Please help me!!!

Hhhhhhhhhhhhhh

Please Help Me!!!Hhhhhhhhhhhhhh

Answers

Answer 1

Answer:

C: -|x| + 3

Step-by-step explanation:

From the graph, we see that when y = 2, x is either +1 or -1

Also,when y = 1, x = +2 or -2

Thus,we can say that;

y = (-x) + 3 or -(x - 3)

So, we can write this in absolute value form as; y = -|x| + 3


Related Questions

why why why do i have to watch ads

Answers

Answer:

Because you didnt pay for brainly.

If you do, no adds :D

Its a lot easier to be honest

Answer: Because the advertisements are corporations' way of making a market with the internet. They pay a fee to have their adds placed on sites and above videos, and by watching them, that generates revenue for the content creator and the hosting domain itself.    

you welcome

Step-by-step explanation:

which tool is not needed to construct a perpendiculer bisecter

Answers

Answer:

a protractor is not needed to constant a perpendicular bisecter

Step-by-step explanation:

please mark brainliest

write five other iterated integrals that are equal to the iterated integral
∫¹₀ ∫¹ᵧ ∫ʸ ₀ f(x, y, z)dx dx dy

Answers

Here are five other iterated integrals that are equal to the given iterated integral:
∫₀ʸ ∫⁺∞ₓ ∫¹₀ f(x, y, z)dz dx dy
∫₀ʸ ∫¹₀ ∫ʸ ∞ f(x, y, z)dz dx dy
∫⁺∞₁₀ ∫₀ʸ ∫ʸ ₀ f(x, y, z)dz dy dx
∫¹ᵧ ∫⁺∞₁₀ ∫₀ x f(x, y, z)dz dx dy
∫⁺∞₀ ∫⁺∞₁₀ ∫ʸ ₀ f(x, y, z)dz dx dy


The given iterated integral ∫¹₀ ∫¹ᵧ ∫ʸ ₀ f(x, y, z)dx dx dy represents the integration of a function f(x, y, z) over a region defined by the limits of integration. To obtain five other equivalent iterated integrals, we can rearrange the order of integration and modify the limits accordingly. Each integral represents the same volume or value as the given iterated integral, but the order of integration and limits may vary.
The key is to ensure that the new integrals cover the same region as the original one. The limits in each integral should define the appropriate range for each variable to maintain the equivalence. By rearranging the order of integration and adjusting the limits accordingly, we can obtain these alternative expressions that are equal to the given iterated integral.

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find an example of a commutative ring R with 1 in R, and a prime ideal P (of R) with no zero divisors but R is not an integral domain.

Answers

An example of a commutative ring R with 1, a prime ideal P, and no zero divisors but R is not an integral domain is the ring R = Z/6Z, where Z is the set of integers and 6Z is the ideal generated by 6.

The ring R = Z/6Z consists of the residue classes of integers modulo 6. The elements of R are [0], [1], [2], [3], [4], and [5], where [a] denotes the residue class of a modulo 6.

In this ring, addition and multiplication are performed modulo 6. For example, [2] + [3] = [5] and [2] * [3] = [0].

R has a multiplicative identity, which is the residue class [1]. It is commutative since addition and multiplication are performed modulo 6.

The ideal P = 2R consists of the elements [0] and [2]. P is a prime ideal since R/P is an integral domain, which means there are no zero divisors in R/P. However, R itself is not an integral domain because [2] * [3] = [0] in R, showing that zero divisors exist in R.

Therefore, the ring R = Z/6Z, with the prime ideal P = 2R, satisfies the given conditions.

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What was different about the Yuan Dynasty? *
I’ll give brainiest answer to the person who gets it right.

Answers

Answer:

One big change during Kublai's reign was that foreigners became the rulers and administrators. Since they didn't trust the local people, they moved in a large number of Muslims and other people to help them rule the empire. The Mongols had their own religious belief called Shamanism.

What is the length of AC?

Answers

Answer:

AC=6

Step-by-step explanation:

You can see that  ABC is 4 times bigger that HIJ because of lines AB and HI. HI(with a value of one) had to be multiplied by four to equal AB (a value of 4). Use this same rule to find the side AC.

1.5(the length of HJ) times 4 =6.

Mario paid $44.25 in taxi fare from the hotel to
the airport. The cab charged $2.25 for the first
mile plus $3.50 for each additional mile. How
many miles was it from the hotel to the airport?
A. 10
B. 11
C. 12
D. 13

Answers

Answer:

C. 12

hope they help

first mile $2.25 plus $3.50 ×12= $42.00+2.25=44.25

Evaluate 4 + (m - n)

When m = 7 and n = 5.

Answers

1. substitute:
4+(7-5)
2. simplify:
4+2
3. evaluate:
6
the answer is 6.

Find the equation for the following parabola. Focus (3,4) Directrix y 2 A. (x-3)2-2 (y-2.5) B. (x-3)2 = 4(y-3) C. (x-3)2 = (y-4) D. (y-3)2-4 (x-3) Enter

Answers

To find the equation of a parabola given its focus and directrix, we use the standard form of the equation of a parabola which is:

[tex]\frac{(y-k)^2}{4a} = x-h[/tex]

Where (h,k) is the vertex of the parabola, and a is the distance between the vertex and the focus (or between the vertex and directrix, they're equal).

Therefore, the answer is option D, (y-3)²-4(x-3).

Using this formula, let's first find the vertex of the parabola. Since the directrix is a horizontal line, the vertex lies halfway between the focus and directrix on the y-axis. Thus, the vertex is at (3,3).

Since the focus is above the vertex, a is positive, and its value is the distance between the vertex and focus:

a = 4 - 3

= 1

Substituting these values into the standard form of the equation of a parabola gives:

[tex]\frac{(y-3)^2}{4(1)} = x - 3$$[/tex]

[tex]\frac{(y-3)^2}{4} = x - 3$$[/tex]

Multiplying both sides by 4 gives:

y - 3 = 2(x - 3)

y = 2x - 3

Therefore, the answer is option D, (y-3)²-4(x-3).

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Is 9.90 equal to greater than or less than 9.9

Answers

Answer:

Equal to.

Step-by-step explanation:

The 0 at the end of 9.90 does not add any value to the number because its 0.

Answer:

It is equal.

Step-by-step explanation:

9.90 = 9.9 , it's the same as the 0 does not count on it.

a new shopping mall records 150150150 total shoppers on their first day of business. each day after that, the number of shoppers is 15\, percent more than the number of shoppers the day before.

Answers

The number of shoppers on the first day is 150, and each subsequent day the number of shoppers increases by 15%.

Number of shoppers on the first day: The shopping mall recorded a total of 150 shoppers on their first day of business.

Increase in shoppers each day: Starting from the second day, the number of shoppers increases by 15% compared to the previous day.

To calculate the number of shoppers on each day, we can use the following steps:

Day 1: The number of shoppers on the first day is given as 150.

Day 2: To find the number of shoppers on the second day, we need to increase the number of shoppers from the previous day by 15%.

Number of shoppers on Day 2 = Number of shoppers on Day 1 + (15/100) * Number of shoppers on Day 1

Day 3: Similarly, to find the number of shoppers on the third day, we increase the number of shoppers from the second day by 15%.

Number of shoppers on Day 3 = Number of shoppers on Day 2 + (15/100) * Number of shoppers on Day 2

We can continue this process for each subsequent day, using the number of shoppers from the previous day to calculate the number of shoppers for the current day.

By following these steps, we can determine the number of shoppers on each day, starting from the first day and increasing by 15% each day compared to the previous day.

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Help me please I have an f in this class I will give you 44 points

Answers

8 x 7s = 56s

8 x (-2) = -16

so 8(7s - 2) = 56s - 16

Rachel has 42 stickers she wants give to her friends. Rachel put the stickers in 7 equal groups. Then Rachel found more stickers and put 3 more in each pile. If Rachel gives 5 stickers to each of her 12 friends, how many stickers does she have left over?

Answers

Answer:

3 stamps

Step-by-step explanation: 42 stamps in equal groups would be 6 stickers/group.

6+3 = 9 stickers in each pile

there was 7 piles so multiply 7 by the 9 stickers in each pile

7· 9 = 63  

5 · 12 = 60, so she gave her friends 60 stickers

63-60 = 3  

Approximate the area under the graph of F(x)=0.2x³+2x²-0.2x-2 over the interval (-9,-4) using 5 subintervals. Use the left endpoints to find the height of the rectangles.

Answers

To approximate the area under the graph of the function F(x) = 0.2x³ + 2x² - 0.2x - 2 over the interval (-9, -4) using 5 subintervals and left endpoints, we can use the left Riemann sum method. The total area under the graph of F(x) over the interval (-9, -4).

To approximate the area using the left Riemann sum method, we start by dividing the interval (-9, -4) into 5 subintervals of equal width. The width of each subinterval can be calculated as (b - a) / n, where b is the upper limit of the interval (-4), a is the lower limit of the interval (-9), and n is the number of subintervals (5 in this case).

Next, we evaluate the function F(x) at the left endpoint of each subinterval to find the height of the rectangles. For the left Riemann sum, the left endpoint of each subinterval is used as the height. In this case, we evaluate F(x) at x = -9, -7, -5, -3, and -1.

Once we have the width and height of each rectangle, we can calculate the area of each rectangle by multiplying the width and height. Finally, we sum up the areas of all the rectangles to approximate the total area under the graph of F(x) over the interval (-9, -4).

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How long will it take for quarterly deposits of $625 to accumulate to be $20,440 at an interest rate of 8.48% compounded quarterly?

Answers

It will take approximately 9 years and 2 months for quarterly deposits of $625, with an interest rate of 8.48% compounded quarterly, to accumulate to $20,440.

To calculate the time it takes for the deposits to accumulate to the desired amount, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the accumulated amount

P = the principal amount (initial deposit)

r = the annual interest rate (converted to a decimal)

n = the number of times interest is compounded per year

t = the number of years

In this case, the principal amount (P) is $625, the interest rate (r) is 8.48% (or 0.0848 as a decimal), the number of times interest is compounded per year (n) is 4 (quarterly compounded), and the desired accumulated amount (A) is $20,440.

We need to solve for t, the number of years. Rearranging the formula, we have:

t = (log(A/P)) / (n * log(1 + r/n))

Plugging in the values, we get:

t = (log(20440/625)) / (4 * log(1 + 0.0848/4))

Calculating this, we find that t is approximately 9.18 years. Converting this to years and months, we get approximately 9 years and 2 months. Therefore, it will take around 9 years and 2 months for the quarterly deposits of $625 to accumulate to $20,440 at an interest rate of 8.48% compounded quarterly.

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g a tank contains 90 kg of salt and 1000 l of water. a solution of a concentration 0.045 kg of salt per liter enters a tank at the rate 8 l/min. the solution is mixed and drains from the tank at the same rate what is the concentration of our solution in the tank initially?

Answers

The final concentration in the tank is 0.045 kg/L, which is the same as the concentration of the incoming solution.

To solve the problem, we can use the formula:

C1V1 + C2V2 = C3V3

where C1 is the initial concentration, V1 is the initial volume, C2 is the concentration of the incoming solution, V2 is the volume of the incoming solution, C3 is the final concentration, and V3 is the final volume.

We know that the initial volume of the tank is 1000 L and it contains 90 kg of salt. To find the initial concentration, we need to convert the mass of salt to concentration by dividing it by the total volume:

90 kg / 1000 L = 0.09 kg/L

This means that initially, the concentration of salt in the tank is 0.09 kg/L.

Next, we need to calculate how much salt enters and leaves the tank during a given time period. Since the incoming solution has a concentration of 0.045 kg/L and enters at a rate of 8 L/min, it brings in:

0.045 kg/L x 8 L/min = 0.36 kg/min

The outgoing solution has the same concentration as the final concentration in the tank, so we can use this formula to find it:

C1V1 + C2V2 = C3V3

(0.09 kg/L)(1000 L) + (0.045 kg/L)(8 L/min)(t min) = C3(1000 L + 8 L/min)(t min)

Simplifying and solving for C3, we get:

C3 = (0.09 kg/L)(1000 L) + (0.045 kg/L)(8 L/min)(t min) / (1000 L + 8 L/min)(t min)

At steady state, when the amount of salt entering and leaving the tank is equal, we can set the incoming and outgoing terms equal to each other:

0.36 kg/min = C3(8 L/min)

Solving for C3, we get:

C3 = 0.045 kg/L

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Identify if they are function or not

Answers

Answer:

1=function

2=not function

3=function

4=function

5=function

6=not function

7=not function

8=function

evan has 4 chocolate bars with a total of 48 pices are in each bar

Answers

Answer:

what is your question? it seems the answer would be 12 just by looking at this, but still what is the question exactly?

Step-by-step explanation:

Answer: if you are dividing the answer will be 12

(i wrote two since it dosent say what we need to do

if you are multiplying you answer will be 192

hope it helped!

Step-by-step explanation:

I’ll give brainless too who ever respond fast and correctly.

Answers

i’ll comment so you can get branliest :)

Each side of a square is increased 3 inches. When this happens, the area is multiplied by 25. How many inches in the side of the original square?

Answers

Answer:

s = 0.75 inches

Step-by-step explanation:

Let s = side length of the original square

s + 3 = side length of the new square

Area of a square = s²

A = s²

A = (s+3)²

A = s² + 6s + 9

Area multiplied by 25 = 25 * s²

So,

s² + 6s + 9 = 25s²

25s² - s² - 6s - 9 = 0

24s² - 6s - 9 = 0

8s² - 2s - 3 = 0

a = 8

b = -2

c = -3

s = -b ± √b² - 4ac / 2a

= -(-2) ± √(-2)² - 4(8)(-3) / 2(8)

= 2 ± √4 - (-96) / 16

= 2 ± √100 / 16

= 2 ± 10/16

s = 2 + 10/16 or 2-10/16

= 12/16 or -8/16

= 0.75 or -0.5

side length can not be negative

Therefore, s = 0.75

A = s²

A = (0.75)²

= 0.5625

A = (s+3)²

= (0.75+3)²

= 3.75²

= 13.95

Determine if the following linear maps are surjective or injective. You may assume each map is linear. (a) The derivative map T : P3(R) → P₂(R); P₂ (R); p(x) → d dx -p(x). (b) The linear map T: R³ → Rª defined by the matrix 1 1 -3 1 1 1 A 0 1 2 1 0 -1 (c) The linear map T: R³ → R³ defined by the matrix 0 5 5 A = 2 1 2 2 3 4

Answers

The linear map is  not surjective but injective.

A linear map is an operation between two vector spaces that preserves the properties of addition and scalar multiplication; therefore, it is a linear transformation.

Here is how to determine if the following linear maps are surjective or injective.

(a) The derivative map T: P3(R) → P₂(R); P₂(R); p(x) → d/dx -p(x) is an example of a linear map,

where P3(R) and P₂(R) are the vector spaces of polynomials of degree at most 3 and 2 with coefficients in R, respectively.

Moreover, d/dx is the derivative operator acting on the polynomial p(x).

The kernel of the linear map T is the subspace of P3(R) consisting of polynomials p(x) with T(p(x)) = d/dx -p(x) = 0, i.e., p(x) is constant.

However, a constant polynomial of degree zero is not in the range of T, since it has no derivative. Therefore, the linear map T is injective and not surjective.

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if 1-3(y+2)=-32 find the value of y/3

Answers

Answer:

7.6

Step-by-step explanation:

-3 multiple by y and -3 multiple by 2 resolve to 7.6....

Which of the following points is not an ordered pair for the function

ƒ(x ) =5/2 x + 6?

(4, 16)
(2, 7)
(-2, 1)

Answers

Answer:

(2, 7) is not an ordered pair for the function.

Step-by-step explanation:

41+98+0000000000000000000000000000000000000000000

Answers

139

ffsahshanjwjsjudke

Answer:

139 because zero is addition identity

A random sample of 50 home theater systems has a mean price of $115. Assume the population standard deviation is $19.50. Construct a 90% confidence interval for the population mean.

Answers

Based on a random sample of 50 home theater systems, the 90% confidence interval for the population mean price is approximately $110.81 to $119.19, assuming a population standard deviation of $19.50.

To construct a 90% confidence interval for the population mean of home theater systems, we can use the following formula

Confidence Interval = Sample Mean ± Margin of Error

The margin of error depends on the level of confidence and the standard deviation of the population. Given that the sample size is large (n = 50) and we know the population standard deviation is $19.50, we can use the z-distribution.

First, we need to find the critical value (z) for a 90% confidence level. Using a standard normal distribution table or calculator, the critical value for a 90% confidence level is approximately 1.645.

Next, we calculate the margin of error (E) using the formula:

Margin of Error (E) = z * (Population Standard Deviation / sqrt(n))

E = 1.645 * ($19.50 / √(50))

E ≈ $4.19

Now we can construct the confidence interval:

Confidence Interval = Sample Mean ± Margin of Error

Confidence Interval = $115 ± $4.19

Confidence Interval ≈ ($110.81, $119.19)

Therefore, we can say with 90% confidence that the population mean of home theater systems is between approximately $110.81 and $119.19.

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Tucker purchased $4,600 in new equipment for a catering business. He estimates that the value of the equipment is reduced by approximately 40% every two years. Tucker states that the function V(t)=4,600(0.4)2t could be used to represent the value of the equipment, V, in dollars t years after the purchase of the new equipment. Explain whether the function Tucker stated is correct, and, if not, determine the correct function that could be used to find the value of the equipment purchased.

show work

Answers

Answer:

The function stated by Tucker is incorrect.

V(t) = 4600(0.8)^t

Step-by-step explanation:

Given the function :

V(t)=4,600(0.4)2t

The initial value of equipment = 4600

Decay rate = 40% of very 2 years

The value of equipment t years after purchase

The exponential decat function goes thus :

V(t) = Initial value * (1 - decay rate)^t

The Decay rate per year = 40% /2 = 20% = 0.2

V(t) = 4600(1 - 0.2)^t

V(t) = 4600(0.8)^t

What is the answer with explanation?

Answers

The value of arc ABD is  determined as 236⁰.

Option C.

What is the measure of arc ABD?

The value of arc ABD is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

Also this theory states that arc angles of intersecting secants at the center of the circle is equal to the angle formed at the center of the circle by the two intersecting chords.

arc BA = 2 x 48⁰ (interior angles of intersecting secants)

arc BA = 96⁰

arc BD = 2 x 70⁰ (interior angles of intersecting secants)

arc BD = 140⁰

arc ABD = arc BA + arc BD

arc ABD = 96⁰  + 140⁰

arc ABD = 236⁰

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Investigators performed a randomized experiment in which 411 juvenile delinquents were randomly assigned to either multisystemic therapy (MST) or just probation (control group). Of the 215 assigned to therapy, 87 had criminal convictions within 12 months. Of the 196 in the control group, 74 had criminal convictions within 12 months. Determine whether the therapy caused significantly fewer arrests at a 0.05 significance level. Start by comparing the sample percentages. Find and compare the sample percentages that were arrested for these two groups. The percentage of arrests for people who received MST was %.

Answers

The percentage of arrests for people who received Multisystemic Therapy (MST) can be calculated by dividing the number of individuals arrested in the MST group (87) by the total number of individuals.

Percentage of arrests for MST group = (87/215) * 100 ≈ 40.47%

To determine if therapy caused significantly fewer arrests at a 0.05 significance level, we need to compare this percentage with the percentage of arrests in the control group.

The percentage of arrests for the control group can be calculated in a similar manner by dividing the number of individuals arrested in the control group (74) by the total number of individuals in the control group (196), and multiplying by 100.

Percentage of arrests for control group = (74/196) * 100 ≈ 37.76%

Comparing the sample percentages, we find that the percentage of arrests for people who received MST (40.47%) is slightly higher than the percentage of arrests for the control group (37.76%).

To determine if this difference is statistically significant at a 0.05 significance level, we would need to perform a hypothesis test, such as a chi-square test, to compare the observed frequencies with the expected frequencies under the assumption that therapy has no effect on reducing arrests.

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solve elimination method 3x+4y=0 and x - 2y =-5​

Answers

Answer:

x=−2 and y=3/2

Step-by-step explanation:

see picture

PLS ANSWER THIS AND GET BRAINLIEST !!!
A grocery store collected sales data. It found that when customers buy less bread, they tend to purchase more rice. What can we conclude?


A. There is no correlation between amount of bread bought and amount of rice purchased.

B. There is a correlation between amount of bread bought and amount of rice purchased. However, there is no causation. This is because there is an increase in the amount of rice purchased with a decrease in the amount of bread bought.

C. There is a correlation between amount of bread bought and amount of rice purchased. There may or may not be causation. Further studies would have to be done to determine this.

Answers

Answer:  C

Step-by-step explanation: C because there is obviously a correlation yet we cannot determine if there is causation or not.

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Mr. Hemsworth is the CFO of Thunder Inc. and he is responsible for managing transaction exposure. The company will need to pay 335,000 Australian dollars to a partner for licensing fees in 30 days. He came up with the probability of the exchange rates of the US dollar per Australian dollar (see the table below). If an Australian dollar sells for 1.9275 U.S. dollars and the 30 days forward rate is USD 2.1231 per AUD, what is the probability of the forward hedging to underperform the unhedged positions? Possible Spot Rate in 30 Days Probability 1.8284 24% 2.0558 16% 2.2904 24% 2.3913 36% a. 40% b. 60% Ec64% d. 36% Raising the required reserved ratio __ the simple deposit multiplier, which will __ the economies money supply? simplify using FOIL method (2x+3)(2x-3) With respect to their nutrition, members of the plant kingdom are usually classified as _________ Which financial statements reflect the costs of production, explain? 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The method is counting the number of even numbers in ray.d. The method is counting the number of odd numbers in ray.e. The method is counting the number of occurrences of x in ray. Now you give this calculation a try with the following subnet entry 66.147.242.171/15 Using the methodology listed in step 1, determine the number of hosts (usable IPv4 addresses) for this subnet. Which of the following is not an additional tax a taxpayer may have to pay?A. Alternative minimum tax.B. Self-employment tax.C.Excess wage tax.D. Net investment income tax. Which of the following statements about supervising unlicensed assistants in Kentucky is correct?A)An unlicensed office manager is permitted to supervise an unlicensed assistant.B)The principal broker isn't permitted to supervise an unlicensed assistant.C)The principal broker may assign supervision of an unlicensed assistant to another licensee.D)The principal broker must supervise unlicensed assistants. Set up a triple integral in cylindrical coordinates to find the volume of the solid whose upper boundary is the paraboloid F2(x,y)=8-x-y and whose lower boundary is the paraboloid F(x,y)=x+y. Do not solve. Which of the following inventories would a company ordinarily hold for sale? a. Work in process. b. Finished goods. c. Raw materials. d. Work in process and finished goods. On October 29, 2014, Lobo Co. Began operations by purchasing razors for resale. Lobo uses the perpetual inventory method. The razors have a 90-day warranty that requires the company to replace any nonworking razor. When a razor is returned, the company discards it and mails a new one from Merchandise Inventory to the customer. The company's cost per new razor is $15 and its retail selling price is $60 in both 2014 and 2015. The manufacturer has advised the company to expect warranty costs to equal 6% of dollar sales. The following transactions and events occurred. 2014 Nov. 11 Sold 70 razors for $4,200 cash. 30 Recognized warranty expense related to November sales with an adjusting entry. Dec. 9 Replaced 14 razors that were returned under the warranty. 16 Sold 210 razors for $12,600 cash. 29 Replaced 28 razors that were returned under the warranty. 31 Recognized warranty expense related to December sales with an adjusting entry. 2015 Jan. 5 Sold 140 razors for $8,400 cash. 17 Replaced 33 razors that were returned under the warranty. 31 Recognized warranty expense related to January sales with an adjusting entry. 1. 1 Prepare journal entries to record these transactions and adjustments for 2014. 1. 2 Prepare journal entries to record these transactions and adjustments for 2015 Let A = {1, 3, 5, 7}, B = {5, 6, 7, 8}, C = {5, 8}, D = {2, 5, 8}, and U={1, 2, 3, 4, 5, 6, 7, 8}. Use the sets above to find B U D. A. B U D = {5, 8} B. B U D = {6, 7} C. B U D = {2,5, 6, 7, 8} D. B U D = {1, 3, 4} E. None of the above The graduate class of the University of Flatland, which only graduates students with majors in mathematics, has 8 graduating seniors majoring in applied mathematics, 7 in statistics, and 6 in pure mathematics. What is the probability of choosing four of these graduates in such a way that they are of the same subdiscipline of mathematics? Find the exact interest for the following. Round to the nearest cent. A loan of $74,000 at 13% made on February 16 and due on June 30 O A. $3,580.78 OB $3,610.79 OC. $3,531,73 OD $3,660.94. earth's atmosphere blocks short wavelengths of the electromagnetic spectrum. which telescopes do not need to be placed in orbit around earth to observe short-length radiation?