Answers
Answer:
5.80^3
Related Questions
A boat is heading towards a lighthouse, whose beacon-light is 108 feet above the water. From point AA, the boat’s crew measures the angle of elevation to the beacon, 8^{\circ}
∘
, before they draw closer. They measure the angle of elevation a second time from point BB at some later time to be 16^{\circ}
∘
. Find the distance from point AA to point BB. Round your answer to the nearest foot if necessary.
Answers
Using the slope concept, it is found that the distance from point A to point B is of 392 feet.
What is a slope?The slope is given by the vertical change divided by the horizontal change.It's also the tangent of the angle of depression.At point A:
The vertical change is of 108.The horizontal change is the position \(x_A\), that we want to find.The angle is of 8º.Hence:
\(\tan{8^\circ} = \frac{108}{x_A}\)
\(x_A = \frac{108}{\tan{8^\circ}}\)
\(x_A = 768.6\)
At point B:
The vertical change is of 108.The horizontal change is the position \(x_B\), that we want to find.The angle is of 16º.Hence:
\(\tan{16^\circ} = \frac{108}{x_B}\)
\(x_B = \frac{108}{\tan{16^\circ}}\)
\(x_B = 376.6\)
Then, the distance is:
\(d = x_A - x_B = 768.6 - 376.6 = 392\)
The distance from point A to point B is of 392 feet.
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what is m1?
a. 42°
b. 48°
c. 96°
d. 138°
Answers
Answer:
b if im not wrong ;-;''
Step-by-step explanation:
Answer:
the answer is a sorry if b it wrong
Compute the linear correlation coefficient between the two variables and determine whether a linear relation exists. Round to three decimal places. A manager wishes to determine whether there is a relationship between the number of years her sales representatives have been with the company and their average monthly sales. The table shows the years of service for each of her sales representatives and their average monthly sales (in thousands of dollars). r = 0.717; a linear relation exists r = 0.632; a linear relation exists r= 0.632; no linear relation exists r= 0.717; no linear relation exists
Answers
The linear correlation coefficient between the number of years of service and average monthly sales is r = 0.717, indicating that a linear relation exists between these variables.
The linear correlation coefficient, denoted as r, measures the strength and direction of the linear relationship between two variables. It ranges between -1 and 1, where a value close to 1 indicates a strong positive linear relationship, a value close to -1 indicates a strong negative linear relationship, and a value close to 0 indicates a weak or no linear relationship.
In this case, the given correlation coefficient is r = 0.717, which is moderately close to 1. This indicates a positive linear relationship between the number of years of service and average monthly sales. The positive sign indicates that as the number of years of service increases, the average monthly sales tend to increase as well.
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Before you can multiply two matrices together, the number of ___ in the first matrix must equal the number of rows in the second matrix.
Answers
Before you can multiply two matrices together, the number of columns in the first matrix must equal the number of rows in the second matrix.
What is the short definition of the Matrix?
Matrix, a collection of numbers lined up in rows and columns to create a rectangular array. The elements of the matrix, also known as the entries, are the integers. In addition to many areas of mathematics, matrices are widely used in the fields of engineering, physics, economics, and statistics.It is called so because it has only one row, and the order of a row matrix will hence be 1 × n.The number of rows in the second matrix must be equal to the number of columns in the first matrix for matrix multiplication to be defined.
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hown to mutiply fractions
Answers
Answer:
The first step when multiplying fractions is to multiply the two numerators. The second step is to multiply the two denominators. Finally, simplify the new fractions. The fractions can also be simplified before multiplying by factoring out common factors in the numerator and denominator.
You’re welcome:)
A certain car's windshield wiper has a total length of 22 inches. As the wiper pivots it clears a sector with a central angle of 120 degrees. If only 18 inches of the wiper cleans the windshield, what is the area (in exact form) of the windshield that is wiped during each swing? 468π inches squared 156π inches squared 160π inches squared 108π inches squared
Answers
Answer: 108π inches squared
Step-by-step explanation:
Formula : Area of sector = \(\dfrac{\theta}{360^{\circ}}\times\pi r^2\)
where , r= radius and \(\theta =\)
Given : A certain car's windshield wiper has a total length of 22 inches. As the wiper pivots it clears a sector with a central angle of 120 degrees.
If only 18 inches of the wiper cleans the windshield, then we take radius of the range of wiper cleaining = 18 inches
The area of the windshield that is wiped during each swing = Area of the sector made by wiper of with a central angle of 120 degrees.
\(=\dfrac{120}{360}\times\pi (18)^2\\\\=\dfrac{18^2}{3}\pi=\dfrac{18\times6}{1}\pi=108\p\text{ inches}^2\)
Hence, the area (in exact form) of the windshield that is wiped during each swing is 108π inches squared.
Convert the number 1681 in base 10 to Roman numerals. Convert the Roman numeral DLXXI to base 10. Note: You can earn partial credit on this problem. Find the sum of the first 20 terms of the arithmetic sequence {0,2,4,6,8,…}. Ahmad has
3
1
of his cash at home and
5
1
of it in his locker at school. The rest of it, which is 49 dollars, he has with him in his wallet. How much cash in total does Ahmad have? Answer (in dollars):
Answers
In conclusion, the number 1681 in base 10 is represented by the Roman numeral MDCLXXXI. The Roman numeral DLXXI is equivalent to 561 in base 10. The sum of the first 20 terms of the arithmetic sequence {0,2,4,6,8,…} is 460. Ahmad has a total of $272.22 in cash.
To convert the number 1681 in base 10 to Roman numerals, we can break it down. The largest Roman numeral that divides evenly into 1681 is M, which represents 1000. So we have M + 681. The next largest Roman numeral that divides evenly into 681 is D, which represents 500.
So we have MD + 181. The largest Roman numeral that divides evenly into 181 is CL, which represents 150. So we have MDCL + 31. The largest Roman numeral that divides evenly into 31 is XXX, which represents 30.
So we have MDCLXXX + 1.
Finally, we have I, which represents 1.
Putting it all together, the number 1681 in base 10 is represented by the Roman numeral MDCLXXXI.
To convert the Roman numeral DLXXI to base 10, we break it down. D represents 500, L represents 50, X represents 10, and I represents 1.
So, we have 500 + 50 + 10 + 1 = 561.
To find the sum of the first 20 terms of the arithmetic sequence {0,2,4,6,8,…}, we can use the formula for the sum of an arithmetic sequence:
Sn = (n/2)(a1 + an),
where Sn is the sum, n is the number of terms, a1 is the first term, and an is the last term.
In this case,
n = 20, a1 = 0, and an = 8 + (20-1)2 = 8 + 19(2) = 8 + 38 = 46.
Plugging in these values, we get
Sn = (20/2)(0 + 46) = 10(46) = 460.
To calculate how much cash Ahmad has, we add up the amounts he has at home, in his locker, and in his wallet. We know that he has 31% of his cash at home and 51% in his locker. Let's call the total amount of cash he has x.
So, he has 0.31x at home and 0.51x in his locker.
Adding these amounts to the $49 he has in his wallet, we have 0.31x + 0.51x + $49 = x.
Simplifying this equation, we have 0.82x + $49 = x.
Subtracting 0.82x from both sides, we get
$49 = 0.18x. Dividing both sides by 0.18, we find x = $49/0.18 = $272.22.
So, Ahmad has a total of $272.22 in cash.
In conclusion, the number 1681 in base 10 is represented by the Roman numeral MDCLXXXI. The Roman numeral DLXXI is equivalent to 561 in base 10. The sum of the first 20 terms of the arithmetic sequence {0,2,4,6,8,…} is 460. Ahmad has a total of $272.22 in cash.
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the alexander family and the chen family each used their sprinklers last summer. the water output rate for the alexander family's sprinkler was 30l per hour. the water output rate for the chen family's sprinkler was 40l per hour. the families used their sprinklers for a combined total of 65 hours, resulting in a total water output of 2250l. how long was each sprinkler used?
Answers
The Alexander family used their sprinkler for 35 hours, and the Chen family used their sprinkler for 30 hours.
To find out how long each sprinkler was used, we can set up a system of equations. Let's say the Alexander family used their sprinkler for x hours, and the Chen family used their sprinkler for y hours.
From the given information, we know that the water output rate for the Alexander family's sprinkler is 30 liters per hour. Therefore, the total water output from their sprinkler is 30x liters.
Similarly, the water output rate for the Chen family's sprinkler is 40 liters per hour, resulting in a total water output of 40y liters.
Since the combined total water output from both sprinklers is 2250 liters, we can set up the equation 30x + 40y = 2250.
We also know that the families used their sprinklers for a combined total of 65 hours, so we can set up the equation x + y = 65.
Now we can solve this system of equations to find the values of x and y, which represent the number of hours each sprinkler was used.
By solving the equation we get,
The Alexander family used their sprinkler for 35 hours, and the Chen family used their sprinkler for 30 hours.
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russell has many dogs in his backyard. which expression below represents the number of dogs he has in his backyard if there are n legs?
Answers
We can say that the total number of dogs in Russell's backyard is equal to n divided by 4, where n is the total number of legs.
"Russell has many dogs in his backyard.
Let's suppose there are x dogs in Russell's backyard. We know that each dog has four legs. As a result, the total number of legs for x dogs will be 4x.
There are n legs in total, according to the problem. This equation can be written as:4x = nNow, let's divide both sides of the equation by 4 to solve for x:x = n/4
Thus, the expression representing the number of dogs Russell has in his backyard if there are n legs is x = n/4.
The Let's suppose there are x dogs in Russell's backyard.
We know that each dog has four legs. As a result, the total number of legs for x dogs will be 4x.There are n legs in total, according to the problem.
This equation can be written as:4x = nNow, let's divide both sides of the equation by 4 to solve for x:x = n/4
Thus, the expression representing the number of dogs Russell has in his backyard if there are n legs is x = n/4.
To summarize, we can say that the total number of dogs in Russell's backyard is equal to n divided by 4, where n is the total number of legs.
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3. On Bob's 10th birthday, his grandmother invested $1,500 in an account * 21
that was locked into a 12.5% interest rate, compounded quarterly. Will he
have enough for a $2500 down payment for his first car on his 16th
birthday?
Answers
Answer: not sure. but as long as he saves his money wisely and doesn't spend frivilously
Step-by-step explanation:
it takes 20 drops of rain to make one milliliter. How many drops would it take to fill a 40-gallon rain barrel?
Answers
Using unit conversion, it is obtained that it would take approximately 3,028,328 drops to fill a 40-gallon rain barrel.
What is unit conversion?
Unit conversion is a process with multiple steps that involves multiplication or division by a numerical factor or, particularly a conversion factor. The process may also require selection of the correct number of significant digits, and rounding.
Use the method of unit conversion.
First, we need to convert 40 gallons to milliliters, since we know the conversion rate of drops to milliliters.
We can use the following conversion factors -
1 gallon = 3,785.41 milliliters (exact)
1 gallon = 3,785,410 drops (since 20 drops = 1 milliliter)
So, 40 gallons is -
40 × 3,785.41 = 151,416.4 milliliters
To find how many drops it would take to fill this amount of space, use operation of multiplication.
Multiply the milliliters by the conversion factor -
151,416.4 × 20 = 3,028,328 drops
Therefore, the value is obtained as 3,028,328 drops.
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Round 25.395 to the nearest hundredths.
Answers
Answer:
25.40
Step-by-step explanation:
Answer:
25.40
Step-by-step explanation:
5 rounds up but 9 rounds up to ten so you add one to the tenths
tially 960m apart and are approaching each other at speeds of 50 m/s and 30 m/s relative to the road. Car B honks its horn, sending a packet of sound traveling at 340 m/s relative to the road towards Car A. The sound wave will bounce off either car and instantaneously keep traveling at 340 m/s relative to the road forwards or backwards at all times. (Note: Many parts of this problem do not require the previous part's solution to solve it) a) (4 points) Find
v
AB
b) (5 points) How long after the horn is sounded until the two cars have collided? c) (4 points) How far will the sound wave have travelled (distance) in that time? d) (7 points) What is Δ
s
Sound
, the displacement of the sound during that time?
Answers
Given data ; Initial distance between cars, d = 960m Speed of Car A, vA = 50 m/sSpeed of Car B, vB = 30 m/sSpeed of sound, vS = 340 m/s
Let's solve the parts given in the question;
a) Find vAB; Relative speed, \(vAB = vA + vBvAB = 50 m/s + 30 m/svAB = 80 m/s\)
b)Let t be the time until the two cars collide.In time t, the distance traveled by Car A = vA0t
The distance traveled by Car B = vBt
The total distance covered by both cars is d:
Therefore, \(vAt + vBt = dd/t = (vA + vB)t = 960 mt = d / (vA + vB)t = 960 / 80t = 12 s\)
Let ΔsSound be the displacement of the sound during that time.
Distance traveled by Car \(A = vA x t = 50 m/s x 12 s = 600 mDistance traveled by Car B = vB x t = 30 m/s x 12 s = 360 m\)
Therefore, the distance between the cars will be \(960 - (600 + 360) = 0 m.\) So, the sound wave will have traveled the displacement of 4080 m from Car B to Car A.
Hence, ΔsSound = 4080 m.
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For a pancake distribution of sin(a), where a = 0, determine the ratio of the average flux for e > 45 to the omnidirectional flux. What I need from here is:Directional Flux, Omnidirectional Flux,Directional Solid Angle, Omnidirectional Solid Angle. Then: Find the Flux per Solid Angle (For both the directional and omnidirectional cases) And find the ratio of those two
Answers
For the ratio of the average flux for e > 45 degrees to the omnidirectional flux, we divide the flux per solid angle for the directional case by the flux per solid angle for the omnidirectional case.
To find the ratio of the average flux for e > 45 degrees to the omnidirectional flux in a pancake distribution of sin(a) where a = 0, we need to calculate the directional flux, omnidirectional flux, directional solid angle, and omnidirectional solid angle.
Directional Flux:
The directional flux is the flux within a specific direction or range of angles. In this case, we are interested in e > 45 degrees.
Omnidirectional Flux:
The omnidirectional flux is the total flux in all directions or over the entire solid angle.
Directional Solid Angle:
The directional solid angle is the solid angle subtended by the specified direction or range of angles. In this case, it would be the solid angle corresponding to e > 45 degrees.
Omnidirectional Solid Angle:
The omnidirectional solid angle is the total solid angle subtended by all possible directions or over the entire sphere.
To find the flux per solid angle for both the directional and omnidirectional cases, we can use the formula:
Flux per Solid Angle = Total Flux / Solid Angle
Finally, to find the ratio of the average flux for e > 45 degrees to the omnidirectional flux, we divide the flux per solid angle for the directional case by the flux per solid angle for the omnidirectional case.
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xcel Online Structured Activity: Required annuilty payments Your father is 50 years old and will retire in 10 years. He expects to live for 25 years after he retires, until he is 85. He wants a fixed retirement income that has the same purchasing power at the time he retires as $50,000 has today. (The real value of his retirement income will decline annually after he retires.) His retirement income will begin the day he retires, 10 years from today, at which time he will receive 24 additional annual payments. Annual inflation is expected to be 5%. He currently has $140,000 saved, and he expects to earn 8% annually on his savings. The data has been collected in the Microsoft Excel Online file below. Open the spreadsheet and perform the required analysis to answer the question below. Open spreadsheet How much must he save during each of the next 10 years (end-of-year deposits) to meet his retirement goal? Do not round your intermediate calculations. Round your answer to the nearest cent.
Answers
The amount that must be saved by him during each of the next 10 years (end-of-year deposits) to meet his retirement goal is $5,280.33 (rounded to the nearest cent).
From the question above, Required retirement income at the time of his retirement = $50,000
Annual inflation rate = 5%
Expected period of receiving payments after retirement = 25 years
Number of annual payments after retirement = 24
The number of years before he retires = 10
Total present value of the annuity = 50,000 / (1 + 0.05)²⁵= $15,144.16
The future value of the annuity at the end of the 25 years period= $15,144.16 x (1 + 0.05)²⁵= $50,000.00
Therefore, the annual payment (PMT) that will allow the present value of the annuity to be $15,144.16 is:
PMT = (0.08)($15,144.16) / (1 - (1 + 0.08)-24)= $1,131.38
Therefore, the total amount that he should save for the next 10 years can be calculated using the Future Value (FV) formula.
FV = PV x (1 + r)n + PMT × [(1 + r)n - 1] / r
Where, PV = the present value of the savings
PMT = the annual payment
r = the interest rate per year (same as the expected annual return on his savings) = 8%
n = the number of years
The total amount of savings required would be:
FV = $0 (he doesn't have any savings now)
PV = -$15,144.16 (since he will need to pay this amount at retirement)
PMT = -$1,131.38r = 8%n = 10 years
FV = 0, PV = -15,144.16, PMT = -1,131.38, r = 8%, n = 10 years
Therefore, the end-of-year deposit (PMT) that he needs to make for the next 10 years to meet his retirement goal is $5,280.33.
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Identify the domain of the function shown in the graph.
Answers
Answer:
C
Step-by-step explanation:
Domain is what x values are allowed in a function
There are 4 yellow, 3 blue, 5 green, 7 red and 2 orange sweets in my bag.
3.1.1 What is the probability of taking out a red sweet? Show all your steps.
3.1.2 What is the probability of taking out a green, blue, or orange sweet? Show all your steps.
please help quick writing test
Answers
Answer:
1/3 ; 10/21
Step-by-step explanation:
total sweets = 4+3+5+7+2 = 21
3.1.1
7/21 = (7:7)/(21:7) = 1/3
3.1.2
(5+3+2)/21
10/21
In Freeport, Illinois, Empire Street runs east to west and route 26 runs north to south.
Zippy’s Pizza parlor is located on route 26, 3 miles south of Empire street.
Zippy’s advertises that it delivers within a 4 mile radius.
Write an equation that represents the radius of delivery for Zippy’s Pizza. Assume that Zippy’s is located at the origin.
- How far east and west from route 26 can you live on Empire street and still receive Zippy’s Pizza delivery?
- Little Cubs Field is located 2 miles west and 4 miles north of Zippy’s. How far is Little Cubs Field from Zippy’s?
- How far is Little Cubs Field from the radius of delivery?
Answers
The area to which Zippy's Pizza makes delivery is 16·π square miles
The responses are;
First Part: x² + y² = 4²Second Part: √5 miles east and √5 miles west from route 26Third Part: 2·√5 milesFourth Part: 2·(√5 - 2) milesReasons:
The radius of the area that Zippy delivers pizza = 4 miles
Direction in which Empire Street runs = East to west
Direction of the route 26 route = North to south
Location of Zippy's Pizza parlor = 3 miles south of Empire street
-First Part:
The equation that represents the radius of delivery for Zippy's Pizza is given by the equation of a circle as follows;
(x - h)²+ (y - k) = r²
Where:
(h, k) = The center of the circle which is the location of Zippy's Pizza
r = The radius of the circle
Zippy's Pizza is at the center of the circular area with coordinates (h, k) = (0, 0)
r = 4 miles
-Which gives;
(x - 0)² + (y - 0)² = 4²
The equation that represent the radius is; x² + y² = 4²
-Second part:
The locations of addresses on Empire street, relative to Zippy's Pizza are given by the equation;
y = 3
Therefore, we have;
The furthest distances east and west on Empire street that can receive Zippy's Pizza delivery are given by the equation;
x² + 3² = 4²
x = √(4² - 3²) = ±√5
The furthest distances that can receive Zippy's Pizza delivery are ±√5 miles (east and west) from route 26
-Third Part:
Location of Little Cubs = 2 miles west and 4 miles north of Zippy's
The distance from Little Cubs Field to Zippy's = √((2² + 4²) = 2·√5
The distance from Little Cubs Field to Zippy's = 2·√5 miles
-Fourth Part:
The distance between Little Cubs Field from Zippy's radius of delivery, d, is found as follows;
d = 2·√5 - 4 = 2·(√5 - 2)
Therefore, d = 2·(√5 - 2) miles
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After making inquiries about credit granting policies, an auditor selects a sample of sales transactions and examines evidence of credit approval. This test of controls most likely supports management's financial statement assertion(s) of
Answers
After making inquiries about credit granting policies, an auditor selects a sample of sales transactions and examines evidence of credit approval. This test of controls most likely supports management's financial statement assertion(s) of "Completeness.
"Explanation: Completeness is one of the financial statement assertions.
It's a category of assertions that an auditor should consider when testing an entity's financial statements. Completeness ensures that all financial information is recorded in the financial statements and that no data is omitted. In other words, completeness ensures that the financial statements are complete.
This test of controls ensures that all sales transactions that have been approved for credit are recorded in the financial statements. By conducting this test, the auditor can verify that all sales transactions that were approved for credit are included in the financial statements.
Therefore, it can be concluded that this test of controls supports management's financial statement assertion(s) of "Completeness."
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Find the area of the figure.
Answers
Answer:
37.5
Step-by-step explanation:
What is in standard form?(7 x 10^-3) (9x10^4)
Answers
Answer:9
Step-by-step explanation:
Hurry ASAP need help nowww
Answers
Answer:
cant help sry
Step-by-step explanation:
Answer:
35
Step-by-step explanation:
80-45=35
When can we say that two triangles are similar?
Answers
The two triangles are similar If they have the same shape, but their sizes are different.
Similar triangles are triangles that have the same shape, but their sizes may be same or different. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion. The similarity of triangles are denoted by ‘~’ symbol
AA (or AAA) or Angle-Angle Similarity
If any two angles of a triangle are equal to any two angles of another triangle, then those two triangles are similar to each other.
SAS or Side-Angle-Side Similarity
If the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle inscribed between those two sides in both the triangle are equal, then two triangles are said to be similar.
SSS or Side-Side-Side Similarity
If all the three sides of a triangle are in proportion to the three sides of another triangle, then the two triangles are similar.
Therefore, two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.
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pls thank you pls explain it
Answers
The surface area of the shed is given as follows:
S = 367.2 m².
What is the surface area of a rectangular prism?The surface area of a rectangular prism of height h, width w and length l is given by:
S = 2(hw + lw + lh).
This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas.
The shed in this problem is composed as follows:
Rectangular prism of dimensions 6m, 10 m and 3 m.Two rectangles of dimensions 6m and 10 m.Two triangles of base 6 m.The height of each triangle is obtained as follows:
h² + 3² = 6²
\(h = \sqrt{6^2 - 3^2}\)
h = 5.2 m.
Hence the surface area is given as follows:
S = 2 x (6 x 10 + 6 x 3 + 10 x 3) + 2 x 6 x 10 + 2 x 0.5 x 6 x 5.2
S = 367.2 m².
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what does the rational of property do
Answers
Answer:
In Mathematics a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. ... Since q may be equal to 1, every integer is a rational Number.
Step-by-step explanation:
To find the total surface area of a cube, you use the
expression 652. What is the surface area of a cube
with a side length of 7 inches?
Answers
\( \Large \underline{\tt Given} :\)
Side of cube = 7 inches\( \\ \)
\( \Large \underline{\tt To \: Find} :\)
Total surface area = ?\( \\ \)
\( \Large \underline{\tt Solution} :\)
As, we have side of cube is 7 inches.
So, to find total surface area, we have a formula :
\( \underline{\boxed{\bf{Total \: surface \: area_{(cube)} = 6(side)^{2}}}}\)
\( \tt : \implies Total \: surface \: area = 6 (7 \: inches)^{2}\)
\( \tt : \implies Total \: surface \: area = 6 \times 49 \: inches^{2}\)
\( \tt : \implies Total \: surface \: area = 294 \: inches^{2}\)
\( \\ \)
Hence, Total surface area of given cube is 294 inches².
a researcher conducts two studies on self-perception. in study 1, 24 participants rate how positively they view themselves (on a 5-point scale) in one of three groups (n
Answers
A researcher conducts two studies on self-perception. Study 1 involves 24 participants who rate their self-perception on a 5-point scale within three groups. However, the content of the question in the second paragraph seems to be incomplete.
In Study 1, the researcher focuses on self-perception and divides the participants into three groups. Each participant rates how positively they view themselves using a 5-point scale. The specific details of the three groups and their purpose or characteristics are not provided in the question, so further information is needed to provide a comprehensive explanation. It is important to understand the specific variables and factors being studied in each group, as well as the objectives and hypotheses of the research. This additional information would allow for a more in-depth analysis of the researcher's approach and the potential insights gained from the study.
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A triangular prism has a base that is an isosceles triangle with sides 14 cm, 14cm , base 9 cm , and height 13 cm. The height of the prism is 32 cm. What is the surface area of this prism?
Answers
Answer:
Surface area of prism = 1301 cm²
Step-by-step explanation:
A triangular pyramid has 3 rectangular sides and 2 triangular sides.
Now, we are told that the triangular side is isosceles.
This means that two of the rectangular sides which share a side with the equal side of the triangle are equal as well as the 2 triangular sides.
Surface area of prism = 2(area of triangular face) + 2(area of rectangle sharing one side with the equal side of the triangle) + (area of rectangle sharing side with the unequal side of the triangle).
Area of triangle = ½ × base × height
Area of triangle = ½ × 9 × 13 = 58.5 cm²
Since height of prism is 32 cm, then;
area of rectangle sharing one side with the equal side of the triangle = 32 × 14 = 448 cm²
area of rectangle sharing side with the unequal side of the triangle = 32 × 9 = 288 cm²
Thus;
Surface area of prism = 2(58.5) + 2(448) + 288
Surface area of prism = 1301 cm²
She concludes that there are no limits within the set of real numbers on the range of this exponential function. Which best explains the accuracy of Geraldine’s statements and her conclusion? Statement 1 is incorrect because the y-values are increased by 2, not doubled. Statement 2 is incorrect because the y-values are doubled, not halved. The conclusion is incorrect because the range is limited to the set of integers. The conclusion is incorrect because the range is limited to the set of positive real numbers.
Answers
Geraldine's conclusion that there are no limits within the set of real numbers on the range of the exponential function is incorrect. The correct explanation is that the range of the function is limited to the set of positive real numbers.
The given statements indicate that Geraldine's conclusions and statements about the function are incorrect. Statement 1 clarifies that the y-values are increased by 2, not doubled. Statement 2 corrects the misconception that the y-values are halved instead of doubled.
The first explanation states that the conclusion is incorrect because the range is limited to the set of integers, which suggests that the function only takes on integer values. However, the correct explanation is that the range is limited to the set of positive real numbers, meaning the function can only produce positive values for y.
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\(3x - 2y = 43x + 2y = 8\)
Answers
3x - 2y = 8 +
===》 46x = 16
43x + 2y = 8
x = 16/46
x = 8/23
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3x - 2y = 8
3(8/23) - 2y = 8
24/23 - 2y = 8
2y = 24/23 - 8
y = 12/23 - 4
y = 12/23 - 92/23
y = - 80/23