The area of the net of the solid figure is 96 square inches
How to determine the area?The image that completes the question is added as an attachment
From the image, we have:
Squares = 6
Length = 4
The area of the net is then calculated as:
Area = Squares * Length^2
This gives
Area = 6 * 4^2
Evaluate
Area = 96
Hence, the area of the net of the solid figure is 96 square inches
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What function is being described Justify each part of your function, explaining how you determined it.
My function has a vertical asymptote at x = -5 and x = 3 , a point discontinuity at x = 2. It has end behavior of f(x) goes to 0 as x goes to negative infinity and f(x) goes to 0 as x goes to positive infinity. The domain is (-inf, -5)U(-5, 2)U(2, 3) U (3,inf).
The end behavior of the function is as x tends to infinity, f(x) tends to zero. It is power function.
What is the end behavior of a polynomial function?The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.
The degree and the leading coefficient of a polynomial function given is determine the end behavior of the graph.
Given that function has a vertical asymptote at x = -5 and x = 3 , a point discontinuity at x = 2.
The end behavior of f(x) goes to 0 as x goes to negative infinity and f(x) goes to 0 as x goes to positive infinity.
The domain is (-inf, -5)U(-5, 2)U(2, 3) U (3,inf).
Hence, we can conclude that the end behavior of the function is as x tends to infinity, f(x) tends to zero.
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Use the limit comparison test to determine whether ∑n=19∞an=∑n=19∞8n3−2n2+196+3n4 converges or diverges.
(a) Choose a series ∑n=19∞bn with terms of the form bn=1np and apply the limit comparison test. Write your answer as a fully simplified fraction. For n≥19,
limn→∞anbn=limn→∞
(b) Evaluate the limit in the previous part. Enter ∞ as infinity and −∞ as -infinity. If the limit does not exist, enter DNE.
limn→∞anbn =
(c) By the limit comparison test, does the series converge, diverge, or is the test inconclusive?
Answer:
Diverges
General Formulas and Concepts:
Algebra I
Exponential Rule [Dividing]: \(\displaystyle \frac{b^m}{b^n} = b^{m - n}\)Calculus
Limits
Limit Rule [Variable Direct Substitution]: \(\displaystyle \lim_{x \to c} x = c\)Series Convergence Tests
P-Series: \(\displaystyle \sum^{\infty}_{n = 1} \frac{1}{n^p}\)Direct Comparison Test (DCT)Limit Comparison Test (LCT): \(\displaystyle \lim_{n \to \infty} \frac{a_n}{b_n}\)Step-by-step explanation:
Step 1: Define
Identify
\(\displaystyle \sum^{\infty}_{n = 19} \frac{8n^3 - 2n^2 + 19}{6 + 3n^4}\)
Step 2: Apply DCT
Define Comparison: \(\displaystyle \displaystyle \sum^{\infty}_{n = 19} \frac{n^3}{n^4}\)[Comparison Sum] Simplify: \(\displaystyle \displaystyle \sum^{\infty}_{n = 19} \frac{1}{n}\)[Comparison Sum] Determine convergence: \(\displaystyle \displaystyle \sum^{\infty}_{n = 19} \frac{1}{n} = \infty , \ \text{div by P-Series}\)Set up inequality comparison: \(\displaystyle\frac{8n^3 - 2n^2 + 19}{6 + 3n^4} \geq \frac{1}{n}\)[Inequality Comparison] Rewrite: \(\displaystyle n(8n^3 - 2n^2 + 19) \geq 6 + 3n^4\)[Inequality Comparison] Simplify: \(\displaystyle 8n^4 - 2n^3 + 19n \geq 6 + 3n^4 \ \checkmark \text{true}\)∴ the sum \(\displaystyle \sum^{\infty}_{n = 19} \frac{8n^3 - 2n^2 + 19}{6 + 3n^4}\) is divergent by DCT.
Step 3: Apply LCT
Define: \(\displaystyle a_n = \frac{8n^3 - 2n^2 + 19}{6 + 3n^4}, \ b_n = \frac{1}{n}\)Substitute in variables [LCT]: \(\displaystyle \lim_{n \to \infty} \frac{8n^3 - 2n^2 + 19}{6 + 3n^4} \cdot n\)Simplify: \(\displaystyle \lim_{n \to \infty} \frac{8n^4 - 2n^3 + 19n}{6 + 3n^4}\)[Limit] Evaluate [Coefficient Power Rule]: \(\displaystyle \lim_{n \to \infty} \frac{8n^4 - 2n^3 + 19n}{6 + 3n^4} = \frac{8}{3}\)∴ Because \(\displaystyle \lim_{n \to \infty} \frac{a_n}{b_n} \neq 0\) and the sum \(\displaystyle \sum^{\infty}_{n = 19} a_n\) diverges by DCT, \(\displaystyle \sum^{\infty}_{n = 19} \frac{8n^3 - 2n^2 + 19}{6 + 3n^4}\) also diverges by LCT.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Convergence Tests (BC Only)
Book: College Calculus 10e
4. A town has a population of 450,000 people. If 60% of the population are under 25 years of age, how many people in the town are 25 years old and over?
Answer: ok so if 60% is under 25 then we can assume 40% is over 25, and then do 40% of 450,000, which is 180,000 .
so we can say that 180,000 people in the town are over 25 years old
A new cream was developed to reduce the irritation caused by poison ivy. To test the effectiveness, researchers put an ad online asking for volunteers to participate in the study. One hundred subjects replied, and they were informed that one group would receive the new cream and the other group would receive a cream with no active ingredient. All 100 subjects were exposed to poison ivy. Fifty were then assigned to the group with the new cream, and 50 were assigned to the group with the cream with no active ingredient. After three days, the subjects’ level of irritation was measured.
Of the 50 subjects that were assigned to the cream with no active ingredient, 15 stated they had less irritation. What is this called?
placebo
control group
placebo effect
placebo control
Answer:
c
Step-by-step explanation:
The effect because of which 15 subjects stated that they had less irritation after having cream with no active ingredient is placebo effect.
What is placebo effect?The placebo effect occurs when a person's physical or mental health appears to improve after receiving a placebo or "dummy" treatment. injections, or even sham surgery.
The placebo effect is caused by an individual's belief in the benefits of the treatment and the expectation that it will make them feel better, rather than by the properties of the placebo.
Given,
50 subjects were assigned to the cream with no active ingredient, 15 stated they had less irritation.
The cream with no active ingredient is placebo, and this effect is called placebo effect.
Hence, 15 subjects stated that they had less irritation is a result of placebo effect.
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can some one answer this plsss
Answer:
D
Step-by-step explanation:
0.2x+5=8
0.2x=3
x=15
Therefore, the correct answer is choice D. Hope this helps!
-2log (6x + 1) = -6.
Bookwork code: N84
Look at the poster below showing the price of pencils in a stationery shop.
Annabel wants to buy exactly 76 pencils. What is the lowest amount she can
pay?
Give your answer in pounds (£).
spar
..
Pencils for sale!
30p each
Pack of 10
pencils for £2
Based on mathematical operations, the lowest amount that Annabel can pay for pencils is $15.20
How is the lowest amount determined?The lowest amount that Annabel can pay for pencils can be determined using the mathematical operations of multiplication and division.
Multiplication and division are two of the four basic mathematical operations, including addition and subtraction.
If Annabel chooses to purchase the first pencil at 30p each, she would pay £22.80 (£0.30 x 76).
If Annabel chooses to purchase the second pencil class of a pack of 10 pencils for £2, she would pay £15.20 [£2 x (76 ÷ 10)].
Pencils for sale
30p each
Pack of 10 pencils for £2
Thus, if Annabel wants to buy the pencils, she can either pay £15.20 or £22.80, but using mathematical operations, the lowest amount she can pay is £15.20.
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2. Mr. Karr resurfaced a sidewalk in the park that was 125.065 meters long. How is this number written in words? one hundred twenty-five and sixty-five hundred thousandths one hundred twenty-five and sixty-five thousandths one hundred twenty-five and sixty-five hundredths D. one hundred twenty-five and sixty-five tenths
Answer:
one hundred twenty-five and sixty-five thousandths
Step-by-step explanation:
The 125 part is simply one hundred twnty five.
The .065 has the 5 in the thousandths place, so it is sixty-five thousandths.
Answer: one hundred twenty-five and sixty-five thousandths
15. Which one of the following is a geometric sequence?
O A. 0, 1, 2, 3,...
O B. 2, -3, 92, -18/4
O C. -7, 10, 23, 36, ...
O D. 8, 4, 2, 1, 1/2, ¹/4....
4 1/8÷2 3/4 convert the mixed numbers to improper fractions
Answer:
Check picture
Step-by-step explanation:
9514 1404 393
Answer:
1 1/2
Step-by-step explanation:
\(\dfrac{4\dfrac{1}{8}}{2\dfrac{3}{4}}=\dfrac{\left(\dfrac{4\cdot8+1}{8}\right)}{\left(\dfrac{2\cdot4+3}{4}\right)}=\dfrac{\left(\dfrac{33}{8}\right)}{\left(\dfrac{11}{4}\right)}=\dfrac{\left(\dfrac{33}{8}\right)}{\left(\dfrac{22}{8}\right)}=\dfrac{33}{22}=\dfrac{3}{2}\)
Then the improper fraction 3/2 can be written as the mixed number 1 1/2.
(4 1/8) / (2 3/4) = 1 1/2
_____
Comment on division of fractions
Fractions can be divided several ways. Two ways that are commonly taught are "invert and multiply", or "match denominators". Here, we have used the second of these methods.
If we were to "invert and multiply", the computation would be ...
(33/8)(4/11) = (33/11)(4/8) = 3(1/2) = 3/2
Instead, we multiplied 11/4 by 2/2 to make it be 22/8, so having a denominator of 8 matching that of the numerator. Then the value of the compound fraction is the ratio of the numerators:
(33/8)/(22/8) = 33/22 = (3/2)(11/11) = 3/2
C The price of milk is believed to increase by 54% over the next 3 years. If 2 gallons of milk costs $2.50 now, what will the price be in 3 years after the increase?
Answer:
The price of 2 gallons of milk will be $3.85 in the next 3 years.
Step-by-step explanation:
So, first, we take the 54% and convert it into 0.54.
Then, we set up this equation: 0.54 x $2.50 = $1.35
Now, $1.35 isn't the answer.
To find the answer, we simply add the $2.50 and the $1.35 to get:
$3.85.
The price of 2 gallons of milk will be $3.85 in the next 3 years.
Mike is overdrawn at the bank by $18. His sister has $23 more than him. How much does
Mike's sister have?
Answer:
$41?
Step-by-step explanation:
Well, if he's overdrawn, then he doesn't have any money, he owes money. But I'm assuming they want to add. The sister has $23 more than he does, so add.
18+23=41.
So his sister has $41.
--
hope it helps
Answer:
The answer will be $41.
Step-by-step explanation:
The answer is 41 because Mike has $18 and his sister has $23 more dollars than him. More = addition. You will add the money Mike has and the amount more than his sister has. When you add it, the answer will turn out to be $41.
Hope that helps! If you somehow get it wrong, please tell me so I could look over my work!! Thanks and have a great rest of your day :) !
Answer ALL the questions, SHOW ALL YOUR WORK. Explain your answers when necessary. Answer ALL questions
in complete sentences.
1. Anthony rode his bike 141 miles in 3 weeks, riding the same distance each week. Malique rode his bloycle 165
miles in 5 weeks, riding the same distance each week. Which statement correctly compares the number of miles per
week they rode?
a. Anthony rode 47 more miles per week than Malique.
b. Malique rode 33 more miles per week than Anthony
c. Malique rode 12 more miles per week than Anthony
d. Anthony rode 14 more miles per week than Malique.
Answer:
d. Anthony rode 14 more miles per week than Malique.
Step-by-step explanation:
Anthony rode (141 mi)/(3 wk) = 47 mi/wk.
Malique rode (165 mi)/(5 wk) = 33 mi/wk.
Anthony rode more miles per week by ...
(47 -33) mi/wk = 14 mi/wk
Anthony rode 14 more miles per week than Malique.
Every 2 centimeters on a floor plan represents
meters of the house. The dining room is 8 cm by
10 cm on the floor plan, and the bedroom is 6cm by10cm on the floor plan. If installing tile costs $34
per square meter and installing carpet costs $21 per
square meter, how much would it cost to install tile
in the dining room and install carpet in the bedroom?
Show your work.
Given statement solution is :- It would cost $680 to install tile in the dining room and $315 to install carpet in the bedroom.
To find the cost of installing tile in the dining room and carpet in the bedroom, we need to calculate the areas of both rooms first.
Given:
Every 2 centimeters on the floor plan represents 1 meter of the house.
Dining Room:
On the floor plan, the dining room is 8 cm by 10 cm.
Converting this to meters, the dimensions of the dining room are 8 cm / 2 = 4 meters by 10 cm / 2 = 5 meters.
The area of the dining room is 4 meters * 5 meters = 20 square meters.
Bedroom:
On the floor plan, the bedroom is 6 cm by 10 cm.
Converting this to meters, the dimensions of the bedroom are 6 cm / 2 = 3 meters by 10 cm / 2 = 5 meters.
The area of the bedroom is 3 meters * 5 meters = 15 square meters.
Now, let's calculate the costs.
Cost of Tile:
The cost of installing tile is $34 per square meter.
The area of the dining room is 20 square meters.
Therefore, the cost of installing tile in the dining room is 20 square meters * $34/square meter = $680.
Cost of Carpet:
The cost of installing carpet is $21 per square meter.
The area of the bedroom is 15 square meters.
Therefore, the cost of installing carpet in the bedroom is 15 square meters * $21/square meter = $315.
Therefore, it would cost $680 to install tile in the dining room and $315 to install carpet in the bedroom.
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In a right-angled triangle the ratio of the two smaller angles is 3:2. Find the sizes of each of the angles.
Answer:
36° , 54° , 90°
Step-by-step explanation:
since the triangle is right then one angle is 90°
the ratio of the smaller angles = 3 : 2 = 3x : 2x ( x is a multiplier )
the sum of the 3 angles in the triangle is 180° , that is
3x + 2x + 90 = 180
5x + 90 = 180 ( subtract 90 from both sides )
5x = 90 ( divide both sides by 5 )
x = 18
Then
3x = 3 × 18 = 54°
2x = 2 × 18 = 36°
the 3 angles measure 36° , 54° , 90°
A snail crawled 3/4 inches in 1/5 of a minute how many inches can a snail crawl in 1 minute
Answer:
a
Step-by-step explanation:
the number greater that 714,587
Answer:
714
Step-by-step explanation:
587,714 they arrange in orderly form
A number greater than 714,587 is 714,588
How to determine the number greater than 714,587?The complete question is added as an attachment
From the attached figure, we have:
Passengers = 714,587
Numbers greater than 714,587 would have a value greater than 714,587
This is represented as:
x > 714,587
The above inequality represents numbers greater than 714,587
An example of such number is 714,588
Hence, a number greater than 714,587 is 714,588
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Evaluate the piecewise function
The solution of the composite function fog(x) = 3x + 3 at x > 2.
What is composite function?Let the two function f(x) and g(x) generate a new function h(x) using an operation.
The operation is composition of functions and h(x) is a composite function.
We have three piecewise function.
First we have to show that,
the composite function,
fog(x) at x > 2.
For that,
g(x) at x > 2 is,
g(x) = 3x.
Now, f(g(x)),
= f(3x)
= 3x + 3 at x > 2.
Therefore, the function is fog(x) = 3x + 3.
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The complete question:
Find the fog(x) at x > 2
Human hair grows an average of 0.7 cm in 2 weeks. How much does it grow in 52 weeks? Round to the nearest tenth
Answer:
18.2 cm
Step-by-step explanation:
Explain how the reaction time and the reaction rate compare to the temperature of the water and the reactants. Revisit your hypothesis from part A, and explain how it compares to your experimental results.
Reaction rate and reaction time are inversely proportional to each other.
Reaction time and reaction rateReaction rate and reaction time are two intertwined concepts. Reaction rate refers to how quickly or slowly a reaction occurs while reaction rate refers to the time taken for a particular reaction to occur.
If the reaction rate increases, the reaction time decreases, if the reaction rate decreases, the reaction time increases hence the both quantities are inversely proportional to each other.
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Li deposited $17,500 into a bank account that earned simple interest each year. After 2 years, he had earned $2975 in interest. No money was deposited into or withdrawn from the account.
What was the annual interest rate?
Enter your answer in the box.
Li's annual interest rate is 8.5%
We know that ,I=Prt.
First, we have to find the interest / I. In the question is asked: '' he had earned $2975 in interest" so we know that the Interest/ I is $2,975.
$2,975= $17,500/P*r*2/t in years (Substitute)
$2,975= 35,000r (Multiply)
$2,975/35,000= $35,000r/$35,000 (Divide each side by $35,000)
$2,975/$35,000=0.085
Covert the decimal 0.085 to a percent.
To do so multiply the decimal by 100 0.085*100= 8.5, add the percent sign and you got the answer 8.5%
Li's annual interest rate is 8.5% (we were finding the rate/r)
Hence , Li's annual interest rate is 8.5% .
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Please help I'll give 100 points to whoever is correct
Answer:
110.5 yd²
Formula's:
Area of triangle:
1/2 × base × height
Area of rectangle:
length × width
Area of the figure:
= area of triangle + area of rectangle's
= 1/2 × 11 × 7 + 3 × 4 + 5 × 3 + 5 × 2 + 7 × 5
= 110.5 yd²
Answer:
110.5 yd²
Step-by-step explanation:
Separate the figure into 1 triangle and 3 rectangles.
(see attached image)
Area 1
Area of a triangle = 1/2 × base × height
= 1/2 × (7 + 2 + 2) × 7
= 1/2 × 11 × 7
= 38.5 yd²
Area 2
Area of a rectangle = width × length
= 3 × (5 + 2 + 2)
= 3 × 9
= 27 yd²
Area 3
Area of a rectangle = width × length
= 5 × (5 + 2)
= 5 × 7
= 35 yd²
Area 4
Area of a rectangle = width × length
= 2 × 5
= 10 yd²
Total Area
Area 1 + Area 2 + Area 3 + Area 2 = 38.5 + 27 + 35 + 10
= 110.5 yd²
Mr. Evans is currently 4 times as old as his son, Dan. If Mr. Evans was 46 years old 2 years ago, how old is Dan now?
Answer:
the son age is 13band Evans age is 52 years old at present day
Dan is 12 years old.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
let the Age of Dan is x years
Mr. Evans Age = 4x
If Mr. Evans was 46 years old 2 years ago
The, Present age of Mr. Evans = 48 years
So, Dan's Age = 48/4
= 12 years.
Hence, Dan is 12 years old.
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Coach Walker has a cooler that can hold 5 gallons of a sports drink. He fills
2
with the sports drink to bring to football practice.
of the cooler
b. How many players can fill their water bottles with the sports drink before the cooler is
empty?
[1 gallon = 8 pints]
Each water bottle can hold 1 1/2
The number of players that can fill their bottle is 13
What is word problem?A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math.
A cooler can have 5 gallons
1 gallon = 8pints
2 gallons = 2 × 10 = 20pints
a water bottle for each player can hold 1 1/2 pints = 3/2 pints
Therefore the number of bottles in 80 pints = 20÷3/2
= 20 × 2/3
= 40/3 = 13 1/3 bottles
therefore 13 players will be able to fill their bottles before the cooler get empty
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Explain the difference between an indefinite integral and a definite integral.
A) An indefinite integral, after evaluating it at the limits of integration, results in a particular number. A definite integral results in a set of functions that share the same derivative and uses an arbitrary constant of integration.
B) A definite integral, after evaluating it at the limits of integration, results in a particular number. An indefinite integral results in a set of functions that share the same derivative and uses an arbitrary constant of integration.
C) An indefinte integral cannot always be integrated analytically and may require numeric integration, while it is always possible to integrate a definite integral. Definite integrals always return a real number after evaluation at its limits of integration.
D) A definite integral is defined and continuous over the interval of integration and has finite limits of integration. An indefinite integral is also defined and continuous over the interval of integration, but may have as a limit of integration.
The answer is A.
An indefinite integral is a function that, when differentiated, equals the original function. It is denoted by ∫f(x)dx, where f(x) is the function to be integrated. An indefinite integral always has an arbitrary constant of integration, which is denoted by C. This is because the derivative of any constant is zero, so the derivative of ∫f(x)dx+C is still equal to f(x).
A definite integral is the limit of a Riemann sum as the number of terms tends to infinity. It is denoted by ∫
a
b
f(x)dx, where a and b are the limits of integration. A definite integral does not have an arbitrary constant of integration, because the limits of integration specify a unique value for the integral.
In other words, an indefinite integral is a family of functions that share the same derivative, while a definite integral is a single number.
What is the difference of
5
6
−
5
12
? Use the fraction strip to help.
One whole fraction strip is equal to six one-sixth fraction strips. It is also equal to twelve one-twelfth fraction strips.
A.
0
B.
5
12
C.
7
12
D.
5
6
The difference of 5/6 - 5/12 is 5/12..
What is a fraction?A fraction consisting of a quotient and a remainder is a mixed fraction. we can convert the mixed fraction to an improper fraction by first dividing the numerator by the denominator and then taking the quotient as whole number and the remainder as the numerator of the proper fraction keeping the denominator same.
In this question, we need to apply real algebra properties to find the result of a basic operation between two fractions, whose procedure is shown below:
Given
5/6 - 5/12
Now multiply by 2 in fraction 5/6
10/12 - 5/12
5/12
The difference is 5/12.
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A straight highway is 100 miles long, and each mile is marked by a milepost numbered from 0 to 100. A rest area is going to be built along the highway exactly 7 miles away from milepost 58. If m is the milepost number of the rest area, which of the following equations represents the possible locations for the rest area?
Answer:
Step-by-step explanation:
The milepost number of the rest area is 7 miles away from milepost 58, so it can be represented by the equation:
m = 58 + 7
This equation states that the milepost number of the rest area is equal to 58 plus 7, or 65. Therefore, the rest area can be located at milepost 65.
there's 20 points for both problems if you could please solve this
What is the solution for 2x + y =12 x = 9 - 2y
Answer:
x=5 and y=2
Step-by-step explanation:
I hope this helps
help me please i would appreciate it so so much
Answer:
w = 120
x = 60
y = 120
z = 60
Step-by-step explanation:
w = 120 (vertically opposite angles)
sum of co interior angles is 180
⇒ w + x = 180 and x + y = 180
w + x = 180
⇒ 120 + x = 180
⇒ x = 180 - 120
⇒ x = 60
x + y = 180
⇒ 60 + y = 180
⇒ y = 180 - 60
⇒ y = 120
z = x (corresponding angles)
z = 60