Answer:
Step-by-step explanation: You start by subtracting the original price from the new price.
Which is $42 from $33.60
$42-$33.60=$8.40
So $8.40 is your discount rate.
Part C
Now you will attempt to copy your original triangle using only two of its sides and the included angle:
Using point E as the center, draw a circle with a radius equal to the length of
, which you calculated in part B.
Using point E as the vertex and
as one side of the angle, create an angle that is equal to the measure of
. Draw ray
.
Locate the intersection of the ray and the circle, and label the point F.
Complete
by drawing a polygon through points D, E, and F.
Take a screenshot of your results, save it, and insert the image below.
Here no figure just go through the definition.
What is a polygon?A polygon is a two-dimensional geometric shape that is defined as a closed figure with straight sides. It is made up of line segments that connect at endpoints called vertices. The term polygon comes from the Greek words "poly" meaning many and "gonia" meaning angle, indicating that polygons have many angles.
Polygons can have different numbers of sides, with the most basic being a triangle, which has three sides and three angles. Other examples of polygons include squares, rectangles, pentagons, hexagons, and octagons. The sides of a polygon do not have to be equal in length or the angles between them do not have to be the same, but they must be straight lines and the polygon must be closed.
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After responding to the prompt, we can deduce that in order to circle and finish the copied triangle, a polygon should be drawn through the coordinates D, E, and F.
What is a polygon?The definition of a polygon, a two-dimensional geometric form, is a closed figure with straight sides. It consists of line segments joined at ends known as vertices. The word "polygon," which means "many angles," is derived from the Greek terms "poly," which means "many," and "gonia," which means "angle."
A triangle is the most basic polygon because it has three edges and three angles. Polygons can have various amounts of sides. Squares, rectangles, pentagons, hexagons, and octagons are additional instances of polygons. In order for a polygon to be considered closed, all of its sides must be straight lines, regardless of whether their lengths or angles are equivalent.
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Homework Progress 19 / 22 Marks Four different sized jerry cans are shown below. A holds 30 litres Write the missing fractions as simply as possible. The first one is done for you. Can D holds of the amount can C holds. Can C holds of the amount can A holds. Can D holds B holds 18 litres of the amount can B holds. Can B holds C holds 6 litres holds 3 litre of the amount can A holds. Answer
The fraction shows that can d holds 1/2 of the amount can c holds.
Can c holds 1/5 of the amount can a holds.
Can d holds 1/6 of the amount can b holds.
Can b holds 1/5 of the amount can a holds.
How to explain the fractionCan d holds 1/2 of the amount can c holds. This is because can d holds 3 litres and can c holds 6 litres, so if you divide the volume of can d (3 litres) by the volume of can c (6 litres), you get 3/6 or 1/2.
Can c holds 1/5 of the amount can a holds. Can c holds 6 litres and can a holds 30 litres, so if you divide the volume of can c (6 litres) by the volume of can a (30 litres), you get 6/30 or 1/5.
Can d holds 1/6 of the amount can b holds: This is because can d holds 3 litres and can b holds 18 litres, so if you divide the volume of can d (3 litres) by the volume of can b (18 litres), you get 3/18 or 1/6.
Can b holds 1/5 of the amount can a holds: This is because can b holds 18 litres and can a holds 30 litres, so if you divide the volume of can b (18 litres) by the volume of can a (30 litres), you get 18/30 which can be simplified as 3/5 or 1/5.
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A student mows lawns on the weekends. It takes him 120 min to mow 4 lawns. What prediction can you make about the time he will spend this weekend if he has 12 lawns to mow?
It will take him 30 hours to mow 12 lawns.
It will take him 9 hours to mow 12 lawns.
It will take him 6 hours to mow 12 lawns.
It will take him 3 hours to mow 12 lawns.
Answer: It will take him 6 hours
Step-by-step explanation: 4 lawns = 120 min
1 lawn = 30 min
12 lawn = 360 min = 6 hours
To mow 12 lawns, the student will spend 6 hours.
Explanation:To predict the time the student will spend mowing 12 lawns, we can use the information given in the question. The student takes 120 minutes to mow 4 lawns. We can calculate the time the student will take to mow 1 lawn by dividing 120 minutes by 4, which equals 30 minutes per lawn. Since the student has 12 lawns to mow, we multiply 30 minutes by 12 to get the total time. The student will spend 360 minutes, or 6 hours, mowing 12 lawns.
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4 feet 4 inch into inch.
Answer:
52 inches
Step-by-step explanation:
1 foot=12 inches
4(12)=48 inches
Then you add the other 4 inches.
48+4=52
52 inches
The quadratic regression corresponding to the number of birds f(x) in a park relative to the number of people x in the same park is given by f(x) = -0.1536x² + 3.3915x +88.738. Use the quadratic regression to estimate the number of people in the park when there are 80 birds. Round your answer to the nearest whole number. en is Provide your answer below: people An
The quadratic regression function f(x) = -0.1536x² + 3.3915x + 88.738, then estimate value for the number of people in the park when there are 80 birds is equals to the 24.
A quadratic regression is the process of finding the equation of the parabola that best fits a set of data. An equation of the form, y = ax² + bx + c where a≠0. We have a quadratic regression function is defined by f(x) = -0.1536x² + 3.3915x +88.738 --(1), where, f(x) = the number of birds in a park relative to the number of people x in the same park. We have to determine quadratic regression to estimate the number of people in the park when there are 80 birds. Now, f(x) = 80, substitute the known value in equation (1),
=> 80 = -0.1536x² + 3.3915x +88.738
=>0.1536x²- 3.3915x -88.738 + 80 = 0
=> 0.1536x²- 3.3915x - 8.738 = 0
=> x² - 22.08x - 56.88 = 0 --(2)
Using the quadratic formula for solution of (2), x = (-b ±√b² - 4ac)/2a, for ax² + bx + c = 0. So, [tex]x =\frac{ -(-22.08) ± \sqrt{(22.08)² + 4× 56.88}}{2}[/tex]
=> x = 24.41 or - 2.3331
but number of people can't be negative hence, the required value is 24.41 ~ 24.
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A contestant on a game show has a 1 in 6 chance of winning for each try at a certain game. Which probability models can be used to simulate the contestant’s chances of winning??
Select ALL of the models that can be used to simulate this event.
A) a fair six-sided number cube
B) a fair coin
C) a spinner with 7 equal sections
D) a spinner with 6 equal sections.
E) a bag of 12 black chips and 60 red chips.
The probability models that represents a probability of winning of 1/6 are given as follows:
A) a fair six-sided number cube.
D) a spinner with 6 equal sections.
E) a bag of 12 black chips and 60 red chips.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
For this problem, we want a probability of 1/6 of winning each trial, hence the events are given as follows:
A) a fair six-sided number cube. -> One out of the six numbers is equivalent to winning.
D) a spinner with 6 equal sections. -> One out of the six regions is equivalent to winning.
E) a bag of 12 black chips and 60 red chips. -> 12/(12 + 60) = 12/72 = 1/6.
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Pls help! I don't know what to do!!
14. The length of AB for the given right-angled triangle is [tex]$24{\sqrt{2}}$[/tex].
15. The value of base GF is √247 or 15.716234
What are Heights and Distances in trigonometry?The ideas of angles, right triangles, and the trigonometric functions of sine, cosine, and tangent are used in trigonometry to calculate heights and distances.
It is possible to determine the height of an object or the distance between two objects by measuring the angle of elevation or depression between the observer's line of sight and the object being observed and the distance between them. These ideas are frequently applied in the engineering, navigation, and surveying industries.
14. In a right-angled triangle, if one angle is 45 degrees, then the other acute angle is also 45 degrees and hence,
Let AB = x
Using the trigonometric ratio for the 45 degree angle in the triangle:
tan(45) = opposite/adjacent
We know that the opposite side is BC = [tex]$24{\sqrt{2}}$[/tex] and the adjacent side is AB = x.
tan(45) = BC/AB
1 = [tex]$24{\sqrt{2}}/x$[/tex]
x = [tex]$24{\sqrt{2}}$[/tex]
15. Using Pythagoras theorem:
HF² = HG² + GF²
16² = 3² + GF²
GF² = 16² - 3²
GF² = 256 − 9
GF² = 247
GF = √247
GF = 15.716234
Thus, The value of base GF is √247 or 15.716234
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If 7 men can finish a work in 84 days , then 12 men can finish the same work in 96 days. True / False?
Answer:
false
Step-by-step explanation:
if there r more men working then it will take less time to finish the same work not more
Decompose the composite figure to find its total area.
Answer:
152 in²
Step-by-step explanation:
Area of rectangle = L x W
1st rectangle area
10 x 8 = 80 in²
2nd rectangle area
Length = 20 - 8 = 12 in
12 x 6 = 72 in²
Total area
80 + 72 = 152 sq. in
So, the answer is 152 in²
Ruby wants to find the height of the tallest building in her city. She stands 190 feet away from the building. There is a tree 31 feet in front of her, which she knows is 20 feet tall. How tall is the building? (Round to the nearest foot.)
To solve this problem, we can use similar triangles. Let's call the height of the building "h". Then, we have two similar triangles: one formed by Ruby, the tree, and the top of the tree; and the other formed by Ruby, the building, and the top of the building.
We know that the height of the tree is 20 feet, and the distance from the tree to Ruby is 31 feet. We also know that the distance from Ruby to the building is 190 feet.
Using these values, we can set up a proportion:
h / (190 + 31) = 20 / 31
Simplifying the proportion, we get:
h / 221 = 20 / 31
Multiplying both sides by 221, we get:
h = (20 / 31) * 221
h ≈ 143.23
Therefore, the height of the building is approximately 143 feet. Rounded to the nearest foot, the height of the building is 143 feet.
A survey of eighty students at a certain college reveals that
36 takes english
32 take history
32 take political science
16 takes political science and history
16 takes history and English
14 takes political science and English
6 takes all three
How many students offer only English
By set theοry the number οf students whο οffer οnly English is 12.
What is Set theοry?In mathematics Set theοry studies with sets, which can be infοrmally described as cοllectiοns οf οbjects. Objects οf any kind can be cοllected intο a set, set theοry, as a branch οf mathematics, is mοstly cοncerned with that which are relevant tο mathematics as a whοle.
Given that,
A survey οf eighty students at a certain cοllege reveals that
36 takes English
32 take histοry
32 take pοlitical science
16 takes pοlitical science and histοry
16 takes histοry and English
14 takes pοlitical science and English
6 takes all three
Sο n(s)=80 [ Since the number οf students is 80]
The number οf students whο takes English is denοted by n(E)=36
The number οf students whο takes Histοry is denοted by n(H)=32
The number οf students whο takes Pοlitical Science is denοted by n(P)=32
By set theοry
The number οf students whο takes Pοlitical Science and Histοry is denοted by n(P∩H)=16
The number οf students whο takes English and Histοry is denοted by n(E∩H)=16
The number οf students whο takes Pοlitical Science and English is denοted by n(P∩E)=14
The number οf students whο takes Pοlitical Science, English and Histοry is denοted by n(P∩E∩H)=6
Frοm set theοry ,
n(P∪E∪H) = n(E)+n(H)+n(P)- n(P∩H)-n(H∩E)-n(P∩E)+n(P∩E∩H)
= 36+32+32-16-16-14+6
= 60
Sο the number οf students whο take nοne οf the subjects is (80-60)=20
Hence the number οf students whο οffer οnly English is 12.
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What is the least common denominator of the fractions in the sum 1/8 + 1/9?
This means that the lowest goal (LCD) is 72 and that the total of 1/8 and 1/9 stated with one common denominator = 72 is 17/72.
What or who is a denominator?The denominator of a fraction, which represents many spaced evenly out parts are utilized to split an object, is the smallest amount inside the fraction. The fraction is divided by it. The denominator in this situation is 4, suggesting there are four parts altogether.
The fractions mentioned have 8 and 9 as their denominators. Multiples of 8 include 8, 16, 24, 32, 40, 48, 56, 64, 72, and 80, while multiples of 9 include 9, 18, 27, 36, 45, 54, 63, 72, and 81.
It is evident that 72 will be the first common number of 8 and 9. Hence, for 1/8 and 1/9, its least common factor (LCD) is 72.
We must express every fraction with denominator 72 in order to sum the fraction with a common denominator:
1/8 Equals 9/72 (with multiplying both the numerator and the denominator by 9)
1/9 Equals 8/72 (with multiplying both the denominator and the numerator by 8)
We can now combine the fractions:
1/8 plus 1/9 = 9/72 plus 8/72
= 17/72
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Decompose the composite figure to find its total area.
Answer: 36 m^2
Step-by-step explanation: I got it correct trust btw can i get brsainliest
How many 4-letter code symbols can be formed with the letters P, D, Q, X
without repetition?
Algebra 2
After answering the presented question, we can conclude that As an expression result, there are 24 4-letter code symbols that may be constructed without duplication using the letters P, D, Q, and X.
what is expression ?
An expression in mathematics is a collection of representations, digits, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a combination of the two can be used as an expression. Mathematical operators include addition, subtraction, rapid spread, division, and exponentiation. Expressions are often used in arithmetic, mathematics, and form. They are employed in the representation of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.
We may use the method for permutations of n items taken r at a time to compute the number of 4-letter code symbols that can be created with the letters P, D, Q, X without repetition:
n! / (n-r)! P(n,r) = n!
where n denotes the number of items (in this example, four letters) and r the number of things taken at once (in this case, 4).
Thus far, we have:
P(4,4) = 4! / (4-4)! = 4! / 0! = 4 x 3 x 2 x 1 / 1 = 24
Hence, As a result, there are 24 4-letter code symbols that may be constructed without duplication using the letters P, D, Q, and X.
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Complete question:
How many 4-letter code symbols can be formed with the letters P, D, Q, and X without repetition?
a machine in a factory makes 2 1/4 pounds of nails in 1 1/2 hours. At what rate in pounds
per hour does the machine makes nails?
Answer:
a machine in a factory makes 2 1/4 pounds of nails in 1 1/2 hours. At what rate in pounds
per hour does the machine makes nails?
wholesale 575.00
marked up 40%
List price?
The drop down options are “greater than”, “less than”, and “equal to”
The length of FG is equal to the length of F'G'.
The perimeter of pentagon CDEFG is equal to the perimeter of pentagon C'D'E'F'G.
What are the properties of a translated shape?The properties of a translated shape are the shape and size of the translated shape are the same as that of the original shape. The orientation of the translated shape is the same as that of the original shape. The distance between the corresponding points of the translated shape and the original shape is constant.
The area and perimeter of the translated shape are the same as that of the original shape. The interior angles of the translated shape are the same as that of the original shape. The coordinates of the vertices of the translated shape are obtained by adding a constant value to the corresponding coordinates of the vertices of the original shape.
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Image transcribed:
Pentagon CDEFG is translated 7 units up and 5 units left, resulting in pentagon C'D'E'F'G' (not shown).
Part A
Select from the drop-down menu to correctly complete this sentence:
The length of FG is ___ the length of F'G'.
Part B
The perimeter of pentagon CDEFG is ____ the perimeter of pentagon C'D'EF'G.
(CO 3) A bottle of water is supposed to have 20 ounces. The bottling company has determined that 96% of bottles have the correct amount. Which of the following describes a binomial experiment that would determine the probability that a case of 36 bottles has all bottles properly filled?
Group of answer choices
a. n=0, p=36, x=98
b. n=20, p=0.98, x=36
c. n=36, p=0.96, x=36
d. n=36, p=0.98, x=1
The parameter to describes a binomial experiment that would determine the probability that a case of 36 bottles has all bottles properly filled is x = 36, p = 0.96 and n = 36. So, the right choice for answer is option (c).
A binomial experiment is an experiment using a fixed number of independent trials with only two outcomes. These experiments'outcomes are defined as either success or failure. The following requirements for experiment are :
Each fixed trial performed in the experiment had only two possible outcomes. One result will be marked as a success and the other as a failure.The probability of success in each trial must remain the same for each trial conducted. It is represented by p.Each trial in the experiment must be independent of the other trials.Water Quantity in a bottle = 20 ounces
According to bottling company, the percentage of bottle with correct amount = 96% = 0.96
so, probability of success, p = 0.96
Probability for 36 bottles has all bottles properly filled, that is x = 36. Now, looking the all choice, we conclude option(c) is correct choice.
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PLEASE GUYS HELP!!
Solve 2(x + 3) = 18
Answer:
[tex]\mathrm{x=6}[/tex]Step-by-step explanation:
[tex]\mathrm{2\left(x+3\right)=18}[/tex]
Divide both sides by 2:-
[tex]\mathrm{\cfrac{2\left(x+3\right)}{2}=\cfrac{18}{2}}[/tex]
Simplify:-
[tex]\mathrm{x+3=\cfrac{18}{2} }[/tex]
[tex]\mathrm{x+3=9}[/tex]
Subtract 3 from both sides:-
[tex]\mathrm{x+3-3=9-3}[/tex]
[tex]\mathrm{x=6}[/tex]
_____________________
Hope this helps!
50 POINTS!!!!! PLEASE HELP ASAP
Example of the Disjunctive Syllogism?
Premise:
Premise:
Conclusion:
disjunctive syllogism = p v q, ~ p / q
example: he wants to be on either the football or wrestling team. he's not on the wrestling team. therefore, he's on the football team.
It was incorrect. A=80-B, C=70-B.
(80-b) +b+(70-b)=100. Therefore:
80-70-b=100
B= - 90. Negative number,
So, A=170
C=160. Correct answer
The values of A, B, and C are 30, 50, and 20, respectively.
What is the sum?
The sum is the result of adding two or more numbers together. The sum is found by performing the operation of addition, which involves combining the values of two or more quantities to find the total or the sum.
If A = 80 - B and C = 70 - B, and the sum of A, B, and C is 100, then we can write:
A + B + C = 100
Substituting A and C with their given values, we get:
(80 - B) + B + (70 - B) = 100
Simplifying and combining like terms, we get:
150 - B = 100
Subtracting 150 from both sides, we get:
-B = -50
Dividing both sides by -1, we get:
B = 50
Now that we know B = 50, we can substitute this value back into the equations for A and C:
A = 80 - B = 80 - 50 = 30
C = 70 - B = 70 - 50 = 20
Therefore, the values of A, B, and C are 30, 50, and 20, respectively.
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A
,
B
and
C
form a triangle where
∠
B
A
C
=
90
∘
.
A
B
=
14.7
mm and
B
C
=
25.9
mm.
Find the length of
A
C
, giving your answer rounded to 1 decimal place.
To find the length of AC, we can use the Pythagorean theorem, which states that in a right triangle. the length of AC is approximately [tex]29.8 mm[/tex].
What is the square of the length of the hypotenuse?the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, we can use AC as the hypotenuse, so:
[tex]AC^2 = AB^2 + BC^2[/tex]
[tex]AC^2 = (14.7 mm)^2 + (25.9 mm)^2[/tex]
[tex]AC^2 = 216.09 mm^2 + 671.61 mm^2[/tex]
[tex]AC^2 = 887.7 mm^2[/tex]
Taking the square root of both sides, we get:
[tex]AC = \sqrt887.7 mm[/tex]
[tex]AC \approx 29.8 mm[/tex] (rounded to 1 decimal place)
Therefore, the length of AC is approximately [tex]29.8 mm[/tex].
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Trey purchases 200 shares of Turner stock for per share. Trey pays in cash to complete the purchase. One year later, Trey sells the stock for per share. Part 2 Calculate the return that Trey earned on his investment of .
Answer: Formula
Step-by-step explanation:
Stocks x per share = return
Trey's return on investment, if the stock paid no dividends during the year, is 14.29%.
We have,
Purchase price per share: $50
Number of shares purchased: 200
Total purchase cost (excluding loan interest):
Purchase price per share * Number of shares purchased
= $50 * 200
= $10,000
Loan amount: $5,000
Loan interest rate: 10%
Interest paid on the loan:
Loan amount * Interest rate
= $5,000 * 10%
= $500
Total purchase cost (including loan interest):
Total purchase cost + Loan interest
= $10,000 + $500
= $10,500
Selling price per share: $60
Total revenue from selling the stock:
Selling price per share * Number of shares sold
= $60 * 200
= $12,000
Return on investment (ROI):
(Total revenue - Total purchase cost) / Total purchase cost
ROI = ($12,000 - $10,500) / $10,500
Simplifying the expression:
ROI = $1,500 / $10,500
ROI = 0.1429 (approximately)
To express the ROI as a percentage:
ROI as a percentage = 0.1429 * 100 = 14.29%
Therefore,
Trey's return on investment, if the stock paid no dividends during the year, is 14.29%.
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The complete question:
Trey purchases 200 shares of Turner stock for $50 per share.
Trey pays $5,000 in cash and borrows $5,000 from his broker at 10 percent interest to complete the purchase.
One year later, Trey sells the stock for $60 per share.
Trey's return, if the stock paid no dividends during the year, is?
Find the value of z such that 0.6318 of the area lies between −z and z. Round your answer to two decimal places.
A standard normal distribution table or a calculator again, we can find that the z-score that corresponds to this area is approximately 0.42.
Describe Standard Normal Distribution?The standard normal distribution is useful because it allows us to calculate probabilities for any normal distribution by converting the distribution to a standard normal distribution using a process called standardization. Standardization involves subtracting the mean of the distribution from each observation and then dividing by the standard deviation. The resulting values are called z-scores, and they represent the number of standard deviations that an observation is from the mean of the distribution.
Assuming a standard normal distribution, we know that 0.5 of the area lies between -z and z, since the normal distribution is symmetric around the mean. Therefore, we need to find the value of z such that the area between -z and z is 0.6318 - 0.5 = 0.1318.
Using a standard normal distribution table or a calculator, we can find that the area between the mean and z is 0.5 + 0.1318/2 = 0.5659. Therefore, the z-score that corresponds to this area is approximately 0.18.
Since the distribution is symmetric, the area between -z and z is twice the area between the mean and z, so we can solve for z:
0.1318/2 = 0.0659 of the area lies between the mean and z
Using a standard normal distribution table or a calculator again, we can find that the z-score that corresponds to this area is approximately 0.42.
Therefore, z = 0.42 rounded to two decimal places.
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Calculate
√4.7² +2.55
Give your answer to 1 significant figure
Answer: 3.53
Step-by-step
True or False. A hypothesis is a speculation.
Justify your answer.
Find the surface area of the rectangular prism below:
3m
2m
2.4 m
- 2.4 m
3 m
The surface area of the rectangular prism is 72 square meters.
Describe Rectangular Prism?A rectangular prism, also known as a rectangular parallelepiped, is a three-dimensional figure that consists of six rectangular faces. It is a polyhedron with two identical and parallel bases, which are rectangles, and four rectangular lateral faces. The height of the prism is the perpendicular distance between the two bases. The volume of a rectangular prism is given by the formula V = l × w × h, where l, w, and h are the length, width, and height of the prism, respectively. The surface area of a rectangular prism is given by the formula SA = 2lw + 2lh + 2wh, where l, w, and h have the same meanings as in the volume formula. Rectangular prisms are commonly encountered in everyday life, such as in the shape of boxes, rooms, and buildings.
The surface area of a rectangular prism can be found by adding up the area of all its faces.
Area of blue rectangles:
= 2 x (length x width)
= 2 x (2.4m x 2m)
= 9.6m²
Area of green rectangles:
= 2 x (length x width)
= 2 x (2.4m x 3m)
= 14.4m²
Area of yellow rectangles:
= 2 x (length x width)
= 2 x (2m x 3m)
= 12m²
Total surface area = sum of all face areas
= (2 x blue rectangles) + (2 x green rectangles) + (2 x yellow rectangles)
= 2(9.6m²) + 2(14.4m²) + 2(12m²)
= 19.2m² + 28.8m² + 24m²
= 72m²
Therefore, the surface area of the rectangular prism is 72 square meters.
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Can someone help me with this please,thanksss
Answer:
gradient= rise \ run
and cuz line is coming downward
it will be negative
so your answer is
- 5\6
Can someone pls help me its delta really annoying
The cost per boxed lunch is $9.46.
For each of the indefinite integrals below, choose which of the following substitutions would be most helpful in evaluating the integral. Enter the appropriate letter (A,B, or C) in each blank. DO NOT EVALUATE THE INTEGRALS.
The substitutions that would be most helpful in evaluating the integral are:
1. C (x = 8 secθ)
2. B (x = 8 sinθ)
3. A (x = 8 tanθ)
4. B (x = 8 sinθ)
5. A (x = 8 tanθ)
What are the substitutions that are most helpful?For problem 1, the substitution x = 8 secθ will be useful because it will transform the integral into a form that can be solved using the substitution u = tanθ.
For problem 2, the substitution x = 8 sinθ will be useful because it will transform the expression inside the integral into a trigonometric function that can be integrated using standard techniques.
For problem 3, the substitution x = 8 tanθ will be useful because it will transform the expression inside the integral into a form that can be solved using integration by parts.
For problem 4, the substitution x = 8 sinθ will be useful because it will transform the expression inside the integral into a form that can be solved using the substitution u = cosθ.
For problem 5, the substitution x = 8 tanθ will be useful because it will transform the expression inside the integral into a form that can be solved using the substitution u = secθ.
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