the standard deviation of the weights of the fish in the lakex will be equal to 0.115 right so that that is approximately 0.12
Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. In graphical form, the normal distribution appears as a "bell curve".
Formula
f(x)= {frac{1}{sigma\sqrt{2\pi}}}e^{- {frac {1}{2}} (frac {x-mu}{sigma})^2}
f(x) = probability density function
sigma = standard deviation
mu = mean
the question is that organizers of a fishing totame believe that the lake whole sizable population of large mouths they assumed the wives of these fish have modeled that is q to the right, with a mean of 2.3 and standard deviation of 1.67. So here the question first part is that why does the skewed model make sense here right? So the for this? The answer will be because a skeeto, the right model makes sense, because it would be expected that there are many small fishes and few larger ones in the lake right. So here the correct option would be the option a right now. The next part of the question here it says that explain why you cannot use the normal model to determine the probability that a large mouth, but some randomly selected from the lake, weighs over 2 pounds. So here the correct option will be option b only. That is because the distribution is not normal and the exact distribution is not given. So it is not possible to determine the probability right so here and the third part of the question. It says here that each contestant catches 15 fish each day. So is it possible to determine the probability that some 1 catches average more than 2 pounds? Okay, so here the answer will be here: the probability cannot be determined, since the distribution is q to the right and the sample size of 15 is not large enough to use the central limit theorem. So the correct option is option b now. The third part for d option is the next part here says that the 14 contestants competing each cot, the limit of 15 fish. So what is the standard? Deviation of the mean weight of the 210 fishes caught right now here the size of the sample is 14 into 15 point. That is equal to 210 point right. So this is the standard. Deviation here. Sorry, okay, so the standard deviation here for the mean will be equal to the population. Standard deviation upon square root of sample size, so this is the population. Standard deviation is 1.67. This is square root of 210 point,
so this will be equal to 0.115 right so that that is approximately 0.12
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the standard deviation of the weights of the fish in the lake will be equal to 0.115 right so that is approximately 0.12
A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.
Formula:
[tex]P(x) = \frac{1}{{\sigma \sqrt {2\pi } }}e^{{{ - \left( {x - \mu } \right)^2 } \mathord{\left/ {\vphantom {{ - \left( {x - \mu } \right)^2 } {2\sigma ^2 }}} \right. \kern-\nulldelimiterspace} {2\sigma ^2 }}}[/tex]
[tex]P(x)[/tex] = probability density function
σ = standard deviation
μ = mean
The issue is that the organizers of a tame fishing tournament think that the lake has a substantial population of large mouth bass, therefore they assumed that the spouses of these fish have modeled that is q to the right, with a mean of 2.3 and a standard deviation of 1.67. The first half of the inquiry is, therefore, why does the skewed model make sense in this situation? then what for this? The correct model, a skeeto, will provide the answer since it is reasonable to assume that the lake has a large number of little fish and few larger ones.
The following portion of the question asks you to clarify why you can't use the normal model to calculate the likelihood that a large mouth, but some randomly selected from the lake, weighs more than 2 pounds. So, in this case, the distribution is not normal and the precise distribution is not provided. Because of this, it is impossible to answer the third half of the question and establish the probability at this time. Each participant in the competition is said to capture 15 fish every day. Can we therefore calculate the likelihood that some 1 catches average more than 2 pounds? Okay, so this is where the response will be: The probability cannot be calculated because of the distribution is q to the right and the sample size of 15 is not large enough to use the central limit theorem.
The next section of this question states that each of the 14 contenders has a catch limit of 15 fish. What then is the norm? The sample size's 14 to 15 point deviation from the mean weight of the 210 fish currently captured here. That is equivalent to 210 correct points. And so, this is the norm. this is a departure. Sorry, yeah, so the population's standard deviation will be the same as the mean in this case. This is the population based on standard deviation of sample size squared. There is a 1.67 standard deviation. This is the square root of 210.
So, this will be equal to 0.115 right so that that is approximately 0.12
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If you were given sticks of the following lengths, how many triangles can you make?
6 inches, 9 inches, 4 inches.
I know you can make a triangle but would it be infinite triangles or just one?
How do you find the distance between two points in 8th grade?
To calculate the distance between two places, we can apply the distance formula d=((x2 - x1)² + (y2 - y1)²).
What is the distance?The distance of an object is its overall motion, regardless of direction.
Distance is the amount of space that an object has covered, regardless of where it began or concluded.
By understanding how far an object is from us, we may calculate its actual size.
It is possible to calculate the area that an object takes up in the sky.
The actual size of an object can then be determined by taking into account its distance.
The further away something is, the smaller it appears.
The distance between two locations on a plane is the length of the line segment connecting them.
The formula d=((x2 - x1)² + (y2 - y1)²) is frequently used to calculate the separation between two points.
Therefore, to calculate the distance between two places, we can apply the distance formula d=((x2 - x1)² + (y2 - y1)²).
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A new car is purchased for $ 50 , 000 $50,000 and over time its value depreciates by one half every 5 years. What is the value of the car 7 years after it was purchased, to the nearest hundred dollars?
The value of the car 7 years after it was purchased to the nearest hundred dollars as required is; $18,900.
What would be the value of the 7 years after?It follows from the task content that the car in discuss depreciates by one half every 5 years.
Hence, since the exponential function which represents the situation can be modelled as;
V = 50,000 (1/2)^(7/5)
V = 50,000 × 0.378929141
V = 18,946.45708.
Hence, the value of the car 7 years after would be; $18,900 (rounded to the nearest hundred dollars).
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Cynthia started an exercise program. During the first week she walked mile every day. 2 1 Every week she increased the distance she walked each day by mile. Which method can be 2 used to determine the number of miles Cynthia walked each day during the ninth week of her exercise program?
Cynthia walked 63 miles during the ninth week of her excercise program.
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here: Cythia walks a mile everyday. Now. Cynthia walk 1 mile on day 1 and 2 miles on day 2 and so on and 9 weeks has 63 days.
Therefore the number of miles she walked coincides with the number of days she walked i.e 63 miles
Hence, Cynthia walked 63 miles.
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What is the distance between the points 2 0 and (- 2 0?
16 units are the distance between the two points (2, 0) and (-2, 0).
What is the distance?An object's distance is determined by its total velocity, regardless of direction.
Regardless of where it started or ended, distance is the amount of space that an object has covered.
We can determine an object's true size by knowing how far it is from us.
Usually, the formula shown below is used to calculate the separation between two points: d=((x2 - x1)2 + (y2 - y1)2)
So, the distance formula is:
d=((x2 - x1)2 + (y2 - y1)2)
Points are: (2, 0) and (-2, 0)
Now, enter the numbers in the formula above and do the following calculation:
d=((x2 - x1)2 + (y2 - y1)2)
d=(-2 - 2)2 + (0 - 0)2)
d=(-4)²
d=16
Therefore, 16 units are the distance between the two points (2, 0) and (-2, 0).
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Correct question:
What is the distance between the points (2, 0) and (-2, 0)?
If <3=<4, which lines must be parallel?
A)line d and line e
B)line a and line d
C)line a and line c
D)line a and line b
If ∠2 = ∠4, then the line a and line b is parallel. So the option D is correct.
In the given question, if ∠2 = ∠4, then we have to find which lines must be parallel.
The graph of the given question is given below:
Lines that are parallel to one another on a plane do not intersect or meet at any point. They are always equidistant from one another and parallel. Non-intersecting lines are parallel lines. Parallel lines can also be said to meet at infinity.
As we can see that in the given graph graph that there have two parallel lines a and b, c and d.
As given that ∠2 = ∠4, then the line a and line b is parallel. So the option D is correct.
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The complete question is:
If ∠2 = ∠4, which lines must be parallel?
A)line d and line e
B)line a and line d
C)line a and line c
D)line a and line b
Given that Justin is collecting data on reaction time, what type of data is he working with?
Select the correct answer below:
A. qualitative
B. discrete quantitative
C. continuous quantitative
D. none of the above
Since reaction time is measured and not constrained to a specific range of numbers, it is continuous quantitative data.
'What is continuous quantitative?'
A continuous data set is a quantitative data set that represents a scale of measurement that includes fractions and decimals in addition to whole integers. Values like height, weight, length, temperature, and other similar metrics would be included in continuous data sets. They are items that can be quantified in decimals and fractions. A continuous data set typically requires the use of a tool, such as a ruler, measuring tape, scale, or thermometer, to create the numbers.
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alice has a bag containing balls that are each colored either red or blue. bob reaches in to pick five of the balls, and says that he hopes to get at least one of each color. alice reveals that this is guaranteed! what is the largest total number of balls that alice could have in the bag?
The largest total number of balls that alice could have in the bag is 5.
Bob wants to pick five balls from the bag and get at least one of each color, red and blue. Alice has guaranteed that this is possible, which means that there must be enough balls in the bag and at least one of each color.
The maximum number of balls in the bag can be achieved when the total number of balls is the same as the total number of balls Bob picks, which is 5.
In this case, Bob could pick one red and four blue, or one blue and four red, and he would still get at least one of each color.
This means that the largest total number of balls that Alice could have in the bag is 5.
It's important to note that this is the maximum number and it's possible that there are less balls in the bag. The maximum number of balls in the bag can only be achieved when Bob picks one red and four blue, or one blue and four red.
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Please help!! circular flower bed is 20 m in diameter and has a circular sidewalk around it that is 2 m wide. Find the area of the sidewalk in square meters.
The area of the sidewalk is 144π square meters.
Describe area of a circle?The area of a circle is a measure of the amount of space inside the circle. It is defined as the product of Pi (π) and the square of the radius of the circle.
A = π × r²
The radius is the distance from the center of the circle to its edge. The area of a circle is a scalar quantity and is typically expressed in square units, such as square centimeters or square meters.
The diameter of the circular flower bed is 20 m, so its radius is 20/2 = 10 m.
The sidewalk around the flower bed is 2 m wide, so the radius of the circular sidewalk is 10 + 2 = 12 m.
The area of a circle can be found using the formula:
A = πr^2
So the area of the circular sidewalk is:
A = π × 12²= π × 144 = 144π m²
Therefore, the area of the sidewalk is 144π square meters.
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Write an equation of the line in point-slope form with the given slope and the point it passes through.
Slope=(2,-1)
y + 1 = -3 (x - 2) an equation of the line in point-slope form with the given slope and the point it passes through, slope=(2,-1)
What is slope?An indication as to how sharp a line is its slope. Slope is computed mathematically as "rise over run" (change in y divided by change in x). The ratio of the increase in elevation between two places to the run in elevation between those same two points is referred to as the slope.
Slope-related equations The "change in y" over the "change in x" of a line is referred to as the slope. By dividing (y₂ - y₁) over (x₂ - x₁) and choosing two locations on the line (x₁, y₁) and (x₂, y₂), you can get the slope.
The point-slope formula states: (y₂- y₁) = m (x₂ - x₁)
where, m = slope and (x₁, y₁) is a point the line passes through.
Substituting the slope and values from the point in the problem gives:
[y₂- (-1)] = -3 (x₂ - 2)
y + 1 = -3 (x - 2)
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The complete question is as follows:
How do you write the equation in point slope form given (2,-1), m= -3?
in a communication system each data packet consists of 1000 bits. due to the noise, each bit may be received in error with probability 0.1. it is assumed bit errors occur independently. find the probability that there are more than 120 errors in a certain data packet.
The probability that there are more than 120 errors in a certain data packet is:
P(X > 120) = 1 - P(X <= 120)
We are given, each data packet consists of 1000 bits. Due to noise, each bit may be received in error with a probability of 0.1. It is assumed that bit errors occur independently. The goal is to find the probability that there are more than 120 errors in a certain data packet.
To find the probability that there are more than 120 errors in a data packet, we can use the cumulative distribution function (CDF) of the binomial distribution:
P(X > 120) = 1 - P(X <= 120)The number of errors in a data packet can be modeled as a binomial random variable with n = 1000 (number of bits in the packet) and p = 0.1 (probability of a bit error).
Where X is the number of errors in the data packet.
The cumulative distribution function of the binomial distribution can be calculated using the formula:
P(X <= k) = Summation(i=0 to k) ( (n choose i) * (p^i) * ((1-p)^(n-i)) )
Plugging in the values we get:
P(X > 120) = 1 - P(X <= 120) = 1 - (summation(i=0 to 120) ( (1000 choose i) * (0.1^i) * (0.9^(1000-i)) ))
This computation can be done using a computer program on the computer.
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Why does the distance formula work?
In addition to many other things, it assists with the construction of new structures and with locating potential places and new routes for emergency situations. As a result, it's important to learn how to calculate the distance between two points in two and three dimensions.
In math, what is a distance?
The length of the segment of the line that connects the supplied two points determines the distance between them.
The shortest segment of a line connecting a point to a line will have a length equal to the distance between them.
Why does the distance formula work?
The Pythagorean Theorem, which states that a side plus a side plus a side equals a side equals a side equals a side equals a side equals a side equals a side equals a side equals a side, is where the Distance Formula actually originates (known as the legs of a right triangle).
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Answer the questions below Alex loves golf. He has kept track of his last 10 shots for 4 different clubs. He wrote down the distance in yards he hit each of the clubs in the table below. Pitching Wedge 7 Iron 3 Iron Driver 1 2 3 4 5 132 143 137 24 134 164 161 237 168 163 198 204 193 198 199 298 293 315 307 322 a) Calculate the mean distance for the four clubs Alex used? Pitching Wedge Mean b) Calculate the median distance for the four clubs Alex used? c) Calculate the mode of each club. 6 136 164 209 299 Mode Median Pitching Wedge Pitching Wedge 7 Iron 3 Iron 7 8 9 132 130 133 168 164 158 42 201 198 303 314 52 7 Iron 3 Iron 604301 7 Iron Driver 3 Iron d) Look for some outliers in the data. What could have caused these outliers? 10 132 153 198 311 Driver Driver e) To calculate the average distance of all four clubs combined, find the mean of the medians for each club.
a) The mean distance for the four clubs Alex used, Pitching Wedge Mean is 133.5
b) The median distance for the four clubs Alex used are:
Pitching Wedge Median: 136
7 Iron Median: 164
3 Iron Median: 298
Driver Median: 42
c) The mode of each club. 6 136 164 209 299 Mode Median are:
Pitching Wedge Mode: N/A (no value is repeated)
7 Iron Mode: N/A (no value is repeated)
3 Iron Mode: N/A (no value is repeated)
Driver Mode: N/A (no value is repeated)
How did we determine the values above?a) Calculate the mean distance for the four clubs Alex used?
Pitching Wedge Mean: (132 + 143 + 137 + 24 + 134 + 136 + 132 + 130 + 133 + 132) / 10 = 133.5
7 Iron Mean: (164 + 161 + 237 + 168 + 164 + 164 + 158 + 201 + 198 + 153) / 10 = 176.5
3 Iron Mean: (198 + 199 + 298 + 293 + 315 + 307 + 322 + 42 + 303 + 314) / 10 = 250.5
Driver Mean: (199 + 604 + 301 + 7 + 604 + 301 + 7 + 42 + 52 + 311) / 10 = 243.2
b) Calculate the median distance for the four clubs Alex used?
Pitching Wedge Median: 136
7 Iron Median: 164
3 Iron Median: 298
Driver Median: 42
c) Calculate the mode of each club.
Pitching Wedge Mode: N/A (no value is repeated)
7 Iron Mode: N/A (no value is repeated)
3 Iron Mode: N/A (no value is repeated)
Driver Mode: N/A (no value is repeated)
d) Look for some outliers in the data. What could have caused these outliers?
Pitching Wedge: 24 yards (could be caused by a poor shot or a mistake in recording)
7 Iron: 237 yards (could be caused by a particularly good shot or a tailwind)
3 Iron: 604 and 301 yards (could be caused by a data entry error)
Driver: 604 and 301 yards (could be caused by a data entry error)
e) To calculate the average distance of all four clubs combined, find the mean of the medians for each club.
(136 + 164 + 298 + 42) / 4 = 165.25
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Help me. Choose IS & IS NOT
Answer:
Yes
Step-by-step explanation:
6(5)+3(-6)=12
30-18=12
12=12
4(5)+(-6)=14
20-6=14
14=14
A movie theater has a seating capacity of 217. The theater charges $5. 00 for children, $7. 00 for students, and $12. 00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 1558, How many children, students, and adults attended?
The probability that the theater had 108 children, 108 students, and 54 adults attend, for a total of $1558 in ticket sales.
Total ticket sales = $1558
Adult ticket sales = $12 x 54 = $648
Remaining ticket sales = $1558 - $648 = $910
Student ticket sales = $7 x 108 = $756
Children ticket sales = $910 - $756 = $154
Children = $154 / $5 = 108
Students = $756 / $7 = 108
Adults = 108 / 2 = 54
The theater had a total ticket sales of $1558, with adults tickets being $12 each. By subtracting the adult ticket sales from the total, we get the remaining ticket sales. We then divide this by the student ticket price of $7 to get the number of students. Subtracting this from the remaining ticket sales gives us the amount of children ticket sales. We divide this by the children ticket price of $5 to get the number of children. Finally, we divide the number of adults by 2 to get the number of adults.
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Need help with this math work
Answer:
Step-by-step explanation:
edit back ur post and put the picture in for help
Express sin x as a fraction in simplest terms.
Sin x = 2sin (x/2)cos (x/2) = 2(sin (x/2))/(cos (x/2)). This fraction is in its simplest form.
What is fraction?Fraction is a mathematical concept that represents a part of a whole or a ratio between two numbers. It is expressed as a numerator (top number) over a denominator (bottom number). A fraction is a way to express a number that is not whole, such as 1/2, which is one half, or 3/4, which is three quarters. Fractions are used in many areas of mathematics, including basic arithmetic, algebra and geometry.
The expression sin x can be rewritten in simplest terms as a fraction using the trigonometric identity sin x = 2sin(x/2)cos(x/2).
Therefore, sin x = 2sin (x/2)cos (x/2) = 2(sin (x/2))/(cos (x/2)). This fraction is in its simplest form.
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A mouse has made holes in opposite corners of a rectangular kitchen. The width of the kitchen is 3 meters and the distance between the mouse's holes is 5 meters. What is the length of the kitchen?
The length of the kitchen given the width and distance between the mouse's holes is 4 meters.
What is the length of the kitchen?The width of the kitchen and the two holes in opposite corners of the rectangular kitchen forms a right angle triangle.
The two holes in opposite corners of the kitchen is therefore the hypotenuse.
Distance between the mouse's holes = 5 meters
Width of the kitchen = 3 meters
Hypotenuse² = opposite² + adjacent²
5² = 3² + x²
25 = 9 + x²
25 - 9 = x²
16 = x²
find the square root of both sides
x = √16
x = 4 meters
Therefore, the length of the kitchen is 4 meters.
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The relationship between attending your classes and passing your classes would best be described as:
Causal
Correlation
Spurious Correlation
No relationship
It will be best defined as a spurious correlation rather a casual correlation.
What is a spurious correlation?
A spurious correlation occurs when two variables are correlated but don’t have a causal relationship. In other words, it appears like values of one variable cause changes in the other variable, but that’s not actually happening.
If you look up the definition of spurious, you’ll see explanations about something being fake or having a deceitful nature. It has the outward appearance of genuineness, but it’s an imitation. With this definition in mind, spurious correlations look like causal relationships in both their statistical measures and in graphs, but it’s not real.
For example, ice cream sales and shark attacks correlate positively at a beach. As ice cream sales increase, there are more shark attacks. However, common sense tells us that ice cream sales do not cause shark attacks. Hence, it’s a spurious correlation.
Now,
As attending classes is not related to passing the class because one can pass an examination without attending classes.
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The Americans with Disabilities Act states that ramps must have an angle less than or equal to 4.8 degrees. Remember, a 4.8 degree angle in a right Americans with Disabilities Act requirements
The angle of elevation will this ramp have 5.74 degree.
What is Angle of Elevation?The angle of elevation is the angle created between the line of sight and the horizontal. The angle created is an angle of elevation if the line of sight is upward from the horizontal line.
The angle of elevation is the angle made by the line of sight and the horizontal when the object is above the level of the horizontal.
Given:
[tex]\theta_{max[/tex] = 4.8 degree
Perpendicular = 2.5 feet
Using Trigonometry
sin [tex]\theta_{max[/tex] = P/ H
sin 4.8 = 2.5/ H
0.084 = 2.5/ H
H= 2.5/ 0.048
H = 29.76.
Hence, 25 feet is not enough for the length of ramp .
Then, the Angle elevation should be
[tex]\theta[/tex] = [tex]sin ^{-1}[/tex](2.5/25)
[tex]\theta[/tex] = 5.74 degree
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The complete is shown below:
A builder needs to install a ramp to reach a door that is 2.5 feet off the ground.
Is 25 feet long enough for the straight line distance of the ramp to meet the requirements? What angle of elevation will this ramp have?
which of the following can be a form of solution of 3x+0y+7=0 in two variables? i)-7/3,m ii) m,-7/3 iii) -7/3,0
If y=x+7 will be the value of the function that crosses the y-axis at position (0, 7).nThe replacement approach refers to determining any variable's value from one equation in terms of another variable. The correct answer is c. -7/3,0
Considering that, the point where the function crosses = (0, 7) Considering that the function's intersection point is now = (0, 7).As a result, the point must fulfil the function.
We have to check whether these pairs satisfy equation 3x+0y+7=0 or not.
So, we will put these pairs one by one.
A) (-7/3,m) x=-7/3 & y=m
Than
3×(-7/3)+0×m+7=0
-7+0+7=0
0=0 so, it satisfies.
B) (m, -7/3) x=m & y=-7/3
Than
3×m+0×-7/3+7=0
3m+0+7=0
3m+7 =0 so, it does not satisfies.
D) (-7/3,0) x=-7/3 & y= 0
Than
3x(-7/3)+0×0+7= 0
-7+7= 0
0=0 so, it satisfies.
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Two forces of 58 newtons and 32 newtons act simultaneously on an
object. The angle between the two forces is 22°. Find the magnitude of
the resultant, to the nearest 10th of a newton. Find the measure of the
angle between the resultant and the smaller force, to the nearest 10th
of a degree.
Answer: 678900 to the 10 power
Step-by-step explanation:
Please answer fast I need help
The correct answer is C. Isosceles; since a rhombus always has 4 equal sides, each triangle must have 2 equal sides.
When a diagonal is drawn in a rhombus, it splits the rhombus into two congruent triangles. Since the diagonal bisects the rhombus, the two triangles are mirror images of each other.
In a rhombus, opposite sides are parallel and equal in length, which means that the two sides of the triangle that are formed by the diagonal are congruent. Therefore, each triangle is isosceles.
A rhombus is a quadrilateral with four equal sides, so we know that the triangles have two equal sides, but we cannot say anything about the other sides and angles, so we cannot say that it is acute, equilateral or obtuse.
Answer:
The correct answer is C. Isosceles; since a rhombus always has 4 equal sides, each triangle must have 2 equal sides.
A rhombus is a quadrilateral with all four sides equal in length. When a diagonal is drawn in a rhombus, it forms two congruent triangles. Since the rhombus has four equal sides, each triangle will have two equal sides. In other words, the two triangles are isosceles triangles.
Option A is incorrect, because a rhombus does not always have 2 acute angles. A rhombus can have acute, right or obtuse angles, and the angles of the rhombus are not related with the triangles formed by drawing a diagonal.
Option B is incorrect, because a rhombus does not always have 4 equal angles. A rhombus can have acute, right or obtuse angles, and the angles of the rhombus are not related with the triangles formed by drawing a diagonal.
Option D is incorrect, because a rhombus does not always have 2 obtuse angles. A rhombus can have acute, right or obtuse angles, and the angles of the rhombus are not related with the triangles formed by drawing a diagonal.
Question 1
Write the function x³ - 13x² + 52x - 60 in factored form knowing that one of the roots is 5.
O(x+6)(x + 2)(x + 5)
O(x+4)(x + 6)(x + 3)
O (x - 5)(x-2)(x-6)
2 pts
O(x-6)(x-3)(x+4)
The factorization of the function us (x-2)(x-5)(x-6).
What is factorization of the expression?
To factorise an algebraic statement, we first identify the terms' highest common factors and then arrange the terms into groups in accordance with those groups. In plain English, factorization is the process through which an algebraic expression gets expanded in the opposite direction.
Here the given function is ,
=> [tex]x^3-13x^2+52x-60[/tex]
=> [tex]x^3-2x^2-11x^2+22x+30x-60[/tex]
=> [tex]x^2(x-2)-11x(x-2)+30(x-2)[/tex]
=> [tex](x-2)(x^2-11x+30)[/tex]
=> [tex](x-2)(x^2-5x-6x+30)\\[/tex]
=> [tex](x-2)(x(x-5)-6(x-5))[/tex]
=> (x-2)(x-5)(x-6)
Hence the factorization of the function us (x-2)(x-5)(x-6).
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Find the focus and directrix of the parabola y=-1/8x^2
y = (-1/8)x^2 is a downward opening parabola with vertex = the origin (0,0) relatively flat.
Parabola points horizontally left and right of the focus = from (4,-2) to (-4,-2) = 2(4) = 8.
what is parabola?
Any point on a parabola is at an equal distance from both the focus, a fixed point, and the directrix, a fixed straight line. A parabola is a U-shaped plane curve.The topic of conic sections includes parabola, and all of its principles are discussed here.Three different parabolas exist. Vertex form, standard form, and intercept form are the three forms.Several examples of parabolas in real life The wheel stance in yoga resembles a parabola. Banana's shape is beginning to resemble a parabola. A parabola is emerging from the Rainbow.A series of points in a plane that are evenly spaced off from a straight line is referred to as a parabola.Focus and directrix are equidistant from the vertex.
Focus has an x coordinate = 0 and y coordinate <0 axis of symmetry is the y axis or x=0.
Find one more point on the parabola, go horizontally from the focus to the parabola, that distance equals the distance from the parabola at that point to the directrix. its x coordinate = -2 times its y coordinate. it helps to graph a rough sketch of the parabola.
y = (-1/8)x^2
y = (-1/8)(-2y)^2
y = -4y^2/8 = -y^2/2
2y = -y^2
2 =- y
x=-2y = -2(-2) = 4
plug that point (4,-2) into y =(-1/8)x^2
-2 = (-1/8)(4)^2 = -16/8 = -2 = the y coordinate of the vertex,
x coordinate = 0
the focus = (0,-2)
distance from the focus to the vertex = 2
distance from the directrix to the vertex = 2
the latus rectum = distance from the parabola points horizontally left and right of the focus = from (4,-2) to (-4,-2) = 2(4) = 8. "Latus rectum" is the math term for that distance.
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y = (-1/8)x² is a downward opening parabola with vertex = the origin (0,0) relatively flat. Parabola points horizontally left and right of the focus = from (4,-2) to (-4,-2) = 2(4) = 8.
What is a parabola?
A parabola is a U-shaped plane curve. Any point on a parabola is at an equal distance from both the focus, a fixed point, and the directrix, a fixed straight line.
The topic of conic sections includes a parabola, and all of its principles are discussed here.
Three different parabolas exist. Vertex form, standard form, and intercept form are the three forms.
Several examples of parabolas in real life The wheel stance in yoga resembles a parabola.
The Banana's shape is beginning to resemble a parabola. A parabola is emerging from the Rainbow.
A series of points in a plane that are evenly spaced off from a straight line is referred to as a parabola.
Focus and directrix are equidistant from the vertex.
Focus has an x coordinate = 0 and y coordinate <0 axis of symmetry is the y axis or x=0.
Find one more point on the parabola, and go horizontally from the focus to the parabola, that distance equals the distance from the parabola at that point to the directrix. its x coordinate = -2 times its y coordinate. it helps to graph a rough sketch of the parabola.
y = (-1/8)x²
y = (-1/8)(-2y)²
y = -4y²/8 = -y²/2
2y = -y²
2 =- y
x=-2y = -2(-2) = 4
plug that point (4,-2) into y =(-1/8)x²
-2 = (-1/8)(4)² = -16/8 = -2 = the y coordinate of the vertex,
x coordinate = 0
the focus = (0,-2)
distance from the focus to the vertex = 2
distance from the directrix to the vertex = 2
the latus rectum = distance from the parabola points horizontally left and right of the focus = from (4,-2) to (-4,-2) = 2(4) = 8. "Latus rectum" is the math term for that distance.
Hence, the distance from the focus to the vertex is 2 and the distance from the directrix to the vertex is 2 of the parabola y=-1/8x².
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Can an equation have more than one extraneous solution?
Yes, a logarithmic equation can have more than one extraneous solution.
An equation involving the logarithm of an expression containing a variable is known as a logarithmic equation. It is possible for a logarithmic equation to have more than one extraneous solution and the logarithms of positive numbers only exist.
For example,
log(x-5) + log(x-2) = 1
log((x-5)(x-2)) = 1
(x-5)(x-2) = 10¹
(x-5)(x-2) = 10
x² - 7x + 10 = 10
x² - 7x = 0
x(x - 7) = 0
x = {0, 7}
0 is an "extraneous" solution because you cannot plug it back into the original equation.
The solution is x = 7.
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What is the slope of 3y =- 5?
The slope of 3y = -5 is -5/3
We know that the slope-intercept form of equation of line is y = mx + c
where m is the slope of the line and c is the y-intercept of the line.
We have been given an equation of line 3y = -5
Consider given equation of line
3y = -5
Divide each side of above equation by 3
(3y)/3 = (-5)/3
y = -5/3
Comparing above equation with the slope-intercept form of equation of line y =mx + c we get,
m = -5/3 and c = 0
So, slope is -5/3
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When Sandra was 8 years old she had 100 dollars in the bank. Each year for her birthday she deposited 25 dollars in the same account.
Sandra is now 28 years old. Assuming Sandra has not withdrawn or deposited anything else into that account, how much money does she
have there now?
(Teacher will mention another example using years. For example, Sandra started depositing money in 2000, how much does she have in 2022
7)
O b
Oc
Od
500 dollars
125 dollars
800 dollars
600 dollars
Sandra has 600 dollars now. The solution is obtained using arithmetic operations.
What are arithmetic operations?
There are four basic operations which are listed as follows:
Addition(‘+’): This operation deals with finding the sum.Subtraction(‘-’): This operation deals with finding the difference. Multiplication(‘×’): This operation deals with finding the product.Division(‘÷’): This operation deals with finding the quotient.We are given that when Sandra was 8 years old she had 100 dollars in the bank and each year for her birthday she deposited 25 dollars in the same account.
This means that Sandra has deposited 25 dollars every year for 20 years because we are provided that she had 100 dollars when she was 8 years and now she is 28 years. So, she has deposited the amount for 20 years.
So, the total money she deposited= 25*20=500 dollars
Also, she had 100 dollars when she was 8 years.
Thus, the total money she has= 500+100= 600 dollars
Hence, Sandra has 600 dollars in the account now.
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in the figure to the right, the two triangles are similar. what is the value of x?
The value of x in the triangle is 55/6
How to determine the value of xFrom the question, we have the following parameters that can be used in our computation:
Similar triangles
From the triangles, we have the following ratio
x : 11 = 5 : 6
Express as fraction
x/11 = 5/6
So, we have
x = 55/6
Hence, the solution is 55/6
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Shayla created two patterns. Pattern X increases by 7 each time. Pattern Y increases by 5 each time. Shayla used the corresponding values in each
pattern to make coordinate pairs. She graphed the coordinate pairs on a coordinate plane.
Answer:
45
Step-by-step explanation:
since you increase the x-value by 7 each time you must figure out how many 7's go into 63, which is 9
to get the matching y-coordinate to 63, multiply 5 by 9 to get 45