On March 30, Century Television received an invoice dated March 28 from ACME Manufacturing for 51 televisions at a cost of $100 each. Century received a 8/5/5 chain discount. Shipping terms were FOB shipping point. ACME prepaid the $91 freight. Terms were 5/10 EOM. When Century received the goods, 3 sets were defective. Century returned these sets to ACME. On April 08, Century sent a $275 partial payment. Century will pay the balance on May 06. What is Century’s final payment on May 06? Assume no taxes

Answers

Answer 1

Century's final payment will be on May 06 is $4,028.

Total cost of televisions:

51 TVs at $100 each = $5,100

8% discount = $100 x 8% x 10 = $80

5% discount  = $100 x 5% x 10 = $50

5% discount  = $100 x 5% x 31 = $155

Total discount = $80 + $50 + $155 = $285

Cost after discount = $5,100 - $285 = $4,815

Shipping cost: no additional cost

Returned sets:

3 *$100  = $300

ACME will issue a credit to Century for $300

Total cost:

$4,815 + $0 - $300 = $4,515

Partial payment:

$275

Final payment:

Balance after partial payment = $4,515 - $275 = $4,240

5% discount if paid within 10 days after the end of the month = $4,240 x 5% = $212

Final payment on May 06 = $4,240 - $212 = $4,028

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Related Questions

Question 10(Multiple Choice Worth 2 points)
(Circle Graphs MC)

A New York City hotel surveyed its visitors to determine which type of transportation they used to get around the city. The hotel created a table of the data it gathered.


Type of Transportation Number of Visitors
Walk 120
Bicycle 24
Car Service 45
Bus 30
Subway 81


Which of the following circle graphs correctly represents the data in the table?
circle graph titled New York City visitor's transportation, with five sections labeled walk 80 percent, bus 16 percent, car service 30 percent, bicycle 20 percent, and subway 54 percent
circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent
circle graph titled New York City visitor's transportation, with five sections labeled subway 40 percent, bus 8 percent, car service 15 percent, bicycle 10 percent, and walk 27 percent
circle graph titled New York City visitor's transportation, with five sections labeled subway 80 percent, bicycle 20 percent, car service 30 percent, bus 16 percent, and walk 54 percent

Answers

So, the circle graph entitled New York City visitor's transportation with five sections labelled walk 40%, bicycle 8%, car service 15%, bus 10%, and subway 27% is the proper option that displays the data in the circular graphs.

Explain about the circle graphs:

A circle represents 360 degrees. A circle can be split up into smaller sections. An arc is a segment of a circle, and arcs are named based on their angles.

To illustrate information and data, use a circle graph or pie chart. Often, a circle graph is used to quickly and proportionately display the findings of an investigation.

Given data:

Type of Transportation      Number of Visitors  Percentage

Walk                                    120                            120*100/ 300 = 40%

Bicycle                                 24                            24*100/ 300 = 8%        

Car Service                         45                            45*100/ 300 = 15%

Bus                                      30                            30*100/ 300 = 10%

Subway                               81                             81*100/ 300 = 27%

Total                                   300

So, the circle graph entitled New York City visitor's transportation with five sections labelled walk 40%, bicycle 8%, car service 15%, bus 10%, and subway 27% is the proper option that displays the data in the circular graphs.

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PLEASE HELP ME FIND DE, EF, and m

Answers

The values of the missing sides and angles of the triangle using sine rule are;

DE = 18.3

<D = 84°

EF = 20.8

How to Use the sine rule?

Sine rule is a method that is used to find the missing angles and sides of triangles.

Thus, it is expressed as;

a/sin A = b/sin B = c/sin C

Thus;

12/sin 35 = DE/sin 61

DE = 12(sin 61)/sin 35

DE = 18.3

Sum of angles in a triangle is 180°. Thus;

<D = 180 - (61 + 35)

<D = 84°

Similarly;

EF/sin 84 = 12/sin 35

EF = 12(sin 84)/sin 35

EF = 20.8

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What is the law of large numbers?
If you were using the relative frequency of an event to estimate the probability of the event, would it be better to use 100 trials or 500 trials? Explain.

Answers

The Law of Large Numbers is a fundamental concept in probability theory and statistics stating the number of trials of a random event increases, the average of the outcomes approaches the expected value of the event. It's better to use 500 trials.

In other words, as we repeat an experiment a large number of times, the proportion of times that a certain outcome occurs will converge to its probability of occurrence. This is an important concept in statistical inference, as it helps to ensure that the results of a sample are representative of the population from which it was drawn.

Now, if you were using the relative frequency of an event to estimate the probability of the event, it would be better to use 500 trials rather than 100 trials. The reason is that the larger the number of trials, the more accurate the estimate of the probability is likely to be.

Using a larger sample size reduces the impact of random variation and provides a more precise estimate of the true probability. The Law of Large Numbers tells us that as the sample size increases, the relative frequency of the event should converge to the true probability, so a larger sample size will generally give a more reliable estimate

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sweets are sold loose,or pre-packed in 120g bags

Answers

Step-by-step explanation:

The option that has the better value is the loose sweets.

What is division?

Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations.

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Which pack has the better value?

Price per gram for the bag = £1.49 / 120 = £0.0124

Price per gram for the loose sweets = £0.89 / 100 = £0.0089

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A glass contains 320cm3 of milk. The mass of the milk is 330g. Calculate the density of the milk in kilograms per cubic metre (kg/m3). Give your answer to the nearest integer

Answers

The density of the milk is 1031.25 kg/m³.

How to calculate the density of milk?

Density refers to the mass of a unit volume of a material substance.

Density (ρ) = mass (m) / volume (V)

Given:

Volume (V) = 320cm³ = 0.00032m³

Mass (m) = 330g = 0.33kg

The Density (ρ) of the milk wll be:

= 0.33kg / 0.00032m³

= 1031.25 kg/m³

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select all values equivalent to -10/7
A.-10/-7
B.-3 1/7
C.1 3/7
D.- -10/-7
E. -1 3/7

Answers

The values that are equivalent to the fraction -10/7 are -(-10/7) and -13/7 which makes options D and E correct.

What are equivalent fractions

Equivalent fractions are fractions that have different numerators and denominators, but represent the same amount or quantity. In other words, equivalent fractions are different ways of representing the same fraction.

-10/-7 = 10/7 {not equivalent to - 10/7}

-3 1/7 = -22/7 {not equivalent to - 10/7}

1 3/7 = 10/7 {not equivalent to - 10/7}

- -10/-7 = - (-10/-7) = - 10/7 {equivalent}

- 1 3/7 = - 10/7 {equivalent}

Therefore, the values that are equivalent to the fraction -10/7 are -(-10/7) and -13/7.

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6. How many times larger is the first number in the pair than the second? a. 34 is times larger than 3³. times larger than 5². times larger than 78. times larger than 17. times larger than 5*. b. 5³ is_____ c. 710 is d. 176 is e. 5 1⁰ is​

Answers

3⁴ is 3 times larger than 3³, 5³ is 5 times larger than 5², 7¹⁰ is 49 times larger than 7⁸ and 17⁶ is 289 times larger than 17⁴.

3⁴ / 3³ = (3 × 3 × 3 × 3) / (3 × 3 × 3) = 3

This means that 3⁴ is 3 times larger than 3³.

5³ is 5 times larger than 5².

5³ / 5² = (5 × 5 × 5) / (5× 5) = 5

7¹⁰ is 49 times larger than 7⁸.

7¹⁰/ 7⁸ = 7² =49

17⁶ is 289 times larger than 17⁴.

17⁶ /17⁴ = 289

Hence, 3⁴ is 3 times larger than 3³, 5³ is 5 times larger than 5², 7¹⁰ is 49 times larger than 7⁸ and 17⁶ is 289 times larger than 17⁴.

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Prove that ST^2=TU*TV

Answers

Hence proved,[tex](ST)^2=(TU*TV)[/tex]for given figure.

What is the right triangle?

A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly called a rectangle triangle, is a triangle in which one angle is a right angle, i.e., in which two sides are perpendicular. The relation between the sides and other angles of the right triangle is the basis for trigonometry.

What is the Pythagoras theorem?

In mathematics, the Pythagoras  theorem or  Pythagorean  theorem is a fundamental relation  in Euclidean geometry between the three sides  of a right triangle. It states that the area of the  square whose side is the hypotenuse is equal to  the sum of the areas of the squares on the other two sides.

Use Pythagoras theorem , in given figure

than we get ,

in ΔTSU,

[tex](TU)^2=(ST)^2+(SU)^2[/tex]......(I)

inΔTVS,

[tex](ST)^2=(TV)^2+(SV)^2[/tex]......(II)

inΔSVU,

[tex](SU)^2=(VU)^2+(VS)^2[/tex].....(III)

from (I),

[tex](TU)^2-(ST)^2=(SU)^2=(VU)^2+(VS)^2[/tex]....(IV)  {by (III)

according to figure,TU=TV +VU

∴ [tex](TV+VU)^2=(VU)^2+(VS)^2+(ST)^2=(VU)^2+(VS)^2+(TV)^2+(SV)^2[/tex]{by (II)

use the identity,is

[tex](a+b)^2=a^2+2ab+b^2\\(TV)^2+2(TV)*(VU)+(VU)^2=(VU)^2+2(SV)^2+(TV)^2[/tex]

after simplification,

⇒[tex](TV)*(VU)=(SV)^2[/tex]

according to figure,TU=TV +VU ⇒VU=TU-TV

[tex](TV)*(TU-TV)=(SV)^2\\(TV*TU)-(TV)^2=(SV)^2\\(TV*TU)-(TV)^2=(SV)^2\\(SV)^2+(TV)^2=(TV*TU)\\(ST)^2=(TV*TU) {by(II)\\ OR (ST)^2=(TU*TV)[/tex]

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Juan walks mile, Jamal walks 0.78 mile,
Lucia walks mile, and Marisol walks
0.62 mile to school each day. Which lists
the students in the order of the lengths
of their walks to school, from shortest to
longest?
A. Juan, Jamal, Lucia, Marisol
B. Lucia, Juan, Marisol, Jamal
C. Marisol, Juan, Lucia, Jamal
D. Jamal, Marisol, Juan, Lucia

Answers

From shortest to longest is:  C. Marisol, Juan, Lucia, Jamal.

How to determined the lengths of their walks?

By comparing the lengths of the students' walks, it is possible to determine the correct order of the students based on their walks.

Marisol walks 0.62 miles, while Juan walks one mile. So Juan's walk isn't the most limited.

Lucia walks one mile, which is shorter than Jamal's walk of 0.78 miles but longer than Marisol's walk of 0.62 miles. Therefore, neither the shortest nor longest walk is Lucia's.

Therefore, Jamal and Marisol remain choices. The correct order, from shortest to longest, is as follows because Jamal's walk is longer than Marisol's:

C. Marisol, Juan, Lucia, Jamal.

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You have been asked to build a scale model of your school out of toothpicks. Imagine your school is 30 feet tall. Your scale is 1 ft:1.47 cm.

If a toothpick is 6.3 cm tall, how many toothpicks tall will your model be?

Answers

7 toothpicks tall
1.47•30= 44.1 (the cm of the model)
then 44.1 divided by 6.3= 7

What is the median?
0 7 27 10 0 3

Answers

Answer: Median is 5

Step-by-step explanation: To find the median, we first need to arrange the numbers in order from least to greatest:

0 0 3 7 10 27

The median is the middle number, or the average of the two middle numbers if there are an even number of values. In this case, there are 6 values, so the median is the average of the two middle numbers:

median = (3 + 7) / 2

median = 5

Therefore, the median of the given numbers is 5.

08.02 MC) The two plots below show the heights of some sixth graders and some seventh graders of a school: Two dot plots are shown one below the other. The title for the top dot plot is Sixth Graders and the title for the bottom plot is Seventh Graders. Below the line for each dot plot is written Height followed by inches in parentheses. There are markings from 52 to 57 on the top line and the bottom line at intervals of one. For the top line there are 2 dots above the first mark, 1 dot above the second mark, 1 dot above the third mark and 2 dots above the fourth mark. For the bottom line, there are 2 dots above the second mark, 3 dots above the third mark, 1 dot above the fifth mark. The mean absolute deviation (MAD) for the first set of data is 1.2 and the MAD for the second set of data is 0.7. Approximately how many times the variability in the heights of the seventh graders is the variability in the heights of the sixth graders? (Round all values to the tenths place.) (1 point) 0.5 1.2 1.7 3.4

Answers

The variability in the heights of the seventh graders is approximately 0.6 times the variability in the heights of the sixth graders.

What is mean absolute deviation?

The variability or dispersion of a set of data is measured by the mean absolute deviation (MAD). By averaging the absolute differences between each data point and the set mean, it is calculated. Because it is less impacted by high values or outliers, the MAD is a more reliable measure of variability than the standard deviation. The MAD is always a non-negative number and is stated in the same units as the data. Greater variability is indicated by a bigger MAD, whereas a smaller MAD suggests that the data points are more variable and are consequently closer to the mean. The MAD is frequently used to track process variation in descriptive statistics and quality control applications.

Given that, MAD for the sixth graders is 1.2 and the MAD for the seventh graders is 0.7.

To determine the relation of variability we take the ratio as:

0.7 / 1.2 ≈ 0.6

Hence, the variability in the heights of the seventh graders is approximately 0.6 times the variability in the heights of the sixth graders.

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The complete question is:

Find the annual percentage yield (APY) for the investment. $8000 at 4.75% compounded daily The annual percentage yield (APY) is%. (Type an integer or decimal rounded to three decimal places as needed.)​

Answers

Answer:

The annual percentage yield (APY) is a measure of the return on an investment that takes into account the effect of compounding interest. To calculate the APY for an investment of $8000 at an interest rate of 4.75% compounded daily, you can use the formula:

APY = (1 + r/n)^(n*t) - 1

where r is the annual interest rate as a decimal (0.0475 in this case), n is the number of times the interest is compounded per year (365 for daily compounding), and t is the number of years (1 in this case).

Plugging these values into the formula gives:

APY = (1 + 0.0475/365)^(365*1) - 1 APY ≈ 0.0486

So, the APY for this investment is approximately 4.86%.

Step-by-step explanation:

PLEASE HELP! PHOTO ATTACHED

The height of a cabinet is twice the width. The depth is 1.5 times the width. The volume of the cabinet is 5.184 in^3. What are the dimensions of the cabinet?

Answers

Answer: Width: 12 Height: 24 Depth: 18

Step-by-step explanation: Width= 12, 12x2=24 and 12x1.5=18. 12x24x18=5184in3

Solve and simplify your answer.


6/7 + 1/8

Answers

Answer: 41/56

Step-by-step explanation:

first you would try to find a common denominator (or LCM) in this case, its 56 so the revised question is 48/56+7/56 because you have to change the numerator as well. if you subtract the numerators it is 41. so its 41/56. 41/56 is already in its simplest form, so the answer is 41/56

The transportation department is resurfacing 12. 75 miles of roadways in Collin County. The crew completes work on ¼ - mile section of roadway each hour. How many hours will it take to complete the resurfacing project?

Answers

The number of hours it will take to complete the resurfacing project is:

51 hours

How to divide fractions?

We are told that the department of  transportation is resurfacing 12. 75 miles of roadways in Collin County.

Now, we are also given that:

Number of miles completed each hour = 1/4 mile in section = 0.25 mile per hour

Thus, the number of hours it will take to complete the resurfacing project is:

That would be 12.75 divided by 0.25 hours

= 12.75/0.25

= 51 hours

Thus, we conclude that is the total time it will take to complete the project

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how many 15 letter arrangements of 5 a's, 5 b's and 5 c's have no a's in the first 5 letters, no b's in the next 5 letters and no c's in the last 5 letters?

Answers

The possible number of letter arrangements of 15 letter with 5 a's, 5 b's and 5 c's have no a's in the first 5 letters, no b's in the next 5 letters and no c's in the last 5 letters are equal to 2252.

Total number of letters for arrangement are 15 in count. Arrangment of 5 A's, 5 B's and 5 C's have no A's in the first 5 letters, no B's in the next 5 letters and no C's in the last 5 letters. In other words, we say that the first five letters must be B's or C's, the next five letters must be C's or A's, and the last five letters must be A's or B's. If there are k number of B's in the first five letters, then there must be (5-k) C's in the first five letters, like that there must be k C's and (5 - k ) A's in the next five letters, and k A's and (5-k) B's in the last five letters. That is number of each letter in each group of five letters is determined completely by knowing the number of B's in the first 5 letters. The number of ways to arrange, 15 letters with this restriction is [tex]$\binom{5}{k}^3$[/tex](since there are [tex]$\binom{5}{k}$[/tex]

ways to arrange k B's and 5-k C's that is arrangements ( 1B + 4C , 2B+ 3C , 3B+2C, 4B+ 1C ),similarly for next five arrangements (1A + 4C , 2A+ 3C , 3A+2C, 4A+ 1C ), ( 1B + 4C , 2B+ 3A , 3B+2A, 4B+ 1A ) and ( 5B, 5C, 5A), ( 5C,5B,A). Thus, the final answer for arrangement is [tex]$\sum_{k=0}^{5}\binom{5}{k}^{3}$[/tex]

Solve the above bionomial expression,

[tex]= \binom{5}{0}^{3} + \binom{5}{1}^{3} + \binom{5}{2}^{3} + \binom{5}{4}^{3} + \binom{5}{5}^{3} \\ [/tex]

[tex]= (\frac{ 5!}{5! 0!})^{3} + (\frac{ 5!}{4! 1!})³ + (\frac{5!}{3! 2!})³ + (\frac{5!}{2! 3!})³ + (\frac{5!}{1! 4!})³ + (\frac{5!}{0! 5!})³ \\ [/tex]

= 1 + 5³ + 10³ + 10³ + 5³ + 1

= 2252

Hence, required value is 2252.

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PLEASE is due very soon please explain

Answers

Answer:

1) The image of the line has the same slope as the pre-image but a different y-intercept.

hope this helps ;)

In circle E with
m

D
E
F
=
4
8

m∠DEF=48

and
D
E
=
6
DE=6, find the area of sector DEF. Round to the nearest hundredth

Answers

The area of sector DEF is 15.09 square units

How to find the area of sector DEF?

The formula for area of a sector is:

A = (θ/360) * πr²

Where θ is the angle subtended at the center and r is the radius of the circle.

In this case, DE is the radius.

Thus r = 6 cm and θ = 48°

Substituting:

A = (48/360) * π * 6²

A = (48/360) * (22/7) * 36

A = 15.09 square units

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Complete Question

Check image attached

Find the distance traveled by a particle with position (x, y) as t varies in the given time interval. x = 3 sin^2 (t), y = 3 cos^2 (t); 0 less than or equal to

Answers

From distance formula, the distance covered by a particle with position (x, y) as time, t is equals to the [tex] 18\sqrt{2}[/tex].

The distance d, traveled by the particle with position vector, r(t) = <x(t), y(t) > over the interval [a,b] is calculated by following

[tex]d = \int_{a}^{b} ( (\frac{dx}{dt})² +(\frac{dy}{dt})² )dt[/tex]. We have a particle with position value (x, y) as t varies in the time interval. The parametric equations are, x = 3 sin² (t), y = 3 cos²(t), on the

time interval [0,3π]. Now the derivative of above parametric equations with respect to time t are [tex]\frac{dx}{dt} = 6 sin(t)cos(t) [/tex] = 3 sin(2t)

[tex]\frac{dy}{dt} = -6 sin(t)cos(t) [/tex]

= - 3 sin(2t)

Therefore, the required distance travelled by particle in the interval [0,3π] is written as [tex]d = \int_{0}^{3π} \sqrt{( (3 sin(2t))² + (-3 sin(2t))²) dt} \\ [/tex]

[tex]= \int_{0}^{3π} \sqrt{ ( 9 sin²(2t) + 9sin²(2t))}dt \\ [/tex]

[tex]= \int_{0}^{3π} \sqrt{18sin²(2t)dt}[/tex]

[tex]= 3\sqrt{2}\int_{0}^{3π} |sin(2t)|dt[/tex]

[tex]= 3\sqrt{2}[ \int_{0}^{\frac{π}{2}} sin(2t)dt - \int_{\frac{π}{2}}^{π} sin(2t)dt + \int_{π}^{\frac{3π}{2}} sin(2t)dt - \int_{\frac{π}{2}}^{2π}sin(2t)dt + \int_{2π}^{\frac{5π}{2}}sin(2t)dt - \int_{\frac{5π}{2}}^{3π}sin(2t)dt \\ [/tex]

[tex]= 3\sqrt{2}([ \frac{cos(2t)}{2}]_{0}^{\frac{π}{2}} - [\frac{cos(2t)}{2}]_{\frac{π}{2}}^{π} + [\frac{cos(2t)}{2}]_{π}^{\frac{3π}{2}} - [\frac{cos(2t)}{2}]_{\frac{3π}{2}}^{2π} + [\frac{cos(2t)}{2}]_{2π}^{\frac{5π}{2} }- [ \frac{cos(2t)}{2}]_{\frac{5π}{2}}^{3π})\\ [/tex]

[tex]= 3\sqrt{2}([ \frac{1}{2} +{\frac{1}{2}] - [\frac{-1}{2}- \frac{1}{2}}] + [\frac{1}{2}+ \frac{1}{2}] - [\frac{-1}{2} - \frac{1}{2}] + [\frac{1}{2} + \frac{1}{2}]- [ \frac{-1}{2} - \frac{1}{2}])\\ [/tex]

[tex]= 3\sqrt{2}(6)[/tex] =[tex]= 18\sqrt{2}[/tex]

Hence, the required distance is [tex] 18\sqrt{2}[/tex].

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Jessie likes to ride her bike around a circular track with a radius of
25.8 yards. If she rides around the track 3 times, about how far
will she ride?
A 162 yards
B 243 yards
C 309 yards
D 486 yards

Answers

Jessie will cover a distance of about 486 yards.

What is the distance covered by Jessie?

The distance that Jessie will ride around the circular track can be calculated as the circumference of the circle.

The formula for the circumference of a circle is:

C = 2πr

Where C is the circumference, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.

In this case, the radius of the circle is 25.8 yards.

We can substitute that into the formula and simplify:

C = 2πr

C = 2 × 3.14 × (25.8)

C = 162.024 yds

Since the circumference of the circular track is approximately 162.024 yards.

If Jessie rides around the track 3 times, the total distance she will ride is:

3 × 162.024 = 486 yards.

Therefore, option D) 486 yards is the correct answer.

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if f(x) = 3 - x^2, find f(-2)

Answers

Based on the function f(x) = 3 - x², the value of f(-2) include the following: f(-2) = -1.

What is a function?

In Mathematics and Geometry, a function can be defined as a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair in tables or relations.

What is a domain?

In Mathematics and Geometry, a domain is sometimes referred to as input value and it can be defined as the set of all real numbers for which a particular function is defined.

When the domain (input value) of the given function f(x) is -2, the output value (range) is given by;

f(x) = 3 - x²

f(x) = 3 - (-2)²

f(x) = 3 - 4

f(x) = -1

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the weekly earnings of bus drivers are normally distributed with a mean of $395. if only 1.1 percent of the bus drivers have a weekly income of more than $429.35, what is the value of the standard deviation of the weekly earnings of the bus drivers?

Answers

The value of the standard deviation of the weekly earnings of the bus drivers is $14.57.

To solve this problem, we can use the standard normal distribution table or a calculator that provides the inverse of the standard normal distribution. Let X be the weekly earnings of the bus drivers, then we have:

P(X > $429.35) = 0.011

Using the standard normal distribution table or calculator, we can find the z-score that corresponds to a probability of 0.011, which is approximately -2.33. We can then use the formula for standardizing a normal variable:

z = (X - μ) / σ

where μ is the mean and σ is the standard deviation of the distribution. Substituting the given values, we have:

-2.33 = ($429.35 - $395) / σ

Solving for σ, we get:

σ = ($429.35 - $395) / (-2.33) = $14.57

Therefore, the value of the standard deviation of the weekly earnings of the bus drivers is $14.57.

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Derek had 10 2/3 ounce of water in a glass He drank 1/4 of an ounce

Answers

After Derek drinks 1/4 ounce of water, he is left with 95/3 ounces of water in his glass.

Derek initially had 10 2/3 ounces of water in his glass. To find out how much water is left after he drinks 1/4 ounce of water, we need to subtract 1/4 from 10 2/3. To do that, we need to convert the mixed number (10 2/3) into an improper fraction.

To convert a mixed number into an improper fraction, we multiply the whole number by the denominator of the fraction and then add the numerator. In this case, we have:

10 x 3 + 2 = 32/3

Therefore, Derek initially had 32/3 ounces of water in his glass.

To subtract 1/4 from 32/3, we need to make sure the denominators are the same. We can convert 1/4 into twelfths by multiplying both the numerator and denominator by 3. This gives us:

1/4 x 3/3 = 3/12

Now that we have a common denominator of 12, we can subtract:

32/3 - 3/12 = 383/12 - 3/12 = 380/12

To simplify, we can divide both the numerator and denominator by 4:

380/12 ÷ 4/4 = 95/3

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Complete question is:

Derek had 10 2/3 ounce of water in a glass He drank 1/4 of an ounce of the water from his glass how much water is left in Derek's glass?

Bri opened up a savings account that earns 1.25% interest, compounded monthly. If she puts $2500 in the account to start, how much money would be in her account 4 years later, assuming no additional money was deposited or withdrawn from the account? Group of answer choices $2377.32 $2620.36 $2628.11 $2510.43

Answers

Answer:

The formula for calculating the future value of an investment with compound interest is:

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

where A is the future value, P is the principal (initial amount), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time period in years.

In this case, P = $2500, r = 0.0125 (1.25% as a decimal), n = 12 (since the interest is compounded monthly), and t = 4.

Plugging these values into the formula, we get:

A = 2500(1 + 0.0125/12)^(12*4) ≈ $2,628.11

Therefore, the answer is $2628.11.

Answer: $ 2628.11

Step-by-step explanation:

Compound interest is nasty.

the formula (which you need to memorize) is:

[tex]A = P(1+\frac{r}{n} )^t^n[/tex]

A is the final amount, P is the principle, (original amount of money invested), r is the rate of return (as a decimal NOT percent), n is the number of times compounded annually, and t is the time, (in years), invested.

With all this information, our formula becomes:

[tex]A = 2500(1+\frac{0.0125}{12} )^4^8[/tex]

solving, we get A ≅ 2628.11

This corresponds to answer choice C

Determined the area of a pentagon with a apothem of 10

Answers

The area of the pentagon with an apothem of 10 units is approximately 353.55 square units.

How to solve for the Apothem

Area = (Perimeter × Apothem) / 2

Central angle = 360° / 5 = 72°

To find the area of a regular pentagon with an apothem of 10 units, we can use the formula:

Area = (Perimeter × Apothem) / 2

Central angle = 360° / 5 = 72°

Now, consider the right triangle formed by half of a side, the apothem, and the radius. The angle between the apothem and the radius (half of the central angle) is:

Angle = 72° / 2 = 36°

In the right triangle, we have:

tan(36°) = (s/2) / 10

Solving for s:

s = 2 * 10 * tan(36°) ≈ 14.142 units (rounded)

Now that we have the length of one side, we can calculate the perimeter of the pentagon:

Perimeter = 5 * s ≈ 5 * 14.142 ≈ 70.710 units (rounded)

Finally, we can find the area of the pentagon using the formula:

Area = (Perimeter × Apothem) / 2

Area = (70.710 × 10) / 2

≈ 353.55 square units (rounded)

The area of the pentagon with an apothem of 10 units is approximately 353.55 square units.

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Which retirement plan comes with a guaranteed retirement benefit at retirement?

401(k)
Fixed Annuity
Roth IRA
Traditional IRA

Answers

Answer: B. Fixed Annuity

Step-by-step explanation: A Fixed Annuity is a type of retirement plan where you make regular contributions to an insurance company, and in return, they guarantee a fixed payout during your retirement years. This guaranteed benefit is typically paid out as a stream of income for a specific period or for the rest of your life, depending on the terms of the annuity contract.

Unlike other retirement plans such as a 401(k), Roth IRA, or Traditional IRA, which are investment-based and subject to market fluctuations, a Fixed Annuity provides a guaranteed benefit regardless of how the financial markets perform.  This can provide peace of mind for individuals who prioritize a stable and predictable income during retirement.

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. A thermometer shows a temperature of -4.5°C. A nearby thermometer shows a temperature of 3.5°C. Explain how absolute value can be used to decide which temperature is warmer.​

Answers

Answer:

Step-by-step explanation:

The concept of absolute value can be used to determine which temperature is warmer between -4.5°C and 3.5°C. Absolute value is a mathematical function that returns the magnitude, or distance, of a number from zero, regardless of whether the number is positive or negative. In other words, the absolute value of a number is always a positive number.

In this case, we can calculate the absolute value of each temperature as follows:

| -4.5°C | = 4.5°C

| 3.5°C | = 3.5°C

The absolute value of -4.5°C is 4.5°C, which is greater than the absolute value of 3.5°C, which is 3.5°C. This means that -4.5°C is further from zero than 3.5°C, and therefore it is a colder temperature. So, the temperature of 3.5°C is warmer than the temperature of -4.5°C.

Therefore, we can use the concept of absolute value to determine which temperature is warmer by comparing the absolute values of the temperatures. The temperature with the greater absolute value is farther from zero, and therefore colder, while the temperature with the smaller absolute value is closer to zero, and therefore warmer.

I need some help please

Answers

Answer:

Step-by-step explanation:

I think is x-1

It is because you need to find f(1) and the formula of x-1 when x is greater and equal to 1.

In 2010, Haiti was hit by a devastating earthquake, which registered at 7.0 on the Richter scale. The largest recorded earthquake since 1900 occurred in 1960 in Valdivia, Chile, and registered at 9.5 on the Richter scale. About how many times greater was the intensity of the Chilean earthquake? a. 2.5 b. 25 c. 150 d. 316

Answers

In 2010, Haiti was hit by a devastating earthquake, which registered at 7.0 on the Richter scale. The largest recorded earthquake since 1900 occurred in 1960 in Valdivia, Chile, and registered at 9.5 on the Richter scale. About 316 times greater was the intensity of the Chilean earthquake.

Hence, the correct option is D.

The Richter scale is a logarithmic scale that measures the magnitude of an earthquake. Each increase of one on the Richter scale represents a tenfold increase in the amplitude of the seismic waves.

To find out how many times greater the intensity of the Chilean earthquake was compared to the Haitian earthquake, we will have to find the difference in magnitude between the two earthquakes.

9.5 - 7.0 = 2.5

Since each increase of one on the Richter scale represents a tenfold increase in the amplitude of the seismic waves, a 2.5 increase represents

10^(2.5) = 316.2

Hence, the intensity of the Chilean earthquake was about 316 times greater than the intensity of the Haitian earthquake.

Hence, the correct option is D.

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Answer:d

Step-by-step explanation:

its d

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