The required solution of the random variable X that follows an exponential distribution is shown below.
To find the expected value, standard deviation, and probabilities associated with the exponential distribution, we'll use the given parameter λ = 1/9.848.
Expected Value (Mean):
The expected value of an exponential distribution is equal to the reciprocal of the rate parameter λ. Therefore, the expected value is given by:
E(X) = 1 / λ
E(X) = 1 / (1/9.848)
E(X) = 9.848
So, the expected value of the random variable X is 9.848.
Standard Deviation:
The standard deviation of an exponential distribution is equal to the reciprocal of the rate parameter λ. Therefore, the standard deviation is given by:
σ = 1 / λ
σ = 1 / (1/9.848)
σ = 9.848
So, the standard deviation of the random variable X is also 9.848.
P(X < 12):
To find the probability that X is less than 12, we can use the cumulative distribution function (CDF) of the exponential distribution. The CDF is given by:
[tex]F(x) = 1 - e^{(-\lambda x)}[/tex]
Substituting the given λ = 1/9.848 and x = 12, we have:
[tex]P(X < 12) = F(12) = 1 - e^{-(1/9.848) * 12)}[/tex]
Calculating this expression, we find:
P(X < 12) ≈ 0.7043
Therefore, the probability that X is less than 12 is approximately 0.7737.
P(8 < X < 12):
To find the probability that X lies between 8 and 12, we subtract the cumulative probability at 8 from the cumulative probability at 12:
P(8 < X < 12) = F(12) - F(8)
= [tex]1 - e^{(-(1/9.848) * 12)]} - [1 - e^{(-(1/9.848) * 8)]}[/tex]
Calculating this expression, we find:
P(8 < X < 12) ≈ 0.2025
Therefore, the probability that X lies between 8 and 12 is approximately 0.2025.
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How do you write 37 million as using the power of ten exponent
37 million can be written as 3.7 × 10⁶ in the power of ten exponent notation.
In scientific notation, a number is written as the product of a coefficient and a power of ten.
To convert 37 million to scientific notation, we need to move the decimal point to the left until we have a number between 1 and 10.
Starting with 37 million, we can move the decimal point six places to the left to obtain the number 3.7:
= 37,000,000 -> 3.7
Now, we express this number as a product of the coefficient (3.7) and 10 raised to the power of the number of places we moved the decimal point.
In this case, since we moved the decimal point six places to the left, the exponent of ten is 6:
37 million = 3.7 × 10⁶
Therefore, 37 million can be written as 3.7 × 10⁶ in the power of ten exponent notation.
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find the equation of the line that passes through the points (-3,-7) (-3,10
The equation of the line that passes through point (-3,-7) and point (-3,10) is x = -3.
What is the equation of the line passing through the given coordinates?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the points through which the line passes: (-3,-7) and (-3,10).
The two given points (-3, -7) and (-3, 10) have the same x-coordinate -3
Hence, the two lines lie on a vertical line.
since the slope of the vertical line is undefined.
The equation of the line passing through these two points is simply the equation of the vertical line:
x = -3
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Write the equation of the ellipse graphed below.
Answer:
(x +4)²/25 +(y -3)²/16 = 1
Step-by-step explanation:
You want the equation of the ellipse with center (-4, 3) and semi-axes 5 and 4 in the x- and y-directions, respectively.
Ellipse equationThe standard form equation for an ellipse with center (h, k) and sem-axes 'a' and 'b' in the x- and y-directions, respectively, is ...
(x -h)²/a² +(y -k)²/b² = 1
Using the given values, we find the equation to be ...
(x +4)²/25 +(y -3)²/16 = 1
__
Additional comment
The longer of the two axes is the "major" axis, and its end points are the "vertices". For the purpose of an ellipse with center, vertices, and co-vertices specified, the equation is not affected by which axis is longer.
Effectively, this is the equation of a circle with different scale factors in the x- and y-directions.
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Five males with an X-linked genetic disorder have one child each. The random variable x is the number of children among the five who inherit the X-linked genetic disorder. Determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied.
Does the table show a probability distribution? Select all that apply.
Find the mean of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Find the standard deviation of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
The standard deviation of the random variable x is 1.1145
Since the Probability distribution of a random variable is the collection of value and its probability pair for values of that considered random variable.
The probability of a value of x is never neg.
The sum of the probabilities is always 1.
The sum of all values of P(X = x) equals 1, which is, considering n values
There are no negative values of P(X = x).
Since we are given the probability distribution as below, we will go and calculate the mean and standard deviation using the formula:
E(X)= ∑xP(X=x)
Standard deviation = √Variance(x)
Var(x) = E(x²) - [E(x)]²
X 0 1 2 3 4 5
p(x=x) 0.032 0.152 0.316 0.316 0.152 0.032
First we have to find E(x)
E(x) = (0x0.032) + (1x0.152) + (2x0.316) + (3x0.316) + (0.152) + (5x0.032)
The mean E(x) = 2.5
To find variance, we use Var(x) = E(x²) - [E(x)]²
But we have to calculate E(x²) first, since we already have found E(x)
So,
E(x²) = (0²x0.032) + (1²x0.152) + (2²x0.316) + (3²x0.316) + (4²x0.152) + (5²x0.032)
therefore, E(x²) = 7.492
Now we have all the values we can find the variance:
Var(x) = E(x²) - [E(x)]²
=7.492 - [2.5]²
= 1.242
With variance now we can find the standard deviation;
S.D = √Var(x)
= √1.242
= 1.1145
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2. Convert the following into a single log statement from the many log statements to 1.
2 Log w+ log 7-3 log x-8 log y
NOTE: You must show this in at least two steps.
1st line should be to convert the 2 the 3 and the 8 only.
2nd line can be the final answer.
A single log statement from the many log statements to 1 is: [tex]log(7wy^{(-8)}/x^3)[/tex]
The exponent that indicates the power to which a base number is raised to produce a given number are called logarithm.
Use the logarithmic identity:
log[tex](a^n)[/tex] = n*log(a)
to convert the coefficients 2, 3, and 8:
log w + log 7 - 3log x - 8log y
= log w + log 7 - log [tex]x^3[/tex] - log [tex]y^8[/tex]
Combine the terms on the right-hand side using the logarithmic identity:
log(a) + log(b) = log(ab)
log w + log 7 - log[tex]x^3[/tex] - log [tex]y^8[/tex]
= log([tex]7wy^{-8}/x^3[/tex])
Therefore, the single log statement is from the many log statements to 1 is: log[tex](7wy^{-8}/x^3)[/tex]
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Find the area of this trapezoid. Be sure to include the correct unit in your answer.
13 in
10 in
5 in
12 in
Answer:
12
Step-by-step explanation:
206
5x10 12x13=206 it may be incorrect but i not sure if it is incorrect
Find the area of the shape
The area of the given figure with rectangle and triangle is 27.5 square centimeters.
The given figure has a rectangle and two triangles.
The area of the rectangle is length times width
Length = 5 cm
Width = 4 cm
Area of rectangle = 5×4
=20 square centimeters
Area of triangle =1/2 base ×height
=1/2×2.5×3
=3.75 square centimeters
As there are two triangles, 2(3.75)=7.5 square centimeters
Total area = 20+7.5
=27.5 square centimeters
Hence, the area of the given figure with rectangle and triangle is 27.5 square centimeters.
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The sector of a circle has an area of 7π/5 square inches and central angle with
measure 56°.
What is the radius of the circle, in inches?
Answer:
3
Step-by-step explanation:
Area = 7pi/5
56/360 × pi r² = 7pi/5
Pi is canceled on both sides.
r² = 7/5 ÷ 56/360 = 9
r = root 9 = 3
What is the slope of this line?
A line passing through the points (negative 4, negative 3) & (0, 1).
© 2017 StrongMind. Created using GeoGebra.
Enter your answer as a number, like this: 42
Or, if the slope is undefined, enter a lowercase letter "u," like this: u
Answer:
[tex]m = \frac{1 - ( - 3)}{0 - ( - 4)} = \frac{4}{4} = 1[/tex]
Hello! Find Domain and range, thank you :-)
There are 3 feet in a yard. How many centimeters are in a yard?
Gavin is working two summer jobs making $14 per hour tutoring and $13 per hour landscaping. Last week Gavin worked a total of 10 hours and earned a total of $137. Determine the number of hours Gavin worked tutoring last week and the number of hours he worked landscaping last week.
Solving a system of equations we can see that Gavin worked 7 hours tutoring.
How to find the number of gours that Gaving worked tutoring?Let's define the variables:
x = number of hours tutoring.
y = number of hours land scaping.
We know that he worked for 10 hours and earned $137, then we can write a system of equations:
x + y = 10
14x + 13y = 137
Isolating y on the first equation we get:
y = 10 - x
Replace that in the second one to get:
14x + 13*(10 - x) = 137
14x + 130 - 13x = 137
x = 137 - 130 = 7
He worked 7 hours tutoring.
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Nadeen bought a 91-day T-bill that has an interest rate of
4.30% p.a. and a face value of $5,000.
a) How much did she pay for the T-Bill?
b) After 40 days, Barbara sold the T-bill to her friend when the interest rate for this T-bill in the market increased to 5.30% p.a. What was her selling price?
The 91-day T-bill that Nadeen bought at an interest rate of 4.30% p.a. and face value of $5,000 indicates;
a) Nadeen paid about $4,946.24 for the T-bill
b) Barbara's selling price for the T-bill is about $4,962.74
What is a T-bill?A Treasury bill (T-bill), is a short-term obligation that is issued by the U.S. Department of Treasury and which is backed by the United States government, and has a maturity of less than a year. T-bills are low risk investment as they are backed by the credit and full faith of the U.S. government.
The formula for the price of the T-bill can be calculated with the formula;
Price = Face Value/(1 + (Interest Rate × Days to Maturity/360))
Plugging in the value from the question, we get;
Price = 5000/(1 + (0.043 × 91/360)) ≈ 4946.24
Therefore, Nadeen paid $4,946.24 for the T-billb) The formula for the selling price can be presented as follows;
Selling Price = Face Value/(1 + (Interest Rate × Remaining Days to Maturity/360))
Plugging in the known values, we get;
Selling Price = 5,000/(1 + (0.053 × (91 - 40)/360)) ≈ $4,962.74
Therefore, Barbara sold the T-bill to her friend for $4,962.74
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The equation of line, L is given by r=3i+3j-k+t 2i-j+3k Find an Cartesian equation for the plane pi which contains L and the origin.
The equation of the plane pi is: -6x-7y-9z=0.
To find the equation of the plane that contains the given line L and the origin as well, we first need to find two vectors that lie on the plane. One vector can be the direction vector of the line L, which is (2i - j + 3k). Now to find the second vector, we can take the vector from the origin to any point on the line L, and this vector will lie on the plane.
Let us now take t=0, and find the point on the line L:
r = 3i + 3j - k + 0(2i - j + 3k)
= 3i + 3j - k
So, the vector from the origin to this point is simply (3i + 3j - k). We can just take (3i + 3j - k) as our second vector.
Now, we can find the normal vector of the plane by taking the cross-product of two vectors that we just found, we get:
n = (2i - j + 3k) * (3i + 3j - k)
= -6i - 7j - 9k
Therefore, the equation of the plane pi is: -6x-7y-9z=0.
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The grid shown below is in the shapr of a rectangle. What is the area innsquare units, of the shaded part of the rectangle? It have 48
Based on the information provided, it seems that you have a rectangular grid with a shaded area, and the grid contains option D. 48 square units.
To calculate the area of the shaded part, we would need to know the dimensions of the rectangle as well as the specific location and size of the shaded region within it.
If you can provide more details about the dimensions of the rectangular grid and the shaded region, I would be happy to help you calculate the area of the shaded part. Once we have that information, we can apply the formula for calculating the area of a rectangle,
which is Area = length × width. The result will give us the area of the shaded part in square units.
The area in square units, of the shaded part of the rectangle It has 48. Therefore the correct option D
The Question was Incomplete, Find the full content below :
The grid shown below is in the shape of a rectangle. What is the area, in square units, of the shaded part of the rectangle? a 14 b 24 c 28 d 48
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Solve each equation by completing the square. Round to the nearest
necessary.
2x² - 2x +7=5
-2x^2 + 10x =14
4x^2 + 6x = 12
All the expressions after completing the square each equation are,
⇒ (x - 1/2)² = 5/4
⇒ (x - 5/2)² + 3/4 = 0
⇒ (2x + 3/2)² = 57/4
Given that;
Expressions are,
⇒ 2x² - 2x + 7 = 5
⇒ -2x² + 10x = 14
⇒ 4x² + 6x = 12
Now, We can completing the square each equation as;
⇒ 2x² - 2x + 7 = 5
⇒ x² - x + 7/2 = 5/2
⇒ x² - x + 1/4 - 1/4 + 7/2 = 5/2
⇒ (x - 1/2)² = 1 + 1/4
⇒ (x - 1/2)² = 5/4
⇒ -2x² + 10x = 14
⇒ - x² + 5x = 7
⇒ x² - 5x = - 7
⇒ x² - 5x + 25/4 - 25/4 = - 7
⇒ (x - 5/2)² = - 7 + 25/4
⇒ (x - 5/2)² = - 3/4
⇒ (x - 5/2)² + 3/4 = 0
⇒ 4x² + 6x = 12
⇒ (2x)² + 2×2x×3/2 + 9/4 -9/4 = 12
⇒ (2x + 3/2)² = 12 + 9/4
⇒ (2x + 3/2)² = 57/4
Thus, All the expressions after completing the square each equation are,
⇒ (x - 1/2)² = 5/4
⇒ (x - 5/2)² + 3/4 = 0
⇒ (2x + 3/2)² = 57/4
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
In a rectangle, the value of x is,
⇒ x = 5
We have to given that;
ABCD is a rectangle.
And, AC = 5x + 2
BD = x + 22
Since, We know that;
Diagonal of a rectangle are equal in length.
Hence, We get;
AC = BD
(5x + 2) = (x + 22)
5x - x = 22 - 2
4x = 20
x = 20/4
x = 5
Thus, the value of x is,
⇒ x = 5
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
The measure,
⇒∠s = 124 degree
In the given figure of kite,
PQRS,
Measure of angle p = 22 degree
And angle R is a right angle
Therefore,
∠R = 90 degree
Now we know that for a kite PQRS
Angle Q and Angle S are equal
Now consider,
Angle s is equal to x degree
Therefore,
∠S = ∠ Q = x degree
We know that,
For a kite the sum of interior angle is equal to 360 degree.
Therefore,
⇒ ∠P + ∠Q + ∠R + ∠S = 360
⇒ 22 + x + 90 + x = 360
⇒ 22 + x + 90 + x = 360
⇒ 2x = 248
⇒ x = 124 degree.
Thus,
Measure of angle s = 124 degree.
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Which statement accurately describes the relationship between JKL and MNP?
The triangles are not similar
Given data ,
Let the first triangle be ΔJKL
Let the second triangle be ΔMNP
Now , the corresponding sides are
JK / JL ≠ NM / MP
where the corresponding sides of similar triangles are not in the same ratio
And , the common angle to both the triangles is ∠J = ∠M
So , ∠J = ∠M and JK / JL ≠ NM / MP
Hence , the triangles are not similar
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The figure shows three tennis balls in a can with each tennis ball having a diameter of 2.5 inches. What is the total volume of the air space around the three tennis balls?
The total volume of the air space of spherical ball is A = 12.265625 inches³
Given data ,
Since each tennis ball has a diameter of 2.5 inches, the radius of each ball is 1.25 inches.
The air space around the balls can be thought of as a cylinder with a height equal to the diameter of one ball and a radius equal to the radius of one ball.
The height of the cylinder is 2.5 inches, and the radius is 1.25 inches.
The formula for the volume of a cylinder is:
V = πr²h
V = ( 3.14 ) ( 1.25 )² ( 7.5 )
V = 36.796875 inches³
where V is the volume, r is the radius, and h is the height.
So, the volume of the one ball is:
V₁ = ( 4/3 )π(1.25)³
V₁ = 8.177083 inches³
The total volume of three balls is = volume of 3 spherical balls
V₂ = 3V₁ = 3(8.177083) ≈ 24.53125 cubic inches
Therefore, the total volume of the air space around the three tennis balls is approximately A = 36.796875 inches³ - 24.53125 inches³
A = 12.265625 inches³
Hence , the volume of air space is A = 12.265625 inches³
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12. Sasha surveys students from her homeroom about the number of
siblings each student has. The results are 1, 0, 2, 2, 3, 0, 1, 1, 4,
and 5. What is the mode(s) of the data? (CC.6.SP.5c)
C 1
(D) 1 and 2
in
(A) 1.5
B 0 and 2
The calculated value of the mode(s) of the data is (a) 1
How to determine the mode(s) of the data?From the question, we have the following parameters that can be used in our computation:
1, 0, 2, 2, 3, 0, 1, 1, 4, and 5
By definition, the mode of a data is the data that has the highest frequency
Using the above as a guide, we have the following:
The data element 1 has the highest frequency of 3
Other data elements have lesser frequencies
Hence, the mode(s) of the data is (a) 1
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Find the area of a triangle whose base (b) is 5 feet and whose height (h) is 2 ft.
(a) 5ft.²
(b) 20ft.²
(c) 100ft.²
(d) 3.5ft.²
Answer:
(a) 5 ft^2
Step-by-step explanation:
The formula for area of a triangle is given by the formula,
A = 1/2bh, where
A is the area in square units,b is the base,and h is the height.Thus, we can plug in 5 for b and 2 for h in the formula to find the area of the triangle in square feet:
A = 1/2(5)(2)
A = (5/2)(2)
A = 10/2
A = 5
Thus, the area of a triangle whose base is 5 ft and whose height is 2 ft is 5 ft^2
50 Points! Multiple choice geometry question. Photo attached. Thank you!
The coordinates of vertex D in the parallelogram are (-7, -10).
We have,
To find the coordinates of vertex D of the parallelogram, we need to use the properties of a parallelogram.
One of these properties states that opposite sides of a parallelogram are parallel and have equal lengths.
Given that A = (8, 2), B = (6, -4), and C = (-5, -4), we can find the coordinates of D as follows:
Find the vector representing one of the sides of the parallelogram.
We can use the vector AB.
Vector AB = (x-coordinate of B - x-coordinate of A, y-coordinate of B - y-coordinate of A)
= (6 - 8, -4 - 2)
= (-2, -6)
Add this vector to point C to find the coordinates of D.
Coordinates of D = (x-coordinate of C + x-coordinate of AB, y-coordinate of C + y-coordinate of AB)
= (-5 - 2, -4 - 6)
= (-7, -10)
Therefore,
The coordinates of vertex D are (-7, -10).
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find the numerical value of the log expression
Answer:
Step-by-step explanation:
The numerical value of the given log expression is -73.
From definitions of logarithms, we know that :
[tex]log(a*b) = log(a) + log(b)\\log(a / b) = log(a) - log(b)[/tex]
[tex]log(a^n) = n*log(a)[/tex]
Therefore,
[tex]log(\frac{\sqrt[3]{b^4}}{a^8c^5 }) = \frac{4}{3}*log(b) - 8*log(a) - 5*log(c)[/tex]
substituting the given values
[tex]log(a) = 10\\log(b) = 9\\log(c) = 1\\[/tex]
we get the value of the given expression
[tex]log(\frac{\sqrt[3]{b^4}}{a^8c^5 }) = \frac{4}{3}*9 - 8*10 - 5*1[/tex]
[tex]log(\frac{\sqrt[3]{b^4}}{a^8c^5 }) = 12 - 80 - 5[/tex]
[tex]log(\frac{\sqrt[3]{b^4}}{a^8c^5 }) = -73[/tex]
Therefore the numerical value of the given log expression is -73.
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PLEASE HELPPP!!!!!!!!!
If tanA= 40/9 and sin B = 45/53
and angles A and B are in
Quadrant I, find the value of tan (A-B).
The value of tan (A-B) is equal to 715/2052.
To find the value of tan(A - B), we can use the trigonometric identity:
tan(A - B) = (tan(A) - tan(B))/(1 + tan(A)tan(B))
Given that tan(A) = 40/9 and sin(B) = 45/53, we can determine the values of cos(B) and tan(B) using the Pythagorean identity:
sin^2(B) + cos^2(B) = 1
cos(B) = sqrt(1 - sin^2(B))
cos(B) = sqrt(1 - (45/53)^2)
cos(B) = sqrt(1 - 2025/2809)
cos(B) = sqrt(784/2809)
cos(B) = 28/53
tan(B) = sin(B)/cos(B)
tan(B) = (45/53)/(28/53)
tan(B) = 45/28
Now we can substitute the values into the formula for tan(A - B):
tan(A - B) = (tan(A) - tan(B))/(1 + tan(A)tan(B))
tan(A - B) = (40/9 - 45/28)/(1 + (40/9)(45/28))
tan(A - B) = [(1120/252 - 405/252)] / (1 + (1800/252))
tan(A - B) = (715/252) / (2052/252)
tan(A - B) = 715/2052
Therefore, tan(A - B) is equal to 715/2052.
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A straight line is given as 2 x+4 -2 y-5=-3 z-6 (a) Determine the vector equation of the straight line. (b) Find the intersection point between the straight line with the plane yz
Answer:
a) r(t) = (10, 5, -5) + (5, 5, 0)*t
b) (0, -5, -5)
Step-by-step explanation:
a) 2x + 4 -2y -5 = -3z -6
2x - 2y +3z +5 =0
(10, 5, -5)
(15, 10, -5)
(5, 5, 0)
r = (10, 5, -5) + (5, 5, 0)*t
b) The yz plane is given by the equation x = 0.
x = 0 in the vector equation of a straight line if and only if t = -2, than r ( - 2) = (0, -5, -5) is the desired intersection point.
can u give me an answer
Answer: 0 , 5
Step-by-step explanation:
Imagine a plane taking off, first it drives to gain speed then flies, thats what you can use for coordinates.
X is the driving and Y is the flight.
The X is at 0, and the Y is at 5.
Find the area of this semi-circle with diameter 5cm.
Use the л (pi) button on your calculator and give your answer rounded to 2 decimal places.
No spam, please.
Answer:
Step-by-step explanation:
make t the subject of the formula k=2(t+3)/t-3
t = (6 + 3k)/(k - 2) is the formula for t in the equation k=2(t+3)/t-3.
The given equation is k=2(t+3)/t-3.
We need to isolate t on one side of the equation.
Let's start by cross-multiplying:
k(t - 3) = 2(t + 3)
Expanding the brackets:
kt - 3k = 2t + 6
Now, let's gather all the terms with t on one side and all the constant
terms on the other side:
kt - 2t = 6 + 3k
Factoring out t on the left side:
t(k - 2) = 6 + 3k
Finally, we can solve for t by dividing both sides of the equation by (k - 2):
t = (6 + 3k)/(k - 2)
Therefore, t is the subject of the formula, and it is given by t = (6 + 3k)/(k - 2).
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What is the equation, in slope-intercept form, of the line parallel to y = 5x + 2 that passes through the point with coordinates (-2, 1)? Show your work on the scratchpad. y = C G City 2 E X
Answer:
y = 5x + 11
Step-by-step explanation:
Step 1: When two lines are parallel, they have the same slope, as indicated by the following equation as m2 = m1, where
m2 is the slope of the line you're trying to find, and m1 is the slope of the line you're given.Thus, since the slope of line 1 is 5, the slope of line 2 is also 5.
Step 2: Now we can plug in (-2, 1) for x and y and 5 for m to solve for b, the y-intercept of the other line:
1 = 5(-2) + b
1 = -10 + b
11 = b
Thus, the equation of the line parallel to y = 5x + 2 and passing through (-2, 1) is y = 5x + 11