A measure of the degree to which capital wears out or becomes obsolete during a period is:________

Answer:

(4 √ 3 + 4 √2 ) m

Step-by-step explanation:

The  insect can travel from one corner directly to opposite corner in four different ways

each can be calculated using Pythagoras theorem

firstly  for one face we need to calculate the diagonal

H² = 1² + 1² = 2

H = √2

then we calculate the diagonal opposite a corner

for example

A to H where A  is at the bottom and H opposite A in another plane at the top in the cubical box

(Interior diagonal for A to H)² = √2² + 1² = 3

Interior diagonal from A to H = √ 3

there are four such corners, the fly will travel 4 √ 3 and it could also go 4 √2 diagonally to the the other corners

maximum possible length in meters = (4 √ 3 + 4 √2 ) m

Answer:

Step-by-step explanation:

Looking at the table,

a) the standard daily rate for a luxury car is $70. Since Lynn wants to rent the luxury car for 3 days, it means that the standard rate for 3 days would be

3 × 70 = $210

She figures she will put on about 400 km during the three

days. The cost of renting the luxury car per kilometer(mileage) is 30 cents. Therefore, the cost for 400 kilometers would be

400 × 30 = 12000 cents.

Converting 12000 cents to dollars, it becomes

12000/100 = $120

Total cost of renting the luxury car would be

120 + 210 = $330

b) the daily cost of the unlimited mileage daily for the luxury car is $105

Total cost of renting the luxury car for 3 days would be

105 × 3 = $315

c) the standard daily rate is better because it is cheaper

To calculate the expected number of applications that went to the right college, we need to consider the probability of each application being placed correctly. Since the applications are placed randomly, each application has an equal chance of going to the right college. The expected number of applications that went to the right college is 1.

To calculate the expected number of applications that went to the right college, we need to consider the probability of each application being placed correctly. Since the applications are placed randomly, each application has an equal chance of going to the right college. Let's say there are n applications and n colleges.

The probability of a specific application going to the right college is 1/n. Therefore, the expected number of applications that went to the right college can be calculated as:

Expected number = Total number of applications * Probability of an application going to the right college

Expected number = n * (1/n)

Expected number = 1

The expected number of applications that went to the right college is 1. This means that, on average, one application will go to the right college.

Answer:

C. $1.80

Step-by-step explanation:

Given:

MSRP of a certain item = $60

Percentage of Selling by store A = 20%

Percentage amount will be = [tex]\frac{20}{100}\times 60 = \$12[/tex]

Sales tax = 5% on purchase price

Amount of sales tax = [tex]\frac{5}{100}\times 60 = \$3[/tex]

Total Cost of item at Store A is MSRP of a certain item plus Percentage amount of selling the item plus Amount of Sales tax.

framing in equation form we get;

Total Cost of item at Store A = [tex]60+12+3 =\$75[/tex]

Also Given:

Percentage of Selling by store B = 30%

Percentage amount will be = [tex]\frac{30}{100}\times 60 = \$18[/tex]

Regular price of item at store B = [tex]60+18 = \$78[/tex]

Percentage of discount of item at store B = 10% on regular price

Amount of discounted item at store B = [tex]\frac{10}{100}\times78 = \$7.8[/tex]

Now regular price of item with discount at store B will be equal to Regular price of item at store B minus Amount of discounted item.

regular price of item with discount at store B = [tex]78-7.8 = \$70.2[/tex]

Sales tax = 5% on purchase price

Amount of sales tax = [tex]\frac{5}{100}\times 60 = \$3[/tex]

Total Cost of item at Store B is regular price of item with discount at store B plus Amount of Sales tax.

framing in equation form we get;

Total Cost of item at Store B = [tex]70.2+3 =\$73.2[/tex]

The result when total cost of the item at Store B is subtracted from the total cost of the item at Store A  = $73.2 - $75 = $1.80.

Hence the result is $1.80.

Final answer:

To find the value of alpha given that alpha and beta are conjugate complex numbers, and alpha/beta^2 is real, we can use the equation |alpha - beta| = 2√3. We can substitute alpha = a + bi and beta = a - bi, and solve for a and b to find the value of alpha.

Explanation:

Let α and β be conjugate complex numbers such that α/β² is a real number and |α - β| = 2√3. We need to find the value of α.

Since α and β are conjugate complex numbers, they have the form α = a + bi and β = a - bi, where a and b are real numbers. Substituting these values into the given equation, we get:

|α - β| = |(a + bi) - (a - bi)| = |2bi| = 2|b| = 2√3

From this, we can conclude that |b| = √3. Since |b| is the absolute value of b, it is always positive. Therefore, we have two options: b = √3 or b = -√3.

If b = √3, then α = a + √3i. We can substitute this into the equation α/β² to check whether it is a real number.

α/β² = (a + √3i)/(a - √3i)² = (a + √3i)/(a² - 2a√3i - 3) = [(a(a² - 3) + √3i(3a - a²)] / (a² - 2a√3i - 3)

This expression is not a real number, so b ≠ √3.

If b = -√3, then α = a - √3i. We can substitute this into the equation α/β² to check whether it is a real number.

α/β² = (a - √3i)/(a + √3i)² = (a - √3i)/(a² + 2a√3i + 3) = [(a(a² + 3) - √3i(3a + a²)] / (a² + 2a√3i + 3)

This expression simplifies to (a(a² + 3) - √3(3a + a²))/ (a² + 3) = a - √3(2a + 1)/ (a² + 3)

For this expression to be a real number, the imaginary term √3(2a + 1) must be equal to 0. So, we have √3(2a + 1) = 0.

Solving this equation, we get 2a + 1 = 0, which implies a = -0.5.

Therefore, the value of α is α = -0.5 - √3i.

Answer:

Step-by-step explanation:

Answer: interest at the end of 3 months is $4.08

Step-by-step explanation:

The formula for simple interest is expressed as

I = PRT/100

Where

P represents the principal

R represents interest rate

T represents time in years

I = interest after t years

From the information given

T = 3 months = 3/12 = 0.25 years

P = $544

R = 3%

Therefore

I = (544 × 3 × 0.25)/100

I = 408/100

I = 4.08

Answer:

No solution

Step-by-step explanation:

-6y - 3 = 3 - 6y     ,     add 6y on both sides to cancel them out

-3 = 3     ,     you're left with -3=3, which is impossible because they're

                   different numbers, therefore not solution.

-3 ≠ 3

Final answer:

To determine which of the given points satisfy the inequality y < (2/3)x + 2, substitute the x and y values of each point into the inequality and check if it is true. The only solution to the inequality is (0, 3).

Explanation:

To determine which of the given points satisfy the inequality y < (2/3)x + 2, we can substitute the x and y values of each point into the inequality and check if the inequality is true.

Taking the first point (0, 3), we substitute x=0 and y=3 into the inequality: 3 < (2/3)(0) + 2. Simplifying, we have 3 < 2, which is true. Therefore, (0, 3) is a solution to the inequality.

Next, let's check the other points: (-3, 1), (3, 5), and (1, 2).

By substituting the x and y values of each point into the inequality, we find that (-3, 1), (3, 5), and (1, 2) are not solutions to the inequality. Therefore, the only solution to the inequality is (0, 3).

The equivalent annual cost of the machine, considering a 10% return, is approximately $309,535 per year.

First, accumulate the total cost over the lifespan of the machine which is $750,000 (initial cost) + ($12,000 * 3 years) = $786,000. The equivalent annual cost can be calculated using the formula for the present value of an annuity: PV = PMT [(1 - (1 + r)^-n ) / r], where 'PMT' is the payment per period, 'r' is the rate of return, and 'n' is the number of periods. Rearrange to calculate PMT: PMT = PV * r / (1 - (1 + r)^-n). Substituting in given values gives us, PMT = $786,000 * 0.1 / [1 - (1 + 0.1)^-3] = $309,535/year.

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Answer:

Option B) Use sample statistics to make decisions about population parameters  

Step-by-step explanation:

Statistical hypothesis testing

Thus, Option B) Use sample statistics to make decisions about population parameters is the correct answer.

Answer:

18 snacks

Step-by-step explanation:

Here we are considering that popcorn,icecreams,chocolate are snacks and each quantity represents each unit of snack.

Given that  they ate 8 buckets of popcorn, 4 ice cream bars, and 6 boxes of chocolate

So the total number of snacks they ate are 8 + 4 + 6 = 18

Final answer:

To calculate the percentage of calories from fat, multiply the grams of fat by the calories per gram of fat and divide by the total calories consumed.

Explanation:

To calculate the percentage of calories from fat in Nadia's daily intake, we need to know the total number of calories she consumed. Let's assume it was 2000 calories. First, we calculate the number of calories from fat by multiplying the grams of fat consumed (60g) by the number of calories per gram of fat (9 calories/g). This gives us 540 calories from fat. Then, we calculate the percentage by dividing the calories from fat (540 calories) by the total calories consumed (2000 calories) and multiplying by 100. So, the percentage of calories from fat in Nadia's day's intake is 27%.

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How I got that answer:

Create a two-way table showing the breakdown of students who like or dislike either vegetable. This is shown in the attached image below. Anywhere there is a letter indicates we aren't able to determine that value. Luckily we dont need to know those values to answer the question.

----------

Let's say we had 3000 students. I picked some large number that is a multiple of 3. That way when we multiply by 2/3, we get a whole number.

Take 2/3 of 3000 and you should get 2000. So there are 2000 students who dislike lima beans. Write "2000" at the end of the "dislike lima beans" row which is where the total is. Above that we'll have 1000 people who like lima beans, but we dont need to use this value.

-----------

Of those 2000 students, 3/5 of them also dont like sprouts either. So (3/5)*2000 = 0.6*2000 = 1200 students do not like both veggies. Furthermore, 2000 - 1200 = 800 like sprouts but dont like lima beans.

Alternatively, 2/5 of the 2000 students like sprouts but dont like lima beans, so (2/5)*2000 = 0.4*2000 = 800.

[tex]\text{Solve:}\\\\(5x^2 + 2x + 11) - (7 + 4x - 2x^2)\\\\5x^2+2x+11-7-4x+2x^2\\\\7x^2+2x+11-7-4x\\\\7x^2-2x+11-7\\\\\boxed{7x^2-2x+4}[/tex]

Answer:

D. 7x2 - 2x + 4

Step-by-step explanation:

5x2 + 2x + 11 - 7 - 4x +2x2

7x2 + 2x + 11 - 7 - 4x

7x2 - 2x + 11 - 7

7x2 - 2x + 4

Answer:

Total number of ways will be 20

Step-by-step explanation:

We have given three identical green shirts and three identical red shirts

So total number of shirts = 3+3 = 5

We have to distribute these shirts to 6 children so that each children got one shirt

Number of ways will be equal to [tex]=\frac{6!}{3!3!}=20[/tex] ( Here we divide by 3!3! because three green shirts and 3 red shirts are identical )  

Answer:

A.) View Image

B.) Not possible. If you look at the graph,the student must work at the cafe at least 80 hours and at the the market for at least 100 hours to earn the minimum $800 they wanted.

60 hours is below the minimum required time of both place. 90 hours can only satisfy the minimum work hour of one of the place, they need to satisfy the minimum of both places.

In other word, they must work at least 180 hours to earn the $800+ they wanted

Step-by-step explanation:

Set up your equation.

let c be hour worked at cafe and m be hours worked at market.

solve for any of the variable. I solved for c because it looked easier. solving for m will give you the same graph as well.

Graph your equation like usual. Since it's a ≥ sign then you must shade above the line. The shaded part represents the hours that the student can work at both place to earn at least $800

Step-by-step explanation:

A rectangular lot whose perimeter is 260 ft is fenced along three sides. An expensive fencing along the​ lot's length cost $ 18per foot. An inexpensive fencing along the two side widths costs only $ 3per foot.

So we have

         l + 2 w = 260 -------------------eqn 1

And total cost is 1800 $

That is

                18 l + 2 x 3 w = 1800

                 3l + w = 300 -------------------eqn 2

eqn 2 x 2

                 6l + 2w = 600 -------------------eqn 3

eqn 3 - eqn 1

              6l + 2w - l - 2w = 600 - 260

                   5l = 340

                     l = 68 ft

Substituting in eqn 1        

                   68 + 2 w = 260    

                     2w = 192

                       w = 96 ft

Lot's dimension is 68 ft x 96 ft    

Answer:

no. of spjeres=10

radius of those cylinders =2cm

radius of the cylinder in which water is poured=10

rise in water water level =10×2÷10 = 2cm

The rise in water level will be 2 centimeters when spheres are fully immersed in a cylinder.

The volume of a cylinder is defined as the space occupied by the cylinder and the volume of any three-dimensional shape is the space occupied by it.

Ten spheres, each with a radius of 2 cm, are fully immersed in a 10 cm cylinder of water.

As per the given question, we have

The number of spheres = 10

The radius of those cylinders = 2cm

The radius of the cylinder in which water is poured = 10

According to the condition, the required solution would be as:

The rise in water level = 10 × 2 ÷ 10

The rise in water level = 20/10

Apply the division operation, and we get

The rise in water level = 2 cm

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Answer: the answers b i think

Good evening ,

Answer:

The right answer is B.

Step-by-step explanation:

If we apply the Pythagorean theorem we get

the length of the other leg is :

√(70^2-35^2)

= √(3 675)

= 60,621778264911.

:)

Answer:

a)%85,5

b)%92,2

Step-by-step explanation:

a) To determine the probability of getting a hand with at least one face, we need to calculate the probability of the hand without any face firstly.

[tex](36/52)*(35/51)*(34/50)*(33/49)*(32/48)=0,145[/tex]

Then, we need to deduct this value from the probability 1

[tex]1-0,145=0,855[/tex]

The probability of the hand with at least one face is %85,5.

b)To determine the probability of a hand with at least one ace and face we will track the same road again.

[tex](32/52)*(31/51)*(30/50)*(29/49)*(28/48)=0,0775[/tex]

Then, we need to deduct this value from the probability 1

[tex]1-0,0775=0,922[/tex]

The probability of the hand with at least one ace and one face is %92,2.

Answer:

C(x,y,z)=6*x*y+10*x*z+10*y*z

Step-by-step explanation:

Lets assume that x is width, y is length and z is height. To find the area of the top and bottom surfaces we need to simply multiply length and width.

x*y

There is a 2 surface exist (top and bottom) we need to multiply this value with 2 again.

2*x*y

and the cost is 3$ for per square foot and the cost for top and bottom is:

6*x*y$

Surface areas of side surfaces are multiply of width, height and length, height:

x*z+y*z

There are 4 side surfaces exist. Therefore the are need to be multiply with 2.

2*x*z+2*y*z

and the cost is 5$ for per square foot and the cost for side surfaces is:

10*x*z+10*y*z

Total equality for cost is C(x,y,z)=6*x*y+10*x*z+10*y*z

To calculate the cost of materials for a closed rectangular box, use the formulas C(x,y) = 2 * (3xy) for the top and bottom and C(z,y) = 2 * (5zy) for the sides. Then, find the total cost by adding the costs together.

To calculate the cost of materials for a closed rectangular box, we need to consider the dimensions of the box. Let's assume the dimensions are given as x, y, and z in feet.

The cost for the top and bottom parts of the box can be calculated using the formula C(x,y) = 2 * (3xy), where 3 is the cost per square foot and xy is the area of the top and bottom.

The cost for the side parts of the box can be calculated using the formula C(z,y) = 2 * (5zy), where 5 is the cost per square foot and zy is the area of the sides.

Finally, the total cost of materials for the box can be found by adding the costs for the top and bottom parts to the cost of the side parts: C(x,y,z) = C(x,y) + C(z,y).

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I don't know.. can you please explain it?

Answer:

option a is correct , watch explanation

Answer:

There are two factors of the function. You already said the first one, x-5. The second factor is Option A

Hope this helps, comment for any questions. If you like this answer please mark me the brainliest! Thanks!

Answer:

Gilda can send 125 messages in one month.

Step-by-step explanation:

Given,

Total bill of 1 month = $50

Fixed charge of 1 month = $40

Charge of 1 message = 8 cents

∵100 cents = $1

∴8 cents = $0.08

Therefore Charge of 1 message = $0.08

We have to find out the number of messages that Gilda can send in 1 month.

Solution,

Let the total number of messages that Gilda can send in 1 month be 'x'.

Total bill of the month is the sum of fixed charge and charge of 1 message multiplied with total number of messages.

So, framing the above sentence in equation form, we get;

Total bill of 1 month =Fixed charge of 1 month+Charge of 1 message× total number of messages

On substituting the given values, we get;

[tex]40+0.08x=50\\\\0.08x=50-40\\\\0.08x=10\\\\x=\frac{10}{0.08}=125[/tex]

Hence Gilda can send 125 messages in one month.

Answer:

Ron's speed = 3 miles/hour

Stevie's speed = 2.5 miles/hour

On comparing we see Ron is walking faster than Stevie.

Step-by-step explanation:

Given:

Ron takes 10 minutes to walk on a track to cover a distance of 0.5 miles

Stevie takes 6 minutes to walk on a track to cover a distance of 0.25 miles

To find their unit rates in mile per hour and choose the faster one.

Solution:

Unit rate in miles per hour signifies their speeds. Thus, we will find out their speeds.

Ron:

Distance= 0.5 miles

Time = 10 minutes = [tex]10\ min\times \frac{1\ hr}{60\ min}=\frac{1}{6}[/tex] hours

Speed = [tex]\frac{Distance}{Time}=\frac{0.5}{\frac{1}{6}}=0.5\times6=3\ miles/hour[/tex]

Stevie

Distance = 0.25 miles

Time = 6 minutes = [tex]6\ min\times \frac{1\ hr}{60\ min}=\frac{1}{10}[/tex] hours

Speed = [tex]\frac{Distance}{Time}=\frac{0.25}{\frac{1}{10}}=0.25\times10=2.5\ miles/hour[/tex]

Thus, we have

Ron's speed = 3 miles/hour

Stevie's speed = 2.5 miles/hour

On comparing we see Ron is walking faster than Stevie.

Answer:

Step-by-step explanation:

They are not similar.  If they were, ∠LMF and ∠GHF would both have the same angle measure and they do not.

Final answer:

Mathematics question on similar triangles; triangles are similar if they have congruent corresponding angles and proportional sides obtained through AA, SSS, or SAS criterion. A similarity statement describes the correspondence of the vertices.

Explanation:

The question provided falls within the subject of Mathematics, specifically within the study of geometry and the concept of similar triangles. To determine if two triangles are similar, we must check if they have the same shape, which implies that their corresponding angles are equal and their corresponding sides are in proportion. In other words, two triangles are similar if their corresponding angles are congruent and the lengths of their corresponding sides are proportional. This can be verified by angle-angle similarity (AA), side-side-side similarity (SSS), or side-angle-side similarity (SAS). The similarity statement provides the order of correspondence of vertices between similar triangles.

When evaluating if triangles BAO and B1A1O are similar, we must compare their corresponding angles and sides. If the given information indicates that at least two angles of one triangle are congruent to two angles of another triangle (AA criterion), or that the sides are proportional (SSS or SAS criterion), then the triangles are similar. For instance, if ∠BAO ≅ ∠B1A1O and ∠BOA ≅ ∠B1O1A1, then by the AA criterion, the triangles are similar, and we could write the similarity statement as triangle BAO ∼ triangle B1A1O.

Answer:

The value of the quotient is always equal to m

Step-by-step explanation:

The values of m and n are whole numbers greater than 1.

We are given a quotient that is [tex]\frac{\frac{m}{n} }{\frac{1}{n}}[/tex].

In this we have fractions in both numerator and denominator.

The given quotient will be the same if we multiply the numerator with the inverse of the denominator.

So we multiply the numerator [tex]\frac{m}{n}[/tex] with the inverse n.

So the quotient will become = [tex]\frac{m}{n} \times n[/tex] = m

Hence the value of the quotient is always equal to m.

The volume of rectangular prism is 6840 cubic centimeters.

Step-by-step explanation:

Given,

Area of base of rectangular prism= l*w = 360 cubic centimeters

Height of rectangular prism = h = 19 centimeters

Volume of rectangular prism = Length * Width * Height

Volume of rectangular prism = l*w*h

Volume of rectangular prism = [tex]360*19=6840\ cubic\ centimeters[/tex]

The volume of rectangular prism is 6840 cubic centimeters.

Keywords: prism, rectangle

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Answer: The first number is [tex]-10[/tex] and the second number is [tex]4[/tex]

Step-by-step explanation:

Let be "x" the first number and "y" the second number.

The word "Twice" indicates multiplication.

By definition, the sum is the result of an addition.

"is" indicates an equal sign.

Therefore, "Twice the sum of a number and three times the second number is four" can be expressed as:

[tex]2(x+3y)=4[/tex]   [Equation 1]

A difference is the ressult of a subtraction, then " The difference of 10 times the second number and five times the first is 90" can be expressed as:

[tex]10y-5x=90[/tex]   [Equation 2]

To find the numbers:

1. Solve for "x" from the Equation 1:

[tex]2(x+3y)=4\\\\2x+6y=4\\\\x=\frac{4-6y}{2}\\\\x=2-3y[/tex]

2. Substitute this equation into the Equation 2 and solve for "y":

[tex]10y-5(2-3y)=90\\\\10y-10+15y=90\\\\25y=100\\\\y=\frac{100}{25}\\\\y=4[/tex]

3. Substitute the value of "y" into the equation [tex]x=2-3y[/tex] and evaluate:

[tex]x=2-3(4)\\\\x=-10[/tex]

Step-by-step explanation:

987 → 789

987 - 789 = 198

876 → 678

876 - 678 = 198

765 → 567

765 - 567 = 198

654 → 456

654 - 456 = 198

543 → 345

543 - 345 = 198

432 → 234

432 - 234 = 198

321 → 123

321 - 123 = 198

Generally it is always like that:

3 ≤ x ≤ 9

100x + 10(x-1) + (x - 2) → 100(x - 2) + 10(x - 1) + x

(100x + 10(x - 1) + (x - 2)) - (100(x-2) + 10(x-1) + x)

= 100x + 10(x - 1) + (x - 2) - 100(x - 2) - 10(x - 1) - x   cancel 10(x - 1)

= 100x + x - 2 - 100x + 200 - x     cancel 100x and x

= 100 - 2

= 198