Answer:
1) [tex]31 < p<37[/tex]
For this case the values that satisfy the inequality are: 32,33,34,35,36
And we can analyze one by one the number:
[tex] a=32= 16*2[/tex] so then is a composite number because 2>1 and 16>1
[tex] a=33= 11*3[/tex] so then is a composite number because 3>1 and 11>1
[tex] a=34= 17*2[/tex] so then is a composite number because 2>1 and 17>1
[tex] a=35= 7*5[/tex] so then is a composite number because 7>1 and 5>1
[tex] a=36= 6*6[/tex] so then is a composite number because 6>1 and 6>1
So then part 1 is correct and we can see that the statement is enough or sufficient all the values on 31<P<37 are composite numbers.
2) For this cas this statement is FALSE, since we have a counterexample on this case:
[tex]a=3=1*3[/tex] and 3 is not a composite number since 1 is not >1
And since we have one element that not satisfy the condition that's FALSE.
Step-by-step explanation:
For this question we need to use the following definition "If an integer p can b expressed as the product of two integers, each of which that is greater then 1, then the integer p can be considered as a composite number". And this number is not the same as prime number.
Part 1
[tex]31 < p<37[/tex]
For this case the values that satisfy the inequality are: 32,33,34,35,36
And we can analyze one by one the number:
[tex] a=32= 16*2[/tex] so then is a composite number because 2>1 and 16>1
[tex] a=33= 11*3[/tex] so then is a composite number because 3>1 and 11>1
[tex] a=34= 17*2[/tex] so then is a composite number because 2>1 and 17>1
[tex] a=35= 7*5[/tex] so then is a composite number because 7>1 and 5>1
[tex] a=36= 6*6[/tex] so then is a composite number because 6>1 and 6>1
So then part 1 is correct and we can see that the statement is enough or sufficient all the values on 31<P<37 are composite numbers.
Part 2
For this cas this statement is FALSE, since we have a counterexample on this case:
[tex]a=3=1*3[/tex] and 3 is not a composite number since 1 is not >1
And since we have one element that not satisfy the condition that's FALSE.
Maggie can paint a fence in 9 hours, but Tom needs 12 hours to paint the same fence. How long does it take them to paint the fence if they work together? Round to the nearest tenth.
Working together, Maggie and Tom can paint the fence in 5.1 hours
Solution:Given that,
Maggie can paint a fence in 9 hours
So in 1 hour maggie paints, [tex]\frac{1}{9}[/tex] of the house
Tom needs 12 hours to paint the same fence
So in 1 hour, tom can paint [tex]\frac{1}{12}[/tex] of the house
To find: time taken to paint the fence if they work together
Let "a" be the time taken to paint the fence if they work together
So working together, in 1 hour, they can paint [tex]\frac{1}{a}[/tex] of the house
We can frame a equation as:
To see how much of the fence they can paint together in one hour, we add these together.
[tex]\frac{1}{9} + \frac{1}{12} = \frac{1}{a}[/tex]
[tex]\frac{1}{a}[/tex] is how much of the fence they can paint together in one hour. Therefore "a" is the number of hours it will take them both to paint the fence
On solving,
[tex]\frac{12 + 9}{12 \times 9} = \frac{1}{a}\\\\\frac{1}{a} = \frac{21}{108}\\\\a = \frac{108}{21} = 5.1428[/tex]
So working together, Maggie and Tom can paint the fence in 5.1 hours
HELP ASAP!!! BRAINLIEST!
its a b and c they all equal 45
Answer:
1 * 45
5 * 9
3 * 15
Hope this helps!
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The manufacturerâs suggested retail price (MSRP) of a certain item is $60. Store A sells the item for 20 percent more than the MSRP. The regular price of the item at Store B is 30 percent more than the MSRP, but the item is currently on sale for 10 percent less than the regular price. If sales tax is 5 percent of the purchase price at both stores, what is the result when the total cost of the item at Store B is subtracted from the total cost of the item at Store A?A. $0B. $0.63C. $1.80D. $1.89E. $2.10
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.
In how many different ways can 3 identical green shirts and 3 identical red shirts be distributed among 6 children such that each child receives a shirt
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 )
State if the triangles in each pair of similar. If so, State how you know they are similar and complete the similarity statement.
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.
Yesterday Nadia consumed 250 grams of carbohydrate, 75 grams of protein, and 60 grams of fat. What percentage of Calories of her day's intake came from fat?
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%.
An egg farm packages 264 total cartons of eggs each month.The farm has three different sizes of cartons.The small carton holds 8 eggs,and 1/6 of the total cartons are small.TThe medium carton holds 12 eggs and 2/3 of the total Cardinals are medium to large carton holds 18 eggs and the rest of the total clients are large determine how many of each size of the curtain is needed each month then determine how many eggs are needed to fill the 264 cartons show your work or explain your answers
I don't know.. can you please explain it?
Ron walks 0.5 mile on a track in 10 minutes. Stevie walks 0.25 mile on the track in 6 minutes find the unit rate for each walker in miles per hour. Who is faster?
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.
Office Furniture Makers, Inc. uses machines to produce high quality office chairs for other firms. The initial cost of one customized machine is $750,000. This machine costs $12,000 a year to operate. Each machine has a life of 3 years before it is replaced. What is the equivalent annual cost of this machine if the required return is 10 percent? (Round your answer to whole dollars.)
The equivalent annual cost of the machine, considering a 10% return, is approximately $309,535 per year.
Explanation: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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At the price of $3 a pound of pork, Jason buys 8 pounds of pork and Noelle buys 10 pounds of pork. When the price rises to $5 a pound, Jason buys 5 pounds of pork and Noelle buys 7 pounds of pork. What is the market demand at $5?
Answer:
Market demand at $5 is 12 pork.
Step-by-step explanation:
In a market, the sum of individual demand for a product from buyers is known as market demand.
It is give that the at the price of $3 a pound of pork, Jason buys 8 pounds of pork and Noelle buys 10 pounds of pork.
So, market demand at $3 is
8 + 10 = 18
When the price rises to $5 a pound, Jason buys 5 pounds of pork and Noelle buys 7 pounds of pork.
So, market demand at $5 is
5 + 7 = 12
Therefore, the market demand at $5 is 12 pork.
Statistical hypothesis testing allows you to: a.Estimate the standard deviation of your sample distribution b.Use sample statistics to make decisions about population parameters c.Eliminate all potential errors in your research d.Use non-probability samples to make inferences about a population
Answer:
Option B) Use sample statistics to make decisions about population parameters
Step-by-step explanation:
Statistical hypothesis testing
Hypothesis testing is a statistical method that is used in making statistical decisions using a sample that is taken from the population. Statistical hypothesis testing is basically an assumption that we make about the population parameter. with the help of sample statistic.Calculations are performed on samples to gather more information about the population.This helps us to know that the particular sample belongs or does not belong to the population and estimate the parameters of the population with the help of this claim.Probability sampling involves random selection from the population and non-probability sampling relies on the selection based on judgement of the researcher.Thus, Option B) Use sample statistics to make decisions about population parameters is the correct answer.
Mary read 42 pages of a book on Monday she read 2/5 of the book on Tuesday if she still had 1/4 of the book to read how many pages are there in the book
Answer: 120 pages
Step-by-step explanation:
42 p on Monday
2/5x on Tuesday
1/4x rest of book
---------------------------------------------------
42+2/5x+1/4x=x
42*20 +8x+5x=20x
840=20x-8x-5x
840=7x
x=840/7
x=120
The required number of pages in the book is given as 120 pages.
Given that,
Mary read 42 pages of a book on Monday she read 2/5 of the book on Tuesday if she still had 1/4 of the book to read how many pages are there in the book is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
here,
let the number of pages in the book be x,
According to the question,
x - 42 - 2/5x = 1/4x
x - 2/5x - 1/4x = 42
x[1 - 2/5 - 1/4] = 42
x[20 - 8 - 5] / 20 = 42
x [7] / 20 = 42
x = 6 × 20
x = 120 pages
Thus, the required number of pages in the book is given as 120 pages.
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A rectangular prism has these dimensions. The area of the base of the prism is 360 square centimeters The height of the prism is 19 centimeters What is the volume, in cubic centimeters, of the rectangular prism?
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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A rectangular lot whose perimeter is 260 ftis 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. The total cost of the fencing along the three sides comes to $ 1800.What are the lot's dimensions?
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
Calculate the simple interest paid on a loan of $544 at 3% for three months.
$48.96
$4.80
$4.90
$4.08
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
Ten spheres each with radius of 2 cm are fully immersed in a cylinder of water with radius 10 cm. find the rise in water level
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.
What is the volume of 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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Twice The sum of a number and three times the second number is four. The difference of 10 times the second number And five times the first is 90 find the numbers
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]
State the postulate or theorem you would use to prove each pair of triangles congruent.
If the triangles cannot be proved congruent, choose "Not Possible."
Answer:
Not possible
Step-by-step explanation:
The only information we are given are the pairs of angles that are congruent which is not enough information to prove that they are congruent
The triangles cannot be proved congruent by AAA postulates. Then the correct option is D which is not possible.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
The two triangles are congruent if two sides are as well and the angle (angle between any of these two sides) among one triangle is congruent to the comparable two sides as well as the angle of a second triangle.
The triangles cannot be proved congruent by AAA postulates. Then the correct option is D which is not possible.
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A right triangle has a hypotenuse of 70 feet and a leg of 35 feet. What is the length of the other leg? A. 51 feet B. 61 feet C. 78 feet D. 80 feet
URGENT!!!!!
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.
:)
can someone help me right now!!!
Which of the following is a solution to this inequality?
y less than two thirds times x plus 2
(0, 3)
(−3, 1)
(3, 5)
(1, 2)
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).
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If (x − 5) is a factor of the polynomial function f(x) = 3x^2 − 23x + 40, which of the following is another factor?
A. (3x − 8)
B. (3x + 8)
C. (8x − 3)
D. (8x + 3)
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
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A bicycle moves approximately 7 feet with each revolution of the wheels. If the bicycle wheels are making 30 revolutions per minute, approximately how many feet will the bicycle travel in 1 hour?
Answer:
[tex]12,600\ ft[/tex]
Step-by-step explanation:
step 1
Find out the number of revolutions in one hour
we know that
The bicycle wheels are making 30 revolutions per minute
One hour are 60 minutes
so
using proportion
[tex]\frac{30}{1}\ \frac{rev}{min}=\frac{x}{60}\ \frac{rev}{min}\\\\x=60(30)\\\\x=1,800\ rev[/tex]
step 2
Find out how many feet the bicycle will travel in one hour
we know that
A bicycle moves approximately 7 feet with each revolution and the number of revolutions in one hour is 1,800
so
Multiply the number of revolutions in one hour (1,800 rev) by 7 feet
[tex](1,800)7=12,600\ ft[/tex]
A lazy high school senior types up application and envelopes to and different colleges, but puts the applications randomly into the envelopes. What is the expected number of applications that went to the right college?
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.
Explanation: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.
A fly trapped inside a cubical box with side length 1 meter decides to relieve its boredom by visiting each corner of the box. It will begin and end in the same corner and visit each of the other corners exactly once. To get from a corner to any other corner, it will either fly or crawl in a straight line. What is the maximum possible length, in meters, of its path?
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
Find a formula C(x,y,z) that gives the cost of materials for a closed rectangular box, with dimensions in feet. Assume that the material for the top and bottom costs $3 per square foot and the material for the sides costs $5 per square foot. Show all work in steps clearly.
Answer:
C(x,y,z)=6*x*y+10*x*z+10*y*z
Step-by-step explanation:
Lets assume that x is width, y is length and z is height. To find the area of the top and bottom surfaces we need to simply multiply length and width.
x*y
There is a 2 surface exist (top and bottom) we need to multiply this value with 2 again.
2*x*y
and the cost is 3$ 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.
Explanation: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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Complete the statement to describe the expression (a+b)(d+e)(a+b)(d+e)left parenthesis, a, plus, b, right parenthesis, left parenthesis, d, plus, e, right parenthesis. The expression consists of factors, and each factor contains 4 terms.
Final answer:
To complete the statement describing the expression (a+b)(d+e)(a+b)(d+e), we expand it by multiplying each term. Simplifying the expression, we get a²*d² + 2a²de + 2abde + b²e².
Explanation:
To complete the statement describing the expression (a+b)(d+e)(a+b)(d+e), we need to expand it. This can be done by multiplying each term in the first factor by each term in the second factor and then multiplying the result by the third factor. So the expression becomes:
(a+b)(d+e)(a+b)(d+e) = (a*d + a*e + b*d + b*e)(a*d + a*e + b*d + b*e)
We can simplify this further by combining like terms:
(a*d + a*e + b*d + b*e)(a*d + a*e + b*d + b*e) = a²*d² + 2a²de + 2abde + b²e²
What is the total interest earned in two years on an account containing $500 at 3.5% interest, compounded annually?
$35.61
$35.16
$35.00
$36.51
Answer: Compound interest is $36.61
Step-by-step explanation:
Initial amount deposited into the account is $500 This means that the principal,
P = 500
It was compounded annually. This means that it was compounded once in a year. So
n = 1
The rate at which the principal was compounded is 3.5%. So
r = 3.5/100 = 0.035
It was compounded for 2 years. So
t = 2
The formula for compound interest is
A = P(1+r/n)^nt
A = total amount in the account at the end of t years. Therefore
A = 500 (1+0.035/1)^1×2
A = 500(1.035)^2 = $535.61
Compound interest = 535.6 - 500 = $35.61
why is it that when you take the squre root of a function that is squared you get an absolute value?
Answer and explanation :
When we square any number then its gives absolute value for example even when we square the negative numbers it will given positive , that is absolute value
So we can conclude that square of any number is absolute number
And then is we take square root of that absolute number it will always positive and absolute
A man flies a kite at a height of 15 ft. The wind is carrying the kite horizontally from the man at a rate of 5 ft./s. How fast must he let out the string when the kite is flying on 32 ft. of string?
Answer:
4.4 ft/s
Step-by-step explanation:
Height = 15ft
Rate= 5 ft/s
Distance from the man to the kite= 32ft
dh/dt = 5 ft/s
h = √32^2 - 15^2
h = √ 1025 - 225
h = √800
h = 28.28ft
D = √15^2 + h^2
dD/dt = 1/2(15^2 + h^2)^-1/2 (2h) dh/dt
= h(225 + h^2)^-1/2 dh/dt
= (h / √225 + h^2)5
= (28.28 / √225 + 28.28^2)5
= (28.28 / √1024.7584)5
= (28.28/32)5
= 0.88*5
= 4.4 ft/s
Let alpha and beta be conjugate complex numbers such that frac{\alpha}{\beta^2} is a real number and alpha - \beta| = 2 \sqrt{3}. Find alpha.
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.