The function r(x) - 3f(x+1) transforms the parent function f(x)=x^2 by shifting it left by 1 unit, vertically stretching it by a factor of 3, and translating it downward by 3 units. The resulting graph is a parabola with vertex at (-1,-3) and a steeper shape.
The function r(x) - 3f(x+1) is a transformation of the parent function f(x)=x^2. Let's consider each transformation step by step.
First, the function f(x+1) represents a horizontal shift of the parent function f(x)=x^2 to the left by 1 unit. This means that the vertex of the parabola is shifted to the point (-1,0).
Next, the function 3f(x+1) vertically stretches the parabola by a factor of 3. This means that the distance between the vertex and the x-intercepts of the parabola is tripled, while the shape of the parabola remains the same.
Finally, the function r(x) subtracts a constant value from the transformed function. This translates the entire graph downward by 3 units.
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For the function , find f' (1).
guys pls help me
The derivative of the function is solved and f' ( 1 ) = 0.183
Given data ,
Let the function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = sinh⁻¹ ( √ (2x + 3 )
On taking the derivative of the function , we get
f' ( x ) = 1/ ( √2x + 4 ) ( √ ( 2x + 3 ) )
On simplifying , we get
when x = 1
f ( 1 ) = 1 / ( √6 ) ( √5 )
f ( 1 ) = 1/√30
f ( 1 ) = 0.18257
f ( 1 ) = 0.183
Hence , the function is solved
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100 Points! Algebra question. Please show as much work as possible. Thank you!
Michio answer was wrong. The correct answer for x in the expression 2(3)ˣ = 34 is 2.5789
How do i determine the correct answer?To know if Michio is correct or not, we shall determine the value of x in the algebraic expression. This is shown below:
Algebraic expression: 2(3)ˣ = 34Value of x =?2(3)ˣ = 34
Divide both sides by 2
3ˣ = 34 / 2
3ˣ = 17
Take the Log of both sides
Log 3ˣ = Log 17
Recall
Log Aⁿ = nLogA
Thus, we have
xLog 3 = Log 17
Divide both sides by Log 3
x = Log 17 / Log 3
x = 2.5789
From the above calculation, we see that Michio was wrong as the correct value of x in the expression is 2.5789
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The choir director wants to divde the choir into groups. There ar 24 Altos and 36 Tenors. Each group must have the same amount of each Alto and Tenors. What is the greates amount of groups the choir director could make?
The greatest number of groups the choir director could make is 12.
To find the greatest number of groups the choir director could make, we need to determine the highest common factor (HCF) of 24 and 36.
First, let's prime factorize both numbers:
[tex]24 = 2^3 \times 3\\36 = 2^2 \times 3^2[/tex]
Next, we identify the common factors between 24 and 36:
The factors common to both numbers are [tex]2^2[/tex]and 3.
To find the HCF, we take the smallest exponent for each common prime factor:
[tex]HCF = 2^2 \times 3 = 12[/tex]
Therefore, the greatest number of groups the choir director could make is 12.
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Suppose that the number of cars manufactured at an automobile plant varies jointly as the number of workers and the time they work. If 85 workers can produce 136 cars in 8 hours, find the number of cars that 125 workers can produce in 7 hours.
125 workers can produce approximately 102.94 cars in 7 hours.Additionally, this assumes that the constant of Proportionality remains the same for different numbers of workers and hours worked.
We are given that the number of cars manufactured at an automobile plant varies jointly as the number of workers and the time they work. This can be expressed as:
C = kWT
where C is the number of cars produced, W is the number of workers, T is the time they work, and k is a constant of proportionality
We can use this formula to solve the problem. We are given that 85 workers can produce 136 cars in 8 hours, so we can set up an equation using this information:
136 = k(85)(8)
Solving for k, we get:
k = 2/17
Now we can use the formula to find the number of cars that 125 workers can produce in 7 hours:
C = (2/17)(125)(7)
C = 102.94
Therefore, 125 workers can produce approximately 102.94 cars in 7 hours.
It's important to note that this is an approximation since we have rounded the answer to two decimal places. Additionally, this assumes that the constant of proportionality remains the same for different numbers of workers and hours worked.
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VNIHO NI es sequence. c). C 9 is 27 km from R on a bearing of 060° town T is 19km from town R on a aring of 3400 draw a diagram showing the relative position of the towns.
The description of the given bearing with the towns and a similar drawing of bearing is given below:
How to solveThe directions to draw the diagram that shows the relative position of the towns is given below:
Town R is at the center of the coordinate system.
Town C is 27km away on a bearing of 060°. Start at R, move 27km at 060° to find C towards east-southeast.
Town T is 19 km away from R on a ring of 3400.
T is on a circular path of radius of 3400 units.
To plot T, draw a circle at R with a 3400 unit radius. Put T on the circle, 19 km from R. Diagram: R center, C ESE, T on a circular path with a 3400 unit radius around R.
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Is Saturn less dense than water which has a density of 997 kg/m³? Find out by calculating the density of Saturn in kg/m³. The mass of Saturn is 5.68 x 1026 kg, and its radius is 5.6 x 107 m.
Density of Saturn:
Answer:
Sure, I can help you with that.
To calculate the density of Saturn, we can use the following formula:
Density = Mass / Volume
We know the mass of Saturn is 5.68 x 1026 kg, and we can calculate the volume of Saturn using the following formula:
Volume = (4/3)πr³
where π is approximately equal to 3.14159 and r is the radius of Saturn, which is 5.6 x 107 m.
Plugging in these values, we get the following:
Density = 5.68 x 1026 kg / (4/3)π(5.6 x 107 m)³
Density = 0.687 kg/m³
Therefore, the density of Saturn is 0.687 kg/m³, which is less than the density of water (997 kg/m³). This means that Saturn would float on water.
Step-by-step explanation:
Which statements describe finding the limit shown?
Check all that apply.
O Multiply by √x +2+3
√x+2+3
Getx-1 in the numerator.
Get (x-7)(√x+2-3) in the denominator.
O Divide out a common factor of x- 7.
Calculate the limit as
The correct statements that apply to the given limits are:
Option A: Multiply by (√(x + 2) + 3)/(√(x + 2) + 3)
Option D: "Divide out a common factor of x - 7."
Option E: The limit of the given expression is 1/6.
How to find the limits of the function?Option: We generally multiply by the conjugate of the expression to eliminate square roots in simplification. Thus, option A applies.
Option B: Get x - 1 in the numerator:
This statement is not correct. The expression does not involve x - 1 in the numerator.
Option C: Get (x - 7)(√(x + 2) - 3) in the denominator:
This statement is not correct due to the fact that we want to simplify the expression, and not introduce a more complex denominator.
Option D: Divide out a common factor of x - 7:
This statement is correct because by factoring out (x - 7) from both the numerator and denominator, we can cancel out the common factor.
Option E: Calculate the limit as 1/6:
After canceling out the common factor of x - 7, the simplified expression becomes:
lim x -> 7 (√(x + 2) - 3)/(x - 7)
= lim x -> 7 1/(√(x + 2) + 3)
To find the limit, we substitute the value x = 7 into the simplified expression:
lim x -> 7 1/(√(7 + 2) + 3) = 1/(√(9) + 3) = 1/(3 + 3) = 1/6
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What is the solution to this system of linear equations?x − 3y = −2x 3y = 16(7, 3)(3, 7)(−2, −3)(−3, −2)
The solution to the system of linear equations is (14, 16/3).
To find the solution to the given system of linear equations, we can use the method of substitution. First, we can solve the second equation for y by dividing both sides by 3, which gives us y = 16/3. .
We can then substitute this value of y into the first equation and solve for x. This gives us x - 3(16/3) = -2, which simplifies to x = 14. This point represents the intersection of the two lines, where they cross over each other on the coordinate plane.
The other answer choices given in the question are not valid solutions to the system of equations.
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Answer:
C
Step-by-step explanation:
Write the equation of a line that is perpendicular to y=7/5 x+6 and that passes throght the point (2,-6)
The equation of line that passes through and is perpendicular toy = (7/5)x + 6 is [tex]y = -\frac{5}{7}x - \frac{32}{7}[/tex].
What is the equation of the perpendicular line?The slope-intercept form is expressed as;
y = mx + b
Where m is slope and b is the y-intercept.
Given the equation of the original line:
y = (7/5)x + 6
Using the slope intercept, slope m is 5/2
Slope m = 7/5
Note: the equation of a perpendicular line to y = (7/5)x + 6 must have a slope that is the negative reciprocal of the original slope.
Slope of perpendicular line = -1 / ( 7/5 )
Slope of perpendicular line = -5/7
Plug the slope m = -5/7 and point (2,-6) into point-slope formula and simplify.
( y - y₁ ) = m( x - x₁ )
[tex]( y - (-6) = -\frac{5}{7}( x - 2 ) \\\\y + 6 = -\frac{5}{7}x + \frac{10}{7} \\\\y = -\frac{5}{7}x + \frac{10}{7} - 6\\\\y = -\frac{5}{7}x - \frac{32}{7}[/tex]
Therefore, the equation of the line is [tex]y = -\frac{5}{7}x - \frac{32}{7}[/tex].
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Sketch BC intersecting KT at point F. F is the midpoint of BC but not KTp
The desired sketch is attached below.
To sketch the scenario where BC intersects KT at point F, with F being the midpoint of BC but not KT, you can follow these steps:
Take a blank sheet of paper or open a drawing application on your device.Draw a straight line segment BC anywhere on the paper, and label the endpoints as B and C.Draw another line segment KT, intersecting BC at some point. Make sure that KT does not pass through the midpoint of BC.Label the intersection point of BC and KT as F.Draw a small line segment perpendicular to BC from point F. This line segment represents the intersection between BC and KT.Add arrows or marks on BC and KT to indicate the directions in which the lines extend.Finally, write the labels B, C, K, and T next to their respective points on the sketch to make it clear which points correspond to each line segment.Learn more about midpoint here:
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Can you expess this answers for me express 625 as a fraction of 1000 in its lowest terms
625 as a fraction of 1000 in its lowest terms is 5/8.
Express 625 as a fraction of 1000 in its lowest terms. Here's a step-by-step explanation:
1. Write the given numbers as a fraction: 625/1000
2. Find the greatest common divisor (GCD) of the numerator (625) and the denominator (1000). The GCD of 625 and 1000 is 125.
3. Divide both the numerator and the denominator by the GCD: (625 ÷ 125) / (1000 ÷ 125)
4. Simplify the fraction: 5/8
So, 625 as a fraction of 1000 in its lowest terms is 5/8.
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find tan s
thank you
Check the picture below.
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=\sqrt{c^2 - o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{40}\\ a=\stackrel{adjacent}{ST}\\ o=\stackrel{opposite}{24} \end{cases} \\\\\\ ST=\sqrt{ 40^2 - 24^2}\implies ST=\sqrt{ 1600 - 576 } \implies ST=\sqrt{ 1024 }\implies ST=32 \\\\[-0.35em] ~\dotfill\\\\ \tan(S )=\cfrac{\stackrel{opposite}{24}}{\underset{adjacent}{32}} \implies \tan(S )=\cfrac{3}{4}[/tex]
Two observation towers A and B are located 10 miles apart scientist at tower A spot an exotic bird at 42° and scientist at tower B spot the same bird at 64° how far away from tower A is the exotic bird
The distance of bird away from the tower is 4.04 miles.
Given that,
Distance between A and B = 10 miles
To solve this problem,
Use the law of tangents and basic trigonometry.
Let the distance from tower A to the bird = x
Then,
tan(180° - 64°) = x / (10 - d)
(where d is the distance from tower B to the bird)
tan(42°) = x / d
We can rearrange the first equation to get,
10 - d = x / tan(116°)
Substituting this into the second equation, we get:
⇒ tan(42°) = x / (x / tan(116°))
⇒ tan(42°) = tan(116°) x / x
⇒ x = 10 tan(42°) / (tan(116°) - tan(42°))
Plugging this into a calculator, we get:
x ≈ 4.04 miles
Therefore,
The exotic bird is approximately 4.04 miles away from tower A.
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which equation is equivalent to 4(2-5x)=6-3(1-3x)?
The equivalent equations of 4(2-5x)=6-3(1-3x) are 4(2 - 5x) = 6 - 3(1 - 3x), 8 - 20x = 6 - 3 + 9x and 29x = 5
Calculating which equation is equivalent to 4(2-5x)=6-3(1-3x)?From the question, we have the following parameters that can be used in our computation:
4(2-5x)=6-3(1-3x)
Express properly
So, we have
4(2 - 5x) = 6 - 3(1 - 3x)
Open the brackets
So, we have
8 - 20x = 6 - 3 + 9x
Evaluate the like terms
This gives
29x = 5
This means that the equivalent equations are 4(2 - 5x) = 6 - 3(1 - 3x), 8 - 20x = 6 - 3 + 9x and 29x = 5
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Heather has a combination of dimes and quarters in her piggy bank. If Heather has a total of 43 coins and the value in the piggy bank is $7.60, how many of each coin does she have?
Answer:
Step-by-step explanation:
5.6
Put these four functions in order from smallest to largest : 1/4,2/3,4/7,1/2
Answer:
1/4, 4/7, 2/3, 1/2
Step-by-step explanation:
Helena lost her marbles but then she found them and put them in 4 bags with m marbles in each bag she had 3 marbles left over that didn’t fit in the bags how many marbles did Helena have in all I need help
Three children have an average age of 7 years 11 months. If The youngest child is not included, the average age increases to 8 years 11 months. Find the age of the youngest child.
Step-by-step explanation:
7 yr 11 mos = 95 mos
8 yr 11 mos = 107 mos
(x + y + z) / 3 = 95 mos z is youngest
(x+y)/2 = 107 or x+y = 214 <=====sub into first equation
(214 + z ) / 3 = 95 solve for 'z'
214+ z = 285
z = 71 months = 5 yrs 11 months
A normal distribution has a mean of 146 and a standard deviation of 4. Find the z-score of the data value of 153
Answer:
To find the z-score of a data value, we use the following formula:
z = (x - μ) / σ
where z is the z-score, x is the data value, μ is the mean of the distribution, and σ is the standard deviation.
Given a normal distribution with a mean (μ) of 146 and a standard deviation (σ) of 4, and a data value (x) of 153, we can plug these values into the formula:
z = (153 - 146) / 4
z = 7 / 4
z = 1.75
Thus, the z-score of the data value 153 is 1.75.
Use a calculator to find the trigonometric ratio. Round your answer to four decimal places
sin 98°~
Using a calculator, the trigonometric ratio of sin 98 is approximately 0.9848.
How to Find the Trigonometric Ratio?One of the trigonometric ratio we have in mathematics is the sine ratio. We can use calculator to find the sine of an angle without making use of tables. To do this on your calculator, enter the sine function followed by the degree of the angle you want to find its sine. You will get your answer.
Using a calculator, we can find the sine of 98 degrees as follows:
sin 98° ≈ 0.9848
Rounding this to four decimal places, we get:
sin 98° ≈ 0.9848
Therefore, sin 98° is approximately equal to 0.9848.
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pls calculate all of this: (one at a time)
The solution to the equations are
1/3(2x - 3/7) + 1/6x = 4/7 is x = 6/7
7/8 x + 3/4 x + 7/16 x - 1/16 = 5/8 is x = 1/3
1 1/5 y + 3/10 y - 1/2 y = 1/3 y + 2/5 is y = 6/10
3/4 * (1/6 x + 16) = 3/7 * (4 3/8 x - 21) is x = 12
4/3x + 9/2y
How to solve for x1. To solve this equation, we can start by simplifying
1/3(2x - 3/7) + 1/6x = 4/7
2/3x - 1/7 + 1/6x = 4/7
Multiplying both sides by the lcm of the denominators which is 42
28x - 6 + 7x = 24
35x = 30
x = 6/7
2. 7/8x + 3/4x + 7/16x - 1/16 = 5/8
Multiplying both sides by the lcm of the denominators which is 16
14x + 12x + 7x - 1 = 10
33x = 11
x = 1/3
3.
6/5 y + 3/10 y - 1/2 y = 1/3 y + 2/5
2/3 y= 2/5
y = 2/5 * 3/2
y = 6/10
4.
3/4 * (1/6 x + 16) = 3/7 * (4 3/8 x - 21)
opening the parenthesis
1/8 x + 12 = 15/8 x - 9
1/8 x - 15/8 x= -12 - 9
-7/4 x = -21
x = 12
5.
2x - 2/3 x + 3 y + 1 1/2 y
4/3 x + 9/2 y
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Question 4
The table below shows the scores of a group of students on a 10-point quiz.
Frequency
Test Score
3
4
5
6
7
8
9
10
4
1
0
3
3
5
1
6
The mean score on this test is:
1 pt194 Details
Enter an integer or decimal number [more..)
The median score on this test is:
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The mean score of the test is 7.13.
The median score of the test is 7.
What is the mean and median score on the test?To get mean score, we have to multiply each test score by its corresponding frequency, sum up products and then divide by the total frequency.
Mean score = EF/ n
Mean score = (34 + 41 + 50 + 63 + 73 + 85 + 91 + 106) / (4 + 1 + 0 + 3 + 3 + 5 + 1 + 6)
= (12 + 4 + 0 + 18 + 21 + 40 + 9 + 60) / 23
= 164 / 23
= 7.13
To find the median score, we will arrange the scores in ascending order: [tex]3, 4, 4, 4, 4, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 9, 10, 10, 10, 10, 10, 10.[/tex]
Since there are 23 scores, the median will be the 12th score (in the middle). So, the median score = 7.
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Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Triangle- m ∠ 2 m ∠ 3 m ∠ 5 = 180 °( by the Triangle Sum Theorem)
The statements are true. still, grounded on the given options, three statements that are always true regarding any triangle are . The sum of the angles of a triangle is always equal to 180 degrees.
This statement is true because the total degrees of any triangle is 180 degrees.
This is known as the Triangle Sum Theorem.
2. The surface angle of a triangle is equal to the sum of its interior contrary angles. This statement is true for any triangle. The surface angle is the angle formed by extending one side of the triangle. The contrary innards angles are the two angles inside the triangle that don't partake a vertex with the surface angle.
3. The measure of each angle of an equilateral triangle is 60 degrees. This statement is true for any equilateral triangle. An equilateral triangle has three equal sides and three equal angles, each measuring 60 degrees. thus, grounded on the given options,
the three statements that are always true regarding the illustration could be
- m ∠ 3 m ∠ 4 m ∠ 5 = 180 °( by the Triangle Sum Theorem)
- m ∠ 5 m ∠ 6 = 180 °( by the sum of the angles of a straight line)
- m ∠ 2 m ∠ 3 m ∠ 5 = 180 °( by the Triangle Sum Theorem)
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when the square of a natural number is multiplied by 5,the product is 125
Answer:The least number by which 125 be multiplied to make it a perfect square is 5.125 = 5 × 5 × 5
The question deals with solving an equation pertaining to natural numbers and their squares. The solution involves finding the square root of 125 divided by 5, which gives us 5. Thus, the natural number whose square multiplied by 5 equals 125 is 5.
Explanation:The subject of this question is Mathematics, specifically working with natural numbers and their squares. Here, you're given that 'when the square of a natural number is multiplied by 5, the product is 125'.
It's a simple application of the basic arithmetic operations. We have to try and find the square root of 125 divided by 5 because multiplication is inverse of division.
The calculation would be: √(125/5) = √25 = 5.
Thus, the natural number in question is 5, as 5 squared (25) times 5 is equal to 125.
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10. Kristen compared the y-intercept of the graph of the function f(x) = 7x - 5 to the y-intercept of the graph of the linear function that includes the points in the table below. X -5,-2,0,3 g(x) -56,-20,4,40
What is the difference when the y-intercept of g(x) is subtracted from the y-intercept of f(x)?
IXL S.10…Geometry…Explain Down Below Please
The area of the shaded region, to the nearest hundredth can be calculated as approximately: 1,195.71 mm².
What is the Area of the Shaded Region?The area of the shaded region can be found using the area of circle, which is: Area = πr²
Therefore, area of the shaded region = area of larger circle - area of smaller circle.
Area of larger circle:
radius (r) = 14 + 6.6 = 20.6 mm
Area of larger circle = 3.14 * 20.6² = 1,332.4904 mm²
Area of smaller circle:
radius (r) = 6.6 mm
Area of larger circle = 3.14 * 6.6² = 136.7784 mm²
Area of the shaded region = 1,332.4904 - 136.7784 = 1,195.71 mm².
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Alex, Bill, Carl and David shared $168. David received 1/7 of the total amount of money received by Alex, Bill and Carl. Alex received 3/4 of the total amount of money received by Bill and Carl. Bill received 2/5 as much money as Carl. How much did Bill receive?
Bill's share = $56 Therefore, Bill received $56.
Let's start by setting up some equations based on the given information:
David's share = 1/7 * (Alex's share + Bill's share + Carl's share)
Alex's share = 3/4 * (Bill's share + Carl's share)
Bill's share = 2/5 * Carl's share
The sum of all four shares is $168.
We can use the fourth equation to solve for one of the shares in terms of the others:
Alex's share + Bill's share + Carl's share + David's share = $168
Alex's share + Bill's share + Carl's share = $168 - David's share
Substituting the other equations into this expression, we get:
Alex's share + (2/5 * Carl's share) + Carl's share + (1/7 * (Alex's share + (2/5 * Carl's share) + Carl's share)) = $168
Simplifying this equation, we get:
(8/7) * Alex's share + (22/35) * Carl's share = $168
Now we can use the other equations to solve for Carl's share, and then for Bill's share:
From Bill's share = 2/5 * Carl's share, we get Carl's share = (5/2) * Bill's share
From Alex's share = 3/4 * (Bill's share + Carl's share), we get Alex's share = (3/4) * ((7/2) * Bill's share) = (21/8) * Bill's share
Substituting these expressions into the equation we derived earlier, we get:
(8/7) * (21/8) * Bill's share + (22/35) * (5/2) * Bill's share = $168
3 * Bill's share = $168
Bill's share = $56
Therefore, Bill received $56.
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The classroom had a 16-centimetre-long glue stick, and then Christina used 2.5 centimetres of it. How long is the stick now?
Answer:
[tex]13.5cm[/tex]
Step-by-step explanation:
You just need to subtract to find your answer!
The information we are given:
We have a 16cm glue stick.
Christina used 2.5cm of it.
Subtracting:
16 - 2.5 = 13.5
Now, dont forget your units :D
[tex]13.5 -- > 13.5cm[/tex]
I hope I helped!~~~Harsha~~~
In a large population, about 70% of families have a pet. A researcher takes a random sample of 6 families and surveys
whether they have a pet.
Use the binomial distribution to compute the probability that exactly 2 of the families have a pet.
Identify the following information required to find the probability of families that have a pet.
If in a large population, about 70% of families have a pet. A researcher takes a random sample of 6 families and surveys whether they have a pet. The probability of families that have a pet is: 0.0595.
How to find the probability?Number of trial= 6
Probability of success = 0.7
Probability of failure = 1 - 0.7 = 0.3
Probability that exactly 2 of the families have a pet
Let make us of binomial distribution formula to determine the probability
P(X = 2) = (6 choose 2) * 0.7² *[tex]0.3^{4}[/tex]
= 15 * 0.49 * 0.0081
= 0.0595
Therefore the probability is 0.0595.
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Using L’Hôpital’s Rule, evaluate
heeeeeelp
The value of the given limit expression is 1.
Given is limit expression [tex]\lim _{x\to \infty }\left(x^{\frac{1}{3x}}\right)[/tex], we need to use L’Hôpital’s Rule to solve it,
So,
[tex]\lim _{x\to \infty \:}\left(x^{\frac{1}{3x}}\right)[/tex]
Using the exponent rule,
[tex]=\lim _{x\to \infty \:}\left(e^{\frac{1}{3x}\ln \left(x\right)}\right)[/tex]
Applying the chain rule,
[tex]\lim _{x\to \infty \:}\left(e^{\frac{1}{3x}\ln \left(x\right)}\right) = 1[/tex]
Hence the value of the given limit expression is 1.
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