 = 130, for the number above; is divisible)

  17: subtracting 5 times the last digit from the rest is divisible by 17

  19: the sum of 4 times the last 2 digits and the remaining number will be divisible by 19

  23: the sum of 3 times the last 2 digits and the remaining number will be divisible by 23

  29: the sum of 9 times the last 2 digits and the remaining number will be divisible by 29

  31: subtracting 3 times the last digit from the rest is divisible by 31

Need help. not in college

Answers

The length of ab is 24

tickets for a concert have been in increadbibly high demand. and as the date for the concert draws closer the price of tickets increases exponentially. the cost of a pair of concert tickets was $96 yesterday and today it is $108.

what is the multiplier

what is the daily percent rate?

using the cost of a ticket today as your initial value write an exponential equation that models this situation

what will be the cost of a pair of concert tickets in one week from today

what was the cost of a pair of tickets three days ago?

Answers

Answer:

multiplier 1.125percent rate 12.5%p(t) = 108·1.125^tp(7) = $246.32p(-3) = $75.85

Step-by-step explanation:

a) The daily multiplier is 108/96 = 1.125

b) The daily percentage change is 1.125 -1 = .125 = 12.5%

c) The function can be written as ...

  price = (initial value)·(daily multiplier)^t

  p = 108·1.125^t

d) for t=7, put the number in and do the arithmetic.

  108·1.125^7 ≈ 246.32 . . . dollar cost in a week

e) same deal, for t=-3

  108·1.125^-3 ≈ 75.85 . . . .dollar cost 3 days ago

Solve for a given 2e^a =4b

Answers

Answer:

a = ln (2b)

Step-by-step explanation:

2e^a =4b

Divide each side by 2

2/2 e^a =4/2b

e^a = 2b

Take the natural log of each side

ln(e^a) = ln(2b)

a = ln (2b)

Select the correct symbol to compare the rates.
22 miles in 20 minutes 38 miles in 30 minutes

Answers

Answer:

<

Step-by-step explanation:

22/20=1.1

38/30=1.27

Answer:

<

Step-by-step explanation:


brainliest quick!

Aiden wanted to model -15 + 15 = 0 on the number line. He first drew an arrow 15 units long starting from zero that pointed to the left. He then draws another arrow 15 units long starting from zero that points to the right. What error did Aiden make?
A. The first arrow he drew should have pointed to the right to represent -15.
B. The second arrow he drew should have pointed to the left to represent 15.
C. The first arrow he drew should have started at -15 instead of 0.
D. The second arrow he drew should have started at -15 instead of 0.

Answers

Answer:

c

Step-by-step explanation:

Answer:

it's D

Step-by-step explanation:

The number never goes over 0 so there is no need to put anything above 0

Find the radius of Circle M, if the area of a sector is 36.07 cm^2 and the central angle of that sector is 58º. Round your answers to the hundredths place if necessary

Answers

Answer:

r = 5.97 cm

Step-by-step explanation:

The area of the sector is given by the following equation:

[tex]A = r*S = 2\pi*r^{2}*\frac{58}{360}[/tex]

Where:

r: is the radius

A: is the area

The radius is:

[tex]r = \sqrt{\frac{A}{2*\pi*58/360}} = \sqrt{\frac{36.07 cm^{2}}{2*\pi*58/360}} = 5.97 cm[/tex]

Therefore, the radius of Circle M is 5.97 cm.

I hope it helps you!

Can a triangle have died of the lengths 2 yd, 9yd and 10 yd?

Answers

Answer:

No it does not work because 85 does not equal 100.

Step-by-step explanation:

so you would try the formula a2+b2=c2

2^2+9^2=10^2

4+81=100

85=100

No it does not work because 85 does not equal 100.

Answer:

Answer:C. 4 m, 3 m, 4 m, 4 m

Step-by-step explanation:

the sides in a parallelogram need to be equal to the opposite side making them the same length.

A parallelogram is a quadrilateral in which the opposite sides are parallel. The opposite sides and opposite angles are also equal.

Looking at the given options,

A) the opposite sides are equal to 2 yards. Therefore, it is a parallelogram.

B) the opposite sides are equal to 2cm and 3cm each. Therefore, it is a parallelogram.

C)A pair of opposite sides is equal to 4 cm and the other pair of opposite sides is unequal because one side is 3m and the other is 4 m. Therefore, it is not a parallelogram.

D) the opposite sides are equal to 5 in and 3 in each. Therefore, it is a parallelogram.

Hope this helps!!!

What is the sum in simplest form I ready diagnostic please hurry

Answers

example:

The value of x is 22

Step-by-step explanation:

We are given that there are two numbers

First number is x

second number is 35

The sum of x and 35 is 57

so, we get equation as

now, we can solve solve x

So, subtract both sides by 35

B(4,8) and C(8,0) are the endpoints of a line segment. What is the midpoint M of that line
segment?
Write the coordinates as decimals or integers.

Answers

Answer:

(6,4)

Step-by-step explanation:

I just did quick math in my head.

The angle of elevation from the top of a building to the top of another is 45°.
The distance between the feet of these two buildings is 402 m.
What is the distance between the top of the two buildings?

Answers

Answer:

402m

Step-by-step explanation:

Set this up as a triangle and use trig to solve it:

tan(45) = y/402

y = 402*tan(45)

substitute: tan(45) = 1

y = 402 * 1

y = 402m


How many unique ways are there to arrange the letters in the word PRIOR?

Answers

Answer:

60

Step-by-step explanation:

Answer:

it is 60

Step-by-step explanation:

Factor.

Z^2- 3z – 18

Answers

Answer:

(z-6)(z+3)

Step-by-step explanation:

Answer:

Step-by-step explanation:

z^2-6z + 3z -18

z(z-6)+3(z-6)

(z+3)(z-6)

What are prime number​

Answers

A prime number is a special number because it means that it only has one factor pair and that factor pair is always 1 and the number itself.

In other words, prime numbers are the numbers

divisible by 1 and the number itself.

For example, let us take 2.

2 has only two factors and those are 1 and 2 so it's prime.

Similarly, 7 is also a prime number because it has only two factors

and these are 1 and the number itself which is 7.

Answer:

A number that is only divisible by itself and 1

Step-by-step explanation:

A University of Florida economist conducted a study of Virginia elementary school lunch menus. During the state-mandated testing period, school lunches averaged 863 calories. The economist claims that after the testing period ends, the average caloric content of Virginia School lunches drops significantly.

Set up the null and alternative hypotheses to test the economist’s claim.

Answers

Answer:

Null hypothesis: u = 863

Alternate hypothesis (H1): u < 863

Step-by-step explanation:

a. Null hypothesis: u = 863

The null hypothesis implies that the average caloric content of Virginia School lunches is equal to 863.

b. Alternate hypothesis: u < 863

The alternate hypothesis implies that the average caloric content of Virginia School lunches is less than 863, that is, it drops significantly.

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