Answer: approximately 68,404 liters.
Step-by-step explanation:
To solve the problem, we first need to find the cross-sectional area of the pipe, which we can calculate using the formula for the area of a circle:
A = πr^2
where r is the radius of the pipe, which is half the diameter. So, in this case, the radius is 2.4 cm / 2 = 1.2 cm.
A = π(1.2 cm)^2
A ≈ 4.5239 cm^2
Next, we can use the formula for volume flow rate to find the volume of water that is discharged per second:
Q = Av
where Q is the volume flow rate, A is the cross-sectional area of the pipe, and v is the velocity of the water. In this case, we have:
Q = (4.5239 cm^2)(2.8 m/s)
Q ≈ 0.01266 m^3/s
To find the volume of water discharged in one and a half hours (which is 5400 seconds), we can multiply the volume flow rate by the time:
V = Qt
V = (0.01266 m^3/s)(5400 s)
V ≈ 68.404 m^3
Finally, to convert the volume from cubic meters to liters, we can multiply by 1000:
V = 68.404 m^3 × 1000 L/m^3
V ≈ 68,404 L
Therefore, the volume of water discharged in one and a half hours is approximately 68,404 liters.
Answer the question below:
A rocket is launched from atop a 76-foot cliff with an initial velocity of 113 ft/s. The height of the rocket
above the ground at time is given by h = -161 +1131+ 76. When will the rocket hit the ground after it is
launched? Round to the nearest tenth of a second.
0.6 seconds
7.7 seconds
3.5 seconds
7.1 seconds
Answer:
t=7.7 s
Step-by-step explanation:
h=ut+1/2gt²
-76=113t+1/2(-32)t²
-76=113t-16t²
16t²-113t-76=0
[tex]t=\frac{113\pm\sqrt{(-113)^2-4 \times 16 \times(-76)} }{2 \times 16} \\t=\frac{113 \pm\sqrt{12769+4864} }{32} \\t=\frac{113 \pm\sqrt{17633} }{32} \\t=\frac{113+\sqrt{17633} }{32} \approx 7.68~s \approx7.7 s\\or\\t=\frac{113-\sqrt{17633} }{32} \approx~-0.62 ~s \approx-0.6~s[/tex]
negative~sign~rejected.
PLEASEE HELP! DUE TONIGHT
Find the perimeter of the figure below, in feet.
Answer:
79.2ft
Step-by-step explanation:
(9+9+10.3+10.3+10+10+10.3+10.3)ft
79.2ft
Which of the ten basic functions in
our toolkit have all real numbers for
their range?
The functions that have all real numbers for their range are the ones in the option B.
Which set of ten basic functions has all real numbers for their range?Remember that for a function y = f(x), we define the range as the set of possible outputs of the function, that is, possible values of y.
Here we can see a lot of functions, first, the option with the absolute value function can be discarded because we know that:
|x| ≥ 0
So it never takes negative values.
We also can discardthe option with the sine and cosine, because the range of these two functions is [-1, 1].
The only remaining option is B, and the range of these 3 functions is (-∞, ∞), so that is the correct option in this case.
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I need help with this
Answer:
(x -14)² +(y -7)² = 1²
Step-by-step explanation:
You want the equation of the circle that represents the border of a logo centered 14 m right and 7 m up from the lower left corner of a soccer field. The logo is 2 m in diameter.
Equation of a circleThe equation of a circle with center (h, k) and radius r is ...
(x -h)² +(y -k)² = r²
Since the origin of the coordinate system is the lower left corner of the field, the center is located at (h, k) = (14, 7). The diameter of 2 m means the radius is 1 m. Using these values in the equation, it becomes ...
(x -14)² +(y -7)² = 1²
C Select the correct answer. Which equation is equivalent to the given eq -4(x - 5) + 8x = 9x - 3
Answer:
-4(x - 5) + 8x = 9x - 3
Simplifying the left side:
-4x + 20 + 8x = 9x - 3
4x + 20 = 9x - 3
Subtracting 4x from both sides:
20 = 5x - 3
Adding 3 to both sides:
23 = 5x
Dividing both sides by 5:
x = 23/5
Therefore, the equation equivalent to the given equation is:
5x - 23 = 0
Uri paid a landscaping company to mow his lawn. The company charged $74 for the service plus
5% tax. After tax, Uri also included a 10% tip with his payment. How much did he pay in all?
Uri paid a total of $85.47 for the landscaping service including tax and tip.
What is tax?Taxes are compulsory payments made by a government organisation, whether local, regional, or federal, to people or businesses. Tax revenues are used to fund a variety of government initiatives, such as Social Security and Medicare as well as public infrastructure and services like roads and schools. Taxes are borne by whoever bears the cost of the tax in economics, whether this is the entity being taxed, such as a business, or the final users of the items produced by the firm. Taxes should be taken into consideration from an accounting standpoint, including payroll taxes, federal and state income taxes, and sales taxes.
Given that company charged $74 for the service plus 5% tax.
The tax is 5%, that is:
Tax = 5% of $74 = 0.05 x $74 = $3.70
Cost after tax = $74 + $3.70 = $77.70
Now, tip is 10%:
Tip = 10% of $77.70 = 0.10 x $77.70 = $7.77
Total cost = $77.70 + $7.77 = $85.47
Hence, Uri paid a total of $85.47 for the landscaping service including tax and tip.
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Chau had 4/5 of a spool of yarn. He used 3/5 of his yarn for a project. What fraction of the spool was used for the project?
Answer: 3/5
Step-by-step explanation:
Chau had 4/5 of a spool of yarn, and he used 3/5 of it for a project.
The fraction of the spool used for the project is:
3/5
So, 3/5 of the spool was used for the project.
Hoang has worked as a nurse at Springfield General Hospital for 5 years longer than her friend Bill. Two years ago, she had been at the hospital for twice as long. How long has each been at the hospital?
5 years longer then Bill, 2x5=10.
10+2=12.
12-5=7
Hoang has be there for 12 years. Bill has for 7 years.
Cells ire approximately round with a diameters ranging from 1 to >100 micrometers. The graph below shows the cross section of half a cell with a diameter of 2μm. The curvature of the cell surface determines if and how vesicles can form. Find the curvature of the cell surface y at the red point x=0.25 from the equation for a circle: y= (2−x)x
The curvature of the cell surface that has a shape of circle y at the red point x=0.25 is 1.75.
What is diameter?Diameter is a line segment that passes through the center of a circle or sphere and has its endpoints on the circumference of the circle or sphere. The diameter of a circle is twice the length of its radius, so if the radius is given, the diameter can be calculated by multiplying the radius by two.
The equation is given as y = (2 - x)2, where x is the distance from the centre of the circle and y is the curvature of the circle at that distance. To calculate the curvature of the cell surface at any given point, the distance from the centre needs to be known. In this example, the distance from the centre is 0.25, and the curvature of the cell surface at this point is 1.75.
A low curvature, such as 1.75, will allow for more vesicles to form on the surface of the cell. A low curvature will allow for more vesicles to form, and a high curvature will prevent the formation of vesicles.
The equation for a circle with a diameter of 2μm is given as y = (2 - x)2. Substituting x = 0.25 into the equation yields y = (2 - 0.25)2 = 1.75.
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The circle-shaped cell surface's (or circumference's) curvature at the red spot x=0.25 is 0.66.
What is diameter?A circle or sphere's diameter is defined as a line segment with its endpoints on the circumference and that travels through the middle of the object. If the radius is known, the diameter can be determined by multiplying the radius by two since the diameter of a circle is twice the length of its radius.
It is possible to compute the cell surface's curvature at x = 0.25 as follows:
Let's look at the circle's calculation.
y = √(2 - x)x
Now, when x = 0.25,
y = √(2 - 0.25)×0.25
y = √1.75×0.25
y = 0.66
As a result, the cell surface's slope at x = 0.25 is 0.66.
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Solve the polynomial equation by factoring and then using the zero-product principle.
2
8x-4=2x-x
Rewrite the equation in factored form.
(Blank)= 0
What is the solution pair?
the factored form of the equation is 2(13x - 2) = 0, and the solution to the equation is x = 2/13.
Why it is and what is Zero-Product formula?
First, we can simplify the equation by combining like terms:
28x - 4 = 2x - x
Simplifying further:
26x - 4 = 0
Now, we can factor out 2 from the left side of the equation:
2(13x - 2) = 0
Using the zero-product principle, we can set each factor equal to zero:
2 = 0 or 13x - 2 = 0
The first equation is impossible since 2 is not equal to zero. Solving the second equation, we get:
13x - 2 = 0
Adding 2 to both sides:
13x = 2
Dividing both sides by 13:
x = 2/13
Therefore, the factored form of the equation is 2(13x - 2) = 0, and the solution to the equation is x = 2/13.
The zero-product property or formula states that if the product of two factors is zero, then at least one of the factors must be zero. In other words, if a and b are real numbers such that ab = 0, then either a = 0, b = 0, or both a and b are zero. This property is often used to solve polynomial equations by factoring the expression and then setting each factor equal to zero.
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An insurance company offers its policyholders a number of different premium payment options. For a randomly selected policyholder, let X = the number of months between successive payments. The cdf of X is as follows:F(x) =0 x < 10.31 1 ≤ x < 30.42 3 ≤ x < 40.46 4 ≤ x < 60.82 6 ≤ x < 121 12 ≤ xa) What is the pmf of X?x 1 3 4 6 12p(x) _____
For the given CDF of X, the pmf of X at 1,3,4,6 and 12 is written as :
P(X = k) = 0.30 for k = 1 , P(X = k) = 0.10 for k = 3,
P(X = k) = 0.05 for k = 4 , P(X = k) = 0.15 for k = 6,
P(X = k) = 0.40 for k = 12.
In order to find the probability mass function (PMF) of X, we need to calculate the probability that X takes on each possible value.
Since X can take on any positive integer value, we can start by calculating the probability that X equals each positive integer.
⇒ P(X = 1) = 0.30,
⇒ P(X = 3) = F(3) - F(1) = 0.40 - 0.30 = 0.10
⇒ P(X = 4) = F(4) - F(3) = 0.45 - 0.40 = 0.05
⇒ P(X = 6) = F(6) - F(4) = 0.60 - 0.45 = 0.15
⇒ P(X = 12) = F(12) - F(6) = 1 - 0.60 = 0.40
Therefore, the required PMF of X is: P(X = 1) = 0.30 , P(X = 3) = 0.10 , P(X = 4) = 0.05 , P(X = 6) = 0.15 and P(X = 12) = 0.40 .
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The given question is incomplete, the complete question is
An insurance company offers its policyholders a number of different premium payment options. For a randomly selected policyholder, let X = the number of months between successive payments.
The CDF of X is as follows:
F(x) = {0 x < 1
{0.30 1 ≤ x < 3
{0.40 3 ≤ x < 4
{0.45 4 ≤ x < 6
{0.60 6 ≤ x < 12
{1 12 ≤ x
What is the pmf of X at 1,3,4,6 and 12?
Can I please get help it's an EMERGENCY!
The number of hours it will take the same dog to run 26 1/10 miles is 7.2 hours
How long will it take the dog to run 26 1/10 miles?7 1/4 miles in 2 hours
26 1/10 miles in x hours
Equate miles ratio hours
7 ¼ miles : 2 hours = 26 ⅒ miles : x hours
7.25 / 2 = 26.10 / x
cross product
7.25 × x = 26.10 × 2
7.25x = 52.20
divide both sides by 7.25
x = 52.20 / 7.25
x = 7.2 hours
Ultimately, it will take 7.2 hours for the dog to run 26⅒ miles.
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(Evaluating Reports MC)
The dot plot below shows the number of hours of sleep preferred by 25 patients chosen randomly in a particular medical office.
Calculate the mean, median, and mode of the data. Based on the results, which list shows a comparison of the measures of central tendency, from least to greatest?
A) Median, mode, mean
B) Median, mean, mode
C) Mode, median, mean
D) Mean, median, mode
Answer:
D
Step-by-step explanation:
Mean- 6.78
Median- 7
Mode- 8
can you find the slope of the given graph?
slope of graph=?
The slope of the graph f(x) = 3x² + 7 at (-2, 19) is -12
What is the slope of a graph?The slope of a graph is the derivative of the graph at that point.
Since we have tha graph f(x) = 3x² + 7 and we want to find its slope at the point (-2, 19).
To find the slope of the graph, we differentiate with respect to x, since the derivative is the value of the slope at the point.
So, f(x) = 3x² + 7
Differentiating with respect to x,we have
df(x)/dx = d(3x² + 7)/dx
= d3x²/dx + d7/dx
= 6x + 0
= 6x
dy/dx = f'(x) = 6x
At (-2, 19), we have x = -2.
So, the slope f'(x) = 6x
f'(-2) = 6(-2)
= -12
So, the slope is -12.
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if A is 20% more than B, by what percent is B less than A?
Answer:
Jika A adalah 20% lebih banyak dari B, maka dapat dituliskan sebagai:
A = B + 0.2B
Dalam bentuk sederhana, hal ini dapat disederhanakan menjadi:
A = 1.2B
Kita dapat menggunakan persamaan ini untuk mencari persentase B yang lebih kecil dari A. Misalnya, jika kita ingin mengetahui berapa persen B lebih kecil dari A, maka kita dapat menggunakan rumus persentase sebagai berikut:
(B lebih kecil dari A) / A x 100%
Substitusikan nilai A = 1.2B dan kita dapatkan:
(B lebih kecil dari 1.2B) / 1.2B x 100%
Maka:
0.2B / 1.2B x 100%
= 0.1667 x 100%
= 16.67%
Jadi, B adalah 16.67% lebih kecil dari A.
Untuk Konsultasi: 0813-7200-6413
6.) The sum of two numbers is 45.
The larger number y is 6 less than twice the smaller number
a.
Write a system of linear equations.
What is the smaller number?
Answer:
x= 13 =smaller number
Step-by-step explanation:
let x=smaller number
y=2x-6=larger number
x+y=45
x+2x-6=45 (equation)
3x=39
x=13
Answer:
[tex]x = 13[/tex] ..... smaller number
and
[tex]y = 32[/tex] ....... larger number
Step-by-step explanation:
Greetings!!!
Let the two numbers be X and Y
[tex]x + y = 45........ \:equation \: 1[/tex]
The larger number is y and is 6 less than twice the smaller number. which means:-
[tex](y - 6) = 2x........... \: equation \: 2[/tex]
so, now solve for y. from equation 2
[tex]y - 6 = 2x \\ y = 2x + 6[/tex]
Substitute equation 1 into equation 2
[tex]x + y = 45 \\ x + (2x + 6) = 45 \\ 3x + 6 = 45 \\ 3x = 45 - 6 \\ 3x = 39....divide \: both \: sides \: by \: 3 \\ x = 13[/tex]
To solve for y substitute x into the first equation
[tex](13) = + y = 45 \\ y = 45 - 13 \\ y = 32[/tex]
Finally, to be more sure make a cross check
[tex]y - 6 = 2x \\ 32 - 6 = 2(13) \\ 26 = 26[/tex]
If you have any questions tag it on comments
Hope it helps!!!
What is the perimeter of the football field without the end zones?
Answer:
30623 yards
Step-by-step explanation:
Answer:
In the NFL, the perimeter of a football field, excluding the end zones, is 30623 yards. The field is how many feet wide... A football field in the United States is 120 yards long (including the end zones).
Step-by-step explanation:
Brainliest pls
The dot plot below shows the number of hours of sleep preferred by 25 patients chosen randomly in a particular medical office.
Calculate the mean, median, and mode of the data. Based on the results, which list shows a comparison of the measures of central tendency, from least to greatest?
A) Median, mode, mean
B) Median, mean, mode
C) Mode, median, mean
D) Mean, median, mode
The list that shows a comparison of the measures of central tendency from the least to the greatest is mean, median and mode. (option D)
What is the correct order?The dataset represented with the dot plot is 2, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8,8, 8, 8, ,8, 8, 8, 8, 8, 8
Mean is the average of the dataset.
Mean = sum of numbers / total number in the dataset
[(2 x 1) + (5 x 4) + (6 x 4) + (7 x 6) + (8 x 10)] / 25 = 6.72
Median is the number at the center of the dataset.
The median = 1/2(n + 1)
1/2 x (26) = 13th number = 7
Mode is the number that occurs most frequently. The number that occurs the most in the dataset is 8.
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Estimate a 15% tip on a dinner bill of $58.12 by first rounding the bill amount to the nearest ten dollars.
Answer: an estimated 15% tip on a dinner bill of $58.12 would be $8.72.
Step-by-step explanation:
First, we can calculate 10% of $58.12 by moving the decimal point one place to the left, which gives us $5.81.
Then, we can calculate half of 10%, which is 5%, by dividing $5.81 by 2, giving us $2.91.
Finally, we add 10% and 5% to get the estimated tip amount:
$5.81 + $2.91 = $8.72
Therefore, an estimated 15% tip on a dinner bill of $58.12 would be $8.72.
Consider the following equation: X3 + 4x2 + 4x + 16 = 0. Solve for x. Your answer should be stored in a variable result , which will be a list containing three sympy expressions. Starter code (click to view) Answer* 1 import sympy
Considering the following equation x³ + 4x² + 4x + 16 = 0 we have the value of x as [-4, -2*I, 2*] in sympy expressions.
Symbolic math is supported by the Python library SymPy (http://www.sympy.org). In symbolic mathematics, mathematical expressions are represented by symbols. This is an illustration of a symbolic arithmetic expression: x2+y2=z. The three variables x, y, and z are present in the formula above.
Considering the following equation x³ + 4x² + 4x + 16 = 0.
CODE:
import sympy #importing SymPy
x = sympy.Symbol('x') #declaring the variable 'x' as the only variable for the expression
result = sympy.solve(x**3 + 4*x**2 + 4*x + 16,x) #using the function solve() to solve the expression.
print(result) #displaying the list 'result'
OUTPUT:
[-4, -2*I, 2*]
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Help I don’t just this
The conditional relative frequency that a student rides the bus, given that the student is in middle school is 0.16 / 0.96 ≈ 0.17.
Describe conditional relative frequency ?Conditional relative frequency is a statistical measure that describes the proportion or percentage of a specific group or category within a subset of data. It is calculated by dividing the frequency of the specific category in the subset by the frequency of the total subset.
To find the conditional relative frequency that a student rides the bus, given that the student is in middle school, we need to divide the frequency of middle school students who ride the bus by the total number of middle school students.
From the table, we see that the frequency of middle school students who ride the bus is 0.16. The total number of middle school students is the sum of the frequencies in the first row, which is 0.20 + 0.16 + 0.12 + 0.48 = 0.96.
So, the conditional relative frequency that a student rides the bus, given that the student is in middle school is:
0.16 / 0.96 ≈ 0.17
Rounded to the nearest hundredth, the answer is 0.17. Therefore, about 17% of middle school students ride the bus.
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two cards are drawn at random from an ordinary deck of 52 cards what is the probability that thee are no sixes
there is an 85% chance that the two cards drawn at random from an ordinary deck of 52 cards will not be sixes.
The probability of drawing a card from an ordinary deck without replacement can be determined using the concept of conditional probability. Conditional probability is the probability of an event occurring, assuming that another event has already occurred.
In order to calculate the probability that the two cards drawn are not sixes, we can use the formula:
P(A and B) = P(A) x P(B|A)
Where A and B represent two independent events, P(A) is the probability of event A occurring, and P(B|A) is the conditional probability of event B occurring given that event A has already occurred.
The probability of drawing the first card that is not a six is:
P(A) = 48/52 = 0.9231
The probability of drawing the second card that is not a six, given that the first card drawn was not a six, is:
P(B|A) = 47/51 = 0.9216
Therefore, the probability of drawing two cards at random from an ordinary deck of 52 cards and having neither of them be a six is:
P(A and B) = P(A) x P(B|A) = 0.9231 x 0.9216 = 0.8503 or approximately 85%.
This means that there is an 85% chance that the two cards drawn at random from an ordinary deck of 52 cards will not be sixes.
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What is 15426.82 rounded to the nearest hundredth
Answer:
Step-by-step explanation:
15426.80
Answer: 15426.82
Step-by-step explanation:
15426.82 is also 15426.82000
Since 2 is the hundredth number (behind the decimal point) and the next number is 0, it will be rounded down.
Therefore 15426.82 to the nearest hundredth is 15426.82
what is the cost of sales
The expense incurred by a cοmpany tο prοduce the gοοds οr services sοld within a specific time periοd is knοwn as the cοst οf sales.
What dοes cοst cοmprise οf ?It cοmprises all cοsts that are directly related tο the prοductiοn prοcess, such as thοse fοr labοr, utilities, raw materials, and manufacturing equipment depreciatiοn.
Grοss prοfit, which is the amοunt οf mοney a firm makes frοm its cοre οperatiοns befοre deducting extra cοsts like marketing, administrative, and financing charges, is calculated by subtracting the cοst οf sales frοm revenue. Tο apprοpriately price their prοducts and assess the prοfitability οf their οperatiοns, firms must have a thοrοugh understanding οf their cοst οf sales.
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Complete question:
What is the definition of cοst οf sales?
Find the standard normal area for each of the following(round your answers to 4 decimal places)
The standard normal area is the region under the standard normal distribution curve, which has a mean of 0 and a standard deviation of 1. One is equal to the entire area under the normal distribution curve.
What is the standard normal area?To determine the probability for the above intervals using a typical normal distribution table or a calculator with a normal distribution function:
[tex]P(1.22 < Z < 2.15) = 0.1143[/tex]
[tex]P(2.00 < Z < 3.00) = 0.0228[/tex]
[tex]P(-2.00 < Z < 2.00) = P(Z < 2.00) - P(Z < -2.00) = 0.9772 - 0.0228 = 0.9544[/tex]
The number of standard deviations the variable is from the mean is shown by the ensuing Z-score. The chance of detecting a certain value of the variable in a given interval can then be determined using the standard normal area.
Therefore, The symmetry of the normal distribution allows us to use the third interval's coverage of 4 standard deviations to simplify the calculation, as illustrated above.
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Help i need this question solved
Answer: D. Square
Step-by-step explanation:
The shape created by the cross section of the cut through a square pyramid is a square.
To see why, imagine the pyramid sitting on a table with its square base flat against the surface. The cut goes through the vertex, which is the point at the top of the pyramid. Since the cut is perpendicular to the base, it divides the pyramid into two smaller pyramids with congruent, but not identical, bases. Each of these smaller pyramids has a triangular base that is an isosceles right triangle. The two triangles share a common hypotenuse, which is the line of the cut.
The cross section of the cut is the shape formed where the two triangles meet along the hypotenuse. Since both triangles are congruent and the hypotenuse is the same for both, the cross section is a square. The sides of the square are equal to the base of the original pyramid, which is one of the legs of the isosceles right triangles formed by the cut. Therefore, the answer is D, a square.
Help what’s the answer
Answer:
Difference=£2.4
Step-by-step explanation:
Here in shop A
130 cm=£1.82
1 cm=£1.82/130
1 cm=0.014
Now
400 cm=0.014*400
=£5.6
Again, In shop B
235cm=£1.88
1 cm=£1.88/235
1 cm=£0.008
Now
400cm=0.008*400
=£3.2
Now,
Difference=£5.6-£3.2
=£2.4
What if the equation of the line that passes through (-4,5) and is parallel to the line 4x+2y=10
Answer: y = -2x -3
Step by step explanation
First, we find the gradient of the line 4x + 2y = 10 by making y the subject of the formula.
4x + 2y = 10
2y = 10 - 4x which is the same as 2y = -4x + 10
Divide each term by 2
2y/2 = -4x/2 + 10/2
y = -2x + 5
From the equation, the gradient (coefficient of x) is -2
Since the line is parallel to 4x+2y=10, therefore the gradient of the lines are the same
The equation of the line can be gotten from y - y1 = m(x -x1)
where y1 = 5, x1 = -4 and m = -2
Therefore subtitiuiting into y - y1 = m(x -x1)
y - 5 = -2(x-(-4))
y - 5 = -2(x + 4)
y - 5 = -2x - 8
y = -2x -8 + 5
y = -2x -3
you can see that the gradients are the same (coefficent of x = -2)
2. Urn A contains 4 black, 3 red, and 3 white balls, whereas urn B contains 3 white, I red, and 3 black balls. A ball is drawn at random from urn A and placed in urn B. A ball is then drawn from urn B. It happens to be red. What is the probability that the ball transferred was red?
The probability that the ball transferred was red, given that a red ball was drawn from urn B, is 21/55, or about 0.382.
What is probability ?
Probability is a mathematical concept that measures the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 means that the event is impossible, and 1 means that the event is certain to happen.
To calculate probability, we usually take the number of favorable outcomes and divide it by the total number of possible outcomes. For example, if we flip a coin, the probability of getting heads is 1/2 because there is only one favorable outcome (heads) out of two possible outcomes (heads or tails).
According to the question:
Let's use Bayes' theorem to find the probability that the ball transferred was red:
Let R be the event that a red ball is drawn from urn B, and T be the event that the transferred ball was red.
Then we want to find P(T = red | R = red).
By Bayes' theorem, we have:
P(T = red | R = red) = P(R = red | T = red) * P(T = red) / P(R = red)
We can calculate each of these probabilities as follows:
P(R = red | T = red): The probability of drawing a red ball from urn B, given that a red ball was transferred from urn A to urn B, is 1/4, since urn B originally contained 1 red ball out of 7 total balls (3 black, 3 white, and 1 red) and we added one more red ball to it.
P(T = red): The probability that a red ball was transferred from urn A to urn B is 3/10, since urn A originally contained 3 red balls out of 10 total balls and we transferred one ball at random.
P(R = red): The overall probability of drawing a red ball from urn B is:
P(R = red) = P(R = red | T = black) * P(T = black) + P(R = red | T = red) * P(T = red)
where T = black means that a black ball was transferred from urn A to urn B. We can calculate each of these conditional probabilities as follows:
P(R = red | T = black): The probability of drawing a red ball from urn B, given that a black ball was transferred from urn A to urn B, is 1/7, since urn B originally contained 1 red ball out of 7 total balls (3 black, 3 white, and 1 red) and we did not add any more red balls to it.
P(T = black): The probability that a black ball was transferred from urn A to urn B is 4/10, since urn A originally contained 4 black balls out of 10 total balls and we transferred one ball at random.
Therefore, we have:
P(R = red) = 1/7 * 4/10 + 1/4 * 3/10 = 1/35 + 3/40 = 11/140
Putting it all together:
P(T = red | R = red) = (1/4) * (3/10) / (11/140) = 21/55
So the probability that the ball transferred was red, given that a red ball was drawn from urn B, is 21/55, or about 0.382.
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Find the surface area of the triangular pyramid. The side lengths of the base are equal.
The surface area of the triangular pyramid is the sum of the lateral surface area and the base area.
Lateral Surface Area: The lateral surface area of a triangular pyramid is equal to the product of the slant height and the perimeter of the base.
Slant height = √ ( (length of side)2 + (height)2 )
Perimeter of the base = 3 x length of side
Therefore, the lateral surface area = √ ( (length of side)2 + (height)2 ) x 3 x length of side
Base Area: The base area of the triangular pyramid is equal to one-half of the product of the three side lengths.
Therefore, the base area = 1/2 x (length of side) x (length of side) x (length of side)
Surface Area: The total surface area of the triangular pyramid = lateral surface area + base area
Therefore, the surface area = √ ( (length of side)2 + (height)2 ) x 3 x length of side + 1/2 x (length of side) x (length of side) x (length of side)