[tex]\begin{cases} x = \frac{4}{3} &\implies 3x=4\implies 3x -4=0\\ x = -1 &\implies x +1=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( 3x -4 )( x +1 ) = 0} \hspace{5em}\stackrel{\textit{now assuming that}}{a=1}\hspace{3em}1( 3x -4 )( x +1 ) = 0 \\\\\\ ~\hfill {\Large \begin{array}{llll} 3x^2-x-4=0 \end{array}}~\hfill[/tex]
please help me with this question
Answer:
V = 3 * 3 * 7 + 2 * 3 * 5 = 63 + 30 = 93 just adding 2 segments
Rafael spins the pointers of the top spinners shown at the right. Find the probability of each possible sum.
After addressing the issue at hand, we can state that Keep in mind that any probability model must have these probabilities sum up to 1, as is the case here.
What is probability?Calculating the probability that an event will occur or that a statement is true is the subject of probability theory in mathematics. A risk is a number between 0 and 1, where 1 denotes certainty and an approximate probability of 0 denotes how likely an event appears to be to occur. A mathematical representation of the likelihood that an event will take place is called probability. You can also express probabilities as percentages ranging from 0% to 100% or as integers between 0 and 1. the proportion of equally plausible options that actually occur when compared to all possible outcomes, leading to a certain event.
A probability model for selecting a bead can be defined as follows:
Let the actions of choosing a glass, wood, or brass bead be represented by G, W, and B, respectively. We can suppose that the likelihood of choosing a particular type of bead is inversely correlated with the quantity of that type of bead in the box. As a result, we have:
P(W) = 96/300 = 8/25 P(B) = 144/300 = 12/25 with P(G) = 60/300 = 1/5
Keep in mind that any probability model must have these probabilities sum up to 1, as is the case here.
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The correct question is -
Write a probability model for choosing a bead.
Choosing Beads
Glass 60
Wood 96
Brass 144
A rectangle has side lengths of x cm and (x+y) cm, where x and y are both positive. The rectangle has an area of 57 cm squared and a perimeter of 44 cm. work out the values of x and y
The value of x and y for the rectangle has side lengths of x cm and (x+y) cm are found as : x = 3 and y = 16.
Explain about the area of rectangle?The total of a rectangle's four sides is its perimeter. The equation Perimeter of Rectangle = 2 (Length + Width) is used to calculate it. The region contained within the boundaries of a rectangle is its area, which may be determined using the formula area of rectangle = length width.Dimensions are:
Length L = x cmWidth w = (x + y) cmArea = 57 cm squared perimeter = 44 cm.Then,
Area = l*w
57 = x(x + y) ....eq 1
Perimeter = 2(l + w)
44 = 2(x + x + y)
22 = 2x + y
y = 22 - 2x ...put in eq 1
57 = x(x + y)
57 = x(x + 22 - 2x)
57 = x(22 - x)
Simplifying:
57 = 22x - x²
Or.
x² - 22x + 57
Factorizing using quadratic formula:
x = 19 ans x = 3
For x = 19
y = 22 - 2*19
y = 22 - 38 (negative value not possible)
So, x = 3
y = 22 - 2*3
y = 22 - 6
y = 16
Thus, the value of x and y for the rectangle has side lengths of x cm and (x+y) cm are found as : x = 3 and y = 16.
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Travis tossed a coin off a bridge into the stream below. The path of the coin can be modeled by the equation where t is the time in seconds and h is the height in feet. How long will it take the coin to reach the stream?
The coin will reach the stream in 5.61 seconds.
How to determine how long it will take the coin to reach the stream?
Since the height of the coin, after t seconds, is given by the equation:
h = -16t² + 72t + 100
The stream is the ground level. Thus, the coin reaches the stream when h(t) = 0.
So we can equate the equation to zero and solve for t:
-16t² + 72t + 100 = 0
Using the quadratic formula:
t = −b ± √(b² − 4ac) 2a
where a = -16, b = 72 and c = 100
t = −72 ± [√(72² − 4(-16)(100))] /2(-16)
t = −72 ± [√11584]/(-32)
t = (-72 ± 107.63)/(-32)
t = (-72 + 107.63)/(-32) or (-72 - 107.63)/(-32)
t = -1.11 or 5.61
Since t cannot be negative. Thus, t = 5.61 seconds
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Complete Question
Travis tossed a coin off a bridge into the stream below. The path of the coin can be represented by the equation h = -16t² + 72t + 100. How long will it take the coin to reach the stream?
Warm-up:
1. -g + 2(3 + g) = -4(g +1)
The solution for g is -2
How to solve the linear equation?[tex]-g+2\left(3+g\right)=-4\left(g+1\right)[/tex]
expand [tex]-g+2\left(3+g\right)[/tex]
= [tex]g+6[/tex]
expand [tex]-4(g+1)[/tex]
[tex]-4g-4[/tex]
[tex]g+6=-4g-4[/tex]
collect like terms:
[tex]5g=-10[/tex]
Divide both side by 5:
[tex]\frac{5g}{5} =\frac{-10}{5}[/tex]
=[tex]g = -2[/tex]
Therefore, the solution for g is -2.
What is linear equation?A linear equation is an algebraic equation in which the highest power of the variable is 1. It can be written in the form of y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept.
The slope is the rate of change of the line, which represents how steeply it rises or falls, and the y-intercept is the point where the line intersects the y-axis.
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Hey triangle area with three sides 26 feet18 feet and 9 feet
The area of the triangle with sides 26 feet, 18 feet, and 9 feet is approximately 125.6 square feet.
To find the area of a triangle while given three aspects, we are able to use Heron's formula, which states that the region of a triangle with facets a, b, and c is given by means of:
area = √(s(s-a)(s-b)(s-c))
where s is the semiperimeter, calculated as:
s = (a + b + c) / 2
plugging inside the given values, we get:
s = (26 + 18 + 9) / 2 = 26.5
area = √26.5(26.5-26)(26.5-18)(26.5-9))
area = √(26.50.58.5×17.5)
area = √(15793.75)
area ≈ 125.6 square feet
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What coordinates on the unit circle are associated with the angle measure? Drag coordinates into each box to match the angle measure.
Angle measure [tex]\frac{23 \pi}{3}[/tex] is associated with the coordinate [tex]\left({\frac{1}{2}}\;-{\frac{\sqrt{3}}{2}}\right)$[/tex]
Angle measure [tex]-\frac{3 \pi}{4}[/tex] is associated with the coordinate [tex]\left(-{\frac{\sqrt{2}}{2}},-{\frac{\sqrt{2}}{2}}\right)[/tex]
Angle measure 150° is associated with the coordinate [tex]\left(-{\frac{\sqrt{3}}{2}},{\frac{1}{2}}\right)$[/tex]
What is angle measure coordinate?An angle is fοrmed when twο lines οr rays meet at a cοmmοn pοint. The cοmmοn pοint is knοwn as the vertex.
In geοmetry, an angle measure can be defined as the measure οf the angle fοrmed by the twο rays οr arms at a cοmmοn vertex.
Angles are measured in degrees (°) using a prοtractοr. A prοtractοr is a measuring device that is used tο calculate οr draw angles in terms οf degrees.
Check the figure given in the attachment to better understand
Angle measure [tex]\frac{23 \pi}{3}[/tex] is associated with the coordinate [tex]\left({\frac{1}{2}}\;-{\frac{\sqrt{3}}{2}}\right)$[/tex]
Angle measure [tex]-\frac{3 \pi}{4}[/tex] is associated with the coordinate [tex]\left(-{\frac{\sqrt{2}}{2}},-{\frac{\sqrt{2}}{2}}\right)[/tex]
Angle measure 150° is associated with the coordinate [tex]\left(-{\frac{\sqrt{3}}{2}},{\frac{1}{2}}\right)$[/tex]
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PLEASE HELP ME WITH THIS PROBLEM !!!
Answer: 24
Step-by-step explanation: 2x2x2 is the volume since 2x2x2 is 8. so the surface area of one side would be 2x2. 4x6= 24. Since there are 6 sides, the answer is 24.
What is the area of a sector with a central angle of 60° and a radius of 16.7 ft?
Use 3.14 for π and round your final answer to the nearest hundredth.
Enter your answer as a decimal in the box.
ft²
Answer:
Step-by-step explanation:
2
Answer:
145.95
Step-by-step explanation:
I took the test and got it right
GIVING 75 POINTS URGENTTTT please help me thanksssss
Matching each number with its name, 1,254 :: whοle number
What is whοle numbers?Whοle numbers are a set οf numbers including all natural numbers and 0. They are a part οf real numbers that dο nοt include fractiοns, decimals, οr negative numbers. Cοunting numbers are alsο cοnsidered as whοle numbers.
Whοle numbers are pοsitive integers (including zerο) withοut any fractiοnal οr decimal parts. They are used tο cοunt whοle οbjects οr things, and cannοt represent a part οf a whοle. Examples are 0, 1, 2, 3, 4, 5, and sο οn.
0.143143143.... :: repeating decimal
0.123456789..... :: nοn-terminating/nοn-repeating
0.13 :: terminating
1,254 :: whοle number
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Determine if the following numbers are rational or irrational.
1. √25
2.4.31
3.-2/2
4. √18
5.7
6. Pi
7.√50
8.-5
9. 1/3
10. 0
Answer:check explanation
Step-by-step explanation:1. √25 is a rational number because it is equal to 5, which is a rational number.
2. 4.31 is a rational number because it can be expressed as the ratio of two integers (431/100).
3. -2/2 is a rational number because it can be simplified to -1, which is a rational number.
4. √18 is an irrational number because it cannot be expressed as the ratio of two integers. It is approximately equal to 4.242640687119285.
5. 7 is a rational number because it can be expressed as the ratio of two integers (7/1).
6. Pi is an irrational number because it cannot be expressed as the ratio of two integers or as a terminating or repeating decimal. It is approximately equal to 3.141592653589793.
7. √50 is an irrational number because it cannot be expressed as the ratio of two integers. It is equal to √(25*2) which simplifies to 5√2.
8. -5 is a rational number because it can be expressed as the ratio of two integers (-5/1).
9. 1/3 is a rational number because it can be expressed as the ratio of two integers (1/3 = 0.33333...).
10. 0 is a rational number because it can be expressed as the ratio of two integers (0/1).
Let (Xn)n≥0 be a branching process (as described in lectures) with X_0 = 1. Let Z denote the common offspring distribution (iid for all individuals) and suppose that Z ∼ Poisson(γ). Write down a general expression for P(X_n = i|X_n−1 = j) for the case that i ∈ N and j > 0.
Hint: Distribution of the sum of independent Poisson distributed RVs is?
The probability as a function of the sum of independent Poisson distributed random variables. We can then obtain the desired expression for P(X_n = i|X_n−1 = j) as follows:P(X_n = i|X_n−1 = j) = P(Z_1 + ... + Z_j = i) = (1/i!)×(γi)×e{-γ}.
What is expression?Expression in math is a combination of numbers, variables, operations and symbols that represent a mathematical relationship or value. Expressions can be used to represent equations, functions, and sequences, and can be evaluated for a result. Expressions can include constants, variables, operators, functions, and other mathematical expressions.
The general expression for P(X_n = i|X_n−1 = j) is given by P(X_n = i|X_n−1 = j) = P(Z_1 + ... + Z_j = i), where Z_1, ..., Z_j are independent and identically distributed Poisson random variables with parameter γ. This follows from the fact that the offspring of each individual follows the same Poisson distribution, and the total number of offspring is the sum of the offspring of each individual. Therefore, we can express the probability as a function of the sum of independent Poisson distributed random variables. We can then obtain the desired expression for P(X_n = i|X_n−1 = j) as follows:
P(X_n = i|X_n−1 = j) = P(Z_1 + ... + Z_j = i) = (1/i!)×(γi)×e{-γ}.
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Interest Rate Basics: How much interest would you pay to borrow $670 for eight months at 12% interest?
Answer:
$53.60
Step-by-step explanation:
The December 31 inventory count of computer supplies shows $660 still available.
Accounting problem
Please help this is due by 11:59 PM
In the Closing Entries, the Income summary, computer service revenue, and retained earnings are given.
What is a Statement of Income?A Statement of Income, also known as an Income Statement or Profit and Loss Statement (P&L), is a financial statement that reports a company's revenues, expenses, and net income or net loss over a specific period of time, usually a month, quarter, or year.
The statement shows the company's ability to generate revenues and manage expenses during the period being reported
It is an essential tool for analyzing a company's financial performance and is used by investors, creditors, and management to make decisions about the company's operations.
The journal entries, adjusted balances, closing entries, unadjusted trial balances, and statements of income have all been solved in the images below.
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4. A stone nudged off the Royal Gorge Bridge near Cañon City, Colorado, falls 1053 feet before hitting water. Because its speed increases as it falls, the distance it travels each second increases. During the first second, it drops 16 feet. During the next second, it drops an additional 48 feet. During the third second, it drops another 80 feet. The distances traveled each second form an arithmetic sequence:
16, 48, 80, ...
Part I: How far does the stone fall during the 5th second? Find and use the explicit formula.
a. What is the first term of the sequence? _____
b. What is d, the common difference? _____
c. Write the explicit formula in function notation. Use f(n) = f(1) + (n – 1)d, where f(1) represents the first term. _______________
d. Use the explicit formula to find the distance the stone travels in the 5th second.
a. The first term of the sequence is 16.
b. the common difference is d = 32
c. the explicit formula is f(n) = 16 + (n - 1)32
d. the stone falls a distance of 144 feet during the 5th second.
How to find the first term in the sequencea. The first term of the arithmetic sequence is given to be 16.
b. To find the common difference, we can subtract the second term from the first term, then the third term from the second term:
48 - 16 = 32
80 - 48 = 32
Therefore, the common difference is d = 32.
c. Using f(n) = f(1) + (n - 1)d,
where
f(1) = 16 and d = 32,
we can write the explicit formula for the distance traveled during the nth second as:
f(n) = 16 + (n - 1)32
d. To find the distance traveled during the 5th second, we plug in n = 5 into the explicit formula:
f(5) = 16 + (5 - 1)32
f(5) = 16 + 4*32
f(5) = 16 + 128
f(5) = 144
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Please solve with proof
Yes, the Median of a triangle is also an altitude and the triangle is isosceles.
What is the altitude of a triangle?The altitude of a triangle is the perpendicular line segment drawn from the vertex of the triangle to the side opposite to it
A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side.
In an isosceles triangle, two sides that are equal meet at a vertex that lies directly above the base midpoint. Because of this altitude from the vertex bisect the base at midpoint median to the base from the vertex.
Therefore, Median of a triangle is also an altitude and the triangle and it is isosceles.
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Question 1
Use the figure below to answer your the following question.
2 feet
The figure above is a cube. What is the total surface area of the cube?
A. 6 square feet
B. 20 square feet
C. 8 square feet
D. 24 square feet
Question 2
A campsite provides a locking rectangular box with the dimensions shown below to secure food from bears.
3 feet
5 feet
2 feet
What is the surface area of the box?
A. 30 square feet
B. 62 square feet
C. 31 square feet
D. 72 square feet
Question 3
Gina is painting the rectangular tool chest shown in the diagram below.
24 in.
12 in.
10 in.
If Gina paints only the outside of the tool chest what is the total surface area in square inches (in.²) she will paint
A. 368
B. 648
C. 1296
D. 2880
Question 5
A triangular prism is pictured below.
6cm
5cm
6.5cm
6.5cm
16cm
What is the surface area of the prism?
A. 240 cm²
B. 318 cm²
C. 270 cm²
D. 348 cm²
Answer 1:
D. 24 sq feet
The formula to find surface area of a cube is [tex]a=6a^{2}[/tex]
Substitute 2 for a, [tex]2^{2} = 4[/tex]
6 x 4 = 24, so 24 sq feet
Answer 2:
B. 62 sq feet
The formula to find surface area of a rectangular prism is [tex]a = 2(wl+wh+hl)[/tex]
Substitute 3 for w, 5 for l, 2 for h and multiply
a = 62 sq feet
Answer 3:
C. 1296 sq inches
The formula to find surface area of a rectangular prism is [tex]a = 2(wl+wh+hl)[/tex]
Substitute 24 for w, 12 for l, 10 for h and multiply
a = 1296 sq inches
Gender Selection The Genetics and IVF Institute conducted a clinical trial of the YSORT method designed to increase the probability of conceiving a boy. As of this writing, 291 babies were born to parents using the YSORT method, and 239 of them were boys. 291/239= a. What is the best point estimate of the population proportion of boys born to parents using the YSORT method? b. Use the sample data to construct a 99% confidence interval estimate of the proportion of boys born to parents using the YSORT method. c. Based on the results, does the YSORT method appear to be effective? Why or why not? Theoretical probability is u. population proportion is o. 90% confidence interval
the 99% confidence interval estimate for the proportion of boys born to parents using the YSORT method is: (0.7584, 0.8820)
what is an algebraic expression?
An algebraic expression is a mathematical phrase consisting of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.
a. The point estimate of the population proportion of boys born to parents using the YSORT method can be calculated as the ratio of the number of boys to the total number of babies:
239/291 ≈ 0.8202
Therefore, the best point estimate of the population proportion of boys born to parents using the YSORT method is approximately 0.8202.
b. To construct a 99% confidence interval estimate of the proportion of boys born to parents using the YSORT method, we can use the following formula:
p ± z*sqrt(p(1-p)/n)
where p is the point estimate of the population proportion, z* is the critical value from the standard normal distribution for the desired confidence level (99% in this case), and n is the sample size.
Using the values from part (a), we have:
p = 0.8202
n = 291
z* = 2.576 (from the standard normal distribution table for a 99% confidence level)
Plugging in these values, we get:
0.8202 ± 2.576sqrt(0.8202(1-0.8202)/291)
Simplifying, we get:
0.8202 ± 0.0618
c. Based on the results, the YSORT method appears to be effective in increasing the probability of conceiving a boy. The point estimate of 0.8202 is significantly higher than the theoretical probability of 0.5 for a randomly selected baby to be a boy.
Therefore, the 99% confidence interval estimate for the proportion of boys born to parents using the YSORT method is: (0.7584, 0.8820)
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in a certain state, 60% of all adults have high blood pressure, 45% have high cholesterol and 20% have both high blood pressure and high cholesterol. what is the probability that a randomly selected adult from the state has high blood pressure but not high cholesterol?
The probability that a randomly selected adult from the state has high blood pressure but not high cholesterol is 0.40 or 40%.
To find the probability that a randomly selected adult from the state has high blood pressure but not high cholesterol, we need to subtract the probability of having both high blood pressure and high cholesterol from the probability of having high blood pressure.
Using set notation, let A be the event of having high blood pressure and B be the event of having high cholesterol. Then, the probability of having both high blood pressure and high cholesterol can be written as
P(A ∩ B)= 0.20
The probability of having high blood pressure can be written as
P(A) = 0.60
Therefore, the probability of having high blood pressure but not high cholesterol is:
P(A) - P(A ∩ B) = 0.60 - 0.20 = 0.40
Thus, the probability that a randomly selected adult from the state has high blood pressure but not high cholesterol is 0.40 or 40%.
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What is the equation of this graphed line?
Enter your answer in slope-intercept form in the box.
Answer:
y = -1/3x - 5
Step-by-step explanation:
The slope-intercept form is y = mx + b
m = the slope
b = y-intercept
Slope = rise/run or (y2 - y1) / (x2 - x1)
Points (-6, -3) (6, -7)
We see the y decrease by 4, and the x increase by 12, so the slope is
m = -4/12 = -1/3
Y-intercept is located at (0, -5)
So, our equation is y = -1/3x - 5
Lake A has a volume of 21,150,427,000 cubic meters. Lake B has a volume that is 2.5 times the volume of Lake A. What is the approximate volume of Lake B? Write your answer as the product of a single digit and a power of 10.
Therefore , the solution of the given problem of volume comes out to be Lake B's volume is roughly as follows is 5.28760675 cubic metres.
Volume : What is it?The volume of a three-dimensional item, which is measured in cubic units, describes how much room it occupies. Cubic measurements are represented by the symbols litre and in3. However, you can calculate an object's measurements using its bulk. In most cases, the item's weight is transformed into mass units like kilogrammes and kilos.
Here,
=> Lake B's capacity is 2.5 times greater than Lake A's.
=> Lake B's volume is 2.5 times that of Lake A.
=> Lake B's volume is 2.5 x 21,150,427,000.
=> Lake B has a volume of 52,876,067,500.
By moving the decimal point until there is only one non-zero digit left of the decimal point, we can represent this number as the sum of a single integer and a power of 10. We need to multiply by 1010 to account for the fact that we shifted it 10 positions to the left.
Therefore, Lake B's volume is roughly as follows:
=> 5.28760675 cubic metres
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Write a system of equations for this-
Cora ran 3 miles last week and will run 7 miles per week from now on. Hana ran 9 miles last week and will run 4 miles per week from now on
The solution to the system of equations is C = 3 and H = 9.
Let C = Cora's miles last week and H = Hana's miles last week
The equation for Cora's miles is C + 7x = 3, and the equation for Hana's miles is H + 4x = 9, where x is the number of weeks.
The solution to this system of equations is C = 3, and H = 9. This can be determined by solving each equation separately and then checking that the answers satisfy both equations.
For Cora's equation, subtract 7x from both sides to get C = 3 - 7x. Solving for x gives x = (3 - C) / 7. Plugging this into Hana's equation gives H + 4((3 - C) / 7) = 9. Simplifying this equation gives H = 9 - 12 + 4C.
Checking the answers, C = 3 - 7(0) = 3, and H = 9 - 12 + 4(3) = 9. Both equations are satisfied by C = 3 and H = 9, so this is the solution to the system of equations.
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helpp -3(0.75x-2y)+6(0.5x-2y) ?????
PLEASE HELP!!!! PLEASE PLEASE PLEASE!!!!
The volume of the cylinder is approximately 753.98 cubic centimeters.and the volume of the cone is approximately 600.98 cubic centimeters.
The solutions of the question are given as following :-
1.To find the radius of a cone with height 19 cm and width (diameter) 12 cm, we can use the Pythagorean theorem to relate the height, radius, and slant height of the cone. The slant height is the distance from the vertex of the cone to any point on the circular base, and it is related to the height and radius by the equation:
slant height² = height² + radius²
We know the height is 19 cm, and the diameter (width) is 12 cm, so the radius is half of the diameter, or 6 cm. We can now substitute these values into the equation for the slant height:
slant height²= 19²+ 6²
slant height² = 361 + 36
slant height² = 397
slant height ≈ 19.92 cm
Therefore, the radius of the cone is approximately:
radius = √(slant height² - height²)
radius = √(397 - 19²)
radius ≈ 5.65 cm (rounded to two decimal places)
2.Volume = (1/3) * π * radius²* height
Substituting the given values, we get:
Volume = (1/3) * π * (5.65 cm)²* 19 cm
Volume ≈ 600.98 cubic centimeters
Therefore, the volume of the cone is approximately 600.98 cubic centimeters.
3.To find the volume of the cylinder with height 15 cm and radius (width/2) 4 cm, we can use the formula for the volume of a cylinder:
Volume = π * radius² * height
Substituting the given values, we get:
Volume = π * (4 cm)² * 15 cm
Volume = π * 16 cm² * 15 cm
Volume ≈ 753.98 cubic centimeters
Therefore, the volume of the cylinder is approximately 753.98 cubic centimeters.
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the sum of the areas of two squares on the legs (a and b) equals the area of the square on the hypotenuse (c)?
This statement is knοwn as the Pythagοrean Theοrem, and it states that the square οf the hypοtenuse οf a right triangle is equal tο the sum οf the squares οf the οther twο sides.
What is the area?The area is the amοunt οf twο-dimensiοnal space that is enclοsed within a given bοundary οr shape. It is measured in square units, such as square inches, square feet, οr square meters. The area is an impοrtant cοncept in mathematics and is used tο calculate the size οf physical οbjects as well as tο measure figures οn a twο-dimensiοnal surface. Knοwing hοw tο calculate area is an essential skill in a variety οf fields, including architecture, engineering, and landscaping.
This relatiοnship was first discοvered by the ancient Greek philοsοpher Pythagοras οf Samοs, whο nοticed that this equatiοn always held true in right-angled triangles. The equatiοn is expressed as, where a and b are the sides οf the triangle and c is the hypοtenuse.
Fοr example, Lets take an example οf twο legs 3 and 4, and the hypοtenuse be 5,
Lets see if the hypοtenuse² = leg a² + leg b²
⇒ 5² = 4² + 3²
⇒ 25 = 16 + 9
⇒ 25 = 25.
Thus, This statement is knοwn as the Pythagοrean Theοrem, and it states that the square οf the hypοtenuse οf a right triangle is equal tο the sum οf the squares οf the οther twο sides.
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The complete question is:
Is it correct that the sum of the areas of two squares on the legs (a and b) equals the area of the square on the hypotenuse (c)?
Let x be a random variable distributed as normal(5,4). Find the probabilities of the following events: (i) p(x::; 6). (ii) p(x > 4 ). (iii) p( ix- 5 1 > 1
From the given information provided, the probability of P(X ≤ 6), P(X˃ 4) and P(|X- 5| ˃ 1) is 0.6915, 0.6915 and 0.3829 respectively.
(i) To find P(X ≤ 6), we need to standardize the value of 6 using the formula:
Z = (X - μ) / σ
where μ = 5 and σ = 2 (since the standard deviation is the square root of the variance, which is 4).
So, we have:
Z = (6 - 5) / 2
Z = 0.5
We can then look up the probability of Z ≤ 0.5 in a standard normal distribution table, or use a calculator to find:
P(X ≤ 6) = P(Z ≤ 0.5) = 0.6915
(ii) To find P(X > 4), we again need to standardize the value of 4:
Z = (4 - 5) / 2
Z = -0.5
Then, we can use the fact that the total area under a normal distribution curve is 1 to find the probability of X being greater than 4:
P(X > 4) = 1 - P(X ≤ 4) = 1 - P(Z ≤ -0.5)
Using a standard normal distribution table:
P(X > 4) = 0.6915
(iii) To find P(|X - 5| > 1), we first need to transform this inequality into a standard normal distribution by standardizing both sides:
|X - 5| > 1
implies:
X - 5 > 1 or
X - 5 < -1
which gives:
X > 6 or X < 4
We can then standardize each inequality separately. For X > 6, we have:
Z = (6 - 5) / 2
Z = 0.5
and for X < 4, we have:
Z = (4 - 5) / 2 = -0.5
Then, using the fact that the total area under a normal distribution curve is 1, we can find the probability of both events occurring:
P(|X - 5| > 1) = P(X > 6 or X < 4) = P(Z > 0.5 or Z < -0.5)
Since the standard normal distribution is symmetric around 0:
P(Z > 0.5 or Z < -0.5) = 2 × P(Z < -0.5)
Using a standard normal distribution table:
P(|X - 5| > 1) = 0.3829
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I can't figure out these questions. I know the answer because I'm using a textbook with answers in the back, but I don't understand *how* to get the answers. (I put 20 points for each question, please help!)
1. The difference of two polynomials is (3d² - 7d + 4).
One polynominal is (-8d² - 5d + 1).
a) What is the other polynomial? Explain how you found it.
b) How many different answers can you find?
I know that for the answer there are only two polynomials, (-5d² - 12d + 5) and (-11d² - 2d - 3), and I know how to get the first polynomial but the -11 one is confusing for me. I don't understand how to get it
2. Write a polynomial for the perimeter of each shape. Simplify the polynomial. Determine each perimeter when a = 3 cm.
Please help!!!
Answer:
Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
The width of a rectangle is 4 units less than the length. The area of the rectangle is 32 square units. What is the length, in units, of the rectangle?
Answer:
Let L be the length of the rectangle.
According to the problem, the width of the rectangle is 4 units less than the length, so the width is L - 4.
The area of the rectangle is given as 32 square units, so we can set up the equation:
A = L(L - 4) = 32
Expanding the left side of the equation, we get:
L^2 - 4L = 32
Rearranging and factoring, we get:
L^2 - 4L - 32 = 0
We can solve for L by using the quadratic formula:
L = (-b ± sqrt(b^2 - 4ac)) / 2a
Where a = 1, b = -4, and c = -32.
L = (-(-4) ± sqrt((-4)^2 - 4(1)(-32))) / 2(1)
L = (4 ± sqrt(16 + 128)) / 2
L = (4 ± sqrt(144)) / 2
L = (4 ± 12) / 2
L = 8 or L = -4
Since the length must be a positive value, we take L = 8.
Therefore, the length of the rectangle is 8 units.
The width and length of the rectangle will be 4 units and 8 units, respectively.
What is the area of the rectangle?Let W be the rectangle's width and L its length.
The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be
Area of the rectangle = L × W square units
The width of a square shape is 4 units less than the length. The region of the square shape is 32 square units. Then the equations are given below.
[tex]W = L - 4[/tex] ...1
[tex]L \times W = 32[/tex] ...2
From equations 1 and 2, then we have
[tex]L \times (L - 4) = 32[/tex]
[tex]L^2 - 4L = 32[/tex]
[tex]L^2 - 4L - 32 = 0[/tex]
[tex]L^2 - 8L + 4L - 32 = 0[/tex]
[tex]L(L - 8) + 4(L - 8) = 0[/tex]
[tex](L - 8)(L + 4) = 0[/tex]
[tex]L = 8, -4[/tex]
Then the width of the rectangle is given as,
[tex]W = 8 - 4[/tex]
[tex]W = 4 \ units[/tex]
The width and length of the rectangular shape will be 4 units and 8 units, separately.
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Evaluate x2 + 2(y ÷ w) for w = 2, x = 5, y = −8
The value of the expression x² + 2y ÷ 2w + 3z for w = 2, x = 5, y = 8, and z = 3 will be; ⇒ 3.15
Mathematical expression is defined as the collection of numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is;
⇒ x² + 2y ÷ 2w + 3z
And, The values are w = 2, x = 5, y = 8, and z = 3.
Now,
The expression is;
⇒ x² + 2y ÷ 2w + 3z
Substitute all the values of w = 2, x = 5, y = 8, and z = 3 in above equation, we get;
⇒ x² + 2y ÷ 2w + 3z
⇒ 5² + 2 × 8 ÷ 2 × 2 + 3 × 3
⇒ 25 + 16 ÷ 4 + 9
⇒ 41 ÷ 13
⇒ 3.15
Thus, The value of the expression x² + 2y ÷ 2w + 3z for w = 2, x = 5, y = 8, and z = 3 will be;
⇒ 3.15
The complete question is-
What is the value of x2 + 2y ÷ 2w + 3z for w = 2, x = 5, y = 8, and z = 3?
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Typically, the y-value in a function is called the ______.
a. output
b. axis
c. expression
d. variable
e. input