(a) A vector v parallel to the line of intersection L is v = <1, 1, -2>. (b) The cartesian equation of the plane is -7x + 10y - 3z = -1
(a) To find a vector v parallel to the line of intersection L, we need to take the cross product of the normal vectors to the two given planes. The normal vectors are the coefficients of x, y, and z in the equations of the planes.
In this case, the equations of the planes are:
x + y - 2z = 1
4x + y + 3z = 4
The normal vectors to these planes are <1, 1, -2> and <4, 1, 3>, respectively. Since the line of intersection is parallel to both planes, a vector parallel to the line must be perpendicular to both normal vectors.
We can find such a vector by taking the cross product of the two normal vectors, which gives us: <1, 1, -2> × <4, 1, 3> = <-7, 10, -3>
Therefore, a vector v = <1, 1, -2>.
(b) To find the equation of the plane through the point (2, -1, 3) and perpendicular to L, we need to find a normal vector to the plane that is also parallel to L.
We can find such a vector by taking the cross product of the normal vectors to the two given planes. The normal vectors are <1, 1, -2> and <4, 1, 3>, so the cross product is: <1, 1, -2> × <4, 1, 3> = <-7, 10, -3>
This vector is parallel to L, so it can serve as the normal vector to the desired plane. The equation of the plane can be written in point-normal form as: -7(x - 2) + 10(y + 1) - 3(z - 3) = 0
Simplifying, we get:
-7x + 10y - 3z = -1
Therefore, the cartesian equation of the plane is -7x + 10y - 3z = -1, and it passes through the point (2, -1, 3) and is perpendicular to the line of intersection between the given planes.
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10% of a competition’s contestants like dogs. 60% of them like rabbits. 90% of them like cats. Liking each of these animals is independent. That means, for example, that whether or not you like dogs does not affect whether you like cats. If we choose a random contestant:
a. What is the probability of this contestant
liking cats and dogs, but not rabbits?
b. What is the most likely outcome of this contestant’s preferences? As in, which animals does s/he like, and which does s/he not like?
To find the probability of a contestant liking cats and dogs but not rabbits, we can use the formula for calculating the probability of independent events. That is, P(A and B and not C) = P(A) * P(B) * P(not C).
So in this case, P(cats and dogs and not rabbits) = 0.1 * 0.9 * 0.4 = 0.036. Therefore, the probability of a contestant liking cats and dogs but not rabbits is 0.036 or 3.6%.
As for the most likely outcome of this contestant's preferences, we can see that 90% of the contestants like cats, so it's very likely that this contestant likes cats. However, only 10% of the contestants like dogs, so it's less likely that this contestant likes dogs.
And 60% of the contestants like rabbits, so it's even more likely that this contestant does not like rabbits. Therefore, the most likely outcome is that this contestant likes cats but does not like dogs or rabbits.
In conclusion, given the probabilities provided, we can calculate the probability of a contestant liking cats and dogs but not rabbits, and we can also determine the most likely outcome of this contestant's preferences. The independence of the events allows us to use simple probability calculations to make these determinations.
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The coach of the soccer team is asked to select 5 students to represent the team in the Homecoming Parade. The coach decides to randomly select 5 students out of the 38 members of the team.
a. What is the population for this problem?
b. What is the sample for this problem?
c. Suggest a method for selecting the random sample of 5 students
The population is 38, and the sample is 5 students.
find out the population, sample, and method for selection?. The population for this problem is the entire soccer team, which consists of 38 members.
b. The sample for this problem is the group of 5 students who are selected by the coach to represent the team in the Homecoming Parade.
c. One method for selecting a random sample of 5 students from the team is to use a random number generator to choose 5 numbers between 1 and 38, representing the 38 team members. The coach can then select the students who correspond to the chosen numbers. Another method is to write the names of all 38 team members on identical slips of paper, place the slips in a container, mix them up, and then randomly select 5 slips to determine the students who will participate in the parade. It is important to ensure that the selection method is truly random to avoid any bias or non-representativeness in the sample.
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20 pt if someone can answer this!!!
Pls help.
The median value is____
Answer:
The median value is 45.
Step-by-step explanation:
"The median is the middle number in a sorted, ascending or descending list of numbers"
The middle number here is 45
50
Step-by-step explanation:
I put the explanation on the attachment. please see it.
As a volunteer at the animal shelter, uma weighed all the puppies. she made a list of the weights as she weighed them. the puppies weights were 3 3/4 lb, 4 1/4 lb, 3 1/2 lb, 3 3/4 lb, 3 1/4 lb, 3 3/4 lb, 3 1/2 lb, 4 1/4 lb, and 3 3/4 lb. draw a line plot of the puppies weights. use the line plot to write and answer a question about the data
Using this line plot, we can answer questions such as:
What is the most common weight for the puppies?
The most common weight is 3 3/4 lb, which occurs 3 times.
What is the range of weights for the puppies?
The range of weights is from 3 1/4 lb to 4 1/4 lb.
How many puppies weigh less than 4 lb?
Four puppies weigh less than 4 lb.
How many puppies weigh exactly 3 1/2 lb?
Two puppies weigh exactly 3 1/2 lb.
What is the frequency?
The number of periods or cycles per second is called frequency. The SI unit for frequency is the hertz (Hz). One hertz is the same as one cycle per second.
The line plot of the puppies' weights is in the attached image.
Each "*" represents a puppy's weight.
The horizontal axis represents the weight values, and the vertical axis represents the frequency of each weight.
Hence, Using this line plot, we can answer questions such as:
What is the most common weight for the puppies?
The most common weight is 3 3/4 lb, which occurs 3 times.
What is the range of weights for the puppies?
The range of weights is from 3 1/4 lb to 4 1/4 lb.
How many puppies weigh less than 4 lb?
Four puppies weigh less than 4 lb.
How many puppies weigh exactly 3 1/2 lb?
Two puppies weigh exactly 3 1/2 lb.
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An administrator of a large middle school is installing some vending machines in the school. She wants to know what type of machine would be most popular.
Conducting a survey among the students would be the best way to determine the most popular type of vending machine.
In order to accurately determine the most popular type of vending machine, it is important to gather data from the intended audience - the students. By conducting a survey, the administrator can gather information on the types of snacks and drinks that the students prefer, as well as their pricing preferences.
This will allow the administrator to make an informed decision on which type of vending machine will be most popular and profitable for the school.
Additionally, by involving the students in the decision-making process, they may feel more invested in the vending machines and be more likely to use them, ultimately leading to a successful vending program.
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Write the equation for shifting the parent function of the absolute value function 3 units down.
The vertex will be at (0, -3), and the graph will be lower than the parent function by 3 units at every point. The parent function of the absolute value function is f(x) = |x|.
To shift this function 3 units down, we need to subtract 3 from the function's output (y) at every point on the graph. This can be expressed as:
f(x) = |x| - 3
The absolute value function is symmetric around the y-axis, which means that any shifts to the left or right do not affect the shape of the graph, only its position on the coordinate plane.
However, a vertical shift up or down will change the location of the vertex, the point where the graph changes direction. In this case, the vertex will be at (0, -3), and the graph will be lower than the parent function by 3 units at every point.
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The edge of a cube-shaped box is 1 yard long. Three students each made an observation about the box. • Janae said that the area of each face of the box is 9 square feet. • Archie said that the perimeter of each face of the box is 3 feet. • Gail said that the volume of the box is 1 cubic yard. Whose observations about the box are correct?
Gail's observations about the box is correct. According to the question the edge of a cube-shaped box is 1 yard.
Now convert the edge length to feet as : 1 yard = 3 feet.
On checking the observations:
1. According to Janae the area of each face is 9 square feet. Calculating the surface area of one face of the cube is given by:
Area = (edge length)² = (3 feet)² = 9 square feet.
Now, Total surface area = 6*9square feet= 54 square feet.
Hence Observations of Janae is not correct.
2. According to Archie perimeter of each face of the box is 3 feet. Calculating the perimeter of each face of the cube is given by:
Perimeter= 4 × (edge length)=4×1 yard= 4×3feet=12 feet
Hence Archie observation is not correct also.
3. According to Gail the volume of the box is 1 cubic yard.
The volume of a cube is given by:
volume= (edge length)³ = (1 yard)³ = 1 cubic yard.
Therefore Gail's observation is correct.
From all the above observations it can be concluded that only Gail's observation is correct.
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The prism shown has a surface area of 1,500 mm squared. What is the height, h, of the prism?
The height of the triangular base prism is 10 mm.
How to find the surface area of a prism?The prism above is a triangular base prism. The surface area of the prism can be calculated as follows:
surface area of the triangular prism = (a + b + c)l + bh
where
a, b, and c are the side of the triangular basel = height of the prismb = base of the triangleh = height of the triangleTherefore,
surface area of the triangular prism = (20 + 30 + 40) + 20 × 30
1500 = 90l + 600
1500 - 600 = 90l
90l = 900
divide both sides by 90
l = 900 / 90
l = 10 mm
Therefore,
height of the prism = 10 mm
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What is the scale factor for the similar figures below?
The value of the scale factor for the similar figures is 1/4
What is the scale factor for the similar figures?From the question, we have the following parameters that can be used in our computation:
The similar figures
The corresponsing sides of the similar figures are
Original = 8
New = 2
Using the above as a guide, we have the following:
Scale factor = New /Original
substitute the known values in the above equation, so, we have the following representation
Scale factor = 2/8
Evaluate
Scale factor = 1/4
Hence, the scale factor for the similar figures is 1/4
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the cost of a taxi ride is $3.00 plus $0.75 for every 0.5km. represent the relation in a table (up to 10km), a graph and an equation
The equation for the cost of a taxi ride as c = 0.75(d - 0.5) + 3.
What is distance travelled?Distance traveled refers to the total distance covered by an object or person over a certain period of time or within a given context. It can be measured in units such as meters, kilometers, miles, or any other unit of length.
According to question:Equation:
Let d be the distance travelled in kilometres, and let c be the cost in dollars. Then we can write the equation for the cost of a taxi ride as:
c = 0.75(d - 0.5) + 3
This equation takes into account the initial $3.00 fee, as well as the additional $0.75 for every 0.5km
Table:
Distance (km) Cost ($)
0.5 3.38
1 3.75
1.5 4.13
2 4.50
2.5 4.88
3 5.25
3.5 5.63
4 6.00
4.5 6.38
5 6.75
5.5 7.13
6 7.50
6.5 7.88
7 8.25
7.5 8.63
8 9.00
8.5 9.38
9 9.75
9.5 10.13
10 10.50
Graph:
The x-axis represents the distance in kilometers, and the y-axis represents the cost in dollars. We start the graph at (0, 3), and then plot a point at (0.5, 3.75), (1, 4.5), (1.5, 5.25), and so on, until we get to (10, 18). We then draw a line connecting all of these points to create a line graph.
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What is the actual perimeter of the kitchen? (ft^2)
Explain
The actual perimeter of the kitchen is 8 inch
How to find the perimeterTo find the perimeter, we have to get the length of all of the sides of the kitchen
The kitchen is a rectangle
perimeter of rectangle = 2(l + b)
= 2 (2 1/4 + 1 3/4)
2(9/4 + 7/4)
2 * 4
= 8
The perimeter of the kitchen is 4 inch
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Which table shows a proportional relationship between x and y?
The set of values for x that satisfies a quadratic inequality is x < -0.5 or x > 1.5
Write down a possible quadratic inequality. Please help - it’s a gcse maths question
Answer: x-0.5y=1.5
Step-by-step explanation:
Evaluate the following limits analytically. Show your work for full credit.
Iim (sin(9x))/x
x->0
The limit of (sin(9x))/x as x approaches 0 is equal to 9.
To evaluate this limit analytically, we can use L'Hopital's Rule.
Taking the derivative of the numerator and denominator with respect to x, we get:lim (sin(9x))/x = lim (9cos(9x))/1as x approaches 0.
Substituting x = 0, we get:lim (sin(9x))/x = 9cos(0)/1 = 9Therefore, the limit of (sin(9x))/x as x approaches 0 is equal to 9.
We know already how to apply or make the procedures mathematically talking so this short program will eventually help you how to find logic.
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A company makes cones out of solid foam. Each cone has a height of inches, and its base has a radius of inches. How much foam is needed to make cones?
The total foam needed to make n cones is (n/3)πr^2h cubic inches.
What is the total volume of foam required to manufacture a certain number of cones with a given height and base radius?The volume of a cone can be calculated using the formula:
V = (1/3)πr^2h
where r is the radius of the base, h is the height, and π is the mathematical constant pi.
In this case, the height of each cone is given as h inches, and the radius of the base is given as r inches. So, the volume of each cone can be calculated as:
V = (1/3)πr^2h
Now, let's assume that the company wants to make n cones. Then, the total amount of foam needed to make these cones would be:
Total foam needed = n × V
Substituting the expression for V, we get:
Total foam needed = n × (1/3)πr^2h
Therefore, the total foam needed to make n cones is (n/3)πr^2h cubic inches.
Note that the given values of h and r are necessary to compute the total foam required.
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Anyone who knows how to do this please help answer!! Fill in the correct numbers in both sides of the chart and answer the bottom questions.
WILL MARK BRAINLIEST!!!
a) Here is the chart showing the number of bacteria after 0 to 4 hours:
| Time (hours) | Number of bacteria |
|--------------|--------------------|
| 0 | 50 |
| 1 | 150 |
| 2 | 450 |
| 3 | 1,350 |
| 4 | 4,050 |
b) To write an expression that models the number of bacteria after a number of hours, n, we can use the formula:
Number of bacteria = Initial number of bacteria x Growth factor^nIn this case, the initial number of bacteria is 50, and the growth factor is 3 (since the number of bacteria triples every hour). Therefore, the expression that models the number of bacteria after n hours is:
Number of bacteria = 50 x 3^nc) To determine the number of bacteria that are present after 12 hours using the expression we derived in part b), we can substitute n = 12 into the expression:
Number of bacteria = 50 x 3^12= 26572050
Therefore, there are approximately 2.7 billion bacteria present after 12 hours.a rectangular poster is to contain 392 square inches of print. the margins at the top and bottom of the poster are to be 2 inches, and the margins on the left and right are to be 1 inch. what should the dimensions of the poster be (in inches) so that the least amount of poster is used? (enter your answers as a comma-separated list.)
The dimensions of the poster with an area of 392 square inches is equal to 14 inches and 28 inches.
Area of rectangular poster to print = 392 square inches
Let us assume that dimensions of the posters are,
Width of the poster is x inches and the length of the poster is y inches.
Area of the rectangular poster is,
xy = 392
Add 2 inches to the top and bottom margins for a total of 4 inches
And 1 inch to the left and right margins for a total of 2 inches.
Total area of the poster including the margins using the following equation,
Total area = (x + 2) × (y + 4)
Minimize the total area of the poster while still satisfying the area constraint.
Use the first equation to solve for one variable
And substitute it into the second equation,
y = 392/x
Total area = (x + 2) × (392/x + 4)
⇒ Total area = 4x + 392 +784/x + 8
⇒Total area = 4x + 400 +784/x
Minimize the total area, take the derivative of this expression with respect to x and set it equal to 0,
d/dx (4x + 400 +784/x ) = 0
⇒ 4 + 0 - 784/x² = 0
⇒ x² = 784 /4
⇒ x = 14
Substituting this value of x back into the equation for y, we get,
y = 392/14
= 28
Therefore, the dimensions of the poster should be 14 inches by 28 inches.
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Find the distance traveled by the top of second hand of a clock in 4 minute if the hand is 8 cm long
The second hand of a clock rotates once around the clock face in 60 seconds or one minute. Therefore, in 4 minutes, the second hand will rotate 4 times around the clock face.
The length of the second hand of a clock is 8 cm. The distance traveled by the top of the second hand in one full rotation is equal to the circumference of a circle with radius 8 cm, which is 2πr = 2π(8) = 16π cm.
The distance traveled by the top of the second hand in 4 rotations (or 4 minutes) is:
4 rotations * 16π cm/rotation = 64π cm
So the distance traveled by the top of the second hand of a clock in 4 minutes if the hand is 8 cm long is approximately 64π cm or about 201.06 cm (when rounded to two decimal places).
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so i need help with this question so please help
Answer:
I believe the answer is D.
Step-by-step explanation:
Her car tires need to be ATLEAST 28. So, the number will be 28 or above.
15. sheila has an eye-height of 5.4 feet and is standing 33 feet from a building. the angle of elevation from her line of
sight to the top of the building is 71 degree how tall is the building? round to the nearest tenth.
The height of the building is approximately 102.3 feet, rounded to the nearest tenth.
Step 1: Draw a right triangle with Sheila's eye-height as the base, the building's height as the vertical side, and the distance between Sheila and the building as the horizontal side.
Step 2: We are given the angle of elevation (71 degrees) and the horizontal distance (33 feet). To find the vertical distance, we can use the tangent function in trigonometry. The formula is:
tan(angle) = (opposite side) / (adjacent side)
Step 3: Plug in the given values into the formula:
tan(71) = (vertical distance) / 33
Step 4: Solve for the vertical distance:
vertical distance = 33 * tan(71) ≈ 96.9 feet
Step 5: Add Sheila's eye-height to the vertical distance to find the total height of the building:
total height = eye-height + vertical distance
total height = 5.4 + 96.9 ≈ 102.3 feet
The height of the building is approximately 102.3 feet, rounded to the nearest tenth.
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1. )Indicate the equation of the given line in standard form. Show all of your work for full credit.
The line containing the median of the trapezoid whose vertices are R(-1, 5) , S(1, 8), T(7, -2), and U(2, 0).
2. )Indicate the equation of the given line in standard form. Show all of your work for full credit.
The line containing the altitude to the hypotenuse of a right triangle whose vertices are P(-1, 1), Q(3, 5), and R(5, -5).
3. ) Indicate the equation of the given line in standard form. Show all of your work for full credit.
The line containing the diagonal, BD, of a square whose vertices are A(-3, 3), B(3, 3), C(3, -3), and D(-3, -3). Find two equations, one for each diagonal.
1) x+y=4. This is the equation of the line in standard form.
2) x+y=4. This is the equation of the line in standard form.
3) The equation of the other diagonal is x=0.
1) The median of a trapezoid connects the midpoints of the non-parallel sides. The midpoint of RT is ((-1+7)/2,(5-2)/2)=(3,1.5) and the midpoint of SU is ((1+2)/2,(8+0)/2)=(1.5,4). The line containing the median passes through these two points, so we can use them to find the equation of the line. The slope of the line is (4-1.5)/(1.5-3)=1.5/(-1.5)=-1. The midpoint formula for a line gives us (y-1.5)=-1(x-3), which simplifies to x+y=4. This is the equation of the line in standard form.
2) To find the altitude to the hypotenuse of a right triangle, we need to find the midpoint of the hypotenuse and the slope of the hypotenuse. The midpoint of PQ is ((-1+3)/2,(1+5)/2)=(1,3), and the midpoint of PR is ((-1+5)/2,(1-5)/2)=(2,-2). The slope of PQ is (5-1)/(3-(-1))=4/4=1, so the slope of the altitude is -1. We can use the point-slope form of a line to get y-3=-1(x-1), which simplifies to x+y=4. This is the equation of the line in standard form.
3) The diagonals of a square are perpendicular bisectors of each other, so we can find the equations of both diagonals using the midpoint and slope formulas. The midpoint of AC is ((3-3)/2,(3-3)/2)=(0,0), and the midpoint of BD is ((-3+3)/2,(3-3)/2)=(0,0). The slope of AC is (3-(-3))/(3-(-3))=6/6=1, so the slope of BD is -1. Using the point-slope form of a line, we can get y-0=-1(x-0), which simplifies to y=-x. This is the equation of one diagonal. To find the equation of the other diagonal, we use the midpoint of AB ((-3+3)/2,(3+3)/2)=(0,3) and the midpoint of CD ((3-3)/2,(-3-3)/2)=(0,-3). The slope of AB is (3-3)/(3-(-3))=0, so the slope of the other diagonal is undefined (since it's perpendicular to AB). The equation of the other diagonal is x=0.
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Scientists measured 24 geodes in kilograms and got the following data: 0.9, 1.1, 1.1, 1.2, 1.5, 1.6, 1.7, 1.7, 1.7, 1.9, 2.0, 0.8, 2.3, 5.3, 6.8, 7.5, 9.6, 10.5, 11.2, 12.0, 17.6, 23.9, and 26.8
How many items belong to the interval 10.1-15
Answer:
the answer to your problem is 3
Liang wants to form a chess club. His principal says that he can do that if Liang can find six players, including himself. How would you conduct a simulated model that estimates the probability that Liang will find at least five other players to join the club if he asks eight players who have a 70% chance of agreeing to join the club? Suggest a simulation model for Liang by describing how you would do the following parts
To conduct a simulated model that estimates the probability that Liang will find at least five other players to join the chess club if he asks eight players who have a 70% chance of agreeing to join.
We can use the following steps:
1. Define the variables:
- n: the number of trials (i.e., the number of times Liang asks eight players to join)
- p: the probability of success (i.e., the probability that a player agrees to join the club, which is 0.7)
- k: the number of successes needed (i.e., the number of players, excluding Liang, that he needs to find to form the club, which is 5)
- success: a counter to keep track of the number of successful trials (i.e., the number of times Liang finds at least five players to join)
2. Set the initial value of the success counter to 0.
3. Start a loop that runs n times. In each iteration of the loop:
- Generate a random number between 0 and 1 using a random number generator.
- If the random number is less than or equal to p, increment a "success count" variable.
- If the success count variable reaches k, break out of the loop.
4. After the loop finishes, divide the success count variable by n to get the simulated probability that Liang will find at least five players to join the chess club.
5. Repeat the simulation multiple times (e.g., 1000 times) to obtain a distribution of simulated probabilities.
6. Calculate the mean and standard deviation of the simulated probabilities to estimate the most likely probability that Liang will find at least five players to join the chess club, and the range of probabilities that he is likely to obtain.
Note: This simulation model assumes that each player's decision to join the club is independent of the other players' decisions and that the probability of success (i.e., agreeing to join) is the same for each player. These assumptions may not always be accurate in practice.
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how do i change a mixed number to a improper fraction and simplify
Answer:
To change a mixed number to an improper fraction quickly we can multiply the whole number by the denominator, add the numerator and then write that over the original denominator.
HELP ME PLEASE ANYBODY I NEED IT URGENTLY
I also have to show my work
Thank you.
In two or more complete sentences, describe the transformation(s) that take place on the parent function F=f(x)=log(x) to achieve the graph of g(x)=log(-3x-6)-2
The transformations that take place on the parent function F=f(x)=log(x) to achieve the graph of g(x)=log(-3x-6)-2 are horizontal compression and vertical shift.
What transformations took place in the function?The transformations are a horizontal compression and a vertical shift.
Horizontal compression: The factor of 3 in the argument of the logarithm function causes a horizontal compression by a factor of 1/3. This means that the graph of g(x) is narrower than the graph of f(x) and it is shifted to the left.Vertical shift: The constant term of -2 is subtracted from the logarithm function, causing a vertical shift downwards by 2 units.Therefore, the transformations can be expressed mathematically as follows:
g(x) = log(-3x - 6) - 2
= log(-3(x + 2)) - 2
= log(1/3)log(-3(x + 2)) - 2
Therefore, the transformations are a horizontal compression by a factor of 1/3 and a vertical shift downwards by 2 units.
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Sylvia Baxterâs Cape Cod home has an assessed value of $64,000 and her land has an assessed value of $4,800. If the rate of assessment in her municipality is 35 percent, what is the market value of her property?
a
$196,571. 43
b
$44,720. 00
c
$68,800. 00
d
$113,520. 00
The market value of Sylvia Baxter's property are $68,800.00. The correct answer is (c)
To find the market value of Sylvia Baxter's property, we need to divide the assessed value by the assessment rate and then multiply by 100.
Assessed value of the home = $64,000
Assessed value of the land = $4,800
Assessment rate = 35% = 0.35 (as given in the problem)
So, the total assessed value of the property = $64,000 + $4,800 = $68,800
Now, to find the market value, we need to divide the assessed value by the assessment rate and multiply by 100:
Market value = (Assessed value / Assessment rate) x 100
Market value = ($68,800 / 0.35) x 100 = $196,571.43 (rounded to the nearest cent)
Therefore, the market value of her property is $68,800.00.
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A cylinder has a height of 4 in and a base circumference of 12. What is the approximate volume of the cylinder? Round to the nearest whole number.
Answer: 48 inches
Step-by-step explanation:
One similar figure has an area that is nine times the area of another. The larger figure must have dimensions that are
times the dimensions of the smaller figure.
three
eighteen
eighty-one
nine
Since the area of a similar figure is proportional to the square of its linear dimensions, if one similar figure has an area that is nine times the area of another, the larger figure must have dimensions that are three times the dimensions of the smaller figure.
This is because the area is the square of the linear dimensions. So, if we increase the linear dimensions by a factor of 3, the area increases by a factor of 3^2 = 9.
Therefore, the answer is 3.
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What is the area of a sector with a central angle of 45° and a diameter of 5. 6 in. ? Use 3. 14 for π and round your final answer to the nearest hundredth. Enter your answer as a decimal in the box. What is the area of a sector with a central angle of 120° and a radius of 18. 4 m? Use 3. 14 for π and round your final answer to the nearest hundredth. Enter your answer as a decimal in the box
The area of a sector with a central angle of 45° and a diameter of 5.6 in. is 1.23 square inches.
To see why, you can use the formula for the area of a sector, which is:
A = (θ/360) x π x r^2
where θ is the central angle in degrees, r is the radius, and π is approximately 3.14.
First, you need to find the radius of the sector, which is half of the diameter:
r = d/2 = 5.6/2 = 2.8 in.
Next, you can plug in the values for θ and r into the formula:
A = (45/360) x 3.14 x 2.8^2 = 1.23 square inches
Therefore, the area of the sector is 1.23 square inches.
The area of a sector with a central angle of 120° and a radius of 18.4 m is 1908.57 square meters.
To see why, you can use the same formula for the area of a sector:
A = (θ/360) x π x r^2
First, you need to convert the radius from meters to centimeters, since π is in terms of centimeters:
r = 18.4 m x 100 cm/m = 1840 cm
Next, you can plug in the values for θ and r into the formula:
A = (120/360) x 3.14 x 1840^2 = 1908.57 square meters
Therefore, the area of the sector is 1908.57 square meters.