The amount of paint needed to cover the wall is 112 square feet
How to determine the amount of paint?The given parameters are:
Parallel bases = 8 feet and 20 feet
Height = 8 feet
The area is calculated as:
Area = 0.5 * (Sum of parallel bases) * Height
So, we have;
Area = 0.5 * (8 + 20) * 8
Evaluate
Area = 112
Hence, the amount of paint needed to cover the wall is 112 square feet
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Angle 1 and Angle 2 are complementary angles. Angle 1 is 5x degrees. Angle 2 is 50 degrees. Find the value of x. Type ONLY the number.
Answer:
x = 8
Step-by-step explanation:
complementary angles sum to 90°
sum the 2 angles and equate to 90
5x + 50 = 90 ( subtract 50 from both sides )
5x = 40 ( divide both sides by 5 )
x = 8
A recent survey suggests that 85% of college students have a job, 54% live on campus, and 42% have a job and live on campus. What is the probability that a randomly chosen college student either has a job or lives on campus
[tex]\frac{97}{100}[/tex] probability that a randomly chosen college student either has a job or lives on campus.
What is probability?
Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.To find the probability that a randomly chosen college student either has a job or lives on campus:
Given: 85% of college students have a job, 54% live on campus, and 42% have a job and live on campus.
So, out of 100 students, 42 students either has a job or live on campus.
43 college students have a job and 12 live on campus.
So, 43 + 42 + 12 = 85 + 54 - 42
85 + 12 = 139 - 42
97 = 97
Therefore, [tex]\frac{97}{100}[/tex] probability that a randomly chosen college student either has a job or lives on campus.
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he function D(t) defines a traveler’s distance from home, in miles, as a function of time, in hours. Which times and distances are represented by the function? Select three options. The starting distance, at 0 hours, is 300 miles. At 2 hours, the traveler is 725 miles from home. At 2.5 hours, the traveler is still moving farther from home. At 3 hours, the distance is constant, at 875 miles. The total distance from home after 6 hours is 1,062.5 miles.
The true statements are (b), (d) and (e)
At 2 hours, the traveler is 725 miles from home.At 3 hours, the distance is constant, at 875 miles.The total distance from home after 6 hours is 1,062.5 miles.How to determine the times and distances are represented by the function?From the function, we have the following piecewise function and the domains
D(t) = 300t + 125, 0 ≤ t < 2.5
D(t) = 875, 2.5 ≤ t ≤ 3.5
D(t) = 75t + 612.5, 3.5 < t ≤ 6
When t = 2, we use the domain 0 ≤ t < 2.5
So, we have
D(2) = 300 * 2 + 125
Evaluate the product
D(2) = 600 + 125
Evaluate the sum
D(2) = 725 --- this is true
When t = 3, we use the domain 2.5 ≤ t ≤ 3.5
So, we have
D(t) = 875
This gives
D(3) = 875 -- this is true
When t = 6, we use the domain 3.5 < t ≤ 6
So, we have
D(t) = 75t + 612.5
This gives
D(6) = 75* 6 + 612.5
Evaluate the product
D(6) = 450 + 612.5
Evaluate the sum
D(6) = 1062.5 --- this is true
Hence, the true statements are (b), (d) and (e)
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Complete question
Select three options. The starting distance, at 0 hours, is 300 miles. At 2 hours, the traveler is 725 miles from home. At 2.5 hours, the traveler is still moving farther from home. At 3 hours, the distance is constant, at 875 miles. The total distance from home after 6 hours is 1,062.5 miles.
Answer:
At 2 hours, the traveler is 725 miles from home.
At 3 hours, the distance is constant, at 875 miles.
The total distance from home after 6 hours is 1,062.5 miles.
Step-by-step explanation:
There is a 40% probability that a student PASSES their first statistics exam. Using a Binomial Distribution, if we randomly select 7 students: What is the probability that more than 5 PASS their first statistics exam
The probability that more than 5 students will pass their exam is 0.0188416.
How to find the probability?The probability that a student passes their examination = 40% = 0.4
The probability that more than 5 students pass their statistics exam = Probability that 6 students pass their exam + Probability that 7 students pass their exam
The probability that 6 students pass their exam =
[tex]7C_{6} (0.4)^{6} (0.6)^{1}\\=7(0.4)^6(0.6)\\=0.0172032[/tex]
The probability that 7 students pass their exam =
[tex]7C_{7} (0.4)^{7} (0.6)^{0}\\=(0.4)^7\\=0.0016384[/tex]
The probability that more than 5 students pass their statistics exam = 0.0172032 + 0.0016384
= 0.0188416
Therefore, we have found the probability that more than 5 students will pass their exam to be 0.0188416.
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thanks!!
1) Now is your chance to find examples of sinusoids. Come up with some examples of natural or man-made phenomena that repeat at predictable intervals.
Search the Internet to find descriptions, and post the link as well as your analysis of why the behavior is periodic. You do not have to find an equation or write one. Examples already given in the lessons for this unit are off limits, so look for something new.
As you ride a ferris wheel, your distance from the ground varies sinusoidally with time. When the last passenger boards the ferris wheel and the ride starts moving, let your position be modeled by the diagram provided.
2) Let t be the number of seconds that have elapsed since you began moving. It takes you 5 seconds to reach the top of the wheel (38 feet above the ground) and 20 seconds to make a complete revolution. The diameter of the wheel is 30 feet.
Work with your classmates to answer the following questions:
What is the lowest you go as the ferris wheel turns?
Why is this number always greater than zero?
Write the equation of a sinusoid that describes this motion.
Predict your height above the ground when t = 3, t = 8, t = 15, and t = 19.
The examples of sinusoids include sound and water waves.
How to illustrate the information?Simple harmonic motion such as that of a pendulum or a weight attached to a spring results in a sinusoidal relationship between position and time.
The angle will be formed after t time of the starting of the motion.
θ = wt = 2πt/20 = πt/10
Radius of the wheel = 30/2 = 15 feet
Distance from the ground = (15 - 15cosθ) + 8 = (15 - 15cosπt/10) + 8
= 23 - 15cos(πt/10)
As we know the minimum value of the cos is -1
-1 ≤ cos(πt/10) ≤ 1
8 ≤ 23 - 15cos(πt/10) ≤ 38
The lowest distance = 8 feet
It should be always greater than zero as the lowest point of what should be above the ground.
d = 23 - 15cos(πt/10)
Plug t = 3 in the above equation:
d(3) = 14.18 feet
For t = 8
d(8) = 35.13 feet
For t = 15
d(15) = 23 feet
For t = 19
d(19) = 8.73 feet
Thus, the lowest distance is 8 feet, and the lowest point of what should be above the ground and the equation is d = 23 - 15cos(πt/10).
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What is equilibrium if autonomous expenditures are $2,000 and the mpe is 0. 5?
The equilibrium level if autonomous expenditures are $2,000 and the mpe is 0. 5 is $4000.
How to calculate the equilibrium?From the information given, the autonomous expenditures are $2,000 and the mpe is 0. 5.
Here, the equilibrium level will be:
= 2000/(1 - 0.5)
= 2000/0.5
= 4000
In conclusion, the correct option is $4000.
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Slope-intercept form?
Answer:
y=3x+4
Step-by-step explanation:
The original formula for slope-intercept is y=mx+b.
b is your y-intercept (where the line crosses the y-axis).
m is your slope which is 3/1 or just 3.
The length of a rectangle is 5 5/3 inches. the width of the rectangle is half of its length. what is the perimeter of the rectangle?
(a) 16.8 inches
(b) 8.4 inches
(c) 2.8 inches
(d) 15.68
(question and answers attached)
The perimeter of the rectangle that has a length of 5 3/5 inches, and the width as half of its length is 16.8 inches. Hence, option A is the right choice.
The perimeter of any object is the total sum length of its boundary.
The perimeter of a rectangle with length l units and width w units is given as:
Perimeter = 2(l + w) units.
In the question, we are given that the length of a rectangle is 5 3/5 inches and its width is half of its length. We are asked to find the perimeter of the rectangle.
The length of the given rectangle (l) = 5 3/5 inches = 28/5 inches.
The width of the given rectangle (w) = Half of length = 1/2 * 28/5 inches = 14/5 inches.
Thus, the perimeter of the rectangle = 2(l + b) = 2(28/5 + 14/5) inches,
or, the perimeter = 2(42/5) inches,
or, the perimeter = 84/5 inches,
or, the perimeter = 16.8 inches.
Thus, the perimeter of the rectangle that has a length of 5 3/5 inches, and the width as half of its length is 16.8 inches. Hence, option A is the right choice.
The given question is incorrect. The correct question is:
"The length of a rectangle is 5 3/5 inches. the width of the rectangle is half of its length. what is the perimeter of the rectangle?
(a) 16.8 inches
(b) 8.4 inches
(c) 2.8 inches
(d) 15.68"
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Calculate the area of triangle abc with altitude bd, given a (-6,0) b (0,0) c (o,6) and d (3,-3)
The area of the triangle abc in which bd is altitude and having coordinates a(-6,0),b(0,0),c(0,6),d(3,-3) is 18 square units.
Given the coordinates of abcd are a (-6,0) b (0,0) c (o,6) and d (3,-3).
We are required to find the area of the triangle when bd is the altitude of the triangle.
When we draw the triangle we will find that that the base is ac and altitude is given bd.
ac=[tex]\sqrt{(6-0)^{2} +(0+6)^{2} }[/tex]
=[tex]\sqrt{36+36}[/tex]
=[tex]\sqrt{72}[/tex]
=6[tex]\sqrt{2}[/tex]
bd=[tex]\sqrt{(-3-0)^{2} +(3-0)^{2} }[/tex]
=[tex]\sqrt{9+9}[/tex]
=[tex]\sqrt{18}[/tex]
=3[tex]\sqrt{2}[/tex]
Area=(Base*Height)/2
=(6[tex]\sqrt{2}[/tex]*3[tex]\sqrt{2}[/tex])/2
=(18*2)/2
=18 square units.
Hence the area of the triangle abc in which bd is altitude and having coordinates a(-6,0),b(0,0),c(0,6),d(3,-3) is 18 square units.
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Clue 1
The number has three digits.
Clue 2 The number is less than 140.
Clue 3 The number has 7 as a factor.
Clue 4 The number is even.
Clue 5 The sum of the digits of the number is less than 9.
Xy has 10 pets: 4 dogs, 3 cats, 2 alpacas and 1 bunny. If he wants to arrange them in a row and make sure the pets are always grouped according to species, how many ways can he arrange the pets?
The number of ways pets can be arranged in group according to the species is in a row 288 ways.
Pets can be grouped by permutation concept as follows.
Total number of pets = 10
Number of dogs = 4
Number of cats = 3
Number of alpacas = 2
Number of bunny = 1
The number of ways pets can be arranged in group according to the species in a row as,
⇒ (4!)(3!)(2!)(1!)
⇒ (24)(6)(2)(1)
⇒ 288
Hence we can conclude that the number of ways pets can be arranged in group according to the species in a row is 288 ways.
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the number 40 cannot be decomposed into prime factors
True
either
False
[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {\large{\textsf{\textbf{\underline{\underline{Answer : \:}}}}}}[/tex]
False, because the number 40 is a composite number, those that cannot be broken down are called Prime Numbers.
Prime numbers are numbers that are used to decompose any number, but prime numbers cannot be decomposed, since they only have two Divisors, which are 1 and itself.
[tex]~\sf{Atte: Murdock:)}[/tex]
Answer: False
Step-by-step explanation:
All whole numbers can be decomposed into prime factors. For the number 40, the prime factorization would be [tex]2 * 2 * 2*5[/tex]. Since all 4 of those numbers are prime numbers, the answer is false.
Identify the domain of the function shown in the graph
Answer:
C. All real numbers.
Step-by-step explanation:
The domain is the set of all x values that are used by points on the graph. This is a sine wave, and we assume it extends infinitely far to the left and right. Even without that assumption, you can eliminate the other answers.
A. This describes the numbers on the x-axis between 0 and 5, inclusive. But the graph includes many more points with x-coordinates beyond that interval.
B. The same sort of thing: the graph extends well beyond the interval of x values between -5 and 5, inclusive.
D. This would mean the graph has only points with positive x-coordinates, but there are many with negative (or 0) x-coordinates.
Can someone help me please and show work !!
Answer:
Step-by-step explanation:
Rectangles have 2 pairs of equal sides that means:
2(4x) and 2(3x+2)
8x and 6x+4
8x+ (6x + 4) = 14x + 4
A piece of plexiglass is in the shape of a semicircle with radius 2m. determine the dimensions of the rectangle with the greatest area that can be cut from the piece of plexiglass
The dimensions of the rectangle having greatest area in the piece of plexiglass which is a semicircle is [tex]2\sqrt{2}[/tex] and [tex]\sqrt{2}[/tex].
Given radius of piece of plexiglass which is a semi circle equal to 2m.
We have to find the dimensions of the rectangle which is inscribed in the semi circle.
Draw a rectangle in a semicircle.
Suppose the length of rectangle be x and width be y.
Draw a line from the center to the vertex of the rectangle which forms a right angled triangle with sides x,y and 2.
[tex](x/2)^{2} +y^{2} =2^{2}[/tex]
y=[tex]\sqrt{16-x^{2} }/2[/tex]
Area of rectangle=2xy
=x[tex]\sqrt{16-x^{2} }[/tex]/2
Finding the derivative of area
d A/dx=1/2[x(-2x)/2[tex]\sqrt{16-x^{2} }[/tex]+[tex]\sqrt{16-x^{2} }[/tex]]
d A/dx=0
1/2[[tex]-2x^{2} /2\sqrt{16-x^{2} }+\sqrt{16-x^{2} } ][/tex]=0
Solving for x
[tex]\sqrt{16-x^{2}[/tex]=[tex]x^{2} /\sqrt{16-x^{2} }[/tex]
16-[tex]x^{2}[/tex]=[tex]x^{2}[/tex]
16=2[tex]x^{2}[/tex]
[tex]x^{2}[/tex]=8
x=2[tex]\sqrt{2}[/tex]
put the value of x in y=[tex]\sqrt{16-x^{2} }/2[/tex] to get the value of y
y=[tex]\sqrt{16-8} /2[/tex]
=[tex]\sqrt{8} /2[/tex]
= 2[tex]\sqrt{2} /2[/tex]
=[tex]\sqrt{2}[/tex]
Hence the dimensions of rectangle which is in a semi circle of radius 2 is [tex]\sqrt{2} and 2\sqrt{2}[/tex].
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Question 14 of 23
Which of the following describes a compound event?
OA. spinning a 3 on a spinner
OB. rolling a 3 on a die
OC. getting tails on a coin toss
OD. rolling a 5 on a die and drawing a 10 from a deck of cards
SUBMIT
Answer:
B
Step-by-step explanation:
If a truck traveled 75 miles in 3 hours, how many miles would the truck have traveled per minute?
The truck travelled 0.42 miles per minute
How to determine the miles per minute?The given parameters are:
Distance = 75 miles
Time = 3 hours
Convert time to minutes
Time = 3 * 60 minutes
Time = 180 minutes
The speed is calculated as:
Speed = Distance/Time
This gives
Speed = 75 miles/180 minutes
Evaluate
Speed = 0.42 miles per minutes
Hence, the truck travelled 0.42 miles per minute
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Suppose matrix B is the inverse of matrix A. Use your knowledge of inverses and matrix multiplication to answer the following: AB
AB will be an Identity matrix.
What is an identity matrix?A square matrix with 1s on the main diagonal and 0s everywhere else is an identity matrix. The identity matrices 22 and 33, for example, are presented below. These are known as identity matrices because they produce the identity matrix when multiplied by a compatible matrix.If the answer to a matrix multiplication problem is an identity matrix, then each of the two matrices is an inverse matrix of the other. When the matrix is multiplied by the original matrix, the result is the identity matrix.As it is given in the description itself, if the answer to a matrix multiplication problem is an identity matrix, then each of the two matrices is an inverse matrix of the other.
Therefore, AB will be an Identity matrix.
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Answer:
AB= I
ABA=A
BBA=B
BBAA=I
Step-by-step explanation:
just took the test on edge. 2022
three decreased by eleven times a number
Step-by-step explanation:
3 - 11x
x is "a number".
so, the request is to multiply it by 11 and subtract the result from 3.
Hi, can you help me with this math problem?
The equation of a hyperbola is shown.
[tex]\frac{(y-7)^2}{3}-\frac{(x+13)^2}{12}=1[/tex]
Determine the area of the central rectangle.
Answer:
24
Step-by-step explanation:
The semi-axis lengths are 'a' and 'b' in the equation ...
(y -k)²/a² -(x -h)²/b² = 1
AreaThe area of the central rectangle will be ...
A = LW
The axis lengths are 2a and 2b, so the area is ...
A = (2a)(2b) = 4ab
In terms of the numbers in the given equation, this is ...
A = 4√(a²b²) = 4√(3×12)
A = 4×6 = 24
The area of the central rectangle is 24 square units.
Determine whether the relationship is an inverse variation or not. Explain.
The relationship is not an inverse variation because the product xy is not a constant.
What is Inverse variation?Inverse variation is the relationship between two quantities whereby an increase in one quantity cause a decrease in the other quantity.
In this type of variation the product of the two quantities is constant.
Analysis:
if x is one quantity and y is the other,
Mathematically, x = [tex]\frac{k}{y}[/tex]
Where, k is a constant,
it means k = xy
from the table, when, x =2, y = 409, xy = 2 x 409 = 818
Also, x = 3, y = 240, xy = 3 x 240 = 720
Therefore, 720 not equal to 818.
In conclusion, The product xy is not a constant, so the relationship is not an inverse variation.
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urgent please help!!!!! will give brainliest
Answer: Read the explanation
Step-by-step explanation:
If the points of a figure are all moved the same, they are congruent.
Point A is moved 9 points right, and 7 points down.
Point B is moved 9 points right, and 7 points down.
Point C is moved 9 points right, and 7 points down.
So, they are congruent.
Three friends owe 18 dollars to another friend for gas if they plan to split the cost evenly which of the following expressions could they use to find how much they each owe
If they plan to split the cost evenly, the expression that could be used to find how much they each owe is 18/3
How to determine the amount paid by each?The given parameters are:
Total amount owed = 18 dollars
Number of friend = 3
If they plan to split the cost evenly, the expression that could be used to find how much they each owe is represented as:
Amount = Total/Friends
This gives
Amount = 18/3
Hence, the expression is 18/3
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If there are fifty raffle tickets in a jar, and only two will be drawn out, and you own two of them, what chance do you have of owning both winning tickets?
Answer:
1/25
Step-by-step explanation:
Answer:
I think it may be 1/1225
Step-by-step explanation:
first chance is 2/50 and second chance is 1/49 as one card decrease at first. So multiplying it we get 1/1225.
Which equation could represent the graph shown below?
F(x) = ^3√x + 2 (sqrt just over the x)
F(x) = ^3√x - 2 (sqrt just over the x)
F(x) = ^3√x + 2 (the sqrt is over the whole equation)
F(x) = ^3√x - 2 ( the sqrt is over the whole equation)
I DONT KNOW HOW TO PUT A PICTURE OF THE GRAPH!!
The equation of the graph is [tex]f(x) = -\sqrt{x -2[/tex]
How to determine the graph equation?The graph is added as an attachment
The form of the graph is
[tex]f(x) = a\sqrt{x + b[/tex]
The graph passes through the points (2, 0) and (6, -2).
So, we have:
[tex]0 = a\sqrt{2 + b[/tex] and [tex]-2 = a\sqrt{6 + b[/tex]
Solve for b in [tex]0 = a\sqrt{2 + b[/tex]
Divide both sides by a
[tex]0 = \sqrt{2 + b[/tex]
Square both sides
0 = 2 + b
Subtract 2 from both sides
b = -2
Substitute b = -2 in [tex]-2 = a\sqrt{6 + b[/tex]
[tex]-2 = a\sqrt{6 -2[/tex]
[tex]-2 = a\sqrt{4[/tex]
Evaluate the square root
-2 = 2a
Divide by 2
a = -1
Substitute b = -2 and a = -1 in [tex]f(x) = a\sqrt{x + b[/tex]
[tex]f(x) = -\sqrt{x -2[/tex]
Hence, the equation of the graph is [tex]f(x) = -\sqrt{x -2[/tex]
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Can someone help me out with these two problems and show work please !!
Answer :
( 6 y^4 + 3 y^2 -7) - (12 y^4 - y^2 + 5)
Step-by-step explanation:
(6 y^4+ 3 y^2-7) - (12 y^4 - y^2 + 5 )
=6 y^4 +3 y ^2 - 7 - 12 y^4 + y^2 - 5
=6 y ^4 - 12 y ^4 +3 y ^2 + y ^2 - 7 -5
= -6 y ^4 + 4 y ^2- 12
Hope this helps!
a cone has a height of 16 centimeters and a radius of 12 centimeters. what is the exact lateral and surface area of the cone? type the correct answer in each box. use numerals instead of words.
The lateral and total surface areas of the given cone are 753.98 cm² and 1206.31 cm² respectively.
What are the formulae for lateral and total surface areas of a cone?A cone has a height 'h', radius 'r', and slant height 'l'.
The slant height of the cone is obtained by the Pythagorean theorem. I.e.,
l² = h² + r²
Then,
Its lateral surface area(LSA) = πr([tex]\sqrt{h^2+r^2}[/tex]) square units and
Its total surface area(TSA) = πr(r + l) square units
Calculation:It is given that,
A cone has a height h = 16 cm and radius r = 12 cm
Then, the slant height is calculated by
l² = h² + r²
l = [tex]\sqrt{h^2+r^2}[/tex]
On substituting,
l = [tex]\sqrt{16^2+12^2}[/tex]
= [tex]\sqrt{400}[/tex]
= 20 cm
So,
LSA = πr([tex]\sqrt{h^2+r^2}[/tex])
= π × 12 × ([tex]\sqrt{16^2+12^2}[/tex])
= π × 12 × 20
= 753.98 cm²
and
TSA = πr(r + l)
= π × 12 × (12 + 20)
= π × 12 × 32
= 1206.37 cm²
Therefore, the lateral and total surface areas of the cone with a height of 16 cm and a radius of 12 cm are 753.98 cm² and 1206.37 cm².
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Answer: The lateral area is 240π square centimeters. The total surface area is 384π square centimeters.
Step-by-step explanation:
The primary goal of a data _____ is to create new questions using data.
The primary goal of a data scientist is to create new questions using data.
Who is a data scientist?In the data ecosystem, a data scientist is one who creates new questions using data.
Who is a data analyst?Unlike a data scientist, a data analyst uses existing data questions to find answers through insightful analysis of data.
Who are data designers?Data designers design databases and database-specific constructs, and the procedures for storing, retrieving, and deleting persistent objects.
Who are data engineers?Data engineers build data systems to collect, manage, and convert data into information for both data scientists and analysts.
Thus, the primary goal of a data scientist is to create new questions using data.
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Question Completion with Answer Options:a) scientist
b) engineer
c) designer
d) analyst
A student missed 45 problems on a mathematics test and received a grade of 39%. If all the problems were of equal value, how many problems were on the test
There were 74 problems in the test.
Rounding-off percentageLet the student got total number of problems in the test to be X.
Percentage of correct answer = 39 %
⇒ 61% of X were incorrect
⇒61/100 x X = 45
⇒61X = 45x100
⇒X = 4500/61
⇒X=73.77
After rounding off 73.77, we get 74.
Hence, we can say that there were total of 74 problems in the test.
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help quick, it's based on polynomials .
Find the area of the shape
Answer:
Step-by-step explanation:
I got you first you want to get some little ceasers