The properties of the least squares line are that the intercept represents the estimated base appraised value for any house in East Meadow, and the slope represents the estimated increase in appraised value for each additional room in the house.
The properties of the least squares line, ? = 74.80 + 19.72x, are as follows:
1. The intercept, ?0, is 74.80. This represents the estimated base appraised value for any house in East Meadow, regardless of the number of rooms. However, there is no practical interpretation for this value, since a house with 0 rooms is nonsensical.
2. The slope, ?1, is 19.72. This represents the estimated increase in appraised value for each additional room in the house. For each additional room in the house, we estimate the appraised value to increase $19,720.
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HEELLPPPP!!!! quickly im being timed.
Fill in the gaps in the following sentences using the options below:
Two objects are similar if they have
Two objects are congruent if they have 1)the same shape.
2) different shapes.
3)the same shape and size.
4)different shapes and sizes
Answer:
Two objects are similar if they have the same shape.
(1): Two objects are similar if they have the same shape.
(2): Two objects are congruent if they have the same shape and size.
(3): Two objects are congruent if they have the same shape and size.
(4): Two objects are congruent if they have different shapes and sizes.
Hope this helps! I'm sorry if it's wrong. If you need more help, ask me! :]
F(x)=4x^2+2
a) F(1)=
B) F(-1)=
C) F(-4)
D) F(-7/2)=
Answer:
F(1) = 6
F(-1) = 6
F(-4) = 66
F(-7/2) = 51
Find the missing information for the triangle. *not drawn to scale
The measure of the angle x is 60 degrees and the sides of the triangle is 4√3 and 8.
What is sum of interior angles of triangle?According to the triangle sum theorem, a triangle's internal angles can be added up to 180 degrees. The triangle sum theorem, often referred to as the angle sum theorem of the triangle, states that the total of the measures of a triangle's internal angles in a Euclidean space adds up to 180 degrees, whether the triangle is acute, obtuse, or right. The smallest polygon with three sides and three internal angles, one at each vertex, and bordered by two neighbouring sides is a triangle.
Given that, angle B = 30 degrees and angle m = 90 degrees.
The sum of all the angles of a triangle is 180 degrees.
Thus,
30 + 90 + angle x = 180
120 + angle x = 180
angle x = 180 - 120
angle x = 60
The sides is thus a triangle with angle 30-60-90.
For this case the sides are in the ratio:
x : x√3 : 2x
From the figure we see that, x = 4.
Thus, the remaining sides are:
x√3 = 4√3 and 2x = 2(4) = 8
Hence, the measure of the angle x is 60 degrees and the sides of the triangle is 4√3 and 8.
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14. EXTENSION QUESTION
A GIVE WAY sign in the shape of an equilateral triangle is 110cm in height. Find the length of one
of its sides. Include a diagram.
The length of one of the sides of the GIVE WAY sign, equilateral triangle is approximately 200.89cm.
What is an equilateral triangle?
An equilateral triangle in geometry is a triangle with equally long sides. The three angles opposing the three equal sides are equal in size because the three sides are equal. As a result, with each angle measuring 60 degrees, it is sometimes referred to as an equiangular triangle. Equilateral triangles have the same area, perimeter, and height formula as other kinds of triangles.
Given that the triangle is an equilateral triangle, thus all sides are equal.
Let us suppose the sides = x.
The height of the equilateral triangle is given by:
height = (√3/2) x side length
Substituting the values:
110 = (√3/2) x (x)
x = 110 / (√3/2)
x ≈ 200.89cm
Hence, the length of one of the sides of the GIVE WAY sign is approximately 200.89cm.
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7. The sides of a rectangle are in the ratio 5:2. If the perimeter of the rectangle is 42 cm, find the area of the rectangle.
Answer:
90 cm²
Step-by-step explanation:
Let the greater side be the length L and the smaller side the width W
Given L : W = 5 : 2
we can rewrite this as a fraction
[tex]\dfrac{L}{W} = \dfrac{5}{2}[/tex]
Cross-multiplying we get
2L = 5W
The perimeter of a rectangle
= 2(L + W)
= 2L + 2W
and we are told it is 42 cm
Therefore
2L + 2W = 42
Substitute 5W for 2L to get
5W + 2W = 42
7W = 42
or
W = 42/6 = 6
Given 2L + 2W = 42, substitute 6 for W to get
2L + 2(6) = 42
2L + 12 = 42
2L = 42 - 12= 30
L = 30/2 = 15
So length L = 15
Just to check
L/W = 15/6 = 5/2 by dividing both numerator and denominator by 3
Area of the rectangle
= L x W
= 15 x 6
= 90 cm²
−
2
x
+
2
y
=
8
6
x
+
y
=
11
If
(
x
,
y
)
is the solution to the system of equations above, what is the value of
7
y
?
Answer:
7y=-91
Step-by-step explanation:
-2x + 2y = 8 (multiply the second equation by 2)
12x + 2y = 22
Adding the two equations, we get:
10x = 30
Therefore, x = 3.
Substituting x = 3 into the second equation, we get:
6(3) + y = 11
Simplifying, we get:
y = -13
Finally, we can find the value of 7y:
7y = 7(-13) = -91
What is the x-coordinate of the midpoint of line segment AB with points A(21, 5) and B(-9, -13).
Answer:
6
Step-by-step explanation:
You want the x-coordinate of the midpoint of segment AB with endpoint coordinates A(21, 5) and B(-9, -13).
MidpointThe midpoint of a line segment has coordinates that are the average of the endpoint coordinates:
M = (A +B)/2
M = ((21, 5) +(-9, -13))/2 = (12, -8)/2
M = (6, -4)
The midpoint of AB is (6, -4).
The x-coordinate of the midpoint is 6.
2p - 5q= 8
3p - 7q = 11
Solve the simultaneous equation using elimination method
Step-by-step explanation:
Paul behavior is not unethical is that the information is firsthand hand factual and
how is a condominium different than a single family dwelling
a. occupants pay rent to the landlord who owns the property
b.occupants are investors who own shares in the entire property and not individual unit
c.occupants individually own both the home and the land
b.occupants jointly own the common parts of the property and individually own their own units
Option d. occupants jointly own the common parts of the property and individually own their own units is the correct answer .A condominium is a type of housing where individuals own their own unit or apartment
what is condominium?
A condominium, often shortened to "condo," is a type of housing arrangement where individuals own their own unit or apartment within a larger building or community, and jointly own the common areas and facilities of the property with other owners.
In the given question,
A condominium is a type of housing where individuals own their own unit or apartment and jointly own the common areas of the property, such as hallways, elevators, and recreation areas. This is different from a single-family dwelling where the occupant individually owns both the home and the land.
In a condominium, occupants are not renting from a landlord who owns the property, nor are they investors who own shares in the entire property. Instead, each occupant owns their own individual unit and has a shared interest in the common areas of the property.
Additionally, in a condominium, occupants are typically required to pay fees to the condo association to cover the maintenance and upkeep of the common areas, which is not typically required in a single-family dwelling.
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When women were allowed to become pilots of fighter jets, engineers needed to redesign the ejection seats because they had been originally designed for men only. The ACES-II ejection seats were designed for men weighing between 140LB and 211LB. Weights of women are now normally distributed with a mean of 165LB and a standard deviation of 45.6LB
a. If 1 woman is randomly selected, find the probability that her weight is between 140LB and 211LB
b. If 36 different women are randomly selected, find the probability that their mean weight is between 140LB and 211LB
The probability that the mean weight of 36 different women is between 140LB and 211LB is approximately 0.9874.
Is it possible for a random variable to have 0 probability across the board?There can only be one value for a random variable. A random variable's value could be zero with a probability of zero. A probability distribution's total probabilities are always equal to one.
a. We must convert the weight to a typical normal distribution using the following formula in order to determine the likelihood that a randomly chosen woman weighs between 140LB and 211LB.
z = (x - μ) / σ
If the weight x, the mean weight, and the standard deviation are all given. The probability can then be determined using a calculator or a typical normal table.
When x=140LB, we get:
z = (140 - 165) / 45.6 = -0.5461
x = 211LB results in:
z = (211 - 165) / 45.6 = 1.0096
The area under the standard normal curve between z = -0.5461 and z = 1.0096 is found to be roughly 0.6267 using a typical normal table or calculator.
Hence, the likelihood that a lady chosen at random weighs between 140LB and 211LB is roughly 0.6267.
b. We must normalise the sample mean to a standard normal distribution using the following method in order to determine the likelihood that the mean weight of 36 individual women is between 140LB and 211LB.
z is equal to (x - ) / (n / sqrt(n)).
When n is the sample size, x is the sample mean weight, is the mean weight, and is the standard deviation. The probability can then be determined using a calculator or a typical normal table.
To solve this issue, we have:
μ = 165LB
σ = 45.6LB
n = 36
If x = 140 LB, we get:
z = (140 - 165) / (45.6 / sqrt(36)) = -2.4994
With x = 211LB, we get:
z = (211 - 165) / (45.6 / sqrt(36)) = 2.4994
The area under the standard normal curve between z = -2.4994 and z = 2.4994 is found to be around 0.9874 using a standard normal table or calculator.
Hence, there is a roughly 0.9874 percent chance that the average weight of 36 individual women falls between 140LB and 211LB.
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Which is better? 8"A" students out of 40, or 9 "A" student out of 50
The first group has a higher proportion of "A" students 0.2
To determine which is better, we need to compare the proportions of "A" students in each group.
For the first group, the proportion of "A" students is:
8/40 = 0.2
For the second group, the proportion of "A" students is:
9/50 = 0.18
Therefore, the first group has a higher proportion of "A" students, and we can say that it is "better" in terms of producing "A" students. However, it is important to note that this is just one aspect of performance and there may be other factors to consider as well.
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The diameter of a circle is 6 kilometers. What is the length of a 30 degree arc
Hence, in answering the stated question, we may say that As a result, the circle length of a 30-degree arc of a 6-kilometer-diameter circle is approximately 1.57 kilometers.
What is circle?Each spot that is a particular distance from yet another point creates a circle in the plane (center). As a result, it is a curve composed of points separated in the plane by a given distance. Furthermore, at all angles, it is circumferentially symmetric the about centre. Every couple of points in such a circle's closed, two at least plane is evenly spaced out from the "centre." A round symmetry line is formed by tracing a line through circle. Furthermore, at all angles, it is rotationally equal about the centre.
The circumference of a circle can be calculated using the formula C = d, where d is the circle's diameter. Because the diameter in this case is 6 kilometres, the circumference is:
C = d = (6) = 18.85 km (rounded to two decimal places)
1/12 = 30 degrees / 360 degrees
As a result, the length of the 30 degree arc is:
1.57 km length = (1/12) * C = (1/12) * 18.85 km (rounded to two decimal places)
As a result, the length of a 30-degree arc of a 6-kilometer-diameter circle is approximately 1.57 kilometres.
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What angle does m make with the x-axis?
Therefore , the solution of the given problem of angle comes out to be x = 30°.
What does an angle mean?In Euclidean geometry, the barrier's centre and top separate two spherical faces, which make both of the sides of a tilt. Two rays may combine to create an angle where they collide. Another result of two things interacting is an angle. They most closely resemble dihedral shape. Two line beams can be arranged in different ways at their extremities to form a two-dimensional curve.
Here,
Given : a line making angle with x axis:
We have to find the angle with x axis.
So,
=> tan x = p/b
=> tanx = 1/√3
=> x = tan⁻¹(1/√3)
=> x = 30°
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Hi. I need to know the answer because one of my friends wanted to know the answer and I knew the answer, but not how to explain it well enough: Adrienne and Evelyn have a pet cat. When they got it as a kitten, as much as it it weighed 0.6 kilograms. Now it weighs 7.3 times did when it was a kitten. How much does their cat weigh now?
So their cat weighs 4.38 kilograms now.
What is an algebraic expression?
An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations. It may also include exponents and/or roots. Algebraic expressions are used to represent quantities and relationships between quantities in mathematical situations, often in the context of problem-solving.
Algebraic expressions can take many different forms, but some common examples include:
3x + 7
2a^2 + 5ab - 3b^2
(x + 2)(x - 5)
4x^2 - 9.
Let's start by figuring out how much the cat weighs now. We know that the cat weighs 7.3 times what it did when it was a kitten, and it weighed 0.6 kilograms when it was a kitten.
To find out how much the cat weighs now, we can multiply its original weight by 7.3:
0.6 kilograms x 7.3 = 4.38 kilograms
Therefore, So their cat weighs 4.38 kilograms now.
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(09.02 MC)
What step is needed when constructing a circle circumscribed about a triangle? (1 point)
Group of answer choices
Construct the angle bisectors of each angle in the triangle.
Construct the perpendicular bisectors of each side of the triangle.
Construct the midpoints of each side of the triangle.
Construct the altitude of each angle in the triangle.
The step needed when constructing a circle circumscribed about a triangle is option B: Construct the perpendicular bisectors of each side of the triangle.
What is the triangle construction about?When constructing a circle circumscribed about a triangle, the center of the circle must lie at the intersection of the perpendicular bisectors of the sides of the triangle.
To construct the perpendicular bisector of a side, you need to find its midpoint and then draw a line perpendicular to the side passing through that midpoint.
By constructing the perpendicular bisectors of all three sides, you can find their point of intersection, which will be the center of the circle. Then, the radius of the circle can be found by measuring the distance from the center to any of the vertices of the triangle.
Therefore, Once you have the center and radius, you can draw the circle circumscribed about the triangle.
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The system of linear equations below has the solution (3, 3), where F, G, H, P. Q, and R are non-zero real numbers.
Fr+ Gy=H
Pr+Qy= R
Which system must also have the solution (3,3) ?
3Fx - 3Gy= H
Pr + Qy = R
[ 3Fx + 3Gy = H
13Px +3Qy = R
((F+3P) x + (G+ 3Q) y = H + 3R
Pr+Qy = R
((F+3G) x + (P+3Q) y = H + 3R
Pr+Qy = R
Answer:
3Fx - 3Gy= H
Step-by-step explanation:
ALGEBRA 2 HELP
(Please show work!)
A student wrote the arithmetic series 8 + 11 + ... + 29 in summation notation as (picture below)
a. Describe and correct the error in the notation.
b. Evaluate the corrected summation of the arithmetic series above.
[tex]S_8=[/tex]
c. Write the explicit and recursive formulas for the arithmetic series above,
Explicit:
[tex]a_n=[/tex]
Recursive:
If [tex]a_1=[/tex]
Then for n > 1
[tex]a_n=[/tex]
Step-by-step explanation:
ALGEBRA 2 HELP
(Please show work!)
A student wrote the arithmetic series 8 + 11 + ... + 29 in summation notation as (picture below)
a. Describe and correct the error in the notation.
b. Evaluate the corrected summation of the arithmetic series above.
�
8
=
S
8
=
c. Write the explicit and recursive formulas for the arithmetic series above,
Explicit:
�
�
=
a
n
=
Recursive:
If
�
1
=
a
1
=
Then for n > 1
�
�
=
a
n
=
a bag of 15 scrabble tiles contains three each of the letters a, c, e, h, and n. if you pick six letters one at a time, what is the chance that you spell c-h-a-n-c-e? (in this order)
The chance of spelling C-H-A-N-C-E in this order with a bag of 15 scrabble tiles containing three each of the letters A, C, E, H, and N is 3/40040.
The chance of spelling C-H-A-N-C-E in this order with a bag of 15 scrabble tiles containing three each of the letters A, C, E, H, and N can be calculated by multiplying the probabilities of picking each letter in the correct order.
we need to calculate the probability of picking the letter C. There are three C's in the bag and a total of 15 tiles, so the probability of picking C is 3/15 or 1/5.
Next, we need to calculate the probability of picking the letter H. After picking the first letter, there are 14 tiles left in the bag and three H's, so the probability of picking H is 3/14. We can calculate the probabilities of picking the letters A, N, C, and E in the correct order:
- Probability of picking A: 3/13
- Probability of picking N: 3/12 or 1/4
- Probability of picking C: 2/11
- Probability of picking E: 3/10
To find the overall probability of spelling C-H-A-N-C-E in this order, we multiply all of these probabilities together:
[tex](1/5) * (3/14) * (3/13) * (1/4) * (2/11) * (3/10) = 18/240240 = 3/40040[/tex]
Therefore, the chance of spelling C-H-A-N-C-E in this order with a bag of 15 scrabble tiles containing three each of the letters A, C, E, H, and N is 3/40040.
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AD and EC are diameters of 0. OB is a radius. Classify each statement as true or false. AOC = 100
Therefore , the solution of the given problem of circle comes out to be this statement is true ∠AOC = 100° .
Circle – what is it?Each area of a plane with a specific distance from this additional spot forms a circle (center). Thus, it comprises of curved spots that are separated from one another and separated by the surface. Additionally, it rotates evenly around the centre from all sides. Every set of endpoints in a circular, constrained double sphere is uniformly spaced apart from the "centre."
Here,
Given :
AD and EC are diameters as we can see they are passing through centre .
So , there are diameter.
=> ∠AOC = ∠A0B + ∠BOC
=> ∠AOC = 100°
thus , this statement is true ∠AOC = 100° .
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to decrease a number by 37% you multiply by 0.63
to decrease a number by 16% what do you multiply it by
To decrease a number by 16%, you should multiply it by 0.84.(1 - 0.16 = 0.84).
When you reduce a number by a percentage, you are subtracting that percentage from it. For example, if you were to decrease 100 by 16%, you would subtract 16 from 100 to get 84.
This is also known as a percentage decrease, which is the opposite of a percentage increase.
Using the formula for percentage decrease, we get:
Percentage decrease = (Decrease in value / Original value) × 100
We're told that to decrease a number by 37%, you multiply it by 0.63.
Therefore, we can write:
0.63 = (Decrease in value / Original value) × 1000.63 × Original value = Decrease in value
We want to find what you multiply a number by to decrease it by 16%, so let's call that value x.
So: x = (Decrease in value / Original value) × 100%
So, we can substitute in the values we know to solve for x:
x = (0.16 × Original value / Original value) × 100%x = 0.16 × 100%x = 16%
Therefore, to decrease a number by 16%, you should multiply it by 0.84.
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in a group more than 1/2 are boys but there are less than 2/3 of the group can there be 4 people
The minimum number of people in the group should be 3.
In a group more than 1/2 are boys but there are less than 2/3 of the group.
Let the number of people in the group be x.
Therefore, the number of boys in the group is greater than 1/2 × x or x/2.
The number of people in the group is less than 2/3 × x or 2x/3.
As per the question, x > x/2 and x < 2x/3
multiply both sides by 2,
so we get:
2x > x and 2x < 4x/3.
Now, simplify the above equations as follows:
2x > x ⇒ x > 0 and
2x < 4x/3 ⇒ 6x < 4x ⇒ 0 < -2x ⇒ x < 0
Thus, it is not possible to have a group of 4 people as the number of people in the group is greater than 0.
Therefore, the minimum number of people in the group should be 3.
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Antonio participa en la restauración del salón comunal. Pinta una pared de 15m² de la siguiente manera 4m² de color melón 5m² de color verde y 6m² de color blanco ¿Que fracción de la pared pinta de cada color ? EXPRESE CADA UNA DE LAS FRACCIONES DEL EJERCICIO EN NOTACION DECIMAL
Antonio painted about 27% of the wall with melon color, 33% with green color, and 40% with white color.
Antonio painted a wall with an area of 15 square meters. He painted 4 square meters with melon color, 5 square meters with green color, and 6 square meters with white color.
To find the fraction of the wall that Antonio painted with each color, we need to divide the area painted with each color by the total area of the wall:
Fraction painted with melon color = 4 / 15 = 0.2666... ≈ 0.27
Fraction painted with green color = 5 / 15 = 0.3333... ≈ 0.33
Fraction painted with white color = 6 / 15 = 0.4
So Antonio painted about 27% of the wall with melon color, 33% with green color, and 40% with white color.
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Complete Question:
Antonio is participating in the restoration of the communal room. He paints a wall of 15m² in the following way: 4m² of melon color, 5m² of green color, and 6m² of white color. What fraction of the wall does he paint with each color? EXPRESS EACH OF THE FRACTIONS IN THE EXERCISE IN DECIMAL NOTATION.
Do you mind if someone would answer number 21 part a and b
I would really appreciate if you would
The value at the 60th percentile is 72°F. According to the given question.
What is whisker plot?
A whisker plot, also known as a box and whisker plot, is a graphical representation of a dataset that shows the distribution of values. It is often used to summarize and compare datasets, and to identify outliers or extreme values.
The plot is constructed using a rectangular box that represents the middle 50% of the data (the interquartile range or IQR). The box extends from the lower quartile (the value below which 25% of the data falls) to the upper quartile (the value below which 75% of the data falls). A line inside the box represents the median (the value below which 50% of the data falls).
Part A:
Here is a box and whisker plot representing the given data:
| + |
75 -+ + |
| | |
70 -+ | |
| | |
65 -+-------------+-------------------+
| S M T W | T F S |
The plot is divided into four sections: the lowest 25% of the data (the lower quartile), the next 25% of the data (the second quartile or median), the next 25% of the data (the third quartile), and the highest 25% of the data (the upper quartile). The box represents the middle 50% of the data, and the whiskers extend to the lowest and highest values that are not outliers.
Part B:
To determine which value is at a given percentile, we need to sort the data in ascending order and count how many values are less than or equal to the percentile we are interested in. Then we find the corresponding value in the sorted list.
For example, to find the value at the 60th percentile, we first calculate 60% of the total number of values, which is:
0.60 * 7 = 4.2
Since we cannot have a fraction of a value, we round up to the next integer, which is 5. This means that the value at the 60th percentile is the fifth value in the sorted list:
65, 66, 68, 70, 72, 74, 75
Therefore, the value at the 60th percentile is 72°F.
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Graph f(x) = -x. Click on the graph until the graph of f(x) = -x appears.
The graph of f(x) = -x is attached.
What is the x-intercept?The intersection of a function or equation's graph with the x axis is known as the x intercept. This can be compared to a point having a value of 0.
For any given curve, the x-intercept is a coordinate that is plotted on the x-axis. To put it another way, the x-intercept is the value of the x coordinate at the point where the graph crosses the x-axis, or we can say that it is the value of the x coordinate at a point where the value of the y coordinate equals zero.
f(x) = -x ----------(1)
Equation (1) can be written as f(x) = -x+0
This is in the form of f(x)=mx+b,
where , m= -1, b=0
this represents a line
Find the x and y-intercepts: ( consider f(x)=y)
Find x-intercept when y=0
=> 0=-x
=> x=0
Thus, x-intercept is (0,0)
Find y-intercept when x=0
=> y=-0 = 0
Thus, y-intercept is (0,0)
We need another point, because both intercepts are same
When x= 1, y= -1
The point is (1,-1)
Plot these points and join them with a line.
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Complete Question:
Which of the following is the graph of f(x) = x2?
Click on the graph until the correct graph appears.
*See image *The number of foxes in a forest increases
by 20% each year.
This year, there are 500 foxes in the
forest.
Calculate the number of foxes that there
will be in the forest
a) after 1 year.
b) after 2 years.
Answer:
a) 600 foxes
b) 720 foxes
Step-by-step explanation:
See attached spreadsheet.
The rate of population increase is 20% each year. To find a new year's population, multiply the previous year's population by 0.20 (20%) and add that to the previous year. Year 1 would be (500)*(0.20) = 100 new foxes which are added to the year 0 population of 500, which means there are (500+100) or 600 foxes in year 1.
Year 2: (0.20)*(600) = 120 new foxes
Add 120 to the existing 600 to find 720 foxes in year 2,
============
A formula that can be used to predict the fox population for any year, n, would be:
P(n) = 500*(1+0.20)^n
where P(n) is the popluation at year n. The 500 is the population at year 0 (the starting population). (1+0.20) is the growth for each year (120%, which means the original population plus 20%). That is raised to the year of interest, n. [When n=0, (1+0.20)^0 = 1]
Please help me find the missing sides to solve this equation
Trigonometry is a branch of mathematics that deals with the relationships and properties of triangles, particularly the relationships between their sides and angles.
What is trigonometry?1) sin 30 = 10/u
u = 10/sin 30
u = 20
Cos 30 = v/20
v = 20cos 30
v = 17
2) cos 30 = 4√3/m
m = 4√3/√3/2
m = 4√3 * 2/√3
m = 8
Sin 30 = n/8
n = 8 sin 30
n = 4
3) sin 60 = x/7
x = 7 sin 60
x = 6
Cos 60 = y/7
y = 7 Cos 60
y = 3.5
4) Tan 30 = v/10√3
v = 10√3 * 1/√3
v = 10
Cos 30 = 10√3/u
u = 10√3/Cos 30
u = 10√3/√3/2
u = 10√3 * 2/√3
u = 20
5) Sin 60 = x/6√3
x = 6√3Sin 60
x = 6√3 * √3/2
x = 3
Cos 60 = y/6√3
y = Cos 60 * 6√3
y = 6√3 * 1/2
y = 3√3
6) Sin 60 = x/4√2
x = Sin 60 * 4√2
x = 4√2 * √3/2
x = 2√6
Cos 60 = y/4√2
y = Cos60 * 4√2
y = 1/2 * 4√2
y = 2√2
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Solve 19(1.12^x)=8(1.18^x). Show work.
Answer:
x≈12.6
Step-by-step explanation:
We have the equation:
19(1.12^x) = 8(1.18^x)
Divide both sides by 8:
19/8 (1.12^x) = (1.18^x)
Take the natural logarithm of both sides:
ln[19/8 (1.12^x)] = ln[1.18^x]
Using the properties of logarithms, we can simplify the left side:
ln(19/8) + ln(1.12^x) = x ln(1.18)
Substituting y = 1.12^x, we get:
ln(19/8) + ln(y) = ln(1.18) y
Now we can solve for y:
ln(y) = ln(1.18) y - ln(19/8)
Using a numerical method or a graphing calculator, we can find that y ≈ 10.584.
Substituting back to solve for x:
1.12^x ≈ 10.584
Taking the logarithm base 1.12 of both sides:
x ≈ ln(10.584)/ln(1.12)
x ≈ 12.6
Therefore, the solution to the equation is x ≈ 12.6.
Let X be a geometric random variable with so that P(X=k)=(1=p)^k-1 p over k=1,2,…and p is the probability of success taking a value between 0 and 1. a) Let
P(A) be the event that X assumes an even number. Compute P(A) . b) Compute the expectation and variance of e^X. c) Compute P(e^x >10)
0.0472 (approx.)
Anwer:
a) P(A) = P(X is even) = P(X = 2) + P(X = 4) + P(X = 6) + ...Let us take p = 1/3, thus P(X = k) = (1 - p)^(k - 1)p, for k = 1, 2, 3, .... Therefore, P(X = 2) = (2 - 1)p(1-p), P(X = 4) = (4 - 1)p(1 - p)^3, P(X = 6) = (6 - 1)p(1 - p)^5, ...So, we haveP(A) = [(2-1)p(1-p)] + [(4-1)p(1-p)^3] + [(6-1)p(1-p)^5] + ...= p(1-p)[1 + 3(1-p)^2 + 5(1-p)^4 + ...]= p(1-p)/(1-(1-p)^2)= 2p(1-p) = 2/9.b) For a geometric random variable, we have E(X) = 1/p and Var(X) = (1 - p)/p^2.The expected value of e^X is:E(e^X) = Σ e^k (1-p)^(k-1) p= p Σ [e^(ln(1-p))]^(k-1) = p Σ (1-p)^(k-1)= p/(1-(1-p)) = 1/pAnd the variance of e^X is:Var(e^X) = E((e^X)^2) - [E(e^X)]^2= E(e^(2X)) - (1/p)^2= Σ e^(2k) (1-p)^(k-1) p - 1/p^2= p Σ [e^(2ln(1-p))]^(k-1) - 1/p^2= p Σ (1-p)^(2(k-1)) - 1/p^2= p/[1-(1-p)^2] - 1/p^2= (2-p)/(p(1-p)^2).c) P(e^X > 10) = P(X > ln(10)) = (1-p)^[ln(10)] = 0.0472 (approx.)
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need help with part A part B and part c
Answer:
4,20,C
Step-by-step explanation:
1/7 of 28 is 4
5/7 of 28 is 20
and if you multiply 4 times 5 you get 20
hope this helped