Enzo’s profit over the last few months has been falling. In December he made $900, in January his profit was $500, and in March, he lost $300. Is the sequence that represents his profit arithmetic? If it is, what is the recursive formula for the sequence?

Answers

Answer 1

Answer:

See explanation

Step-by-step explanation:

Enzo’s profit over the last few months:

In December, he made profit $900;In January, his his profit was $500; In February - unknown;In March, his loss was  $300.

Find the difference between given data

Dec - Jan [tex]\$900-\$500=\$400[/tex]

Jan - Feb [tex]\$500-\$x[/tex]

Feb - Mar [tex]\$x-(-\$300)=\$x+\$300[/tex]

If this sequence is arithmetic, then

[tex]\$500-\$x=\$x+\$300=\$400\\ \\\$x=\$100[/tex]

So, if the profit in February was $100, then this sequence is arithmetic sequence. In this case,

[tex]a_1=900\\ \\a_2=500\\ \\a_3=100\\ \\a_4=-300\\ \\...\\ \\d=-400[/tex]

The recursive formula is

[tex]a_n=a_{n-1}-400[/tex]


Related Questions

A rectangle is 25 feet long.Its area is 375 square feet. What is the width of the rectangle?

Answers

Answer:

Width of rectangle is 15 ft !

Step-by-step explanation:

Given :-

Area of rectangle = 375 ft²

Length of rectangle = 25 ft

Let width of the rectangle be b ft

Formula for area of rectangle

= ( lenght ) ( width )

Substituting the value ,

375 ft² = 25ft ( b ft )

[tex] \frac{375 {ft}^{2} }{25ft} = bft[/tex]

15 = b

So, the width of rectangle is 15 ft

The required width of the rectangle is  15 feet which is 25 feet long and the area is 375 square feet.

Given that,
A rectangle is 25 feet long. Its area is 375 square feet. What is the width of the rectangle is to be determined.

What is a rectangle?

The rectangle is 4 sided geometric shape whose opposites are equal in lengths and all angles are about 90°.

Here,
The area of the rectangle = length * width
                                     25 =  375 * width
                                      width = 375 / 25
                                      width = 15

Thus the required width of the rectangle is  15 feet.

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The cost, C, of ground beef varies directly with its weight in ounces, W. If 16oz of ground beef cost $3.20, what is the equation that would allow you to find the cost of any weight of ground beef?

A. C=0.2w
B. C=3.2w
C. C=5w
D. C=8w

Answers

Answer:

The answer would be B.

Step-by-step explanation:

The answer is b. C=3.2w because the cost of the beef is $3.20 and the amount of weight would be w and the cost would be C so the answer would be Cost = 3.2 • a number (w) which is c=3.2w . Hope you understand it now:) I explain things weird sorry

Write each fraction or mixed number as a decimal 7/20

Answers

Answer:

[tex]\large\boxed{\dfrac{7}{20}=0.35}[/tex]

Step-by-step explanation:

[tex]\bold{METHOD\ 1}\\\\\dfrac{7}{20}=7:20=0.35\\\\\text{Use a calculator or long division}\\\\.\qquad\underline{0.35}\\.\ \ 20|7\\.\ \ \ \ \ \underline{\ 0}\\.\qquad70\\.\ \ \ \ \ \underline{\ 60}\\.\qquad100\\.\qquad\underline{100}\\.\qquad==[/tex]

[tex]\bold{METHOD\ 2}\\\\\dfrac{7}{20}=\dfrac{7\cdot5}{20\cdot5}=\dfrac{35}{100}=0.35[/tex]

How do I plot this equation on the graph ?

Answers

Answer:

y = ¼x + 2

Step-by-step explanation:

x - 4y = -8

-x - x

__________

-4y = -x - 8

___ _____

-4 -4

y = ¼x + 2

I am joyous to assist you anytime.

Help me thank you!!!!!

Answers

Answer:

x= 31 degrees

Step-by-step explanation:

A triangle's angles add up to 180 degrees. Look at the 123, it's not part of the triangle. Subtract it from 180. You should get 57 degrees. Now, make an equation. You know it equals 180, so you add up all the sides like this: 57+92+x=180. After solving the equation, you should get 31 degrees.

Round 42395 to the nearest ten thousand

Answers

Answer:

40000

Step-by-step explanation:

4(2)395

if it smaller than 5 round down

if its lager than 5 round up

For what value of x will 55 and x have the mean (average) as 67? explain how you got your answer

Answers

Answer:

X=79

Step-by-step explanation:

The answer can be found by finding the difference of 67 and 55 which would be 12, then adding 12 and 67 to get 79. I can do this because if 2 numbers are split equally between them, then adding an number to get one will get you the other. It may seem confusing, comment if you still need help.

What is 4/16 simplify

Answers

Answer:1/4

Step-by-step explanation: divide both numbers by 4

[tex]\huge\boxed{\frac{1}{4}}[/tex]

You can simplify a fraction by dividing its numerator and denominator both by a factor from both of the numbers.

In this case, [tex]4[/tex] is a factor of the numerator and the denominator.

Divide both the numerator and the denominator by [tex]4[/tex].

[tex]\dfrac{4}{16} \div \dfrac{4}{4} = \dfrac{4 \div 4}{16 \div 4} = \boxed{\dfrac{1}{4}}[/tex]


A hiking club charges $60 to join and $12 for each hiking trip. Write an expression to model the total
cost. Find the cost of six hikes.​

Answers

Answer:

4,320 dollars. Expression is 60 × 12(6)

Answer:The trip will cost 132$

can i get brainlyest

Step-by-step explanation:60(to join) + 12(per hike)x6(hikes)

12 x 6 = 72 + 60 =132

what is 4 9/20 as a decimal

Answers

Answer:

4.45

Step-by-step explanation:

4 9/20

4 + 9/20

1/20 = 0.05

so 9/20 = 9 × 0.05

9/20 = 0.45

4 9/20 = 4 + 0.45

4 9/20 = 4.45

15 points
What is the value of x in the equation ?


StartFraction one-half EndFraction left-parenthesis n minus 4 right-parenthesis minus 3 equals 3 minus left-parenthesis 2 n plus 3 right-parenthesis.
2
13

Answers

Answer:

x=2

Step-by-step explanation:

isolate the variable by dividing each side by factors that dont contain the variable

Answer:

the answer is C (2)

Step-by-step explanation:

Solve A = a+b/2 for b

Answers

Answer:

Step-by-step explanation:

I'm not sure if the right side is [tex]\frac{a + b}{2}[/tex] or [tex]a + \frac{b}{2}[/tex], so I'll provide an answer for both:

[tex]A = \frac{a + b}{2}[/tex]

[tex]2A = a + b[/tex]

[tex]2A - a = b[/tex]

[tex]A = a + \frac{b}{2}[/tex]

[tex]A - a = \frac{b}{2}[/tex]

[tex]2(A - a) = b[/tex]

[tex]2A - 2a = b[/tex]

A = a +b/2
A -a =b/2
2(A-a) = b

4. If DF = 9x - 39, find EF.

Help I’m so confused!!!!

Answers

Answer:

EF =58

Step-by-step explanation:

from the illustration,

EF =DF - DE

given that DF =9x-39 , DE =47 EF=3x +10

substitute them into the formula,

3x +10=9x-39 - 47

solving for x

3x +10 =9x -86

grouping like terms

3x - 9x =-86 -10

-6x=-96

dividing through by -6

[tex] \frac{ - 6x}{ - 6} = \frac{ - 96}{ - 6} [/tex]

[tex]x = \frac{96}{6} [/tex]

[tex]x = 16[/tex]

but EF=3x+10

substitute x=16 into it to get the EF

EF= 3(16)+10

EF=48+10

EF=58

[tex]\huge\boxed{58}[/tex]

First of all, we know that [tex]DE+EF=DF[/tex], because these are two segments that make up one larger segment.

Write this as an equation.

[tex]DE+EF=DF[/tex]

[tex]47+(3x+10)=9x-39[/tex]

Remove the parentheses. [tex]47+3x+10=9x-39[/tex]

Combine the like terms. [tex]3x+57=9x-39[/tex]

Subtract [tex]9x[/tex] from both sides. [tex]-6x+57=-39[/tex]

Subtract [tex]57[/tex] from both sides. [tex]-6x=-96[/tex]

Divide both sides by [tex]-6[/tex]. [tex]x=16[/tex]

Now, find [tex]EF[/tex].

[tex]3x+10[/tex]

[tex]3(16)+10[/tex]

Multiply. [tex]48+10[/tex]

Add. [tex]\boxed{58}[/tex]

What is the solution to this system of equations?

Answers

Answer:

First choice.

Step-by-step explanation:

You could plug in the choices to see which would make all the 3 equations true.

Let's start with (x=2,y=-6,z=1):

2x+y-z=-3

2(2)+-6-1=-3

4-6-1=-3

-2-1=-3

-3=-3 is true so the first choice satisfies the first equation.

5x-2y+2z=24

5(2)-2(-6)+2(1)=24

10+12+2=24

24=24 is true so the first choice satisfies the second equation.

3x-z=5

3(2)-1=5

6-1=5

5=5 is true so the first choice satisfies the third equation.

We don't have to go any further since we found the solution.

---------Another way.

Multiply the first equation by 2 and add equation 1 and equation 2  together.

2(2x+y-z=-3)

4x+2y-2z=-6 is the first equation multiplied by 2.

5x-2y+2z=24

----------------------Add the equations together:

9x+0+0=18

9x=18

Divide both sides by 9:

x=18/9

x=2

Using the third equation along with x=2 we can find z.

3x-z=5 with x=2:

3(2)-z=5

6-z=5

Add z on both sides:

6=5+z

Subtract 5 on both sides:

1=z

Now using the first equation along with 2x+y-z=-3 with x=2 and z=1:

2(2)+y-1=-3

4+y-1=-3

3+y=-3

Subtract 3 on both sides:

y=-6

So the solution is (x=2,y=-6,z=1).

is 15 a perfect square​

Answers

No its not. the square root of 15 is about 3.873. Thus, the square root of 15 is not an integer, and therefore 15 is not a square number.

Answer:

No.

Step-by-step explanation:

No.

16 is a perfect square because 4 times itself is 16.

9 is a perfect square because 3 times itself is 9.

So there are no whole numbers such that when yoy square it (times it by itself) gives you 15.

Whole numbers are numbers contained within the following set:

{0,1,2,3,4,5,...}

So here are the first few perfect squares:

0 because 0(0)=0

1 because 1(1)=1.

4 because 2(2)=4.

9 because 3(3)=9.

16 because 4(4)=16.

25 because 5(5)=25.

36 because 6(6)=36.

49 because 7(7)=49.

64 because 8(8)=64.

81 because 9(9)=81.

As you can see 15 isn't in that list.

Please help me with this equation

Answers

Answer: The answer is 2 10/27

the complementary angle of 45

Answers

Answer:

45°

Step-by-step explanation:

Complementary angles sum to 90°, thus

90° - 45° = 45° ← is the complement of 45°

Alexis left her house at 7:45 p.m. to go shopping for clothes. She returned at 10:30 p.m.

a) express the time in hours that Alexis spent away for home.

Answers

Final answer:

Alexis spent 2 hours and 45 minutes away from home, which is equivalent to 2.75 hours.

Explanation:

To calculate how long Alexis spent away from home, we need to find the difference between the time she left and the time she returned. She left her house at 7:45 p.m. and returned at 10:30 p.m.

First, we'll convert both times to a 24-hour format to make it easier to compute the time difference. The time Alexis left remains the same as 19:45 (since p.m. times are already in the second half of a 24-hour day), and the time she came back is 22:30.

Next, we subtract the time Alexis left from the time she returned:

22:30
-19:45
______

The difference in the minutes column is 30 - 45, which would be negative, so we need to borrow an hour from the hours column.

22:30
-19:45
______

Convert the borrowed hour into 60 minutes and add to the 30 minutes: 60 + 30 = 90 minutes.

21:90
-19:45
______

Now we can subtract the minutes:

90 - 45 = 45 minutes.

And subtract the hours:

21 - 19 = 2 hours.

Therefore, Alexis spent 2 hours and 45 minutes away from home.

To express this time purely in hours, we convert 45 minutes into hours by dividing by 60:

45 minutes ÷ 60 minutes per hour = 0.75 hours.

Adding this to the 2 hours, we find that Alexis was away from home for 2.75 hours.

Final answer:

Alexis was away from home for 2 hours and 45 minutes, which is equivalent to 2.75 hours. The calculation involves subtracting the time she left from the time she returned and converting minutes to hours for an accurate measure.

Explanation:

The student is asking how to calculate the time Alexis spent away from home while she went shopping for clothes. To solve this, we need to calculate the difference in time between when she left and when she returned.

Alexis left her house at 7:45 p.m. and returned at 10:30 p.m.. To find the number of hours she spent away from home, we can follow these steps:

Convert the times into a 24-hour format if necessary, but here it's not required as both times are in the p.m.

Subtract the start time from the end time.

In this case, 10:30 p.m. is the same as 22:30 in a 24-hour format, and 7:45 p.m. is the same as 19:45. So,

22:30 (End Time)
- 19:45 (Start Time)
----

We have a difference of 2 hours and 45 minutes. To express this time purely in hours, we convert 45 minutes to a decimal by dividing by 60 (since there are 60 minutes in an hour).

45 minutes / 60 = 0.75 hours

Therefore, Alexis was away for 2.75 hours.

Which expression is equivalent to 34 ⋅ 3−9?

Answers

Answer:

93

Step-by-step explanation:

PEMDAS

parenthesis, exponents, multiplication, division, addition, subtraction

34 x 3 - 9

102 - 9

93

Answer:

93

Step-by-step explanation:

First we have to use pemdas

so we multiply

34*3=102

the we subtract

102-9=93

so 93 is your answer.

The sum of two numbers is 15 and their product is 54.What are the two numbers?

Answers

6 and 9. 6+9=15 and 6x9=54. hope this helps! :))

Find the slope of the lines passing through th points (-9,-3)and (7,-7)

Answers

Answer:

slope = - [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 9, - 3) and (x₂, y₂ ) = (7, - 7)

m = [tex]\frac{-7+3}{7+9}[/tex] = [tex]\frac{-4}{16}[/tex] = - [tex]\frac{1}{4}[/tex]

Answer:

Step-by-step explanation:

-y₁ + y₂\-x₁ + x₂ = m

[tex] \frac{3 - 7}{9 + 7} = - \frac{4}{16} = -\frac{1}{4} [/tex]

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contestants on a popular game show have an opportunity to randomly select a cash prize in 6 hidden containers. the highest possible cash prize is 25,000. the next highest prize is 5,000 and the one after that is 1000.
a. think about how the value of the prize changes from one container to the next. describe the pattern.
b. determine the prize values in the remaining containers.
c. represent the prize values in all six containers as a numeric sequence. then represent the sequence using table values

Answers

Answer:

A. The pattern is you multiply by 5

B. All 6 prizes are 25,000 and 5,000 and 1,000 and 200 and 40 and 8

C. ??

Step-by-step explanation:

Final answer:

The cash prize values in the game show reduce by a multiple of 5 each time from $25,000 to $5,000, $1,000, $200, $40, and $8. This forms a declining sequence and can be represented in a tabular form.

Explanation:

Contestants on a popular game show have six containers from which to select a hidden cash prize. The pattern of the prize values seems to exist in multiples of 5, with each prize being 5 times smaller than the previous one.

a. 25,000 is the highest cash prize. The next highest prize is 5,000, which is 5 times smaller than 25,000. The third prize, 1,000, is again 5 times smaller than 5,000. Thus, there seems to be a pattern where each subsequent prize is 1/5th of the preceding one.

b. Continuing this pattern, the prize values in the remaining containers would be 200, 40, and 8. Each of these values is 1/5th of the preceding value.

c. We can represent the values in a numeric sequence as follows: 25,000, 5,000, 1,000, 200, 40, 8. Our table representation would look as follows:

ContainerPrize Value125,00025,00031,000420054068

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PLZ HELP! ASAP 25 POINTS! AND BRAINLEST!!!

Add 113+(−56) using the number line. Select the location on the number line to plot the sum. -2 -12 3 -11 3 -1 -2 3 -1 3 0 1 3 2 3 1 11 3 12 3 2

Answers

THE Answer is 67

Step-by-step explanation:

Answer:

The Correct Answer Is 57

Step-by-step explanation:

According To Research

=113+(-56)

=113-56

=57

A parcel has a mass of 500g. Calculate its weight. (Assume the gravitational field strength is 10N/kg).

Answers

Answer:5n

Step-by-step explanation:

Final answer:

The weight of a 500g parcel, with a gravitational field strength of 10 N/kg, can be calculated using the formula w = mg, giving a weight of 5 N.

Explanation:

To calculate the weight of a parcel with a mass of 500g (0.5 kg), we will use the formula for weight, which is w = mg, where w is the weight in newtons (N), m is the mass in kilograms (kg), and g is the gravitational field strength in newtons per kilogram (N/kg). Given that the gravitational field strength is 10 N/kg, the weight of the parcel can be calculated as follows:

First, convert the mass from grams to kilograms: 500g is equal to 0.5 kg.Next, use the formula w = mg with m = 0.5 kg and g = 10 N/kg.Calculate the weight: w = 0.5 kg × 10 N/kg = 5 N.

Therefore, the weight of the parcel is 5 N.

someone please help ASAP will give brainliest

Answers

Answer:

Step-by-step explanation:

Zareen has 24 minutes to work on her math homework, and each problem is taking her 2/3 of a minute, on average, to complete. Which expression can be used to determine the number of math problems she will be able to complete in the time she has?

Answers

Answer is  24 divided by 2/3

Answer:

24 ÷ 2/3

Step-by-step explanation:

(3 x _) + (2 x 2)= 3x(5+2)
I don’t know how to get both sides the same

Answers

3•n+4=3x10

3n+4=30
3n=26
n=26/3=8.6

Therefore, the answer for that blank is about 8.6

Evaluate the expression.
38 +16 - 12 - 2 - (302)
Enter your answer in the box.

Answers

Answer:

-262

Step-by-step explanation:

Evaluate Subtraction & Addition from right to left [or left to right, as long as you know what you are doing]:

38 + 16 - 12 - 2 - 302

|_______||____________|

[tex]44 - 316 = -262[/tex]

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Sophie earns $18 for working 2 1/4 hours how much can she earn per hour

Answers

Sophie would earn jajnsbzbxxbxbbxbxbdbd1118388

Sophie earns $8.00 per hour. To find this, dividends of $18 by 2.25, representing the total hours worked, result in the per-hour earning.

To calculate how much Sophie earns per hour, we need to divide her total earnings by the total number of hours she worked. Sophie earns $18 over 2 1/4 hours.

First, we express the hours worked as an improper fraction or a decimal for ease of calculation. Since 1/4 hour is equivalent to 15 minutes, and 2 1/4 hours are the same as 2 + 0.25 which equals 2.25 hours. Now we divide $18 by 2.25 hours to find the hourly wage:

Hourly Wage = Total Earnings / Total Hours Worked

Hourly Wage = $18 / 2.25 hours

Hourly Wage = $8.00 per hour

So, Sophie earns $8.00 per hour.

If 12% of a number is 24, what is the number?

Answers

The answer is 200. Your welcome

Answer:

The number is 200.

Step-by-step explanation:

12% of a number = 24

Let the number be x.

[tex]\frac{12}{100}[/tex] of x = 24

0.12x = 24

x = [tex]\frac{24}{0.12}[/tex] = 200

So the number (x) is 200.

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