The following figures were entered on a checking-account record. Add or subtract them to keep the running total correct. Balance forward $643.72 Check #5734 to Lupe's Market, for food, for $68.29 $ Deposit of $341.80, a paycheck $ Check #5735 to Broadmoor Community Center in the amount of $34.18 $ Check #5736 to Bill Baughman, for plumbing services, for $60.00 $

Answers

Answer 1

It is given Balance forward $643.72 in the account. An amount of $68.29 is given to to Lupe's Market, for food. In the account a Deposit of $341.80 is made.A Cheque of $34.18 is given to Broadmoor Community Center .Charge for for plumbing services, is $60.00 .

Transactions made in the account = $643.72-68.29+341.80-34.18-60.00

Amount left in the account =$823.05.

Answer 2

Answer:

Running Total = $823.05

Step-by-step explanation :

When the figures were entered on a checking account record to keep the running total correct :

Balance forward = $643.72

Check #5734 to Lupe's Market for food = $68.29

A deposit = $341.80

Check #5735 to Broadmoor Community Center = $34.18

Check #5736 to Bill Baughman for plumbing services = $60.00

Total Transactions :

643.72 - 68.29 + 341.80 - 34.18 - 60 = $823.05

Total balance = $823.05

Related Questions

wanda rode her bike 21/10 miles. Which mixed number shows how far Wanda rode her bike?

Answers

2 1/10 as a mixed number or 2.1 as a decimal

Hope that helps

To convert the improper fraction 21/10 to a mixed number, divide 21 by 10 to get 2 with a remainder of 1. The mixed number is 2 1/10.

The student is asking for help converting an improper fraction to a mixed number. An improper fraction is one where the numerator is greater than the denominator. To convert 21/10 to a mixed number, we divide the numerator by the denominator.

Divide 21 by 10, which equals 2 with a remainder of 1.

The whole number part of the mixed number is the quotient, which is 2.

The remainder becomes the new numerator, and the original denominator stays the same, making it 1/10.

Therefore, the mixed number is 2 1/10.

An item is called "price elastic" if you drop the price and revenue goes up. Last week you sold 10 sodas for $2 each; this week you sold 30 sodas for $1 each. Is soda price elastic?

Answers

Final answer:

Soda is price elastic because lowering the price from $2 to $1 resulted in an increase in total revenue from $20 to $30, indicating that a decrease in price caused a larger increase in quantity sold.

Explanation:

When determining whether an item is price elastic or not, we look at the effect that changing the price has on the total revenue. If a decrease in price leads to an increase in total revenue, the demand for the product is considered price elastic. In the example given, soda was sold at different prices and quantities: 10 sodas at $2 each last week, and 30 sodas at $1 this week. We use these numbers to calculate the total revenue for each week:

Last week: 10 sodas × $2/soda = $20

This week: 30 sodas × $1/soda = $30

Since the total revenue increased from $20 to $30 when the price was lowered from $2 to $1, we can see that the revenue increased as a result of the price drop, indicating that the demand for soda is indeed price elastic.

what is the solution -10 + sqrt x+8=-4

Answers

- 10 + √(x + 8) = - 4

Add 10 to both sides to get:
√(x + 8) = 6

Square both sides to get our binomial out of the square root:
x + 8 = 6²
x + 8 = 36

Subtract 8 to both sides to get:
x = 28

Answer:

[tex]x=28[/tex]

Step-by-step explanation:

[tex]-10+\sqrt{x+8}=-4[/tex]

⭆ Add 10 to both sides:-

[tex]-10+\sqrt{x+8}+10=-4+10[/tex]

[tex]\sqrt{x+8}=6[/tex]

⭆ Square both sides:-

[tex]x+8=36[/tex]

⭆ Subtract 8 from both sides:-

[tex]x+8-8=36-8[/tex]

[tex]x=28[/tex]

OAmalOHopeO

Can someone please answer all these please?

a) When Lucia buys olives at the deli, the scale shows 0.325 kg at $18.88 per kg. How much should she pay?

b) John’s weekly wage is $1510.99 and he pays 2/3 of his weekly income in rent. How much rent does he pay each week?

c) A farmer owns 780 hectares of land. During a bushfire, 195 hectares are burnt. What percentage of his land was burnt?

d) Candles are $14.95 each. Estimate how much I need if I want to buy 17 of them.
Show your working.

e) Decrease 5000 by 13 %.

f) Ray bought a computer for $1600 and then a year later sold it for $1200.
Calculate his loss =
Calculate his loss as a percentage of the original price of the computer =

g) John spent $80 on dinner last Friday night. If this $80 is equal to 40% of his weekly income, calculate his weekly income.

h) Mr Jenkins invested $7500 at his local bank at 6.5% Simple Interest per annum.
What was his investment worth at the end of the first year?

Question 5

a) Express this ratio in lowest terms: 50 minutes : 2 ½ hours

b) Divide $120 in the ratio 5:7

c) Jane and Ben share in their lottery win in the ratio of 7: 3.
If Jane’s share of the money is $5600, how much does Ben receive?

Answers

a) $6.136
b) $997.25
c) 25%
d) $254.15
e) 4350
f) $400, 25% loss
g) $200
h) $7,987,50
5
a) 1min: 3min
b) $50:$70
c) $2400

what is the surface area of a sphere with a radius of 3m

Answers

The area is 113.1m If you want to double check go on google and look up surface area of a sphere. A calculator will come up. Hope this helped.

A pair of dice are rolled. What is the probability of rolling 4 or greater?

A: 5/36
B: 1/18
C: 1/36
D: 11/12

Answers

Answer: option D: 11/12

Explanation:

1) The sample space is formed by 36 pairs: 6×6 = 36.

2) Roolling 4 or more is the same that not rolling 3 or less

3) Rolling 3 or less are (1,1), (1,2), and (2,1). Those are 3 outcomes out of 36.

4) Therefore, not rolling 3 or less (the same that rolling 4 or more) has 36 - 3 = 33 outcomes out of 36.

5) The probability of 33 out of 36 is 33/36

6) Simplify the fraction 33/36 = 11/12

And that is the answer.

Use the substitution method to determine whether the system of equations has one solution, no solution, or infinitely many solutions. 2x-y=10 x = y + 5

Answers

We have the equations:
2x-y = 10, x = y + 5
To solve the system we substitute x = y + 5 in the first equation and it remains:
2 (y + 5) - y = 10
2y +10 -y = 10.
y = 0
Then we substitute y = 0 in any of the two equations to find x
Finally we have left that x = 5

Jason wants to choose 9 players for his track team. There are 12 players to choose from. How many different teams can Jason make?

Answers

220
12C9 = 12!/(12-9)!*9!
= 12*11*10/6 = 220

Jason wants to form a team of 9 players out of total 12 players.

Here the order of selection does not matter because there is no particular post for any player. So we need to use Combinations and choose 9 players out of 12 players.

We know the formula for Combinations is given as follows :-

[tex]nCr=\frac{n!}{r!*(n-r)!} \\\\ Choosing \;9 \;out \;of \;12 \\\\ 12C9 = \frac{12!}{9!*(12-9)!} =\frac{12!}{9!*3!} =\frac{12*11*10*9*8*7*6*5*4*3*2*1}{(9*8*7*6*5*4*3*2*1)*(3*2*1)} \\\\ 12C9 = \frac{12*11*10}{3*2*1} =\frac{1320}{6} =220 \;combinations[/tex]

Hence, all the possible number of different teams = 220 combinations.

for her bedroom Marisol is buying a rug that is 6 feet by 8 feet her room is 9 feet by 11 feet how many square feet of floor will not be covered by Rug?

Answers

51 feet i think because the area of the room is 99 feet the area of the rug is 48 feet 99-48=51

Final answer:

Marisol's bedroom is 99 square feet, and the rug area is 48 square feet. By subtracting the rug area from the total room area, we find that 51 square feet of floor will not be covered by the rug.

Explanation:

To find out how many square feet of Marisol's bedroom floor will not be covered by the rug, we must first calculate the area of her entire room and then the area of the rug. The area of a rectangle is found by multiplying the length by the width. The area of Marisol's room is 9 feet × 11 feet = 99 square feet. The area of the rug is 6 feet × 8 feet = 48 square feet.

Next, we subtract the area of the rug from the area of the entire room to find the uncovered floor area.

Uncovered floor area = Total room area – Rug area
= 99 square feet – 48 square feet
= 51 square feet

Therefore, 51 square feet of Marisol's bedroom floor will not be covered by the rug.

Calculate the surface area of the portion of the surface z=x^2 + y that lies above the triangular region t wth vertices 0,0 4,0 and 4,2

Answers

Z=x^2+y

Z=(0)^2+0=0

Z=(4)^2+0=16

Z=(4)^2+2=18

Z total = 34

What are the lateral area and the surface of the cone shown below?

Answers

[tex]\bf \textit{lateral surface area of a cone}\\\\ LA=\pi r\stackrel{slant~height}{\sqrt{r^2+h^2}}~~ \begin{cases} r=radius\\ h=height\\ -------\\ r=11\\ \stackrel{slant~height}{\sqrt{r^2+h^2}}=24 \end{cases}\implies LA=\pi (11)(24) \\\\\\ \boxed{LA=264\pi }\\\\ -------------------------------[/tex]

[tex]\bf \textit{total surface area of a cone}\\\\ SA=\pi r\stackrel{slant~height}{\sqrt{r^2+h^2}}+\pi r^2~~ \begin{cases} r=radius\\ h=height\\ -------\\ r=11\\ \stackrel{slant~height}{\sqrt{r^2+h^2}}=24 \end{cases} \\\\\\ SA=\pi (11)(24)+\pi (11)^2\implies SA=264\pi +121\pi \\\\\\ \boxed{SA=385\pi }[/tex]

How does the graph of y=1/2(x+4)^2compare to the graph of y=(x-1)^2 -3?

Answers

[tex]\bf ~~~~~~~~~~~~\textit{function transformations} \\\\\\ % templates f(x)= A( Bx+ C)+ D \\\\ ~~~~y= A( Bx+ C)+ D \\\\ f(x)= A\sqrt{ Bx+ C}+ D \\\\ f(x)= A(\mathbb{R})^{ Bx+ C}+ D \\\\ f(x)= A sin\left( B x+ C \right)+ D \\\\ --------------------[/tex]

[tex]\bf \bullet \textit{ stretches or shrinks horizontally by } A\cdot B\\\\ \bullet \textit{ flips it upside-down if } A\textit{ is negative}\\ ~~~~~~\textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if } B\textit{ is negative}[/tex]

[tex]\bf ~~~~~~\textit{reflection over the y-axis} \\\\ \bullet \textit{ horizontal shift by }\frac{ C}{ B}\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is negative, to the right}\\\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is positive, to the left}\\\\ \bullet \textit{ vertical shift by } D\\ ~~~~~~if\ D\textit{ is negative, downwards}\\\\ ~~~~~~if\ D\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{ B} [/tex]

and now with that template in mind,

bearing in mind the parent function for both is just y = x², or y = 1(1x + 0)² + 0.

[tex]\bf y=\stackrel{A}{\cfrac{1}{2}}(x\stackrel{C}{+4})^2[/tex]

is x² but expanded by twice as much vertically, and has a horizontal shift of +4, namely 4 units to the left.

y=(x-1)² - 3

is just x² but with a horizontal shfit of -1, namely 1 unit to the right, and a vertical shift of -3, namely 3 units down.

You put $400 in an account. The account earns $18 simple interest in 9 months. What is the annual interest rate?

Answers

The annual interest rate is 0.06 or 6%.

thats the answer hope this helps

Answer:

Step-by-step explanation:

Let's start by finding the amount earned per month:

[tex]\frac{18}{9}[/tex]=2

Now let's find the % per month

[tex]\frac{2}{400} =.005[/tex], or .5%

Now let's multiply by 12 months to get the annual interest rate

[tex].005 * 12 = .06[/tex] or 6%

the number of bacteria in a container increases at the rate of R(t) bacteria per hour. If there are 1000 bacteria at time t=0 , which of the following expressions gives the number of bacteria in the container at time t=3 hours?

Answers

The expression for the total number of bacteria at t = 3 hours, given an initial 1000 bacteria at t = 0, is: [tex]\[ 1000 + \int_0^3 R(x) \, dx \][/tex]

To find the number of bacteria in the container at time t = 3 hours, given that the rate of increase is [tex]$ R(t) $[/tex] bacteria per hour and there are 1000 bacteria at time t = 0, you can use the following steps:

Start with the initial condition :

You are given that there are 1000 bacteria at t = 0.

So, the initial condition is [tex]$ N(0) = 1000 $,[/tex] where N(t) represents the total number of bacteria at time t.

Integrate to find the change in number of bacteria over time :

Since the rate of increase is R(t), the total increase in bacteria from time t = 0 to t = t is given by integrating R(t) with respect to time.

This integral provides the cumulative increase in bacteria:

[tex]\[ \int_0^t R(x) \, dx. \][/tex]

Add the initial bacteria to the increase :

Since there are already 1000 bacteria at t = 0, the total number of bacteria at time t is given by:

[tex]\[ N(t) = 1000 + \int_0^t R(x) \, dx. \][/tex]

Find the expression for t = 3 hours :

To find the total number of bacteria at t = 3 hours, you substitute t = 3 into the expression derived in step 3:

[tex]\[ N(3) = 1000 + \int_0^3 R(x) \, dx. \][/tex]

Thus, the expression [tex]$ 1000 + \int_0^3 R(x) \, dx $[/tex] gives the number of bacteria in the container at time t = 3 hours.

Question :

The correct expression that gives the number of bacteria in the container at time t = 3 hours is D. [tex]1000 + \int_0^3 R(t) \, dt[/tex]

The problem asks us to find the number of bacteria in a container at t = 3 hours, given that the number of bacteria increases at a rate of R(t) bacteria per hour and there are 1000 bacteria at time t = 0.

To solve this, we need to integrate the rate function R(t) to find the total change in the number of bacteria over the interval from t = 0 to t = 3.

1. Initial number of bacteria:

At t = 0, the number of bacteria is 1000.

2. Change in number of bacteria:

The rate of change of the number of bacteria is given by R(t) bacteria per hour.

To find the total number of bacteria added over the time interval from t = 0 to t = 3, we need to integrate R(t) from 0 to 3.

Total change in number of bacteria = [tex]\int_0^3 R(t) \, dt[/tex]

3. Total number of bacteria at t = 3 hours:

This is the sum of the initial number of bacteria and the total change in the number of bacteria over the 3 hours.

Number of bacteria at t = 3 hours = [tex]1000 + \int_0^3 R(t) \, dt[/tex]

Complete Question:

The number of bacteria in a container increases at the rate of R(t) bacteria per hour. If there are 1000 bacteria at time t=0, which of the following expressions gives the number of bacteria in the container at time t=3 hours?

(A) R(3)

(B) 1000+R(3)

(D) [tex]$1000+\int_0^3 R(t) d t$[/tex]

PLZ HELP ASAP CIRCLES WILL GIVE BRANLIEST

Answers

From the given, it is obvious that angle I is the opposite angle of angle D. This means that the sum of the measures of these two should be equal to 180°.

If we are to look closely to the figure, angle I intercepted the arc BDR. Also, the angle D intercepted arc BIR. The sum of the measures these two arcs is 360°. Hence, the sum of the measures of the angles intercepting these arcs is 180°.

m∠I + m∠D = 180°
117° + m∠D = 180°

The measure of angle D is 63°.

Answer: 63°

Which of the following is a service that banks provide? A. Printing paychecks B. Insuring vehicles C. Access to cash D. Printing money

Answers

Hey There! Your answer is C, In a bank you can store money in a savings account and later take it out. Or you can apply for a Loan. So you have access to money in a bank. Have a nice day! Hope this helped!

Answer:

C. Access to cash

Step-by-step explanation:

Bank provides access to cash in multiple manners, you can debit the money from your savings account, apply for different type of loans, draft your DD etc.

While for the other options like printing paychecks are done by any company in order to provided paychecks to its employees, Insurance companies provides vehicle insurance services to anyone will to get their vehicle insured and printing money is provided only by central bank of any country, not every bank is allowed to print money.

simplify this problem

Answers

[tex] \dfrac{49 - \frac{1}{r^2} }{7 - \frac{1}{r} } [/tex]

Rewrite the fraction as division:
[tex]= (49 - \dfrac{1}{r^2}) \div (7 - \dfrac{1}{r} )[/tex]

Make them into single fraction:
[tex]= \dfrac{49r^2 - 1}{r^2} \div \dfrac{7r - 1}{r} [/tex]

Change the divide fraction into multiplication fraction:
[tex]= \dfrac{49r^2 - 1}{r^2} \times \dfrac{r}{7r - 1} [/tex]

Factorise the difference of square a² - b² = (a + b) (a - b) :
[tex]= \dfrac{(7r+ 1)(7r - 1)}{r^2} \times \dfrac{r}{7r - 1} [/tex]

Cancel the common factors:
[tex]= \dfrac{(7r+ 1)}{r}[/tex]

Comment. The best way to do this is to let 1/r = a and 1/r^2 = a^2. Now rewrite the problem.

Solution
[tex] \frac{49 - a^2}{7 - a} \\ \frac{(7 - a)(7 + a)}{7 - a}\text{ Notice a cancellation can take place} [/tex]

There is a 7 - a in both numerator and denominator, so that cancel providing a does not equal 7. a cannot equal 7 because that will put a 7 in the denominator and that makes the whole fraction = something over 0 which is undefined.

Answer
So far what we have is
7 + a

But a = 1/r
So the answer can be 7 + 1/r

r can be anything but 0 [for this answer]
and 1/7 for the cancellation.

what integer and-8 have the product of -96

Answers

That would be 12
12 times -8 = -96!

:) Have a nice day and maybe consider grading this answer brainliest? <3

Your answer is 12.

12 * (- 8) = - 96.

Polygon ABCDEF is the result of a translation of polygon GHIJKL . GL¯¯¯¯¯ is parallel to HI¯¯¯¯¯ in the pre-image. please help

Answers

Since GL and HI are parallel to each other, then in the translation this condition is going to be kept. So that, we can write in these gaps that AB and FE are parallel to each other.

GL parallel to HI in the pre-image ensures AB remains parallel to FE in the translation.

Given that GL and HI are parallel, we can infer that AB and FE will also remain parallel in the translation. The parallelism of lines GL and HI suggests that their corresponding sides, AB and FE, will exhibit the same parallel relationship during the translation process. This is a consequence of the consistent geometric transformation applied to all points on lines GL and HI. As each point on GL undergoes translation, its corresponding point on HI experiences the same displacement, preserving the parallelism.

Therefore, we can confidently state that AB and FE maintain their parallel orientation, aligning with the geometric properties of the translation that preserves parallel lines. The parallelism observed in the original configuration persists throughout the translation, ensuring that AB and FE remain parallel to each other.

For more such questions on parallel:

https://brainly.com/question/30195834

#SPJ6

What is the probability that at least 2 students in a class of 36 have the same birthday?

Answers

Given a group of n students, and given the fact that there are 365 days in one year, the probability that there are no students with the same birthday is given by
[tex]p_{no} (n) = \frac{364}{365} \cdot \frac{363}{365} \cdot ... \cdot \frac{365-n+1}{365} = \frac{364!}{365^{n-1} (365-n)!} [/tex]
Therefore, the probabilty that there are at least 2 students with same birthday is the complementary of this value:
[tex]p_{yes} (n) = 1 -p_{no}(n) =1- \frac{364!}{365^{n-1} (365-n)!}[/tex]

And if we use n=36 (number of students), we find
[tex]p=1- \frac{364!}{365^{36-1} (365-36)!} \sim 0.83[/tex]
So, the probability that there are at least 2 students in a group of 36 with same birthday is approximately 83%.

Explain why the ratio 3 feet / 1 yard has a value of one

Answers

Because There are 3 feet in 1 yard, so 3 feet and 1 yard are the same thing, hence a 1:1 ratio.

Which five values would be used to graph a box-and-whisker plot for the following set of data? 36, 14, 27, 27, 33, 22, 41, 29

Answers

First put all the number in order from least to greatest:
Q1 Q2 Q3
{14,22,27,(27}{,29),33,36,41}
add/div. by 2 add/div. by 2
28.5 34.5

Minimum: 14 (smallest number)
Quartile 1: 28.5 (middle number of q1)
Quartile 2: 28 (middle number) when you have and even amount of numbers you end up having 2 middle numbers, so you just add them then divide by 2. 27+29=56 56/2=28
Quartile 3: 34.5 (middle number of q3)
Maximum: 41 (biggest number)

I hope this helped you! :)

Answer:

Lower value: 14

Highest value: 41

Lower quartile: 24.5

Upper quartile: 34.5

Median: 28

Step-by-step explanation:

Hey can you please help me posted picture of question

Answers

Parent function is F(x) = |x|

Two transformations occur on F(x)

1) Shift 8 units left
So, the expression will be | x + 8 |

2) Shift 3 units down
So, the expression will be |x + 8| - 3

Thus,

G(x) = |x +8| - 3

So, option D is the correct answer

Comment
A minus number on the right of an equal sign (where f(x) or y or something like it is on the left of the equal sign) that is negative means that the function is going down. So any positive number in the answer is wrong if it greater than 0.

f(x) = | x | - 3 is going down.

Comment 2
Anything inside the | | which is plus goes left (not right) so you want y = |x + 8| - 3

D<<<< answer

Which is equivalent to sin^-1(tan(pi/4)) ? Give your answer in radians.

Answers

We are to find the value of [tex]sin^{-1}(tan( \frac{ \pi }{4})) [/tex]

First we evaluate tan(π/4). The value of tan(π/4) is 1.

So,

[tex]sin^{-1}(tan( \frac{ \pi }{4})) =sin^{-1} (1)[/tex]

sin(π/2) = 1
So,
[tex]sin^{-1}(1)= \frac{ \pi }{2} [/tex]

Thus, we can write:

[tex]sin^{-1}(tan( \frac{ \pi }{4}))= \frac{ \pi }{2} [/tex] radians.

So, the answer to this question is π/2 radians.

Answer:

the answer is b

Step-by-step explanation:

Adams sister want to watch her intake of fat per day.he estimate that the dinner will have 48grams of fat.what percentage of her total daily allowance of fat will the dinner be round your answer to a whole number.the recommended daily allowance of fat is70g

Answers

You have to figure out what 48 percent of 70 is.
Use the formula percent/of = x/100.
So, 48/70 and x/100 you cross multiply the numbers; 48*100 and 70*x and end up with 70x=4800.
Divide both sides by 70, which gives you 68.57.
Round the number up to 69 percent.

hello can you please help me posted picture of question

Answers

The area of the spinning board is divided into 10 equal sections.

Probability in this case will be = Area of favorable outcome/Total Area

Let the total area be A.
Area of each section will be A/10

So probability of landing on 3 will be = (A/10) / A = 1/10

So the correct answer will be option C

What are the zeroes of y = x^2 – 4x – 5?

Answers

Start by factoring [tex] x^2 - 4x - 5[/tex]. Your two factors will be in the form (x + a) and (x + b). You want two numbers a and b to multiply to -5 and add to -4. Test out various numbers, and you'll find that -5 and 1 work!

That means your factors are (x - 5) and (x + 1). You can double check this by foiling and seeing if you get your original equation.

Since you want to find the zeroes for that equation, that means y = 0. Remember that anything multiplied by 0 is 0, so you can set each of your factors equal to zero and solve for x. The x-values are your zeros:
x - 5 = 0
x = 5

x + 1 = 0
x = -1

-----

Answer: 5 and -1

Answer:

x=5 or x=-1

Step-by-step explanation:

The zeroes of the equation is when the x values when y=0.

We can determine this using a method that when we times out the brackets of our simplification we arrive at the original equation. We know that we must get -5 and -4x and x^2:

We can write:

[tex]y=x^2-4*x-5=0[/tex]

[tex](x-5)*(x+1)=0[/tex]

If we use the rules of algebra and multiply each term with each other:

[tex]x*x+x*1-5*x-5*1=0[/tex]

We can simplify:

[tex]x^2-4*x-5=0[/tex]

We end up with the original equation:

Therefore the zeros of the equation is when:

[tex](x-5)*(x+1)=0[/tex]

[tex]x-5=0[/tex] and [tex]x+1=0[/tex]

[tex]x=5[/tex]

[tex]x=-1[/tex[

x=5 or x=-1

A fluorite crystal is shaped like a regular octahedron with edges that are 2.1 inches. Which of these is the volume of the fluorite crystal in cubic inches? Round to the nearest hundredth

Answers

To solve this problem you must apply the proccedure shown below:

1. You have the following information given in the problem above: The regular octahedron with edges that are 2.1 inches.

2. Therefore, you must apply the formula for calculate the volume of a octahedron, which is:

V=(a^3√2)/3

3. Therefore, you have:

V=((2.1 inches)^3√2)/3
V=178.30 inches^3

To find the volume of the fluorite crystal, you can use the formula for the volume of an octahedron with the given edge length of 2.1 inches, rounded to the nearest hundredth to be approximately 7.69 cubic inches.

The volume of the fluorite crystal can be calculated as follows:

Identify the formula for the volume of an octahedron: V = (1/3) × [tex]\sqrt{2}[/tex] × a³, where 'a' is the edge length.

Substitute the given edge length: V = (1/3) × [tex]\sqrt{2}[/tex] × 2.1³.

Calculate the volume: V = 7.69 cubic inches (rounded to the nearest hundredth).

Angela owns a set of 6-inch tall glasses. Each glass has a diameter of 3 inches. Angela has three people over for dinner. Each guest will be served a full glass of milk. How much milk will Angela need ?

Answers

Dimensions of the glasses: Diameter, d = 3 in; depth, h = 6 in

Volume of 1 glass = (πd^2/4)*h = (π*3^2/4)*6 = 42.41 in^3

Each of the three guests will be served a glass full of milk.

Volume of milk required = 3*volume of 1 glass = 3*42.41 = 127.23 in^3
But,
1 in^3 = 0.0163871 liters

Therefore,
127.23 in^3 = 127.23*0.0163871 ≈ 2.09 liters will be required.

A book club offers a choice of 8 books from a list of 40. In how many can a member make a collection?

Answers

Final answer:

This is a math combination problem. The number of ways a member can choose 8 books from a list of 40 is 76,904,685 ways.

Explanation:

This is a combinatorics problem, specifically a combination problem. A combination is a selection of items from a larger set where the order does not matter. In this case, we have a set of 40 books and want to know how many ways one can select 8 books from those 40. The formula for calculating combinations is nCr = n! / [(n - r)! * r!] where 'n' represents the total number of items, 'r' represents the number of items to choose, 'nCr' represents the number of combinations of n items taken r at a time, and '!' denotes factorial, the product of all positive integers up to that number.

Applying the combination formula, a member can make the choice of 8 books from a list of 40 in:

40C8 = 40! / [(40 - 8)! * 8!] = 76,904,685 ways

Learn more about Combinations here:

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